Optimizing time resolved phosphorimetry

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OPTIMIZING TIME RESOLVED PHOSPHORIMETRY


BY

CHARLES GLENN BARNES














A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA
1980














ACKNOWLEDGEMENTS

I wish to first express my belief in the guidance

of Jesus Christ in my life, and in my career. In

addition, I would like to take this opportunity to

express my gratitude to those people who have assisted

me in this endeavor. To my research director,

Dr. James D. Winefordner, go my appreciation and thanks

for his patience and support, and for his willingness

to make himself readily accessible to students. To

Dr. John Legg of Mississippi College go my sincere thanks

for his friendship and guidance, and for the example

that he sets for myself and other students.

I would like to express my loving gratitude to

my wife, Joyce, who continued to love me even through

the ultimate test of a marriage --the writing of a

dissertation; and to my parents and family who have con-

tributed their love and financial support for these 25

years. Many thanks to my friends at the Baptist Student

Center for making me a part of your fellowship.

Thanks are due to Art Grant and the Machine Shop

gang for their artistry, and to the JDW group for their

knowledge and the willingness to share it.















TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS --------------------------------- ii

LIST OF TABLES ----------------------------------- iv

LIST OF FIGURES ---------------------------------- v

ABSTRACT -----------------------------------------vii

CHAPTER

I. INTRODUCTION ------------------------1----- 1

Historical ----------------------------- 1
Time Resolved Phosphorimetry ---------------- 5

II. THEORETICAL CONSIDERATIONS ----------------- 28

Kinetic Analysis of Molecular Processes -- 28
Intensity Expressions --------------------- 30
Response Profiles -------------------------- 61
Summary ---------------------------------- 100

III. EXPERIMENTAL------------------------------- 102

Instrumentation -----------------------------102
Reagents ---------------------------------112
Instrumental Procedure --------------------- 113
Sampling Procedure -----------------------114

IV. RESULTS AND DISCUSSION ---------------------118

Validation of Theoretical Analysis ------- 118
Time Resolution of Phosphor Mixtures ----- 141

V. CONCLUSIONS --------------------------------155

APPENDIX --- ------------------------------------157

LIST OF REFERENCES -----------------------------------164

BIOGRAPHICAL SKETCH ------------------------------167


iii















LIST OF TABLES


TABLE Page

1. FINAL WORKING EQUATIONS FOR THE EXPONENTIAL
METHOD OF TIME RESOLUTION FOR A BINARY
MIXTURE ----------------------------------- 24

2. FINAL WORKING EQUATIONS FOR THE EXPONENTIAL
METHOD OF TIME RESOLUTION FOR A TERNARY
MIXTURE ----------------------------------- 25

3. DEFINITION OF PARAMETERS ------------------ 38

4. KEY TO GATE WIDTH FOR FIGURES 5-7 -----------51

5. PARAMETERS FOR RESPONSE PROFILES ----------- 63

6. EXPERIMENTAL EQUIPMENT AND MANUFACTURERS ---- 105

7. PRELIMINARY LIFETIME MEASUREMENTS -----------119

8. PARAMETERS FOR EXPERIMENTAL VALIDATION ------ 121

9. COMPARISON OF THEORETICAL AND EXPERIMENTAL
INTENSITY RATIOS FOR THIORIDAZINE HC1 ----- 125

10. COMPARISON OF THEORETICAL AND EXPERIMENTAL
INTENSITY RATIOS FOR VANILLIN -------------- 126

11. COMPARISON OF THEORETICAL AND EXPERIMENTAL
INTENSITY RATIOS FOR NUPERCAINE HCl --------- 127

12. AVERAGE RESULTS OF INTENSITY MEASUREMENTS FOR
THREE PHOSPHORS --- ----------------------------128

13. ANALYSIS OF BINARY MIXTURE I ----------------147

14. ANALYSIS OF BINARY MIXTURE II -------------- 149

15. ANALYSIS OF TFRP.APY MIXTURE I ---------------152

Al. KINETIC EVENTS IN A RIGID GLASS SYSTEM
CONTAINING ONE SOLUTE ----------------------158














LIST OF FIGURES


Figure


1. Schematic diagram and molecular electronic and
vibrational energy levels------------------

2. Schematic representation of the operation of
a pulsed source gated phosphorimeter------

3. Schematic representation of the excitation
process with a pulsed source ---------------

4. A typical relative response profile---------


5. Optimum delay versus

6. Optimum delay versus

7. Optimum delay versus


8. Response profile


Response

Response

Response

Response

Response

Response

Response

Response

Response

Response


profile

profile

profile

profile

profile

profile

profile

profile

profile

profile


19. Response profile


(tg

(tg

(tg

(tg

(tg

(tg

(tg

(tg

(tg

(t
g
(tg

(tg
(t


lifetime (f = 1 Hz) --


lifetime (f =

lifetime (f =


5x -3 ,
5x10 s,


= 5x10- 3S,

= 5x103,
= 5xl0-3s,
= 5x10- s,

= 5xl-4,

= 5x10 s,

= 5x10 5,
-4
= 5x10 5s,



= 5xlO-4s,
-5
= 5x10 s,
-5
= 5x10 s,
-5
= 5x10 S,
-5
= 5x10 s,


10 Hz)

50 Hz)


f = 1 Hz)


f = 10 Hz) --

f = 50 Hz) -

f = 100 Hz)--

f = 1 Hz)----

f = 10 Hz)---

f = 50 Hz)---

f = 100 Hz)--

f = 1 Hz)----

f = 10 Hz)---

f 50 Hz)---

f = 100 Hz)--


--55

--- 57

--- 65


9.

10.

11.

12.

13.

14.

15.

16.

17.

18.


Page








20. Schematic representation of phosphorescence
growth during the excitation pulse for two
phosphors with different lifetimes ---------- 92

21. Schematic representation of the effect of
gate width on observed phosphorescence
signal --------------------------------------95

22. Schematic representation of the effect of
frequency on pulse-to-pulse phosphorescence
intensity growth ---------------------------- 98

23. Block diagram of the experimental system ----- 104

24. Growth profile for thioridazine HC1 at 1 Hz 132

25. Growth profile for thioridazine HC1 at 10 Hz 134

26. Growth profile for thioridazine HC1 at 100 Hz- 136

27. Growth profile for nupercaine HC1 at 10 Hz --- 138

28. Growth profile for nupercaine HC1 at 100 Hz -- 140

Al. Kinetic processes occurring during growth and
decay of phosphorescence -------------------- 160













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

OPTIMIZING TIME RESOLVED PHOSPHORIMETRY

By

Charles Glenn Barnes

December, 1980

Chairman: James Dudley Winefordner
Major Department: Chemistry

Time resolved phosphorimetry (TRP) is an analytical

method with primary application to analysis of multi-

component mixtures of spectrally similar species. The

resolution of such a mixture is attained by utilizing

differences in the phosphorescence decay lifetimes (T)

of the mixture components. Earlier work has relied

heavily upon multichannel detection systems which scan

the entire emission decay curve as a function of time.

However, a phosphorimeter incorporating a pulsed excita-

tion source with a single channel gated detection system

(boxcar average or integrator) has several characteris-

tics that make it attractive for TRP. These include

relatively low cost and flexibility in selection of

the operating parameters of gate width (t ), delay time

(td), pulse repetition rate (f), and integration time

constant. This flexibility should allow resolution of

mixtures over a large range of phosphorescence lifetimes.

vii







In this work, the potential for applying such a

system to TRP is examined. Theoretical expressions

are derived which demonstrate the relationships of

observed phosphorescence intensity on the phosphorescence

lifetime and on the characteristic parameters of the

experimental system. Plots of relative response versus

lifetime under various sets of parameters are presented

and are used to predict and interpret the effect of

excitation peak width, t td f and T on the observed

signal level. At a fixed set of parameters, there is a

lifetime to which the system has optimum response, T
max"

An expression is presented which allows positioning this

maximum at any selected lifetime.

A pulsed-laser source boxcar average phosphorimeter

is described. Experimental results are presented to

demonstrate the validity of the theoretical expressions.

The expressions are used to optimize the experimental

system for TRP analysis of binary and ternary mixtures

of spectrally similar species. Results indicate that

this type of analysis requires a mixture with two or

three components, the lifetimes of which differ by a

factor of two or more. The major errors are due to

photodecomposition of the samples and excessive

source flicker noise.


viii














CHAPTER I
INTRODUCTION

Historical

Phosphorimetry was first proposed as a method of

chemical analysis by Lewis and Kasha (1). They reviewed

the little that was known about phosphorescence at that

time, and based upon their own research, wrote "for every

substance, there is a unique phosphorescent state" (p.2102).

