Time-resolved opto-acoustic spectroscopy

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TIME-RESOLVED OFTO-ACOUSTIC SPECTROSCOPY


By

JOSEPH J. WROZEL











A D)ISSERTATION PR~ESENTED TO THIE CrGRADUAT ClOUNCLIL OF- THEif
UNIVERSITY OF FLORIDA
IN PARTIIAL FULFIFLLMENT OF THE RlajEQUIEMENTS FOR THIE
DEGREE ;F' DOCTOR OF PHIILOSOPHiY






UNIVERSITY OF FLO~RI~DA


1976




















To my parents



















...The investigations of chemistry have about
them all the fluctuating fortunes of a deep and
subtle game. There are the same vacillations of
good and bad luck; the same tides of hope and fear:
the almost certain prospect of success dashed and
darkened by failure; the grief and disappointment
of failure dispelled by glimpses of bright hope.
So many are the disturbing influences, so subtle
the causes that derange experiments, where some
infinitesmal excess or deficiency, some minute
accession of heat or cold, some chance adulteration
in this or that ingredient, can vitiate a whole
course of enquiry, requiring the labour of weeks to
be all begun again, that the pursuit at length
assumes many of the features of a game, and a game
only to be won by securing every imaginable condi-
tion of success.

Charles Lever in his novel,
"One of Them," written
in the miiddle of the 19th
Century.














A~~CKNWLE1:DGMELN TS


I would like, to acknrowJledge Dr. Martin Vala for the

guidance, encouragement and assistance he provided through-

out the course of this work. His confidence in me anid the

remarkable understanding he displayed over the long period

of our association made the completion of this work pos-

sible.

I would like to acknowledge my wife Mlargaret, whose

peanut butter, jelly, patience and love kept my body and

soul together, and miy daughter Jennifer, whose welcome-

hior:1e smile could make the world go aw2ay.

I would also lik-e to acknowledge those fellow gradlu-

ate students, with whom I worked and with whom I played,

for helping to lighten the burden and, likewis-e, Che staff

of the Depart~ment of Ch~emi.stryj both in the offices and inl

the shops for their essential contributions.















TABLE OF CONTENTS


ACKNOWLEDGMENTS iv

LIST OF TABLES vii

LIST OF FIGURES viii

KEY TO SYMBOLS x

ABSTKRCT xiii

CHAPTER ONE. INTRODUCTION 1

CHAPTER TWO. THEORETICAL CONSIDERATIONS 10
Introduction and Direction 10
The Solution of the Heat-Flow Equations 13
Simple Two-State Model 13
Multi-State Model 17
Neglect of density fluctuations 21
Neglect of thermal conductivity 22
The Extraction of Mol~ecular Parameters from the
Gross Pressure Signal 32
Excitation into the First Excited Triplet
State 33
Excitation into the First Excited Singl~et
State 38
Consideration of the Total Disturbance:
Pressure Wave Plus Acoustic Harmonics 47
Evaluation of: the Expansjon Coefficients 47
Computer Simulation of Opto-acoustic
Signlal 50
Limitations and Extensions of the Theory 57
Limitations on Experimental Design 62
Cell construction 62
Pressure transducer 64
Illumination source 66
Extensions of Theory to Additional Effects 67
Effect of window absorption 67
Effect of luminescence heating 67
Effect of a second gas 68
Effect of photochemistry 69

CHAPTER THREE. EXPERIMENTAL SYSTEM 72
Equipment 72
Opto-acoustic Cell and Vaccuum System 72
Excitation Source 76
Pressure Detection System 115









Data Gathering and Processing System 125
Operating Procedure 132

CHAPTER FOUR. OB3SERVAlTIONS 136
Flashlamp Experiments 136
Laser Experiments 138
Choice of Sample 138
Pyridazine 138
Oxaly1 chloride 140
Results 151

CHAPTER FIVE. COMMENTS 160

LIST OF REFERENCES 164

BIOGRAPHICAL SKETCH 169














LIST OF TABLES


Table Description Page

1. Triplet a and b 36

2. Singlet a and b 44

3. J(s.,B). 54
4. Characteristics of laser system. 113















LIST OF FIGURES


Figure

1.


Description

Experimental pressure signal of 02.


y-


Page

12

15

35

40

41

56

59

61

74


80

83

85

87

90


93


98

100

103

109


112


2. Diagram of two-state model.

3. Diagram of triplet state processes.

4. Form of pressure rise for triplet excitation.

5. Diagram of singlet state processes.

6. Plot of expression (18), high absorptivity.

7. Plot of expression (18), moderate absorptivit!

8. Plot of expression (18), low absorptivity.

9. Diagram of opto-acoustic cell.

10. Plot of calculated pulse energy versus wave-
length.

11. Spectra of dye No. 386.

12. Reflectivity of R1 reflector.

13. Diagram of laser alignment.

14. Diagram of laser-monochromator alignment.

15. Plot of nitrocon emission lines versus dis-
tance on photograph.

16. Plot of wavelength of laser output versus
micrometer setting.

17. Schematic of photodiode circuit.

18. Effect of intercavity reflector.

19. Absorption spectrum of optical filter.

20. Oscilloscope tracinig of phototube signal from
laser pulse.


Vll3









Figure Des;cription Page

21. Schematic of standard Pitran circuit. 117

22. Cross-section of Pitran mounted in cell. 120

23. Block diagram of Pjtran circuit. 123

24. Plots of channel count: versus dwell time. 129

25. Block diagram of elements of opto-acoustic
experiments. 134

26. Absorption spectrum of pyridazine vapor,
4.6m path. 142

27. Absorption spectrum of oxalyl chloride
vapor, 10cm path. 145

28. Absorption spectrum of oxalyl chloride
vapor, 6.4mn path. 148

29. Plot of absorbance of S *T. band of oxaly1
chloride versus path le~gtA. 150

30. Plot of pressure rise due to oxalyl chloride
decomposition. 155

31. Signal generated by laser firing. 158





KEY TO SYMBOLS


Symbol Definition

a Expansion coefficient of n.

A Absorptivity; A = ECC



B Beam size correction factor

c Speed of sound; c2 = yp/p

c ~Heat capacity at constant
volume

C Concentration

C ,Cy Molar heat capacity at
constant pressure, volume

E Energy

f Oscillator frequency

h Planck's constant

H(x) Heaviside function

I Energy flux


J ,J1 J2 Zero, first and second
order Bessel functions

k First-order rate constant

K Thermal conductivity

L Length of sample cell

M Molecular weight

n. Number density of molecules
in state j

N Number of mloles


Units
-3
mol cm

none
-3 -1
erg cm a

none

cm s1

erg g- deg-


mole 1-

erg mole- deg-


erg
s-1

erg s mol-1

none
-2 -1
erg cm s

none


s-1

-1 -1 -1
erg cm deq s

cm

g mole-1
-3
mol cm


mole











Symbol


N

O3D




myl

q~r,z)




Q

r


rb
r
c



SoS1,S2


t




Tl

U

v

V

W

W.

3

x.


Definition


Avogadro's number

Optical density; OD=AL

Pressure

Expansion coefficients of p

Spatial dependence of Q

Expansion coefficients
of q~r,z)

Source term

Radial coordinate

Beam radius

Cell radius

Maolar gas constant

Ground, first and second
singlet states

Time

Temperature

First excited triplet state

Internal energy

Flow velocity

Sample cell volume

Power

Rate of heat release from
molecule in state j

Root i of J



Axial coordinate


Units


mol mole-1

none

erg cm3
-3
erg cm

none

none


-3 -1
ergl cm s

cm

cm

cm

erg mole-1 deg-1

none





deg

none

erg g
-1
cm s

cm3
-1
erg s

erg s mol


none
--1
cm

cm








Symbol

a








6(t)



E




K



m,l








X

.

m,l


Definition U

Absorption coefficient; a = EC cm1

Ratio of beam to cell radli; none
8 =rb/rc

Heat_capacity ratic; none
y = C /C
p v
Delta function none

Molar extinction coefficient cm2` m

Molar coefficient of cm2 n
absorption; E = Eln 10

Angular coordinate rad

Thermal diffusivity; cm
K =K/pcV

Acoustic resonance frequency; s-
h2 = C~y2 + (mw/L) ]
-1
Frequency of transition from s
state j to state 1

Mean free path cm

Density g cm

Yield of process X; from none
state j
-1
Acoustic resonance frequency; s
2 Y2[y (2mw/L) i
Wy 1


Inits












nole1

mole1




-1


-3










Abstract of Dissertation Presented to
the Graduate Council of the University of Florida
in Partial Fulfillment of the Requirements for the
Degree of Doctor of Philosophy


TIME-RESOLVED OPTO-ACOUSTIC SPECTROSCOPY

By

Joseph J. Wrobel

August, 1976

Chairman: Martin T. Vala
Major Department: Chemistry

A new approach to the study of excited state radiation-

less processes of large molecules in the vapor phase is

proposed. The basis of the approach is the opto-acoustic

effect, the generation of temperature and pressure fluc-

tuations in a sample upon absorption of optical energy.

The set of heat flow equations governing this effect are

constructed and solved, under certain restrictions, for a

sample in an isothermal cylindrical cell acted on by a

short pulse of light. Computer simulations of the expected

pressure signals are presented, and it is shown how molec-

ular parameters can be extracted from experimental meas-

urements.

Limi-tations on experimental design imposed by theoret--

ical assumptions are discussed and applied to the construc--

tion of an experimental system for performing time-resolved

opto-acoustic spectroscopy. The properties of oxalyl

chloride are examined, and it is chosen as the object of

experi~mental study. An attempt to verity the theo~recicallly


X1.11











predicted opto-acoustic signals using oxaly1 chloride is

made but is unsuccessful due to insufficient pulse energy

from the excitation source employed. Improvements of the

experimental system are suggested, and areas for future

work are designated.















CHAPTER ONE
INTRODUCTION



In the past several years a great deal of work has been

done exploring the theory of radiationless processes in

polyatomic molecules [1-7]. Although differing theories

have posed the problem in different frameworks, they all

have in common the goal of explaining and anticipating the

influence of temperature [8,9], isotopic substitution

[10,11), excitation energy [12,13], singlet-triplet energy

gap [14,15] or vibrational state of the molecule [16,17],

on the nonradiative decay rate.

As in all branches of science, previous experimental

work led to current theoretical interest which now demands

more experiments on which to judge the merit of the theory.

In this case, since all the theories of radiationless tran-

sitions deal with "isolated" molecules, the need grew for

experimental studies of vapor phase molecules at pressures

low enough so as to preclude collisions of an excited

molecule during the lifetime of its excitation. Also, since

the deactivation rates were known to be dependent upon the

excitation wavelength at these low pressures [18-20},

restrictions had to be made on the band width of the inci-

dent light thus decreasing its available intensity.









Although the advent of the tunable laser [21] will

serve to compensate for the diminished intensity of irradia-

tion at first caused by the second restriction, experi-

mentalists studying excited states by their ~igh~t emission

must still reckcon with the small number of photons which

are emitted from the low density vapor. The sensitive

light detection required in these cases initiated the use

of photon counting techniques to measure lifetimes and

yields. However, photon counting has its share of pitfalls

[22] which add to the already difficult problem of measuring

accurate radiative yields from which the non-radiative

yields are derived [23].

There is a somewhat separate problem associated with

studying molecular de-excitation solely by light emission.

Even if one can accurately measure the lifetime and radia-

tive yield of the monitored state anid thus derive the over-

all non-radiative yield, the distribution of the excitation

energy among the available non-radiative pathways remains

unknown. Even if photochemical reactions are excluded, one

cannot tell, for example, upon excitation into an upper

singlet state, what portion~ of the non-radiative yield is

due to intersystem crossing to the triplet manifold and

what portion derives from internal conversion to the ground

electronic state.

It is because of the need for more information on

excited state properties in the low pressure vapor and

because of the problems associated withh the usual spectro-





scopic methods for getting this information that we sought

an alternative approach. The most appealing approach, of

course, would be some course of experimentation that would

allow us to examine the radiationless behavior of a molecule

directly, rather than through its radiative properties. At

the same time, it would have to be sensitive enough to pick

up the small amounts of hieat given off during non-radiative

decay. This line of thinking led us to investigate the

application of the opto-acoustic effect to this area of

research.

Initial investigations of the opto-acoustic effect date

back almost a century. Following the invention of the tele-

phone, Alexander Graham Bell continued his investigation in

the area of voice transmission. Specifically, in 1880, he

was involved with the production and reproduction of sound

by light, i.e. transmitting sound not through wires but

through air using an undulatory beam of light [24]. Taking

advantage of the then recently discovered effect of light on

selenium's electrical resistance, Bell constructed a receiv-

ing circuit comprised of a telephone, a battery and a piece

of selenium. Using such a device and a proper transmitter,

he found he could communicate over long distances.

Bell then questioned whether the molecular disturbance

causing the effect required the telephone and battery to be

heard, and, further, whether the sound generation was

specifically a property of selenium or rather one which

would occur in a variety of substances. After a series of









experiments using samples in the form of thin diaphragms, he

concluded that sound could indeed be produced by substances

of all kinds. Further experiments by Bell [25] and others

[26-30] established that the effect was a general phenomenon

as long as the substance was irradiated with a source whose

radiation it could absorb. They reasoned, and correctly so,

that the absorbed energy wras degraded in the sample to heat

pulses which caused pressure pulses to occur in the surround-

ing gas. Thus if the incident light were chopped at a fre-

quency in the sound region, the sample could be heard to

emit sound of the same frequency.

In 1881 Bell [25] introduced a device by which one

could examine the absorption spectrum of a sample by noting

the intensity of the sound produced when the sample was

irradiated by chopped radiation from different regions of

the spectrum. This device Bell called the spectrophone.

Although Bell noted the promise of the spectrophone in his

1881 paper, especially in examining infrared absorption, it

was not until 1938 that the device was rediscovered by

Veingerov [31], and later by others [32-34], who sought to

exploit the opto-acoustic effect for both qualitative and

quantitative analyses of gases based on their infrared

absorptivity. Several types of radiation detectors were

built at this timie incorporating the effect as an integral

part of the detection scheme (35]. As the spectrophone

technique was established for vapor analysis in the infra-

red, the application of' the method broadened. The spectro-










phone was used to measure- absorptivities in the microwave

region of the spectrum 136!, and its use in the visible and

untraviolet regions was investigated [737. More recently,

the use of the spectrophone technique for detection and

analysis has brought high senisitivi-ty to mm and cm spec-

troscopy of gases [38-39]. It has also proven to be a very

sensitive method for detection of air pollutants [40-42].

Further, since this type of spectroscopy does not require

that samples be translucent, it has opened the door to the

study of absorption spectra of solids, biological materials

and other opaque substances [43].

As the use of the spectrophone for analyses grew, a

second use for this technique was discovered and investi-

gated. In 1946 Gorelik [44] proposed that the spectrophone

could be used to measure vibrational relaxation times of

gases. Slobodskaya [45] did the first work along these

lines on carbon dioxide and his results were subsequently

given a theoretical analysis by Stepanov and Girrin [46].

Two methods of determining vibrational relaxation times

using the spectrophone were investigated both theoretically

and experimentally [47]. The phase shift method relates

the vibrational relaxation time to the phase shift between

the sinusoidal excitation and the resultant sinusoidal

pressure changes. The amplitude- or frequency-response

method measure the amplitude of the pressure response as a

function of the frequency of the excitation which theory

shows is related to the vibrational relaxation rate.










Both methods have the advantage over previous methods in

that they can be made specific to a particular molecular

vibration by using incident radia~tion limited to a single

spectral band.

Interest in opto-acoustic effect has boon revived

again in recent years [48)] as a tool for studying molecules
under the action of visible and ultraviolet radiation.

The interest here lies in the fact that while polyatomic

molecules which are vibrationally excitedly relax almost

totally by nonradiative patchwayn, electronically excited

molecules typically deactivate along numerous pathways

including those which lead to light emission as well as

photoreaction. Since the response of an opto-acoustic

cell1 is only to that protion of the absorbecd energy which

is released as heat, opto-acoustic spectroscopy allows one

to measure the yield of nonradiative pathways directly,

and in this way it complements the standard method of

studying molecular excited states by light emission alone.
In 1967, employing broadband excitation Hey 149)

applied the standard spectrophone amplitudo-response
technique to the measurement of relaxation rates of dye

molecules in solution with some success. In 1969, two

studies were performed on similar compounds in solution.

In the first, Seybold et al. used steady-state illumination

and detected pressure increases by a capillary rise tech-

nique [501. In the second Colllis et al. employed broadband
flashlamp excitation and a cell. equipped with a capacitance





microphone to detect the resultant pressure pulse [51). In

the latter study, the quantum yield of triplet formation

was calculated by comparing the fast heating due to singlet

state deactivation with the slow heating resulting from the

triplet state decay.

Since the inception of the present work, investi-

gations of excited state kinetics employing the opto-

acoustic effect have been extended to the gas phase.

deGroot et al. uncovered details of aldehyde photochemistry

which could not have been easily detected if standard

photochemical methods had been employed [52]. Other photo-

chemical studies were later carried out by Harshbarger and

Robin on NO2 and SO2 [48). Quenching of iodine atoms has

also been studied opto-accustically by these same authors

[53]. Another quenching study was carried out by Parker

and Ritke who concerned themselves with deactivation of

the first vibrational level of the lowest electronic sing-

let state of 02 [54-56].

Recently, Kaya et al. have examined the opto-acoustic

spectra of biacetyl [57] and the azabenzenes [581 using a

spectrophone technique. Their qualitive interpretation of

these spectra provides new insight into the radiationless

processes which affect the excited state kinetics of these

molecules.

Also recently, Hunter and Stock began a series of

papers on photophysical processes in the vapor-phase

measured by the opto-acoustic effect. The first of these





papers [59] developed a multi-state relaxation model to be

used as a basis for the study of radiationless processes

from excited electronic states. This model essentially

incorporates the complex deactivation schemes available to

electronically excited polyatomic molecules into the basic

spectrophone theory. Later papers by the same authors

applied this model to the study of excited benzene [601

and biacetyl [61]. Although each compound was studied at

only one particular wavelength of excitation, the results

show the usefulness of the opto-acoustic approach. Using

both phase shift and amplitude-response data, the lifetime

and yield of formation of the triplet state of both

compounds were determined in agreement with previously

reported values where available for comparison.

In this work it is our intention to further explore

the application of the opto-acoustic effect to the exam-

ination of photophysical processes. Our approach, how-

ever, differs from that of previous workers who used the

standard spectrophone technique to study indirectly the

course of energy flow in the sample. In the present work,

a pulsed excitation source will be employed in conjunction

with suitable transient recording instrumentation to study

directly the time-evolution of the resultant pressure

wave which appears in the gaseous sample upon irradiation.

As will be shown in the following chapter, such an

approach should allow us to gain both lifetime and yield

information in what we consider to be a more convenient





manner than the traditional spectrophone technique.

Further, by utilizing a tunable dye laser as the source of

the incident radiation, the manner in which these quanti-

ties vary as a function of excitation wavelength may be

explored.















CHAPTER TW~O
THEORETICAL CONSIDERATIONS

Introduction and Direction



Although no formal theory describing the pulsed opto-

acoustic effect has previously been reported, the effect has

been observed in molecular oxygen by Parker and Ritke (54].

They used a Nd: glass laser to pulse-excite molecular oxygen

in a high-pressure cell and monitored the pressure changes

using a capacitance type microphone. The pressure response

to the optical pulse (reproduced in Figure 1) was found to

be fundamentally an exponential rise to a limiting value

followed by a slow return to the initial value. The rise

time of the pressure signal was found to correspond to the

lifetime of the initially excited 02 vibronic level as

determined by Parker and Ritke from a frequency-response

opto-acoustic approach [54]. Superimposed upon this rise

was an oscillatory component corresponding to an acoustic

resonance of the cell. This secondary signal was ascribed

to absorption of the excitation beam by the cell windows.

In this chapter, these observations will be given a

theoretical foundation by constructing a model describing

the pressure disturbance which occurs in a vapor upon the





Od
LA
rQ



rd



COnc




(d cU M-


MOrd








Ro
-a -Hm
V) rl CI
C t




*Hc-




12







I~EV
r


1 t~









absorption of a pulse of optical energy. Also, the depen-

dence of the magnitude and time-evolution of this pressure

fluctuation upon the molecular parameters of the sample

will be examined. Further, the effects of the solution on

experimental design will also be discussed.



The Solution of the Heat-Flow Equations


Simple Two-State Model

To prepare for dealing with the complexities of the

model for a real experimental system, a simplified model is

first considered. In it, it is assumed that the molecules

of the sample vapor possess only two energy states (see

Figure 2) a ground state and an excited state which can be

populated from the ground state by absorption of a photon

with energy hu. Further, it is assumed that a molecule in

the excited state can lose energy and relax back to the

ground state in two ways, either by radiation of the

absorbed photon with first-order rate constant kr or by

nonradiative loss with first-order rate constant kn

What we wish to predict is how the pressure in the sample

vapor will change with time if it is allowed to absorb an

amount of radiative energy Ba'

Let us start by examining the rate at which heat energy

is given up by the excited molecules. If we let E = heat

energy released and nex(t) = number density of excited

molecules at time t, then



























h-
rQ
M





~I





ri-

PIO

(D






(cD





rt

(D





(D

























a,
id 00
t 0 O




to cO




O6 r
a -H





Oa
-Hd
4 3 o
*H
m rit
r
0a




ARx









dE/dt = k nrnx(t)hy VJ,


where V is the sample volume. Since the excited state

decays by first-order processes only, it is a simple matter
to show that


nexct) nec(0)xp((kn+kr)t) = (Ea/hy)exp(-kt)


by which we obtain dE/dt = knrEaexp (-kt) where k = kr~n

Integrating this expression, we find that the heat released

as a function of time is given by


E = knrEa(1-exp(-kt))/k = OnrEa(1-exp(-kt)),

whre#r = nr/k is the nonradiative yield of the state

initially excited.

The change in pressure p' produced in the sample can

be related to E through the ideal gas law and the relation

between E and the resultant temperature change T' brought

about in a constant volume system. Thus


p' = NRT'/V = (NR/V)(E/NC ) = (y-1)#nrEa(1-exp(-kt))/V (1)

where N is the number of moles of the sample, y is the heat

capacity ratio C /C Cp is the molar heat capacity at
constant pressure, C6 is the molar heat capacity at constant

volume and R is the gas constant which is equal to C -CV
for an ideal gas.

Equation (1) shows how, in this simple model, the

pressure change in a sample upon absorption of a pulse of

optical energy is related to parameters of the excited state.










It makes clear that the lifetime of the excited state (k-1)

can be determined directly from the rise time of the

pressure jump. Further, if V, Ea and y can be evaluated

independently, it shows that the value of On can be deter-

mined from the amplitude of the pressure jump.

This is the basic result of time-resolved opto-acoustic

spectroscopy; it relates the time-evolution of the radiation-

induced pressure signal to an excited state lifetime and

provides from the pressure amplitude information relating

to yields of radiationless processes. In the next section

the theory of the opto-acoustic effect will be treated more

rigorously. It will be shown that the multiplicity of

states in real molecules and the spatial nonuniformities of

the absorbed radiation cause the form of the pressure signal

to become somewhat more complex than that given in equation

(1). However, the method of extracting excited state

parameters from this signal will not differ significantly

from that used on the simple model examined above.

Multi-State Model

Let us consider a molecular vapor at equilibriumn con-

tained in a cylindrical cavity of length L and radius r .

Let the initial state of the gas be defined by the density

po, the pressure po and the temperature To. If the vapor
is now pulsed with optical energy in an absorption region,

the resultant heating brought about by the molecular

relaxation will cause the gas to undergo local variations

in pressure, density and temperature and to assume the new









values of these parameters p, p and T respectively. Also,

in response to these local variations, the gas will assume

a flow/ velocity v *.

All these changes must occur under the constraints

imposed by the equation of state of thle gas ** as well as

the following three partial differential equations which

reflect the quantities conserved in molecular collisions

in thie absence of external forces [62, p. 698]:

1. conservation of mass


Dp/Dt = -p(a/ar~v)


2. conservation of momentum


Dv/Dt = -(d/drp)/p


3. conservation of energy


DUto/Dt = -(a/ar*(I+I RM p- p~v r)/p.


In the above equations, t = time, p = pressure tensor,

Utot = total molecular energy per gram, = energy flux

vector' fR = radiative energy flux vector and D/Dt =


In the general case, this system of equations is not

solvable; thus, some simplification through reasonable


* The dependence of the functions v, p, p and T on time
and position will be in general not written explicitly.

** The assumption of gas ideality will be accepted through-
out and justified by restricting our considerations to
sufficiently low pressures.










assumptions is in order. First, we ignore the dissipation

of energy due to viscous effects. This action is rigorously

justified only if the product of the shear viscosity times

the divergence of the flow velocity is much less than the

pressure [62, p. 521;631. If the divergence of v is approx-

imated by v/re and thle simple kinetic theory definition of

the coefficient of viscosity as one-third the product of

density, average molecular speed and mean free path is

adopted (62, p. 13), then an equivalent requirement for

ignoring viscous effects can be stated. This requirement

is that the flow velocity be less than or comparable to the

speed of sound in the gas while at the same time the mean

free path in the gas be much smaller than the cell radius.

The restriction on the flow velocity should be easily met

since the effect of the pressure pulse will be slight. As

for the other condition, for a molecule the size of

biacetyl, at a pressure of one torr, the mean free path is

calculated as 2xl0-3cm (58]. Since the cell to be used in

this work has a radius almost three orders of magnitude

greater than this value, we are justified in ignoring vis-

cous effects. This allows the replacement of the pressure

tensor with the scalar pressure p times the unit tensor.

