Title Page
 Table of Contents
 Key to Symbols
 Thermal desorption of physisorbed...
 Experimental equipment and...
 Catalyst surface area measurement...
 Catalytic gasification of...
 Determination of heat of adsorption...
 Conclusions and recommendation...
 Biographical sketch

Title: experimental method for measurement of catalyst surface area by thermal desorption of physisorbed gases
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 Material Information
Title: experimental method for measurement of catalyst surface area by thermal desorption of physisorbed gases
Series Title: experimental method for measurement of catalyst surface area by thermal desorption of physisorbed gases
Physical Description: Book
Creator: Miller, Dennis John.
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Bibliographic ID: UF00090212
Volume ID: VID00001
Source Institution: University of Florida
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Table of Contents
    Title Page
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        Page ii
    Table of Contents
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    Key to Symbols
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    Thermal desorption of physisorbed gas: theory
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    Experimental equipment and methods
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    Catalyst surface area measurement by thermal desorption
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    Catalytic gasification of carbon
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    Determination of heat of adsorption by thermal desorption
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    Conclusions and recommendations
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    Biographical sketch
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Full Text








The author wishes to thank Dr. Stanley Bates, Dr. John

Hren, and Mr. E. J. Jenkins of the Materials Science and

Engineering Department at the University of Florida for

performing the scanning and transmission electron micro-

scope studies on the supported catalysts. Their long hours

of tedious labor are greatly appreciated. Dr. Bates and

Mr. Wayne Akery also did an X-ray line broadening study of

the impregnated samples of K2CO3 and carbon black.

The author thanks Mr. Eric Kaler of the Department

of Chemical Engineering at the University of Minnesota for

performing small angle X-ray scattering studies (SAXS) on

the carbon black and K2CO3 impregnated samples.

The author thanks Mr. Anthony Gonzalez for performing

the gasification experiments in the thermobalance.

The author would like to acknowledge the members of

the supervisory committee: Dr. K. Fahien, Dr. G. Hoflund,

Dr. M. Vala, and especially Dr. H. H. Lee for guidance in

this research.

The author thanks Mr. Ron Baxley and Mr. Tracy Lambert

for assistance in obtaining materials for and construction

of the experimental equipment.

Finally, the author expresses a special thank you to

Miss Pam Victor for diligence and cooperation in the prep-

aration of the manuscript.



ACKNOWLEDGEMENTS ....................... ............. ii

KEY TO SYMBOLS ..................................... vi

ABSTRACT ............................................. xii


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


2.1 Physical Adsorption ........................ 8
2.2 Nature of Physisorption Forces ............. 11
2.3 Kinetic Model of Thermal Desorption ........ 15


3.1 Introduction ............................... 27
3.2 Apparatus ................................... 29
3.3 Procedure ............... ....... ............ 36
3.3.1 Sample Preparation .................. 36
3.3.2 Instrument Warm-Up .................. 37
3.3.3 Adsorption ......................... 38
3.3.4 Thermal Desorption .................. 39
3.3.5 Post-Experimental Measurements ...... 39
3.3.6 Modification of Procedures for BET
Surface Area Measurements .......... 41
3.4 Experimental Data--Analysis and Sample
Calculations ......... ................... 41
3.4.1 Analysis of BET Experiments ......... 41
3.4.2 Analysis of Thermal Desorption ...... 43
3.5 Verifications of Assumptions Made in the
Thermal Desorption Model .................. 50
3.5.1 Constant Adsorbate Partial Pressure.. 50
3.5.2 Negligible Inter- and Intra-Particle
Diffusion Resistance ............... 52
3.5.3 Dynamic Equilibrium ................. 54
3.5.4 Bed Isothermality ................... 56
3.5.5 Negligible Axial Dispersion Between
Sample Cell and Detector ........... 57
3.6 Summary .................................. 58


Table of Contents continued



DESORPTION .................................... 59

4.1 Introduction ............................ 59
4.2 Theory .................................... 62
4.2.1 Criterion for Catalyst Area
Measurement ....................... 62
4.2.2 Choice of Adsorbate ................ 66
4.2.3 Monolayer Volume Ratio ............. 69
4.2.4 Calculation of Catalyst Surface
Area ............................. 71
4.3 Results ................................... 76
4.3.1 Carbon Black and Potassium Carbonate
(K2C03) ........................... 78
4.3.2 Carbon Black and Silver ............ 97
4.3.3 Platinum and Alumina ............... 115
4.3.4 Silver and Alumina ................. 121
4.4 Discussion and Conclusions ............... 139


5.1 Introduction .............................. 146
5.2 Thermobalance ............................. 147
5.2.1 Design Concepts .................... 147
5.2.2 Safety Considerations .............. 148
5.2.3 Detailed Description ............... 150
5.2.4 Experimental Procedure ............. 154
5.3 Measurement of Intrinsic Kinetics ......... 158
5.3.1 Flow Rate Criteria ................. 160
5.3.2 Solid Reactant Configuration ....... 170
5.4 Collection and Analysis of Data ........... 175
5.5 Results of Gasification ................... 181
5.6 Discussion ................................ 185
5.7 Conclusions ........................... ... 193

DESORPTION ....................... ............ 196

6.1 Introduction ......................... 196
6.2 Theory .................................... 199
6.3 Data Analysis and Calculations ............ 210
6.4 Results ................................... 214
6.5 Application to Equilibrium Data .......... 221
6.6 Discussion of Results ..................... 223


Table of Contents continued



I EXPERIMENTAL DATA .............................. 235

ADSORPTION .......................... .... . 243

LITERATURE EQUILIBRIUM DATA ................... 247

BIBLIOGRAPHY ........................................ 254

BIOGRAPHICAL SKETCH ................................. 257


Al, A2 areas of sample basket and tube wall, respectively,
in Equation (5-6)

b parameter defined in Equation (2-22)

c dimensionless concentration

C concentration

Cij constant in Equation (2-1)

C basket or pellet centerline methane concentration
Cs basket or pellet surface methane concentration

C total gas concentration

C total concentration of surface adsorbing sites

C ideal gas constant pressure heat capacity

C ideal gas constant volume heat capacity

d spherical diameter of supported catalyst particles

De effective gas diffusivity

D.. constant in Equation (2-2)
Ea activation_ energy of adsorption

Ed activation energy of desorption

E.. constant in Equation (2-2)

f. fraction of total surface sites with heat of
I adsorption AHi

f partition function of adsorbed activated complex

fads partition function of adsorbed species

f minimum flow rate necessary to gasify solid

f solid surface partition function

F local electric field of solid around adsorbing

FG gas phase partition function per unit volume

F12 parameter in radiation heat transfer, defined in
Equation (5-6)

h Planck's constant in Equation (2-17)

h height of sample basket in Equation (5-7)

-HA heat of reaction of Reaction (5-1)

-AH heat of adsorption
AH. heat of adsorption of group i of sites
AH enthalpy of adsorption in Appendix II

I1, I2 integrals defined in Equation (4-10), area under
6 T curve

I integral defined in Equation (4-10), area under
9 T curve

k Boltzmann constant in Equation (2-7)

k gas phase thermal conductivity, Equation (5-3)

k first order reaction rate constant in Equation (5-9)

k adsorption rate constant
k adsorption rate constant pre-exponential factor
kd desorption rate constant

kdo desorption rate constant pre-exponential factor

K thermal conductivity of sample bed in Equation (5-15)

K(T) ratio of rate constants, k /kd, in Equation (2-11)

K ratio of rate constants, kd/ka, in Equation (6-11)

K ratio of pre-exponential factors, kdo/kao

Ki ratio of rate constants, kd/ka, for group i of sites

K. ratio of pre-exponential factors, k do/k for group
i of sites


L depth of sample bed

m linear heating rate in Equation (2-12)

m mass of adsorbing molecule in Equation (2-16)

n moles of ideal gas in Equation (A2-2)

N total number of groups of sites in Equation (6-8)

p partial pressure of adsorbate

po saturation pressure of adsorbate

P total gas pressure

qc heat flux by conduction

qR heat flux by radiation

q total heat flux

Q total heat liberated per step change in 6

r distance between adsorbing molecule i and surface
in Equation (2-4)

r radial coordinate in annulus (Equation (5-2)) and
in basket (Equation (5-10))

r.. distance between adsorbing molecule i and surface
atom j
r ol rate of adsorption by collision theory
r trans rate of adsorption by transition state theory
r trans rate of. desorption by transition state theory
R ideal gas constant

R radius of spherical particle in Equation (5-9)

R1, R2 radius of sample basket and tube wall in Chapter V

R1, R2 monolayer volume ratio of adsorbate in Chapter IV
on pure components

RA,CH4 rate of methane production

RCL rate of catalyst loss

S surface area


S surface area of pure component from BET experiment

S1, S2 surface area of components 1 and 2 in supported
catalyst (two-component solid)

S total surface area of supported catalyst (two-
component solid)

t time

T temperature

Ta minimum temperature of adsorption

Tm temperature at which desorption rate is a maximum

Ts surface temperature of reactor tube wall

T1, T2 limits of integration in Equation (4-10)

T1 surface temperature of pellet or sample basket

U internal energy, Appendix II

U .. dispersion potential between adsorbing molecule i
'dj and surface atom j

U dispersion potential between adsorbing molecule
d,i and entire surface

U rd orientation potential of a rigid dipole

U orientation potential of a rigid quadrupole
Upd orientation and induction potential of a polarizable

U induction potential between a non-polar molecule and
an ionic surface

UR repulsive potential between adsorbing molecule and

UT total net potential

V gas volume, Appendix II

V volume adsorbed
Vdes volume desorbed during thermal desorption

Vm monolayer volume of gas per unit weight

W1 weight fraction of component

W weight of carbon
WC weight of catalyst

x axial coordinate in sample bed

z dimensional axial coordinate in sample bed

Greek Symbols

a polarizability of gas molecules

B angle of dipole or quadrupole with solid surface

A change in

E:i,2 emissivities of basket and tube wall surfaces

a sticking coefficient in collision theory, Equation

a parameter in radiation heat transfer, Equation (5-6)

n parameter in Equation (2-6)

sn first-order isothermal effectiveness factor for
spherical pellets

Pi density of component 1

s0 Thiele modulus for first-order reaction in a spheri-
s cal pellet

V monolayer volume of adsorbate per unit area

8 fractional coverage

ea fractional coverage at temperature T
T fraction of volume adsorbed

T permanent quadrupole moment of adsorbing molecule

T dimensionless time

P permanent dipole moment of adsorbing molecule



BET Brunauer, Emmett, and Teller; refers to experiments
for measuring total exposed surface area

ID inside diameter

NPT national pipe taper

OD outside diameter

S.S. Stainless Steel

STP standard temperature and pressure

TC thermal conductivity

TPD temperature programmed desorption

I microns

Component Subscripts

a silver

Al alumina

c carbon

p platinum

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



Dennis John Miller

August 1982

Chairman: H. H. Lee
Major Department: Chemical Engineering

A new experimental method for the measurement of total

supported catalyst surface area is developed utilizing the

transient thermal desorption of physically adsorbed gases.

The method takes advantage of the limited selectivity of

certain physisorbed gases, allowing calculation of the cata-

lyst surface area as a fraction of the total exposed area of

catalyst and support.

Theoretical and experimental analyses of the transient

desorption of physisorbed gas show that a dynamic equilibrium

between adsorption and desorption is maintained at all times

during the thermal desorption, allowing the desorption kin-

etics to be described by the Langmuir isotherm. Experiments

in the continuous flow sorptometer at constant partial pres-

sure result in the fractional coverage's being described as a

function solely of temperature. The resulting fractional


coverage vs. temperature curve fully characterizes the adsorp-

tion of gas onto the solid surface, and is used to calculate

heat of adsorption and for catalyst surface area measurements.

The method for determining catalyst surface area exploits

differences in adsorption characteristics of the adsorbate on

the catalyst and support surfaces, manifested as differences

in the fractional coverage vs. temperature curves for the two

surfaces. The thermal desorption experiments are performed

for the pure catalyst (in powder or gauze form), pure support,

and the supported catalyst; the fractional surface area of

the supported catalyst is calculated by a level-rule expres-

sion utilizing the three fractional coverage vs. temperature

curves. The underlying assumption of the calculation is that

the adsorption onto catalyst and support surfaces of the sup-

ported catalyst can be described by adsorption onto the pure

catalyst and pure support surfaces.