Further, they ascribed phosphorescence to the triplet state

of the unsaturated molecule. The next significant work on

phosphorimetry was that of Keirs, Britt and Wentworth

thirteen years later (2), which first demonstrated the

enormous potential of phosphorimetry for chemical analysis.

The authors discussed the experimental and theoretical

aspects of phosphorimetry and demonstrated that binary

mixtures of phosphors could be spectrally resolved by

judicious selection of excitation and emission wavelengths.

For mixtures of phosphors whose excitation and emission

spectra were similar, they used a technique called "phos-

phoroscopic resolution," which resolved the components by

utilizing differences in their phosphorescence decay rates.

The technique was applicable to phosphors having lifetimes

in the millisecond region.








O'Haver and Winefordner in 1966 discussed the in-

fluence of mechanical phosphoroscope design on the

detected phosphorescence intensity (3). Expressions were

derived which related the measured and instantaneous

phosphorescence intensity to the decay time of the phos-

phorescent species and to the characteristic parameters

of the phosphoroscope used in the measurement system.

Numerical results were given for two different phos-

phoroscopes. The expressions were later extended (4) to

apply to pulsed sources and gated detection systems,

specifically, to a pulsed flash tube and a pulsed photo-

multiplier tube, using an average-reading DC meter for

output. They were able to predict the "sample-to-inter-

ferent ratio enhancement" under differing sets of experi-

mental conditions, based upon the relative lifetimes of

the analyte and interferent.

St. John and Winefordner (5) published the results

of a study on "Time Resolved Phosphorimetry," in which

binary mixtures of phosphors were resolved based upon

differences in lifetime. The method employed a CW source

and a DC readout system coupled with a logarithmic con-

verter to display log-phosphorescence intensity versus

time, following the cessation of excitation via a manual

guillotine shutter. Hollifield and Winefordner (6)

designed a unique single-disk phosphorimeter to measure

intensity at small intervals along the emission decay








curve and used it to time resolve several binary mixtures.

The overall error was found to be largest when the lifetimes

of the components were similar, or when one component was

present in great excess.

Winefordner suggested the potential advantages of

utilizing a pulsed source fast (gated) readout system for

time resolved phosphorimetry (7). Fisher and Winefordner

(8) built such a system and applied it to the analysis of

binary and ternary mixtures of phosphors. The system was

designed primarily for rapidly decaying n-ir* phosphors

and utilized a pulsed flash tube for excitation and a

multichannel signal average coupled to a logarithmic

converter for output. Expressions were derived which related

measured phosphorescence signal to the concentration of

each analyte phosphorr) in a multi-component mixture of

spectrally similar organic molecules. Three specific methods

of data reduction were described and employed for estimating

concentrations from phosphorescence signals measured at

different times after the termination of excitation.

O'Donnell et al. (9) modified the Fisher phosphorimeter by

using a higher powered xenon flashlamp and a rotating sample

cell, and quantitated mixtures of halogenated biphenyls.

Harbaugh, O'Donnell, and Winefordner measured phosphor-

imetric lifetimes and qualitatively and quantitatively

identified drug mixtures with this system (10,11).








Wilson and Miller (12) described a versatile

computer-controlled laser phosphorimeter. The phos-

phorescence spectra were recorded on magnetic tape as

a family of signal averaged decay curves. The system

would average one hundred decay curves at 1 nm intervals

over a 150-200 nm range. The technique of component-

resolved spectrometry was discussed in detail and

illustrated by resolution of the phosphorescence spectra

of a binary mixture. The data reduction involved a non-

linear least squares fit in n-dimensional space (12,13).

O'Donnell and Winefordner (14) reviewed advances in

instrumentation and methodology for phosphorimetry, and

discussed the potential of the pulsed source gated detec-

tion system over standard systems. Goeringer and Pardue

(15) designed a silicon intensified-target vidicon (SIT)

camera for phosphorescence studies and described applica-

tions to room temperature phosphorimetry of salts of

organic acids. The spectral decay data were processed by

a variety of regression methods, which were based in part

upon the work of Ridder and Margerum (16), Mieling and

Pardue (17), and Willis et al. (18) on simultaneous kinetic

analysis. In addition, the authors applied the internal

standard method to phosphorimetry for the first time and

reduced overall imprecision by two to five times. Boutilier

and Winefordner (19) described a laser-source time resolved

phosphorimeter and applied it to investigating the external




5


heavy atom effect on the phosphorescence lifetimes,

relative intensities, and limits of detection of drugs.

Time Resolved Phosphorimetry

Phosphorescence is the long-lived luminescence

observed following excitation of some types of molecules

with an external light source. The physical basis for

phosphorescence can be seen in Figure 1, which is a

schematic diagram of the processes taking place during

excitation/emission of molecular luminescence (2,20).

Absorption of a photon (A) excites the molecule to some

vibrational level of an excited singlet state (10 15s).

(Absorption to a triplet state is extremely unlikely,

because the transition is spin-forbidden.) Usually, the

first excited singlet, Si, is the state that is optically

pumped, but not always. Within the electronic state thus

populated, vibrational relaxation (VR) (plus solvent-

relaxation), efficiently deactivates the molecule to the

lowest vibrational level of that electronic state (10 13s).

Further deactivation to a lower electronic level occurs by

internal conversion (IC), which is a nonradiative relax-

ation to a lower electronic state of the same multiplicity
-12
(10 12s). Once the molecule is in the S1 state, further

deactivation can occur by further internal conversion to

the ground state. However, because the energy gap between

S and S1 is usually larger than that between the higher

electronic states, the process is less efficient, and a


























Figure 1. Schematic diagram of molecular electronic
and vibrational energy levels.


















I


-- ---^ -j
----1 t



II
II


A A I


SC




ISC P/
ISC P


TRIPLET MANIFOLD


SINGLET MANIFOLD








spin-allowed radiative transition, fluorescence (F), can

compete effectively for depopulation of the S1 state.

There is, however, another pathway for de-excitation

of the S1 state. Due to spin-orbital coupling, the less

energetic T1 state can be populated from the S1 state.

This nonradiative process, occurring between states of

differing multiplicity,is intersystem crossing (ISC).

The efficiency of ISC varies greatly from molecule to

molecule, and is extremely dependent upon the molecular

environment.

The T1 state can be depopulated by further ISC to

the ground state singlet, or by a spin-forbidden radiative

transition, T1-* S0. This spin-forbidden radiative tran-

sition between states of different multiplicity is phos-

phorescence (P). The probability of a spin-forbidden
-3 -6
transition is 10 to 10 smaller than that of the

corresponding spin-allowed transition. Therefore, the

mean lifetime of the T1 state is usually 10 3s to several

seconds in duration, while the mean lifetime of the S
8
state is approximately 10 8s.

Observation of molecular luminescence requires that

the radiative processes compete effectively with the non-

radiative processes for depopulation of the excited states.

Therefore, molecules possessing rigid molecular skeletons

and large separations between the ground state and lowest

excited states most often exhibit fluorescence/phosphores-

cence (20). Note that the two luminescence processes








compete indirectly for depopulation of the T1 state.

Aromatic molecules, possessing rigid-ring structures,

form the largest class of compounds to exhibit lumines-

cence.

Due to the long lifetime of the triplet state,

many other processes compete with phosphorescence for

depopulation of the triplet. These include collisional

deactivation by solvent molecules; quenching by para-

magnetic species, especially oxygen; and photochemical

processes. For this reason, phosphorescence is normally

observed with the phosphorescent species phosphorr)

frozen rigidly into a solvent matrix at or below liquid

nitrogen temperatures (77 K). This minimizes collisional

processes (20).

The instrument used to measure phosphorescence is

known as a phosphorimeter. The sample is irradiated with

a suitable source, and the phosphorescence is usually ob-

served at 90 to the excitation axis. Because phospho-

rescence has a longer lifetime (i.e., persists for a longer

time following termination of excitation) than scatter and

fluorescence, phosphorescence can be measured without

interference from either process by using an experimental

system that excites the sample for some period of time,

stops the excitation, and waits for fluorescence and scatter

to disappear before making the intensity measurement (14).

Normally, a mechanical shutter system (phosphoroscope) is

employed, but pulsed systems have been applied to advantage

(8-11,21).








In order for phosphorescence to be used for quanti-

tative chemical analysis, there must be a well-defined

relationship between analyte concentration and observed

phosphorescence intensity. An approximate relationship

is given by Equation (1), which assumes a dilute

solution of the analyte, monochromatic radiation, and no

prefilter or postfilter effects:

P = P 2.3 abc Y (1)
p 0 p

In Equation (1), P is defined to be the radiant phospho-
P
rescence power (W) emitted under a given set of experimental
conditions, Y is the power efficiency (ratio of radiant
P
power emitted to radiant flux absorbed), a is the molar
-i -I
absorptivity (L mole cm ), b is the absorption path length

(cm), and c is the molar concentration of the absorber

(mole L- ). The approximation (2.3 abc) < 0.05 is required

for this linear relationship to be valid, and is normally

met at the low concentration levels encountered in

analytical phosphorimetry. This expression is strictly

valid only when the excitation and emission have reached

steady state (21,22,23).