Next, we assume that the disturbances caused by thle

optical pulse will be very small. That is, we let p =

p, + p', p = po + p' and T = To + T' where the primed terms

represent small local changes from the initial bulk values

which occur upon absorption of the optical pulse. Upon









insertion of these expressions for p, p and T in the

general conservation equations and subsequent deletion of

terms second-order in p', p', T' or v, we arrive at the

following set of equations;


ap'/3t = -p V~ (2


9 /at = p'/po 3

and


DUelec/Dt + c BT'/at = -;*(1+IRipp~:p o 0

Uto has been divided into a sum of two terms; Uee

represents the energy per gram stored in electronically

excited molecules, and c ~T' represents the internal energy

per gram expended in translation motion and the population

of electronic ground state rovibrational levels.

Recognizing that I= -KVT' [62, p. 717] where K is the

gas thermal conductivity and, from equation (2), that $*v

-(dp'/dt)/po, we can rearrange equation (4) to obtain:


pocy(aT'/at) -KV T'-po(dp'/dt)/po -'R Po(D~elc/Dt) (5)

The series of equations (2), (3) and (5) still, in

general, do not yield to analytical solution because the

left side of equation (5) cannot be reduced to a function

of one variable. For this reason, one further assumption

must be made, namely, that either the dp'/dt term or the

V T' term in equation (5) can be ignored. We will examine

both alternatives.










Neglect of density fluc-tuations

K~err and Atwood [40] based their theoretical consid-

eration of the opto-accustic phenromenon onl an equation

similar to equation (5), but with the ap'/dr term deleted.

They omitted this term without explanation, thus leaving

it unclear as to whether this was done by design or by

oversight. The latter is possible since most texts on heat

conduction delete the dp'/dt term from the equation in

question without stating the fact that it is truely insig-

nificant only in solids. Regardless of the reason, however,

removal of the dp'/dt term from the problem allows for

solution of (5) in terms of T', and Kerr and Atwood arrive

at such a solution for the case of a time-independent source.

Their solution predicts that upon illumination the

average cell pressure undergoes a more-or-less exponential

rise to a steady-state pressure, p(m), given by p(m)

(1 + AWB/4xrKT)po where A is the absorptivity of the sample

at the exciting wavelength, W is the beam power and B is a

correction factor dependent upon beam size. The rate of the

pressure rise, as that of the decay upon cessation of

illumination, is related to the thermal time constant r 2/K,

where K is the thermal diffusivity given by K/pc .

Although the observations of Kerr and Atwood agree

reasonably with the theoretical predictions for p(N), there

are some drawbacks to their solution. For example, their

solution does not predict the acoustic disturbances which

have been found to occur upon pulsed excitation. Further,










due to their choice of boundary condiitions, their theory

predicts that T', and hence p' since p is taken as a con-

stant, is zero at the cell walls. This clearly contradicts

the pressure behavior which has been observed (54,64,65].

Incorporating a time-dependent source into their theoretical

framework does not remove the major problems.

Neglect of thermal conductivity

Deletion of the thermal conductivity term of equation

(5) has been considered by Longaker and Litvak [63]. They

conclude that omission of this term is justified for short

times after excitation, explicitly when Kh/rc <
physical terms, the solution is limited to times which are

small compared to the time it would take to cool the

excited gas by thermal diffusion. For benzene vapor at a

pressure of one torr, this limits the solution to times

much less than 20 msec. At longer times thermal damping

due to diffusion becomes important and the assumption

becomes invalid. Accepting this time limitation, this

approach to the problem has shown to be most satisfactory

in explaining infrared spectrophone phenomena [66], and so

it will be applied to the case at hand. The following

method of solution follows closely that of Bates et al. [64]

but differs significantly in the time-dependence and

complexity of the source terms (those on the right of

equation (5)).

After deleting the V T' term from equation (5), the

relation aT = (dT/dp) Sp + (dT/dp) Bp is used to eliminate









the remaining T' dependence yielding


ap'/3t -(Tp /p, )(ap'/at) = 3p'/at -c2(3p'/9t) = (r-1)Q (6)

where c is the speed of sound in the sample gas and Q

represents the source term:


*~R ODUelec/Dt.

Differenitiating (2) with respect to time, we have


32p'/3t2 = -p *3 ~/at (7)


and upon substitution of equation (3) into equation (7),

we obtain





Differentiating equation (6) with respect to time and

substituting the above relation, the following equation

is obtained solely as a function of p':

32p'/at2 c2 2p=(-10/t (8)


The solution to equation (8) for a particular form of Q

will yield the spatial and temporal dependence of p'

which we seek.

First let us consider the spatial dependence of p'.

In our experiments an illumination beam will be employed

which reflects the cylindrical symmetry of the excitation

cell, and logically p' is expected to do so also. Because

of this, p' will have no dependence on the angular










cylindrical coordinate 0. The dependence of p' on the

radial coordinate r may be expanded in terms of the Bessel

functions J (yir) where r y. = x., the roots of the first-

order Bessel function. The expansion of p' in terms of

Bessel functions of zero order only is due to the absence

of 6 dependence in p'. The presence of the roots of Jl in

the argument of the expansion functions reflects the

boundary condition of the radial component of the flow

velocity vr, i.e. vr(r=rc)=0. Thus equation (3) requires

that


-(ap'/arrr, P o (ar rt~r = 0,
c c

and since


(J(r)r) = (-y.J (y r)) =~ -y.J (x.) = 0
c c

the boundary condition is satisfied.

Likewise, boundary conditions on the longitudinal

component of v fix the set of functions in which p' can be

expanded to express its z-dependence. The two boundary

conditions of importance here are vz(z=0)=v2(z=L) = 0.

That these boundary conditions are satisfied by the set of

expansion functions given by


cos(maz/L) ; m = 0, 1, 2,..


will now be shown. Again using equation (3) it is found

that it requires of p' that









-(ap'/3z)z=0,/,L o (az )Z=0,L = 0.

The above relation is satisfied by expanding p' in cos

(muz/L) since


(a(cos(mwZZL)]a)/3)=, = (-mwsin(muz/L)/L)z=, = 0.


Thus, p' can be written as the expansion


p' = E~ip' .(t)J (yir~cos~maz/L),


where the coefficients p'm,i(t) must be determined so as
to solve equation (8). Substituting the above expression

for p' into equation (8), we see that this requires solving

the following equation given a particular form for the

source term:


mli o(y r) cos(maz/L) [ (t) + X2~ m'(ti


(v-i)aQ/at (9)

where


m12 = c2 2+ (ma/L2)2

The solution of equation (9) requires that jQ/3t be

expressed as an expansion over the same set of eigen-

functions as used for p'. Since, in general, the temporal

and spatial portions of aQ/3t are spearable, aQ/at may be

written as the product q(r,z)Q(t), where Q(t) is defined as

the volume-averaged time derivative of Q, i.e.





Q(t) = icel(a0/at)dV/V.


The term q(r,z) represents the spatial dependence of aQ/at

deriving from that of the excitation source. From the above

two equations, it fol~low~s that


celq(r,z)dV = V. (10)


Separation of variables allows the expansion of dQ/dt to

be of the form


aQ/at = mEim~q .0J(ti)Js(y~zr)osmzL


where the q .i are determined such that


q(r.~z) = ~m i mi o (ir)COS(m'iz/L), (11)

The expression in brackets in equation (9) can now be set

equal to the coefficients of the source term expansion, and

the resulting differential equation solved for the

p'm (t). Before this can be done, of course, an expression
for Q must be derived. We will now examine individually

the two terms which comprise Q.

The divergence of the radiative energy flux vector is

given by [62, p. 721]


V*IR e aQ

where Qe is the rate of radiation energy emission per unit

volume and Qa is the rate of radiation energy absorption

per unit volume. In general Qe can be written as a sum?-









mation over al~l the emitting levels of the molecule. For

the jth level, the contribution to Qe will be dependent on

the number density of mo~lecules in thle jth level, n., the
rate of radiative emission from state j to some lower state

1, kjl' and the energy of thle emitted photon, hyjl. Hence

Qe = E nj 1 j kjl hyjl

where the upper limit on the first summation refers to the

level s which is the uppermost level initially populated

by the excitation source.

As regards to Qa a similar summation could be written:


Q, = 1032 n. .(I. E. u)/N

where E.U is the molar coefficient of absorption for the

transition from level j to an upper level u, I is the
source radiation energy flux at the frequency of the j~u

transition and NA is Avogadro's number.* In the case of the

proposed experiments, we will attempt to excite only a

single transition, that being from the ground state to
state s. If we let E bc thle merlar extinction coefficient

for this transition and define the absorption coefficient

a by a = EC where C is the bulk; concentration, then Qa = al,
where I is the intensity of the excitation source.

W~e now turn our attention to anl expression for

is related to the molar extinction coefficient a by
the e~quati~on E = Elnl0.









D~elec/Dt. Quite simply,


elec j=0 nj 30 0o

so that

s s
DUelec/Dt = n hvj0/ o- + (v n )hyj0 o'

The second summation in the above equation is second-

order in two small quantities and can be ignored, allowing

us to write


p DU le/Dt = E njhy. .

Thus, for the case in question, the source term is


Q = al I (n hvj + nj 1 j kl hyjl '

At low pressures second-order decay processes of

excited electronic states are negligible. Thus we can

write as the rate equation for state s


ns = al/hys ns 1 s ks1


and in general


n. = E.j k .nu n. E k.l (12)

where kj kj + kj is the sum of both the radiative and

nonradiative first-order rate constants for the transition

from state j to state 1. After substitution of equation

(12) into the expression for Q and simplification, the

source term is given by










snrs
3 1F kj 31313


The W. defined by equation (13) represent the total heat

energy per unit time being released per molecule residing

in state j via all nonradiative pathways and is a constant.

The sought-after time-dependence of aQ/at thus could be

written explicitly if it were known for the n..

When only first-order processes are operative and

n.(t=0) = 0 for all j 0O, the n. take the form of
solutions to a system of linear differential equations

which reflects the various transitions between different

energy levels occurring during molecular relaxation.

Assuming pulsed excitation of the sample the general form

for these solutions is

s-k t
n. = ( E a .e u ) q (r,Z).
3 =j u

The spatial dependence of the n. has been withheld from

inclusion in the a for convenience. If the time
derivative of equation (13) is now taken, we have that



s

s s -k t
= -q(r,z)EW. E a At e u
jD u~ju
s u -k t
= -q(r,z)E (Ea ,W.)k e u
u j u

-k t
= -q(r,z)Cb k e u









where we have defined for convenience


b = a FW..
u .j u

Using the last expression for a0/8t, the bracketed part of

(9) can be rewritten as

2 s-k t
g (t) + X .p (t) =-(Y-1)q Eb k e u.
m,i m,mP,lim u uu

Solving this second-order differential equation will give

a form for the p' which will provide a general expression

for p'.

Applying the standard methods of solving differential

equations to the bracketed equation, one can solve for the

p'.and obtain for p':
Pm,1
s 2 2
p' = (y-1) EqC i, {Elb k/k /( + m .)] x



[cos(Am~it)-exp(-kut)-(im~i/ku~sin(Am,it)] x



J (yir) cos(maz/L) (14)

Before applying this equation to specific cases of

molecular excitation in which the bu will be evaluated in

terms of actual excited state parameters, it will prove

informative to examine the general expression for p'.

Note that for all terms of the summation except the m = i = 0

term, the long-term time-dependence is periodic in nature,

with a frequency of oscillation for a particular i and m

dependent on the speed of sound in the sample gas









and the cell dimensions. What these terms represent is,

in fact, not a true "pressure" wave since their long-term

time-average amplitude is zero. Rather, what they

describe is the infinite set of resonances available in

the cell for radial and transverse acoustic wave prop-

agation. The amplitude of these acoustical disturbance

terms and their relative contribution to the total sum,

as we shall see later whefn the qm~i are evaluated, are

very sensitive to the degree of uniformity of absorption of

the exciting illumination throughout the cell, becoming

increasingly large as the absorption becomes less uniform.

The i = m = 0 term of the summation in equation (14)

thus carries the body of the "pressure" information. One

can write for the contribution of this term to the p'

summation the expression


p' =O (Y-1)q Eb (1--e u)/ku (15)

There is a noteworthy resemblance of an individual term

of this summation to the form of p' derived in the simple

two-state nodel. See equation (1). The terms of the sum

merely represent the individual contributions to p' from

each of the molecular levels. As in the simple solution

for p', equation (15) predicts that p' increases asymp-

totically to a nonzero value, thus implying that the sample

pressure does not return to its preexcitation equilibrium

value. This is, of course, not true; the cell is not

adiabatic and heat transfer through its walls quickly










returns the sample vapor to its original pressure. The

reason the solution does not reflect this physical reality

is the neglect of the thermal diffusion term of equation

(5) on which the derivation of this section is based.

The Extraction of Molecular Parameters
from the Gross Pressure Signal

To this point, the derivation of the theory of time-

resolved opto-acoustic spectroscopy has been kept as general

as possible. Now, to calculate the actual form of the au

(and from them the bu), the set of equations which define

the time-evolution of the states which participate in the

electronic excitation and relaxation of polyatomic molecules

must be solved. To do so, a specific model must be con-

structed and necessarily generality is lost. The important

point is, though, that just as this model is constructed

assuming certain characteristics of excited state kinetics,

so others might be constructed based on other assumptions.

Thus, the following model, though applicable to a great

number of actual cases, should be considered as just an

example of how time-resolved opto-acoustic spectroscopy

may be applied to the study of molecular excited states.

Only two electronic states besides the electronic ground

state will be considered explicitly, these being the first

excited singlet S1 and the first excited triplet T1. In

general, population of higher excited states leads only to

rapid nonradiative decay to the vibrational manifolds of

these lowest states. Thus, for our purposes, excitation









to mnore highly excited electronic states is equivalent to

excitation of higher vibrational levels of S1 and TI'
deactivation of these vibronic levels is considered in the

discussion below. Because the form of the a will depend
on that level which is initially populated, two cases will

be treated which encompass the two possible choices for the

initially populated level (level s) in our narrowed scheme.

Excitation into the First Excited Triplet State

The electronic states and their first-order decay

constants which are typically of importance in this case

are shown in Figure 3. Tl represents the initially pop-

ulated vibronic level of the lowest triplet state T1,

represents the vibrationless level of T1 and So represents
the molecular state before excitation. For this case

equation (12) takes the form:


nTV = al/hy v -n v(k2+k3)
1 1 1


nTo = k2n v kln o
I 1 1

where


kl = kr + knr

To solve this coupled set of equations, a form for

I must be chosen which expresses expli~ci-tly the time-

dependence of the source illumination. Since the excit-

ation will consist of a very short duration laser pulse,

a valid and convenient approximation to its temporal form









is the delta function, 6(t). This function assumes a value

of unity when its argument is zero and equals zero for all

other values of t. Allowing I to assume this functional

dependence on t, the above set of differential equations

can be solved in the standard manner to yield:

ov -(k2 + k )t
n v = nve2
T 1

o vk/k+2k~ (-kl t .-(k +k )t)
no = n v2(3k-l] e1-e 23)
1 1

nTV is the initial population of T1 equal to nTv q (r,z)
1 1
where nPV is the cell-averaged initial number density of
1 v -al
molecules excited into T ivnbE(- )/yvVwhr

E is the laser pulse energy.

The forms for the a and the bU can now be derived
in a straightforward manner and are listed in Table 1.

Using these values, the gross time-dependence of the

pressure pulse expected to occur upon excitation into T;
can be determined by expanding equation (15) to obtain


P'o~ = (y-1)qo~onTI [ klnkhy o(1-e-k1 )/(k3+k2-kl)k1

1, 1 1



Since the vibrational relaxation time of TI is ordinarily

much shorter than the spin-forbidden deactivation of To,

k1 can be assumed to be much less than kc2, and the above
equation can be simplified to the form:
























excitation


Figure 3. Diagram of energy levels typically of
importance for first excited triplet
state excitation and decay.
























~.--



I EI

II

I O











NI








O I I --

Mm I

NN
+









~ IIn
0 > I
n I II XI


rd










9 o,o = (Y-1)qo~0onTI 1rChy 1 l(1-e-(k2+kC3)t)

IC ISC
+ d hv ,o (1-e 1 l)]
T1v Tlo -1

where knr/k1 has been recognized to be eI C, the intersystem
crosingyied o To and k2/(k2+k3) is represented by $T ,

the internal conversion yield of T .One sol oeta

this equation applies equally well to direct excitation of

the vibrationless level of TI' in which case v v is replaced
IC1
by v o, # C goes to unity and hv v o goes to zero. These
1 1 1'
changes cause the first term in the brackets to be deleted

and the second to be somewhat simplified.

The above equation predicts the main pressure signal

to be a sum of two exponentially rising components, each

of different amplitude. In general a response of this

type would be difficult to deconvolute. However, because

of the large difference in the magnitudes of kl and k2, the

two exponential rises should be well separated temporally.

In fact, the first term in the brackets above will most

likely appear as a step-rise in pressure at t=0 with the

second exponential rise building with time on top of it,

as pictured in Figure 4.
IC
The figure indicates that q v can be evaluated only if

the true magnitude of the pressure rise is known, as well

as the values of y,a, E and go~o. However, if hqvT.E is
ISC
known as is usually the case, 4 o can be determined in a









more straightforward manner. If we let p'f be the ampli-

tude of the fast rise and p's be that of the slow rise,
then


IS~C = (huT To/hyTo) ps/'sf.
1 1' 11

Since k1 can be extracted solely from the time-evolution
r nr
of the pressure rise, this indicates that k1 and kl can be

evaluated individually without critical measurement of

either intensity of the beam or absorption and specific

heat of the sample vapor.

Figure 4, is, to be sure, an idealized version of the

pressure response of the sample vapor; built upon this

signal will be the acoustic "bumps" discussed earlier. The

presence of these periodic disturbances is not solely

deleterious, however, and they can in fact provide needed

information about the vapor under study.

Excitation into the First Excited Singlet State

The molecular levels and decay channels which are

generally of importance in this case are displayed in

Figure 5. S~ is the initially populated vibrational level

of Sl, So the vibrationless level of Sl, To the vibration-
less level of T1 and so represents the molecular state
before excitation. For this case, equation (12) takes

the form

n c lI/hy v n nvkSv
1. 1 1 1



































cr-













ad
rl
tP

O -

o
Icr









to













O r-I
.C



r- I
I
I~ ~ r




















OIO-
IC
I r

































Sr--


OH








Or

to -
i O
04
-r 0 *
OOI~2
90% R
00 0

tn 5


LA)~

tP
m2~


Ori
vl





In
X



13


X


0 oo


>H
HI C










nSo = k n v -k on o
1 1 1 1



nTo = kgn o + k7n v kTon a
1 1 1 1 1

where


kSv = k6 + k7 + k8 + knr



k k + kn+k


and


k o = kr + knr


Again approximating the time dependence of I by a delta

function, the above set of differential equations can be

solved in the standard manner to obtain:

o -k v t
n~v =n~ve 1
1 1


nSo = k n v (e-k e- t)( v kSo
1 1 1 1


nTo = n V(k7-kgk6/(kSv-krSo)) (eT Tl -e 51 )/(kSv-k 0)
1 1 1 1 1 1

o (-kT ot -k o
+ k~6nSv~ Tl 1 )/(k v-k c) (k o-k o)
1 1 1 1 1

where n fv= nv q(r,z) and Fi~v is defined similarly to the
1 1 1
analogous term in the triplet case.

As in the previous case, the forms of the a aend b










are listed in tabular form in Table 2. Equation (15) can

now be expanded using these values in order to obtain an

idea of the gross formn of the pressure pulse expected upon

excitation into S1 Before this is done, however, let us

take advantage of the fact that kn and k1 are extremely

small with respect to the remainder of the rate constants

under consideration. This circumstance allows the deletion

of terms in equation (15) which because of it become insig-
nificant. Further, the e-kS an e-k ot temar

discarded to reflect the "step" nature of the pressure rise

due to the fast processes. By doing this, p'o~ for the

case considered here takes the form

-0VD ISC
oP o (y-1)nS~ "o,o [Sv hS ,So S hS To

IC VD ISC IC v0
+ #Sv hLS S S~o hv o o ++ ohyo
1 1 1 1 1' I 1 1


+ISBChyJ oD IS I SC) (1-e-kTo t)
1 1 1 1 1

where

VD
4Sv = k/kSv
1 1

is the vibrational deactivation yield of S1 to So

ISC
QSv= k7/kSv
1 1

is the intersystem crossing yield of S to To

IC nr
#Sv k /kSIJ
1 1










T'ABLE 2. SINGLAT::! a AND b



Tl S




1 k5k6 k5k6
Tl Sv-k~o)l7 1 ko+kTo1 (k v-k o) (kS 0-
1 1 1 1 1 1 1 1





ks

S; k~v-k o
1 1












knrho k6k (k6k I)k1rh
bu1 nS1 (k v-k o)[k k4-k ]
1 1 1 1
ik~vlilk+ kkh a o]
1' I

nr
-L k~kk hv o
561 1
(k v-k o)(k o-k 0)
1 Sl


















-1G k 36 nr
[k. k hv o
(k~v-k, o) 7 k v-k o I TI
1 1 1 1







-k knrhy o + k hv o a
k v-k o 1 1' 1
1 1



kghvqv So + k7hys' mo
1' 1 1' 1


+ k hySr


11 1



+ k hySv


6 nr
(~S-k o)(kq hv o +
(k~~ vk o) 4 S
11


knrhT kk6
S(k)
kv-kTo7kvko
11 11


TAB3LE 2 extended









is the internal conversion yield of S; to So'

IC nr
gSo = kq /kSo
1 1

are the internal conversion yield of S to So and

ISC = nr ISC
o 1/k o and 4 o = 5/k o
1 1 1 1

is the intersystem crossing yields of To to So an fot

To, respectively.
The expression above for p'o~ is quite a bit more com-

plex than that derived in the previous case and the reason

for the added complexity is simply the greater number of

states and decay channels involved. Obviously, for a molecular

system in which all the deactivation paths considered here

play a significant role, none of the radiationless yields in-

cluded in the expression for p'o~ can be uniquely determined

by the sole opto-acoustic experiment involving excitation into

S.Some of these yields may be evaluated by other (optical)
methods or may be deemed insignificant based on previous work

on molecules having similar excited state characteristics to

the sample being investigated. It is more interesting in the

present context that some may also be evaluated by further

opto-acoustic experiments involving excitation into To' TV or

So. In the previous case for example, we have shown how (IC
1'1
coul beeautdb xiaio noT. t hti
So is excited directly instead of S










-o ISC IC v
P'o~ (Y-1)nSo go [o So hv o To + Q q
1 ~1 1 1 1


+ #So g o hy o (1.-e IS I ) J
1 1 1

This equation indicates that both QISC and #S6 can be
1 1
evaluated with an accuracy determined by the accuracy to

which p'o~ a, E and goq are known. Since these

parameters can be determined with reasonably good accuracy,

this avenue of approach promises significant insight into

the dominant processes in excited states.

Consideration of the Total Disturbance:
Pressure Wave Plus Acoustic Harmonics

In the last section we limited our view to the gross

pressure change in the cell in order to examine how impor-

tant molecular parameters might be extracted from its

behavior. In this section we will investigate the total

summation of equation (14). To do so, we must derive a

form for the qmi which, in turn, requires that a spatial

dependence for the n. be specified. Essentially, an
explicit form must be determined for q(r,z).

Evaluation of the Expansion Coefficients

As was noted in a previous section, q(r,z) represents

the spatial distribution of the initially excited molecules.

The radial part of this distribution will be determined by

the radial shape of the illumination beam. For simplicity

we shall assume a uniform intensity to exist over the beam

cross-section which drops to zero outside the beam. For a









dye laser such as employed in this work which operates in

many high order modes, this is a quite good approximation

of its shape [64]. This dependence can be expressed in

mathematical form using the Heaviside function, H(x), which

is zero for negative values of its argument and unity other-

wise. Hence, for a beam of radius rb, the spatial distri-

bution to be used here can be written as H((rb-r)/rc '

Alternative beam distribution functions may be used, e.g.

gaussian, but in general the small variations they intro-

duce into the calculated form of p' is not worth the added

complexity which they introduce in the qm~
The longitudinal, or z-axis, dependence of beam inten-

sity is due to attenuation of the beam by the sample vapor.

For low to moderate power lasers where saturation or two-

photon absorption effects are not important, the diminution

of the excitation beam as it travels through the sample

vapor can be expressed according to the familiar Beer-

Lambert expression, 10Az In this expression, A is the

absorptivity and is related to the absorption coefficient

a by the equation A = a/In 10.

An expression for q(r,z) is thus of the form


q(o,o) H((rb-r)/rc) e-a

where q~o,o) is a normalization constant. The normalization

integral (equation (10)) can be easily evaluated yielding


q (o,o) = rc aL/rb (1_-e ).









Having now given explicit form to q (r,2), we must determine

the set of qmi which will solve equation (ll).
Multiplying both sides of that equation by cos(mw~rz/L) dz

and integrating over the length of the cell, we obtain


H((r-r)/ ) -(-1)me-aL L(1+6 (m))
qtolo) 2 Cmi o Yir)
a J+(mw/aL) 2 i


Letting


qm = 2q(o~o) (1-(-1)me-aL)/ aL(l+6(m)) (1+mn/aL)2~

we now have


9m H((rb-r)/rc) m~,i' o ii'r)

If we now~ take the derivative of both sides with respect

to r, then multiply both sides by rJl ijr)dr and integrate
over the cell radius we have


qm oc rJl Yir) dH((rb-r)/rc)dr = -Cqm,i Yi ocrJl ir)J1 Yir)dr.