The catalyst surface area has been measured for supported

catalysts in four systems. Substantial effort has been put

into the verification of the calculated areas by independent

measurements such as microscopy and chemisorption. The best

results have come from oxygen chemisorption on silver cata-

lysts and through the use of physically mixed samples of the

pure components for which the fractional area is known.

A preliminary application of the method has been applied

to a kinetic study of the K2CO3-catalyzed gasification of

carbon. The carbon gasification rate has been found not to

depend on the K2CO3 surface area, but rather only on the

catalyst weight.



The use of thermal desorption for the study of both

physically and chemically adsorbed species on solid sur-

faces has long been recognized as an important experimental

technique. The process consists of heating a solid sample

from a temperature at which gas is adsorbed to a higher

temperature where all gas is removed from the surface, and

collecting or measuring the total volume of gas desorbed

from the surface. Two types of information are derived from

thermal desorption, depending upon the way in which the ex-

periments are carried out. The two types of experiments are

generally referred to as total desorption and temperature

programmed desorption, and differ in the way that the solid

is heated during the experiment.

The traditional application of thermal desorption to

both physical and chemical adsorption is total desorption,

in which a single piece of information, the total volume of

gas adsorbed on a solid, is obtained. For physical adsorp-

tion, which is reversible under all conditions, the volume

of gas adsorbed on a solid at equilibrium is a function only

of the pressure of the adsorbate and the system temperature.

The volume of gas adsorbed can be determined as a function

of temperature and/or pressure by performing the total thermal

desorption experiments at various initial temperatures and

pressures. Since the volume adsorbed depends only on the

initial temperature and pressure, the rate at which the

sample is heated has no effect on the resulting volume mea-

surement, provided that all gas is ultimately desorbed from

the solid surface. In contrast tophysisorption, the chemi-

cal adsorption of gas is highly irreversible and site-

specific, so that a surface which is saturated with a

chemisorbed gas will have a single layer of molecules ad-

sorbed at specific sites on the solid surface. The satura-

tion takes place very rapidly at adsorption conditions, and

the total amount adsorbed is a function only of the number

of active sites on the solid surface. Therefore, the total

volume of gas which is chemisorbed on a solid can also be

measured independently of the way in which the sample is

heated, as long as conditions are reached where all gas is

desorbed from the surface. Thus it is seen that the total

desorption yields the value for the total amount of gas ad-

sorbed, regardless. of the way in which the sample is heated.

The applications of total thermal desorption are far

too numerous to mention here. Langmuir (1918) was a pioneer

in studying and modeling thermal desorption of physisorbed

gas. The most powerful application in physical adsorption

is the measurement of total solid surface area via the theory

of multilayer adsorption set forth by Brunauer et al. (1938).

Their theory is the most widely used and accepted in physical

adsorption. The application of total thermal desorption to

chemisorption allows calculation of the total number of

active sites of a supported catalyst. Chemisorption studies

are applicable only to certain gas-solid pairs, such as

hydrogen on platinum (Hunt, 1971; Spenadel and Boudart,

1960; Adler and Kearney, 1960), hydrogenon nickel (Taylor

et al., 1964), carbon monoxide on palladium (Scholten and

Montfoort, 1962),and nitric oxide on oxides of copper,

nickel, and iron (Ghandi and Shelef, 1973), and others.

In contrast to the relatively simple experiments in-

volved with the measurement of total volume adsorbed, the

method of temperature programmed desorption allows infor-

mation about the kinetics and transient behavior of gas

desorption to be obtained, but only with the added expense

of rather difficult and sophisticated experimentation.

Temperature programmed desorption (TPD) involves the heat-

ing of a solid (with adsorbed gas) in a programmed manner,

while the volume of gas desorbing from the solid is contin-

uously recorded. The data are analyzed to determine the

desorption rate coefficient and the activation energy of

desorption, so that the kinetics of desorption can be


The applications of TPD have focused entirely on chemi-

sorbed gases. The basic theory for TPD of chemisorbed

species was developed by Smith and Aragnoff (1958) and re-

quired a linear rate of temperature increase in experiments.

Many studies have been carried out for gas-solid pairs,

notably Cvetanovic and Amenomiya (1963, 1967), Redhead (1962),

Hill et al. (1972), and Ehrlich (1961). The utility of TPD

for characterizing desorption kinetics of chemisorbed

species is well recognized.

The application of TPD to physisorbed gases has not

been reported in the literature because the existing theory

for determining kinetics requires assumptions which do not

hold true for physisorbed gases. Further, there has tradi-

tionally been little interest in the kinetics of physisorp-

tion, since practical applications require only total volume

measurements. There are, however, several potential uses

for a theory of the TPD of physisorbed gases, particularly

in the area of characterizing the gas-solid interactions

of the first layer of physically adsorbed gas. Such a

theory and its subsequent applications are the subject of

this research.

The theory and application of programmed desorption of

physisorbed gas originated from a need to measure the sur-

face area of a non-metallic supported catalyst, for which

no general method of measurement was available. Several

studies have met with limited success in measuring oxide

catalyst surface area (Ghandi and Shelef, 1973; Parekh

and Weller, 1977), but no universal method of surface

area measurement has been developed. The theory and ex-

perimental method which have resulted from the study not

only allow the calculation of the supported catalyst area,

but also represent a general theory for the thermal de-

sorption of physisorbed gas. The experimental method

described in Chapter III utilizes a simplification of TPD,

and requires only that the solid sample be heated in a mono-

tonic fashion. The important feature, as in TPD, is the

continuous measurement of the volume of gas desorbed from

the solid as the temperature is increased. The theory de-

veloped in Chapter II shows that the relationship between

the instantaneous volume of gas adsorbed on the solid and

the solid temperature entirely describes the gas-solid inter-

actions at monolayer coverage. This relationship allows the

heat of adsorption to be calculated from the thermal desorp-

tion experiments (Chapter VI) thus quantifying the gas-solid


Most importantly, however, the experimental method devised

allows the catalyst surface area to be determined. The con-

cept of using physisorbed gases to measure actual catalyst

surface area, given in Chapter IV, has previously been undis-

covered. It has been found through the thermal desorption

experiments that certain physisorbed gases (with heats of

adsorption greater than five kilocalories per mole) exhibit

different adsorption behavior on different solid surfaces

at monolayer or sub-monolayer coverages. The difference in

adsorption characteristics results in a given adsorbate show-

ing selective adsorption toward one surface or the other when

two different solids are simultaneously placed in an adsorbing

environment. The selective adsorption allows the individual

surface area of each component in a two-component solid to

be determined, by performance of thermal desorption experi-

ments on each pure solid and on the two-component mixed solid.

The application of the method to the measurement of

catalyst surface area is an important breakthrough in cata-

lyst characterization. Knowledge of the actual catalyst

surface area is all important in characterizing the cata-

lytic reaction and in understanding physical processes

such as sintering that the catalyst undergoes during

reaction. While there are other methods available for

catalyst area measurement such as microscopy, X-ray analy-

sis, and chemisorption, such methods either are limited

to specific types of catalysts or require assumptions which

greatly reduce the quality of information obtained. The

experimental method developed here has several advantages,

the most important being that the experiments are based on

physical adsorption, which takes place on all solid surfaces.

All types of catalysts can be analyzed use.of this method,

especially non-metallic catalysts where chemisorption methods

yield little or no information. Other advantages are the

relative ease of experimentation and the non-destructive

nature of the analysis.

The successful application of thermal desorption to

the measurement of catalyst surface arearequires careful

experimentation and proper choice of adsorbate, both of

which are discussed in much detail in the text. Also,

the experimental results obtained from this method must

somehow be verified by independent means, to assure valid-

ity of the experimental technique. Much of Chapter IV of

the text is devoted to the various methods of verification

of the experimental results obtained.

Finally, the catalyst surface area is expected to be

related to the observed rate of a catalytic reaction. To

test this hypothesis, the catalytic gasification of carbon

has been studied in a high pressure thermobalance. The

rate of carbon gasification is compared to the catalyst

(K2CO3) surface area measured by this thermal desorption

method. The results are given in Chapter V.


2.1 Physical Adsorption

The phenomenon of physical adsorption is a direct result

of low energy interactive forces between molecules in the

gas phase and a solid surface. Because the magnitude of the

interactive forces is much less than the forces involved in

a chemical bond formation, physisorption forces are referred

to as non-bonding forces. Physisorption takes place in sig-

nificant quantities only when the energy of gas molecules is

low enough that the physisorption forces significantly alter

the behavior of gas molecules. It is, therefore, a low temp-

erature phenomenon observed only when the temperature of the

adsorbing gas and solid approaches the saturation or lique-

faction temperature of the adsorbing gas. At low temperature,

gas molecules collide with and remain attached to the solid

surface as a result of the gas-solid interactions. Because

the interactions are relatively weak, the time an individual

molecule remains attached to the solid surface is short, and

there results a constant flux of molecules adsorbing and de-

sorbing from the solid surface. The amount of gas adsorbed

at constant conditions is a consequence of equilibration of

the adsorption and desorption rates, and for a given surface

depends only on the system temperature and gas pressure.

Physisorption is therefore a reversible process.

At high pressure of adsorbate and sufficiently low temp-

erature, an adsorbing gas can form multiple layers on the

solid surface, and a mobile, multiple-layered film of adsor-

bate molecules results. For this reason, physisorption is

sometimes thought of as an accelerated condensation of gas

onto a solid surface at low temperature, in much the same

way that water vapor condenses on the surface of a cold

object. In multilayer physisorption, the dominating forces

of adsorption for more than the first few layers of molecules

are not gas-solid interactions but gas-adsorbed gas

interactions. The magnitude of the gas-adsorbed gas inter-

actions is close to the heat of vaporization of the adsorb-

ing species. In multiple layer adsorption, therefore, the

nature of the solid surface is relatively unimportant, and

gas condensation properties determine the adsorption behav-

ior of the gas. This non-specific adsorption, occurring in

virtually the same way on all solids, has traditionally been

used for total surface area and pore volume measurements

with nitrogen as adsorbate.

The theory presented in this chapter departs from the

traditional treatment of multilayer physisorption, and in-

stead focuses on the adsorption of only a single layer of

adsorbate on the solid surface, and the subsequent forces

of interaction between the first layer of adsorbed gas and

the solid surface. In order to study these interactions,

experimental conditions must be adjusted so that only a

single layer of gas molecules is adsorbed on the solid

surface. The adsorption-desorption behavior of this adsorbed

monolayer characterizes the interactive forces of the parti-

cular gas-solid pair, and allows information such as heat of

adsorption and surface heterogeneity to be obtained through

analysis of data. All that is necessary to obtain such in-

formation is the appropriate experimental technique and con-

ditions such that a monolayer coverage of the solid surface

is assured, and a model describing the adsorption-desorption

behavior of the monolayer on the surface which allows calcu-

lations to be made. The experimental technique, thermal

desorption, has been briefly described in the introductory

chapter. The conditions necessary to achieve the monolayer

adsorption are discussed in detail in the following chapters.

The model describing the behavior of the physically adsorbed

monolayer of gas during the thermal desorption is presented

in this chapter, for adsorption of gas on a single surface.

The model will allow the solid surface and the gas-solid

interactions to be characterized from the data collected in

thermal desorption experiments, and is perhaps the first

model describing the transient desorption behavior of physi-

sorbed species.

Before the theory is developed, a discussion of the

various types of forces involved in physisorption is

presented. An understanding of the forces involved in

physisorption will be very useful in Chapter IV, where

the theory for thermal desorption is applied to the deter-

mination of catalyst surface area. The relative importance

of the physisorption forces and differences in the forces

for different gas-solid pairs is what allows measurement

of the catalyst surface area by the thermal desorption


2.2 Nature of Physisorption Forces

Thorough descriptions of physisorption forces are

available in Brunauer (1943), Young and Crowell (1962), and

Clark (1970), and will not be discussed here. However, an

introduction to the types and relative magnitudes of physi-

sorption forces which are important for various types of

gases and solid surfaces is necessary for further develop-

ment and application of the thermal desorption technique.

Such an introduction is presented here.

