Flor rebeca siperstein thermodynamic excess functions for mixture adsorption on zeolites

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THERMODYNAMIC EXCESS FUNCTIONS
FOR MIXTURE ADSORPTION ON ZEOLITES
FLOR REBECA SIPERSTEIN
ADISERTATION
in
Chemical Engineering
Presented to the Faculties of the University of Pennsylvania in Partial
Fulfillment of the Requirements for the Degree of Doctor of Philosophy
2000
Alan L. Myers, Su
Uvmond/J. Gone. Supervisor ofRaymond/J. Gone, Supervisor of Dissertation
Talid R. Sinno, Graduate Group Chairperson

UMI Number 9965568
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To my father's memory, he would have been proud of this.
To my mother and her contagious love for science.

ACNOWLEDGMENTS
I acknowledge with personal and professional gratitude my advisor Professor Alan L.
Myers, whose support helped me thorough difficult times. His guidance and constant
encouragement made this work not only possible, but also an enjoyable quest. I thank
him for his patience with my lack of eloquence and for understanding my Spanglish as if
it was English. I sincerely value his example of scholarship. I could not have asked for a
better advisor. Thank you Professor Myers.
A special thanks to my other advisor Professor Raymond Gorte for all his help with the
experimental work and for always having interesting explanations of why the equipment
was not working properly.
It was an honor to count with Dr. David Olson's help on everything related to zeolites.
His inexhaustible enthusiasm was always like a breath of fresh air. I am grateful to the
members of my dissertation committee, Professors Eduardo Glandt and Don Berry for
having interesting inputs from different perspectives.
I was fortunate to interact with Professor Ornan Talu from Cleveland State University
who was very generous in sharing his simulation code with me. Meeting someone with
such high values and strong passion for good research made me a better person and a
better scientist.
The completion of this thesis would not have been possible without thefinancialsupport
of the Department of Chemical Engineering and the Department of Mathematics at the
University of Pennsylvania. Financial support provided by NSF and Air Products and
Chemicals is gratefully acknowledged.
iii

The invaluable contributions from former members of the Myers group made smoother
my startup in research. Dr. Jude Dunne, for building the calorimeter that was used for this
research, Dr. Scott Savitz for showing me how to use the calorimeter, Dr. Albert Stella
for always being willing to give advice. Christoph Borst and Max Engelhardt for always
being a good sport.
Colleagues and friends made memorable my years at Penn: Dr. Vicki Booker, my first
officemate and a true friend; Angel Caballero, for always listening when I was drowning
in a glass of water and for all the endless discussions about absolutely irrelevant subjects;
Dr. Beatrice Gooding, for her friendship and for tireless constructive criticism to all my
presentations.. Finally, to some very special friends that made me forget about research
once in a while: Dr. Marisa Ramírez Alesón, Dr. Maria Rubio Misas, Dr. Raquel Sanz
and Mar Socas. To Isaac Skromne for 20 years of friendship.
iv

ABSTRACT
THERMODYNAMIC EXCESS FUNCTIONS
FOR MIXTURE ADSORPTION ON ZEOLITES
Flor R. Siperstein
Alan L. Myers and Raymond J. Gorte
Thermodynamic excess functions have been widely used to describe liquid properties be-
cause they quantify deviations from ideal behavior. In this work, thermodynamic excess
functions are used as a tool to understand and predict the behavior of mixtures in micro-
porous materials such as zeolites. The use of excess functions for describing deviations
from ideal mixing in the adsorbed phase differs from liquid solutions in several subtle but
important ways.
Prediction of mixture adsorption is a key factor in the design of adsorption separation
processes. Measuring single-component adsorption properties is easy compared to multi-
component properties. Therefore it is important to have a reliable method of calculating
mixture behavior from pure-component properties. The main obstacle to progress is a
'scarcity of accurate and consistent experimental data over a wide range of temperature
v

and loading for testing theories. Almost no data are available on the enthalpy of adsorbed
mixtures, even though such information is necessary for the modeling of fixed bed adsor-
bers.
A custom-made calorimeter was used to measure mixture properties. Thermodynamic
excess functions such as excess enthalpy (heat of mixing) and excess free energy (activity
coefficients) provide a complete thermodynamic description of the effect of temperature,
pressure and composition variables.
The mixtures studied are described within experimental error by a 3-constant equation,
which is thermodynamically consistent and has the correct asymptotic properties at high
and low coverage for gases adsorbed in zeolites. More importantly, it is shown that pure
component properties such as heats of adsorption and saturation capacity can be used to
predict the magnitude of the non-idealities in mixture adsorption.
Predictions of mixture properties for SF6-CH4 mixtures on silicalite using molecular
simulation agree with experimental measurements. Molecular simulation results show
segregation of SE5 and CH4 molecules in different sections of the silicalite pore network.
Deviations from ideal solution are consequence of a non-uniform composition of the ad-
sorbed phase.
vi

TABLE OF CONTENTS
ACKNOWLEDGMENTS üi
ABSTRACT v
TABLE OF CONTENTS vii
LIST OF TABLES xi
LIST OF FIGURES xiii
Chapter 1
Introduction 1
l.I Adsorption 2
1.2 Adsorbents 5
1.2.1 Zeolites 6
1.3 Thesis outline 9
Chapter2
Adsorption thermodynamics 11
2.1 Heats of Adsorption 12
2.2 Multicomponent adsorption 22
2.3 Empirical models 28
2.4 Conclusions 33
vii

Chapter3
Adsorption Calorimetry..............................................................................................35
3.1 Introduction 36
3.2 Design Criteria 37
3.3 Theory 39
3.3.1 Idealized Calorimeter 39
3.3.2 Practical Calorimeter 42
3.4 Description of Instrument 43
3.5 Thermopile calibration 47
3.6 Spurious Heat of Compression in Sample Cell 48
3.7 RGA calibration 50
3.8 Verification of Adsorption Equilibrium 54
3.9 Determination of Differential HeatsfromFinite Doses 56
3.10 Alternating Dosings of Each Component 59
3.11 Sample calculation 60
3.12 Conclusion 61
Chapter 4
Experimental measurements of adsorption equilibria and heats of adsorption........64
4.1 Materials 66
4.2 Method 69
4.3 Results 70
viii

4.3.1 Single-Gas Isotherms and Isosteric Heats 70
4.3.2 Binary mixtures 78
4.3.3 Ternary mixture 88
4.4 Discussion 92
4.5 Conclusion 104
Chapters
Molecular Simulation of Mixture Adsorption ..........................................................105
5.1 Statistical mechanics 107
5.1.1 Grand Canonical Ensemble 109
-5.1.2 Monte Carlo Simulation 111
5.1.3 Grand Canonical Monte Carlo 113
5.1.4 Radial Distribution Function 118
5.2 Molecular Model 121
5.2.5 Adsorbent-adsorbate interactions 122
5.2.6 Zero coverage properties 127
5.2.7 Adsorbate-Adsorbate 129
5.3 Simulation method 133
5.4 Results and Discussion 137
5.4.1 Pure component 137
5.4.2 Binary Mixture 147
5.5 Conclusion 156
ix

Chapter 6
Conclusions and Future Work ..................................................................................158
6.1 Summary and Conclusions 158
6.2 Future Work 163
References .................................................................................................................165
Appendix 1.................................................................................................................182
Appendix 2 190
x

LIST OF TABLES
Table 1.1 Unit cell composition of industrially important zeolites.................................. 8
Table 2.1 Adsorbe phase heat capacity at high temperature ...........................................18
Table 3.1 Key to Figure 3.1 .44
Table 3.2 Sample calculation of heats of adsorption from alternating dosings A and B of
the pure components. .............................................................................................62
Table 4.1 Properties of the gases studied .......................................................................69
Table 4.2 Constants of Eq. (4.1) for single gas isotherms. P is given in kPa for n in
mol/kg 74
Table 4.3 Constants of Eq. (4.2) for isosteric heats of adsorption of pure gases at 25°C.
Qu is given in kJ/mol for n in molAg. ................................................••••••«•«•••••••••75
Table 4.4 Binary gas mixtures studied.......«.«...««««.......««»«««..«««.»««.«•«»««•«.«78
Table 4.5 Parameters of ABC equation for adsorption of binary mixtures. .»........»...»».83
Table 5.1 General positions for space group Puma»»»»».»»»...»»»» 125
Table 5.2 Lennard-Jones parameters for adsorbate-adsorbate interactions »»».».»»».»131
Table 5.3 Zeolite-adsorbate interaction parameters».»».»..»».„»».»».»»...»»..«»»»»»138
Table 5.4 Parameters for mixtures of SEs and CH» on silicalite for Eq. (2.31). »»«.».»150
xi