Conventional phosphorimetry, as an analytical method,

exhibits excellent sensitivity, low limits of detection,

and large linear dynamic ranges for many phosphors.

Selectivity is inherent in the nature of phosphorimetry;

both the excitation and emission wavelengths can be varied

to selectively excite/monitor the phosphorescence due to

one particular species. The principal Value of








phosphorimetry was pointed out by O'Donnell and Winefordner

in 1975 in a review article on phosphorimetry in clinical

analysis. They stated:

the greatest use of phosphorimetry in the clinical
laboratory will not be for the analysis of very large
numbers of samples for one species via automatic
instrumentation, but rather will be for the analysis
of those species impossible to measure by conven-
tional methods. . (14, p. 285)

This statement summarizes quite well the contribution of

phosphorimetry towards analytical chemistry as a whole.

Although phosphorimetric analysis does have a high

degree of inherent selectivity, cases obviously arise in

which interfering phosphors cannot be adequately

minimized by spectral resolution. Molecular emission bands

are quite broad, and so spectral overlap occurs frequently.

Increased selectivity is required to solve this problem,

and the additional selectivity is achieved in the time

domain.

The observed phosphorescence intensity following an

excitation pulse decays away slowly. In most cases, the

shape of the "emission decay curve" is an exponential

function, with the intensity at any time, t, given by

I = I0 exp (-t/T) (2)

where I is the observed phosphorescence intensity at time

t, I0 is the initial (t = 0) intensity, and T is the phos-

phorescence decay lifetime(s). In this work, T or

"lifetime" will refer exclusively to the experimentally

observed phosphorescence decay lifetime. Any other type








of lifetime will be distinguished from T by a

subscript or superscript.

The experimental lifetime is a function of both

the specific molecule phosphorr) and the specific

environment and temperature. Fortunately, it does not

vary greatly with temperature in the vicinity of 77 K.

Neither does T show substantial variation with concentra-

tion over a limited concentration range, although changes

in the solvent system, or even in the sampling/freezing

process, can cause T to vary. However, for one specific

set of experimental conditions, T is characteristic of

the particular molecule under study, and is independent

of analyte concentration in dilute solutions (7,21,24).

Phosphors tend to fall into two relatively distinct

categories with regard to lifetime. Molecules involving

an n-f* transition carbonylss, thiocarbonyls, and some

azo compounds) tend to have lifetimes on the order of

milliseconds. Those involving 7-'T* transitions typically

exhibit lifetimes ranging from tenths of a second to tens

of seconds (25). The entire range of phosphorescence

lifetimes is thus approximately 10 4s to 10 s. The

probability of two different phosphors in a sample mixture

possessing identical excitation maxima, emission maxima,

and lifetimes is small, although this does occur. Resolu-

tion of spectrally similar phosphors based upon differences

in phosphorescence lifetime is known as time resolved

phosphorimetry (TRP). TRP is of value when instrumental








or spectroscopic methods for resolution fail, or are not

available; and if prior chemical treatment of the sample

would not effect the desired separation, would result in

lengthy analysis, or would introduce contamination (21).

Conventional mechanical shutter phosphorimeters do

not have the versatility required for application to TRP.

Instead, a pulsed source gated detection system (which

has advantages even for conventional phosphorimetry) is

required.

A pulsed source TRP system employing a conventional

single channel ("boxcar" average or integrator)

measurement system is shown schematically in Figure 2

(4). The source is pulsed on for a period of time of

t the excitation pulse width (s). Phosphorescence

is excited from the sample and decays exponentially follow-

ing termination of the excitation pulse. After a suitable

delay time, td(s), the signal from the detector is sampled

for a fixed period of time, known as the aperature dura-

tion or gate width, t (s). The excitation/measurement
g
cycle occurs at a repetition rate or frequency of f (Hz).

The output signal level is proportional to the area under

the emission decay curve bounded by the gate width. The

exact nature of the relationship between signal level and

area depends upon the specific measurement system employed.

The theoretical advantages of the pulsed system over the

conventional have been pointed out previously (7,8,14).



























Figure 2. Schematic representation of the operation of a pulsed source gated
phosphorimeter.


























< AIISN2HINI


I
T









These include increased precision resulting from increased

signal-to-noise ratios (SNR), due to minimization of non-

source-induced noise,and similar signal levels; lower

detection limits resulting from increased SNR; and the

ability to monitor phosphors having short lifetimes without

interference from the slowly decaying trailing edge of

a mechanically chopped excitation pulse. The most important

advantage for application to TRP, however, is the versa-

tility of the system, due to the relatively independent

variability of the gate width, delay time, and repetition

rate. It must be noted that in practical applications,

the predicted increase in SNR has never been fully realized

(26,27).

The recent trend in TRP instrumentation has been

towards multichannel detection systems, such as the multi-

channel signal average and the computer-controlled

phosphorimeter, which monitor the entire emission decay

curve following each excitation pulse (8-10,12,15).

Sophisticated data handling techniques are also becoming

common (15-18). However, there seems to be an enormous

potential for applying less complex single channel in-

strumentation to TRP. This potential has never been ade-

quately explored. The single channel or boxcar system

can be used to monitor the entire emission decay curve

by scanning the gate in time, but this is a time-consuming

process. The strength of this type of system lies in








measuring intensities at a few carefully selected times

on the decay curve. Reasons for utilizing the pulsed

source single channel gated detection system for TRP

are as follows:

(i) Boxcar averager/integrators are "relatively"
inexpensive and readily available;

(ii) The versatility of this type of instrument is
enormous, due to the aforementioned independent adjust-
ability of operating parameters;

(iii) Boxcar instruments are available to work on
almost any time scale, from seconds to less than nano-
seconds; this, coupled with the versatility, make possible
a TRP analysis over a large range of sample lifetimes;
some earlier systems were limited to either very rapidly
decaying species (8) or very slowly decaying species (5),
but not to both; and

(iv) The data manipulation can be as simple or as
sophisticated as desired, while multichannel systems
require manipulation of very large quantities of data,
if the full potential of such an instrument is to be
realized. This work is concerned with the application
of a pulsed-laser source boxcar average phosphorimeter
to TRP. The advantages of the laser as a pulsed excitation
source are well known, and include high peak powers,
short pulse widths, variable repetition rate, and nearly
monochromatic output.

It is important to realize that in most cases it is

not possible to eliminate directly by time resolution the

intensity contributions of all phosphors other than the

one of interest; that is, one can not make a single intensity

measurement and relate this to analyte concentration.

What is usually necessary is to make intensity measurements

at several times along the emission decay curve of the

mixture, and then to extract mathematically (via simultaneous

equations) the intensity contributions of the individual







components. These deconvoluted intensities can then

be related to the concentrations of the individual

mixture components.

Fisher and Winefordner (8) described three methods

for this type of data reduction, two of which are suitable

for TRP using a single channel detection system. Both

require that the individual phosphors comprising the

sample mixture behave independently of one another, which

must be true for all multicomponent phosphorimetric

analyses. In the multiple-analytical-curve method (MAC),

it is assumed that the analytical calibration curve (in

linear coordinates) for a given phosphor has a slope which

is dependent upon the delay time at which the intensity

is measured (with f, t and t constant). By setting
P g
up simultaneous equations stating that the total intensity

at any one delay time is equal to the sum of the inten-

sities of the individual components, expressions can be

obtained which relate the concentrations of the individual

phosphors to the intensity measurements obtained for the

mixture. This method does not require knowledge of the

lifetimes of the phosphors, but it is very time consuming,

because it requires a calibration curve for each component

at each delay time (n delay times required for an n-compo-

nent mixture).

The exponential method (EM) is the technique chosen

for this work. It does require measurement of the life-

times of the individual components of the mixture, but








these can be determined by scanning the single channel

system. As mentioned earlier, this scanning process is

relatively slow, but is required only for the initial

determinations, and not for the actual intensity

measurements on the mixture. The advantage of this

method is that only one calibration curve is required

per component, and thus the exponential method should

be less time consuming overall than the MAC method,

even when preliminary lifetime measurements are considered.