Physisorption forces, which can be measured as heats

of adsorption, are of the order of one-half to ten kcal/mole,

and are divided into three general groups: dispersion

forces, induction forces, and orientation forces. The quan-

titative description of these gas-solid interactions has

evolved directly from that of the binary gas-phase molecular


In general, the interaction of a gas molecule with a

solid surface is taken as the weighted sum of the binary

interactions between the gas molecule and individual sur-

face atoms. Dispersion forces first explained by London

(1937) are important in all gas-solid interactions. These

forces result from in-phase oscillations of electron clouds

of adjacent molecules. The net attraction energy due to

these fluctuating dipoles is given (.London, 1937) by

d,ij -Cij/r (2-1)

where C.. is a constant depending on the energy and polariza-
ability of the ith and jth molecules. In addition, fluctuat-

ing quadrupoles that molecules possess also contribute to

the dispersion forces in the form of interaction between a

fluctuating quadrupole and a fluctuating dipole and between

two fluctuating quadrupoles:

8 10
U = D /r E /r 1 (2-2)
d,ij 13 i 1.3 ij

These interactions are approximately 20% of the dipole-

dipole interactions. Summing over all solid atoms for the

dispersion interaction between a gas molecule and the solid

surface results in the total dispersion potential:

6 8 10
Ui = -E[C ./r. + D/r + E/r 1 (2-3)
d,i ij 13 1ij j ij/rij

Dispersion forces are the predominant forces in the physi-

sorption of non-polar molecules on covalent and metallic

surfaces, and they are significant in all gas-solid


Orientation forces arise from the interaction of polar

molecules with a metallic or ionic crystal surface. Dipoles

tend to align so that the opposite charges are in closest

proximity, resulting in a net molecular attraction caused by

the opposite charges. Molecules with permanent quadrupoles

also exhibit net attractive forces toward these surfaces.


According to Brunauer (1943), these forces can be quantified

by substituting for the surface a mirror image of the polar

molecule with the charges reversed. The resulting expres-

sion for the attractive energy between a dipole and the

solid surface is

Ur 3( + cos28) (2-4)
rd 3

The similar expression for a rigid quadrupole is

2 2 2 4
U = 4r) 5 (1 + cos + cos48) (2-5)
rq 4(2r)

The average potential can be found by integrating over all

angles 6, using anangular weighting function which takes

into account the preferred angles of orientation. Once again,

the total orientation force must be found by summing the in-

dividual gas molecule-solid atom interactions.

Induction forces arise from the induced dipole produced

in both polar and non-polar molecules when they are in the

vicinity of a metallic or ionic surface. Using the model of

a mirror image dipole, the combined orientation and induction

attractive energy is calculated to be

Up= 2os2 + _--sin n = a/8r3 (2-6)
pd 8r3 -2

In general, the interaction energy of a non-polar molecule

with a solid surface, metallic or ionic, can be described

in terms of the local electric field F of the solid:

U1 aF2 (2-7)
I 2

These induction forces can be significant for both polar

and non-polar molecules.

In most treatments of physisorption, the repulsive

forces between molecules have not been well defined. Several

simple expressions have been used for approximate calcula-


UR = (2-8)

where A, b, C and m are adjustable parameters. The quantum

mechanical treatment suggests the exponential form, but

quantitative calculations yield little information because

of the extremely short range of these forces.

The total interaction force between gas molecules and

a solid surface is the sum of all attractive and repulsive


U =U +U +U. -U
T dispersion orientation induction UR (2-9)

From these forces, various potential models have been devel-

oped, such as the Lennard-Jones model which accounts only

for dispersion attractive and repulsive forces.

From this brief introduction, it can be seen that for

various types of solid surfacesand adsorbing molecules dif-

ferent interactive forces will predominate. For covalent

surfacesand non-polar molecules, dispersion forces alone

describe physisorption behavior. For the adsorption of

non-polar molecules on metallic or ionic crystals, both

dispersion and induction effects are important. For polar

molecules on ionic and metallic surfaces, all three types

of forces must be taken into account including quadrupole

interactions for molecules with permanent quadrupoles. The

relative magnitudes of attractive physisorption forces on

the ionic crystal potassium chloride have been calculated

by Lenel (1933). These are given in Table (2-1). While

these values are only for a single system, they illustrate

the relative magnitudes of the various forces. Calculation

of attractive physisorption forces for several gases are

given in Chapter 8 of Ross and Olivier (1964), and in Chapter

7 of Flood (1967). These authors also give parameters neces-

sary for calculating attractive physisorption forces.

2.3 Kinetic Model of Thermal Desorption

With the brief introduction to physical adsorption

forces, the kinetic model describing the thermal desorption

behavior of adsorbed gas is now presented for monolayer or

sub-monolayer coverage of the solid surface.

The adsorption kinetics of a single layer of molecules

on a solid surface were first modeled by Langmuir (1918),

who postulated that the. adsorption and desorption were

occurring simultaneously on the solid surface. The model

he developed is still regarded as useful for the character-

ization of single layer adsorption, and is the basis for

the development of the transient thermal desorption model.

For unsteady state adsorption, the Langmuir kinetic

equation is

Table 2-1
Adsorption of Gases on KCla

Gas energy














heat of




aLenel, 1933

bUsing adjusted parameter

mS d _= pk S (1-6) k S (2-10)
mo dt ao do

where v is the volume of gas occupying one square meter at
monolayer coverage, S is the total surface area of a single

solid, p is adsorbate partial pressure, and ka and kd are

adsorption and desorption rate constants respectively. At

constant temperature and pressure, the transient term d6/dt

becomes zero when the adsorption-desorption equilbirum is

established, and the familiar Langmuir isotherm results:

6 = K(T)p (2-11)
1 + K(T)p

where K = ka/kd. In this study, however, not the equilibrium

value of surface coverage 6 but the change in 8 during thermal

desorption is of primary interest.

One method of studying the transient desorption by

Equation (2-10) is the temperature programmed desorption (TPD)

technique proposed by Cvetanovic and Amenomiya (1963) and

described in Chapter I. For the desorption of chemisorbed

gas, the readsorption of gas is assumed negligible for rapid

heating of the solid sample, thus reducing Equation (2-10) to

-m de = k (2-12)
m dT d


kd = kdoexp[- Ed/RT] (2-13)

and m = dT/dt, the heating rate of the sample during pro-

grammed desorption. For experimental analysis, the sample

must be heated in a linear fashion, so m is a constant in

Equation (2-12). If the derivative with respect to time of

Equation (2-12) is taken and the term d26/dT2 set equal to

zero at the time where the rate of desorption is a maximum,

the final expression for determination of the components Ed

and kdo of the desorption rate constant kd is obtained:

Ed -In + ln(od)m (2-14)
Rm \\RT

where Tm is the temperature at which the rate of desorption

is a maximum for a given value of m. By carrying out a

series of experiments using different values of m, the para-

meters can be determined from a straight-line plot of

In[m/RT ] vs. 1/T.

The two major assumptions of the TPD method are an ener-

getically homogeneous solid surface and negligible readsorp-

tion of sample. For chemisorbed species and low surface

coverages, these assumptions are somewhat justified. For

physisorption, however, the highly reversible nature of the

adsorption renders invalid the assumption of negligible re-

adsorption of gas under usual experimental conditions. This

was shown by carrying out TPD of physisorbed gases in the

laboratory. The TPD analysis gave results which were totally

unreasonable for the gas-solid pairs studied,showing that the

assumptions of the TPD analysis which result in Equation (2-14)

are invalid for physically adsorbed gases.

To better understand the physisorption process, it is

necessary to examine the relative magnitudes of each of the

terms in Equation (2-10) during the thermal desorption

process. The thermal desorption experiments are carried out

in a continuous flow sorptometer described in Chapter III,

and it is sufficient at this point to state that the typical

time necessary for the desorption process is one minute.

This allows calculation of the relative magnitude of each

term in Equation (2-10). Carbon dioxide is used as a sample


The transient term (vmdO/dt) is estimated by assuming

that the volume adsorbed per area, vm, is 6 x 10-6 moles of

CO2 per square meter, which corresponds to a molecular area

of 25 square Angstroms. The typical time for desorption of

a monolayer is one minute, therefore dO/dt is of the order

of 1/minute, and the magnitude of the transient term is

v de 10-7 moles/m2 s (2-15)
m dt

The adsorption term [ra = pka(1-0)] can be calculated

by two methods (Thomas and Thomas, 1967): collision and

transition state theory. According to the collision theory,

the rate of adsorption ra is

coll = p f()exp(-E /RT)molecules (2-16)
a (2TmkT)1/2 a area-s

where a is sticking coefficient and m is mass of CO2 molecule.

For f(6) = 1 6, Ea z 0, and T = 3000K, the rate becomes

coll 2
r = 850a(l 6) moles/m -s

For coverages less than unity and a reasonable value of a,

the adsorption rate is several ordersof magnitude larger

than the transient term. The transition state theory gives

trans kT f
rra = CgCt(1 6)kT fexp(-Ea/RT) (2-17)

where the concentration in gas phase C is equal to p/kT and

the total surface sites per area is equal to vm. The parti-

tion function for the adsorbed activated complex f' is equal

to or greater than unity, and the solid surface partition

function f can be set to unity. Here F is the partition

function of gas molecules per unit volume. For Ea = 0 and

T = 3000K, the rate of adsorption becomes

trans moles
ra 1.425 x 10 (1 e) moles(2-18)
m sec

where it has been assumed that the gas phase partition function

has only translational and vibrational degrees of freedom.

Again, the rate is several orders of magnitude greater than

the transient form.

The desorption rate is best described by the transition

state theory, and can be written as

trans kT
r = k6 = C f
d ct h exp(-Ed/RT) (2-19)

where fads is the partition function of adsorbed species.

Assuming that f /fads Z 1, the rate for T = 2000K becomes

rtrans= 2.76 x 107 exp(-Ed/RT) (2-20)

The value of the desorption rate as a function of Ed at 2000K

is shown in Table (2-2). It is seen that the desorption rate

is much larger than the transient term even at Ed equal to 9

kcal/mole, which is seldom exceeded in physisorption.

Table 2-2
Desorption Rate as a Function
of Desorption Activation Energy











The theoretical calculations for the adsorbate carbon

dioxide show that the magnitudes of the individual rates of

adsorption and desorption are several orders of magnitude

larger than the magnitude of the transient term for all

temperatures in the range of the thermal desorption

experiments. As a result, the transient term in Equation

(2-10) can be neglected in comparison with the individual

rates of adsorption and desorption, and the transient de-

sorption behavior during therraldesorption is characterized

solely by the adsorption and desorption terms, which result

in Langmuir's isotherm, Equation (2-11). There exists,

therefore, at all times during the thermal desorption a

'dynamic equilibrium' between the free gas phase and the

gas adsorbed on the solid surface. Because the transient

term is small, the value of the surface coverage 6 at any

instantaneous temperature and pressure is not far removed

from the equilibrium value of surface coverage given by the

Langmuir isotherm at the instantaneous temperature and pres-

sure, and the Langmuir isotherm therefore gives an accurate

representation of the thermal desorption behavior.

To examine the dynamic equilibrium in more detail,

Equation (2-10) can be solved for a step change in tempera-

ture or pressure to give

k p
(t) = a [1 exp(-bt)] + O exp(-bt) (2-21)
(d + ka


b = (kaP + kd)/Vm


This equation describes the relaxation of 8 from the initial

value 6 to the equilibrium value given by the Langmuir

isotherm. For the values of k and kd determined above, the
a d
exponential term exp(-bt) decays to zero very rapidly, in

the order of 10- to 106 seconds. Thus as temperature and

pressure change during thermal desorption, the value of 6

will remain very close to the equilibrium value. This obser-

vation of rapid decay of the transient term has also been

made by Golka and Trzeblatowska (1976) and Brunauer (1943),

who stated that the half time for equilibrium coverage to

be reached is always less than the average residence time

of an adsorbed molecule on the surface, which is of the
order of 10 seconds.

It is seen that the instantaneous value of 6 during

thermal desorption is described by the Langmuir isotherm,

and therefore depends only on the instantaneous temperature

and partial pressure of the system. Furthermore, if the

partial pressure of adsorbate can be held constant during

the thermal desorption, the value of surface coverage will

depend only on temperature. Experiments performed in the

laboratory using a continuous flow sorptometer in which

partial pressure is held constant have verified these

postulates: the coverage at constant partial pressure is

a sole function of temperature, and is independent of the

heating rate dT/dt during desorption. The desorption be-

havior can then be modeled in this final form for experi-

ments carried out at constant partial pressure:

pk (T)
6 = (T) (T) + kd(T) (2-23)
ka(T + k(T)

As discussed earlier in this chapter, the adsorption

behavior of the monolayer on the solid surface character-

izes the gas-solid interactions at the surface. It is seen

from the preceding derivation, therefore, that the gas-solid

interactions can be totally described by the generation of

the functional dependence of fractional coverage on tempera-

ture, since the adsorption behavior is fully described by

the surface coverage as a function only of temperature.