Integrating the left side of the above equation by parts
and applying the appropriate Bessel function relations 1671

to the integral on the right, we obtain


qm[rJ (y r)H( (rb-r)/rc, oc- ocH((rb-r)/rc) ir Jo yir)dr]


= -q .lyire J: (yir )/2

The first term~ on the left of the above equation equals

zero; the second term can be evaluated from standard





Bessel function relations [67]. This allows us to write

the following general expression for the


1-(1)m-aL 2q(0,0) rb2 J(x ,B)

m~i 14 mw/L)2 aL (1+6 (m)) r 2 Jo (yjr )

where we define


J (Yir ) + J (yir ) J (x.0) + J (x.8)
J(x ,B)
J (yir ) J (x.)


with B = rb/rc'

Computer Simulation of Opto-acoustic Signal

With the form of the qml ow determined, an expression
for the pressure change in the sample cell upon optical

illumination can now be written which contains the explicit

dependence of p' on cell coordinates and time.


rb y-1 2q(0,0) 1()m-LJ(x ,B)
p' = -2 2 Jo ir) x
rc "L m,i 1+6 (m) 1+ (ma/aL) J (Yjr )

-k t
scosh .t -e u -(, i/k )sinX .t
Eb k m, mX ~ o~r/)
u~~ u uk2
u mI(16)

To test the degree of correspondence between equation (16)

and the actual pressure response in anl opto-acoustic cell,

a computer simulation of the equation was undertaken. The

objective of the simulation was to provide a theoretical

form for p' which could be subsequently checked by exper-

imental observation. In practice, this meant that the









simulation should calculate the predicted temporal evolution

of p' at a particular point chosen on the cell surface

where a suitable detector might be placed.

Examination of equation (16) suggests two unique

choices of r and z coordinates which might be of special

interest with regards to simplifying the simulation.*

Placement of the detector at the end of the cell and on

the cell axis (2 = L; r = 0) would reduce the J [yir) term

to unity for all i and allow the replacement of cos(mwz/L)

with (-1)m. However, placement of the detector in the

light path would certainly rule out measurement of beam

energy directly and might cause secondary problems such as

reflecting the beam back down the cell. The alternative

choice of detector placement is at the cell wall midway down

the length of the cell (r = rc, z = L/2). There are no

experimental problems with placing the detector in the cell

wall, although some nonuniformity in cell wall curvature

may be introduced depending on the relative size of the

detector surface and wall cross-section. As shall be dis-

cussed later, however, the small dimensions of the detector

employed cause these deviations to be minor. Insertion

of this set of coordinates into equation (16) brings

about a significant simplification in the expression;


* A third choice,r = 0 and z = 0, would certainly provide
simplification but would just as certainly dramatically
increase the problem of getting light into the cell.








most notably, for all odd values of m, the summation is

zero. The summation canl be rewritten taking this effect

into account, leaving the following equation:


p' (r ,L/ 2,t) =(r-1) E J (x ,0) C 2 (-1)m
1 m 1+6 (m) l+(2mwi/aL)2

-k t 2 2
gb k (cosw m .t-e u -(w, /k )sinw m .t)/kU +w .i), (17)

where

2 2 2y 2mn 2]
m,i i L;

For the simulation, only a single term in the

bracketed summation in equation (17) is kept. This simple

tw~o-state model would correspond in practice to excitation

into To. Higher states were not included since their

effect on the form of p', besides the initial step rise,

would be only to alter slightly the appearance of the

acoustic bumps and add to their peak-to-peak amplitude.

The actual expression evaluated in the simulation, then is

-kt
m cosm .t-e -(W ,/k )sinw .t
CJgx ') 7 (1 m,i m,i u m,i
i 1+6 (m) 2msn22
m 1+ (r ) 1+ (Um /k)

which is the temporal form of p'(rc,L/2,t) normalized to
the long-time amplitude of the pressure rise,


(y-1) #nrE(1-e-a)V

A simple Fortran program was written to evaluate the










J(x ,8) on an IBM (360/75) computer. Representative values

of this parameter for i = 1 to 20 and 13 = 0.25, 0.50 and

0.75 are listed in Table 3. The Jfxi,B) values for a chosen

value of B were incorporated into a program written for

execution on a WANG 700c Programmable calculator. This

program is capable of calculating the expression of interest

for i running from 0 to 20. It was found, however, that

in all the cases investigated, only the first few partial

sums were significant, and the sum could be truncated at

much smaller values of i. The number of significant terms

in the m summation is found to vary considerably with the

choice of a. Because of this, the summation over m was

terminated at no set value of m, but rather when a partic-

ular term caused a change in the current i sum of less than

0.1%. As the values of expression (18) are calculated at

time increments At, they are plotted, point-by-point, by a

WANG 702 Output Plotter.

A typical plot is shown in Figure 6. This plot displays

the signal calculated for excitation of a sample in the

opto-acoustic cell used in this work (to be described

later) with B=0.5, k=1 ms, c=L/k and a=2x/L. As expected,

it shows the gross exponential rise and the periodic

acoustical undulations which have been observed in pulsed

excitation experiments. On close observation, one notes

that the acoustic signal appears to be a sum of two waves

with different amplitude and frequency. The higher frequency

smaller amplitude oscillation is due to the radial modes of














Table 3. J(x.,P).


0.25 0.50 0.75


I .~I. ~L-s~------


-2.209

2.205

-1.531

0.572

0.271

-0.714

0.684

-0.317

-0.134

0.426

-0.441

0.219

0.088

-0.304

0.326

-0.167

-0.065

0.236

-0.258

0.135


-1.505

0.255

0.529

-0.147

-0.323

0.103

0.232

-0.079

-0.182

0.064

0.149

-0.054

-0.126

0.047

0.110

-0.041

-0.097

0.037

0.087

-0.033


-0.664

-0.437

-0.174

0.041

0.154

0.154

0.076

-0.022

-0.088

-0.094

-0.049

0.015

0.061

0.068

0.036

-0.011

-0.047

-0.053

-0.028

0.009

































O








II







U] II
O,




WOh
O c






















., r .


#* 1






















'"L.











" -.


z**









.. co O










standing wave formation. The larger amplitude component is

formed by the action of the longitudinal standing waves.

The frequency ratio of the two waves is "L/rc, and their

absolute frequencies are determined by both the cell dimen-

sions and the speed of sound in the gas. Because of this,

the speed of sound in the sample gas can be determined rather

accurately by measuring the period of the acoustic "bumps."

This is a very convenient happenstance because it allows a

simultaneous determination of the heat capacity ratio since


y= c2p/p = Mc2/RT (19)


where M is the molecular weight of the sample [68].

Figures 7 and 8 are two further plots derived from

expression (18). The parameters chosen are identical to

those used to generate Figure 6 except for the value of a

which is 2nr//16 L in Figure 7 and 2vr/10L in Figure 8. The

most noticeable effect on the plots due to this change is

the decrease in amplitude of the longitudinal acoustic

waves. This decrease occurs because as a decreases, the

distribution of excited molecules down the cell axis becomes

more uniform. This results in a reduced longitudinal

pressure differential occurring after molecular relaxation,

an~d hence the longitudinal resonances are driven less strongly,

Limitations and Extensions of the Theory

The purpose of this section is to tie together the

previous sections with regards to the general applicability

of the method therein described. The many assumptions made





































HO

r-1

m d






co 0
r--




-Hro
ro II


X-
Q LA \
'CON
O
II II





ct
*Ht































41r


C C






E:~~~icr~-' L'Jui5-r~_)


____YYYC1~I I~U~-YIX+~-B-CCII9C~-r


~____I _


C


II?
I
I

I

I
1
1L?


I
1
I
I
I
I
I
13


I
I
I



I
,c?
i
r?







3
c






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IJ1
c
-r






I
I=
r
Iri
I
I

I
I
I

i n

I,.
I
I
I
I
I
I
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13
C
I
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I
I
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Irr)

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i
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'1. '
~-H-c~cccccc~






































O











-rl





S11


co
co In
a,


ICON
O
II 11






to




-r-I










61






~C I
~52
s
I. a
~f'
~
I~

:r t
r.
f;:
.I
i

r. io
~


~I
:r
'r
C it?

:r

~
.

io
:r +
!rr,
r
~



1 L) iJ


P



~

I r,



;e

,,
~:

.~
lr:
c;


~ +

b'
;i,
A.
%.

ILo
~ +




'6 ..
c..
u~-~ccccecct~tcr-c*~crcct --ct~-cccm- -~us~rc:
C cO n cu









set restrictions on the type of experiments which can be

performed and the kind of equipment needed to carry them out.

These restrictions will be re~viewed~ below and their effect

on experimental design will be discussed. Also, many

effects were purposefully excluded from previous sections

for simplicity. Therefore, a discussion of how the theory

might be extended and corrected to include these effects is

provided.

Limitations on Experimental Design

Cell construction

In the foregoing sections, the sample was assumed to

be contained in an isothermal cell of perfect cylindrical

symmetry. In practice, the symmetry of the cell is upset

by ports through which the cell can be evacuated and through

which the sample can be introduced. Further, a port for

the pressure transducer must be provided; a side-viewing

port for the attachment of a light detection device is

optional. By employing a transducer which is externally

translatable, a single port can serve both to connect the

cell with the remainder of the sample handling system and

provide an access port for the transducer. This arrange-

ment does add considerably to the complexity of cell con-

struction, however, In general, one can approach suffi-

ciently close to the ideal geometry if care is taken to

limit cell connections to minimal length and to limit port

size to a small fraction of the circumference of the cell.

So that the cell has no initial temperature variation, it









should be built from materials of high thermal conductivity

and have a high thermal capacity.

The volume of the cell is determined by its length and

radius. The length is certainly the less critical of the

two dimensions; it will be shown in the next section that

the samples of low to moderate absorptivity, the pressure

pulse amplitude is independent of cell length. Optimum cell

length is thus determined by "second order" effects. In-

creasing cell length increases the useful cell volume and

minimizes the effect of "dead" space in the connectors and

ports. The cell must be short enough, however, so beam

divergence over the cell length can be disregarded and no

significant temperature variations exist at the walls.

From these considerations, it is clear that there is much

attitude in the choice of cell length.

This is not the case for the cell radius. Noting

the strong dependence of p' on rc, one might assume that

the smaller r_ is chosen, the better. We must, however,

recall that two very important assumptions depend on the

size of r Sample viscosity was neglected only under

the condition that rc be much greater than the mean free

path of the sample. More importantly, the neglect of

thermal conductivity, the ultimate basis for equation (5)

being solvable, is strictly justifiable only for times

less than r /K. Thus, choosing a larger re increases

the upper limit on the available observation time of thle

experiment. There is a lower limit of observation time










sample pressure will be determined very much by sample

volatility and the nature of the investigation, larger

pressures tend to relax the restrictions on r Both 5

and Kc are inversely proportional to pressure, so at higher

pressures lower values of rc become justifiable.

Pressure transducer

The only explicit restriction placed on the pressure

sensing device in previous sections is that it be small

with respect to the cell circumference, so as not to inter-

fere significantly with the cylindrical symmetry of the

cell. A reasonable interpretation of this restriction

would be to require that the diameter of the transducer

port be comparable to or smaller than the cell radius.

Since the transducer itself must be placed so that its

sensor is positioned directly at the cell wall, this will

cause only a small amount of nonideality.

Besides the above explicit assumption about the

transducer, two implicit ones have been presumed. The

first is that the response time of the device is short

enough to adequately transduce the rapidly fluctuating

pressure level at the cell wall. This requires a response

time of about two orders of magnitude smaller than the

rise time of the gross pressure signal. For a molecule

with a triplet lifetime of 5ms, this translates into a

response time on the order of 50ps.

A second implicit requirement on the performance of

the pressure transducer is that it is sensitive enough









to respond to the small pressure fluctuations involved.

These have been assumed to be very small with respect of

po. To help determine the sensitivity required of the
transducer, an estimate can be made of the magnitude of the

opto-acoustic pressure pulse expected. For this purpose,

the long-time value of the gross pressure pulse for a

simple two-state case can be calculated. The explicit form

for this value is obtained by evaluating equation (15) for

u = s and t very large


p' =t- (y-1)q ~b /k = (Y-1)a W 'l/ks

=(y-1)noknrh /
s s hs ks

=(y-1)#nr(1-e a)E/V (20)


where E = output energy of the excitation beamn and V = cell

volume. For small values of a, the 1-e-a term is approx-

imately equal to GL; in particular, letting po = 1 torr,

E = 10 liter/mole-cm, L = 10 cm and T = 300K, less than

three per cent error is introduced by rewriting the above

equation as


p'o~ ~ (Y-1)$nrE~po/Tr2RT (21)


where the relation a = ZC = Epo/RT has been used. If we

now let y = 1.10, nr = 1.10, r = 0.5cm and E = 5 mJ, a
S C
value of 26 mtorr is calculated for the longterm pressure

rise. This value both verifies the assumption that the

experiment causes a small change in pressure and aids in









quantitatively specifying the sensitivity needed in the

transducer. It is of further importance that a satisfactory

device should not only respond to pressures as small as or

smaller than that calculated above but also should do so

while limiting its pressure equivalent noise level to a

reasonable level.

Illumiination source

The illumination source assumed in deriving equation

(16) has been fairly well defined. It must deliver a

sharply-collimated narrow-bandwidth short-duration pulse

of optical energy. In general, the restrictions on beam

profile and bandwidth may be relaxed; these would require,

however, a redetermination of the qm~i in the former case

and in the latter case a change in the deactivation scheme

to one involving multiple-level initial population. Devi-

ation of the temporal form of the excitation source from

that of a delta pulse can also be accommodated, but this

involves a resolution of equation (12) using the new time-

dependence. One characteristic of the excitation source

which has not been discussed as yet is the pulse energy

which it must be capable of delivering. Although the abso-

lute pressure developed in an opto-acoustic experiment

depends strongly on the absorption and emission characteris-

tic of the sample, even for large values of E and (n the

excitation beam must be relatively energetic (_1 m J).

Ordinary flashlamps can provide this excitation, but when

the requirements of narrow-bandwidth and short pulse dur-










ation accompany the energy requirements, it appears that

only laser sources will suffice.

Extensions of Theory to Additional Effects

Effect of windows absorption

Absorption of the exciting light by the inner surface

of either cell window will cause local heating of the sample

in the vicinity of the surface [70). The effect of this

heating will be the production of an acoustic wave whose

amplitude will depend on the extent of window absorption.

The presence of this unwanted absorption is most easily

determined by illuminating a gas, such as N2, which does

not absorb in the wavelength region employed. If the win-

dow material is satisfactory and no traces of absorbing

substances are adhering to its surface, then no signal

will occur. In experiments in which the cell is heated to

increase the vapor pressure of the sample, special care must

be taken to avoid condensation on the windows which can

also cause this spurious effect.

Effect of luminescence heating

In our development of the molecular deactivation

scheme, decay paths were, divided ~into nonradiative and

radiative types with the former ostensibly being the sole

heat producers. Radiative decay paths do give off heat,

however, because radiative transitions to vibrational levels

of the ground state produce a non-Boltzmann distribution

of these vibrational levels. Although the amount of heat

energy produced by a molecule undergoing a radiative










deactivation is a small fraction of that produced by an

initially identical molecule undergoing totally nonradiative

decay, the problem is significant when dealing with a mole-

cule possessing a large luminescence yield.

To correct for this effect required some knowledge

of the emission characteristics of the sample. In par-

ticular, the average frequency of emission, v, must be

determined from the emission spectrum of the sample for

the emitting state in question. Then, for a state u which

undergoes radiative decay to the ground state, the term

61um(hy -hS) is added to the term in p' which accounts

for the heat produced by the corresponding nonradiative
lum.
process. In the above expression, qu is the luminescence

yield of the state u. Addition of this further term to p'

may cause some difficulties; specifically it may now become

impossible to derive the yields of all decay processes for

all the states of interest from opto-acoustic measurements.

In these cases, the problem will require the use of optical

methods to complement the information gained from the opto-

acoustic studies.

Effect of a second gas

The effect of a second nonabsorbing or buffer gas on

the excited state decay parameters of an absorbing vapor

is easily studied using the opto-acoustic method. As noted

in the introduction, several quenching studies have already

been published. The only direct changes in the theoretical

formulation which accompany the study of a gas mixture is










that the heat capacity ratio used in equation (16) and

elsewhere must now be that of the mixture, and po in

equation (21) is now taken to be the equilibrium partial

pressure of the absorbing species.

In general, the addition of a buffer gas will affect

the rates of the various relaxation processes occurring

in the excited sample and may also open new channels for

release of excitation energy. These actions will change

both the amplitude and time evolution of the opto-acoustic

signal relative to that observed in the pure sample. Aside

from these changes, the amplitude will also be affected by

the change in y noted above. Further, since the mixture

of a buffer gas plus sample may have a significantly dif-

ferent thermal diffusivity than that of the sample gas alone,

especially if He, Ne or H2 are used, the temporal part of
the signal will also be affected. Specifically, an increase

in thermal diffusivity will cause the sample to cool more

rapidly and thus limit the available observation time.

Effect of photochemistry

Inclusion of the possibility of a photo-induced

chemical reaction adds another decay path to those already

available to the excited state. Predicting the effect on

the pressure signal in the cell of a molecule traversing

this path is much more difficult, however, than for a

standard radiative or nonradiative process. The reason

for this difficulty is that a molecule undergoing photo-

reaction can contribute to the overall pressure response









in several ways. Firstly, the endo- or exothermicity of

the reaction step must be considered. Depending on this

value, the products of the reaction will have more or less

energy available for heating than the energy of the

initially absorbed photon. Secondly, the products of the

photoreaction may not be formed in their ground electronic

state. Thus, a whole new set of excited state decay

kinetics must be investigated to determine how that elec-

tronic energy is dissipated. Finally, the initially excited

molecule may break up into a number of products. Thus,

regardless of the heat released or potentially available,

the pressure of the vapor increases solely due to the

increase of the number of molecules in the cell.

It is clear, then, that studying photochemically

reactive systems via time-resolved opto-acoustic spec-

troscopy is a complex matter. This is not to say that such

a study can not be done, but rather that one must carefully

investigate the probable pathways open to a system before

such a study is undertaken. If a well-defined model can

be constructed for the decay kinetics of a photochemically

reactive species which does not involve a change in the

number of gaseous molecules in the cell, then this model

in conjunction with the theory developed in this chapter

can be used to predict the pressure behavior of a sample of

this species upon pulsed optical illumination.

If a change in the number of molecules in the vapor

phase accompanies photoreaction, then the detailed










prediction of the pressure response of the sample upon

optical illumination is beyond the scope of this work.
However, one might expect that the overall response should

not be greatly different than what might normally be

observed in the absence of photoreaction, with one signi-

ficant exception. Where photoreaction takes place accom-

panied by a change in the number of gaseous molecules, the

long-time pressure in the cell will not return to its

initial level. The change in pressure can be written by

analogy with equation (20) as
N'RT ~pr -al E
Pp~r It-+m N hv 4 1e

where N' is the difference between the number of moles of

reactants and the number of moles of products per mole of

excited molecules which react, and $pr is the yield of the

photoreaction (number molecules reacted/number molecules

excited). If one calculates a typical value of ppr t~m
one finds it is about one order of magnitude smaller than

p'o~olta. for comparable values of mpr an nr dwt
N' = 1. In general, this presents no problem, since the

device used for the steady-state measurement involved in

evaluating ppr t~m usually will have a much greater sen-
sitivity than the device required to follow the rapid

fluctuation of p' during transient heating.





CHAPTER TIIREE
EXPER.IMENTAL SYSTEM



Equipment



Opto-accustic Cell and Vacuum System

During the course of this work, several opto-acoustic

cells were constructed and used for preliminary studies.

As work progressed, design changes were made to increase the

ruggedness of the cell and especially to provide better

access and shielding for the dynamic pressure sensor. The

final result of this refinement process is diagrammed in

Figure 9. The cell consists basically of two chambers:

the experimental chamber in which the sample is optically

excited and a second larger reference chamber. These

chambers are mounted together on a height-adjustable alumi-

num platform which can be leveled.

The experimental chamber is fashioned from a block of

aluminum 3" x 4" x 6 1/2" by drilling a 1/2" diameter hole

down the center of the long axis of the block. At either

end of the chamber are attached l" diameter Suprasil quartz

windows with vacuum-tightness insured by rubber "O"-rings.