The working equations for EM are derived in the

following manner (21). Let a hypothetical binary mixture

consist of components A and B with lifetimes T and T ,

and let the intensities be measured at delay times t and

td Equation (2) can be rewritten specifically for the
"2
intensity contribution of A at delay time td
"1
IA = I exp (-td /TA) (3)
A A0 1 A

where I is the initial intensity (at arbitrary or actual
A0
td= 0) of A. The equivalent expression for component B is
IB = I exp (-t /TA) (4)
1 B 0 d1B

Similar expressions can be written for the intensity con-

tributions of A and B at delay time td Because the

total intensity, IT at any time is the sum of the inten-

sities of A and B at that time,

I = I exp (-t /TA)+I exp (-tA ) (5)
T1 A0 d1 A B0 d1 B


and







I = I exp (-td /TA)+ IB exp (-t d/T ) (6)
2 0 "2 0 "2 B

These two equations can be solved simultaneously for IA
A0
and TB and these values, when substituted into Equations
B0
3 and 4, yield I and I Actually, once I and I are
A! B!
,I1 I1 A0 IB0

known, the intensities of A and B at any delay time, td,
N
can be found by multiplying by exp (-td /T). The intensities
N
so obtained can be used to determine the concentration of A

and B from calibration curves prepared for pure solutions of

A and B at delay time td. Fisher and Winefordner (8) and
N
Fisher (21) derived the working equations for the two com-

ponent mixture. These are presented in Table 1, in a form

that will allow calculation of the intensity of that com-

ponent at any delay time. The symbolism I refers to the
XN
intensity contribution of component X at delay time N.

Note that the quantity in brackets is equal to the intensity

of component X at td = 0 (I x), and that this is multiplied

by an exponential term to yield the intensity at various t 's.

This same approach can be applied to a three component

ternaryy) mixture. In this case, there are three components,

A, B, and C, with lifetimes TA, TB, and TC and three delay

times, t, t and td. Fisher calculated one of
d1 d2 d3
the expressions; the others were derived in this work.

The three working equations are given in Table 2. It

should be noted that, due to the complexity of the

simultaneous equations, Cramer's Rule was required for








their solution (28). Although the expressions appear

formidable, if the exponential terms are calculated in

advance, and inserted with the experimentally determined

mixture intensities IT IT2 and I3 the mathematics

is easily handled on a pocket calculator.

An interesting question arises here. Only one cali-

bration curve per component is required for the exponential

method. However, the intensity contribution of any

component can be calculated at any delay time. Under what

conditions, then, should the single calibration curve be

prepared? Certainly, the largest intensity would occur

at td = 0 (although there are some practical limitations

on using td = 0), and one would expect that preparing all

calibration curves at the shortest delay time would yield

optimum results. This minor point will be examined

(experimentally) to some extent.

In order to insure that the results of such a multi-

component analysis have validity, there are several require-

ments that must be met. These were stated very clearly by

Ridder and Margerum (16):

multiple component analysis performed by the direct
measurement of the physical properties of the com-
ponents . must meet several general require-
ments. First, the number of measurements obtained
at different values of the independent variable
(i.e., wavelength, time, etc.) must be at least
equal to the number of components to be determined
(however, additional data may improve precision).
Second, the relative contributions of the components
at each measurement must not be redundant (i.e.,
there must be at least as many non degenerate equations








as there are components). Third, the absolute
and relative contributions of each component to
the measurement must be large enough to achieve
the sensitivity desired. . (p. 2098)

In TRP, the first requirement is met by taking

measurements at as many different delay times as there

are components to be quantitated. The second and third

conditions for TRP may be explained as follows. Intensity

measurements are made at different points in time, with

the aim of correlating these mathematically to the ex-

perimental decays of the individual components. Obviously,

each measurement must have significance (i.e., a good

SNR). In addition, the delay times must be chosen in

such a way as to insure a significant difference in total

signal at the various points, because it is indirectly

the difference in signal levels that contains the desired

information. For experimental work, this requires that

the difference in signal levels between the different times

must be larger than the uncertainty of any of the measure-

ments. Thus, it is necessary that the relative intensities

of the mixture components differ significantly at the

various delay times, and also that the total intensity

varies significantly. Knowing in advance that the second

and third conditions will be met is much more difficult,

because it requires some prior knowledge of the relative

intensities of the components, as well as the total

intensities, at several sets of experimental conditions.

Because the actual number of measurements required for








a TRP analysis is large, and sampling in phosphorimetry

is normally time consuming, it is obvious that trial

and error selection of experimental conditions is not

a viable choice, although this has been done (8).

Therefore, a large part of this work has explored

how the choice of experimental conditions affects the

relative intensity contributions from the individual

components of a mixture, and how the conditions can be

optimized for a particular separation.

The overall goal of this work is to examine the

potential of a pulsed-laser source boxcar average

detection system for time resolved phosphorimetry. This

is accomplished in part by deriving expressions relating

observed phosphorescence intensity to the operating

characteristics of the experimental system and to the

lifetimes of sample components. This allows prediction

of the relative effects of the various adjustable param-

eters, and gives insight into how the general require-

ments for multicomponent analysis can best be met for a

given analysis. Experimental results are presented to

verify the conclusions drawn from the theoretical work,

which are then used to optimize the experimental system

for TRP analysis of two-component and three-component

mixtures of spectrally similar molecules.












TABLE 1
FINAL WORKING EQUATIONS FOR THE EXPONENTIAL METHOD OF
TIME RESOLUTION FOR A BINARY MIXTURE


SITexp(-td /TA) I T exp(-td/TA)

ixp(-td /TA)exp(-td /TB)-exp(-td /TB)exp(-td /TA)
1 2 1 A


exp(-t d /T)



Nexp(-td/B



exp(-t /AB)
'N


'AN






BBN











TABLE 2
FINAL WORKING EQUATIONS FOR THE EXPONENTIAL METHOD OF
TIME RESOLUTION FOR A TERNARY MIXTURE


+ (Y)IT


+(Z) IT
T3


Sexp(-td /TA )


(Y)exp(-t /T A)+(Z)exp(-t d/TA)
A^ A


where


X = exp(-td /TB)exp(-td /1 C)-exp(-td2/CC)exp(-td/B)


Y = exp(-td /TC) exp(-td /TB)-exp(-t /TB )exp(-t d/tc)


Z = exp(-t d/T B)exp(-td /Tc)-exp(-td /Tc)exp(-t /B)


continued


IAN











TABLE 2-continued


IBN



where


(X)I T + (Y)I T + (Z)I

(X)exp(-td /TB)+(Y)exp(-t dAB)+(Z)exp(-td /B)
1d23/


exp(-t /TB )
(d B


X = exp(-t d/Tc )exp(-td /TA )-exp(-t d/TA)exp(-td /TC)


Y = exp(-t /TA)exp(- /T)-e(xp(-t /TC )exp(-t /TA)


Z = exp(-t /TC )exp(-t d/TA )-exp(-t /TA )exp(-td /T)



continued


(10)










TABLE 2-continued


(X)IT + (Y)IT2 +(Z)I T
(X)exp(-T1 )+(Y)exp(-t /)+(Z)exp(-t3 /
(X) exp (-tdl/Tc) +(Y) exp (-td2/TC)+(Z) exp (-td3/Tc)j


exp(-t /TC )
N


X = exp(-td /TA)exp(-td /TB)-exp(-td /TB)exp(-td /TA)
2j 3 2~ 3J
Y = exp(-td/TB)exp(-td/TA)-exp(-td/TA)exp(-td3/TB)

Z = exp(-t /TA )exp(-t d/TB)-exp(-td /TB)exp(-td /TA)
AL d2 1 2


I =

CNwhere
where


(11)














CHAPTER II
THEORETICAL CONSIDERATIONS

In this chapter, the theoretical aspects of TRP

will be dealt with. First, the kinetic events occurring

during excitation and initiation of phosphorescence

emission will be discussed. The results of this analysis,

coupled with the knowledge of how the gated detection

system responds to the emitted luminescence, yields an

expression which relates measured signal level to the

parameters of excitation pulse width, repetition rate,

delay time, gate width, and phosphorescence lifetime,

T, of the analyte. This expression is used as a basis

for predicting the effects of the individual parameters,

and how these parameters may be optimized for a particular

phosphorimetric analysis.

Kinetic Analysis of Molecular Processes(29)

This section is a summary of the conclusions reached

by McGlynn, Srinivasan, and Maria (29) in a superb paper

on the kinetic processes occurring during phosphorescence.

The details of the mathematical model and the derivations

employed are presented in the Appendix. Tables and figures

are reprinted by permission of the publisher.

The system studied is a phosphor species frozen into

a glassy matrix. This matrix gives good optical








characteristics, and minimizes solute-solute interactions.

In this matrix, decay is usually first order (exponential),

and the concept of mean phosphorescence lifetime is valid.