The problem of characterizing the transient desorption of

physisorbed gases therefore reduces to one of generating a

curve of 6 vs. temperature from the thermal desorption ex-

periments, and analyzing this curve to obtain the information

desired, such as heat of adsorption. The remainder of this

research report will focus on the application of the thermal

desorption model to single surface characterization and cata-

lyst area measurement.

In conclusion, it must be noted that there are many

assumptions necessary to arrive at the final result of sur-

face coverage depending only on temperature. Most are in-

volved in the derivation of the Langmuir isotherm, which is

the basis of this model. These assumptions include an ideal

gas phase, immobile adsorbed molecules, simple adsorption

kinetics, energetically homogeneous solid surface, and most

importantly, adsorption onto and desorption from a free

surface without any diffusional resistances. The first

three of these assumptions are taken without further consid-

eration to hold. The assumption of a homogeneous solid sur-

face cannot be assumed to hold for even a single solid, and

much less so when two solid surfaces are present as in the

catalyst area measurement. An energetically heterogeneous

surface will change the functional form of the dependence of

6 on temperature, because adsorption will be favored for

sites of higher energy. A modified form of the Langmuir

equation, in which the activation energy of desorption is

a function of 6, is used to model the heterogeneous surface.

The derivation is given in Chapter VI. However, if the

dynamic equilibrium exists during thermal desorption, and

constant partial pressure is maintained, 6 will still depend

solely on temperature regardless of the model used to de-

scribe the adsorption behavior. Furthermore, for the appli-

cation to catalyst surface area measurement only the plot

of 6 vs. temperature is necessary for analysis. Thus the

assumption of an energetically homogeneous solid surface

is not necessary for application to catalyst surface area,

and can be taken into account by a modified Langmuir iso-

therm for heat of adsorption measurements.

The assumption of negligible diffusional resistances

during thermal desorption requires that the solid sample

is configured so as to minimize any intraparticle or inter-

particle diffusion. The types of solid samples studied

and the way the sample is placed in the experimental appa-

ratus are the factors determining the extent of diffusional

resistance. These factors are studied in the following

chapter, and a thorough analysis of the sample configuration

is presented, showing that diffusional resistances are un-

important for a proper sample.

The experimental verification of the assumptions of

dynamic equilibrium and constant adsorbate partial pressure

must be presented for the derived model to be accepted. The

analyses verifying these assumptions will be presented in

the following chapter, after a thorough description of the

experimental apparatus and procedure are given.

In conclusion, it is recognized that the basis of this

model, the Langmuir kinetic equation and Langmuir isotherm,

are not the work of this author. The theory of Langmuir

is the most widely used in adsorption, and the isotherm

established by the adsorption-desorption equilibrium was

one of the first analytical expressions describing adsorp-

tion behavior. The originality of this work is the contin-

uous application of the Langmuir isotherm to the thermal

desorption process. The realization of the dynamic equi-

librium between adsorption and desorption allows the desorp-

tion process to be characterized in a very simple manner.

Moreover, the application of the theory to catalyst surface

area measurement is a very important contribution, which will

lead to further study and use of the thermal desorption of

physisorbed gases. The application of this theory to catalyst

surface area measurement is given in Chapter IV, along with

guidelines for choosing an adsorbate which facilitates. cata-

lyst area measurement.


3.1 Introduction

The theory developed in Chapter II makes it possible to

characterize gas-solid interactions and thus adsorption be-

havior by carrying out the thermal desorption experiments.

The two major assumptions, which are dynamic equilibrium

and constant adsorbate partial pressure, allow the adsorp-

tion to be fully characterized solely by a plot of frac-

tional coverage, 6, vs. temperature for a particular solid

surface. The problem of characterizing adsorption behavior

therefore reduces to one of determining the 0 vs. tempera-

ture curve via the appropriate thermal desorption experiment.

This chapter describes the apparatus, procedure, and methods

of analysis developed for obtaining the thermal desorption 6

vs. T curve used in the adsorption characterization.

All adsorption experiments in this study have been car-

ried out using a continuous flow sorptometer, in which a

mixed stream of carrier gas and adsorbate flow continuously

over a solid sample which is at a measured temperature.

The amount of gas adsorbing or desorbing from the solid

surface is measured as a difference in composition between

the gas stream before and after it has passed over the sample.

Continuous flow sorptometers have been in existence for over

twenty years, and are used both in physisorption and chemi-

sorption studies. They have important advantages over other

types of adsorption apparatus, most notably in ease and effi-

ciency of the experiments. Very precise measurements are pos-

sible with the electrical detecting devices such as the

thermal conductivity cell. Other types of adsorption appa-

ratus such as gravimetric or constant volume systems require

sensitive balances or pressure gauges which are difficult to

use, fragile, and expensive. Continuous flow sorptometers

are low in cost and easy to maintain because of their simple


The experimental procedures developed for measurement

of the 6 vs. T curve have evolved from both the traditional

thermal desorption experiments for BET surface area measure-

ments and the temperature programmed technique described in

Chapter II. The procedure entails the continuous recording

of volume of gas desorbed during the thermal desorption,

and requires only that the solid sample be heated in a mono-

tonic fashion during desorption. Particular detail is given

in this chapter to the actual operation of the instrument,

to assure the acquisition of precise data. The accurate re-

production of the 0 T curve is of primary importance in

thermal desorption, as the application to catalyst surface

area requires the ability to distinguish between similar

e T curves for different solid surfaces.

The method of analysis of the raw data from both the

thermal desorption and BET surface area measurements is

presented, and a sample calculation of actual experimental

data is included for clarity. Finally, the experimental

justification of some of the assumptions made in the thermal

desorption model is given, along with calculations support-

ing the assumptions. An understanding of the experimental

equipment and procedure is necessary for the verification

of the assumptions, hence their inclusion in this chapter.

3.2 Apparatus

The sorptometer used in this study is a Perkin-Elmer

continuous flow sorptometer which has been modified for the

thermal desorption experiments. The major components of

the sorptometer are valves, flowmeters, and regulators for

individual flow control of carrier gas and adsorbate, a

sample cell in which the powdered solids used as adsorbents

are placed, a thermal conductivity cell for detecting amounts

of gas adsorbed or desorbed, and a calibration valve for in-

jection of known amounts of gas into the flowing stream. A

schematic of the sorptometer is shown in Figure (3-1).

The carrier gas used in all thermal desorption experi-

ments ishelium (Airco Grade 5, 99.999% purity); the adsor-

bates include nitrogen (Airco Grade 5, 99.999%), ethylene

(Matheson, 99.98%), carbon dioxide (Airco Grade 4, 99.99%),

and nitrous oxide (Matheson 99.9%). The carrier and adsor-

bate gases enter the sorptometer from their respective cyl-

inders and pass through a bed of 4A molecular sieves to

remove water. The gases then flow through Fairchild Model

10 low pressure regulators, which reduce the gas pressures

Figure 3-1
Schematic of continuous flow sorptometer


A molecular sieve dryer
B low pressure regulators, 0 2 psig
C shut-off valve
D capillary tube
E gas rotameter
F mixing tank
G cold trap
H TC cell, reference side
I calibration injection valve
J sample cell
K TC cell, detector side
L soap bubble flowmeter


Carrier (10 psig) E

Adsorbate (10 psig)

Figure 3-1. Schematic of continuous flow sorptometer.


from 10 pounds per square inch (psig) to the range of 0 2

psig. The gases then pass through on-off valves and approxi-

mately six feet of .060 inch OD capillary tube, which is the

major constriction to flow in the sorptometer.

The flow rate of each gas is controlled by setting the

pressure at each low pressure regulator, thus fixing the

pressure drop across the capillary tubing and thereby fixing

the flow rate. Because the capillary tube is the major flow

constriction in the sorptometer, the downstream side of the

capillary tubing is essentially at atmospheric pressure, and

the flow rates of the two gases can be set independently.

The flow rates are estimated by setting the low-pressure

regulators at the desires values; the precise measurement

of the flows is done with the 10 ml (milliliter) soap bubble

flowmeter located at the instrument exhaust. In all experi-

ments, the individual flows of carrier and adsorbate were

set to give a total mixed flow rate of 30 to 40 milliliters

per minute.

After the gases pass through the capillary tubes, they

mix and then pass through a cold trap to remove impurities

not adsorbed by the molecular sieves. The coolants used in

the trap are liquid nitrogen for nitrogen as adsorbate, and

dry ice-acetone for ethylene, carbon dioxide, or nitrous

oxide as adsorbates.

The detector used in the sorptometer is a thermal con-

ductivity cell, which measures differences in the composition

of two gas streams by measuring the difference of their ther-

mal conductivities. The detector is a very sensitive

Wheatstone bridge, with four tungsten filaments exposed to

the flowing gases as resistors, and can measure changes in

compositions as small as 0.02%.

The gas stream entering the thermal conductivity (TC)

cell is of fixed composition and at atmospheric pressure.

It is seen from Figure (3-1) that this mixed stream flows

through one side (reference) of the TC cell, through the

sample cell, and then through the other side (detector) of

the TC cell and out the instrument exhaust. Thus the ther-

mal conductivity cell measures the difference in composition

of the same gas stream before and after it passes through

the sample cell. The difference in composition represents

the amount of gas adsorbing or desorbing from the sample

cell at a given instant. This difference in composition is

converted to an electrical output and plotted on an inte-

grating strip chart recorder (ImV full scale). The area

under the output signal is proportional to the total volume

of gas desorbed from the solid sample during thermal

desorption. The proportionality constant to convert the

area to volume of gas is determined by injecting a known

volume of adsorbate into the flowing gas stream via the

calibration injection valve, and recording the subsequent

peak on the strip chart recorder. Simple division gives

the proportionality constant. The volumes of gas used for

calibration in our experiments were 0.179 and 0.875 ml.

The sample cell in the sorptometer has been designed

and built to assure that the assumptions made in the theory

of thermal desorption will hold as well as possible, and

to allow easy changing of solid samples in the experiments.

It consists of two vertical coencentric Pyrex tubes of dif-

ferent lengths jointed at the top by a ground glass fitting,

as shown in Figure (3-2). The outer tube is sealed at the

bottom; the powdered sample (100 mg) is placed in the bottom

of this tube and forms a shallow bed approximately 1.0 cm in

diameter and 0.3 cm in depth. The gas stream flows into the

sample cell through the annulus between the two tubes, over

but not through the solid sample bed, and out the inside of

the inner tube. Two microthermocouples (0.020 inch OD) are

placed directly in the solid sample, one near the outer

radius and one directly in the center of the sample bed.

The signals from the thermocouples are recorded on strip

chart recorders; the dual thermocouples allow detection of

thermal gradients in the sample bed.

The outside of the sample cell is wrapped with a high-

temperature Nichrome heating wire to facilitate heating of

the sample. The heating wire is connected to a DC power

supply, through which the voltage and heating rate can be

controlled during the thermal desorption experiment.

The sample cell is immersed into a cold bath during

the adsorption experiments. The cold bath consists of a

Dewar flask, the appropriate coolant, and a thermocouple

to monitor the temperature of the coolant.

All tubing used in the sorptometer, other than the

capillary tubing, is 0.25 inch OD copper or teflon tubing,

joined with Swagelok fittings.

---- Gas outlet

S/ < Gas inlet

Ground glass joint

S/Outer tube

/ Inner tube

Heating wire

SSample bed

Thermocouple sensors

Figure 3-2. Schematic of sorptometer sample cell.

3.3 Procedure

The desired result from the thermal desorption experi-

ments is the fractional coverage of gas adsorbed as a func-

tion of the temperature of the solid sample. The volume of

gas is determined from the area under the thermal conductivity

cell output, and the solid temperature is measured and re-

corded by the microthermocouples. Simultaneous recording of

these outputs, and knowledge of the monolayer volume from

BET experiments, allows the desired curve of fractional cov-

erage e vs. temperature to be calculated and plotted.

To ensure the collection of useful data, a well-defined

experimental procedure is necessary. Of particular impor-

tance in thermal desorption is the output of the thermal

conductivity cell; any drift or instability in the baseline

before or after desorption will induce uncertainties into

calculation of volume of gas adsorbed. The procedure de-

scribed here explains the preparations necessary to ensure

the collection of good data, and is applied to both the

thermal desorption measurements and the BET surface area


3.3.1 Sample Preparation

The samplesanalyzed by thermal desorption are generally

fine powders of relatively low surface area. Sample weights

of 0.1 to 0.5 grams are used in the sample cell; the amount

of sample placed in the cell should allow gas to flow unre-

stricted over the sample and not through it, as shown in

Figure (3-2).

