AN EXPERIMENTAL METHOD FOR MEASUREMENT OF
CATALYST SURFACE AREA BY THERMAL DESORPTION
OF PHYSISORBED GASES
BY
DENNIS JOHN MILLER
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL
OF THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1982
ACKNOWLEDGEMENTS
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 Xray 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 Xray 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.
TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS ....................... ............. ii
KEY TO SYMBOLS ..................................... vi
ABSTRACT ............................................. xii
CHAPTER
I INTRODUCTION .................................... 1
II THERMAL DESORPTION OF PHYSISORBED GAS: THEORY .. 8
2.1 Physical Adsorption ........................ 8
2.2 Nature of Physisorption Forces ............. 11
2.3 Kinetic Model of Thermal Desorption ........ 15
III EXPERIMENTAL EQUIPMENT AND METHODS .............. 27
3.1 Introduction ............................... 27
3.2 Apparatus ................................... 29
3.3 Procedure ............... ....... ............ 36
3.3.1 Sample Preparation .................. 36
3.3.2 Instrument WarmUp .................. 37
3.3.3 Adsorption ......................... 38
3.3.4 Thermal Desorption .................. 39
3.3.5 PostExperimental Measurements ...... 39
3.3.6 Modification of Procedures for BET
Surface Area Measurements .......... 41
3.4 Experimental DataAnalysis 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 IntraParticle
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
iii
Table of Contents continued
Page
CHAPTER
IV CATALYST SURFACE AREA MEASUREMENT BY THERMAL
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
V CATALYTIC GASIFICATION OF CARBON ............... 146
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
VI DETERMINATION OF HEAT OF ADSORPTION BY THERMAL
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
VII CONCLUSIONS AND RECOMMENDATIONS ................ 230
Table of Contents continued
Page
APPENDIX
I EXPERIMENTAL DATA .............................. 235
II COMPARISON OF ISOTHERMAL AND ISOBARIC HEATS OF
ADSORPTION .......................... .... . 243
III CALCULATIONS OF HEAT OF ADSORPTION FROM
LITERATURE EQUILIBRIUM DATA ................... 247
BIBLIOGRAPHY ........................................ 254
BIOGRAPHICAL SKETCH ................................. 257
KEY TO SYMBOLS
Al, A2 areas of sample basket and tube wall, respectively,
in Equation (56)
b parameter defined in Equation (222)
c dimensionless concentration
C concentration
Cij constant in Equation (21)
C basket or pellet centerline methane concentration
c
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 (22)
13
Ea activation_ energy of adsorption
Ed activation energy of desorption
E.. constant in Equation (22)
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
reactant
f solid surface partition function
F local electric field of solid around adsorbing
molecule
FG gas phase partition function per unit volume
F12 parameter in radiation heat transfer, defined in
Equation (56)
h Planck's constant in Equation (217)
h height of sample basket in Equation (57)
HA heat of reaction of Reaction (51)
AH heat of adsorption
a
AH. heat of adsorption of group i of sites
1
AH enthalpy of adsorption in Appendix II
I1, I2 integrals defined in Equation (410), area under
6 T curve
I integral defined in Equation (410), area under
9 T curve
k Boltzmann constant in Equation (27)
k gas phase thermal conductivity, Equation (53)
k first order reaction rate constant in Equation (59)
k adsorption rate constant
a
k adsorption rate constant preexponential factor
ao
kd desorption rate constant
kdo desorption rate constant preexponential factor
K thermal conductivity of sample bed in Equation (515)
K(T) ratio of rate constants, k /kd, in Equation (211)
K ratio of rate constants, kd/ka, in Equation (611)
K ratio of preexponential factors, kdo/kao
Ki ratio of rate constants, kd/ka, for group i of sites
K. ratio of preexponential factors, k do/k for group
i of sites
vii
L depth of sample bed
m linear heating rate in Equation (212)
m mass of adsorbing molecule in Equation (216)
n moles of ideal gas in Equation (A22)
N total number of groups of sites in Equation (68)
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 (24)
r radial coordinate in annulus (Equation (52)) and
in basket (Equation (510))
r.. distance between adsorbing molecule i and surface
atom j
coll
r ol rate of adsorption by collision theory
a
r trans rate of adsorption by transition state theory
a
r trans rate of. desorption by transition state theory
d
R ideal gas constant
R radius of spherical particle in Equation (59)
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
viii
S surface area of pure component from BET experiment