As stated earlier in this work, T refers to the experimen-

tally observed phosphorescence decay lifetime. The

analysis in the Appendix approximates T as a function of

fundamental rate constants for the processes involved in

excitation/de-excitation of the triplet state. There is,

however, another lifetime associated with a phosphor,

this being the phosphorescence growth lifetime, designated
R
T (R for rise). The growth lifetime describes the rate

of phosphorescence intensity increase when a phosphor

sample is irradiated. What is predicted theoretically,

and observed experimentally, is that the observed phos-

phor intensity grows exponentially while the excitation

continues, eventually reaching a steady state value. This

steady state intensity level is designated 10 and is the

maximum intensity observable for that sample and experi-

mental system.

The actual relationship describing the growth of

phosphorescence when the sample is subjected to constant

intensity irradiation is

I = [l-exp(-t/T ) ]I0 (12)

where I is the intensity at time t. In addition to
RD
Equation 12, the difference between T and T is of great
Interest. It has been found that in many cases, T and T
interest. It has been found that in many cases, T and T








are not identical, but that T < T. The magnitude of the

difference between the two is expected to increase when

T is large, when the quantum efficiency for intersystem

crossing is large, and when the excitation intensity is

large. In the limit of very small excitation intensity,
R
the difference between T and T approaches zero. Experi-

mental comparisons of the growth and decay of a number

of phosphors were cited, and the results included values
R
for naphthalene, with T = 16.6 s and T = 19.9 s; for

triphenylene, with T = 10.4 s and T = 13.4 s; and for
R
phenanthrene, with T = 3.3 s, and T = 3.9 s. The

difference between T and T varies from 8% to 25% for

these phosphors.

Intensity Expressions

O'Haver and Winefordner (3,4) derived an expression

which related the observed phosphorescence intensity to

the temporal characteristics of the luminescence and to

the operating parameters of the measurement system.

The system discussed was an averaging DC meter. The re-

sulting expression containrB observed luminescence intensity

dependence upon T, t p, f, td, and t Plots of relative
g
intensity versus lifetime (other parameters constant)

showed distinctive features, the most significant of which

was that under various combinations of experimental pa-

rameters, there was a point of maximum intensity, correspond-

ing to a particular phosphorescence lifetime. The lifetime

corresponding to the point of maximum instrumental response








is designated T max. By using simplifying assumptions, it

was possible to derive an expression that enabled one to

choose the experimental conditions to shift that point of

maximum response to a given phosphor lifetime. Possible

applications were given, such as calculating theoretical

analyte/interferent intensity ratios based on their life-

times. No experimental evidence for validation of the

underlying model was given. In addition, the expression

allowing calculation of optimum experimental conditions

was based on an assumption which invalidates the expres-

sion for some very useful practical cases.

In this chapter, a similar expression will be de-

rived. There will be several major differences,however.

The measurement system employed for this derivation is

the gated (boxcar) average. In the initial derivation,

a distinction is made between phosphorescence growth life-

time, T and phosphorescence decay lifetime, T. Later,

the expression for optimization will be derived in such

a way as to be valid over a much wider range of conditions.

Most importantly, major emphasis will be placed upon

trying to explain on a physical basis the trends pre-

dicted from this theoretical analysis. The underlying

factor throughout this chapter is the search for results

of practical applicability.

The concept of exponential growth of phosphorescence

during irradiation is critical to the following derivations.








Although the previous section states the reality of

this growth process, it is somehow difficult at first

inspection to rationalize the premise of a long life-

time for phosphorescence growth. It seems to contradict

what is known about the rapid population of the triplet

state by intersystem crossing following the absorption

of photons.

The fallacy is, of course, that although the ex-

citation process for one molecule is very fast, what is

observed experimentally is the luminescence emitted from

a very large number of excited molecules. One could

simplistically visualize an excitation pulse beginning

at time t = 0 and continuing indefinitely. Let the ex-

citation be temporally subdivided into a very large number

of small segments of excitation intensity. By assuming

only that the excitation process is very rapid, the

following rationalization emerges. During the first

excitation segment, a number of molecules,n, undergo

absorption and subsequent population of the triplet state.

Species in the triplet state will undergo deactivation

via the characteristic exponential phosphorescence decay,

exp(-t/T). During each subsequent excitation segment,

a population of n molecules are excited and phosphorescence.

Although the excitation process for any subset of n

molecules is very rapid, what is actually observed is the

sum of phosphorescence intensity decays from a very large








number of subsets of excited molecules. It can be seen

that the overall phosphorescence intensity will continue

to increase until the intensity contributed by the very

first subset of excited molecules disappears. After

this occurs, i.e., all of the molecules excited during

the first excitation segment have returned to the

ground state, the observed phosphorescence intensity will

reach a steady state, because equal numbers of molecules

are excited and deactivated at each instant. This steady

state intensity is the I0 described earlier and will not

be exceeded, regardless of how much longer the sample

is irradiated. I represents the phosphorescence intensity

level resulting from continuous (CW) excitation. Almost

five phosphorescence decay lifetimes are required for

phosphorescence intensity to decay to 1% of its initial

value. Thus, it could take only milliseconds of excitation

for a short-lived phosphor to reach 10, but a long-lived

phosphor might require ten seconds or longer. If the

excitation is terminated (as with a pulsed source) before

a sufficient time period has elapsed, the observed

phosphorescence intensity will be some fraction of I .

This same reasoning can be used to describe the ex-

citation process in a pulsed system. Figure 3 illustrates

a train of excitation pulses of width t occurring at the
P
rate of f pulses per second. During each excitation pulse

Rthe phosphorescence grows proportionately to T and the
the phosphorescence grows proportionately to r and the



























Figure 3. Schematic representation of the excitation process with a pulsed source.












































TI IME








intensity at the end of the first pulse is given by

I0[l-exp(-t p/TR)]. When this pulse ends, the phos-

phorescence intensity decays. This takes place in-

dependently on each successive excitation pulse, with

each pulse contributing the same amount of additional

phosphorescence intensity. The observed intensity is

the sum of the intensities resulting from all the

preceding pulses. Therefore, one would expect that if

a train of excitation pulses is incident upon a

non excited"phosphorescent" sample, the phosphorescence

intensity would rise rapidly during each pulse, and

would decay between pulses. Also, that the intensity

immediately following the pulse would increase steadily,

as "new"intensity (that due to the latest pulse) is added

to the intensity still present from the previous pulses.

Again, after some number of pulses, the pulse-to-pulse

intensity would reach some "pulsed source steady state,"

with the additional intensity from any pulse balancing

the loss of intensity due to decay. The time required

to reach this steady state should be independent of

repetition rate, but should depend on the decay lifetime,

T, of the phosphor. It is not improper, then, to speak

of "pulse-to-pulse phosphorescence intensity growth,"

when the intensity is observed at the same time relative

to each pulse.








The operation of the pulsed source gated detection

system of Figure 2 can now be examined further. The

intensity and time axes are not to scale. The excitation

pulse, of width t is an extremely short, high intensity

burst of radiation, which is assumed to have the shape

of a step function. That is, it goes instantaneously

from zero intensity to maximum intensity, and maintains

this level for t seconds. The phosphorescence intensity
P
grows during t and decays between pulses as previously
P
discussed. If the excitation pulse had sufficient dura-

tion, the intensity would reach I For this derivation,

it is assumed that a sufficiently large number of pulses

have been incident on the sample, that the "pulse-to-

pulse steady state" has been attained. This means that

in Figure 2,the loss of intensity due to decay from I
P1
to I is equal to the increase in intensity from I to
P3 P3
I For convenient reference, important variables

are listed in Table 3.