Table ALI CO2 on NaX 182
Table A1.2 CO2 on NaX 183
Table A U C2H4 on NaX 183
Table A1.4 C2H4 on NaX 184
Table AL5 C2H4 on NaX 184
Table A1.9 SF6 on NaX 187
Table ALIO SF6 on NaX. 187
Table ALU CR, on silicalite 188
Table A1.12 SF6 on silicalite 188
Table A1.13 SF6 on silicalite 189
Table A2.1 SF6-C2H6 on NaX 190
Table A2.2 C02-C2H8 on NaX 191
Table A2J SF6-CH4 on Silicalite 192
Table A2.4 C2H4-C2H6 on Silicalite 193
Table A2.5 CO2-C2H6 on NaX 194
Table A2.6 CO2-C2H4 on NaX 195
Table A2.7 Ternary equilibrium data for CO2-C2H4-C2H6 on NaX. .„»..»„.»..»„.».„.»196
Table A2.8 Ternary enthalpies of adsorption for CO2-C2H4-C2H6 on NaX ............197
xii

LIST OF FIGURES
Figure 1.1 Density of a fluid near a solid surface...................................................... 3
Figure 1.2 Density of argon adsorbed on TON and VPI zeolite structures at 295 K and 10
kPa. Bulk argon density is given as a reference....................................................... 4
Figure 2.1 Zero coverage isosteric heats of Lennard-Jones spheres on idealized
geometries 19
Figure 2.2 Isosteric heats of adsorption of CO2 on a faujasite model pore with cations of
charges z at different temperatures 21
Figure 3.1 Schematic of the calorimeter and auxiliary equipment 44
Figure 3.2 Picture of the glass sample cell and connections to the pressure head, vacuum
line, dosing loop and RGA leak valve. The glass sample cell is surrounded by
thermopiles (not shown) set into an aluminum heat sink 45
Figure 3.3 Linear correlation of a spurious sensible heat term for adding a dose of gas.
The difference in pressure is the pressure in the dosing loop minus the pressure in
the sample cell before opening the valve 49
Figure 3.4 Effect of pressure on RGA calibration ATof Eq. (3.15) for mixtures of SF6 and
CH4 53
xiii

Figure 3.5 Calibration of the composition for mixtures of C2H4 and C2H6 based on Eq.
(3.16). The calibration is independent of pressure....„.„».»»...„............»».».»»»„»54
Figure 3.6 Loci of loading by alternate paths for mixtures of SFs and CH4. Black circles
and open circles indicate different paths that intersect at point A............................55
Figure 3.7 Selectivity of SF6 relative to CH4 at 21.5°C. Symbols are the same as those in
Figure 3.6 The selectivity at point A is independent of the order of contacting the
components„„...».»..„.......„„.„.„„.„...».....„„.„.».„„.„„„„..»..„„.».»..»».««««..«.56
Figure 3.8 Comparison of the differential heat of adsorption with experimental heats
determined withfinitedoses of gas 58
Figure 3.9 Thermopile response, voltage versus time 60
Figure 4.1 MFI structure (view along 010) 67
Figure 4.2 NaX structure indicating ion positions 68
Figure 4J Isotherms on NaX: CO2 at 293 K, C3H8 at 293 K, C2H4 at 293 K, C2H6 at 293
K, and SF6 and 295 K 72
Figure 4.4 Isotherms on Silicalite. C2H6 at 296 K, SF6 at 298 K, and CH4 at 297 K. Data
from Golden and Sircar for CH» is used to extrapolate at high pressure„„.„.»»»»»73
Figure 4.5 Single component differential enthalpy (isosteric heat) on NaX....................76
Figure 4.6 Single component differential enthalpy (isosteric heat) on silicalite..............77
Figure 4.7 Error in calculated pressure and selectivity plotted in parameter space for the
binary mixture CO2-C2H« on NaX using constants A, fi, and C in Eq. 2.31 »„„..„».81
xiv

Figure 4.8 Experimental and calculated pressure for the systems (A) CO2-C3H8 on NaX;
(B) CO2-C2H6 on NaX; (C) C2H4-C2H6 on NaX; (D) SF6-CH4 on MFI; (E) SE3-C2H6
on NaX; (F) CO2-C2H4 on NaX 84
Figure 4.9 Experimental and calculated gas-phase composition for the systems (A) CO2-
C3H8 on NaX; (B) CO2-C2H6 on NaX; (C) C2H4-C2H6 on NaX; (D) SEs-CH* on
MH; (E) SF5-C2H6 on NaX; (F) CO2-C2H4 on NaX 86
Figure 4.10 Experimental and calculated differential enthalpies for CO2-C2H6 on NaX..
86
Figure 4.11 Experimental and calculated differential enthalpies for CO2 in a CO2-C3H8
mixture adsorbed on NaX 87
Figure 4.12 Comparison of experimental pressure for the ternary system CO2-C2H4-C2H6
on NaX with pressure calculated values „„......„.„.„„„„„„„.„..«..»«..»..»««.««•••«89
Figure 4.13 Comparison of experimental selectivity for the ternary system CO2O) -
C2H4 (2) - C2H6 (3) on NaX with selectivity predicted using IAS (dashed line), and
ABC Eq. (2.31) (solid line) 90
Figure 4.14 Comparison of experimental enthalpy for the ternary system C02(l) - C2H4
(2) - C2H<5 (3) on NaX with predicted values using Eq. (2.27) and Eqs.(2.34)-(2.37).
91
Figure 4.15 Isothermal (295K), isobaric (13.3 kPa) xy diagrams for the systems: (A)
CO2-C3H8 on NaX; (B) CO2-C2H6 on NaX; (C) CO2-C2H4 on NaX; (D) C2H4-C2H6
on NaX; (E) SF6-CH4 on MH; (F) SF6-C2H6 on NaX 94
xv

Figure 4.17 Comparison of infinite dilution differential enthalpies (dashed lines) for the
system CO2-C2H6 on NaX with pure-component heats of adsorption at the same
total loading as the mixture (solid lines).„„.„„»»„„„„„„.„„„„.«..„„„„„„„„„„.„„96
Figure 4.18 Isothermal (295K), isobaric (13.3 kPa) excess enthalpy and excess free
energy for the systems: (A) CO2-C3H8 on NaX; (B) CO2-C2H6 on NaX; (C) C2H4-
C2H6 on NaX; (D) SF6-CH4 on MFI. x is the molefractionof thefirstcomponent
in the adsorbed phase 97
Figure 4.19 Isothermal (295K), isobaric (13.3 kPa) activity coefficients for the systems:
(A) CO2-C3H8 on NaX; (B) C02-C2H6 on NaX; (C) C2H4-C2H6 on NaX; (D) SF6-
CHionMFI 98
Figure 4.20 Excess chemical potential as a function of fractional coverage (6) at the
equimolar composition (xi=0.5) 100
Figure 4.21 Excess enthalpy as a function of fractional coverage (8) at the equimolar
composition (xt=0.5) 101
Figure 4.22 Correlation of constant A¿=A+BT in Eq. (2.31) with pure component
properties. h° is the enthalpy of adsorption (isosteric heat) at the limit of zero
loading; h* is the molar integral enthalpy of adsorption from Eq (4.2) at saturation;
Vc is the molar critical volume.„.....„..„.„„......„..„.„..„....»....«.».«»»»»»««««»»103
Figure 4.23 Correlation of constant C in Eq. (2.31) with pure component properties, mn
is the saturation capacityfromEq. (4.10) 103
xvi