S1, S2 surface area of components 1 and 2 in supported
catalyst (twocomponent 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 (410)
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
rq
Upd orientation and induction potential of a polarizable
dipole
U induction potential between a nonpolar molecule and
an ionic surface
UR repulsive potential between adsorbing molecule and
surface
UT total net potential
V gas volume, Appendix II
V volume adsorbed
ads
Vdes volume desorbed during thermal desorption
Vm monolayer volume of gas per unit weight
W1 weight fraction of component
W weight of carbon
c
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
(216)
a parameter in radiation heat transfer, Equation (56)
n parameter in Equation (26)
sn firstorder isothermal effectiveness factor for
spherical pellets
Pi density of component 1
s0 Thiele modulus for firstorder reaction in a spheri
s cal pellet
V monolayer volume of adsorbate per unit area
8 fractional coverage
ea fractional coverage at temperature T
a
T fraction of volume adsorbed
T permanent quadrupole moment of adsorbing molecule
T dimensionless time
P permanent dipole moment of adsorbing molecule
Abbreviations
Sangstroms
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
AN EXPERIMENTAL METHOD FOR MEASUREMENT
OF CATALYST SURFACE AREA BY THERMAL
DESORPTION OF PHYSISORBED GASES
By
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
xii.
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 levelrule 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 K2CO3catalyzed 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.
xiii
CHAPTER I
INTRODUCTION
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 gassolid 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
predicted.
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 gassolid 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 gassolid 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 nonmetallic 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 gassolid 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 gassolid
interactions.
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 submonolayer 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 twocomponent solid to
be determined, by performance of thermal desorption experi
ments on each pure solid and on the twocomponent 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, Xray 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 nonmetallic catalysts where chemisorption methods
yield little or no information. Other advantages are the
relative ease of experimentation and the nondestructive
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.
CHAPTER II
THERMAL DESORPTION OF PHYSISORBED GAS: THEORY
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 nonbonding 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 gassolid 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, multiplelayered 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 gassolid interactions but gasadsorbed gas
interactions. The magnitude of the gasadsorbed 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 nonspecific 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 adsorptiondesorption behavior of this adsorbed
monolayer characterizes the interactive forces of the parti
cular gassolid 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 adsorptiondesorption
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 gassolid
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 gassolid pairs is what allows measurement
of the catalyst surface area by the thermal desorption
technique.
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 onehalf to ten kcal/mole,
and are divided into three general groups: dispersion
forces, induction forces, and orientation forces. The quan
titative description of these gassolid interactions has
evolved directly from that of the binary gasphase molecular
forces.
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 gassolid interactions. These
forces result from inphase 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 (21)
where C.. is a constant depending on the energy and polariza
1j
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 (22)
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 (23)
d,i ij 13 1ij j ij/rij
Dispersion forces are the predominant forces in the physi
sorption of nonpolar molecules on covalent and metallic
surfaces, and they are significant in all gassolid
interactions.
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.
13
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) (24)
rd 3
8r
The similar expression for a rigid quadrupole is
2
2 2 2 4
U = 4r) 5 (1 + cos + cos48) (25)
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 moleculesolid atom interactions.