I is the instantaneous intensity at the start of
3
any excitation pulse, and includes the intensity resulting

from many previous excitation pulses. During the pulse,

the intensity level will continue to decay, and at the

end of t the remaining intensity will be
p
I exp(-t /T) (13)
P3 p














TABLE 3
DEFINITION OF PARAMETERS

Symbol Definition

t excitation pulse width, s
p

td delay time, s

t gate width, s
g
I0 CW phosphorescence intensity

I/I'0 Relative phosphorescence
intensity, unitless

T Phosphorescence decay
lifetime, s
R
T Phosphorescence growth
lifetime, s

I Instantaneous phosphorescence
intensity

I I immediately following t

I PI at the leading edge of t
P2 P g

I I at the leading edge of t
p3 P P

P Integrated luminescence
P intensity observed (per
excitation/emission cycle)








However, during t ,intensity growth occurs, and the

intensity added per pulse is given by Equation 12,

I = 10I[l-exp(-t p/TR)]

Therefore, the instantaneous intensity immediately

following t is the sum of these two contributions,
p
I = I exp(-t /T)+I0[l-exp(-t /T ] (14)
p1 3

However, I is simply I after decay for a period of
p3 P!
time equal to the total time per cycle, 1/f, minus

the pulse width, t :
p
I = Ip exp[-(l/f-t p)/T] (15)


Substituting for I in Equation 14,
P3 R
IPl= I exp[-(l/f-t )/T]exp(-t /T)+I[l-exp(-t /T)] (16)
1 1 p p 0t1-e p(t/)]16

By combining exponentials and solving, one finds

R)
I 0[l-exp(-t p/T )] (17)

1 [l-exp(-l/f T)]

I is the maximum instantaneous phosphorescence obtained

per cycle. However, the instantaneous intensity present

at the leading edge of the gate, IP2 is less than I ,
"2 1!
due to decay over a period of time equal to td Thus,

I = Ip exp(-td/T) (18)
2and substituting into Equation 17 for I yields
and substituting into Equation 17 for Ip yields
"1









I [l-exp(-t /TR )]exp(-t d/T)
I = 0 d (19)
2 [l-exp(-l/f T)]

At any time during the gate, the instantaneous

intensity is given by

Ip = I exp(-t/r) (20)
2

The observed integrated phosphorescence intensity per
cycle, P (the shaded area in Figure 2), is the integral

of the intensity during the gate width:
t t
g g
p = f I dt I exp(-t/T)dt (21)
p 0 0 2

t
g
P = I I exp(-t/T)dt (22)
2 0


P = I T[l-exp(-t /t) ] (23)
p p2

Substituting for I from Equation 19 yields
"2

10 T[l-exp(-t /T) ] [l-exp(-t /TR) ]exp(-td/T) (24)
p = ___g___P___-
P [l-exp(-l/f T)]

The boxcar or gated average measures signal levels

by averaging the intensity over each gate, and thenaverag-

ing the average intensity per gate over many gates (30,31).

Thus, for the boxcar average the signal level is

proportional to P /t Therefore, for the pulsed source

gated average system,









I0 T[l-exp(-t p/TR )] [l-exp(-t /T)]exp(-t d/T) (25)

t [l-exp(-l/f T)]
g

Equation 25 is the basis from which all remaining

expressions will be derived. Thus far, no assumptions

have been made regarding the relative magnitudes of the

various parameters, and Equation 25 is quite general.

Note that Equation 24 for P can also be validly applied

to the boxcar or gated integrator. The integrator sums

the integrated observed phosphorescence intensity per

cycle, and

I = P f t (26)
p c

where t is the counting time. The signal level is
c
simply equal to the area per gate times the number of gates

summed. For the averaging DC meter (4),

I = f P (27)
P

At this point, several assumptions will be made

to simplify Equation 25 and to put it in a form more

conducive to practical application. The first assumption

is that the phosphorescence growth lifetime, T is

approximately equal to the phosphorescence decay lifetime,

T. This is done for several reasons. First, in the

majority of cases, the error introduced by this assumption

should be negligible. The difference between T and T

could easily lie within the standard deviation of the

normal lifetime determination in many cases. Also, the








thrust of this work is to study primarily the relative

dependencies of intensity upon experimental parameters,

and an absolute relationship is not essential. Finally,

a relationship containing only T would be more easily

applied than if both lifetimes were required. Phospho-

rescence decay lifetimes are readily available in the

literature for many compounds, and are easily measured

with standard phosphoroscopic instrumentation, while

growth lifetimes are seldom quoted and require modifica-

tion of the phosphorimeter for measurement.

It is certainly important to realize that T and T

may differ, and under what conditions this difference is

maximized. As the difference between T and T increases,

the expressions may begin to show error. This is the

reason for including the kinetic summary in the preceding

section.

The second assumption is easily met by most pulsed

source phosphorimeters. We assume that the excitation

pulse width, t is much smaller than the sample lifetime,
-4
t << T Thus, the excitation pulse is limited to 104 s
P

for the shortest lived phosphors (T %lms). Most pulsed

sources have pulse widths of microseconds or less, and

so this assumption should be valid. If the case should

arise where T t Equation (25) would be necessary.
%X p
With the assumptions T = T and t << T the growth term
P
[R
[l-exp(-t /T )] can be expanded and approximated by t /T.








Therefore, Equation 25 reduces to


t [l-exp(-t /T)]exp(-td/T) (28)
1=1 _-~ _________________3_____________
0t
0 g [l-exp(-l/f T)]


It should be possible to derive a similar expression

by relying upon the additivity of intensity from pulse

to pulse. Each excitation pulse yields phosphorescence

intensity as given by Equation 12. Let this intensity

growth per pulse be designated IG. Let the last pulse
G
be designated as pulse "N," and preceding pulses as "N-l,"

"N-2," etc. At the termination of pulse N, the intensity

decays resulting from preceding pulses have decayed for

various periods of time, given by some number of 1/f (s)

periods. Intensity resulting from pulse N has decayed

for zero cycles, pulse N-l for 1 cycle, and so on.

Therefore, after N pulses, the total intensity, I ,

could be given by

IT=IG+IG[exp(-l/f T)]+I G[exp(-2/f T) ]+...+i G[exp(-M/f T)](29)

or
N -i/f T
I = I e (30)
T i=O

If N is large,
00 1/f
IT = IG f/ e di (31)
0

But

eax dx = e ax/a (32)


so, if a = -1/f T ,







1= t -/f T _
IT = G e -1' (-f T)] 0 (33)

Substitution and evaluating yields

IT = IG f T (34)

Since I is the intensity following t at steady
T p
state (N large), IT = I in Figure 2, and since I is

defined by Equation 12,

IP= f T I0[l-exp(-t /TR)] (35)

The remainder of the derivation would then follow that

already presented in Equations 17-28. Comparing Equations

35 and 17 shows that they are not identical; however, in

the limit of small 1/f T (large f or large T), the two

converge. Why this difference occurs is not clear.

However, the similarity of the results for the limiting

case indicates that there is validity in the underlying

principle of the second derivation.

Applications

From a practical point of view, Equation 28 is very

important, for it allows one to ascertain the relative

effects of tp t td f and T on the observed in-
p g
tensity. Note that the observed intensity, I is some

fraction of 10. Dividing I by I 0 would essentially

normalize to a constant CW intensity level,


t [l-exp(-t /T) ]exp(-td/T)
I/I =t -P 2 (36)
S g [l-exp(-l/f T)]

I/I0 can be termed the "relative response" of the detection
u0








system, and is actually the effective duty factor for

the measurement (26,30). A plot of I/I0 versus T with

t tg td and f fixed gives a plot of the relative

response of the instrumentation as a function of sample

lifetime. The terms "relative response" and "relative

intensity" will be used interchangeably.

A typical "relative response profile" resembles

Figure 4. The most significant feature is that there

is a lifetime corresponding to an optimum response, des-

ignated T Relative intensity falls off rapidly
max
towards longer (T ) and shorter (T ) lifetimes. The

"enhancement ratios," or ratios of relative intensity

values, for Tmax over T and TL can be approximated by

reading off the intensities Imax IS and I and

calculating Imax /IS and I max/I There is a lower
-'max S max' L
boundary on relative intensity at long T. This occurs

when T >> 1/f t td and t Under these conditions,
p g
[l-exp(-t /T)] is approximately equal to t /T exp(-td/T)

approaches unity, and [l-exp(-l/f T)] is approximately

equal to 1/f T Therefore, Equation 28 reduces to

I/I0 = t f (37)
P

The gated detection system has enhanced response to
T and discriminates against other lifetime components,
max
both longer and shorter. The time resolution system is,

in effect, a "time filter," and the relative response

profile could be compared to the wavelength response profile



























Figure 4. A typical relative response profile.

























I I
max








s I





CO 1 I
L









TS max TL

LIFETIME (s)








of an optical filter, or the frequency response profile

of an electrical filter.

It would be very useful to be able to alter the

shape of the response profile, and to change Tmax as

desired. This would make it much easier to tailor

the experimental system for a particular analysis.

A way to attack this is to take the derivative of I/10

with respect to T and set the derivative equal to zero.