The sample preparation involves weighing a sample to

the nearest 0.1 milligram, placing it into the lower half

of the sample cell, joining the cell, and sealing it with

stopcock grease. The sample is degassed in the sample cell

by heating it to 1500C for 30 minutes in the flowing gas

stream. This degassing removes water and other adsorbed

impurities from the sample. Because physisorption experi-

ments are being carried out, it is not necessary to rigor-

ously "clean" the surface before experimentation, as

impurities at very low surface coverages (< 0.01) will have

little affect on the adsorption behavior. The sample de-

gassing procedure is carried out during the instrument

warm-up, described below.

3.3.2 Instrument Warm-Up

To start an experiment or a series of experiments, the

carrier gas and adsorbate flows are turned on and the approx-

imate composition is set up by adjusting the two low pressure

regulators. The partial pressure of adsorbate in the mixed

stream during thermal desorption must be low enough to assure

that at most a monolayer of gas is adsorbed onto the solid

sample, so that the experiments can be analyzed by the model

given in Chapter II. This partial pressure can be determined

from BET experiments. After the regulators have been set,

the system is allowed to stand for 15 minutes to flush impur-

ities from the cold trap. The cold trap can be placed in hot

water during this period to hasten the purging. Following

this flushing, the appropriate coolant is applied to the

cold trap for removal of impurities during the experiment.

The power is then switched on to the recorders and the ther-

mal conductivity cell to allow them to warm up. The entire

apparatus is allowed to stand for one hour until all flow

rates have stabilized and a steady TC cell output (seen as

a stable recorder baseline) is observed. The adsorption-

desorption cycle of thermal desorption can now proceed.

3.3.3 Adsorption

With the instrument at steady state, the sample cell

wrapped with heating wire (not necessary for use with nitro-

gen) is immersed into the coolant to a depth of about one

inch. The adsorption of gas is recorded on the strip chart

to give an estimate of total gas adsorbed, allowing the de-

sorption cycle to be properly attenuated. The sample temp-

erature and TC cell output are monitored until all three

have reached steady state at the adsorption temperature, Ta

It is necessary at this point to collect data such as the

total flow rate, pressure regulator settings of each gas,

temperature of adsorption, recorder and sorptometer atten-

uations, and so on. At this point the two temperature

recorders and the TC cell recorder are set to the same

chart speed (precalibrated) with the chart drives off, and

the starting positions of the three pens are marked so that

simultaneous recording of volume desorbed and temperature

are assured during thermal desorption.

3.3.4 Thermal Desorption

With the instrument at steady state at the adsorption

temperature Ta, all three recorders are turned on

simultaneously. The power supply to the heating wire is

then turned on to give the desired heating rate (30 to 600C/

min) and the sample cell is immediately removed from the

coolant. The desorption is allowed to proceed until all

gas has desorbed and the recorder baseline again stabilizes.

At this point the power supply is turned off, and the sam-

ple cell is immersed in the coolant to repeat the cycle.

Several cycles are done for each sample studied.

3.3.5 Post-Experimental Measurements

Three additional measurements must be done in order to

analyze the thermal desorption data. First, the TC cell

output, which is a measure of volume desorbed, is inte-

grated by the recorder and the result is given in arbitrary

area units. In order to convert these units to a volume of

adsorbate, a known volume of adsorbate must be injected into

the gas stream via the calibration injection valve, and the

resulting peak used as a calibration to determine the volume

desorbed in thermal desorption. This injection of adsorbate

must take place at the same flow conditions as the experi-

ment, and is done immediately following the thermal desorp-

tion while the sample is at room temperature.

The second piece of information takes into account the

fact that the TC cell is actually measuring the volume of

gas desorbing from the sample at a point downstream from

the sample. Thus, even though the recorders are working

simultaneously, there is a finite length of tubing between

the sample and the TC cell which causes the TC cell output

to "lag" behind the temperature output. This "lag" time

can be measured by immersing the tip of the sample cell

into the coolant for a fraction of a second, and recording

the resulting small adsorption peak on the TC cell output.

By marking the point on the TC cell recorder chart where

the sample cell was immersed, and recording the peak, the

actual lag time can be read directly from the chart. The

measurement of lag time allows the TC cell output to be

shifted with respect to the temperature output so that the

data collected is a true representation of volume desorbed

as a function of temperature.

The final piece of information is the gas phase compo-

sition, which is measured by the soap bubble flowmeter.

This measurement is always deferred until the thermal de-

sorption runs for all samples being studied have been com-

pleted, for it is necessary to shut off one of the gas

flows in order to measure the other. Disturbing the gas

flow rates is not recommended during the thermal desorption

experiments. Once all experiments have been completed, the

total gas flow rate is determined by the soap bubble meter,

and then the carrier gas flow rate is measured after the

adsorbate flow has been shut off. The adsorbate flow rate,

and hence the partial pressure,is determined from the differ-

ence of carrier gas and total gas flow rates.

3.3.6 Modification of Procedures for
BET Surface Area Measurements

The continuous flow sorptometer is also well suited for

total surface area and monolayer volume measurements. The

theory and analysis of data collected in the BET experiments

are well defined. The determination of BET surface area re-

quires the generation of a plot of volume adsorbed on a sam-

ple as a function of the adsorbate partial pressure. Thus

the partial pressure of adsorbate is changed in the experiment.

The experimental procedure for the surface area measurement

is nearly the same as for the thermal desorption at a given

partial pressure, except that a higher heating rate can be

used, the simultaneous recording of volume and temperature

is not necessary, and the lag time need not be determined.

Of course for the surface area measurement, the desorption

must be done at several partial pressures, and the instru-

ment must be allowed to stabilize at each of the partial

pressures beforemeasurements can be made. The most important

difference is that thermal desorption requires the continuous

recording of volume desorbed, while the surface area measure-

ment only requires the total volume desorbed.

3.4 Experimental Data--Analysis
and Sample Calculations

3.4.1 Analysis of BET Experiments

For a given solid sample, the BET experiment must be

carried out to determine the volume of gas necessary to

provide a monolayer coverage on the solid surface, and to

find the partial pressure at which the monolayer is present.

Table 3-1
Experimental Data: BET Experiment

Sample Weight = 0.075 grams

Run 1 2 3

He Regulator Pressure, inches H20 26.2 24.0 21.1
CO2 Regulator Pressure, inches H20 0.5 3.5 5.7

Area of Desorbed Peak 43.5 46.7 69.5
Attenuation of Desorbed Peak xl x2 x2
Area of Calibration Peak 150.2 76.5 77.0
Attenuation of Calibration Peak xl x2 x2
Volume of Calibration Pulse, ml .179 .179 .179
Volume of Adsorbed Gas, ml .052 .109 .162

Total Flow Rate, ml/min 34.5 34.5 34.3
He Flow Rate, ml/min 32.2 29.4 26.4
CO2 Flow Rate, ml/min 2.3 5.1 7.9
Volume Fraction CO2 .065 .147 .232

Total Pressure, mm Hg 760 760 760
Partial Pressure CO2p, mm Hg 49.4 111.7 176.3

Adsorption Temperature, OK 195.9 196.0 195.8
Saturation Pressure, po, mm Hg 851 851 851

p/po .058 .131 .207
p/(v(po p)) 1.19 1.38 1.62

The data collected are the volumes adsorbed at several par-

tial pressures, which are analyzed by plotting the quantity

P/(V(po-p))vs. p/po to find the monolayer volume Vm:

V 1 (3-1)
m m+ b

where m is the slope and b is the intercept of the above

plot. As an example, the complete set of data collected

from the BET experiment to determine the monolayer volume

of carbon dioxide on carbon black is given in Table (3-1).

The partial pressure po of carbon dioxide has been calcu-

lated using Antoine's equation. The monolayer volume of

carbon dioxide was found to be Vm = 3.15 ml(STP) per gram,

occurring at a partial pressure of 0.3 atm (atmospheres).

3.4.2 Analysis of Thermal Desorption

The data collected from the desorption experiments in-

clude strip chart recorder outputs for the two sample temp-

eratures and the TC cell output which is a plot of gas

desorbed as a function of time. From this data, the plot

of fractional coverage vs. temperature is the desired result

for each sample tested.

From the several thermal desorption runs made for each

sample, the run with the smallest baseline drift from the

beginning to the end of a run should be chosen for analysis.

The shift in baseline distorts the measurement of the volume

of gas desorbed,' and must be taken into account in the data

analysis. If it is assumed that the recorder baseline

changes linearly with time, then the contribution of the

baseline shift to the total area recorded by the integrator

can be taken into account along the entire desorption curve.

The desorption curve can be divided into a number (usu-

ally 10 to 12) of intervals, and the area under the desorp-

tion curve can be found in each interval using the integrator

and taking into account the baseline shift. By using the

proportionality constant determined in the area calibration,

the volume desorbed in each interval can be calculated.

These incremental volumes can be summed to give the total

volume desorbed as a function of time for the run. The cor-

responding value of the fractional coverage can be obtained

by dividing the volume desorbed by the monolayer volume de-

termined in the BET experiments. This completes the analysis

of the TC cell output.

Once the value of the fractional coverage has been de-

termined at each of the intervals, the corresponding tempera-

tures of the sample must be determined. The two temperature

outputs are analyzed individually in the following way and

then averaged to give the overall average sample temperature.

To begin, the same intervals marked off on the TC cell output

are marked off on the temperature outputs. Next, the lag

time determined at the end of the experiment is subtracted

from the original times marked off on the temperature chart

to give a new set of times at which the temperatures corre-

spond to the volumes desorbed at each increment on the TC

cell output. This shift of the entire temperature curve

toward the start of the run takes into account the lag

between the sample cell and the TC detector. Once the new

marks have been made, the correct temperatures may be read

off of each chart and averaged to give the overall sample


Thus the fractional coverage of the solid sample and

the corresponding temperatures have been determined at a

number of points during the thermal desorption run. The

curve of 6 vs. temperature can now be plotted.

A sample calculation of the thermal desorption analysis

has been carried out for the thermal desorption of carbon

dioxide from carbon black. The output of the TC cell and

the temperatures are shown in Figure (3-3); these data are

representative of most thermal desorption experiments.

Table (3-2) is a reproduction of the data sheet for the

three thermal desorption runs carried out for this sample;

only Run 3 is shown in Figure (3-3) and only Run 3 is ana-

lyzed to obtain the 6 T curve for CO2 on carbon black.

It should be noted that the partial pressure of CO2 is

approximately 0.1 atm, which is much less than the partial

pressure necessary to form a monolayer coverage on the


The TC cell and temperature outputs in Figure (3-3)

are analyzed at ten discrete times (At = 0.25 min) during

the thermal desorption. The results of the analysis are

shown in Table (3-3). The area under the TC cell output

in each interval (ti -ti_l) is found from the integrator

on the recorder or by counting squares in the interval.



= 0.20


o 0.10


0.5 1.0 1.5 2.0

Time, min



0 -20




0.5 1.0 1.5


Time, min

Figure 3-3. Sample of raw data collected in thermal
desorption experiments.

Table 3-2
Experimental Data: Thermal Desorption

Sample Weight = .1202 grams

Run 1 2 3

He Regulator Pressure, inches H20 26.9 26.9 26.9
CO2 Regulator Pressure, inches H20 1.3 1.3 1.3

Area of Desorbed Peak 278.6 278.3 278.7
Attenuation of Desorbed Peak xlA xlA xlA
Area of Calibration Peak 94.8 94.8 94.8
Attenuation of Calibration Peak x4A x4A x4A
Volume of Calibration Pulse, ml .179 .179 .179
Volume of Desorbed Gas, ml .133 .133 .130

TC Cell Recorder Chart Speed,
inches/min 2.0 2.0 2.0
Temperature 1 Chart Speed,
inches/min 2.0 2.0 2.0
Temperature 2 Chart Speed,
inches/min 2.0 2.0 2.0

DC Voltage to Heater, V 17 17 17

Total Flow Rate, ml/min 36.1
He Flow Rate, ml/min 32.3
CO2 Flow Rate, ml/min 3.8

Adsorption Temperature, OC -77.1 -77.1 -77.0
Lag time, min .135

Table 3-3
Sample Calculation: Thermal Desorption

Time, ti, Area under
min output in
ti- ti-1



Baseline area
in interval
ti ti-l
area units


Area of de-
sorbed gas
in ti- ti_-
area units


Volume de-
sorbed up to
ti, ml
(at 250C)


Time of
0 Temperature





This area does not yet represent the volume of gas desorbing

from the sample, because the shift in the recorder baseline

during the thermal desorption also contributes to the area

under the curve. Because the shift is assumed linear (for

lack of better information) and the area is known at the

beginning (0 units) and end (1 unit/0.25 min) of the run

from the recorder integrator, the contribution of the area

under the baseline in each interval can be calculated and

subtracted from the total area under the TC cell output in

each interval to give the true area which represents the

volume of gas desorbing from the sample. This is shown

in columns 2, 3, and 4 of Table (3-3).