At the midpoint of the chamber length a 0.1934" diameter

hole is drilled perpendicular to the chamber axis on the




~~~_~~, _~.ts-l*;i s~ son~ve. E ^i..i6_ )- L~Li IC~ I.(-lrl IC I.-. ---i (--)X --. ---(II1_I-l r _--_5~I; I-ws 4-e L








74





















ME~












oa ad







-H m .-

's **- I lI II4


r(O I 0) I~
a, C




- C --l r


ct rl C











large face of the blocks to provide a port for the pressure

transducer. Provisions for mounting a phototube on the

opposite face of the aluminum blcck are provided and a

second 0.1934" diameter hole is drilled diametrically

opposite the first to allow light output through a third

Suprasil window. A 3/16" diameter port for gas transfer

from the reference chamber is placed 3/4" from the cell

end on the same side as the transducer port.

The transducer which measures the excitation-induced

dynamic pressure fluctuations is attached to the experi-

mental chamber after mounting it in its own special holder.

Because the transducer is a differential device, its refer-

ence side must be held at the initial pressure of the

sample vapor. To accomplish this, the transducer mount is

covered by an aluminum cup which, when fastened to the cell

wall, provides a vacuum-tight compartment. This cup is then

connected by copper tubing through bias vacuum valve (A) to

the reference chamber.

Gas flow between the two chambers takes place through

1/4" copper tubing and is regulated by the action of brass

vacuum valve (B). A capacitance manometer is connected

in parallel with this valve and measures any pressure

differential which may exist between the experimental and

reference chambers. This manometer also serves to measure

the initial pressure of the sample as part of the procedure

which shall be discussed later.










The reference chamber is basically a 5" long, 1 3/4"

diameter closed cylinder with three radial ports and one

port at each end. The uses of the radial ports have al-

ready been discussed. One end port is employed for vapor

entry of samples and this port is controlled by vacuum

valve (C). The valve is connected :o a metal "quick-

connect" which allows facile attachment and removal of

sample containers. Cell evacuation takes place through

the reference chamber port controlled by valve (D). Through

this valve the opto-accustic system is connected to a

glass vacuum line and gas handling manifold. The vacuum is

provided by a mercury diffusion pump used in conjunction

with a liquid nitrogen cold trap and mechanical roughing

pump. Line pressure is monitored by an ionization gauge,

and pressures down to 2 x 10-6 mm of Hg are attainable

in the line.



Excitation Source

As discussed in the previous chapter, the requirements

for the excitation source for time-resolved opto-accustic

experiments are most fittingly satisfied by a pulsed laser.

Especially useful for general work of this type is the tun-

able laser, which would allow excitation of electronic

transitions over a broad range in the visible and ultraviolet

spectral regions. In general this type of laser employs a

solution of an organic dye which, upon excitation in a










cavity equipped with suitable reflectors, has the ability

to lase over a broad band of 10 to 50 nm in the optical

spectrum. By replacing the rear reflector of the laser

cavity with an element whose reflectivity is sharply peaked

at one wavelength in the lasing band, e.g. a grating,

lasing will occur only at this particular wavelength with

only slight loss of optical energy [71]. Thus, by tuning

the cavity's selective reflector to a particular wavelength,

monochromatic output can be achieved anywhere within the

lasing region of the dye being employed.

The optical energy by which the lasing dye is excited

or "pumped" can be supplied either by a fixed frequency

pulsed laser, e.g. nitrogen or argon lasers, or by a flash-

lamp which emits high intensity broad band excitation. A

laser pump would allow for very high repetition rates as

well1 as provide very short lasing pulsing. On the other

hand, a flashlamp excited device provides much more ener-

getic optical pulses and is considerably less expensive

than a laser-pumped system. As was shown in a previous

section, the pressure fluctuation produced in an opto-

acoustic experiment is quite small and linearly dependent

on pulse energy. So, primarily on the basis of the pulse

energy available, the decision was made to utilize a flash-

lamp-pumped dye laser system in this work.

The system chosen (Model DL 1200, Phase-g Co.) is a

complete dye laser system including flashlamp, power supply,





dye circulation, cavity reflectors, tuning grating and

control electronics. This system is primarily designed

for use with dyes lasing in the 320 to 420nm region but

will also accept dyes lasing throughout the visible if

the cavity is fitted with reflectors optimized for the

visible region. The rated pulse energy from the system

(for Rhodamine 6B at 588n1m) is 150mJ, and the manufacturer's

literature describes this rating as "conservative." The

data presented on ultraviolet dyes indicates output energies

in the 330 to 420nm region of from 5 to 15mJ depending on

wavelength and dye chosen (see Figure 10). Bandwidth is

given as 0.1-0.2nm when the laser cavity is grating tuned.

The laser pulses are provided in a beam nominally 5mm in

diameter and with a stated pulse width of less than 250

ns (full width at half maximum). The firing mod~e is either

manual or by external trigger pulse, and the maximum rep-

etition rate is given as ten pulses per second.

We elected to purchase this commercial laser system

rather than construct one of our own design so as to

minimize time spent on laser research at the expense of

the major interest of our investigation. As it occurred,

this was not the case. Component failures in the laser

system were numerous and continued to occur from time to

time throughout the course of this study. These problems

aside, however, the laser, under the best conditions, fell

far short of expected performance in three citiical areas:






























mrm -H I
He a,) al ,C &

a d '0 0~~

0 rd OH 6) 0
OO >I 'C -:0
Q 0 0~ He


O -M 4-1 IN
UN 'Ur r
HUU H < 61
a, a0 N
> pi 5'0 L 4
a 0 IQ OcoH
gw Fa ,CM
to 0 RIOH
to CO rJ *l ~ -A L
rd 0~ ,CO .0 L-r -
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a4 OW 0 0o
o N-I HO rl .n
'0 > .0-0 IO m
a) id N N V
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4d a, a0- II -H0O
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pulse repetition rate, optical bandwidth and output energy.

Because these reduced performance levels so affected the

course of this research, we will describe here our efforts

to achieve the expected laser operation and report the final

performance obtained.

Preliminary work with the laser system was performed

using the ultraviolet laser dye No. 386 (New England Nuclear)

in dimethyl formamide (DMF) solution, as per manufacturer's

suggestion. This dye is supplied as a 10-3M1 concentrated

solution and is diluted to 5 x 10-4M using Spectroquality

DMF (Matheson Coleman and Bell). Absorption and emission

spectra of this dye are shown in Figure 11. The front

reflector used in conjunction with this dye, hereafter

referred to as R1, is matched to the output characteristics

of No. 386, having a peak reflectance of 85% at 389nm. The

spectral variation of the reflectance of RI is indicated in

Figure 12.

Before losing can be attempted, the laser cavity must

be aligned. This is accomplished with the use of a 1mW He-Ne

laser (Metrologic). The He-Ne laser is first adjusted so

that its beam is co-linear with the flashlamp using the pin-

hole caps provided. When a mirror is used as the rear re-

flector of the cavity, the front and rear reflectors are

then adjusted so that they direct the He-Ne beam back upon

itself. See Figure 13. The laser is now roughly aligned.

At this point, the He-Ne laser is removed and the dye laser



























-0 O
4d *H -H
LI 0 0





Em4



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0 I -HMd

O X 0 r
UNHl



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LA
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O C

rl O


































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r-1








:--I
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LD







LA




LA
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of

00O


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E("

PAGE 1

TIME-RESOLVED OPTOACOUSTIC SPECTROSCOPY By JOSEPH J. WROBEL A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FCR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1976

PAGE 2

To my parents

PAGE 3

...The investigations of chemistry have about them all the fluctuating fortunes of a deep and subtle game. There are the same vacillations of good and bad luck; the same tides of hope and fear; the almost certain prospect of success dashed and darkened by failure; the grief and disappointment of failure dispelled by glimpses of bright hope. So many are the disturbing influences, so subtle the causes that derange experiments, where some infinitesmal excess or deficiency, some minute accession of heat or cold, some chance adulteration in this or that ingredient, can vitiate a whole course of enquiry, requiring the labour of weeks to be all begun again, that the pursuit at length assumes many of the features of a game, and a game only to be won by securing every imaginable condition of success. Charles Lever in his novel, "One of Them," written in the middle of the 19th Century.

PAGE 4

ACKKOWLE DGMENTS I would like to acknowledge Dr. Martin Vala for the guidance, encouragement and assistance he provided throughout the course of this work. His confidence in me and the remarkable understanding he displayed over the long period of our association made the completion of this work possible. I would like to acknowledge my wife Margaret, whose peanut butter, jelly, patience and love kept my body and soul together, and my daughter Jennifer, whose welcomehome smile could make the woxld go away. I would also like to acknowledge those fellow greiduate students, with whom I worked and with whom I played, for helping to lighten the burden and, likewise, the staff of the Department of Chemistry both in the offices and in the shops for their essential contributions.

PAGE 5

TABLE OF CONTENTS ACKNOWLEDGMENTS i v LIST OF TABLES vii LIST OF FIGURES viii KEY TO SYMBOLS x ABSTRACT xiii CHAPTER ONE. INTRODUCTION 1 CHAPTER TWO. THEORETICAL CONSIDERATIONS 10 Introduction and Direction 10 The Solution of the Heat-Flow Equations 13 Simple Two-State Model 13 Multi-State Model 17 Neglect of density fluctuations 21 Neglect of thermal conductivity 22 The Extraction of Molecular Parameters from the Gross Pressure Signal 32 Excitation into the First Excited Triplet State 33 Excitation into the First Excited Singlet State 38 Consideration of the Total Disturbance: Pressure Wave Plus Acoustic Harmonics 47 Evaluation of the Expansion Coefficients 47 Computer Simulation of Opto-acoustic Signal 50 Limitations and Extensions of the Theory 57 Limitations on Experimental Design 52 Cell construction 62 Pressure transducer 64 Illumination source 66 Extensions of Theory to Additional Effects 67 Effect of window absorption 67 Effect of luminescence heating 67 Effect of a second gas 68 Effect of photochemistry 69 CHAPTER THREE. EXPERIMENTAL SYSTEM 7 2 Equipment 72 Opto-acoustic Cell and Vacuum System 72 Excitation Source 76 Pressure Detect ion System 115

PAGE 6

Data Gathering and Processing System ^25 Operating Procedure 132 CHAPTER FOUR. OBSERVATIONS 136 Flashlamp Experiments 135 Laser Experiments 133 Choice of Sample 138 Pyridazine 138 Oxalyl chloride 340 Results 151 CHAPTER FIVE. COMMENTS 160 LIST OF REFERENCES 164 BIOGRAPHICAL SKETCH 169

PAGE 7

LIST OF TABLES Table Description Page 1. Triplet a . and b . 36 uj u 2. Singlet a . and b . 44 uj u 3. J(s.,3). 54 4. Characteristics of laser system. 113 vi x

PAGE 8

LIST OF FIGURES Figure Description Page 1. Experimental pressure signal of 0~. 12 2. Diagram of two-state model. 15 3. Diagram of triplet state processes. 35 4. Form of pressure rise for triplet excitation. 40 5. Diagram of singlet state processes. 41 6. Plot of expression (18), high absorptivity. 56 7. Plot of expression (18), moderate absorptivity. 59 8. Plot of expression (18), low absorptivity. 61 9. Diagram of opto-acoustic cell. 74 10. Plot of calculated pulse energy versus wavelength. 80 11. Spectra of dye No. 386. 83 12. Reflectivity of Rl reflector. 85 13. Diagram of laser alignment. 87 14. Diagram of laser-monochromator alignment. 90 15. Plot of nitrogen emission lines versus distance on photograph. 9 3 16. Plot of wavelength of laser output versus micrometer setting. 98 17. Schematic of photodiode circuit. 100 18. Effect of intercavity reflector. 103 19. Absorption spectrum of optical filter. 109 20. Oscilloscope tracing of phototube signal from laser pulse. 112

PAGE 9

Figure Description Page 21. Schematic of standard Pitran circuit. 117 22. Cross-section of Pitran mounted in cell. 120 23. Block diagram of Pitran circuit. 123 24. Plots of channel count versus dwell time. 129 25. Block diagram of elements of opto -acoustic experiments. 134 26. Absorption spectrum of pyridazine vapor, 4 . Cm path. 142 27. Absorption spectrum of oxalyl chloride vapor, 10cm path. 145 28. Absorption spectrum of oxalyl chloride vapor, 6.4m path. 14 8 29. Plot of absorbance of S ->T. band of oxalyl chloride versus pai~h lengtn. 150 30. Plot of pressure rise due to oxalyl chloride decomposition. 155 31. Signal generated by laser firing. 158

PAGE 10

KEY TO SYMBOLS Symbol a Uj C ,C P v E f h H(x) I Definition Expansion coefficient of n . Absorptivity; A = eC u Z a .W. Beam size correction factor Speed of sound; c' YP/P Heat capacity at constant volume Concentration Molar heat capacity at constant pressure, volume Energy Oscillator frequency Planck's constant Heaviside function Energy flux J ,J, ,J Zero, first and second order Bessel functions First-order rate constant Thermal conductivity Length of sample cell Molecular weight Number density of molecules in state j Units mol cm none -3 -1 erg cm s none -1 cm s -1 , -1 erg g deg mole 1 -1 1 1 A 1 erg mole deg erg

PAGE 11

Symbol N A OD P P q(r, z) *m, 1 R S o' S l' S 2 t T T l U -> v V w w. x. X Definition Avogadro's number Optical density; OD=AL Pressure Expansion coefficients of p Spatial dependence of Q Expansion coefficients of q(r, z) Source term Radial coordinate Beam radius Cell radius Molar gas constant Ground, first and second singlet states Time Temperature First excited triplet state Internal energy Flow velocity Sample cell volume Power Rate of heat release from molecule in state j Root i of J, x , /r 1 c Axial coordinate

PAGE 12

Symbol Definition Units a Absorption coefficient; a = eC cm 3 Ratio of beam to cell radii; none 3 = r. /r b c y Heat_ca£acity ratio; none Y = C /C 6(t) Delta function none ? -1 e Molar extinction coefficient cm mole 2 -1 e Molar coefficient of cm mole absorption; e = eln 10 6 Angular coordinate rad 2 ] k Thermal diffusivity; cm s < = K/pc K v A . Acoustic resonance frequency; s m ' 1 A 2 . = c?[y? + (irnr/L) 2 ] m, l J i v . Frequency of transition from s *' state j to state 1 5 Mean free path cm ^ • -3 p Density g cm Yield of process X from state j 0) . Acoustic resonance freguency; s m ' 1 w 2 . = c 2 [y 2 + (2m7T/L)^]

PAGE 13

Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy TIME-RESOLVED OPTO-ACOUSTIC SPECTROSCOPY By Joseph J. Wrobel August, .1976 Chairman: Martin T. Vala Major Department: Chemistry A new approach to the study of excited state radiationless processes of large molecules in the vapor phase is proposed. The basis of the approach is the opto-acoustic effect, the generation of temperature and pressure fluctuations in a sample upon absorption of optical energy. The set of heat flow equations governing this effect are constructed and solved, under certain restrictions, for a sample in an isothermal cylindrical cell acted on by a short pulse of light. Computer simulations of the expected pressure signals are presented, and it is shown how molecular parameters can be extracted from experimental measurements. Limitations on experimental design imposed by theoretical assumptions are discussed and applied to the construction of an experimental system for performing time-resolved opto-acoustic spectroscopy. The properties of oxalyl chloride are examined, and it is chosen as the object of experimental study. An attempt to verify the theorecica.My

PAGE 14

predicted opto-acoustic signals using oxalyl chloride is made but is unsuccessful due to insufficient pulse energy from the excitation source employed. Improvements of the experimental system are suggested, and areas for future work are designated.

PAGE 15

CHAPTER ONE INTRODUCTION In the past several years a great deal of work has been done exploring the theory of radiationless processes in polyatomic molecules [1-7] . Although differing theories have posed the problem in different frameworks, they all have in common the goal of explaining and anticipating the influence of temperature [8,9], isotopic substitution [10,11], excitation energy [12,13], singlet-triplet energy gap [14,15] or vibrational state of the molecule [16,17], on the nonradiative decay rate. As in all branches of science, previous experimental work led to current theoretical interest which now demands more experiments on which to judge the merit of the theory. In this case, since all the theories of radiationless transitions deal with "isolated" molecules, the need grew for experimental studies of vapor phase molecules at pressures low enough so as to preclude collisions of an excited molecule during the lifetime of its excitation. Also, since the deactivation rates were known to be dependent upon the excitation wavelength at these low pressures [18-20] , restrictions had to be made on the band width of the incident light thus decreasing its available intensity.

PAGE 16

Although the advent of the tunable laser [21] will serve to compensate for the diminished intensity of irradiation at first caused by the second restriction, experimentalists studying excited states by their light emission must still reckon with the small number of photons which are emitted from the low density vapor. The sensitive light detection required in these cases initiated the use of photon counting techniques to measure lifetimes and yields. However, photon counting has its share of pitfalls [22] which add to the already difficult problem of measuring accurate radiative yields from which the non-radiative yields are derived [23]. There is a somewhat separate problem associated with studying molecular de-excitation solely by light emission. Even if one can accurately measure the lifetime and radiative yield of the monitored state and thus derive the overall non-radiative yield, the distribution of the excitation energy among the available non-radiative pathways remains unknown. Even if photochemical reactions are excluded, one cannot tell, for example, upon excitation into an. upper singlet state, what portion of the non-radiative yield is due to intersystem crossing to the triplet manifold and what portion derives from internal conversion to the ground electronic state. It is because of the need for more information on excited state properties in the low pressure vapor and because of the problems associated with the usual spectre-

PAGE 17

scopic methods for getting this information that we sought an alternative approach. The most appealing approach, of course, would be some course of experimentation that would allow us to examine the radiationless behavior of a molecule directly, rather than through its radiative properties. At the same time, it would have to be sensitive enough to pick up the small amounts of heat given off during nonradiative decay. This line of thinking led us to investigate the application of the opto-acoustic effect to this area of research. Initial investigations of the opto-acoustic effect date back almost a century. Following the invention of the telephone, Alexander Graham Bell continued his investigation in the area of voice transmission. Specifically, in 1880, he was involved with the production and reproduction of sound by light, i.e. transmitting sound not through wires but through air using an undulatory beam of light [24] . Taking advantage of the then recently discovered effect of light on selenium's electrical resistance, Bell constructed a receiving circuit comprised of a telephone, a battery and a piece of selenium. Using such a device and a proper transmitter, he found he could communicate over long distances. Bell then questioned whether the molecular disturbance causing the effect required the telephone and battery to be heard, and, further, whether the sound generation was specifically a property of selenium or rather one which would occur in a variety of substances. After a series of

PAGE 18

experiments using samples in the form of thin diaphragms, he concluded that sound could indeed be produced by substances of all kinds. Further experiments by Bell [25] and others [26-30] established that the effect was a general phenomenon as long as the substance was irradiated with a source whose radiation it could absorb. They reasoned, and correctly so, that the absorbed energy was degraded in the sample to heat pulses which caused pressure pulses to occur in the surrounding gas. Thus if the incident light were chopped at a frequency in the sound region, the sample could be heard to emit sound of the same frequency. In 1881 Bell [25] introduced a device by which one could examine the absorption spectrum of a sample by noting the intensity of the sound produced when the sample was irradiated by chopped radiation from different regions of the spectrum. This device Bell called the spectrophone. Although Bell noted the promise of the spectrophone in his 1881 paper, especially in examining infrared absorption, it was not until 1938 that the device was rediscovered by Veingerov [31], and later by others [32-34], who sought to exploit the opto-acoustic effect for both qualitative and quantitative analyses of gases based on their infrared absorptivity. Several types of radiation detectors were built at this time incorporating the effect as an integral part of the detection scheme [35] . As the spectrophone technique was established for vapor analysis in the infrared, the application of the method broadened. The spectro-

PAGE 19

phone was used to measure absorptivi ties in the microwave region of the spectrum [36], and its use in the visible and untraviolet regions was investigated [37] . More recently, the use of the spectrophone technique for detection and analysis has brought high sensitivity to mm and cm spectroscopy of gases [38-39] . It has also proven to be a very sensitive method for detection of air pollutants [40-42] . Further, since this type of spectroscopy does not require that samples be translucent, it has opened the door to the study of absorption spectra of solids, biological materials and other opaque substances [43] . As the use of the spectrophone for analyses grew, a second use for this technique was discovered and investigated. In 19 4 6 Gorelik [44] proposed that the spectrophone could be used to measure vibrational relaxation times of gases. Slobodskaya [4 5] did the first work along these lines on carbon dioxide and his results were subsequently given a theoretical analysis by Stepanov and Girrin [46] . Two methods of determining vibrational relaxation times using the spectrophone were investigated both theoretically and experimentally [47] . The phase shift method relates the vibrational relaxation time to the phase shift between the sinusoidal excitation and the resultant sinusoidal pressure changes. The amplitudeor frequency-response method measure the amplitude of the pressure response as a function of the frequency of the excitation which theory shows is related to the vibrational relaxation rate.

PAGE 20

,„,-.ynmvious methods in Both methods have the advantage over previou • r *-« 1 narlicular molecular that they can be made specific to a paruoj ,3j,H nn limited to a single vibration by using incident radiation mux spectral band. , • -.-rr^rHhns been revived Interest m opto-acoustic etieci nu_> r„o-i * fnnl for studying molecules again in recent years [48] as a tool roi i . ., , ^ uu-rwinlot radiation, under the action of visible and ultravxOM.u r~^h -i-ViA-twhile polyatomic The interest here lies in the fact that wnu r y -ii,7 ovfifod relax almost molecules which are vibrational ly excitcu . totally by nonradiative pathways, electronically excited molecules typically deactivate along numerous pathways including those which lead to light emission as well as -,,-^cr. nf an opto-acoustic photoreaction. Since the response or an n c 4-v.o ihcmrbcd energy which cell is only to that protion of the aDsorot. yj ..+-•;,Qn^f-troscopy allows one is released as heat, opto-acoustic spectr j. vi to measure the yield of nonradiative pathways directly, and in this way it complements the standard method of s, +-^c hv 1-iaht emission alone, stydying molecular excited states Py ns riL In 1967, employing broadband excitation Hey [49] applied the standard spectrophone amplitude-response t: ^ni3Y3 4 -inn rates of dye technique to the measurement of reiaxatxun molecules in solution with some success. • -I-,-,nnmnnnnds i" solution, studies were performed on similar compound A r ,joa ^v-qtate illumination In the first, Seybold et al . used steady sw u,r 3 nnillorv rise techand detected pressure increases by a capii -> rem x ^ a r^^\e et al . employed broadband nique [50] . In the second CainHi—Si.' ti Q nninnpd with a capacitance flashlamp excitation and a cell equipped wi 1

PAGE 21

microphone to detect the resultant pressure pulse [51] . In the latter study, the quantum yield of triplet formation was calculated by comparing the fast heating due to singlet state deactivation with the slow heating resulting from the triplet state decay. Since the inception of the present work, investigations of excited state kinetics employing the optoacoustic effect have been extended to the gas phase. deGroot et a l. uncovered details of aldehyde photochemistry which could not have been easily detected if standard photochemical methods had been employed [52] . Other photochemical studies were later carried out by Karshbarger and Robin on N0 2 and SC> 2 [48]. Quenching of iodine atoms has also been studied opto-acoustically by these same authors [53] . Another quenching study was carried out by Parker and Ritke who concerned themselves with deactivation of the first vibrational level of the lowest electronic singlet state of 2 [54-56]. Recently, Kaya et al . have examined the opto-acoustic spectra of biacetyl [57] and the azabenzenes [58] using a spectrophone technique. Their qualitive interpretation of these spectra provides new insight into the radiationless processes which affect the excited state kinetics of these molecules. Also recently, Hunter and Stock began a series of papers on photophysical processes in the vapor-phase measured by the opto-acoustic effect. The first of these

PAGE 22

papers [59] developed a multi-state relaxation model to be used as a basis for the study of radiationless processes from excited electronic states. This model essentially incorporates the complex deactivation schemes available to electronically excited polyatomic molecules into the basic spectrophone theory. Later papers by the. same authors applied this model to the study of excited benzene [60] and biacetyl [61]. Although each compound was studied at only one particular wavelength of excitation, the results show the usefulness of the opto-acoustic approach. Using both phase shift and amplitude-response data, the lifetime and yield of formation of the triplet state of both compounds were determined in agreement with previously reported values where available for comparison. In this work it is our intention to further explore the application of the opto-acoustic effect to the examination of photophysical processes. Our approach, however, differs from that of previous workers who used the standard spectrophone technique to study indirectly the course of energy flow in the sample. In the present work, a pulsed excitation source will be employed in conjunction with suitable transient recording instrumentation to study directly the time-evolution of the resultant pressure wave which appears in the gaseous sample upon irradiation. As will be shown in the following chapter, such an approach should allow us to gain both lifetime and yield information in what we consider to be a more convenient

PAGE 23

manner than the traditional spectrophone technique. Further, by utilizing a tunable dye laser as the source of the incident radiation, the manner in which these quantities vary as a function of excitation wavelength may be explored.

PAGE 24

CHAPTER TWO THEORETICAL CONSIDERATIONS Introduction and Direction Although no formal theory describing the pulsed optoacoustic effect has previously been reported, the effect has been observed in molecular oxygen by Parker and Ritke [54]. They used a Nd: glass laser to pulse-excite molecular oxygen in a high-pressure cell and monitored the pressure changes using a capacitance type microphone. The pressure response to the optical pulse (reproduced in Figure 1) was found to be fundamentally an exponential rise to a limiting value followed by a slow return to the initial value. The rise time of the pressure signal was found to correspond to the lifetime of the initially excited 2 vibronic level as determined by Parker and Ritke from a frequency-response opto-acoustic approach [54]. Superimposed upon this rise was an oscillatory component corresponding to an acoustic resonance of the cell. This secondary signal was ascribed to absorption of the excitation beam by the cell windows. In this chapter, these observations will be given a theoretical foundation by constructing a model describing the pressure disturbance which occurs in a vapor upon the 10

PAGE 25

0)

PAGE 26

12 GO E

PAGE 27

13 absorption of a pulse of optical, energy. Also, the dependence of the magnitude and time-evolution of this pressure fluctuation upon the molecular parameters of the sample will be examined. Further, the effects of the solution on experimental design will also be discussed. The Solution of the Heat-Flow Equations Simple Two-State Model To prepare for dealing with the complexities of the model for a real experimental system, a simplified model is first considered. In it, it is assumed that the molecules of the sample vapor possess only two energy states (see Figure 2) a ground state and an excited state which can be populated from the ground state by absorption of a photon with energy hv. Further, it is assumed that a molecule in the excited state can lose energy and relax back to the ground state in two ways, either by radiation of the absorbed photon with first-order rate constant k or by nonradiative loss with first-order rate constant k What we wish to predict is how the pressure in the sample vapor will change with time if it is allowed to absorb an amount of radiative energy E . Let us start by examining the rate at which heat energy is given up by the excited molecules. If we let E = heat energy released and n (t) = number density of excited molecules at time t, then

PAGE 28

C M fD

PAGE 29

15

PAGE 30