Figure 5.1 Adsorbent in contact with a reservoir that imposes constant chemical
potential, temperature and composition by exchanging particles and energy. Adapted
from Frenkel and Smit (1996) 109
Figure 5.2 Algorithm for Monte Carlo simulation on a grand canonical ensemble for
adsorption from a mixture..»»»»»»»»».»...»»..»».»»»»».»».»»»»»»»»».»»„»»»115
Figure S3 Representation of the SÍO4 tetrahedra»»».».»»„»»»».»»...«.««»»».«...««»123
Figure 5.4 Asymmetric unit cell for MFI structure»»»»»».»»»»»».»»....... 125
Figure 5.5 Representation of a two dimensional grid for nodes where the summations to
calculate the energy are stored.».».»»»....».»».»».»»»»»»....„»...«..»»«.«.«.»»».126
Figure 5.6 Second virial coefficient for methane .„»»„„»».»»»»»».»».».»„.„„„.„»»„131
Figure 5.7 Second virial coefficient for SF6».«».»»»»»»»»»»»»».««»»»»»»»»»»»"»132
Figure 5.8 Single component isotherms. Experimental measurements are white symbols
and simulation results are black symbols ......„„.„„.„„»»»»»..»»».».».»»»»»».»»137
Figure 5.9 Single component heats of adsorption. Experimental measurements are white
symbols and simulation results are black symbols. ».»»»»»»„».»»»»»»»»»».»»»138
Figure 5.10 Probability distribution on (a) pure SF6, and (b) pure CH4 at 298 K and
loadings of approximately 4 molecules/unit cell. Black regions represent the volume
of the pore network where there is a probability of 90% to find an adsorbed
molecule, white spheresrepresenttheremaining10%. »»»„».»»»».»»».»»»»«««140
Figure 5.11 Distribution for pure SF6 and pure CH» along the straight channel in
silicalite, for approximate loadings or 4 molecules/unit cell..............................„..141
Figure 5.12 Pure SF6-SF6 radial distribution function».».»..»».»..»»...».. 142
xvii

Figure 5.13 Pure CH4-CH4 radial distribution function 142
Figure 5.14 Approximate distance of 5.2 Â: (a) distance between an intersection and the
center of the straight channel (b) distance between an intersection and the center of
the sinusoidal channel 144
Figure 5.15 Approximate distance of 7.9 Â: distance between the straight channel and
the sinusoidal channel 144
Figure 5.16 Approximate distance of 10.5 A: (a) distance between two intersections, (b)
distance between two straight channel sections, (c) distance between two sinusoidal
channels................................. 145
Figure 5.17 Approximate distance of 12.2 Â: (a) distance between straight and sinusoidal
channel, (b) between intersections of different straight channels, and (c) between
two sinusoidal channels................... 145
Figure 5.18 Approximate distance of 13.4 Â: distance between an parallel straight
channels in the [001] direction 146
Figure 5.19 Gas-gas dispersion energy contribution for pure components 147
Figure 5.20 Comparison between experimental and simulatedresults:(a) total loading of
SF6(1) and CH4(2) on silicalite, (b) adsorbed phase mole fraction 148
Figure 5.21 Excess chemical potential as a function of spreading pressure 149
Figure 5.22 Individual enthalpy of adsorption in a mixture of SEs and CH» on silicalite
obtained from simulation...................»».»»..».»».......» 150
Figure 5.23 Probability distribution of: (a) SF6, and (b) CH4 in an almost equimolar
mixture of approximately 4 SEs and 4 CH4 molecules/unit cell, at 298 K and 100
xviii

kPa (yt=0.035, xi=0.56). Black spheresrepresentthe volume of the pore network
where there is a probability of 90% tofindan adsorbed molecule, white spheres
represent the remaining 10%. ...........„..»„„.„...„..........„„....».........«.„„„„«...».»151
Figure 5.24 Probability distribution along the straight channel for SF6and CH4 in
silicalite, at 298 K and 100 kPa (yi=0.035, xi=0.56). Solid line is SF6, dashed line is
CH4 152
Figure 5.25 Composition along the straight channel for a mixture of SEs - CH» on
silicalite at 100 kPa and 298 K (y,=0.035, x,=0.56) 153
Figure 5.26 SE5-SE3 radial distribution function in a binary mixture «—155
Figure 5.27 CH4-CH4 radial distribution function in a binary mixture 155
Figure 5.28 SE5-CH4 radial distribution function 156
xix

Chapter 1
Introduction
When asked about the most important technology for the chemical process industries,
most people might assume chemical reactor design. Actually, separation and purification
of the products is more likely to be where value is really added. In the last few years, ad-
sorption separation technologies have become increasingly important. On-site gas gen-
eration is possible, instead of purchasing liquefied gases [Crittenden and Thomas, 1998].
The synthesis of microporous materials has played an important role in the development
of new adsorption technologies. Perhaps the most fundamental issue in tailoring porous
materials is the nature of adsorbent-adsorbate interactions and the relationship between
these interactions and sorption kinetics and thermodynamics. [Barton, et al. 1999].
For adsorption separation technologies, the essential question is the behavior of adsorbed
mixtures. The prediction of mixture adsorption has been studied from different angles:
classical thermodynamic models, statistical mechanics, molecular simulation, and density
functional theory. Nevertheless, the prediction of mixture adsorbed propertiesremainsan
important problem [Talu, 1998]. Any method used to predict mixture adsorption proper-
tiesrequiresat some point a comparison with experimental measurements to validate the
predictions. The main obstacle to progress is a scarcity of accurate and consistent ex-
1

perimental data over a wide range of temperature and loading for testing theories. Almost
no data are available on the enthalpy of adsorbed mixtures, although such information is
necessary for the modeling of fixed bed adsorbers.
In this thesis, the adsorption of multicomponent systems on microporous adsorbents
(zeolites) was investigated through molecular simulation and experiment. In particular,
emphasis was placed on the prediction of mixture properties taking as a starting point
single component experimental data, because measuring single-component adsorption
properties is easy compared to multicomponent properties. The combined approach of
experiment and molecular simulation allows the interpretation of experimental measure-
ments on a molecular level.
The remainder of this chapter introduces some generalities about adsorption on micropo-
rous materials. Finally, an outline of the thesis is also presented.
1.1 Adsorption
Adsorption is the increase in density (or composition) of a fluid in the vicinity of a solid
surface. Experimentally, the amount adsorbed corresponds to the excess material in a
given volume compared to the bulk phase density that results of the interaction of the
fluid with a solid surface. Figure 1.1 shows the density profile of a fluid adsorbed on a
2

flat surface. The amount adsorbed, represented by the shaded areas, is known as the
Gibbs surface excess amount adsorbed.
"S3
e
&
Figure 1.1 Density of a fluid near a solid surface. Integral of shaded
areas represent the surface excess amount adsorbed. Bulk
density is p? .
In microporous adsorbents, the density of the fluid inside the pores may never approach
bulk density because the pore opening is of molecular size. Figure 1.2 shows the density
of adsorbed argon at 295 K and 10 kPa in two different zeolite structures, TON and VPI.
These zeolites have almost cylindrical pores with pore openings of approximately 5 and
12 Â respectively. The density of argon at the same pressure and temperature in a box
with no adsorbent is also shown as a reference. In the small pore zeolite, the density of
the fluid in the center of the channel is large compared to the bulk density. In contrast, in
the large pore zeolite, the fluid density near the solid surface is higher than in the bulk
phase but in the center of the pore, the fluid density is comparable with the bulk density.
3
Distance
from the wall

I
(a) (b) (c)
Figure 1.2 Density of argon adsorbed on (a) TON and (b) VPI zeolite structures at
295 K and 10 kPa. (c) Bulk argon density is given as a reference.
The Gibbs surface excess amount adsorbed (per unit mass of adsorbent), nf, is defined
as:
nf = nt-VtPg (1.1)
where nt is the total moles contained in dead space volume V, and pg is the density of
the bulk fluid. Surface excess properties can be defined for any extensive quantity, Ai*,
as:
Me
= M-Vtpgmg (1.2)
where M is the value of the extensive property for the system and mg is the molar prop-
erty for the bulk phase. With these definitions, it follows that the surface excess volume
is zero.
**e
* w
'•(*>'m
•f
r ***^»*
[
mr.
Wk
4