Induction forces arise from the induced dipole produced
in both polar and nonpolar 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 (26)
pd 8r3 2
In general, the interaction energy of a nonpolar molecule
with a solid surface, metallic or ionic, can be described
in terms of the local electric field F of the solid:
U1 aF2 (27)
I 2
These induction forces can be significant for both polar
and nonpolar 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
tions:
Aebr
UR = (28)
Crm
Cr
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
forces
U =U +U +U. U
T dispersion orientation induction UR (29)
From these forces, various potential models have been devel
oped, such as the LennardJones 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 nonpolar molecules, dispersion forces alone
describe physisorption behavior. For the adsorption of
nonpolar 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 (21). 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
submonolayer 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 21
Adsorption of Gases on KCla
Dispersion
Gas energy
(cal/mole)
1,500
1,930
2,900
C02
Induction
energy
(cal/mole)
370
550
740
Quadrupole
Inter
action
(cal/mole)
Total
calculated
energy
1,870
2,480
6,340
Experi
mental
heat of
adsorption
2,080
2,620
6,350
aLenel, 1933
bUsing adjusted parameter
mS d _= pk S (16) k S (210)
mo dt ao do
where v is the volume of gas occupying one square meter at
m
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 adsorptiondesorption equilbirum is
established, and the familiar Langmuir isotherm results:
6 = K(T)p (211)
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 (210) 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 (210) to
m de = k (212)
m dT d
where
kd = kdoexp[ Ed/RT] (213)
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 (212). If the derivative with respect to time of
Equation (212) 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 (214)
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 straightline 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 gassolid pairs studied,showing that the
assumptions of the TPD analysis which result in Equation (214)
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 (210) 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 (210). Carbon dioxide is used as a sample
adsorbate.
The transient term (vmdO/dt) is estimated by assuming
that the volume adsorbed per area, vm, is 6 x 106 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 107 moles/m2 s (215)
m dt
The adsorption term [ra = pka(10)] 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 (216)
a (2TmkT)1/2 a areas
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) (217)
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(218)
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) (219)
ads
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) (220)
The value of the desorption rate as a function of Ed at 2000K
is shown in Table (22). 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 22
Desorption Rate as a Function
of Desorption Activation Energy
rd(moles/m2.s)
1.5x104
1006
0.696
5x103
Ed(kcal/mole)
3.0
5.0
7.0
9.0
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
(210) 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 (211). 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 (210) can be solved for a step change in tempera
ture or pressure to give
k p
(t) = a [1 exp(bt)] + O exp(bt) (221)
(d + ka
where
b = (kaP + kd)/Vm
(222)
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
5
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) (223)
ka(T + k(T)
As discussed earlier in this chapter, the adsorption
behavior of the monolayer on the solid surface character
izes the gassolid interactions at the surface. It is seen
from the preceding derivation, therefore, that the gassolid
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 adsorptiondesorption 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.
CHAPTER III
EXPERIMENTAL EQUIPMENT AND METHODS
3.1 Introduction
The theory developed in Chapter II makes it possible to
characterize gassolid 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
design.
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 PerkinElmer
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 (31).
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 31
Schematic of continuous flow sorptometer
LEGEND
A molecular sieve dryer
B low pressure regulators, 0 2 psig
C shutoff 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
Exhaust
Carrier (10 psig) E
Adsorbate (10 psig)
Figure 31. Schematic of continuous flow sorptometer.
Exhaust
from 10 pounds per square inch (psig) to the range of 0 2
psig. The gases then pass through onoff 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 lowpressure
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 iceacetone 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 (31) 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 (32). 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 32. 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 welldefined
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
measurements.
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 (32).
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
warmup, described below.
3.3.2 Instrument WarmUp
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 PostExperimental 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 DataAnalysis
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 31
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(pop))vs. p/po to find the monolayer volume Vm:
V 1 (31)
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 (31).
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
temperature.
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 (33); these data are
representative of most thermal desorption experiments.
Table (32) 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 (33) 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
sample.
The TC cell and temperature outputs in Figure (33)
are analyzed at ten discrete times (At = 0.25 min) during
the thermal desorption. The results of the analysis are
shown in Table (33). 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.