16 dE/dt = k nr n exc (t)hv V, where V is the sample volume. Since the excited state decays by first-order processes only, it is a simple matter to show that n (t) = n (0)exp(-(k nr +k r )t) = (E /hv) exp (-kt) exc exc a V nr r nr by which we obtain dE/dt = k E exp (-kt) , where k = k +k Integrating this expression, we find that the heat released as a function of time is given by E k nr E (l-exp(-kt))/k 4> nr E (l-exp(-kt)) , a a where = k nr /k is the nonradiative yield of the state initially excited. The change in pressure p' produced in the sample can be related to E through the ideal gas lav/ and the relation between E and the resultant temperature change 1" brought about in a constant volume system. Thus p' = NRT'/V = (NR/V) (E/NC ) = (y-D 4» nr E (1-exp (-kt) ) /V (1) V 3. where N is the number of moles of the sample, y is the heat capacity ratio C /C , C is the molar heat capacity at constant pressure, C is the molar heat capacity at constant volume and R is the gas constant which is equal to C ~C for an ideal gas. Equation (1) shows how, in this simple model, the pressure change in a sample upon absorption of a pulse of optical energy is related to parameters of the excited state.

PAGE 31

17 It makes clear that the lifetime of the excited state (k ) can be determined directly from the rise time of the pressure jump. Further, if V, E and y can be evaluated nr independently, it shows that the value of $ can be determined from the amplitude of the pressure jump. This is the basic result of time-resolved opto-acoustic spectroscopy; it relates the time-evolution of the radiationinduced pressure signal to an excited state lifetime and provides from the pressure amplitude information relating to yields of radiationless processes. In the next section the theory of the opto-acoustic effect will be treated more rigorously. It will be shown that the multiplicity of states in real molecules and the spatial nonuniformities of the absorbed radiation cause the form of the pressure signal to become somewhat more complex than that given in equation (1). However, the method of extracting excited state parameters from this signal will not differ significantly from that used on the simple model examined above. Multi-State Model Let us consider a molecular vapor at equilibrium contained in a cylindrical cavity of length L and radius r c . Let the initial state of the gas be defined by the density p , the pressure p and the temperature T . If the vapor is now pulsed with optical energy in an absorption region, the resultant heating brought about by the molecular relaxation will cause the gas to undergo local variations in oressure, density and temperature and to assume the new

PAGE 32

values of these parameters p, p and T respectively. Also, in response to these local variations, the gas will assume a flow velocity v *. All these changes must occur under the constraints imposed by the equation of state of the gas ** as well as the following three partial differential equations which reflect the quantities conserved in molecular collisions in the absence of external forces [62, p. 698]: 1. conservation of mass Dp/Dt = -p 0/8r«v) 2. conservation of momentum Dv/Dt = (d/dr
PAGE 33

19 assumptions is in order. First, we ignore the dissipation of energy due to viscous effects. This action is rigorously justified only if the product of the shear viscosity times the divergence of the flow velocity is much less than the pressure [62, p. 521;63]. If the divergence of v is approximated by v/r and the simple kinetic theory definition of the coefficient of viscosity as one-third the product of density, average molecular speed and mean free path is adopted [62, p. 131, then an equivalent requirement for ignoring viscous effects can be stated. This requirement is that the flow velocity be less than or comparable to the speed of sound in the gas while at the same time the mean free path in the gas be much smaller than the cell radius. The restriction on the flow velocity should be easily met since the effect of the pressure pulse will be slight. As for the other condition, for a molecule the size of biacetyl, at a pressure of one torr , the mean free path is _3 calculated as 2x10 cm [58] . Since the cell to be used in this work has a radius almost three orders of magnitude greater than this value, we are justified in ignoring viscous effects. This allows the replacement of the pressure tensor p with the scalar pressure p times the unit tensor. Next, we assume that the disturbances caused by the optical pulse will be very small. That is, we let p = P n +P'/P = P +P 1 and T = T + T" where the primed terms represent small local changes from the initial bulk values which occur upon absorption of the optical, pulse. Opon

PAGE 34

20 insertion of these expressions for p, p and T in the general conservation equations and subsequent deletion of terms second-order in p' , p 1 , T 1 or v, we arrive at the following set of equations; 3p'/3t = -p Q V-v (2) 9v/3t -Vp'/P (3) and DU -, /Dt + c 3T'/3t = -V-(I + I rj )p -p V«v/p (4). elec' v ' R K o ^o ' H o U. . has been divided into a sura of two terms; U , tot elec represents the energy per gram stored in electronically excited molecules, and c T" represents the internal energy per gram expended in translation motion and the population of electronic ground state rovibrational levels. Recognizing that 1= -KVT" [62, p. 717] where K is the gas thermal conductivity and, from equation (2), that v*V = -(dp'/dt)/p , we can rearrange equation (4) to obtain: P o c v OTV3t) -KV T'-p o (dp'/dt)/p o = -V'I R -P (DU elec /Dt) (5) The series of equations (2), (3) and (5) still, ingeneral, do not yield to analytical solution because the left side of equation (5) cannot be reduced to a function of one variable. For this reason, one further assumption must be made, namely, that either the dp'/dt term or the 2 V T" term in equation (5) can be ignored. We will examine both alternatives.

PAGE 35

21 Negle c t of d ensity flu ctu a tions Kerr and Atwood [40] based their theoretical consideration of the opto-acoustic phenomenon on an equation similar to equation (5), but with the dp'/clr terra deleted. They omitted this term without explanation, thus leaving it unclear as to whether this was done by design or by oversight. The latter is possible since most texts on heat conduction delete the dp'/dt term from the equation in question without stating the fact that it is truely insignificant only in solids. Regardless of the reason, however, removal of the dp'/dt term from the problem allows for solution of (5) in terms of T', and Kerr and Atwood arrive at such a solution for the case of a time-independent source, Their solution predicts that upon illumination the average cell pressure undergoes a more-or-less exponential rise to a steady-state pressure, p(°°), given by p (°°) = (1 + AWB/4irKT)p where A is the absorptivity of the sample at the exciting wavelength, W is the beam power and B is a correction factor dependent upon beam size. The rate of the pressure rise, as that of the decay upon cessation of 2 illumination, is related to the thermal time constant r /k , c where tc is the thermal diffusivity given by K/pc . Although the observations of Kerr and Atwood agree reasonably with the theoretical predictions for p (°°) , there are some drawbacks to their solution. For example, their solution docs not predict the acoustic disturbances which have been found to occur upon pulsed excitation. Further,

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22 due to their choice of boundary conditions, their theory predicts that T' , and hence p' since, p is taken as a constant, is zero at the ceil walls. This clearly contradicts the pressure behavior which has been observed [54,64,65]. Incorporating a time-dependent source into their theoretical framework does not remove the major problems. Neglect of thermal conductivity Deletion of the thermal conductivity term of equation (5) has been considered by Longaker and Litvak [63] . They conclude that omission of this term is justified for short 2 times after excitation, explicitly when Kt/r <<1. In physical terms, the solution is limited to times which are small compared to the time it would take to cool the excited gas by thermal diffusion. For benzene vapor at a pressure of one torr , this limits the solution to times much less than 20 msec. At longer times thermal damping due to diffusion becomes important and the assumption becomes invalid. Accepting this time limitation, this approach to the problem has shown to be most satisfactory in explaining infrared spectrophone phenomena [66] , and so it will be applied to the case at hand. The following method of solution follows closely that of Bates et al . [64] but differs significantly in the time-dependence and complexity of the source terms (those on the right of equation (5) ) . After deleting the V'T 1 term from equation (5), the relation 3T = (dT/dp) 3p + (dT/dp) 3p is used to eliminate P P

PAGE 37

23 the remaining 1" dependence yielding 3pV3t -(YP Q /P ) Op'/9t) 3p'/3t -c 2 (3p'/9t) (y-l)Q (6) where c is the speed of sound in the sample gas and Q represents the source term: $«i_ p DU , /Dt, R K o elec' Differentiating (2) with respect to time, we have 9 2 p'/3t 2 = -p V3v/3t (7) and upon substitution of equation (3) into equation (7) , we obtain ? 2 2 Differentiating equation (6) with respect to time and substituting the above relation, the following equation is obtained solely as a function of p* : 9 2 p'/9t 2 c 2 V 2 p' (Y-U3Q/3t. (8) The solution to equation (8) for a particular form of Q will yield the spatial and temporal dependence of p' which we seek. First let us consider the spatial dependence of p' . In our experiments an illumination beam will be employed which reflects the cylindrical symmetry of the excitation cell, and logically p 1 is expected to do so also. Because of this, p' will have no dependence on the angular

PAGE 38

2 4 cylindrical coordinate G. The dependence of p' on the radial . coordinate r may be expanded in terms of the Bessel functions J (y.r) where r y. = x., the roots of the firstorder Bessel function. The expansion of p' in terms of Bessel functions of zero order only is due to the absence of 9 dependence in p' . The presence of the roots of J-, in the argument of the expansion functions reflects the boundary condition of the radial component of the flow velocity v , i.e. v (r=r )=0. Thus equation (3) requires that -OpV3r) /p = Ov _/3t) = 0, c c and since. OJ (y.r)/3r) = (-y.J, (y.r)) -y.J, (x.) = o J i ' r=r J x 1 J i r=r 2 1 1 l c c the boundary condition is satisfied. Likewise, boundary conditions on the longitudinal component of v fix the set of functions in which p' can be expanded to express its z-dependence. The two boundary conditions of importance here are v (z=0)=v (z=L) = 0. That these boundary conditions are satisfied by the set of expansion functions given by COS(lTl7TZ/L) ; m = 0, 1, 2, ... will now be shown. Again using equation (3) it is found that it requires of p' that

PAGE 39

25 z=0,L /M o vov z /ow z=0,L The above relation is satisfied by expanding p' in cos (mirz/L) since O (cos (mTTz/L) )/3z) z=0 = (-imrsin (mirz/L) /L) z=0 L = . Thus, p' can be written as the expansion p 1 = Z.p 1 . (t)J (y . r)cos (nmz/L) , v m,i r m,i o J i where the coefficients p 1 . (t) must be determined so as to solve equation (8) . Substituting the above expression for p 1 into equation (8) , we see that this requires solving the following equation given a particular form for the source term: ^.J o (y r) cos(mu Z /L)[p' mf .(t) + X^.p'^ ± ] = (Y-l)9Q/9t (9) where 2 2 2 2 A . = c (yf+ (nnr/L) ) . m,i J i The solution of equation (9) requires that 3Q/3t be expressed as an expansion over the same set of eigenf unctions as used for p'. Since, in general, the temporal and spatial portions of 3Q/3t are spearable, 3Q/3t may be written as the product q(r,z)Q(t), where Q (t) is defined as the volume-averaged time derivative of Q, i.e.

PAGE 40

26 Q(t) = / cell OQ/3t)dV/V. The term q(r,z) represents the spatial dependence of 8Q/3t deriving from that of the excitation source. From the above two equations, it follows that ; Cell q(r, Z )dV = V. (10) Separation of variables allows the expansion of dQ/dt to be of the form 3Q/3t = E.q .Q(t)J (y.r)cos(mirz/L) III f JIII f JL v_J -L where the q . are determined such that m, 1 q(r,z) = E.q .J (y . r) cos (mirz/L) . (11) MV ' m,x m,i o J l The expression in brackets in equation (9) can now be set equal to the coefficients of the source term expansion, and the resulting differential equation solved for the n 1 . (t) . Before this can be done, of course, an expression r m,i for Q must be derived. We will now examine individually the two terms which comprise Q. The divergence of the radiative energy flux vector is given by [62, p. 721] M R V Q a where Q is the rate of radiation energy emission per unit e volume and Q is the rate of radiation energy absorption a per unit volume. In general Q^ can be written as a sum-

PAGE 41

2 7 mation over all the emitting levels of the molecule. For the jth level, the contribution to Q will be dependent on e the number density of molecules in the jth level, n., the rate of radiative emission from state j to some lower state r r 1, k . ., , and the energy of the emitted photon, hv . , . Hence il JJ r ll s r Q = E n. .L k.. hv,. e . j l*j jl jl where the upper limit on the first summation refers to the level s which is the uppermost level initially populated by the excitation source. As reqards to Q a similar summation could be written: J a = 10 3 ! n. E. (I. e. )/N A a . ju>j ]u ]u A where e . is the molar coefficient of absorption for the transition from level j to an upper level u, I . is the source radiation energy flux at the frequency of the j-»-u transition and N is Avogadro ' s number.* In the case of the proposed experiments, we will attempt to excite only a single transition, that being from the ground state to state s. If we let £ be the rrr.lar extinction coefficient for this transition and define the absorption coefficient a by a = eC where C is the bulk concentration, then Q a = ctl, where I is the intensity of the excitation source. We now turn our attention to an expression for £ is related to the molar extinction coefficient e by the equation e -elnlO.

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2 8 DU , /Dt. Quite simply, elec' c J r s U , = .£. n .hv . _/p elec 3 = 3 jO 7 K o so that s s -> -+• DU , /Dt = E n.hv. n /p + E (v • Vn . ) hv . n /p . elec 3 3O K o . 3 3O K o The second summation in the above equation is secondorder in two small quantities and can be ignored, allowing us to write s p DU , /Dt = I n.hv ... o elec . 3 3O 3 Thus, for the case in question, the source term is s Q = al Z (n.hv. A + n. ,E. k r , hv..). j D DO ] 1*!] 3I Dl At low pressures second-order decay processes of excited electronic states are negligible. Thus we can write as the rate equation for state s n = al/hv n , E k , s s s l3 u] u 3 1*3 l jl (12) n3r r where k. n = k . .. +k., is the sum of both the radiatxve and Dl Dl Dl nonradiative first-order rate constants for the transition from state j to state 1. After substitution of equation (12) into the expression for Q and simplification, the source term is given by

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29 s s Q = En. , E. k.r hv., = E n.W. (13) j 3 1*3 31 }1 j 3 3 The W. defined by equation (13) represent the total heat energy per unit time being released per molecule residing in state j via all nonradiative pathways and is a constant. The sought-after time-dependence of 3Q/3t thus could be written explicitly if it were known for the n.. When only first-order processes are operative and n,(t=0) = for all j^O, the n. take the form of solutions to a system of linear differential equations which reflects the various transitions between different energy levels occurring during molecular relaxation. Assuming pulsed excitation of the sample the general form for these solutions is S -k t n . = ( E a .e u ) q (r, z) . j . ut ^ ' J u=j J The spatial dependence of the n. has been withheld from inclusion in the a . for convenience. If the time U3 derivative of equation (13) is now taken, we have that 3Q/3t = Z (3n./3t)W. j 3 3 s s = -q(r,z)EW. E a .k e~ k u t ^ . j . ui u 3 J u=j J S u -k t = -q(r,z)E (Ea W )k e V u j 1 1 s -k t -q (r , z) Eb k e u u u u

PAGE 44

30 where we have defined for convenience u b = Ea .W.. 3 J J Using the last expression for 3Q/3t, the bracketed part of (9) can be rewritten as p' . (t) + X 2 .p' . (t) = -(Y-Dg • ^b k e~ k u t . p m,i v m,i F ra,i v ' '^m,i u u u Solving this second-order differential equation will give a form for the p' . which will provide a general expression for p ' . Applying the standard methods of solving differential equations to the bracketed equation, one can solve for the p' . and obtain for p': s 2 . ,2 p. = ( Y -l) Eg {^b u k u /(k u+ A )] x m,i u [cos(A in ^t)-exp(-k u t)-(X mfi /k u )sin(X m ^ i t)]} x J (y.r) cos(mTTz/L) (14) ox Before applying this equation to specific cases of molecular excitation in which the b will be evaluated in terms of actual excited state parameters, it will prove informative to examine the general expression for p 1 . Note that for all terms of the summation except the m = i = term, the long-term time-dependence is periodic in nature, with a frequency of oscillation for a particular i and m dependent on the speed of sound in the sample gas

PAGE 45

31 and the cell dimensions. What these terms represent is, in fact, not a true "pressure" wave since their long-term time-average amplitude is zero. Rather, what they describe is the infinite set of resonances available in the cell for radial and transverse acoustic wave propagation. The amplitude of these acoustical disturbance terms and their relative contribution to the total sum, as we shall see later when the q . are evaluated, are m, 1 very sensitive to the degree of uniformity of absorption of the exciting illumination throughout the cell, becoming increasingly large as the absorption becomes less uniform. The i = m = term of the summation in equation (14) thus carries the body of the "pressure" information. One can write for the contribution of this term to the p 1 summation the expression S -k t p' = (y-l)q lb (1-e u )/k (15) ^o,o '^o,ou " U ' ' U There is a noteworthy resemblance of an individual term of this summation to the form of p 1 derived in the simple two-state nodel. See equation (1) . The terms of the sum merely represent the individual contributions to p' from each of the molecular levels. As in the simple solution for p', equation (15) predicts that p' increases asymptotically to a nonzero value, thus implying that the sample pressure does not return to its preexcitation equilibrium value. This is, of course, not true; the cell is not adiabatic and heat, transfer through its walls quickly

PAGE 46

32 returns the sample vapor to its original pressure. The reason the solution does not reflect this physical realityis the neglect of the thermal diffusion term of equation (5) on which the derivation of this section is based. The Extraction of Molecular Parameters from the Gross Pressure Signal To this point, the derivation of the theory of timeresolved opto-acoustic spectroscopy has been kept as general as possible. Now, to calculate the actual form of the a . (and from them the b ) , the set of equations which define the time-evolution of the states which partici.pate in the electronic excitation and relaxation of polyatomic molecules must be solved. To do so, a specific model must be constructed and necessarily generality is lost. The important point is, though, that just as this model is constructed assuming certain characteristics of excited state kinetics, so others might be constructed based on other assumptions. Thus, the following model, though applicable to a great number of actual cases, should be considered as just an example of how time-resolved opto-acoustic spectroscopy may be applied to the study of molecular excited states. Only two electronic states besides the electronic ground state will be considered explicitly, these being the first excited singlet S, and the first excited triplet T.. . In general, population of higher excited states leads only to rapid nonradiative decay to the vibrational manifolds of these lowest states. Thus, for oui purposes, excitation

PAGE 47

33 to more highly excited electronic states is equivalent to excitation of higher vibrational levels of S, and T, ; deactivation of these vibronic levels ij> considered in the discussion below. Because the form of the a . will depend on that level which is initially populated, two cases will be treated which encompass the two possible choices for the initially populated level (level s) in our narrowed scheme. Excitation into the First Excited Tr i plet State The electronic states and their first-order decay constants which are typically of importance in this case are shown in Figure 3. T represents the initially populated vibronic level of the lowest triplet state T, , T represents the vibrationless level of T and S represents the molecular state before excitation. For this case equation (12) takes the form: n T v = aI/hv T v -n T v(k 2 +k 3 ) no = k 3 n v k n o 1 1 x x l where k x =k^ + k» r . To solve this coupled set of equations, a form for I must be chosen which expresses explicitly the timedependence of the source illumination. Since the excitation will consist of a very short duration laser pulse, a valid and convenient approximation to its temporal form

PAGE 48

34 is the delta function, 6 (t) . This function assumes a value of unity when its argument is zero and equals zero for all other values of t. Allowing I to assume this functional dependence en t, the above set of differential equations can be solved in the standard manner to yield: n v« n°v e(k 2 + k 3 )t: T l h n T o = [n^vk 2 /(k 3 +k 2 -k 1 )J. (e _k l t e" (k 2 +k 3 )1: ). n„v is the initial population of T. equal to n v q (r,z) 1 1 J. i-L where n?v is the cell-averaged initial number density of 1 molecules excited into T given by E(l-e ) /hv v V, where 1 " i l E is the laser pulse energy. The forms for the a . and the b can now be derived u j u in a straightforward manner and are listed in Table 1. Using these values, the gross time-dependence of the pressure pulse expected to occur upon excitation into T, can be determined by expanding equation (15) to obtain P'o,o = ^-l)q 0f0 H5 iV [k 1 "k 2 hv T o(l-ek l t )/(k 3+ k 2 -k 1 )k 1 + (k 2 hv T v, T o/(k 2 +k 3 ) kJ r hv T o/(k 3 +k 2 -k 1 )) (l-e" (k 2 +k 3 )t )]. Since the vibrational relaxation time of T is ordinarily much shorter than the spin-forbidden deactivation of T , k can be assumed to be much less than k„ , and the above equation can be simplified to the form:

PAGE 49

35 excitation "2 nr Figure 3. Diagram of energy levels typically of importance for first excited triplet state excitation and decay.

PAGE 50

3C ft O Eh

PAGE 51

37 , ,, -o r ISC, ,, -(k„+k_)t. P 0,0 = (Y 1)q o,o n T 1 v ty^v.y 11 6 2 3 ) IC ISC . + tj) (J) hv o (1-e '1 ) ] T,v To 1 ISC where k, /k, has been recognized to be $ 8 , the intersystem 11 -L-i crossing yield of T°, and k 2 /(k 2 +k_) is represented by T v, the internal conversion yield of T.. . One should note that this equation applies equally well to direct excitation of the vibrationless level of T , in which case v v is replaced 1 1 IC by v„o, tf> m v goes to unity and hv v „o goes to zero. These L l T l " i l ,1 l changes cause the first term in the brackets to be deleted and the second to be somewhat simplified. The above equation predicts the main pressure signal to be a sum of two exponentially rising components, each of different amplitude. In general a response of this type would be difficult to deconvolute. However, because of the large difference in the magnitudes of k.. and k_, the two exponential rises should be well separated temporally. In fact, the first term in the brackets above will most likely appear as a step-rise in pressure at t=0 with the second exponential rise building with time on top of it, as pictured in Figure 4 . IC The figure indicates that $_v can be evaluated only if i l the true magnitude of the pressure rise is known, as well as the values of y,OL, E and q . However, if hv T v o is o,o i , , i, ISC " known as is usually the case, (j> o can be determined in a 1

PAGE 52

38 more straightforward manner. If we let p' be the amplitude of the fast rise and p' be that of the slow rise, then ISC <]> T o = (hv v o/hv o) p' /p'. i 1 i l' i l J l Since k can be extracted solely from the time-evolution r nr of the pressure rise, this indicates that k, and k, can be evaluated individually without critical measurement of either intensity of the beam or absorption and specific heat of the sample vapor. Figure 4, is, to be sure, an idealized version of the pressure response of the sample vapor; built upon this signal will be che acoustic "tumps" discussed earlier. The presence of these periodic disturbances is not solely deleterious, however, and they can in fact provide needed information about the vapor under study. Excitation into the First Ex c i ted Sin g let State The molecular levels and decay channels which are generally of importance in this case are displayed in Figure 5. S^ is the initially populated vibrational level of S, , S° the vibrationless level of S,, T the vibrationless level of T n and S represents the molecular state 1 o before excitation. For this case, equation (12) takes the form n v = al/hv v n vk Q v S l b l b l b l

PAGE 53

+J -p w p CD H •H M -P o m Q) tn •H SH a) u p tn M c; n w • tn a o o n -H tn-P (0 4-1 4J O-H U e x o M H P4

PAGE 54

4 a, > rH

PAGE 55

> -H CO 41

PAGE 56

42 r> o = k,n_v k c on o S 1 6 S 1 S 1 S 1 no = k n o + k n v k on o where k s v = k 6 + k 7 + k£ + k* r k s o = k* + kf + k 5 and k o = k r + k nr K T o K x + K x . Again approximating the time dependence of I by a delta function, the above set of differential equations can be solved in the standard manner to obtain: o -k„v t n v = n v e S, b l b l L n s o = k 6 n°v (e" k sj fc -e" k sJ ^/(kgV k g o) n T o = n°v(k 7 -k 5 k 6 /(k s v-k s o)) (e~ k T° fc -e~ k sJ t )/(k s v-k rp o) + k 5 k 6 n°v(e~ k T° t -e" k sJ t ) / (kgV-kgO) (k s o-k T o) where n°v = n?v q(r,z) and r7?v is defined similarily to the 11 -L analogous term in the triplet case. As in the previous case, the forms of the a . and b ^ u, j u

PAGE 57

43 are listed in tabular form in Table 2. Equation (15) can now be expanded using these values in order to obtain an idea of the gross form of the pressure pulse expected upon excitation into S^. Before this is done, however, let us take advantage of the fact that kj r and k£ are extremely small with respect to the remainder of the rate constants under consideration. This circumstance allows the deletion of terms in equation (15) which because of it become insignificant. Further, the e~ k S^ t and e~ k S° t terms are discarded to reflect the "step" nature of the pressure rise due to the fast processes. By doing this, P' Q f ° r the case considered here takes the form p« = (Y-l)H^v q n _ [> hv v o + v hV v o r 0,0 S^ 0,0 b-^ b l'°l b I 1' 1 + (J)Jv hv c v + |.!v (] T l T l S l "1 b l where >l\ = V k sJ is the vibrational deactivation yield of S^ to S^, ISC *S^ = k 7 /k S^ is the intersystem crossing yield of S^ to T^, X IC , nr ,, *sY = k s /k sY

PAGE 58

44 TABLS 2. MINGI..5T a . AND b U'l u V 5 ?! 1 f , , k 5 k 6 (k s v-k T b) lK 7 k s o+k T o J t nr, 1 T ? k 5 k 6 ±— rk + 5 6 i (k g v-k T o) LK 7 k s o-k T o J k,k. (k v~k o) (k o-k m o) b l b l b l x l k v-k o t> 1 b 1 -7i i rlk, hv o (k v-k o 4 S 1 + k c hv_o m o] 5 S 1 ,x 1 " k 5 k 6 k l hV T° TkZv-k'o) (k-o^TL.o) S l S-, b l J l

PAGE 59

TABLE 2 . extended s l

PAGE 60

46 is the internal conversion yield of S. to S . J 1 o' ,IC . nr .. o = k /k o fa l 4 b l are the internal conversion yield of S, to S and 1 o .ISC . nr ,, , ,ISC , ,, cj> T o = k ± A T o and s o = k 5 A g o is the intersystem crossing yields of T.. to S and of S, to T 1 , respectively. The expression above for p' is quite a bit more complex than that derived in the previous case and the reason for the added complexity is simply the greater number of states and decay channels involved. Obviously, for a molecular system in which all the deactivation paths considered here play a significant role, none of the radiationless yields included in the expression for p 1 can be uniquely determined by the sole opto-acoustic experiment involving excitation into v S.. . Some of these yields may be evaluated by other (optical) methods or may be deemed insignificant based on previous work on molecules having similar excited state characteristics to the sample being investigated. It is more interesting in the present context that some may also be evaluated by further opto-acoustic experiments involving excitation into T° tY or o ISC S, . In the previous case for example, we have shown how o 1 could be evaluated by excitation into tY. Note that if S, is excited directly instead of S^

PAGE 61

47 P « « = (Y-Dn c o q [$ 5 hv o o + <£ c o hv c o o,o S-^O/O S, S , T, S ., S, ,ISC .ISC . ,, -k_,o t. , + o q> o hv o (1-e T ) ] . b l l l l l 1 This equation indicates that both o" and c o can be b l fa l evaluated with an accuracy determined by the accuracy to which p* , y» a, E and q are known. Since these o , o o , o parameters can be determined with reasonably good accuracy, this avenue of approach promises significant insight into the dominant processes in excited states. Consideration o f the Total Disturbance: Pressure Wave Plus Acoustic Harmonics In the last section we limited our view to the gross pressure change in the cell in order to examine how important molecular parameters might be extracted from its behavior. In this section we will investigate the total summation of equation (14) . To do so, we must derive a form for the q . which, in turn, requires that a spatial dependence for the n. be specified. Essentially, an explicit form must be determined for q(r,z). Evaluation of the Expan sio n Coef f i c ion ts As was noted in a previous section, q(r,z) represents the spatial distribution of the initially excited molecules. The radial part of this distribution will be determined by the radial shape of the illumination beam. For simplicity we shall assume a uniform intensity to exist over the beam cross-section which drops to zero outside the beam. For a

PAGE 62

48 dye laser such as employed in this work which operates in many high order modes, this is a quite good approximation of its shape [64]. This dependence can be expressed in mathematical form using the Heaviside function, H(x), which is zero for negative values of its argument and unity otherwise. Hence, for a beam of radius r, , the spatial distribution to be used here can be written as H((r,-r)/r ). b ' c Alternative beam distribution functions may be used, e.g. gaussian, but in general the small variations they introduce into the calculated form of p' is not worth the added complexity which they introduce in the q m, 1 The longitudinal, or z-axis, dependence of beam intensity is due to attenuation of the beam by the sample vapor. For low to moderate power lasers where saturation or twophoton absorption effects are not important, the diminution of the excitation beam as it travels through the sample vapor can be expressed according to the familiar Beer— Az Lambert expression, 10 . In this expression, A is the absorptivity and is related to the absorption coefficient a by the equation A = a/In 10. An expression for q(r,z) is thus of the form q(o,o) H((r b -r)/r c ) e~ aZ , where q(o,o) is a normalization constant. The normalization integral (equation (10) ) can be easily evaluated yielding q (o,o) = r 2 c aL/r£ (l-e~ aL ) .

PAGE 63

49 Having now given explicit form to g(r,z), we must determine the set of q . which will solve equation (11) . J m, 1 Multiplying both sides of that equation by cos (miTz/L) dz and integrating over the length of the cell, we obtain H((r, -r)/r ) l-(-l) m e" aL L(l + <5(m)) q(0f0 ) b C — 2 = — Hn^o^ a 1-r (m7T/aL) 2 i Letting q = 2q(o,o) (l-(-l) m e" aL )/ aL (1+6 (m) ) (l+imr/aL) 2 ) , we now have q H((r,-r)/r ) = Eq . ,J (y.,r). M m b c . ,m, i' o x' If we now take the derivative of both sides with respect to r, then multiply both sides by rJ. (y.r)dr and integrate over the cell radius we have Vo c r V y i r) dH((r b -r)/r c )dr = -Eq^.y^cr^ (y.r) J ± (y.r)dr, Integrating the left side of the above equation by parts and applying the appropriate Bessel function relations [67] to the integral on the right, we obtain q m [rJ 1 (y.r)H((r b -r)/r c )|^c /^cH ( (r b -r) /xj y.r J (y.r)drJ 2 2 = -q .y.r J_ (y.r )/2 ^m,i J i c 2 J i c The first term on the left of the above equation equals zero; the second term can be evaluated from standard