Optimization Expression for td

From Equation 28,
exp (-td/T) [l-exp(-t /T) ]
(I/I0) (t/t ) = (38)
0 P [l-exp(-l/f T)]

Taking the derivative with respect to T and setting it

equal to zero,

exp (-t/T) [1-exp(-tg/) ]
dI/dT = 0 = d Td (39)
T [l-exp(-l/f T)]

By using standard calculus techniques (28), we obtain

[exp(-td/T)(td/T2)-(exp[-(td+t g)/T]) (td+t )/T2 ] x

[l-exp(-l/f T)]=[-exp(-l/f T)] (1/f T2) ([exp(-td/T)]-

exp[-(td+tp)/T]) (40)

Factoring yields

[l-exp(-l/f T)] [exp(-td/T)] [(td/T2 )-exp(-t /T) (td+t)/T2 ]=

[-exp(-l/f T)] (1/f T2) [exp(-td/T] [l-exp(-t /T)] (41)

Further simplification is algebraic, and the necessary

manipulations are:








(1) division by exp(-td/T)
2
(2) multiplication by T

(3) division by [l-exp(-l/f T)]

(4) expansion of the first term

(5) addition of t exp(-t /T) to both sides; and

(6) division by [l-exp(-t /T)]

These steps yield


t (-1/f) [exp(-l/f T)] + t [exp(-t/T) (42)
d [l-exp(-l/f T)] g [l-exp(-t /T)]


By dividing out each term, the final result is obtained:


(td)op t= [ 1 ]li/f)l 1 1 (43)
g exp(t /T)-l exp(l/f T)-I

This expression calculates the optimum delay time, (td)opt

required to optiiLze the response of the instrumentation to

any given lifetime, T at fixed t and f. There is no
g
dependence upon t due to the earlier assumption regarding

t Equation 43 is also valid for the gated integrator

system, since the conversion factor is multiplicative,

and disappears when the derivative is set equal to zero.

O'Haver and Winefordner (4) give a similar expression

for the DC averaging meter system, but with the assumption

that t < p
(td)opt = t 1 1 ] (44)
iit < tg exp(t /T)-li


If the limitation T 1/f is applied to Equation 43,








1/f T grows large, exp(l/f T) approaches infinity, and

the frequency dependent term drops out. T.hus, within the

limits of Equation 44, the two expressions are identical.

Equation 43 is also of practical importance, because

it allows rapid evaluation of instrumental parameters

for a sample of given lifetime. For further study and

convenience of application, plots of (td)opt versus T at

constant f and t were prepared. The plots were obtained
g

by programming Equation 43 into a Hewlett-Packard 25

calculator, and evaluating the various terms. The results

were plotted on oversize sheets of log-log graph paper,

and were later photographically reduced.

The sets of parameters were chosen to be representa-

tive of the operating characteristics of practical experi-

mental systems, and specifically those of the source/de-

tection system used later in this work. Repetition rates

of 1, 10, and 50 Hz were chosen, and a wide range of gate

widths was used. The plots are keyed to the various gate

widths as shown in Table 4. One microsecond was taken

as the lower limit on gate width. The results are shown

in Figures 5-7. Each figure gives the curves correspond-

ing to the various gate widths at constant repetition

rate.

Examination shows several interesting features.

Distinct regions can be observed for each curve, roughly

corresponding to long, intermediate, or short lifetimes.














TABLE 4
KEY TO GATE WIDTH FOR FIGURES 5-7

Gate width (t), s Legend

lxl05 A

5x105 B

-4
ixlO04 C

5x10-4 D
-3
lxl03 E

5x103 F

lxl0-2 G

5x102 H

9x10-2 I


























Figure 5. Optimum delay versus lifetime (f = 1 Hz).
































-1C2

.10
E


lo'


Optimum Delay (s)


























Figure 6. Optimum delay versus lifetime (f = 10 Hz).














































10' I


Optimum


























Figure 7. Optimum delay versus lifetime (f = 50 Hz).












































Optimum Delay (s)







In the 50 Hz plot, Figure 7, gate widthsH and I do not

appear. This is due to the physical boundary conditions

of the real system. The total time between successive

excitation pulses is 1/f (s). This must be larger than

the sum of the pulse width, delay time, and gate width.

At 50 Hz, 1/f = 0.02 s, and therefore no gate widths

larger than this are possible.

At the long lifetime limit, the optimum delay is

asymptotic, and shows little change with lifetime. The

asymptote is gate width dependent, and shifts the optimum

delay to smaller values at higher frequencies. The

implication of this asymptotic behavior is that at long

lifetimes, since (t d)opt is independent of lifetime,

the gated detection system will not be able to discriminate

between phosphors with lifetimes in this region.

Mathematically, the reason for this behavior can be

explained. By expanding the exponential terms in Equation

43 and retaining first and second order terms, we obtain

( [1 1 1 1- 1 1 ]= -1 (45)
exp(l/f T)-l f + 2(f T)2 + 2fT


and

t 1 ]= t [ 1]= T (46)
i 2 t/2T
Sexp(t /T)-i g t /T + (t /T)2 1 + t /2T

Therefore,

(t )pttT (47)
dopttl9t/2Tr 1 + 1/2f T








Finding the common denominator and combining terms

gives
2 i/f t
(td)opt = 2T [ 1f -- (48)
opt (2T + t ) (2T + 1/f)


if the assumption is made that 2T>>t 1/f,


2 /f-t 1/f t
(t)opt = 2T 1[- (49)
d opt 4T 2 2

Thus, for very long lifetimes (relative to t and 1/f),
g

(td)opt is constant, and is exactly one-half of the

maximum possible delay, 1/f t (t negligible).
g p

Equation 49 does predict correctly the asymptote in

Figure 5-7.

In the limit of shorter lifetimes (left-hand section),

the curves are frequency independent. This is expected,

because in this region, Equation 44 is valid. In the

central region of the Figures, the curves for longer

gate widths exhibit curvature. However, as the gate-

widths decrease, the curves approach linearity, with

(t d) = T. This can be shown to occur when t d opt g
T< 1/f.

Because the left-hand boundary of the figures

represents the smallest delay time attainable on a prac-
0-6
tical level, the lifetime corresponding to (t ) 10ot s
d opt
is the smallest lifetime that can be realistically opti-
mized at that f and t As t decreases (curves I to A),
the (t for smaller lifetimes becomes accessible.
the (td)opt for smaller lifetimes becomes accessible.







There is another physical constraint of great

significance. As noted earlier, the boxcar average

averages the signal over a large number of gate widths.

If enough gates are averaged, random fluctuations (noise)

in the signal should cancel, and the output should

approach the average signal level of P /t This signal-

to-noise ratio (SNR) enhancement is accomplished by using

an RC filter. Most measurement instruments possess a

time constant, which indicates how rapidly the instrument

can respond to an applied signal. The normal measurement

procedure is to actually measure the signal for a period

of time equal to five time constants, to insure adequate

time for the instrument to respond. In the gated system,

the signal is only sampled during the gate width, which

is a small fraction of the total measurement time. The

fraction, actual measurement time divided by total measure-

ment time, is known as the duty factor, Df = f x t The

RC filter in the system necessitates that the signal be

actually applied to the filter section for 5 x RC. Because

the signal is actually sampled only a fraction, Df, of the

total time, with the boxcar average the total measurement

time required is

5[]RC
ft
g
where the quantity in brackets is known as the observed

time constant, OTC. Thus, the actual measurement time for

the boxcar average is five timesOTC.








Since the value of RC selected effectively deter-

mines the SNR of the measurement, if the noise is not

directly related to f or t the measurement time
g
required to obtain the same SNR decreases as f or t
g
increases. Conversely, as f or t is decreased, the
g
OTC, and thus the actual measurement time, increases

proportionately.

Response Profiles

If t tg, and f are known, (td)opt can be cal-

culated, which will give maximum enhancement to intensity

at the lifetime, T, chosen. The parameters thus selected

can be used in conjunction with Equation 28 to calculate

response profiles with maxima at selected lifetimes, under

various experimental conditions. Such profiles will be

presented here, and are used to ascertain the effects of f,

t and t on the observed intensity levels.

The plots are prepared in a similar fashion to those

shown previously. The values of the parameters represent

realistic experimental conditions. It was necessary to

limit the number of values studied per parameter, but those

values selected for each factor cover a fairly broad

range. Four repetition rates (f = 1, 10, 50, 100 Hz) and
-3 -4 -5
three gate widths (5x103 5x10, 5x105 s) are employed.
-8
The excitation pulse width, t is 10 s, and is rep-

resentative of the nitrogen laser pulse used later in

this study.








For each combination of frequency and gate width,

(td)opt 's are calculated to yield a family of response

profiles, with maximum response occurring at lifetimes

of 9, 0.9, 9x10- 2, 9x10- 3, 9x10 4, and 9x10 s. The

optimum delays calculated for the various combinations

of f, t and T are given in Table 5, which also

contains the legend used to identify the curves. Every

curve marked "A" should have maximum response at T = 9 s,

curves marked "B" at 0.9s, and so on. In addition, a

curve marked "G" appears on one figure. For this curve,

the delay time used was the maximum physically attainable

delay, 1/f t (remember the asymptote at long T is
g
equal to 1/2 of this quantity). This was included to

demonstrate that delays other than the (td)opt predicted

at long lifetimes can be used.