0.30
E
4>
= 0.20
0
Fl
o 0.10
0
0
0.5 1.0 1.5 2.0
Time, min
20
0
0 20
0
40
60
80
0.5 1.0 1.5
2.0
Time, min
Figure 33. Sample of raw data collected in thermal
desorption experiments.
Table 32
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 33
Sample Calculation: Thermal Desorption
Time, ti, Area under
min output in
interval,
ti ti1
0.25
0.50
0.75
1.0
1.25
1.50
1.75
2.0
2.25
2.75
2.0
29.7
49.7
69.6
59.5
31.7
18.6
11.1
6.2
3.9
Baseline area
in interval
ti til
area units
0
.1
.3
.4
.5
.6
.7
.8
.9
+2.0
Area of de
sorbed gas
in ti ti_
area units
2.0
29.6
49.4
69.2
59.0
31.1
17.9
10.3
5.3
1.9
Volume de
sorbed up to
ti, ml
(at 250C)
.001
.015
.038
.071
.099
.113
.122
.127
.129
.130
Time of
0 Temperature
Intervals,
min
.312
.278
.222
.143
.075
.041
.019
.007
.003
0
.115
.365
.615
.865
1.115
1.365
1.615
1.865
2.115
2.615
Average
Temper
ature
C
76.2
73.8
68.1
58.2
45
31.3
14
+1.2
+19
+41.2
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 (33).
The volume desorbed up to the time t. is found by add
1
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 (32)
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 = (33)
i = V
m
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 (33), 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 gassolid 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 (211)
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
experiments.
3.5.2 Negligible Inter and IntraParticle
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 nonporous 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 onedimensional
solid. The dimensionless form of the equation is
2
_c = c (34)
T z2 2
where
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
2
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 (34). 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
0.8
0.6
0.4
0.2
0 
I I I I I
80 60 40 20 0 20
Temperature, C
Figure 34. 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 (34) are solely a result of the difficulty in mea
suring the small volumes of gas desorbed during the step
changes.
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 (33). 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
analysis.
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.
CHAPTER IV
CATALYST SURFACE AREA MEASUREMENT
BY THERMAL DESORPTION
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, xray 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 severalfold. 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 catalystsupport
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 catalystsupport
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 (21) for ad
sorption onto KC1 (Lenel, 1933). As stated in Chapter II,
the different forces will be present for different types of
gassolid 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 (41) and (42). Figure (41)
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 (42) where
a component 1
component 2
a
62
T
a Temperature
Figure 41. Linearly dependent 6 T curves for two
pure components.
a
a component 2
T
a Temperature
Figure 42. 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 catalystsupport 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 trialanderror 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 gassolid 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 (41).
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 (41), and would
therefore be a possible adsorbate to be used in thermal
Table 41
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 (41)
i V
m,N2
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
surfaces.
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 adsorbatesurface interactions
and adsorbateadsorbate 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 adsorbateadsorbate 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 twocomponent 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 (41) and (42). A
special case is presented following this derivation for the
linearly independent 6 T curves.
The volume adsorbed at any temperature on a twocomponent
(supported catalyst) surface is given by
Vads(T) = vm,1S1a1(T) + vm,2S262(T) (42)
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
1
R. = mi i = 1,2 (43)
where v is the volume of nitrogen monolayer per unit area.
m,N2
Substituting R1 and R2 into Equation (42) yields
Vads(T) = m,N2 (R1S1(T) + R2S2 2(T)) (44)
The total surface area of the supported catalyst is
St = S1 + S2 (45)
from which it follows that
2 1
S= 1 (46)
S S
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
a.d
ads a
(T) = (47)
Substituting Equations (46) and (47) into Equation (44)
gives
G(T)Vads(Ta) = m,N2St(RI61(T)Sl/St +
R2 2(T)(1S1/St) ) (48)
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
result
V (T )
ads( a T
V I R2 2
S m,N2
S1 VmN2 (49)
St R11 R2I2
where
T 2
I = (T)dT
S 1
T
f 2
I2 = 2(T)dT (410)
1
T2
jT2
T = 6(T)dT
1
and Vm,N is the monolayer volume of nitrogen per gram of
m,N2
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 (41) and (42), 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 (42).