PAGE 64

50 Bessel function relations [67] . This allows us to write the following general expression for the l-(-l) m e" aL 2q(0,0) r b 2 J(x.,B) m,i l4(nuT/aL) 2 aL (1+6 (m) ) r c J ^ i r c ) where we define J (y^) + VYi-V W! ^ J 2 (x lB ) j(x. , B) = ; ; 1 J (y.r ) J n {x ^ O 2 X C O 1 with 8 = r t/ r c ' Computer Simulation of Opto-acoustic Sig nal With the form of the q . now determined, an expression for the pressure change in the sample cell upon optical illumination can now be written which contains the explicit dependence of p' on cell coordinates and time. r 2 y-1 2q(0,0) l-(-l) m e" aL J(x. ,&) p. = * — Z 2 — J o ( *i r) X r a L m,i 1+6 (m) 1+ (mir/aL) J ^i T c ' s cosX .t -e" k u fc -(X ./k ) sinX .t Eb k Ez2__ EVL_u 5^— cos (mirz/L) . u u u k 2 + X 2 . u m,i (16 ) To test the degree of correspondence between equation (16) and the actual pressure response in an opto-acoustic cell, a computer simulation of the equation was undertaken. The objective of the simulation was to provide a theoretical form for p 1 which could be subsequently checked by experimental observation. In practice, this meant that the

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5] simulation should calculate the predicted temporal evolution of p 1 at a particular point chosen on the cell surface where a suitable detector might be placed. Examination of equation (16) suggests two unique choices of r and z coordinates which might be of special interest with regards to simplifying the simulation.* Placement of the detector at the end of the cell and on the cell axis (z = L; r = 0) would reduce the J Q (y i ^) teriri to unity for all i and allow the replacement of cos (nnrz/L) with (-l) m . However, placement of the detector in the light path would certainly rule out measurement of beam energy directly and might cause secondary problems such as reflecting the beam back down the cell. The alternative choice of detector placement is at the cell wall midway down the length of the cell (r = r , z = L/2) . There are no experimental problems with placing the detector in the cell wall, although some nonuniformity in cell wall curvature may be introduced depending on the relative size of the detector surface and wall cross-section. As shall be discussed later, however, the small dimensions of the detector employed cause these deviations to be minor. Insertion of this set of coordinates into equation (16) brings about a significant simplification in the expression; * A third choice, r = and z = 0, would certainly provide simplification but would just as certainly dramatically increase the problem of getting light into the cell.

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52 most notably, for all odd values of m, the summation is zero. The summation can be rewritten taking this effect into account, leaving the following equation: p' (r ,L/2,t) (Y-DE J(x. ,B) Z 2 (-1) (-• l Til 1 m 1 + 6 (m) l+(2rrnr/aL) 2 l\K {ma m.i t ^"** t -K.±*n )B ^m,L t)/{ *Z +aJ m,i> ' (17) where 2 2 , 2 , ,2mTr,2 , a) . = c [y. + (— — ) ] . m,i J i L ' J For the simulation, only a single term in the bracketed summation in equation (17) is kept. This simple two-state model would correspond in practice to excitation into T . Higher states were not included since their effect on the form of p', besides the initial step rise, would be only to alter slightly the appearance of the acoustic bumps and add to their peak-to-peak amplitude. The actual expression evaluated in the simulation, then is -kt -, , u m costo . t-e (oj . /k ) sinco .t r.T fv p) ? (--U m,i m,i u m,i LJ(x ± ,V) L 1+ 2mu.2 7~. TT2 m 1+ (-v— ) l+(w ./k) aL m ' 1 (18) which is the temporal form of p' (r ,L/2,t) normalized to the long-time amplitude of the pressure rise, (Y-D nr E(l-e~ aL )/V. A simple Fortran program was written to evaluate the

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53 J(x.,3) on an IBM (360/75) computer. Representative values of this parameter for i = 1 to 20 and 3 0.25, 0.50 and 0.75 are listed in Table 3. The J(x.,3) values for a chosen value of 3 v/ere incorporated into a program written for execution on a WANG 7 00c Programmable calculator. This program is capable of calculating the expression of interest for i running from to 20. It was found, however, that in all the cases investigated, only the first few partial sums were significant, and the sum could be truncated at much smaller values of i. The number of significant terms in the m summation is found to vary considerably with the choice of a. Because of this, the summation over m was terminated at no set value of m, but rather when a particular term caused a change in the current i sum of less than 0.1%. As the values of expression (18) are calculated at time increments At, they are plotted, point-by-point, by a WANG 7 02 Output Plotter. A typical plot is shown in Figure 6. This plot displays the signal calculated for excitation of a sample in the opto-acoustic cell used in this work (to be described later) with B=0.5, k=l ms, c=L/k and a=2ir/L. As expected, it shows the gross exponential rise and the periodic acoustical undulations which have been observed in pulsed excitation experiments. On close observation, one notes that the acoustic signal appears to be a sum of two waves with different amplitude and frequency. The higher frequency smaller amplitude oscillation is due to the radial modes of

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54

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O m +J CO (0 w ,.y H \ > II TO o to o •H rH w II x a, x -^ (2) in \ • fc= Won II II OcQ8 ft M tn H

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• • r " *•... "V v.. c -x V ./ v.C "N.. V.., V. "v.. I <: **••.. "^, <: > ..} | i e I I I I I 4-1 I I I I I i-l I I I » I I I I I » » ' * « I ' ' ' » ' ' ' ' ' ' I ' ' ' ' ' ' ' ' ' ' ' * * ***+ SC U.1 -J < H i1 > iU W *-* t3 Z < -J

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57 standing wave formation. The larger amplitude component is formed by the action of the longitudinal standing waves. The frequency ratio of the two waves is ^L/r , and their absolute frequencies are determined by both the cell dimensions and the speed of sound in the gas. Because of this, the speed of sound in the sample gas can be determined rather accurately by measuring the period of the acoustic "bumps." This is a very convenient happenstance because it allows a simultaneous determination of the heat capacity ratio since Y = c 2 p/p Mc 2 /RT (19) where M is the molecular weight of the sample [68] . Figures 7 and 8 are two further plots derived from expression (18) . The parameters chosen are identical to those used to generate Figure 6 except for the value of a, which is 2tt//T0 L in Figure 7 and 2it/10L in Figure 8. The most noticeable effect on the plots due to this change is the decrease in amplitude of the longitudinal acoustic waves. This decrease occurs because as a decreases, the distribution of excited molecules down the cell axis becomes more uniform. This results in a reduced longitudinal pressure differential occurring after molecular relaxation, and hence the longitudinal resonances are driven less strongly Limitations and Extensions of the Theory The purpose of this section is to tie together the previous sections with regards to the general applicability of the method therein described. The many assumptions made

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M 141 -P w A! > oo u rH £ g •H rH to tQ II ,• M Mo Ch (rH Q) m \ IHON o II II +J rH ft (1) rl tn •H

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59 i < I \ s .•;• *7 .;* < *.. >.. "V. «£.. "Vr ".?. '<£. **. '*... *.. . *••• v. '•«.. Hl I t I l -< a u -5 < j> 1 > — whu^< -j

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O u-i 4J G > cx> U rH tn c e o •rH rH w W ll H ,* • 04 J X -o a; m rH • t= o II II -p Oca 3 rH Hi 0) H 3 tn

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61 1 ! «*** •£. ,/* v.. V. *.. #.. *"*... >... '<• .. I— (-< I t I < I I I I I I t I I I I I I 1 I .-»-»>< I I I I I tK t'J -5 U

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62 set restrictions on the type of experiments which can be performed and the kind of equipment needed to carry them out. These restrictions will be reviewed below and their effect on experimental design will be discussed. Also, many effects were purposefully excluded from previous sections for simplicity. Therefore, a discussion of how the theory might be extended and corrected to include these effects is provided. Limitations on Experiment a l Design Cell construction In the foregoing sections, the sample was assumed to be contained in an isothermal cell of perfect cylindrical symmetry. In practice, the symmetry of the cell is upset by ports through which the cell can be evacuated and through which the sample can be introduced. Further, a port for the pressure transducer must be provided; a side-viewing port for the attachment of a light detection device is optional. By employing a transducer which is externally translatable, a single port can serve both to connect the cell with the remainder of the sample handling system and provide an access port for the transducer. This arrangement does add considerably to the complexity of cell construction, however. In general, one can approach sufficiently close to the ideal geometry if care is taken to limit cell connections to minimal length and to limit port size to a small fraction of the circumference of the cell. So that the cell has no initial temperature variation, it

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62 should be built from materials of high thermal conductivity and have a high thermal capacity. The volume of the cell is determined by its length and radius. The length is certainly the less critical of the two dimensions; it will be shown in the next section that the samples of low to moderate absorptivity, the pressure pulse amplitude is independent of cell length. Optimum cell length is thus determined by "second order" effects. Increasing cell length increases the useful cell volume and minimizes the effect of "dead" space in the connectors and ports. The cell must be short enough, however, so beam divergence over the cell length can be disregarded and no significant temperature variations exist at the walls. From these considerations, it is clear that there is much lattitude in the choice of cell length. This is not the case for the cell radius. Noting the strong dependence of p' on r , one might assume that the smaller r is chosen, the better. We must, however, c ' recall that two very important assumptions depend on the size of r . Sample viscosity was neglected only under the condition that r be much qreater than the mean free c 3 path of the sample. More importantly, the neglect of thermal conductivity, the ultimate basis for equation (5) being solvable, is strictly justifiable only for times 2 less than r /«. Thus, choosing a larger r increases the upper limit on the available observation time of the experiment. There is a lower limit of observation time

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64 sample pressure will be determined very much by sample volatility and the nature of the investigation, larger pressures tend to relax the restrictions on r ^. Both £ and k are inversely proportional to pressure, so at higher pressures lower values of r become justifiable. Pressure transducer The only explicit restriction placed on the pressure sensing device in previous sections is that it be small with respect to the cell circumference, so as not to interfere significantly with the cylindrical symmetry of the cell. A reasonable interpretation of this restriction would be to require that the diameter of the transducer port be comparable to or smaller than the cell radius. Since the transducer itself must be placed so that its sensor is positioned directly at the cell wall, this will cause only a small amount of nonideality. Besides the above explicit assumption about the transducer, two implicit ones have been presumed. The first is that the response time of the device is short enough to adequately transduce the rapidly fluctuating pressure level at the cell wall. This requires a response time of about two orders of magnitude smaller than the rise time of the gross pressure signal. For a molecule with a triplet lifetime of 5ms, this translates into a response time on the order of 50us. A second implicit requirement on the performance of the pressure transducer is that it is sensitive enough

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65 to respond to the small pressure fluctuations involved. These have been assumed to be very small with respect of p . To help determine the sensitivity required of the transducer, an estimate can be made of the magnitude of the opto-acoustic pressure pulse expected. For this purpose, the long-time value of the gross pressure pulse for a simple two-state case can be calculated. The explicit form for this value is obtained by evaluating equation (15) for u = s and t very large P' u = (Y-Dq b /k = (Y-Ua W /k ^OjOlt-*1 : ' ^0,0 S S S,0 S S = (Y-l)n°k nr hv A ' s s s s = (Y-D4)" r (l-e~ aL )E/V (20) where E = output energy of the excitation beam and V = cell — ctL volume. For small values of a, the 1-e term is approximately equal to aL; in particular, letting p = 1 torr, e = 10 liter/mole-cm, L = 10 cm and T = 300K, less than three per cent error is introduced by rewriting the above equation as P' L = (Y-lH nr Eep Ar 2 RT (21) r o,o ' t->°° s ^o c where the relation a = eC = ep /RT has been used. If we now let y = 1.10, 4 nr = 1.10, r = 0.5cm and E = 5 mJ, a value of 26 mtorr is calculated for the longterm pressure rise. This value both verifies the assumption that the experiment causes a small change in pressure and aids in

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C ; 5 quantitatively specifying the sensitivity needed in the transducer. It is of further importance that a satisfactory device should not only respond to pressures as small as or smaller than that calculated above but also should do so while limiting its pressure equivalent noise level to a reasonable level. Illumination source The illumination source assumed in deriving equation (16) has been fairly well defined. It must deliver a sharply-collimated narrow-bandwidth short-duration pulse of optical energy. In general, the restrictions on beam profile and bandwidth may be relaxed; these would require, however, a redetermination of the q . in the former case and in the latter case a change in the deactivation scheme to one involving multiple-level initial population. Deviation of the temporal form of the excitation source from that of a delta pulse can also be accommodated, but this involves a resolution of equation (12) using the new timedependence. One characteristic of the excitation source which has not been discussed as yet is the pulse energy which it must be capable of delivering. Although the absolute pressure developed in an opto-acoustic experiment depends strongly on the absorption and emission characterisnr tic of the sample, even for large values of e and 4> the excitation beam must be relatively energetic (>1 m J) . Ordinary flashlamps can provide this excitation, but when the requirements of narrow-bandwidth and short pulse dur-

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G? ation accompany the energy requirements, it appears that only laser sources will suffice. E xtensions of Theory to Additional Effects Effect of window absorption Absorption of the exciting light by the inner surface of either cell window will cause local heating of the sample in the vicinity of the surface [70] . The effect of this heating will be the production of an acoustic wave whose amplitude will depend on the extent of window absorption. The presence of this unwanted absorption is most easily determined by illuminating a gas, such as N 2 , which does not absorb in the wavelength region employed. If the window material is satisfactory and no traces of absorbing substances are adhering to its surface, then no signal will occur. In experiments in which the cell is heated to increase the vapor pressure of the sample, special care must be taken to avoid condensation on the windows which can also cause this spurious effect. Effect of luminescence heating In our development of the molecular deactivation scheme, decay paths were divided into nonradiative and radiative types with the former ostensibly being the sole heat producers. Radiative decay paths do give off heat, however, because radiative transitions to vibrational levels of the ground state produce a non-Boltzmann distribution of these vibrational levels. Although the amount of heat energy produced by a molecule undergoing a radiative

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Gb deactivation is a small fraction of that produced by an initially identical molecule undergoing totally nonradiative decay, the problem is significant when dealing with a molecule possessing a large luminescence yield. To correct for this effect requires some knowledge of the emission characteristics of the sample. In particular, the average frequency of emission, v, must be determined from the emission spectrum of the sample for the emitting state in question. Then, for a state u which undergoes radiative decay to the ground state, the term
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6<.' that the heat capacity ratio used in equation (16) and elsewhere must now be that of the mixture, and p Q in equation (21) is now taken to be the equilibrium partial pressure of the absorbing species. In general, the addition of a buffer gas will affect the rates of the various relaxation processes occurring in the excited sample and may also open new channels for release of excitation energy. These actions will change both the amplitude and time evolution of the opto-acoustic signal relative to that observed in the pure sample. Aside from these changes, the amplitude will also be affected by the change in y noted above. Further, since the mixture of a buffer gas plus sample may have a significantly different thermal diffusivity than that of the sample gas alone, especially if He, Ne or H are used, the temporal part of the signal will also be affected. Specifically, an increase in thermal diffusivity will cause the sample to cool more rapidly and thus limit the available observation time. Effect of photochemistry Inclusion of the possibility of a photo-induced chemical reaction adds another decay path to those already available to the excited state. Predicting the effect on the pressure signal in the cell of a molecule traversing this path is much more difficult, however, than for a standard radiative or nonradiative process. The reason for this difficulty is that a molecule undergoing photoreaction can contribute to the overall pressure response

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70 in several ways. Firstly, the endoor exothermicity of the reaction step must be considered. Depending on this value, the products of the reaction will have more or less energy available for heating than the energy of the initially absorbed photon. Secondly, the products of the photoreaction may not be formed in their ground electronic state. Thus, a whole new set of excited state decay kinetics must be investigated to determine how that electronic energy is dissipated. Finally, the initially excited molecule may break up into a number of products. Thus, regardless of the heat released or potentially available, the pressure of the vapor increases solely due to the increase of the number of molecules in the cell. It is clear, then, that studying photochemically reactive systems via time-resolved opto-acoustic spectroscopy is a complex matter. This is not to say that such a study can not be done, but rather that one must carefully investigate the probable pathways open to a system before such a study is undertaken. If a well-defined model can be constructed for the decay kinetics of a photochemically reactive species which does not involve a change in the number of gaseous molecules in the cell, then this model in conjunction with the theory developed in this chapter can be used to predict the pressure behavior of a sample of this species upon pulsed optical illumination. If a change, in the number of molecules in the vapor phase accompanies photoreaction, then the detailed

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71 prediction of the pressure response of the sample upon optical illumination 1g beyond the scope of this work. However, one might expect that the overall response should not be greatly different than what might normally be observed in the absence of photoreaction, with one significant exception. Where photoreaction takes place accompanied by a change in the number of gaseous molecules, the long-time pressure in the cell will not return to its initial level. The change in pressure can be written by analogy with equation (20) as N'RT A pr ,, -al, E Ppr|t-H» = N~Ev (1_e } V r ' a where N' is the difference between the number of moles of reactants and the number of moles of products per mole of PIT excited molecules which react, and <|r is the yield of the photoreaction (number molecules reacted/number molecules excited). If one calculates a typical value of p ' r i t ^ OT one finds it is about one order of magnitude smaller than p' k for comparable values of pr and nr and with r o , o 1 t-* 00 c s N' = 1. In general, this presents no problem, since the device used for the steady-state measurement involved in evaluating p' ., usually will have a much greater senpr 1 1-*°° sitivity than the device required to follow the rapid fluctuation of p' during transient heating.

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CHAPTER THREE EXPERIMENTAL SYSTEM Equipment Opto-acoustic Cell and Vacuum System During the course of this work, several opto-acoustic cells were constructed and used for preliminary studies. As work progressed, design changes were made to increase the ruggedness of the cell and especially to provide better access and shielding for the dynamic pressure sensor. The final result of this refinement process is diagrammed in Figure 9. The cell consists basically of two chambers: the experimental chamber in which the sample is optically excited and a second larger reference chamber. These chambers are mounted together on a height-adjustable aluminum platform which can be leveled. The experimental chamber is fashioned from a block of aluminum 3" x 4" x 6 1/2" by drilling a 1/2" diameter hole down the center of the long axis of the block. At either end of the chamber are attached 1" diameter Suprasil quartz windows with vacuum-tightness insured by rubber "0"-rings. At the midpoint of the chamber length a 0.19 34" diameter hole is drilled perpendicular to the chamber axis on the 7 2

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G< U o H 4J 0) P o rj I O +J a o IH O e H a: n H

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7 4 o £) -P u H 5 H o h a -P -H H £ G o -p o 0< r.j x; a H -P cd E H M a) a Q) (0 -p p •h o 0) u n c
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75 large face of the block to provide a port for the pressure transducer. Provisions for mounting a phototube on the opposite, face of the aluminum block are provided and a second 0.1934" diameter hole is drilled diametrically opposite the first to allow light output through a third Suprasil window. A 3/16" diameter port for gas transfer from the reference chamber is placed 3/4" from the cell end on the same side as the transducer port. The transducer which measures the excitation-induced dynamic pressure fluctuations is attached to the experimental chamber after mounting it in its own special holder. Because the transducer is a differential device, its reference side must be held at the initial pressure of the sample vapor. To accomplish this, the transducer mount is covered by an aluminum cup which, when fastened to the cell wall, provides a vacuumtight compartment. This cup is then connected by copper tubing through bias vacuum valve (A) to the reference chamber. Gas flow between the two chambers takes place through 1/4" copper tubing and is regulated by the action of brass vacuum valve (B) . A capacitance manometer is connected in parallel with this valve and measures any pressure differential which may exist between the experimental and reference chambers. This manometer also serves to measure the initial pressure of the sample as part of the procedure which shall be discussed later.

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76 The reference chamber is basically a 5" long, 1 3/4" diameter closed cylinder with three radial ports and one port at each end. The uses of the radial ports have already been discussed. One end port is employed for vapor entry of samples and this port is controlled by vacuum valve (C) . The valve is connected to a metal "quickconnect" which allows facile attachment and removal of sample containers. Cell evacuation takes place through the reference chamber port controlled by valve (D) . Through this valve the opto-acoustic system is connected to a glass vacuum line and gas handling manifold. The vacuum is provided by a mercury diffusion pump used in conjunction with a liquid nitrogen cold trap and mechanical roughing pump. Line pressure is monitored by an ionization gauge, and pressures down to 2 x 10~6 mm of Hg are attainable in the line. Excitation Source As discussed in the previous chapter, the requirements for the excitation source for time-resolved opto-acoustic experiments are most fittingly satisfied by a pulsed laser. Especially useful for general work of this type is the tunable laser, which would allow excitation of electronic transitions over a broad range in the visible and ultraviolet spectral regions. In general this type of laser employs a solution of an organic dye which, upon excitation in a

PAGE 91

77 cavity equipped with suitable reflectors, has the ability to lase over a broad band of 10 to 50 nm in the optical spectrum. By replacing the rear reflector of the laser cavity with an element whose reflectivity is sharply peaked at one wavelength in the lasing band, e.g. a grating, lasing will occur only at this particular wavelength with only slight loss of optical energy [71]. Thus, by tuning the cavity's selective reflector to a particular wavelength, monochromatic output can be achieved anywhere within the lasing region of the dye being employed. The optical energy by which the lasing dye is excited or "pumped" can be supplied either by a fixed frequency pulsed laser, e.g. nitrogen or argon lasers, or by a flashlamp which emits high intensity broad band excitation. A laser pump would allow for very high repetition rates as well as provide very short lasing pulsing. On the other hand, a flashlamp excited device provides much more energetic optical pulses and is considerably less expensive than a laser-pumped system. As was shown in a previous section, the pressure fluctuation produced in an optoacoustic experiment is quite small and linearly dependent on pulse energy. So, primarily on the basis of the pulse energy available, the decision was made to utilize a f lashlamp-pumped dye laser system in this work. The system chosen (Model DL 1200, Phase-R Co.) is a complete dye laser system including flashlamp, power supply,

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7 8 dye circulation, cavity reflectors, tuning grating and control electronics. This system is primarily designed for use with dyes lasing in the 320 to 420nm region but will also accept dyes lasing throughout the visible if the cavity is fitted with reflectors optimized for the visible region. The rated pulse energy from the system (for Rhodamine 6B at 588nm) is 150mJ, and the manufacturer's literature describes this rating as "conservative." The data presented on ultraviolet dyes indicates output energies in the 330 to 420nm region of from 5 to 15mJ depending on wavelength and dye chosen (see Figure 10) . Bandwidth is given as 0.1-0.2nm when the laser cavity is grating tuned. The laser pulses are provided in a beam nominally 5mm in diameter and with a stated pulse width of less than 250 ns (full width at half maximum) . The firing mode is either manual or by external trigger pulse, and the maximum repetition rate is given as ten pulses per second. We elected to purchase this commercial laser system rather than construct one of our own design sc as to minimize time spent on laser research at the expense of the major interest of our investigation. As it occurred, this was not the case. Component failures in the laser system were numerous and continued to occur from time to time throughout the course of this study. These problems aside, however, the laser, under the best conditions, fell far short of expected performance in three citiical areas:

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80

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01 pulse repetition rate, optical bandwidth and output energy. Because these reduced performance levels so affected the course of this research, we will describe here our efforts to achieve the expected laser operation and report the final performance obtained. Preliminary work with the laser system was performed using the ultraviolet laser dye No. 386 (New England Nuclear) in dimethyl formamide (DMF) solution, as per manufacturer's suggestion. This dye is supplied as a 10~3 M concentrated solution and is diluted to 5 x 10" 4 M using Spectroquality DMF (Matheson Coleman and Bell) . Absorption and emission spectra of this dye are shown in Figure 11. The front reflector used in conjunction with this dye, hereafter referred to as Rl, is matched to the output characteristics of No. 386, having a peak reflectance of 85% at 389nm. The spectral variation of the reflectance of Rl is indicated in Figure 12. Before lasing can be attempted, the laser cavity must be aligned. This is accomplished with the use of a lmW He-Ne laser (Metrologic) . The He-Ne laser is first adjusted so that its beam is co-linear with the flashlamp using the pinhole caps provided. When a mirror is used as the rear reflector of the cavity, the front and rear reflectors are then adjusted so that they direct the He-Ne beam back upon itself. See Figure 13. The laser is now roughly aligned. At this point, the He-Ne laser is removed and the dye laser

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8 3

PAGE 98

u

PAGE 99

85

PAGE 100

tn

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U d) 0) ,Q w B r-1 y j 8 7 M O P U V Q) r-\ U U-l 4J C O O d) m m 0)

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8 8 is turned on. With a solution of dye circulating in the laser, the spark gap is pressurized with dry nitrogen gas, the voltage across the flash capacitor is raised and the flashlamp is manually fired. Fine tuning of laser alignment consists of observing the laser output pulse on a white card and making small adjustments in reflector positions so as to achieve an output beam which is circular in cross-section and uniform in intensity. In the aligned cavity formed by Rl and a total reflector, the onset of lasing of a freshly-prepared circulating solution of dye No. 386 is found to occur at 15kV with a spark gap pressure of 20psi. To measure the spectral range of this broad band lasing, as well as to monitor tuned output pulses, a 3/4 meter monochromator (Spex) with Polaroid camera attachment was used. See Figure 14. In this mode, dye laser alignment was preceded by alignment of the He-Ne laser to the monochromator. This was accomplished by directing the He-Ne laser into the center of the exit slit of the monochromator, then, with the monochromator wavelength setting at 632 8a, adjusting the He-Ne laser so that its beam exited the monochromator at the center of its entrance slit. This exiting beam is then used (as described previously) to align the dye laser cavity to the monochromator. To photograph the laser output, the monochromator wavelength setting is adjusted to a value close to where lasing is expected and