The volume desorbed up to the time t. is found by add-
ing the area of desorbed gas in all intervals up to ti and

multiplying by the proportionality constant determined from

the calibration pulse injection, which is in this case

volume(ml) 0.179 ml (3-2)
area(units) (94.8 units)(4)

It is necessary to take into account the different attenu-

ations when calculating the proportionality constant.

Finally, the value of 6 is calculated by dividing the

amount of gas remaining on the surface at time ti by the

monolayer volume at the same temperature

V -V
t des,tot des,ti
ti = (3-3)
i = V

where V = (3.44 ml/g)(0.1202 g) = 0.413 ml at 25C.

The average value of sample temperature which corre-

sponds to the value of e determined at each ti must now be

found. In this experiment, the lag time was 0.135 min (8

seconds), which meant that the gas desorbed as read at the

TC cell actually desorbed at a time 0.135 minutes earlier.

Thus the temperature corresponding to each ei is found at

a time (ti 0.135) minutes on the temperature charts.

These times are shown in Table (3-3), and the corresponding

temperature which is the average of the two thermocouple out-

puts is shown at each time (ti 0.135) minutes.

Thus the curve of 6 vs. temperature can be found from

the experiments, and use for any desired application. The

calculations are straightforward, and the 6 T curves for

a given gas-solid pair are accurately reproducible for a

wide range of conditions, using the methods given here.

3.5 Verification of Assumptions Made
in the Thermal Desorption Model

With a thorough understanding of the experimental

equipment and methods, it is now possible to address the

assumptions made in the development of the thermal desorp-

tion model. These assumptions have been briefly discussed

at the end of Chapter II, and will be thoroughly examined

here in light of the experimental methods.

3.5.1 Constant Adsorbate Partial Pressure

The sample cell used in the continuous flow sorptometer

is designed to minimize adsorbate concentration gradients in

the vicinity of the solid sample. As gas desorbs from the

sample, it enters the flowing stream, raising the local ad-

sorbate partial pressure in the sample cell before being

swept away to the TC detector. The extent to which the

local partial pressure changes during thermal desorption

determines the validity of the assumption of constant adsor-

bate partial pressure.

For the thermal desorption runs performed in the labor-

atory, the maximum rate of gas desorption during thermal

desorption was 0.18 ml/min. For a total gas flow rate of

35 ml/min, and an adsorbate flow rate of 2.8 ml/min, the

partial pressure at baseline conditions was 0.08 atm. For

the maximum desorption rate, the adsorbate flow rate became

2.98 ml/min, corresponding to a partial pressure of 0.085

atm, an increase of 6%.

The effect of adsorbate pressure on the value of frac-

tional coverage is roughly given by the Langmuir isotherm

S K(T)p (2-11)
1 + K(T)p

A change in adsorbate partial pressure of 6% changes the

value of 6 a maximum of 0.014 at e = 0.5, a change of about

3%. This change of 6 of .014 is within the experimental

uncertainty for a given run. Thus, even for this extreme

case the small change in partial pressure has a negligible

effect on the value of 6, and the assumption of constant

partial pressure is valid for the thermal desorption


3.5.2 Negligible Inter- and Intra-Particle
Diffusion Resistance

The thermal desorption is assumed to take place at a

free surface, above which the gas phase concentration is

the same as the flowing gas stream concentration. For this

to be true there must be no diffusional resistances within

the porous solid particles or within the sample bed itself.

The intraparticle diffusion resistance poses a serious

threat to the validity of the assumption of desorption from

a free surface. Porous particles with micropores and very

high surface areas can have diffusion times (L2/De) on the

order of minutes in extreme cases. For the thermal desorp-

tion studies carried out in this work, only non-porous or

macroporous solids of low surface area and small particle

sizes have been used. Thus diffusion within particles has

been eliminated by a proper choice of sample.

The sample cell has been constructed to minimize any

diffusional effects within the sample bed, by providing

space for a shallow bed of loosely packed particles. The

extent of diffusion resistance can be determined by examin-

ing the extreme case of all gas desorbing instantaneously

from the solid sample. This instantaneous desorption could

be caused by a large step change in temperature from the

adsorption temperature Ta to a high temperature, and results

in a step change in concentration of adsorbate in the sample

bed at the instant of temperature change. If the relaxation

or decay time of the step change in concentration is small

compared to the time of a thermal desorption run, diffusion

within the bed can be justifiably neglected.

The decay of the step change can be examined by solving

the unsteadystate diffusion equation for a one-dimensional

solid. The dimensionless form of the equation is

_c = c (3-4)
T z2 2


T = D t/L2

z = x/L

D = effective diffusivity of adsorbate in packed bed

L = bed depth

The derivation of this equation and the boundary conditions

for a step change in a finite slab are given in Carslaw and

Jaeger (1959, p. 101). The solution is given in graphical

form for the step change in concentration. For a value of

T = 1.0 sec, the concentration in the bottom of the sample

bed (farthest from the gas stream) has decrease to only 10%

of the magnitude of the step change above the bulk gas
concentration. For values of D = 0.1 cm /sec and L = 0.3

cm (which are typical sample bed parameters), the value of

T = 1.0 is reached in t = 0.9 seconds. Thus, about 95% of

the gas desorbed during the instantaneous desorption has

entered the gas stream after only one second, signifying

that the rate of diffusion is large. Because the rate of

diffusion is much faster than the rate of thermal desorp-

tion, the effects of diffusion can be neglected in the

thermal desorption.

3.5.3 Dynamic Equilibrium

The existence of a dynamic equilibrium between the ad-

sorption and desorption processes during the thermal desorp-

tion has been shown to be theoretically justifiable, based

on the relative magnitude of the terms in Equation (2- 10).

To verify the dynamic equilibrium, it is necessary to measure

the equilibrium value of 0 at a number of temperatures and

pressures and compare it to the value at the same tempera-

tures and pressures determined from thermal desorption. If

the two values of 6 coincide, then the equilibrium must be

established throughout the thermal desorption. This verifi-

cation has been done experimentally by first running the

thermal desorption in the usual way and obtaining the 6 T

plot, and then carrying out the desorption with the same

sample at the same partial pressure but by step changing

the temperature and allowing the equilibrium value of 6 to

be reached at each step. The value of 6 at each temperature

can be plotted along with the 6 T curve from thermal de-

sorption for comparison. One such plot, for the thermal

desorption of carbon dioxide from alumina, is shown in

Figure (3-4). The discrete values of 0 lie close to the

6 T curves from thermal desorption, and show no deviation

in a particular direction. If the dynamic equilibrium did

not exist during the thermal desorption, the value of 9 at

any temperature would be higher than the equilibrium value

of 0 because of the resulting transient nature of the de-

sorption, and all the discrete points would fall below

1.0 Thermal desorption
Step changes





0 -----------------------------
-80 -60 -40 -20 0 20

Temperature, C

Figure 3-4. Comparison of e T curve from thermal
desorption with equilibrium values of
6 from temperature step changes.

the 6 T curve. The deviations of the discrete points in

Figure (3-4) are solely a result of the difficulty in mea-

suring the small volumes of gas desorbed during the step


This experimental evidence is convincing proof that

the dynamic equilibrium does hold during the thermal

desorption. Further evidence is given by plotting the 6 -

T curves for thermal desorption runs made at different heat-

ing rates. Such curves have been found to be the same within

experimental error. This evidence, and the previous verifi-

cation of negligible diffusion resistances and constant adsor-

bate partial pressure, show that the value of 8 depends only

on the sample temperature, and is independent of the rate or

method of heating the sample, for moderate rates of heating

and relatively small volumes of gas adsorbed. These assump-

tions will not universally hold true, but because the thermal

desorption apparatus, experimental methods, and solid samples

have been carefully chosen, the assumptions do hold up for

the experiments performed in this work.

3.5.4 Bed Isothermality

The Langmuir model assumes that the solid sample is

heated uniformly during the thermal desorption so that no

temperature gradients are present in the sample. This

assumption can be seen not to hold upon examination of

the temperature profiles in Figure (3-3). The two temper-

atures recorded during the thermal desorption, one at the

outside edge and one at the center of the bed, differ by

as much as 100C in some thermal desorption experiments.

This thermal gradient is a direct result of the high heat-

ing rates (30 600C/min) used in thermal desorption.

Fortunately, this temperature gradient within the bed has

been found to be almost the same for all solid samples,

provided the same heating rate is used, so that it has lit-

tle effect when comparing the thermal desorption results

for different solids. Good results are obtained by using

the same heating rate for different solids being studied,

and taking the overall bed temperature to be the average

of the two temperatures recorded.

3.5.5 Negligible Axial Dispersion Between
Sample Cell and Detector

When gas desorbs from the solid sample during thermal

desorption, it must travel through a length of tubing before

being detected in the TC cell. Since the volume desorbed

vs. temperature is of primary interest, the peak recorded

by the TC cell should be identical to the peak evolved at

the sample cell. If there is any axial diffusion or mixing

between the sample cell and detector, the peak recorded by

the detector will be different from the true desorption

peak, giving erroneous results. However, since the typical

time for a desorption run is greater than one minute, and

the time required for gas to flow from sample cell to detec-

tor is only about eight seconds, the concentration gradient

in the tube between cell and detectormust be small in com-

parison with the overall peak and axial dispersion can be

neglected. There can be no gross distortion of the desorp-

tion peak because the time available for diffusion between

cell and detector is much less than the time necessary to

distort the peak by axial diffusion. Therefore, axial

dispersion can be neglected in the thermal desorption


3.6 Summary

The apparatus and procedure for obtaining the 6 T

curve for an adsorbate on a given solid has been outlined

in this chapter. The calculation of the 0 T curve from

the raw data obtained has been carefully done, using a

sample calculation to clarify the calculation.

With a complete understanding of the thermal desorption

apparatus and procedure, the assumptions made in the deriva-

tion of the model describing thermal desorption have been

scrutinized. In some cases the assumptions have been found

to hold in general; in other cases the experimental equipment

and procedure have been tailored to assure that the assump-

tions are valid. Overall, the assumptions have been shown to

hold true, so that the model developed in Chapter II is valid

for describing the thermal desorption experiments.


4.1 Introduction

The surface area of a supported catalyst is perhaps the

most desired parameter in catalyst research. Dispersion and

specific activity, derivable from the knowledge of catalyst

area, are essential for the characterization of catalytic

reactions. There are several established methods of catalyst

area measurement: electron microscopy, x-ray techniques, and

gas chemisorption. A review of the gas chemisorption methods

is provided by Farrauto (1974), and details of the other meth-

ods are provided by Pulvermacher and Ruckenstein (1974). The

utility of these methods has been illustrated for several

catalyst systems given in Chapter I, but there is at this

point in time no universal and reliable method for catalyst

surface area measurements. Such a method of measurement

applicable to all types of catalysts would be of tremendous

practical importance in catalytic research.

The primary objective of the development of the thermal

desorption technique is toward the application to the measure-

ment of catalyst surface area. The development of the tech-

nique was a direct result of the need to measure the catalyst

surface area in the study of the catalytic gasification of

carbon. Through extensive experimentation and refinement,

the thermal desorption method thus developed has been shown

to be applicable to several types of catalysts. Within lim-

itations, primarily in the form that the samples studied can

take, this thermal desorption method should be applicable to

all types of supported catalysts.

The measurement of catalyst surface area by thermal de-

sorption is based on the limited selectivity of certain

physisorbed gases toward certain solid surfaces. The exper-

imental technique examines the adsorption characteristics of

a gas separately on a catalyst (in pure powder or crystalline

form), a support, and a supported catalyst via the thermal

desorption technique. The adsorption characteristics of the

gas on the separate (pure component) catalyst and support

are used to determine the total exposed catalyst area as a

fraction of the total catalyst plus support surface area of

the supported catalyst.

The experimental method consists of a series of thermal

desorption experiments as described in Chapter III. The ad-

vantages of the thermal desorption method over other methods

of catalyst area measurement are several-fold. First, phys-

isorption experiments are inherently easy to carry out, and

show good reproducibility. The sample preparation techniques

are much less rigorous in physisorption than in chemisorption.