This nomenclature becomes confusing when we introduce mixture excess variables.
Mixing excess extensive properties are defined as the difference between the actual prop-
erty value of a solution and the value it would have as an ideal solution holding the inten-
sive properties of the system constant. Throughout this thesis, surface excess properties
will bereferredsimply by the property name; excess will be reserved for properties like
excess free energy and excess entropy of mixing.
1.2 Adsorbents
To be effective in a commercial separation process, an adsorbent must have a large pore
volume, high selectivity, and be stable over long periods.
Adsorbents are usually classified depending on their pore structure or pore sizes. Amor-
phous adsorbents such as activated carbons, silica gels and aluminas contain complex
networks of interconnected micropores, mesopores and macropores. Crystalline or regu-
lar adsorbents such as zeolites and carbon nanotubes contain pores or channels with well
defined dimensions. It is customary to refer to macropores when the pore diameters are
larger than 50 nm, mesopores when diameters are in the range 2-50 nm, and micropores
for diameters that are smaller than 2 nm.
Different properties of an adsorbent can be used for mixture separation. Equilibrium
separations are possible due to the difference in compositions of an adsorbed and a bulk
5

phase at equilibrium. Differences in adsórbate diffusivities are used for kinetic separa-
tions. Molecular sieving is considered an extreme case of kinetic separations, where pore
openings may be too small to allow penetration by one or more of the adsorbates.
Equilibrium separation factors depend upon the nature of the adsorbate-adsorbent inter-
actions (that is, on whether the surface is polar, non-polar, hydrophilic, hydrophobic, etc.)
and on the process conditions such as temperature, pressure and concentration. Kinetic
separations are generally, but not exclusively, possible only with molecular sieve adsorb-
ents such as zeolites and carbon sieves. The kinetic selectivity in this case is largely de-
termined by the ratio of micropore diffusivities of the components being separated. For a
separation based on kinetics, the size of the adsorbent micropores must be comparable to
the dimensions of the diffusing adsórbate molecules.
This work was focused on mixture adsorption in zeolite type materials. Following is a
brief description of the structure and properties of zeolites.
1.2.1 Zeolites
Zeolites are crystalline microporous solids whose primary building unit consists of a
central atom (T atom) tetrahedrally bonded to four neighboring oxygen atoms. T atoms
are generally Si, Al or P, but may include Ga, Ge, B, Be or Ti [Vaughan, 1988]. These
tetrahedra are connected to form a three dimensional crystalframework.This framework
6

endoses a well-defined pore network that may be one, two or three-dimensional. The
pore network consists of an array of almost cylindrical pores or interconnected cages.
The pore size is determined by the number of atoms that form the pore openings. For ex-
ample, pore openings may be formed by rings of 6, 8, 10 or 12 T atoms connected
through the same number of oxygen atoms. Pore openings formed by rings of 5 T atoms
can admit only the smallest molecules such as water and ammonia. Zeolites containing 8,
10, and 12 oxygen atom rings have pore openings of approximately 0.42, 0.57 and 0.74
nm, respectively, and are penetrable by molecules of increasing size. It is possible for
molecules slightly larger than the pore opening to enter the pore network because of vi-
bration of the crystal lattice [Meier and Olson, 1992; Crittenden and Thomas, 1998].
The empirical formula of a zeoliteframeworkis [MynAhOi ' JSÍO2] where x is greater or
equal to 2, and n is the cation valence. Typical compositions of industrially important
zeolites are in Table 1.1. The ratio of oxygen atoms to combined silicon and aluminum
atoms is always equal to two and therefore each aluminum atom introduces a negative
charge on the zeoliteframeworkwhich is balanced by an exchangeable cation. Changing
the type of the cation may change the channel size and properties of the zeolite, including
its selectivity in a given chemical system. In addition, the Si/Al ratio can be varied. Thus,
zeolites with widely different adsorptive properties may be tailored by the appropriate
choice offrameworkstructure, cationic form and Si/Al ratio.
7

Table 1.1 Unit cell composition of industrially important zeolites
Zeolite
NaX
NaA
Silicalite
Na-Mordenite
Unit cell composition
Na«5Al85Sii07O384
Nai2Al|2Sii2048
SÍ96O192
Nag Al8SÍ4o096
Zeolites are widely used commercially as adsorbents in the petroleum and chemical in-
dustries in both bulk separation and purification processes. Adsorptive zeolite applica-
tions have been discussed by Ruthven (1984). More than 100 synthetic zeolite types are
known; the most important commercial adsorbents are the synthetic types A X, Y, syn-
thetic mordenite and their ion-exchanged varieties. Zeolite A is used as a desiccant, to
remove CO2 from natural gas, and for air purification. Zeolite X is used for pressure
swing H2 purification, and bulk separation of air. X and Y zeolites are used for xylene
purification. Silicalite is used for removal of organics from water [Crittenden and Tho-
mas, 1998].
The naming of the zeolites can be rather confusing. Although there is no standard naming
system for the composition of the material, the International Zeolite Structure Commis-
sion specifies 3-letter codes that identify zeolite structure types. While these codes offi-
cially designate a structure, in general they have little relation to the common name. For
example, ZSM-5 (Zeolite Synthesized by Mobil) has a code structure of MFI, but both
8

silicalite (aluminum-free ZSM-5) and TS-1 (titanium silicate), also have MFI type struc-
ture. For X and Y zeolites, all have a FAU type structure, independent of the aluminum
content or the nature of the non-framework cation present.
1.3 Thesis outline
Prediction of mixture adsorption is the key factor in the design of adsorption separation
processes. Measuring single-component adsorption properties is easy compared to multi-
component properties. Therefore it is extremely important to have a reliable method of
calculating mixture behaviorfrompure-component properties.
The purpose of this work is to develop new methods for predicting mixture adsorption
behavior based exclusively on pure component information. Two approaches were used:
experimental and computer simulation.
The fundamental thermodynamic concepts necessary for this study are discussed in
Chapter 2. The thermodynamic description of adsorbed mixtures is presented and the
models used in this work are derived. Definitions for heats of adsorption are presented
and the temperature dependency of the heats is discussed.
As mentioned before, to test any method for predicting mixture adsorption it is necessary
to compare its performance with experimental measurements. Chapter 3 contains a de-
9

tailed description of the combined calorimeter-volumetric apparatus used for the meas-
urement of the properties needed to study mixture adsorption, as well as the operation
procedure of the apparatus.
In Chapter 4, the main results from the experimental measurement of pure-component
and mixture adsorption properties are presented. The mixture properties are correlated
using an excess free energy model which allows us to determine the magnitude of the de-
viations from ideal solution observed in the different systems. By identifying the causes
of the non-idealities it is possible to find a relationship between pure-component proper-
ties and the non-ideality observed in adsorbed mixtures. Thisrelationshipcan be used to
predict mixture adsorption properties.
Molecular simulation was the second approach used to study mixture adsorption. Chapter
5 describes the methodology used for simulating mixtures of SEs and CH4 on silicalite
type zeolite. Comparisons between simulation results and experimental measurements
show good agreement. Molecular simulation results were used to understand the behavior
of mixtures in zeolite type materials from a molecular level. Preferential adsorption in
specific sites, as well as segregation of the adsorbates in a mixture was observed. Pack-
ing effects were observed only at high loadings, resulting in CH» molecules packed be-
tween SE5 molecules.
10

Chapter2
Adsorption thermodynamics
Adsorption separation equipment design requires an accurate description of the behavior
of fluids in microporous adsorbents. The fluid adsorbed on a solid surface constitutes a
distinguishable phase in the thermodynamic sense although there is no physical boundary
that separates the adsorbed phase from the bulk phase. Then, phase equilibrium may be
considered between the adsorbed phase and unadsorbed fluid in a bulk phase.
A rigorous treatment of adsorption thermodynamics can be found elsewhere [Ruthven,
1984]. In this chapter an overview of the thermodynamics of heats of adsorption and
mixture adsorption is presented. The concepts and equations presented in this chapter
constitute a theoreticalframeworkfor the design of the calorimeter (Chapter 3) and will
be used to analyze experimental and molecular simulation results in Chapters 4 and 5 re-
spectively.
This chapter is divided in three sections: section 2.1 deals with the definitions and as-
sumptions for heats of adsorption, section 2.2 contains a general thermodynamic descrip-
tion of mixture adsorption, and finally section 2.3 contains some specific models that
were used for this research.
11

2.1 Heats of Adsorption
The term heat of adsorption is commonly understood as the heat released upon the ad-
sorption of a fluid on a surface. The amount of heatreleasedmay be significant and may
influence the performance of the adsorption process in adiabatic units, as in the case of
gas separation. There are several definitions for heats of adsorption. Hill (1949) defines
integral, differential, isothermal and isosteric heats of adsorption.
2.1.1 Heat or Enthalpy of Adsorptionfor Single Gases
The heat of adsorption used mostfrequentlyin the literature is the isosteric heat, usually
written qtt. Unfortunately the terminology "heat of adsorption" is vague and there is dis-
agreement on the definition of isosteric heat. The fact that several other heats of adsorp-
tion (equilibrium, integral, differential) can be defined adds to the confusion. In this
work, well-defined enthalpy variables are used instead of the conventional terminology of
heats of adsorption. In this section is shown how enthalpies of adsorption are related to
the isosteric heats (qa) under certain special conditions.
Consider first the enthalpy H for n moles of pure gas adsorbed at temperature T. H is the
experimental (Gibbs excess) integral enthalpy measured in Joules per kilogram of ad-
sorbent and n is the experimental (Gibbs excess) amount adsorbed in moles per kilogram
of adsorbent. Let h* be the molar enthalpy of the pure, perfect gas at the same tempera-
ture T. The integral enthalpy of adsorptionrelativeto the perfect-gas reference state is:
12