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5 V qLe# J j, u W >1

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9] a movable mirror is dropped into the light path to direct the beam to the camera. Spectral position of the laser output is usually determined by comparison to a photograph of a standard source taken in the same manner. Alternatively, it is possible to record the standard spectrum on the same photograph as the laser output. For the region around 390nm, a nitrogen Geissler tube was used to standardize the photographs. Portions of the second positive band of nitrogen lie in this region [72]. With the monochromator set at 387. 5nm, a photograph is made of the dispersed nitrogen emission. If one nov; plots the known wavelength of the transition band vs. the distance of this band in nm from the left edge of the photo, one obtains the plot shown in Figure 15. The plot shows that wavelength is linear with distance across the photo. A least squares fit of the line gives the intercept as 344.04nm and the slope as 1. 09nm/mm; this latter value correlates well with the stated dispersion of the instrument, Since distances on the photo can be read to + 0.1mm, wavelengths derived from them are thus good to + O.lnm. Photos taken in this manner of the unfiltered broad band output of dye No. 386 show detectible intensity over a 50nm band from about 320 to 420nm with bright areas centered at 387 and 400nm. To achieve narrow-band output, the rear reflector assembly is removed and replaced with a grating (1200 1/mm)

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Figure 15. Plot of wavelength of nitrogen emission lines versus distance from edge of photograph taken with monochromator mounted camera.

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410 400 -. 390 _ X (nm) 380 / 370 / / / 93 360 / ./ 10 30 50 70 d (min)

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94 in a gimbal mount. Set screws on the mount are available for adjusting the grating about its horizontal axis and for rotating it in the vertical plane. A micrometer drive is used for rotating the grating about its vertical axis and it is this motion which is used to select the lasing wavelength. The micrometer is calibrated so that one small division represents 0.2nm. A fine adjust micrometer is also available with vernier adjustment to 0.005nm, but it was not used. Alignment of the laser when using the grating mount is slightly more involved than when using a rear reflector. First, the flashlamp and front reflector are aligned with the He-Ne laser as described previously. A glass microscope slide used as a beamsplitter is now placed in the He-Ne beam in front of the front reflector so as to direct the return beam to the ceiling or a far wall. Using the micrometer drive, the grating is now rotated so as to best align the zeroth order He-Ne beam with the return beam off the front reflector. If exact alignment cannot be achieved solely by micrometer adjustment, the grating is tilted about the horizontal axis through the grating using the appropriate adjustment screws. Next the micrometer drive is used to select the I s order beam and align it as well as possible. If exact alignment of this beam cannot be achieved solely by micrometer adjustment, the grating is rotated about the hori-

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95 zontal axis perpendicular to its face by adjusting the appropriate set screws. Alignment of the zero order and first order beams is now repeated until both can be aligned exactly using the wavelength drive only. The micrometer is now set to select the wavelength of peak lasing for the dye in the laser. In doing so, one must take into account any zero shift in the micrometer drive. If the micrometer scale does not read zero when the zeroth order beam is aligned, this reading must be added to the wavelength desired to determine the appropriate micrometer setting. Lasing is now attempted. Fine adjustment of the alignment involves tilting the grating about its horizontal axis in small, incremental steps and observing the effect on lasing threshhold and spot size. This procedure was followed using a freshly prepared circulating solution of dye No. 386 (1 x 10" 4 M in DMF) to produce very intense lasing over a large spectral region. To calibrate the micrometer readings in terms of actual lasing wavelengths, the monochromator-mounted camera was used. To reduce the amount of scattered flashlamp light entering the monochromator , the laser beam was passed through a visible light filter, a 10% transmitting neutral density filter and a diffuser screen. On a single photo, a series of 16 laser exposures was made with the grating micrometer drive increased one unit after each exposure. The wavelength of each pulse was then determined from the

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96 photograph using the calibration data. A plot of output wavelength vs. micrometer setting is shown in Figure 16; the solid line is the best fit assuming a slope of unity. The plot in Figure 16 verifies the tunability of the laser system. However, the photograph from which the plot was made, as all the photographs taken of tuned laser pulses, cast doubt on the narrowness of the bandwidth of the individual pulses. All the photographs of laser pulses indicate bandwidths of approximately 2 nm. Although photographs of Geissler tube emissions show that the photographic technique used here is capable of capturing and reproducing much smaller line widths, to completely rule out the possibility of the photographic technique displaying falsely broadened spectra, an alternate measuring procedure was employed. A simple photodiode circuit (see Figure 17.) was placed at the exit slit of the monochromator to monitor pulse intensity. With the laser aligned to the entrance slit, the output of the photo circuit was monitored during laser firings as the monochromator was made to scan across the beam. Large variations in pulseto-pulse intensity were found and this made accurate determination of bandwidth impossible; however, the accumulated data bears out the photographic data. Both indicate much larger bandwidths than expected. A technique has been suggested for use with tunable lasers to provide narrower line widths [73]. In a grating

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Cfl

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98

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o o 4> o p. CD U a) :• o f>: ! >( M a) •p 41 td M ! o O -P -p 3 rtj u ii u

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100 a o u to o o -P rH rH H U [fl o

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101 tuned system, this technique involves placing a mirror of intermediate reflectivity in the laser cavity between the active medium and the grating. The grating-mirror combination now acts similarly to a Fabry-Perot etalon to reduce the bandwidth of the reflected light while at the same time increasing the reflectivity to the tuned wavelength over that of the grating alone. This technique was tried on our system using a variety of reflectors, none of which produced the desired result. Of those which did affect the output, all had the same undesired effect: tunability was lost and lasing occurred at 389nm. It is felt that the cause of this finding is that although addition of the added reflector does fractionally increase the reflectivity of the tuning element at the wavelength of interest, it also introduces a reflective element which acts at all wavelengths as opposed to the narrow band of the grating itself (see Figure 18). Thus, if the lasing system has potentially high gain at a particular wavelength, introduction of the partial reflector will cause lasing at this wavelength rather than the one selected by the grating. As we see from Figures 11 and 12, dye emission and Rl reflection both peak at 389nm. Thus, sufficient gain exists at this wavelength when a reflective element is introduced that lasing is required to occur here. If a sufficiently poor reflector is used so as to overcome the 389nm lasing, its ability to produce bandwidth reduction becomes lost. Because of this situation,

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103 s< O o H >, +J H > •H 4J U a 5 H IH
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104 further work was done without an intracavity reflector and with an output bandwidth of ^2nm. A simpler approach to bandwidth reduction was also attempted, but without success. It involved merely reducing the flow rate of the laser dye solution through the flashlamp with the rationale that if flow turbulence was at the root of the large bandwidth observed, this would diminish its effect. As noted, this approach was not fruitful, but it is mentioned here because it drew our attention to the repetition rate of the laser. At reduced flow rates it is found that 20 to 30 seconds must be allowed between laser firings for lasing to occur. The reason for this can be observed quite well when aligning the laser using the beamsplitter technique. As mentioned previously, in this technique the He-Ne beam which is reflected off the rear reflector (or grating) is observed on the ceiling or a far wall. This beam is normally very steady. However, when the laser is fired, turbulence in the dye cavity causes the beam to bounce about erratically for ten seconds or so before again becoming steady. If the laser is fired during the turbulent period, lasing will not occur. This is not surprising. However, we did find that even at the highest flow rates, this turbulence followed a laser firing for a period of several seconds. Thus, even tliough the laser flashlamp could be fired at a rate approaching lOpps, actual lasing could not. be repeated at a rate exceeding . lpps . Other

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105 investigators [74] have increased the maximum repetition rate for this system to about lpps but only after considerable alteration and replacement of original equipment. Thus, our laser system is restricted to a very low repetition rate. Although not a crucial restriction in an opto-acoustic system, for experiments which suffer from a high background noise, it. becomes difficult to markedly enhance the overall signal-to-noise by increasing the number of observations. Having characterized the tunability, bandwidth and repetition rate of the laser system, the measurement of pulse energy was next approached. Preliminary measurements were attempted using a ballistic thermopile (Hadron Model 101) connected to a digital multimeter (Keithley Model 150) . However, the thermopile was found too insensitive to the laser's output and the multimeter too sensitive to the electromagnetic interference produced by the laser during a flash to be of any use. The next approach to measuring output pulse energy was by means of a chemical actinometer. This method has the advantages of being quite sensitive to light, totally insensitive to electrical interference and able to integrate a number of pulses to smooth out the observed pulseto-pulse variation in output energy. This last feature is especially attractive for a multiple shot opto-acoustic experiment. Instead of having to monitor the energy in

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106 each pulse, only a single measurement need be made at the experiment's conclusion to determine the average pulse energy delivered. The chemical actinometer used is the potassium ferrioxalate system of Hatcbard and Parker [75] . Specifically, a 5cm long quartz cell is filled with 14ml of a solution 0.006M in potassium ferrioxalate and 0.005M in sulfuric acid. It is then placed in front of the laser output reflector and the laser is fired a number of times. A 3x5 card held behind the absorption cell gives no indication of any light being transmitted. Equal portions of the exposed solution and an identical unexposed one are then each processed identically. The processing forms the highly absorbing 1 , 10-phenanthroline complex of the photogenerated ferrous ion. Using the value of 1.11 x 10 1/mole-cm as the extinction coefficient of the iron-phenanthroline complex at 510nm, the energy per laser pulse can be computed from the formula E = 377J x 22 (22) Fe N x A x <$> S A where OD is the optical density of the irradiated sample vs. the blank at 510nm in matched 1cm quartz cells, N g is the number of laser shots absorbed by the actinometer, X is the Fe +2 lasing wavelength in nanometers and . in the quantum

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10 7 yield of ferrous ion at X in molecules/photon. With Fe +2 N = 10, A = 386. 4nm and extrapolating
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u

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109 "^

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110 connected to an oscilloscope (Tetronix Model 5 35A) through a 50 ohm termination (actual resistance: 51.5ft). The oscilloscope is triggered by the laser firing unit and the resultant sweep is photographed for analysis. With the laser tuned to 386. 4nm and adjusted for optimum output, a number of shots were made and recorded at a firing voltage of 20kV. A typical scope trace is reproduced in Figure 20. The occurrence of the laser pulse takes place approximately 500 nanoseconds after the sweep is triggered. The full width of the trace at half height is 100 nsec, however this value may be affected somewhat by the rise time (^20 nsec) of the oscilloscope. There is considerable variation in peak amplitude from pulse to pulse, however, the majority of sweeps showed peaks in the range from 5 to 8 volts. The energy in a single pulse can be estimated as the product of peak power and full width at half-height. Correcting for filter losses and using the calibrated phototube sensitivity at the lasing wavelength, the pulse energy in the most energetic pulse observed can be calculated as F = i 15v M -100ns ' 3.07 x 10 2 / (57.5 mA/watt) = 125yJ. ** [ 51.5JT This finding corroborates the actinometer results and would appear to place the upper limit of pulse energy obtainable from dye No. 386 at around 0.15mJ for our laser operating at 20 kV. Table 4 summarizes the important parameters of our

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4J O JJ • O Q) D.H M-l O. O M CX> i (1) H •H Cm

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112

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113 Table 4. Characteristics of laser system using laser dye No. 386. E xpected Achieved Pulse width 250 ns 100 ns Repetition Rate 10 pps . 1 pps Tuning Range 375-401 nm 383-399 nm Bandwidth 0.1-0.2 nm 1.5-2.0 nm Pulse Energy 10-15 mJ 0.15 mJ

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114 laser system, both expected and achieved, when dye No. 386 is used for lasing in the ultraviolet region. Two other ultraviolet lasing dyes, p-terphenyl (New England Nuclear) and p-quaterphenyl (Eastman Kodak laser grade) were also examined in our system with appropriate reflectors and grating settings, however no lasing could be achieved under a variety of conditions. With p-terphenyl a dye concentration series was run to determine whether lasing might occur only for solutions within a certain concentration range. In particular, it was questioned whether the suggested lasing concentration _ ~i of 10 M was too high. This is indicated when one considers the absorption depth of a 10 M p-terphenyl solution in dime thy lformamide. From a spectrum of this solution, the molar extinction coefficient at the absorption 4 peak (283. 2nm) is found to be 3.3 x 10 lit/mole-cm. In _ > a 10 M solution, this means that 90% of the flash energy is absorbed in the first 0.3mm of the solution. Since the dye tube has a radius of 2.5mm, the central portion of the solution is hardly excited at all. For the concentration series, the concentration was varied in ten steps starting -5 -3 from 9 x 10 M and increasing up to 1.0 x 10 M. At the lowest concentration, almost 20% of the incident light has not been absorbed after passing through 2.5mm of solution. For each concentration of dye solution, the laser was aligned, and lasing was attempted but not observed.

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11! Pre s sure Detection Syste m To satisfy the size and responsivity requirements imposed on the opto-acoustic pressure detector, a Pitran pressure sensitive transducer (series PT-L, Stow Laboratories, Inc.) was chosen [77]. Basically the device is a silicon NPN planar transistor that has its emitter-base junction mechanically coupled to a metal diaphragm. Displacement of this diaphragm causes stress-induced variation in the transistor's gain. In a suitable circuit, this change in gain causes a change in voltage output which is linearly proportional to the pressure differential across the device. The unit is small; the diaphragm is only 3/16" in diameter. Yet it is sensitive. In its standard circuit (figure 21), it provides a linear 2 volt output over a 0.1 psi differential pressure range. This converts to a sensitivity of almost 400mV/torr. Pressure equivalent noise is usually less than 10 torr, and the device has a typical rise time of 10 seconds. The device does show a considerable temperature coefficient; for a fixed bias voltage and zero pressure differential across the Pitran, the output voltage will vary with temperature up to 400mV/ C for some models. This drift can be minimized by constructing a suitable temperature-compensation circuit. However, we have found that such a circuit causes a significant increase in noise at the output. In practice, since the temperature drift is of

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-p H 'J •H O -P • •H G CM ^ O T3 M iti -P W W S-l U-l 4J O en -H o w P ^1 (1) H CO 0) H fa

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117

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113 such low frequency, it is sufficient to monitor the zeropressure output and adjust it manually just prior to a run. The actual data-gathering period of a pulsed opto-acoustic experiment is so short that temperature drift during this time is insignificant. In mounting the Pitran in the opto-acoustic cell, precautions must be taken to avoid exerting mechanical strain on the device and at the same time properly shielding the electrical connections against electromagnetic interference. A cross-sectional view of the Pitran mounted in the opto-acoustic cell is given in Figure 22. Mounting begins by carefully applying a thin layer of soft-cure epoxy (Eccobond 45, Emerson and Cuming, Inc.) around the rim of the head of the Pitran. It is then set into a Teflon seat and the epoxy is room-temperature cured overnight. (The Teflon seat is used to electrically insulate the Pitran case (=collector) from the grounded cell.) The seat is then carefully attached to the Pitran holder by means of six small counter-sunk screws. An airtight connection is provided by a rubber gasket. A Teflon sleeve with four small diameter holes drilled parallel to its axis is now slid into the bottom of the Pitran holder. Three of the channels in the sleeve fit loosely over the Pitran leads, the fourth insures airflow to the reference (rear) side of the Pitran. With the sleeve in positon, three small set screws are now tightened to hold the sleeve in place. A

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120

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121 single drop of hard-cure epoxy (Shell Epon Resin 828) is then put into each of the three holes in the Teflon sleeve which encompass a Pitran head. After room-temperature curing, this epoxy helps to absorb any stress put on to the exposed Pitran leads and keeps it from transferring to the Pitran itself. The Pitran holder is now mounted to the opto-acoustic cell with six screws, vacuum-tightness insured by the use of an "0"-ring. Socketed flexible wires are then slipped over the Pitran leads. These wires are permanently soldered to vacuum tight coaxial cable connectors (Amphenol, #82-843) mounted in the aluminum cup which can now be attached to the cell. Coaxial BNC cables are used to connect the Pitran to its control electronics in order to minimize electromagnetic pickup. The control electronics for this device (basically the circuit of Figure 21) were purchased from Stow Laboratories (Model 850) and modified to minimize line and background noise. The output of this circuit is then fed into a second circuit, schematically shown in Figure 23. For biasing, the Pitran output is switched into a long time constant RC filter which presents a stable DC output level to be read with a voltmeter. The bias adjust potentiometer is used to set this level to 2.000 volts. During a run, the Pitran signal is switched into an AC amplifier with selectable voltage gains of 1, 2.5,

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T3

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123 u a I X

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124 5, 7.5 or 10 thousand. This degree of amplification is necessary in order to provide the high level signal required by the data logging instruments. The other pressure measuring device used in the opto-acoustic experiments is a capacitance manometer (Datametrics Barocel Model 1173 Electronic Manometer + Model 523-10 pressure sensor) . As mentioned in a previous section, this instrument is used to measure static pressure differences between the experimental and reference cells. The manometer is capable of full scale measurement of pressures from 10 torr down to 10~ 3 torr, with an accuracy of 0.1% of reading + 2% of full scale. Such accurate measurement of static pressure can be of use in determining the presence and extent of any decomposition or photochemical reaction which changes the number of gaseous molecules in the experimental chamber relative to the reference chamber . Pressure readings are taken directly from the analog panel meter on the manometer, or a digital voltmeter is used to monitor the high level analog output available at the rear of the manometer electronics. This output varies from to 1 volt full scale and is linear with the panel meter reading. Because of these characteristics, it can also be used as input to the data logging equipment when a static or slowly varying pressure is to be monitored for a long period of time.

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125 Da t a Gat he rin g a nd P rocess i ng System The instrument used to capture and accumulate the analog signals generated in the course of the opto-acoustic experiments is a CAT (Computer of Averaged Transients) . This instrument consists of a Model CN-1024 Pulse Analyzer System (Technical Measurements Corporation) equipped with a Model 202 Logic Unit which provides signal averaging capability. The CAT has 1024 channels which it scans sequentially at the onset of a trigger pulse. Each channel accumulates data in the form of counts which are stored in a nonvolatile magnetic core memory which has a capacity of 17 binary bits (131, 071 counts) per channel. As a repetitive waveform is generated for a number of times, at each occurrence it is sampled 1024 times and each sample is added to the appropriate channel in the CAT ' s memory. When sufficient signal is accumulated, scanning is stopped and the stored signal is divided by the number of sweeps N s to obtain the average waveform. The benefit of this averaging procedure is that any random noise which was present in the original signal tends to cancel itself out. This leads to the signal-to-noise ratio in the averaged signal being greater than in a single signal by a factor of N ' . The CAT provides for selection of the dwell time per channel, t, -,-,, from one of the 16 values given by the expression t Q x 2^ x 10 n

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126 where both ra and n range from to 3 and t is the minimum dwell time. Using a Time-Mark Generator (Tetronix) t Q was determined as 30.61usec, only 2% below its nominal value of 3.1. 25 usee. During CAT operation as each channel is addressed, the current count must be transferred from memory to an arithmetic register in the CAT, then the contents of this register returned to memory before the cycle repeats for the next channel. Thus, a fixed portion of the dwell time, t dead , is used for internal data manipulation so that the actual time for which a channel is active is slightly less than the dwell time. During the active channel time, while the count is in the arithmetic register, pulses generated by a voltage controlled oscillator (VCO) in the logic unit are added to it. The frequency of the VCO is dependent in a linear fashion on the instantaneous input voltage. Thus, in the course of one sweep, a number of counts C is added to each channel which is directly related to the average voltage, V, applied to the CAT input during the period for which the channel is active. This relationship can be expressed in a mathematical form as C = (f Q + f v • V) (t dw£ll t^^) (23) where f is the zero voltage frequency of the VCO and f v is the change in VCO frequency per volt change in input signal .

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127 To determine the values of the parameters f , f y and ^dead' a pulse generator was used to provide 1 volt square wave input pulses as the CAT was synchronously triggered for a pre-determined number of sweeps. This was repeated for the ten shortest dwell times. After each set of sweeps the average channel reading for the low (0 volts) and high (1 volt) level of the square wave was determined. These data are plotted in Figure 24. A least squares fit of the data to equation (23) provide the following values: t dead = 13.3ysec, f Q = 3.42 x 10 5 sec" 1 and f v = -5.79 x 10 4 sec'-'-v"-. The sign of f v indicates that the signal is inverted as stored. The input to the CAT is limited to + 3 volts. It is advantageous to amplify the input signal so that its maximum peak-to-peak excursion covers this input range since conversion accuracy is fixed by the linearity of the VCO as + 0.5% of full scale, or + 15 millivolts. For very small dwell times, uncertainty is also introduced by the possible error of + 1 count always present in digital counting schemes. This becomes clear when C is calculated from equation (23) for t = t . The average count per channel for zero voltage input is just under six counts. Conversely, an error of + 1 count converts to an uncertainty of + 1 volt. This latter source of inaccuracy is overcome by increasing the final count, either by increasing tj we ii or by running many sweeps. The number of

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129

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130 sweeps required to reduce the digital counting uncertainty to equal that of the converter is given by 1.15 msec/(t dwe n -tdead*' which for tdwell = fc o comes out to 67 swee P s * Once the averaged signal is in the CAT, it must be transferred out to be processed. The Wang 700C Programmable Calculator which was used to generate the simulation plots was also available to process the CAT data and to control its plotting. The 700C is equipped with a Wang 705-1 Microface for remote data entry. However, the Microface accepts only TTL level, parallel binary-coded-decimal (BCD) data whereas the CAT output is either parallel binary (-12v level) or in the form of a pulse train (-20v level) . To interface the CAT output to the Microface, a device given the name of Picoface (from Practical Interface for CAT Output) was designed and built. The principle operations of the Microface-Picoface-CAT system during data readout are as follows. With the CAT manually set in the decimal readout mode, the programmable calculator instructs the Microface to initiate data transfer. The Microface unit sends out a pulse (execute command) through the Picoface to the CAT, signalling it to begin readout. The CAT responds by sending a pulse train into the Picoface where it is level shifted and counted by a series of one binary and five decimal counting units. The number of pulses in the train is equal to the count in the channel being interrogated; the address of this channel is indicated by a series of

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131 light-emitting diodes on the front panel of the Picoface. 7iS the pulse train ends, the CAT sends a signal (print command) back to the Microface through the Picoface signifying that counting is complete. After the Microface accepts the BCD count data, the counting units are automatically reset, the CAT is advanced to the next channel and the system is ready for another counting sequence. Data transferred in this fashion can now be digitally plotted, stored on magnetic tape or processed in a number of ways by the programmable calculator to extract pertinent information. One additional element which should be considered in this section is a device called Diamux (for dual input analog multiplexer) . This is a device which was designed and built to provide the capability of recording two simultaneous analog signals in the CAT. It would be useful, for example, for simultaneously recording the transient signals generated by both the Pitran and a photomultiplier tube. The Diamux does this by alternately gating two field-effect transitors which connect the two signals to the CAT input. By synchronizing this gating with the CAT channel advance, one signal is averaged in the 512 even-numbered channels and the other in the 512 odd-numbered channels. Though the signals are intermixed in this fashion, it is quite simple to program the calculator to process just one at a time. Thus both can be individually plotted, stored, etc.

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132 Operating Procedure A block diagram of all the elements involved in the pulsed opto-aooustic experiments discussed in this work is shown in Figure 25. The solid arrows connecting the blocks represent signal flow in the basic experimental setup. Dotted lines are used to show possible additional elements and alternate connections. Before initiating an experiment, the following conditions must be satisfied. The sample vapor is present in the optoacoustic cell at the desired pressure. The dye laser is aligned, its grating turned to the desired wavelength, its spark gap pressurized and its flash capacitor charged to the proper voltage. The Pitran is biased at. 2.000v and is switched to the amplification circuit. The CAT is cleared and in the count mode. The oscilloscope is set to single-sweep and armed to accept a trigger pulse. A single opto-acoustic experiment can now begin by manually firing pulse generator #1. This triggers both the CAT and pulse generator #2. This second generator delays firing for a set period to allow the CAT to establish a "baseline." When it does fire, it triggers both the dye. laser and the oscilloscope. The latter is used to display the output of the photodiode monitoring the laser. The scope display can be photographed or its peak value can simply be observed and recorded. The pressure variation in the cell induced by the laser pulse is picked up by the Pitran, amplified and directed to the CAT where it is

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r r.

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134 "~1 0) tn ro +J rH o > (-1 I Q> +1 •P U 1 0) •4-» > C, C 0> O M V U V L 1