Second, the method can be applied to any catalyst-support

system, since gases physisorb on all solid surfaces at temp-

eratures near their liquefaction temperature. All that is

necessary for successful measurement is a selective adsorbate.

Third, the total catalyst area is determined directly from

the experiments. The 'stoichiometry' of physical adsorption

is determined in the experiments, so no additional assump-

tions are necessary to obtain a value for the surface area.

This is in contrast to chemisorption for which knowledge of

stoichiometry is necessary to obtain catalyst surface area.

It must be remembered that the surface area determined

by this method is the total catalyst surface area, not the

number of active sites. While the number of active sites,

obtained by chemisorption, is often desirable in character-

izing catalyst activity, the total catalyst surface area is

usually proportional to the number of active sites, and

therefore also serves as a measure of catalyst activity.

Further, properties of sintering and catalyst dispersion can

only be studied with the knowledge of the total catalyst area.

The theory and experimental results for the measurement

of catalyst surface area are presented in this chapter. The

experiments have been performed on four catalyst-support

pairs. In addition to the thermal desorption catalyst area

measurements, several 'established' methods of catalyst area

measurement have been carried out in an attempt to gain an

independent measure of the catalyst surface area. These

supplementary methods have met with varying degrees of suc-

cess in the verification of the catalyst area by thermal

desorption. Enough evidence has been obtained, however, to

show the general validity of the thermal desorption method.

4.2 Theory

4.2.1 Criterion for Catalyst
Area Measurement

The measurement of catalyst surface area by thermal

desorption requires that the adsorbate distinguish in some

way between the catalyst and support surfaces. The selec-

tivity of the adsorbate toward one or the other of the two

surfaces is a direct result of the different types and mag-

nitudes of the various forces which are responsible for

physical adsorption. The nature of these forces has been

discussed in Chapter II; the relative magnitudes and occur-

rence of the forces is illustrated in Table (2-1) for ad-

sorption onto KC1 (Lenel, 1933). As stated in Chapter II,

the different forces will be present for different types of

gas-solid pairs. Thus the adsorption characteristics of a

gas onto two solid surfaces can differ only if the types and

magnitudes of forces are different on each of the solid sur-

faces, as a result of differences in the two solid surfaces.

It is the difference in these adsorption characteristics

which allows the calculation of the catalyst surface area

using the thermal desorption technique.

As stated in Chapter II, the adsorption characteristics

of a gas onto a solid surface can be fully described by a

plot of fractional coverage, 6, vs. temperature, determined

at constant pressure by the thermal desorption experiment.

Because the dynamic equilibrium is assumed to hold through-

out the thermal desorption, the value of 6 is a function

only of the instantaneous temperature and pressure. At

constant pressure, e becomes a function only of temperature.

With the description of adsorption characteristics given

solely by the e vs. T curve from thermal desorption, it is

clear that any measurement of catalyst surface area which de-

pends on differences in adsorption characteristics must require

that the e vs. T curves for the catalyst surface and the support

surface be different during thermal desorption. Just as the e

vs. T curve is a measure of adsorption characteristics for a

single surface, the differences in the 0 vs. T curves for two

components is a measure of the differences in the adsorption

characteristics of a gas on the two components. Such a differ-

ence in the 6 vs. T curves is absolutely essential if the cata-

lyst area is to be determined by thermal desorption. If there

is no difference in the coverage vs. temperature plots for the

two surfaces, no distinction can be made between adsorption

characteristics on the two surfaces and the method fails. Thus

the difference in the functional form of coverage vs. tempera-

ture of the two components is the necessary and sufficient con-

dition for the successful application of this method for

catalyst area measurement.

The differences in functional dependence can take two

forms, as shown in Figures (4-1) and (4-2). Figure (4-1)

represents the case where the initial value of coverage,

6, are difference for each component, but the two curves are

linearly dependent, differing only by a multiplicative

constant. The second form is shown in Figure (4-2) where

a component 1

component 2

a Temperature

Figure 4-1. Linearly dependent 6 T curves for two
pure components.


a component 2

a Temperature

Figure 4-2. Linearly independent 6 T curves for
two pure components.

the initial values of 8 are different and the curves are

linearly independent. The methods of analysis can be dif-

ferent for the two forms. Expressions for calculating the

catalyst surface area will be developed for both cases.

4.2.2 Choice of Adsorbate

Before the theory for calculating the catalyst surface

area is presented, some thought must be given as to the

choice of an adsorbate for thermal desorption. In the cat-

alyst area measurement, it is necessary to choose an adsor-

bate which will selectively adsorb and distinguish between

a given catalyst and support. Because it is usually de-

sired to study a particular catalyst-support pair, the

only variable which will determine the success or failure

of the thermal desorption measurements is the choice of a

proper adsorbate. The adsorbing gas which gives the maxi-

mum difference in the 6 T curves between the two solid

surfaces should of course be chosen. The maximum differe-

ence in the e T curves allows the maximum accuracy of

measurements in thermal desorption.

While the choice of a suitable adsorbate is usually

made on a trial-and-error basis, an idea of the differences

in types of interactive forces which can be manifested with

the proper choice of adsorbate can help make the selection

process more efficient. Differences in adsorption forces

arise when the adsorbate exhibits significantly large

values of certain properties, such as dipole moment, quad-

rupole moment, and polarizability. Extreme values of such

properties will accentuate certain gas-solid interactive

forces, thus magnifying any differences in properties of

the solid surfaces being studied.

As an example, the adsorption of nitrogen, ethylene,

and carbon dioxide on carbon black and potassium carbonate

has been studied by the thermal desorption method, to iden-

tify differences in the adsorption characteristics of each

of the gases on the two surfaces. The only significant

difference in adsorption characteristics between the two

surfaces occurred with carbon dioxide, which exhibits two

properties that nitrogen and ethylene do not: i) a large

quadrupole moment, and ii) large asymmetry of the directional

polarizabilities of the molecule. The directional polariza-

bilities of the three gases and several others are given by

Ross and Olivier (1964) and are reproduced in Table (4-1).

The directional polarizability of carbon dioxide along its

principal axis is twice the magnitude of the polarizability

along the other two axes, in contrast to nitrogen and ethy-

lene which exhibit only mild asymmetry of the directional

polarizabilities. In addition, nitrogen and ethylene have

small quadrupole moments. It is postulated that properties

such as asymmetry of the polarizabilities and quadrupole

moment are responsible for the differences in adsorption

characteristics of a gas on different solid surfaces. For

instance, nitrous oxide exhibits a large asymmetry in direc-

tional polarizabilities, as shown in Table (4-1), and would

therefore be a possible adsorbate to be used in thermal

Table 4-1
Directional Polarizabilities of Molecules

a 24c3 24 3 24 3
Gas Formula acxlOcm3 2x10 4,cm 3x 024,cm

Carbon dioxide CO2 4.01 1.97 1.97

Nitrogen N2 2.38 1.45 1.45

Ethylene C2H4 5.61 3.59 3.59

Argon A 1.63 1.63 1.63

Ammonia NH3 2.42 2.18 2.18

Nitrous Oxide N20 4.86 2.07 2.07

Sulfur Dioxide SO2 3.49 2.72 5.49

a 1 is along axis of highest symmetry

desorption. It would be a more likely candidate than argon

or ammonia which have nearly symmetrical polarizabilities,

although ammonia also has a significant dipole moment which

must be considered. Gas properties such as dipole moment,

quadrupole moment, and polarizability are the primary infor-

mation for the choice of an adsorbate which maximizes the

differences in adsorption characteristics of the gas on the

two solids during thermal desorption. The choice of an ad-

sorbate can therefore be made more easily by taking these

properties into account.

4.2.3. Monolayer Volume Ratio

The derivation of the expression for the catalyst sur-

face area utilizes the concept of monolayer volume ratios to

aid in the calculations. The monolayer volume ratio for a

given adsorbatee on the ith pure component is defined as

V .
R = i i = 1,2 (4-1)
i V

where V is the monolayer volume of adsorbate from the BET
m, i
experiment, and Vm2 is the nitrogen monolayer volume deter-

mined by BET experiment on the pure component. The nitrogen

monolayer volume is an effective measure of surface area;

thus the monolayer volume ratio gives the area occupied by

one molecule of adsorbate on each of the individual component


The existence of different values of the monolayer volume

ratio for different solid surfaces has been observed in

experiments performed in the laboratory, from the BET runs

using nitrogen and the chosen adosrbate. The monolayer vol-

ume ratios for an adsorbate differ by as much as 30% on dif-

fernt solid surfaces. The difference in the volume adsorbed

per unit area is a result of adsorbate-surface interactions

and adsorbate-adsorbate interactions. For instance, a low

value of the monolayer volume ratio results in a large surface

area per molecule. This implies that there are repulsive in-

teractions between adsorbate molecules on the surface or that

the adsorption site density is low. In the case of a high

value of Ri, the molecules are closely packed on the surface,

indicative of attractive adsorbate-adsorbate interactions.

In general, the relative volume ratio is the parameter in the

theory which takes into account adsorbate properties on the

solid surface.

The existence of monolayer volume ratios is by no means

a theoretical assumption, only an empirical observation.

The above discussion is only a brief justification of their

use, based on arguments which augment the discussion of

physisorption forces earlier in the paper. The point is

that the forces of physisorption determine not only the

strength which which molecules of adsorbate are bound to the

surface, but also the way in which the molecules are packed

onto the surface. The use of monolayer volume ratios allows

one to avoid assigning a value of the surface area per mole-

cule of adsorbate which must be applied to all surfaces.

4.2.4 Calculation of Catalyst Surface Area

In order to develop the expression for calculating the

catalyst surface area from thermal desorption, several as-

sumptions are necessary. The first is that the dynamic

equilibrium exists individually for each surface. The sec-

ond is that the total volume adsorbed on the support catalyst

is the sum of the volumes adsorbed on the catalyst and support.

Third, and most important, it is assumed that the support and

catalyst surfaces of the supported catalyst are the same as

the pure support surface and the pure catalyst surface. This

is strictly true only if each of the components in the two

component solid has the same surface structure as the pure

component alone. However, unless a component (catalyst)

forms very small crystals (< 50R) or spreads out very thin

on the other component surface, it can be assumed that the

surface structures will not differ greatly for a given com-

ponent, regardless of whether it is pure or in a multicom-

ponent solid. Care must be taken, of course, to prepare the

pure components and supported catalysts in exactly the same

manner (whenever possible) to assure that the surfaces will

be as similar as possible. This assumption of similar sur-

face structures for pure and supported components allows

the thermal desorption e T curves obtained for the pure

components to be used as the 6 T curves for the catalyst

and support in the two-component supported catalyst.

To determine the catalyst surface area, the e T re-

lationships must be obtained for the catalyst, support, and

the supported catalyst from the thermal desorption experi-

ments at the same partial pressure. The partial pressure

must be low enough to assure that there is less than mono-

layer coverage of adsorbate (6 < 1) on both pure components.

Since there is a unique dependence of e on temperature, the

temperature during the thermal desorption experiment can be

increased in any way provided the increase is monotonic.

In addition, the volume of adsorbate occupying a monolayer

coverage per gram of solid must be determined by a standard

BET experiment for both pure catalyst and support, in order

to calculate the fractional coverage for the pure components.

The general expression derived here for the catalyst sur-

face area applies to both the linearly dependent and indepen-

dent curves of 6 T given in Figure (4-1) and (4-2). A

special case is presented following this derivation for the

linearly independent 6 T curves.

The volume adsorbed at any temperature on a two-component

(supported catalyst) surface is given by

Vads(T) = vm,1S1a1(T) + vm,2S262(T) (4-2)

where Vml and vm2 are the volumes of gas adsorbed at mono-
mil m,2
layer coverage on one square meter of pure components 1 and

2. The monolayer volume ratio R. can be expressed as

R. = mi i = 1,2 (4-3)

where v is the volume of nitrogen monolayer per unit area.

Substituting R1 and R2 into Equation (4-2) yields

Vads(T) = m,N2 (R1S1(T) + R2S2 2(T)) (4-4)

The total surface area of the supported catalyst is

St = S1 + S2 (4-5)

from which it follows that

2 1
S= 1 (4-6)
t t

The quantity 9 is now defined as the ratio of gas adsorbed

on the supported catalyst at any temperature to that ad-

sorbed at the initial temperature, Ta

ads a
(T) = (4-7)

Substituting Equations (4-6) and (4-7) into Equation (4-4)


G(T)Vads(Ta) = m,N2St(RI61(T)Sl/St +

R2 2(T)(1-S1/St) ) (4-8)

This is the expression which can be rearranaged to yield

the fractional catalyst surface area Si/St. Since this

equation gives a result at any temperature, the equation

can be integrated over the temperature range of desorption

and retain its validity. The integration cancels the

scatter in the experimental data and gives an average value

of the catalyst surface area over the temperature range.