HA
=H-nh* (2.1)
The molar integral enthalpy of adsorption is:
ftA=«i=«_A.
n n
(2.2)
The differential enthalpy of adsorption is:
hA
=
r
BHA
(dH )
dn
J
9« i*
- Ä ' (2.3)
It should be noted that hA
*• P*even in the case of a pure component. Since the differen-
tial enthalpy is the quantity measured by calorimetry, the molar integral enthalpy is ob-
tained by integration:
* " =
_Jo
hn
dn
(2.4)
Since adsorption is normally exothermic, the integral and differential enthalpies of ad-
sorption (/tA
and hA
) are negative quantities. The enthalpies of desorption are positive
quantities:
13

A0
*-A* (2.5)
Henceforth we shallreferto the positive enthalpies of desorption (AD
and h ) without the
superscriptD
to simplify notation.
Without making any assumptions whatsoever, it can be shown that (Karavias and Myers,
1991):
r - « ^
This exact relation allows the differential enthalpy of desorption to be calculated from
adsorption isotherms. In the special case of perfect-gas behavior in the bulk gas phase,
f=P and Eq. (2.6) simplifies to:
*2
h=RV
r
dnP
I 3T )n
(2.7)
This special case provides a connection with the isosteric heat of adsorption (q«)» for
which there is general agreement that
- • < ¥ ) .
14

when the bulk gas obeys the perfect gas law.
The isosteric heat defined by Eq. (2.8) has not been extended to the general case of a
multicomponent, real gas mixture. Eq. (2.6) for differential enthalpy applies to a real gas
and can be generalized for gas mixtures, as shown in the following section.
2.U Enthalpy of adsorptionfor Mixtures
The integral enthalpy of adsorption in Eq. (2.1) may be extended to a multicomponent
mixture:
//M
=//-X^; (2.9)
Defining total adsorption n, = ^.n,-, the molar integral enthalpy of adsorption is:
h*= = 2*x
ih
i (2.10)
nt nt
where x¡ = n¡/n, is the molefractionof /th component in the adsorbed phase. The differ-
ential enthalpy of adsorption for the ith component is:
hiA
=
f
wA
^
{*ni
)T.n, Va
"/Jr.„,
-h¡ (2.11)
15

As before, the molar integral enthalpy is obtained by isothermal integration of the differ-
ential enthalpy:
XJ0V^
hA
=-i- (2.12)
"t
Since integral enthalpy is a state function, the integration in Eq. (2.12) is independent of
the path.
Continuing as before, the negative enthalpies of adsorption (A/4
and A,- ) arereplacedby
positive enthalpies of desorption (A,0
and A,0
), and the superscript ° is dropped to sim-
plify the notation.
It can be shown that the rigorous extension of Eq. (2.6) for the differential enthalpy of
desorption in a multicomponent mixture is (Karavias and Myers, 1991):
^*r 2
fêk) (2
-13)
In the special case of a perfect gas, the fugacity is equal to the partial pressure in the gas
phase (ft = Py¡). In the following discussion, we shall refer to the differential enthalpy of
desorption (h¡) instead of isosteric heat, with the understanding that the two quantities are
the same for a perfect gas.
16

2.1.3 Heat capacity
Heats of adsorption measured experimentally are typically obtained by differentiation of
isotherms based on Eq. (2.7). Typically, three adsorption isotherms are measured at inter-
vals of 30°C, so that the behavior of the system is determined within a band of 60°C, a
region of ±30°Cfromthe middle isotherm.
Another method is to use a calorimeter [Dunne et al. 1997; Siperstein et al. 1999b; Sircar
et al. 1999]. In general, calorimetric measurements are at a single temperature, so the
temperature dependence within the same band of temperature (±30°C) is provided by
thermodynamic equations linked to the heat of adsorption.
Although it is generally accepted that enthalpies or heats of adsorption are constant over
some range of temperature, little is known about the accuracy of the approximation.
Whether the isosteric heat increases or decreases with temperature is also unknown.
The heat capacity at constant loading is obtained by differentiating Eq. (2.3) with respect
to temperature:
Mn-iw<-dT
(2.14)
//!
Thus the derivative of the isosteric heat with respect to temperature at constant excess
amount adsorbed is the difference of two heat capacities: the perfect-gas molar heat ca-
pacity less the differential heat capacity in the adsorbed phase.
17

Estimates of heat capacity for non-polar gases on homogeneous surfaces by computer
simulation [Engelhardt, 1999] show that these systems have small positive heat capaci-
ties, which means that isosterk: heats increase with temperature. Al-Muhtaseb and Ritter
(1999a) estimated the magnitude of adsorbed phase heat capacities for localized and mo-
bile fluids of monatomic, diatomic and polyatomic molecules. Table 2.1 summarizes their
results. They also found that the contribution of the heat capacity is more important at
low temperatures.
Table 2.1 Adsorbe phase heat capacity at high temperature (La-Muhtaseb and Ritter, 1999a)
Monatomic
Diatomic
Linear-Polyatomic
Localized Adsorption
R/2
3R/2
3R/2 to 2R
Mobile Adsorpition
-R/2
-R/2
-R/2
At the limit of zero loading, isosteric heats can be calculated by differentiating the ad-
sorption second virial coefficient (¿is) with respect to temperature:
Bxs-v{e-UlkT
-)dV (2.15)
18

< 7 í r = *
rflnß
ÍL+kT = --M-
Ue-U
'kT
dV
MT) J {e-W-)dV
+ kT (2.16)
Differential enthalpies (isosteric heats) calculated for Lennard-Jones molecules adsorbed
on a flat surface, in a cylindrical pore and in silicalite type zeolite are shown on Figure
2.1. The isosteric heat increases with temperature and the dimensionless quantity AcJR
is less than unity for these systems, which agrees with the result in Table 2.1 for localized
adsorption of monatomic molecules. It is interesting that the heat increases with tem-
perature and that the increase comes from the IcT term in Eq. (2.16). Thus the first de-
rivative with respect to temperature of the average energy is negative and very small for
homogeneous systems such as Ar or CHt on silicalite at room temperature.
25
20
ô
E
3 15
1o
O
0
__ CH4 on silicalite
cylindrical pore
flat surface
100 200 300 400
Temperature, K
500 600
Figure 2.1 Zero coverage isosteric heats of Lennard-Jones spheres on idealized
geometries. Solid lines are for a flat surface and a cylindrical pore and
dashed line is for silicalite.
19

Results from molecular dynamics (MD) simulation of adsorption of p-xylene on NaY
zeolite [Schrimpf et al. 1995] indicate that the largest contribution to the heat capacity is
the gas-solid interaction, not the gas-gas interaction. Lattice gas models have also been
used [Al-Muhtaseb and Ritter, 1999b] to show that laterat interactions play a small roll in
heat capacities; surface heterogeneity and coverage are more important.
Systems such as CO2 on NaX display energetic heterogeneity induced by high energy
sites adjacent to sodium cations and low energy sites elsewhere in the supercavity. The
isosteric heats on Figure 2.2 was calculated for a spherical Lennard-Jones molecule con-
taining a point quadrupole moment at its center, adsorbed in a smooth spherical super-
cage decorated with cations [Soto and Myers, 1981; Karavias and Myers, 1991b]. The
heat of adsorption decreases with temperature and values of cJR as large as -5 were cal-
culated at low coverage. However, the theoretical heat curve fails to reproduce experi-
mental data for C02 on NaX at 298 K [Dunne et al. 1996b]. Instead of the plateau ob-
served on Figure 2.2, the experimental heats decrease exponentially from 50 to 36 kJ/mol
over the range 0-5 mol/kg. Since the shape of the heat curve on Figure 2.2 is unrealistic,
the large values calculated for heat capacities are questionable.
If the heat capacity en is of order unity (positive for homogeneous systems and negative
for heterogeneous systems), then it can be shown by integration of Eq. (2.8) that the con-
stant isosteric heat approximation over a temperature band of 100 degrees Kelvin (plus or
minus 50 degrees from the isothermal measurements) generates an error of 1% or less in
20

the calculated pressure.
t±
278 K z=0.58
298
^ 2 9 ^ = t = : : = : : d t :
=
198 K
298 K
50 2 3 4
Loading, molecules/pore
Figure 2.2 Isosteric heats of adsorption of C02 on a faujasite model pore with ca-
tions of charges z. Solid symbols are at low temperature and open sym-
bols are at high temperature.
21