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135 digitized and accumulated. Before beginning another sequence, sufficient time must be allowed for the turbulence in the laser dye cavity to diminish. During this time the Pitran DC bias can be checked and re-adjusted if necessary. The run can then be repeated by re-arming the oscilloscope and again firing pulse generator #1. As long as there is no decomposition of the sample vapor, as would be indicated by a rise in the capacitance manometer reading with time, data accumulation can continue indefinitely. The practical restriction on the number of runs made is the number of shots of reasonably high pulse energy which the laser can deliver from a single dye solution.

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CHAPTER FOUR OBSERVATIONS Flashlamp Experiments Before the laser experiments were begun, a small xenon flashlamp apparatus in conjunction with an early version of the opto-acoustic cell was used to determine whether our pressure detection system was indeed sensitive enough to detect minute pressure signals. Acetone was used as the sample vapor because of its availability and high vapor pressure. With regards to signal strength, the high room temperature vapor concentration obtainable with acetone is offset by the very low extinction coefficient for acetone absorption (^14 lit mole" cm at ^ max ~ 280 nm ) t 76 /P377 1 and the small fraction of flashlamp radiation available in this wavelength region. Experiments were run with 50 to 100 torr of acetone in the sample cell. The flashlamp radiation was passed through a filter before entering the cell to remove infrared radiation. The pressure variations were detected by the Pitran, amplified and either displayed on an oscilloscope or averaged in the CAT. The observed signals showed a very fast rise (<0.3 msec) independent of pressure followed by a slow return to the pre-flash level. The rate at which the signals decayed 136

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137 varied inversely with pressure as expected. The averaged signal (25 flashes) shows a signal-to-noise of 1 for voltages corresponding to peak-to-peak pressure changes of 1 mtorr. The "bumps" expected in the pressure signal due to the logitudinal acoustic wave are quite evident. They do not appear equally spaced as in Figures 6-8, because the version of the cell used does not have the Pitran mounted at the center of the cell. It is situated instead 3.8 cm from the front cell window and 8.9 cm from the rear. As the wave resonates in the cell, it thus takes a shorter time to pass the detector, reflect off the near window, and return than it does for the similar trip to the far window. Thus, the acoustic bumps appear grouped in pairs where the ratio of the time between the occurrence of two paired bumps and the time between successive pairs equals the ratios of the two trip distances [64]. With time, as the signal decreases, the bumps tend to broaden so that after several milliseconds the paired-bump structure is no longer present. At this point, the time between successive maxima in the signal is the round-trip travel time of the acoustic wave in the cell. For 100 torr of acetone this time is measured as 1.17 ms in the 5" cell. From this measurement the speed of sound in the vapor can be calculated as 2.17 x 10 4 cm/s . With this value Y can now be calculated from equation (19) as 1.10 which is in good agreement with reported data on acetone vapor [78].

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138 Laser Ex perimen ts Choice of Sample In choosing a sample to which the pulsed opto-aco'ustic technique could be applied, several points had to be considered. Since the technique itself is new, it was felt that it should be applied to a molecular system about which there already existed a reasonable amount of knowledge. In this way results could be at least partially verified by previous data while opto-acoustic spectroscopy, by virtue of its unique approach, would certainly provide added insight. On the practical side, to be suitable a sample has to satisfy certain criteria with regard to vapor pressure, extinction coefficient and wavelength of absorption. Based on the latter many otherwise suitable samples were ruled out because their absorption bands lay outside the region accessible to our dye laser. This criterion grew even more restrictive as the narrowed lasing band of our laser became apparent. On the basis of the above criteria, two molecules were examined for suitability. Pyridazine Pyridazine belongs to a class of compounds, the diazines, whose excited state characteristics have been the object of numerous investigations [79]. Of the diazines, pyridazine alone has an allowed electronic transition which appeared to be excitable by the dye laser. The transition, which is actually to the second excited singlet state, is n->TT* in nature and has its origin at 375 nm [80] . The deactivation of this state is known tc be dominated bv

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139 radiationless processes, so that it is an efficient "heat producer" [81]. The major question concerning pyridazine's suitability was its absorptivity. A 5g sample of pyridazine (Aldrich Chemical Co.) was obtained and trap-to-trap distilled twice under vacuum using liquid nitrogen. It was then distilled a third time from potassium hydroxide pellets, as suggested by Cohen and Goodman [81]. The first two distillations removed some solid residue; the third removed an impurity which gave the sample its original reddish-orange color. The sample was then put through five f reezepumpthaw cycles. The distilled and degassed sample is not colorless but is slightly yellowish. A gas chromatograph indicated the presence of only a single component in the sample. A fraction of the sample was distilled into a 10cm gas absorption cell and its spectrum taken on the Cary 14 spectrophotometer using the 0.2 slidewire. The absorption was too small to be detected. For this reason, a selectable path length multipass gas cell (Beckman Instruments) was employed. A modified sample compartment was attached to the spectrophotometer which allowed the cell to be introduced into the sample beam from the side. Since the cell is intended for use in the infrared, it is fitted with KBr windows. These windows cause no problem, although the front surface mirrors in the cell do introduce some background absorption, evidently due to contamination. This absorption is structureless, however, and equivalent to a sloping

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140 baseline. Figure 26 shows the absorption spectrum of pyridazine at its room temperature vapor pressure (subsequently measured as ^0.3 torr) over a 4.6 m path. The small peak at 375nm corresponds to the origin of the S Q +S 2 transition. Other prominent peaks in the spectrum are also observed and their assignments [80] noted in the figure. The strongest transition, the band at 357. 5nm, has an optical density of at most 0.03. This corresponds to an absorptivity of 6.5 x 10~ 5 cm" 1 . Even with a pulse energy of lOmJ, absorption into this "peak" would produce a maximum pressure rise of less than lm torr. For this reason, pyridazine was ruled out as a prospect for experimentation. Oxalyl chloride Oxalyl chloride is also a member of a well-studied class of molecules, the a-dicarbonyls . Though not studied in nearly as much detail as some other members of the class, e.g. glyoxal, biacetyl, the absorption spectrum of oxalyl chloride has been reported and some things are known of its excited state behavior. In particular, both the S Q ->S 1 [82] and S -*T [83] bands have been analyzed. Since oxalyl chloride has a relatively high vapor pressure at 25°C (89 torr) , it was hoped that both the singlet and triplet absorption systems would be suitable for opto-acoustic study. The singlet system has its origin at 368nm. The transition, though formally allowed ( A + A ) is weak, as expected for an n-*Tr * transition. As also expected of a n+ir * transition, a progression in the carbonyl stretching mode

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14; rH

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143 (^1450 cm" ) is quite evident with each member of the progression acting as a pseudo-origin for other vibrational bands. The origin of the triplet system is at 410nm. This transition too is A +A (n-^*), however, because it is sping u forbidden, it is considerably less intense than its singlet counterpart. The triplet system shows much vibrational structure and extends upward in energy to the onset of the singlet system. Triplet emission has been observed both in the crystal at 4.2K and in a cyclohexane matrix at 77K with lifetimes of 7.4 and 13 ras, respectively [84]. A 12. 7g sample of oxalyl chloride (Aldrich Chemical Co.) was obtained. The sample was carefully transferred to a special sample container which was fitted with a Teflon stopcock due to oxalyl chloride's reportedly high reactivity towards stopcock greases [85], Purification was accomplished via trap-to-trap distillation. After two such distillations the sample lost its original reddish-orange tint leaving behind a reddish residue. After degassing, the purified sample was stored in the dark. To measure the absorptivity of the singlet vibronic bands, a room temperature spectrum was taken of oxalyl chloride vapor in a 10 cm gas cell. The spectrum is shown in Figure 2 7 from 310 to 390nm. The prominent bands are marked with the assignments of Balfour and King [82]. The diffuseness of the spectra at shorter wavelengths has previously been reported and tentatively ascribed to the presence of a higher-lying dissociative A (nir*) state. The proposed explanation for

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Figure 27. Oxalyl chloride vapor absorption spectrum in 10 cm gas cell, 310 to 390 nm.

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145 0.7 0.5 J OD 0.3 -J 0.] 310 330 350 X (run)

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146 the continuum underlying the spectral peaks is absorption due to •C0C1 radicals produced during exposure to light [86]. The absorptivity of the 0-0 transition at 36 8nm can be -2-1 estimated from Figure 27 as 2.3 x 10 cm . This transition is certainly sufficiently strong to be examined by the opto-acoustic approach, however because of the narrow tuning range of our laser, it is inaccessible. The same applies to the other bands of the singlet spectrum. To examine the region of oxalyl chloride triplet absorption, the multipass cell was again utilized. This time, however, the KBr windows were replaced with quartz windows. A spectrum was taken of the evacuated cell from 360 to 420nm using the one meter path which showed a rather linear increase in absorbance over this range of about 0.1. The degassed sample was then allowed to enter the evacuated cell and come to equilibrium. The triplet spectrum oxalyl chloride vapor from 380 to 420nm is shown in Figure 28 for a 6.4 m absorption path. All the prominent peaks have been previously assigned [83] . Sample absorbance in the triplet region is sizable, but it cannot be read directly because of the cell mirror absorption. For this reason, all optical densities were measured with respect to the absorption at 420nm where oxalyl chloride is transparent. The absorbance of the S ->T origin band (410nm) was measured in this fashion for several path lengths and this data plotted in Figure 29. The plot is linear as expected from Beer's law and has a

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u

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148 E c X i. ':> z W -J GO

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C CJ tn-H H +J o H<* 0) t O (1) a, o om c co > nj CD CD 4J -H ^a M O OH X! J2 tJ +) cu o c en O 3 G CH O (!) ra >i ^ h £5 H C7> XOjJ 01 O « Hi X) Xi Cu td 4-i O 4-1 O 11 4-> fC O X! rH Pi cu co x\ 2 CO > 0) n en H P<4

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150

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151 slope of 6.12 x 10" cm" J ' which is the absorptivity of oxalyl chloride at 410nm. The intercept of this plot is not zero and apparently arises from the increased absorbance of the mirrors at the lower wavelength. Even accounting for this effect, the bands around 385nm are more intense than the origin band by a factor of two or three. One can calculate that in the experimental cell these bands will absorb approximately 5% of the incident radiation. Being positioned directly in the region where the dye laser is active, these bands appeared to make oxalyl chloride an excellent candidate for opto-acoustic examination. Results The experimental equipment was arranged as diagrammed in Figure 25. The Diamux unit was not used and the amplified Pitran output was connected to the CAT input. With the sample cell evacuated, the sequence of steps which would be followed in an actual run were carried out. It was found that the firing of the laser caused sufficient electromagnetic interference (EMI) to cause a "spike" to be inserted in the otherwise flat signal being sampled by the CAT. This artifact, though of significant magnitude, affected the input for only 0.1 ms or so and thus was a minor problem. A second effect of the laser interference on the CAT was quite more troublesome and involved the read/write cycle of the signal averager. When this problem occurred, laser firing caused the CAT to either retrigger, i.e. immediately

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152 begin a new sweep, or cease operation in mid-sweep. Several steps were taken to reduce this interference. A number of grounding schemes were used in an attempt to avoid ground loops. An aluminum box was built to house the laser and was grounded to hinder transmission of EMI. The CAT was moved to an adjacent room and connected to the other equipment solely by shielded cables which were fed through the common wall. All these approaches did not restrain the CAT from sporadically being affected by the laser firing. One measure which did provide a definite improvement, though not a complete solution, was to insert a reed switch in the CAT's trigger line. Output from the second pulse generator was connected both to the reed coil and to one reed switch contact; the other contact led to the. CAT trigger input. Approximately 3 ms after the first pulse generator is fired, the second delivers a 1 ms 7v positive pulse which serves the dual purpose of both closing the reed switch and triggering the CAT. Ten milliseconds later, the pulse from the first generator makes its positive transition and fires the laser. This sequence causes the trigger input of the CAT to be totally unconnected during laser firing and avoids any spurious signal being coupled to it. Once the equipment appeared to be working as planned, a sample of oxalyl chloride was allowed into the cell. It was noted that whenever the valve separating the two chambers of the cell was closed, the pressure in the experimental

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153 chamber would slowly begin to rise relative to that of the reference chamber at a rate far exceeding that of the leak rate of the cell. Since this pressure rise occurred in the dark and even when an hour was allowed for sample equilibration, it appeared that some form of thermal decomposition of the sample was taking place. To determine the nature of this reaction and the rate at which it was occurring, it was examined more closely. Approximately 1.5 torr of oxalyl chloride was allowed to enter the cell, valve (B)was closed, the reference chamber was evacuated and the variation of the pressure in the experimental chamber was followed using the capacitance manometer. A plot of pressure versus time is given in Figure 30. The straight line drawn at the bottom of the figure represents the pressure rise which occurs under similar circumstances in an evacuated cell due to the leak rate of the cell. One observes that (1) the pressure rise in the presence of oxalyl chloride is far greater than could be ascribed to a leak, (2) the rise is at first linear then asympototically approaches the final pressure and (3) the final pressure (attained after 137 minutes and marked by the arrow in the figure) is very close to twice the initial pressure. The conclusion to be reached from these observations is that the oxalyl chloride undoubtedly decomposes in the aluminum ceil to produce two moles of volatile product per mole of reactant. The shape of the pressure versus time plot is indicative of a surface reaction [87], showing at

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0)

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155 r I u U H O -P CM \ \ \

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156 first zero-order, then first-order reaction. From the linear portion of the plot, a value of 2 2.3 mtorr/rain is extracted for the rate of depletion of the oxalyl chloride. After reaction, the product vapor is transferred to an infrared gas cell and its spectrum recorded on an infrared spectrophotometer (Perkin-Elmer, Model 237B) . Only the absorption characteristic of carbon monoxide is observed. The thermal decomposition of oxalyl chloride has been studied [88] at elevated temperature. The decomposition is found to be predominantly decarbonylation with one molecule each of carbon monoxide and phosgene (C0C1 2 ) being formed per molecule of oxalyl chloride. Evidently, in the aluminum cell the reaction proceeds further with the chlorines apparently being lost to the walls and a second molecule of carbon monoxide forming. Before the means was available for measuring the laser output, several actual opto-acoustic experiments were performed using oxalyl chloride and exciting into the 386. 4nm band. These were all done in the dark to avoid photochemical decomposition. Also, laser firing took place within minutes of the sample being introduced into the cell so little thermal decomposition could occur. In general, no response to the excitation could be obtained from the Pitran. However, the capacitance manometer when set to 10 mtorr full scale was found to produce a signal, the general form of which is shown in Figure 31. The shape of the signal was found to vary only slightly from run-to-run although

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c

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153

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159 different initial pressures of oxalyl chloride were used. When data on laser pulse energy became available, it was realized that the signal was an artifact. It could be produced, it was found, even with the laser beam blocked as long as the manometer was on a sensitive scale. This check for an artifact signal had been run previously, but for that test the manometer had been set on its least sensitive (10 torr) scale.

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CHAPTER FIVE COMMENTS In the previous chapters the ground work has been set for a useful new approach to the study of excited state rate processes. A theoretical foundation has been derived for pulsed opto-acoustic spectroscopy and the application of the technique to real molecular systems has been discussed, An experimental system was designed and assembled, and preliminary experiments run. The failure of the attempted experiments to produce any new information on molecular excited states or, indeed, to even experimentally establish the feasibility of the timeresolved opto-acoustic technique is greatly disappointing. It would be more disappointing by far, however, if the usefulness of the technique described in this work was dismissed on the basis of the present results. Even a cursory analysis of the experimental facts makes it quite obvious that the experimental approach undertaken to observe the opto-acoustic signals failed because of the uniquely poor performance of the dye laser system, which fell far short of its expected capabilities in every critical area, although hundreds of man-days were spent attempting to improve its performance. The dozens of conversations held 160

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161 with the manufacturer plus the visit by their representative to our laboratory were helpful, but the improvements they affected allowed us only to achieve the performance characteristics previously outlined in Table 4. The most important failing of the laser was that insufficient optical energy was supplied to the experimental cell. Even if the most energetic laser pulse observed (150uJ) were completely converted to thermal energy in the cell, a pressure rise of only 5.6 mtorr would result. This would produce a signal not significantly above the overall singleshot noise. Of course, not all the impinging light is absorbed and converted to heat. The role of the sample is of central importance in heat generation. But, here too, laser performance played an important role since its narrow active band greatly limited the choice of sample. Further work employing the present detection system will certainly require pulses significantly more energetic than 150yj being delivered to the cell. Even with the present laser system, this has been achieved in the visible region (150mJ, Rhodamine 6G) [89] . So for these larger wavelengths, attaining sufficient pulse energies appears to be problem. However, at shorter wavelengths the laser dyes tend to be less efficient. For this region, one must either obtain one of the existing dye lasers which can provide the pulse energies required [90] or resort to frequency doubling of the laser output. This latter technique is somewhat inefficient, but with energetic pumping it could provide

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162 ultraviolet pulses with energies several times the maximum observed in this work [91]. A final alternative would be to use a fixed frequency laser as the pump beam, but this would sacrifice wavelength tunability. With regards to the pressure detector employed, although in our hands it did appear rather short-lived, it is hard to fault the Pitran on its performance. However, another type of detector has appeared which exhibits an order of magnitude greater sensitivity and significantly less output noise, though with a reduced frequency response [92]. This general type of detector is known as a capacitance microphone and consists of a thin layer of a pliable dielectric material sandwiched between two electrodes, one being typically a metal foil. Pressure variations across the dielectric cause it to deform and hence change the overall capacitance of the microphone. In a constant voltage system, the change in capacitance causes a current to flow which is detected by a low-noise, high-sensitivity charge amplifier. For the foil electret variety of condenser microphone, an external voltage source is not even required since polarization charges in the dielectric maintain a bias in the device [933 • The condenser microphones are not "point" detectors as is the Pitran, and because of this equation (17) does not accurately describe the surface-averaged signal they would produce. It is easy to show, however, that if a condenser microphone of length A is placed at the outer surface of a cylindrical cell with its center at L/2, the pressure

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163 signal it "sees" is given by a modification of equation (17) with the term sin (nnrA/L)/ (imrA/L) introduced into the summation for m>0. This added factor tends to smooth out the acoustic bumps as A increases. An interesting result is with A=L; no acoustic bumps should be observed, but rather just, the gross pressure rise. With improvements in laser performance and detector response, the application of pulsed opto-acoustic spectroscopy to the study of excited states can become a rather important technique. For the study of molecules which show either a very high or very low luminescence yield, the approach offers some unique advantages. A molecule with a very low level of luminescence is quite difficult to study by light emission. However, this molecule necessarily has a high radiationless yield so it is a good object of study for the opto-acoustic technique. For a molecule with a high level of luminescence, it is in general very difficult to determine radiationless yields accurately, since they are calculated indirectly from luminescence yields. Yet in some cases, evaluation of laser dyes for example, it is important to know these quantities accurately. In this case, opto-acoustic spectroscopy is a means of measuring this small quantity directly as opposed to estimating it as a difference of two larger quantities. Also, it possesses the capability of distinguishing between the different pathways of radiationless decay.

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165 23. G. A. Crosby, J. N. Demas and J. B. Callis, J. Res. Nat. Bur. Stand., Sect. A 76, 561(1972). 24. A. G. Bell, Proc . Am. Assoc. Advance. Sci. 29_, 115 (1880) and J. Soc . Telegraph Eng. 9, 404(1880). 25. A. G. Bell, Philos. Mag, 11, 510(1881). 26. E. Mercadier, C. R. Acad. Sci, 91, 929(1880). 27. W. H. Preece, Proc. R. Soc. London 31, 506(1881). 28. W. H. Preece, A. G. Bell and J. Tyndall, J. Soc. Telegraph Eng . 9 , 3 6 3 ( 1 8 B0 ) . 29. W. C. Rontgen, Ann. Phys . Chem. 12, 155(1881). 30. J. Tyndall, Proc. R. Soc. London 31, 307(1881). 31. M. L. Veir.gerov, Dokl. Akad. Nauk SSSR 19, 687(1938). 32. A. H. Pfund, Science 90, 326(1939). 33. K, r. Luft, Z. Tech. Phys. 7A_, 97(1943). 34. M. J. E. Golay, Rev. Sci. Instrum. 2j0, 816(1949). 35. V. N. Smith, Instruments 26, 421(1953). 36. W. D. Hershberger, E. T. Bush and G. W. Leek, RCA Rev. 7, 442(1946) . 37. Y. I. Gerlovin, Opt. Spectrosc. 7, 352(1959). 38. S. P. Belov, A. V. Burenin, L. I. Gershtein, V. V. Korolikhin and A. F. Krupnov, Opt. Spectrosc. 3_5, 172(1973). 39. V. L. Rudin, Opt. Spectrosc. 24_, 316(1968). 40. E. L. Kerr and J. G. Atwcod, Appl . Opt. 7, 915(1968). 41. L. B, Kreuzer, N. D. Kenyon and C. K. N. Patel, Science 177, 347(1972). 42. L.-G. Rosenaren, E. Max and S. T. Eng, J. Phys. E 7, 125(1974). 43. A. Rosencwaig, Science 181, 657(1973) and Opt. Commun. 7, 305(1973). 44. G. Gorelik, Dokl. Akad. Nauk SSSR 54, 779(1946).

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166 45. P. V. Slobodskaya, Izvest. Akad. Nauk SSSR, Ser. Fiz. 12, 656(1948) . 46. B. I. Stepanov and 0. P. Girrin, J. Exp. Theor. Phys. 20, 947(1950). 47. For a review of this early work see R. Kaiser, Can J. Phys. 37, 1499(1959) and M. E. Delaney, Sci. Prog. (Oxford) 47, 459(1959). 48. W. R. Harshbarger and M. B. Robin, Ace. Chem. Res. 6, 329(1973) . 49. E. Hey, Ph. D. Thesis, Univeristy of Heidelberg (1967). 50. P. G. Seybold, M. Gouterman and J. Callis, Photochem. Photobiol. 9, 229(1969). 51. J. B. Callis, M. Gouterman and J. D. S. Danielson, Rev. Sci. Instrum. 40, 1599(1969). 52. M. S. deGroot, C. A. Emeis, I. A. M. Hesselman, E. Drent and E. Farenhoxst, Chem. Phys. Lett. 17/ 332(1972) and Chem. Phys. Lett. 27, 17(1974). 53. W. R. Harshbarger and M. B. Robin, Chem. Phys. Lett. 21, 462(1973) . 54. J. G. Parker and D. N. Ritke, J. Chem. Phys. 5_9, 3713 (1973) . 55. J. G. Parker and D. N. Ritke, J. Chem. Phys. 61, 3408 (1974) . 56. J. G. Parker, J. Chem. Phys. 6_2, 2235(1975). 57. K. Kaya, W. R. Harshbarger and M. B. Robin, J. Chem. Phys. 60, 4231(1974) . 58. K. Kaya, C. L. Chatelain, M. B. Robin and N. A. Kuebler, J. Am. Chem. Soc. 9J7, 2153(1975). 59. T. F. Hunter, D. Rumbles and M. G. Stock, J. Chem. Soc, Faraday Trans. 2 7£, 1010(1974). 60. T. F. Hunter and M. G. Stock, J. Chem. Soc, Faraday Trans. 2 7_0, 1022(1974) and Chem. Phys. Lett. 2_2, 368(1973) . 61. T. F. Hunter and M. G. Stock, J. Chem. Soc, Faraday Trans. 2 70, 1028(1974). 62. J. 0. Hirschfelder, C. F. Curtiss and R. B. Bird,

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167 "Molecular Theory of Gases and Liquids," John Wiley & Sons, Inc., N. Y. (1967). 63. P. R. Longaker and M. M. Litvak, J. Appl . Phys . £0, 4033(1969) . 64. R. D. Bates, Jr., G. W. Flynn, J. T. Knudtson and A. M. Ronn, J. Chem. Phys. 53, 3621(1970). 65. T. Aoki and M. Katayama, Jpn. J. Appl. Phys. 10_, 1303(1971) . 66. D. R. Siebert, F. R. Grabiner and G. W. Flynn, J. Chem. Phys. 60, 1564(1974). 67. P. W. Berg and J. L. McGregor, "Elementary Partial Differential Equations," Holden-Day, Inc., San Francisco, 1966, p. 376, and J. B. Marion, "Classical Electromagnetic Radiation," Academic Press, New York, 1965, p. 86. 68. G. Shortley and D. Williams, "Elements of Physics," Prentice-Hall, Inc., New Jersey, 1965, p. 448. 69. R. D. Present, "Kinetic Theory of Gases," McGrawHill Book Company, Inc., New York, 1958, pp. 66-69. 70. J. G. Parker, Appl. Opt. 12, 2974(1973). 71. P. P. Sorokin, J. R. Lankard, V. L. Moruzzi and E. C. Hammond, J. Chem. Phys. 4_8, 4726(1968). 72. G. Biittenbender and G. Herzberg, Ann. Phys. 21, 577 (1934) . 73. J. E. Bjorkholm, T. C. Damen and J. Shah, Opt. Commun. 4, 283(1971) . 74. N. Carbone, Los Alamos Research Laboratory, private communication . 75. C. G. Hatchard and C. A. Parker, Proc. R. Soc . London, Ser. A 23_5, 518(1956) . 76. J. G. Calvert and J. N. Pitts, Jr., "Photochemistry," John Wiley and Sons, Inc., New York, 1967. 77. D. J. Curran and S. J. Swarin, Anal. Chem. 43_, 1338 (1971) . 78. B. T. Collins, C. F. Coleman and T. DeVries, J. Am. Chem. Soc. 71, 2929(1949).

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16 8 79. K. K. Innes, J. P. Byrne and I. G. Ross, J. Mol. Spectrosc. 2_2, 125(1967). 80. K. K. Innes, W. C. Tincher and E. F. Pearson, J. Mol. Spectrosc. 3:6, 114(1970). 81. B. J. Cohen and L. Goodman, J. Chem. Phys . 4_6, 713 (1967) . 82. W. J. Balfour and G. W. King, J. Mol. Spectrosc. 2_6, 384(1968) . 83. W. J. Balfour and G. W. King. J. Mol. Spectrosc. 27, 432(1968) . 84. H. Shimada, R. Shimada and Y. Kanda, Spectrochim. Acta, Part A 23, 2821(1967). 85. K. B. Krauskopf and G. K. Rollefson, J. Am. Chem. Soc. 58, 443(1936) . 86. B. D. Saksena and G. S. Jauhri, J. Chem. Phys. 3j5, 2233(1962) . 87. K. J. Laidler, "Chemical Kinetics," McGraw-Hill Book Company, Inc., New York, 1955, pp. 267-8. 88. Z. G. Szabo, D. Kiraly and I. Bardi, Z. Phys. Chem. (Frankfurt am Main) 2J7, 127(1961). 89. J. Eyler, University of Florida, private communication 90. Anon., Electro-Optical Systems Design _7 f121 ' 25(1975). 91. F. M. Johnson and M. W. Swagel, Appl. Opt. 10_, 1624 (1971) . 92. L.-G. Rosengren, Appl. Opt. 14, 1960(1975). 93. G. M. Sessler and J. E. West, J. Acoust. Soc. Am. 4_0, 1433(1966) .

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169 BIOGRAPHICAL SKETCH Joseph J. Wrobel was born March 18, 19 4 7 in Chicago, Illinois. In 196 8 he received a Bachelor of Science degree in Chemistry ( cum laude ) from Loyola University of Chicago and in the fall of that year entered the Graduate School of the University of Florida. In December, 19 74, he accepted his current position as Research Physicist at the Eastman Kodak Research Laboratories in Rochester, New York. Dr. Wrobel was married in September, 1970, and has one child. He was the recipient of a National Science Foundation Traineeship from 196 8 to 19 72 and a Graduate Council Fellowship for 19 72-73. He is currently a member of the American Chemical Society.

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. IfifaiA'pi til&iMartin T. Vala, Chairman Associate Professor of Chemistry I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. William Weltner, Jr. \\ Professor of Chemistry I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Gardiner H. Myers Associate Professor of Chemistry

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I certify that I have read this study and that m my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as 'a dissertation for the degree of Doctor of Philosophy. Raymond Pepinsky Professor of Physics I cer+ifv that I have read this study and that in my ooinion it conforms to acceptable standards of scholarly nr—.~ntation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. ?7i a*sL o
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"What's that you're in again, Joe?" "Chemical Physics, Ma." "I've got to write that down." 1972

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