Integrating and rearranging this equation gives the final


V (T )
ads( a T
V I R2 2
S m,N2
S1 VmN2 (4-9)
St R11 R2I2


T 2
I = (T)dT
S 1
f 2
I2 = 2(T)dT (4-10)

T = 6(T)dT

and Vm,N is the monolayer volume of nitrogen per gram of
supported catalyst, determined from a standard BET experiment.

Here T1 and T2 are the temperatures chosen for integration in

the range of the desorption temperatures, and can take values

over any range where the pure component 6 T curves do not

intersect. Thus the catalyst surface area S1 can be calcu-

lated, since St is known from the nitrogen BET experiments.

The above derivation applies to both functional forms

shown in Figures (4-1) and (4-2), but requires that nitro-

gen BET experiments be performed on the catalyst, support,

and the supported catalyst. These experiments are in addi-

tion to the thermal desorption and adsorbate BET experiments,

and can be quite time consuming. The derivation that follows

is a modification of the previous one, and holds only when

the 6 T curves are linearly independent, as in Figure (4-2).

This modified method does not require that nitrogen BET ex-

periments be carried out for the supported catalyst, if only

the fractional surface area S1/St is desired.

If Equation (4-2) is evaluated at the initial temperature

of desorption, Ta, the definition of 6(T) given in Equation

(4-7) can be written

6(T) = Vads(T)/Vads(T)

= (R1S161(T) + T2S2 2(T))/(R1S119(Ta) +

R2S2 2(Ta)) (4-11)

If the numerator and denominator are divided by St and Equation

(4-6) is substituted into (4-11), the result can be rearranged

and integrated over the desired temperature range to yield the

desired expression for linearly independent 6 T curves.

S1 R22 R2 a a
1 22 2 = 6.(T ) (4-12)
a a + 1 1 a
t (R1j R22 R1 + R 2

This result applies to the 6 T curves shown in Figure (4-2),

and does not require that the nitrogen BET experiment be per-

formed on the supported catalyst in order to determine the

quantity S1/St. This expression is particularly useful in

the characterization of several supported catalysts of the

same catalyst and support but of different loadings of dis-

persion, where comparisons of catalyst area are of primary

interest. However, to find the actual catalyst area S1

the nitrogen BET experiment must be performed to obtain St,

after which S1 can be calculated.

In summary, Equations (4-9) and (4-12) essentially rep-

resent the level rule for the fractional surface areas SI/St

and S2/St. Equation (4-9) can be used for all two-component

systems shown in Figures (4-1) and (4-2) once all the neces-

sary experimental data have been obtained. Equation (4-12)

can be used when the 6 T curves are linearly independent,

with the advantage that relative information among the same

types of catalysts can be obtained without the need for nitro-

gen BET experimentation on each sample. However, calculations

using Equation (4-12) rely on the linear independence of the

6 T curves, and become very sensitive to small changes in

61 or 62 as the difference in functional forms between 61 vs.

T and 62 vs. T decreases. In all cases, the accuracy and

reproducibility of the method increase as the difference in

the 6 T curves increases.

4.3 Results

The measurement of the total catalyst surface area using

the thermal desorption technique has been carried out with

the continuous flow sorptometer described in Chapter III.

The experimental results for four catalyst-support pairs are

presented in this section for the adsorbates nitrogen, car-

bon dioxide, and ethylene.

In addition, many "established" methods of catalyst area

measurement have been applied to the supported catalysts ana-

lyzed by the thermal desorption, to verify the catalyst sur-

face area measurements made by thermal desorption. These

methods include x-ray studies, electron microscopy, and

chemisorption. Some or all of these methods have been applied

to each of the catalyst-support pairs in an attempt to obtain

an independent measure of catalyst surface area for comparison

with the thermal desorption results. Because the thermal de-

sorption method presented here is an original and untested

method, much work has been done using the established methods

to measuring catalyst area, in order to give positive proof

of the validity of the thermal desorption technique. This

verification is absolutely essential if the thermal desorption

method is to become widely accepted as a reliable method for

catalyst surface area measurement.

The four catalyst-support pairs which have been studied

by thermal desorption are carbon black and K2C03, carbon black

and silver, alumina and silver, and alumina and platinum.

The information necessary for each of the systems is the total

surface area measured by nitrogen BET experiment for each pure

component and each supported catalyst, the monolayer volume

of adsorbate by BET experiment for each pure component, the

6 T curves from thermal desorption for each pure component

at a given pressure, and the volume adsorbed vs. temperature

curves for each supported catalyst at the same pressure.

All of this information is reported in the section for each

catalyst-support pair.

Because the pure compounds have been altered or put

through catalyst preparation procedures to maintain the

similarity of pure and supported component surfaces, the

surface area and volumes adsorbed are different for pure

components which have been put through different preparation

procedures. Thus information for the pure components is pro-

vided for each catalyst-support pair, for each method of

sample preparation.

The complete sets of raw data and references to actual

experiments are given in Appendix I for all systems.

4.3.1 Carbon Black and Potassium Carbonate (K2CO3)

The greatest potential of the thermal desorption method

is the measurement of the area of non-metallic catalysts,

for which a generally accepted method of area measurement is

not available. One such non-metallic catalyst is potassium

carbonate,which is an effective catalyst for steam and hydro-

gen gasification of coal. Until this time no method has been

developed for measuring surface area of potassium carbonate

supported on the carbon reactant. Knowledge of the catalyst

surface area will lead to a better understanding of the cata-

lytic nature of potassium carbonate.

The carbon black used in the experiments consists of

non-porous particles of diameter 0.05 to 0.2p. The carbon

black is graphitized, as evidenced by a hexagonal particle

shape under the electron microscope and the hydrophobic

nature of the surface.

Potassium carbonate was prepared for surface area mea-

surement by grinding 1 to 3 mm crystals overnight in a ball

mill grinder purged with nitrogen. The resulting powder was

sieved to collect particles less than 0.042 mm (-325 mesh)

in diameter, and the collected particles were stored in an

inert or vacuum environment to prevent uptake of moisture

prior to use in the experiments.

Five samples of potassium carbonate impregnated on car-

bon black were prepared by first dissolving the desired quan-

tity of K2CO3 into water, and then adding an equal amount of

acetone to the solution. The prescribed amount of carbon

black was then added to the solution to form a slurry. This

slurry was stirred for 15 minutes and then dried for 24 hours

under partial vacuum at 900C. It was found that 2 ml of

water per gram of carbon gave a good slurry. The addition

of acetone was necessary for the carbon to be wetted. In

addition to the preparation of the impregnated samples,

potassium carbonate was prepared by crystallization from the

acetone-water solution, and pure carbon black was also sub-

jected to the impregnation process in a solution which had

no K2CO3 added. Following preparation, part of each sample

was heated in air at 7000C to oxidize all carbon. The resi-

due was weighed to give the weight percent of potassium

carbonate. The pure carbon black contained only 0.1%

residue. The weight percent of potassium carbonate for the

five samples from the pyrolysis is given in Table (4-3).

The BET experiments have been carried out on carbon

black and K2CO3 with nitrogen and carbon dioxide as

adsorbates. The monolayer volumes per unit weight, BET

surface area, and monolayer volume ratios are given in

Table (4-2). The source from which each pure component

was obtained is also given in Table (4-2).

Table 4-2
Results of BET Experiments
for K2CO3 and Carbon Black



9, m2/g

Carbon Black


6.66 -








Fisher Scientific

Fisher Scientific

Vm, CO2


As an initial investigation, the possibility of using

nitrogen as the adsorbate for the measurement of K2CO3 sur-

face area was examined. The 6 T curves for nitrogen on

carbon black and K2CO3 were obtained by thermal desorption

according to the procedure and analysis outlined in Chapter

III. The 6 T curves for the two components at a nitrogen

partial pressure of 0.1 atm are given in Figure (4-3). It

is seen from the figure that the 8 T curves are almost

identical for the two components, signifying that nitrogen

shows almost no selectivity between the two surfaces.

Nitrogen is therefore unsuitable as an adsorbate for the

thermal desorption experiments, because of its inability

to distinguish between the two surfaces upon adsorption.

The use of carbon dioxide as an adsorbate has proven

to be successful for the measurement of catalyst surface

area. The thermal desorption experiments using carbon diox-

ide as the adsorbate were carried out consecutively for the

two pure components and the five impregnated samples. The

experiments were performed in a single twelve-hour period

after the sorptometer had reached steady state, to assure

that the adsorbate partial pressure was the same for all

samples. In addition, a similar sample weight and heating

rate were used for all samples to minimize unforeseen ef-

fects caused by diffusion or temperature gradients in the

sample bed.

Carbon black

0.8 K2C03




O --------------

-80 -60 -40 -20 0 20

Temperature, OC

Figure 4-3. e vs. T for K^CO3 and carbon black pure
components with nitrogen as adsorbate.

The raw data from the seven thermal desorption runs were

analyzed by the methods given in Chapter III to give the e T

relationships for the pure components and the 0 T relation-

ships for the impregnated samples. The carbon dioxide partial

pressure during the experiments was .105 atm. The 6 T

curves for carbon dioxide on K2CO3 and carbon black are given

in Figure (4-4), and the 6- T curves for four of the impreg-

nated samples are given in Figure (4-5). The 0 T curves

for 1.4% and 4.6% K2CO3 are nearly identical, so only one

is shown in the figure.

The e T curves for the pure components are seen to be

linearly independent, allowing the fractional surface area

of potassium carbonate on each of the impregnated samples to

be calculated without determining the total surface area of

each sample. It was therefore not necessary to carry out the

nitrogen BET experiments on each of the impregnated samples.

The equation used to calculate the fractional areaof K2CO3 is

S RI -R 9a
k cI c c (4-12)
S t a
t (Rk -Rca-RI +R I
tk c c kk c c

where the values of the monolayer volume ratios Rk and Rc are

given in Table (4-2). The integrals I and Ik, and I are

determined numerically using the trapezoid rule with AT

2.50C over the range -750C to 0C. The values of 6a and

0a are determined from the total volume adsorbed on the pure
components at the start of the thermal desorption. The data

and results for the five impregnated samples are given in

Table (4-3).


SCarbon black

0.8 K2CO3


0.4 -

0.2 -

0-------------------------------------- -
-80 -60 -40 -20 0 20

Temperature, C

Figure 4-4. e vs. T for carbon black and K CO3 pure
components with CO2 as adsorbate.

0.8 0-- 0.40
0 .8 \.\\- ---------- O 1
0 .8 ...................... 0 .10
". \ 0. 15



0.2 "-

0 -------------------

-80 -60 -40 -20 0 20

Temperature, C

Figure 4-5. vs. T for K CO and carbon black with
impregnated samples with CO2 as adsorbate.
Numbers in the key refer to K2CO3 loading,
g K2CO3/g carbon black.

Table 4-3
Thermal Desorption Results
and Carbon Black Impregnated

Catalyst Loading,
g K2C03/g carbon







Weight %
















of K CO3




Ic, Ik, T






















Only the fractional K2CO3 area Sk/St is calculated by

Equation (4-21). In order to calculate the absolute cata-

lyst area, it is necessary to determine the total surface

area St of the impregnated sample by the nitrogen BET exper-

iment. Of the five impregnated samples analyzed, the total

surface area was determined only for Sample 4, 16.7 weight %

K2CO3. For this sample, the BET result gave Vm,N2 5.06

ml(STP)/g, and St = 22.1 m2/g. The total surface area of

K2CO3 for Sample 4 is therefore 5.08 m2/g.

With the value for the nitrogen monolayer volume, the

fractional catalyst surface area can be calculated by the

general expression for the catalyst area, Equation (4-9).

adsCO (T )
VmN2 c c
= (4-9)
St RkIk RcIc

Upon applying Equation (4-9) to Sample 4, the resulting

fractional area is Sk/St = .17, which is in fairly good agree-

ment with the value obtained from Equation (4-12). The two

results are determined independently of each other; Equation

(4-12) calculates the area based on the linear independence

of the e T curves for the pure components, and Equation

(4-9) is based on differences in the value of 6 for the two

components. The result given shows the consistency of the


Several analytical methods have been attempted in order

to obtain an independent measure of potassium carbonate sur-

face area and thus verify the results obtained by thermal

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