2.2 Multicomponent adsorption
Models or correlations for mixed gas adsorption are crucial to the design of adsorptive
gas separation processes. They should be capable of predicting the equilibrium amount
adsorbedfrompure gas isotherms for each constituent in the mixture, within given ranges
of operating temperature and total pressure.
The theories for mixed gas adsorption fall into three general categories:
1. Langmuir type equations and correlations [Hill, 1986] including extensions to
heterogeneous adsorbents, different size adsorbates on homogeneous and hetero-
geneous adosorbents [Nitta, et al. 1984], and statistical mechanics models for ad-
sorption [Ruthven, 1982; Martinez and Basmadjian, 1996].
2. Two-dimensional equation of state [Appet, et al. 1998 and references therein].
3. Potential theory [Grant and Manes, 1966].
4. The ideal adsorbed solution theory [Myers and Prausnitz, 1965] and models de-
rived from it, like heterogeneous ideal adsorbed solution [Valenzuela et al. 1988;
Moon and Tien, 1988], and the multispace adsorbed solution [Gusev, et al. 1996].
5. Non-ideal adsorbed phase models for activity coefficients, incluiding the vacany
solution theory [Suwanayuen and Danner, 1980], and the spreading pressure de-
pendant model [Talu and Zweibel, 1986].
The ideal adsorbed solution theory is constructed on the assumptions of an inert homoge-
22

neous adsorbent. This theory does not require a specific functional form of the pure com-
ponent isotherm, but it requires a constant slope of the isotherm at the limit of zero cov-
erage (Henry's Law regime). Following is a detailed treatment for non-ideal adsorption
that reduces to ideal adsorption when the activity coefficients are unity.
2.2.1 Non ideal Adsorption
For adsorption of a gas mixture containing Nc components, the equilibrium condition is
equality of fugacity in the adsorbed and gas phases:
Pyi^fiXiYi « = 1,2,.../Vc (2.17)
where P is pressure, y and x are mole fractions in the gas and adsorbed phase, respec-
tively, $¡ is the fugacity coefficient of component i in the gas phase, f¡ is the fugacity of
the pure component in its standard state, ) ¡ is the activity coefficient of component i in
the adsorbed phase, which is unity for ideal solutions. The standard state is the surface
potential (<I>) given by
<¡> = -RT¡ ndnf (constant T) (2.18)
Jo
for single-component adsorption. For a perfect gas, fugacity (/) is equal to pressure (P)
and:
23

<P = -RT¡P
ndnP=-RT ^^-dn (constantT) (2.19)
JO Jovdln/iy
For adsorption at temperature T, the surface potential is the chemical potential of the
solid adsorbent relative to its pure state in vacuo at the same temperature.
As shown later, a variable that arises frequently in adsorption thermodynamics is:
m=-— (2.20)
RT
since the surface potential (<&) has units of J/kg, yt has units of mol/kg, the same as
loading.
It is convenient to define the excess chemical potential of the adsorbed solution by:
Nc
p e
= RT^Xiny¡ (2.21)
so that adsorbed-phase activity coefficients are determined by partial-molar derivatives:
24

RTnn = (2.22)
Note that the variables held constant for the differentiation are temperature and ¡p, unlike
the partial molar quantities of solution thermodynamics for which temperature and pres-
sure are fixed. Let the excess reciprocal loading be defined as:
UJ n, yn
a
i
(2.23)
The excess reciprocal loading vanishes for an ¡deal solution. It can be shown [Talu and
Zwiebel, 1986] that Eqs. (2.21) and (2.23) arerelatedby:
(lY Jè/f/FT
UJ [ Bw )
(2.24)
T,x
The prominence of the reciprocal loading variable (I//i) in adsorption thermodynamics
arises from the Gibbs adsorption isotherm, which for single-gas adsorption is obtained
from Eqs. (2.18) and (2.20):
r
ain/i =J_ (2.25)
25

The concept of selectivity id useful to quantify the ability of an adsorbent to target ad-
sorption of one of the components in a mixture. The selectivity of component 1relativeto
component 2 is defined as:
s _ x
/y _ fiYiki
1,2
xi/yi tfn/h
(2.26)
The temperature dependence of the selectivity is given by the temperature dependence of
the fugacities in the standard state, the activity coefficients and the fugacity coefficients.
For the special case of an adsorbed phase in equilibrium with an ideal gas, the tempera-
ture dependence of the selectivity is given by the difference in differential enthalpies of
adsorption of each component in the mixture:
r
aimu> _fain/2>2>
l fiïL/Qil _fa.i-fa.i »zn
< dT
h » "I ar
J 37* RT2
. ar .
The previous equations are well known [Valenzuela and Myers, 1989]. In this work, the
equilibrium equations are extended to the differential enthalpy (isosteric heat) in order to
introduce the temperature variable in a systematic way. For the general case of a multi-
component mixture, a real gas, and a nonideal adsorbed solution, it can be shown from
Eq. (2.13) that the differential heat of desorption of the rth component (A,) is equal to:
26

S-V+^pS^)r.JC
+<
X^-Aj^rfacv»)''
87/ }
y,x
2*fii-
r
B(/nf
I ** )T,x
(2.28)
where
c;=
1 |9lnn°
(nffldtoFT,
The superscripts ° refers to the standard state of pure adsórbate at the same temperature
and surface potential as the mixture. A,0
is the differential heat of desorption of the pure
component and hf is the molar integral heat of desorption of the pure component from
Eq. (2.4).
For the special case of an ideal adsorbed solution, }¡ = 1, (l/ri)e
= 0, and Eq. (2.27) re-
duces to [Karavias and Myers, 1991]:
A,=A?+-L
X^;-(à7-A;)G;
i
(2.29)
27

In the rare case when the differential enthalpy of desorption is constant (independent of
loading), it follows from Eq. (2.4) that hf = h° and ideal solution theory predicts that the
mixture enthalpies are equal to their (constant) pure component values. There are no sim-
plifications of Eqs. (2.27) and (2.29) for the typical case when the differential enthalpy of
the pure gas varies with loading. The empirical approximation that the differential mix-
ture enthalpy is equal to the value for the pure component at the same loading appears to
have no theoretical basis.
2.3 Empirical models
Models for activity coefficients for an adsorbed phase are available in the literature.
Some of them are not thermodynamically consistent. Othersrequireso many adjustable
parameters that a physical interpretation is practically impossible for the model, so it be-
comes an exercise in parameterfitting.The purpose of this work is to present a model of
activity coefficients (excess chemical potential) in the adsorbed phase that can be inter-
preted in terms of enthalpy and entropy of mixing.
2.3.1 ABC equation
The simplest composition dependence for the excess functions is quadratic and a system
with Afie
= A>xXi is called a quadratic mixture (Rowlinson and Swinton, 1982). If in
addition A0 is independent of temperature, then the excess entropy is zero, a definition
close to that of a regular solution (Hildebrand et al. 1970).
28

For an adsorbed quadratic mixture (Valenzuela and Myers, 1989; Talu et al. 1995):
/íe
*A3x,Jc2(l-<"C
*') (2-30)
which assumes that the excess chemical potential is independent of temperature and equal
to the excess enthalpy. A three- constant model of binary adsorption is proposed in this
work. All of the equilibrium properties of the mixture may be calculated from the excess
chemical potential:
fle
=(A + BT)xlx2(-e-Cv
') (2.31)
where A, B, and C are constants. Eq.(2.30) will be referred to as the ABC equation to
emphasize that it contains three constants which are independent of temperature, loading,
and composition. This empirical equation is the simplest possible representation of equi-
librium which obeys all of the limits required of any theory [Valuenzuela and Myers,
1989; Talu et al. 1995], especially thermodynamic consistency and reduction to an ideal
adsorbed solution at the limit of zero loading. Although the excess chemical potential has
a quadratic (symmetrical) form for the composition dependency at constant surface po-
tential, the composition dependence at constant pressure has the complicated asymmetric
form observed experimentally.
29