The resulting families of response profiles of

relative intensity versus lifetime are presented in

Figures 8-19. Each figure represents a fixed frequency

and gate width, with the individual curves varying only

in delay time. Any one curve represents the relative

response of the experimental system under one fixed set

of experimental conditions.















T (s) =
max
Legend:

Fig. t (s)

8 5x103

9 5x103

10 5x103

11 5x103

12 5xlO-4

13 5x104

14 5x104

15 5x104

16 5x105

-5
17 5xl0 5

18 5x105

19 5x105


f(Hz)

1

10

50

100

1

10

50

100

1

10

50

100


4.88x10

4.74x10

7.50x10

2.50x10

4.91x10

4.97x10

9.75x10

4.77x10

4.90x10

4.92x10

9.98x10

4.98x10


TABLE 5
PARAMETERS FOR RESPONSE PROFILES

9x10- 9x10-2 9xl0-3

B C D

Optimum Delays (s)
-i-i -2 -3
1 4.07xl01 8.75xl02 6.73xl03
-2 -2 -2 -3
2 4.66xl02 3.84xl02 6.73xl03
-3-3 -3 -3
3 7.47xl03 7.15xl03 4.30xl03
-3-3 -3 -3
3 2.49xl03 2.43xl03 1.82xl03

1 4.09xl0-1 8.97x10-2 8.75x10-3
*2 -2 -2 -3
2 4.88x102 4.07xl02 8.75xl03
-3-3 -3 -3
3 9.71x103 9.38xl03 6.32xl03
-3-3 -3 -3
3 4.74xl03 4.66x103 3.84xl03
-I-i -2 -3
1 4.09xl01 9.00x102 8.98xl03

2 4.91x10-2 4.09x10-2 8.97x10-3
--3-3 -3
3 9.94xl03 9.60xl03 6.54x103

3 .97xl03 4.88xl-3 4.07xl-3
S4.97xi03 4.88x103 4.07xi0


9x104

E


1.94x105

1.94xl05

1.94xl05

1.93x105

6.73xl0~4

6.73xl04
-4

6.73xl04

6.73xl04

8.75xl0~4

8. 75xl04

8.75xl04

8.75xl04


9x105

F


-6
1.94x10 6

1.94x10-6

1.94x10-6

-6
1. 94xl0 6

6.73x105

-5
6.73x105

6.73xl05

6.73xl0~5


























-3
Figure 8. Response profile (t = 5x10 s, f = 1 Hz).













10-4


io-5


i0

o -10
CD
w


10-I1


10 "13 i .. ..I I i ,n 1 ,tnL m il..Lf i e I(l
10-5 Ci4 10-3 10-2 10"2
Lifetime (s)

























Figure 9. -3Response profile (t = 5x s, f = 10 Hz).
Figure 9. Response profile (t =5x10 s, f 1 0 Hz).
g























10"r



10-8


I0-3
Lifetime (s)


102 10- I





















Figure 10. -3Response profile (t = 5x s, f = 50 Hz).
Figure 10. Response profile (tg = 5x10 s, f = 50 Hz).










10-4




101.1




10-E

IO-e

10-7




10-8


Lifetime (s)


























-3
Figure 11. Response profile (t = 5x10 s, f = 100 Hz).
g




71





I0-5




105
)E

SB
10-7_
/


0-8 /


_1 0-9-
_)

io-10



i0-1o







10-13
I-5 I0-4 I0-3 10-2
Lifetime (s)


3
r-
4-
.c
C
4-
a


S10-I

























Figure 12. Response profile (t = 5x10 4s, f = 1 Hz).





73








F

10-5_-^N














cc
IO-
10-6












10 1-









10-r- 0 10' 1 1





Lifetime (s)


























-4
Figure 13. Response profile (t = 5x10 s, = 10 Hz).
g



































































. . . .. .. ., I I I i J L Ii I *, I


10-3
Lifetime (s)


10-4


10-5





10-6





10-7-





10-8



4-
in



0)
_ lO-9

C:


)10-
10)10[


10-"





10-12


IC


10-4


10-2


)-5


























Figure 14. Response profile (t = 5x10 4s, f = 50 Hz).
g






















































Lifetime (s)



























Figure 15. Response profile (t = 5x10 4s, f = 100 Hz).
g














10-0



10-6



10-7



i O8


Sj10-9
idr9




J
I)








1012




10-5 10-4 1073 10-2 10-1 I 10

Lifetime (s)

























Figure 16. Response profile (t = 5x10 5s, f = 1 Hz).




81



io-4
F





10"6





10-8






I0I
cnc





I~a










10 13 . .. . ..._ . ... . . .. . ... . . ..
1c.E Bo

40-9

-10 1










105 I04 103 102 10- I 10
Lifetime (s)



























Figure 17. Response profile (t = 5x10- s, f = 10 Hz).
g























































10-3 IC
Lifetime (s)


1013



























-5
Figure 18. Response profile (t = 5x10 s, f = 50 Hz).
g





















































Lifetime (s)



























-5
Figure 19. Response profile (t = 5x10 s, f = 100 Hz).
g





















































Lifetime







Results and Discussion

Initially, one figure will be discussed, before

comparisons are made from figure to figure. Figure 8

shows the response for t = 5x103 s and f = 1 Hz. It
g
is evident that the intensity enhancement at the

maximum increases as the Tmax decreases. That is, as

one goes from A, optimized for T = 9s, towards E,optimized
for 9x1-4
for T = 9x10 s. Curve A has a very broad, flat maximum,

while curve E has a very sharp, well pronounced peak.

It is important to note that (t d)opt is not the td of
d opt -
maximum attainable intensity. In all cases, decreasing

td gives increased intensity, but simultaneously increases

response to shorter lived components.

As mentioned earlier, the degree of enhancement (or

discrimination) for phosphors of various lifetimes can be

estimated by comparing their relative intensities. It can

be seen that in all cases, except for lifetimes lying very

closely together, discrimination over shorter lived

components, IT /I is drastic. The reason for this
max s
is simply that the chosen delay time is so long that phos-

phorescence intensity due to shorter lived species has

decayed significantly before the gate opens to sample the

intensity. At longer lifetimes, the relative intensities

approach the previously described limit of t f which
p
-8 f
is 108 for Figure 8. It is obvious that, since the

intensity contributions from long-lived components never







drop below this level, in most cases, the ratio of

IT /IT will be substantially less than the ratio
max long
of max/I T short This occurs because, regardless of
max short
where the gate is positioned for measurement of intensity

from a particular lifetime component, the intensity

resulting from phosphors of longer lifetime will always

be present, and will always underliethe intensity decays

for short-lived components.

Effect of excitation pulse width, t
P

The effect of t is not illustrated directly in any

of the figures, because the earlier assumption concerning

the relative magnitude of t makes it a strictly multi-
P
plicative factor in all cases presented here. The

relative intensity is directly proportional to t as

long as t << T. This simple dependency is deceptive,
P
however. The t factor enters the intensity expression
P
as the term describing phosphorescence growth during the

pulse, [l-exp(-t /T)]. Within the limit of t T,

this growth term reduces to I = I t /T. This growth

factor is solely responsible for the observed intensity

enhancement of short over long lifetime components.

At a fixed t the phosphorescence intensity level
p
attained due to growth during t is inversely proportional

to the phosphorescence lifetime, T Therefore, for two

components of identical I1 the component of shorter

lifetime is excited to a greater fraction of I and the

intensity due to the shorter lived component immediately








following the excitation pulse (I in Figure 2) is
p1
greater than that of the long-lived component. However,

this intensity due to the short-lived component also

decays more rapidly following t Therefore, for some
p
period of time immediately after the excitation pulse,

the intensity contribution of the shorter lived component

is greater than that due to any longer lived components.

This is shown by the shaded area in Figure 20, which

illustrates the phosphorescence intensity growth/decay

for two phosphors of differing lifetime. Thus, the

maxima in the instrumental response profiles occur

because the shorter lived components actually do have

greater intensity along the earlier portion of the

emission decay curve.

If t is increased, all lifetime components attain
P
a larger fraction of I As t approaches T in value,

the multiplicative effect gradually becomes exponential.

As t continues to increase, components with very short

lifetimes will completely attain I0 and further length-

ening of t will not further increase the intensity due
P
to those components. However, longer lived components

will still increase in intensity with increasing t ,
p
until the pulse width is so long that they too attain I 0.

This is, of course, what occurs in a CW system, and

I/I0 = 1 for all lifetimes. Therefore if t is large,

and all components reach 10 during the excitation pulse,


























Figure 20. Schematic representation of phosphorescence growth during the
excitation pulse for two phosphors with different lifetimes.


























Short