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 (42) is evaluated at the initial temperature
of desorption, Ta, the definition of 6(T) given in Equation
(47) can be written
6(T) = Vads(T)/Vads(T)
= (R1S161(T) + T2S2 2(T))/(R1S119(Ta) +
R2S2 2(Ta)) (411)
If the numerator and denominator are divided by St and Equation
(46) is substituted into (411), 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 ) (412)
a a + 1 1 a
t (R1j R22 R1 + R 2
This result applies to the 6 T curves shown in Figure (42),
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 (49) and (412) essentially rep
resent the level rule for the fractional surface areas SI/St
and S2/St. Equation (49) can be used for all twocomponent
systems shown in Figures (41) and (42) once all the neces
sary experimental data have been obtained. Equation (412)
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 (412) 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 catalystsupport 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 xray studies, electron microscopy, and
chemisorption. Some or all of these methods have been applied
to each of the catalystsupport 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 catalystsupport 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
catalystsupport 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 catalystsupport 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 nonmetallic catalysts,
for which a generally accepted method of area measurement is
not available. One such nonmetallic 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
nonporous 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
acetonewater 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 (43).
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 (42). The source from which each pure component
was obtained is also given in Table (42).
Table 42
Results of BET Experiments
for K2CO3 and Carbon Black
Component
Vrn,N2
ml(STP)
g
9, m2/g
Carbon Black
K2C03
6.66 
3.15
.113
.118
2.91
.08
.47
.62
Fisher Scientific
Fisher Scientific
Vm, CO2
ml(STP)
g
Source
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 (43). 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 twelvehour 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.
1.0
Carbon black
0.8 K2C03
0.6
0.4
0.2
O 
80 60 40 20 0 20
Temperature, OC
Figure 43. 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 (44), and the 6 T curves for four of the impreg
nated samples are given in Figure (45). 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 (412)
S t a
t (Rk RcaRI +R I
tk c c kk c c
where the values of the monolayer volume ratios Rk and Rc are
given in Table (42). 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
c
components at the start of the thermal desorption. The data
and results for the five impregnated samples are given in
Table (43).
1.0
SCarbon black
0.8 K2CO3
0.6
0.4 
0.2 
0 
I I I I I I
80 60 40 20 0 20
Temperature, C
Figure 44. e vs. T for carbon black and K CO3 pure
components with CO2 as adsorbate.
1.0
0.20
0.8 0 0.40
0 .8 \.\\  O 1
0 .8 ...................... 0 .10
". \ 0. 15
0.05
0.6
0.4
0.2 "
0 
80 60 40 20 0 20
Temperature, C
Figure 45. 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 43
Thermal Desorption Results
and Carbon Black Impregnated
Catalyst Loading,
g K2C03/g carbon
0
.015
.05
.10
.20
.40
Weight %
K2CO3
0
1.4
4.6
10.1
16.7
26.8
100.0
Vads,CO2
ml(STP)
g
1.013
1.125
1.110
1.035
.966
.885
.067
of K CO3
Samples
a.
.322
.593
Ic, Ik, T
7.05
22.3
22.3
24.2
27.7
25.7
21.6
Sample
Carbon
1
2
3
4
5
K2CO3
Sk/St
.01
.01
.07
.21
.13
Only the fractional K2CO3 area Sk/St is calculated by
Equation (421). 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 (49).
adsCO (T )
V I R I
VmN2 c c
= (49)
St RkIk RcIc
Upon applying Equation (49) to Sample 4, the resulting
fractional area is Sk/St = .17, which is in fairly good agree
ment with the value obtained from Equation (412). The two
results are determined independently of each other; Equation
(412) calculates the area based on the linear independence
of the e T curves for the pure components, and Equation
(49) is based on differences in the value of 6 for the two
components. The result given shows the consistency of the
data.
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