The exponential dependence upon surface potential (4> = -RTy ) gives the correct as-
ymptotes at zero loading and at high loading. It has been shown previously that the expo-
nential dependence upon surface potential agrees with experiment and molecular simula-
tion from zero loading up to saturation [Talu et al. 1995]. The linear dependence of ex-
cess chemical potential upon temperature implies an enthalpy that is independent of tem-
perature, an approximation consistent with the assumption that the differential enthalpies
("heats") are constant over the temperature range of interest.
The excess reciprocal loading is obtainedfromEq. (2.23):
{${^l/w^™^ <2
-32)
This excess function is required to calculate the total loading (/if) from Eq. (2.24). (1/n)'
is finite at the limit of the zero loading as noted previously [Talu et al. 1995]. Although
this may seem incorrect since loading is calculated for ideal solutions by setting (l/rif =
0, note that Eq. (2.24) has the form (~ - <») as n-»0. Eq. (2.31) predicts that the limit of
(1/ nf is zero at high loading (^ -» ~), which is consistent with the existence of a satu-
ration capacity for loading.
The activity coefficients are given by Eq. (2.22):
30

RT In yi = (A+BT)xj(l - e~c
* ) (i * y) (2.33)
This equation satisfies the requirement that the activity coefficient is unity at the limit of
zero loading (i/t -*0). At high loading (fi -»«), the activity coefficients approach a
constant value corresponding to saturation.
The four partial derivatives in Eq. (2.27) were calculatedfromEqs. (2.31) and (2.32):
T,x
A±BLCe-Crx2
RT J (/*;) (2.35)
B(/n)e
)
BT
y,x
AC -cw
Te x
x
2
RT2
(2.36)
r
31nZL
>
=-l±BLAtX,e-cr
T,x RT
C-xxx2e~ (2.37)
Application of the Gibbs-Helmholtzrelationto Eq. (2.31) yields:
31

I>'=-Á^T -A«w(l--Cr
) (2.38)
Physically, the excess enthalpy is the molar enthalpy of mixing of the adsorbed solution
at constant surface potential. Note that the enthalpy of mixing is independent of tem-
perature for our model, which is consistent with the assumption that differential enthal-
pies (heats) are independent of temperature.
2.3.2 Multicomponent systems
In preparation for a discussion of experimental data obtained for a ternary mixture, the
previous equations for the binary case are next extended to a multicomponent mixture.
Our assumption of a quadratic composition dependence for the excess functions implies
the dominance of pairwise interactions, so the ABC equation for multicomponent systems
(ternary and higher) is additive in the constituent binaries [Prausintz, et al., 1999]. The
excess chemical potential can be written:
. Ne Nc
«e
={ll(A
ü+B
^h4]
-e vW
) (2
-39)
where Aij, B¡¡, and C¡¡ are the binary parameters for the ABC equation and the constants
vanish for i =/. Specifically, for a ternary mixture:
32

p6
= (Al2 + Bl2T)xlx2(l-e-C
»V) +
(A,3 + Bl3T)xlx3[-e-C
^)+ (2.40)
(A23+ß23r)A:2X3(l-e-C
^)
2.4 Conclusions
Two main concepts were treated in this chapter: heats of adsorption and thermodynamics
of adsorption equilibria.
It is convenient to abandon the nomenclature of heat of adsorption, and adopt well-
defined thermodynamic functions such as enthalpy and internal energy. This will prove to
be important in the following chapters to understand the performance of the calorimeter.
The assumption that heats of adsorption are independent of temperature is valid for ho-
mogeneous adsorbents but it may not be a good assumption on heterogeneous adsorbents.
Unfortunately there is little experimental information about the magnitude and sign of
heat capacities in adsorbed phases [Morrison et al. 1951] to compare it with results of
different models.
33

Relationships for non-ideal adsorption equilibira and enthalpy of adsorption were derived
using as a reference the ideal adsorbed solution. A model with three constants (ABC
equation) is proposed for describing non-ideal adsorption equilibria. This equation con-
tains composition, temperature and surface potential dependence of the excess chemical
potential and can be used to calculate activity coefficients in the adsorbed phase as well
as mixture excess properties (reciprocal loading, enthalpy and entropy). The relationship
between mixture excess properties and the parameters in the ABC equation will help to
understand the causes of non-ideal behavior.
34

Chapter 3
Adsorption Calorimetry
Calorimetry has proven to be an accurate and reliable method to measure heats of ad-
sorption [Dunne et al. 1997]. The importance of knowing the heats of adsorption of a
system is because the temperature dependence of the isotherms and selectivity are given
by the single component heats of adsorption and individual heats of adsorption in a mix-
ture, respectively.
Optimal design of pressure swing adsorption (PSA) units for separation of gaseous mix-
tures is based on experimental equilibrium data for loading and selectivity as a function
of pressure, temperature, and composition. The modeling of thermal effects accompa-
nying adsorption and desorption cyclesrequiresan energy balance based on the heats of
adsorption of individual components of the mixture.
Measurements of loading, selectivity, and heats using conventional methods are expen-
sive and difficult. Heats of adsorption of pure gases, which are usually obtained from
isotherms using the Clapeyron equation, are unreliable unless extra precautions are taken
to ensurereversibilityand reproducibility. The calculation of mixture heats from exten-
sions of the Clapeyron equation is impractical [Sircar 1985].
35

This chapter summarizes the design criteria and construction of the combination calo-
rimeter-volumetric apparatus, as well as the procedure developed to study mixture ad-
sorption.
3.1 Introduction
Adsorption calorimetry has been applied extensively to characterize solid adsorbents
[Dios-Cancela et al. 1970], for the characterization of solid acid catalysts by chemisorp-
tion [Parrillo and Gorte, 1992; Chen, et al. 1994], and for studying heterogeneity of zeo-
lite type adsorbents [Masuda, et al. 1980]. Literature surveys of chemisorption calorime-
try [Cardonna-Martinez and Dumesic 1989] and physisorption calorimetry [Morrison,
1987] have been published.
Different types of calorimeters and heats of adsorption associated with them were de-
scribed by Hill (1949). The difference between differential and isosteric heats (internal
energy and enthalpy) is of the order of RT, which is small or negligible for chemisorp-
tion, but it can account for more than 10% of the physisorption energy of light gases.
Calorimetric studies have been performed on commercial and specially built calorime-
ters. Most experiments have been conducted at room temperature and moderately low
pressure, but some work at low temperature and high pressure are alsoreportedin the lit-
erature [Roquero11999]
36

3.2 Design Criteria
The desired equilibrium information for adsorbed mixtures is the pressure and composi-
tion of the gas phase above the adsorbent for a given loading, as well as the heat evolved
for differential increases in the loading. Because we considered direct, calorimetric
measurements of differential heats to be morereliablethan differentiation of isotherms at
various temperatures, the instrument was based on a Tian-Calvet calorimeter. Practical
limitations on the ability to integrate the heat flux in the calorimeter as a function of time
required that equilibrium be established in 30 minutes or less. In order to avoid signifi-
cant perturbations of the system during measurement of the gas-phase composition, we
used a quadrupole mass spectrometer.
The necessity of establishing equilibrium within 30 minutes of changing the sample
loading placed a stringent limitation on the design. First, we excluded adsorption systems
for which diffusion of one of the components was too slow to establish equilibrium
quickly. For most systems of importance in PSA, which requires reversible adsorption,
this is not a severe limitation. To minimize concentration gradients in the sample bed, a
thin layer of adsorbent (»3 mm) was placed on the bottom of calorimeter cell. In addi-
tion to minimizing diffusion time within the bed, the use of a thin adsorbent bed also de-
creased the time necessary for the heat generated by adsorption to be collected by the
thermopiles at the walls of the cell. The size of the calorimeter cell, a one-inch cube, rep-
resents a compromise between sensitivity of the instrument (which increases with the
amount of adsorbent) and the rate of equilibration (which decreases with the cell size).
37

Equilibration within the adsorbent bed is rapid for this configuration: based on a typical
Knudsen diffusion coefficient of 0.01 cm2
/s for mixing in the gas phase of the sample
bed, the mixing time is L2
/D « (0.3)2
cm2
/(0.01) cm2
/s = 9 s. While diffusion coefficients
within the particles making up the adsorbent may be much smaller than the Knudsen co-
efficient, particularly for a zeolite, the size of crystals making up a typical zeolite sample
are also quite small. For crystallites on the order of 1 mm, the diffusion coefficient
would have to be significantly below 10"8
cm2
/s for mixing to be a limiting factor for
equilibration.
The major limitation for the attainment of adsorption equilibrium is gas-phase mixing in
the region above the sample. Based on a typical gas-phase diffusion coefficient of 0.1
cm2
/sec, a tube length of even 10 cm will result in mixing times of 1000 sec. This im-
poses significant challenges on the instrument design. While imposed circulation would
alleviate this problem, forced flow would also complicate the design of the calorimeter
because of convective heat losses. The maximum distance within our apparatus (from the
bottom of the sample cell to the diaphragm of the pressure transducer) was approximately
10 cm. The pressure transducer was chosen for its small dead volume. The leak valve
for the composition measurements was welded directly on the top of the cell to minimize
the dimensions of the apparatus. These design criteria could only be met by a custom-
made calorimeter. The total equipment cost of the apparatus was about $20,000, of which
the major components are the RGA, the pressure transducer, the thermopiles, and the
computer.
38

3.3 Theory
Different heats of adsorption were defined in Chapter 2. The actual heat measured in a
particular calorimeter must berelatedto the thermodynamic definition of isosteric heat or
differential enthalpy:
As mentioned before, qa is the heat of desorption and it is not a heat but the difference of
two state functions, but the name is well established.
3.3.1 Idealized Calorimeter
An idealized batch calorimeter consists of a dosing cell, sample cell, and valve between
the dosing cell and sample cell completely enclosed in an isothermal calorimeter at tem-
peraure T0. At the start, the valve is closed, both cells are at temperature r0, the pressure
in the dosing loop is P¿ and the pressure in the sample cell is P* with P¿ > Pc.
When the value is opened, an increment of gas expands from the dosing cell into the
sample cell and a portion of the increment adsorbs. The total energy is:
U=U*+U* = ut
n* + u*n* (3.2)
39

The total energy U includes that of the adsorbent, the walls of the sample cell and dosing
cell, and the valve. However, since the temperature is fixed at T& these energies are
omitted from Eq. (3.2) because they are constant and do not contribute to the change in
energy. The total amount of gas in both cells is n*. The differential of the total energy is:
dU = u* dne
+ n* du* + u* dn* + n* du* (3.3)
where dU refers to the differential energy change after attainment of adsorption equilib-
rium. Since the temperature is T0 before and after adsorption, du* = 0 and
dU = u*dn* + n*du* + u*dn* + rii
dut
(3.4)
The mass balance is:
n* + n* = constant (3.5)
so
dn* = -dn* (3.6)
Substituting Eq. (3.6) into (3.4):
dU = -u* dn* + «' dn* + n* du* (3.7)
40

The first law for the combined closed system consisting of the dosing cell, sample cell,
and valve is:
dU = dQ (3.8)
where dQ is the heat absorbed by the combined system. For adsorption, dQ is a negative
quantity. Combining Eqs. (3.7) and (3.8):
-dQ = u*dn*-u*dn*-n'dü (3.9)
or
dQ = g
dna
ua
+na d^_
dna
(3.10)
Since A" « «' and h* = u* + zRTo, comparison of Eqs. (3.1) and (3.10) gives:
1st dna (3.11)
This result was derived by Hill (1949). Thefirstterm is the differential heat measured by
the idealized calorimeter and the second term is the difference between the enthalpy and
the internal energy in the equilibrium gas phase, z - PV/RT, the compressibility factor in
the gas phase, is close to unity for sub-atmospheric measurements of isosteric heat. The
RTo term at 25°C is 2.5 kJ/mol and typical isosteric heats of adsorption are in the range
10-50 kJ/mol.
41

332 Practical Calorimeter
In the idealized calorimeter, the temperature of the gas in the sample loop decreases upon
expansion while the temperature of the gas in the sample cell increases as it is com-
pressed by the incoming gas. In the absence of adsorption, heat is absorbed by the dos-
ing loop and heat is liberated by the sample cell until the pressures equalize and the tem-
peraturereturnsto RT0. For a perfect gas, the two effects cancel because the enthalpy of a
perfect gas is a function only of temperature.
Our design is a modification of the idealized calorimeter in which only the sample cell is
placed in the calorimeter. Since the dosing loop and valve are external to the calorimeter,
adding a dose of gas to the sample cell generates an exothermic heat of compression in
the sample cell which is not cancelled by absorption of heat in the dosing loop. The spu-
rious heat of compression must be subtracted from the total heatregisteredby the calo-
rimeter in order to obtain the heat of adsorption. A correction, which typically is about
2% of the total heat, is derived below.
42

3.4 Description of Instrument
A diagram for the calorimeter apparatus is shown in Figure 3.1. A picture of the sample
cell and its connections is shown in Figure 3.2. The glass (Pyrex) cube is the sample cell
for the adsorbent and adsórbate. The use of glass to minimize heat conduction through
the top of the cell is a crucial element of the design. The glass cube is surrounded on all
four sides and on the bottom by square thermal flux meters (not shown in the picture)
obtained from the International Thermal Instrument Company, Del Mar, CA. Each ther-
mopile is a 1-in square polyimide plate with about 100 embedded thermocouples for de-
tecting temperature differences across the plate.
The five thermopiles were connected in series and a similar set in thereferencecell was
connected in opposition to improve baseline stability. The combined signal from these
transducers was input to an amplifier on the data acquisition board of a computer. The
sample cell slides into cubical holes cut into an aluminum block (27x 18x 10 cm, mass 13
kg). A silicone-based heat-sink compound was used to ensure good thermal contact be-
tween the Al block and the transducers, and between the transducers and the pyrex cell.
43

Figure 3.1 Schematic of the calorimeter and auxiliary equipment
Table 3.1 Key to Figure 3.1.
No. Description Model No.
1 Gas I inlet
2 To vacuum pump
3 Inlet valve to dosing loop
4 Pressure transducer for dosing loop
5 Outlet valve from dosing loop
6 Valco 6-way valve
7 Calibrated dosing loop (10 cm3
)
8 0.01 ID tube
9 Cell outlet valve
10 Reference ceil
11 Calorimeter cell
12 Pressure transducer for cell
13 Variable leak valve
14 Thermopiles
15 Heat sink (aluminum block)
16 K-type thermocouple
17 Mass spectrometer (RGA)
18 Turbopump
19 Data acquisition board
20 Computer
21 Liquid nitrogen trap
MKS 626A
Omega PX425
International Thermal Instrument C-783
Leybold Inficon TSP C100F
Balzers TSU062
44

8 in extension
To dosing
1/16 in vain)
1/4 in female
VCR fitting
Leak Valve
diaphragm
Connection to leak
valve. 1/4 in 0 0
1/4 in NPT thread
Topressu
head
Cajon ultra
torr fitting
1/2 in 00
Qlas8cell
Figure 3.2 Picture of the glass sample cell and connections to the pressure
head, vacuum line, dosing loop and RGA leak valve. The glass
sample cell is surrounded by thermopiles (not shown) set into an
aluminum heat sink.
45

The cubical glass cell shown in Fig. 3.2 was made with a 1/2-in glass tube on the top
which was inserted into a Cajonfitting.This provides a vacuum seal by compression of a
Viton O-ring. The Cajon fitting connects to a custom-made r-connection onto which are
welded the leak valve, the pressure head, the connection to vacuum, and the 0.01-in bore
tube from the dosing loop. The leak valve is connected through a l/4-in0D
stainless-steel
tube; the pressure head is connected through a 1/4-in NPT fitting; the valve that opens to
vacuum is connected through a 1/4-in VCR fitting. The pressure head was chosen for its
small dead space (1.2 cm3
). The total dead space is 20.6 cm3
for the (empty) sample cell,
the dead space inside the pressure head, and the lines to vacuum, the dosing loop, and the
RGA leak valve.
Gas was introduced to the sample cell from the dosing loop using a six-port Valco sam-
pling valve connected to a small bore (0.01 inID
) tube. The small diameter of the tube
prevents backmixing of the mixture into the dosing loop. This tube enters the T-shaped
connector from the back (the welded connection does not appear on Fig. 2) and extends
downward with the opening 5 cm above the bottom of the sample cell. Two small metal
cylinders with a Viton O-ring between them were inserted in the NPT connection to the
pressure head to make a vacuum seal. The adsorbent was covered with a 0.5 cm layer of
glass chips to minimize heat loss through the top of the cell andregeneratedin situ.
46

3.5 Thermopile calibration
The primary calibration of the calorimeter (0.0540 W/mV) is based upon the Clapeyron
equation [Dunne96a] applied to a series of adsorption isotherms measured in a separate,
high-precision volumetric apparatus for ethane on silicalite (MFI structure). The calibra-
tion constant for ethane was confirmed by excellent agreement of calorimetric data with
the Clapeyron equation for SFs, CO2, and CH4. The calibration constant was found to be
independent of the amount of adsorbent in the cell.
A secondary calibration based on electrical heating (0.059 W/mV) was 9% higher than
the primary calibration. The voltage signal from the calorimeter was determined as a
function of the rate of heat dissipation dQ/dt - l2
R in a platinumresistancewire wrapped
around the outside of the cell in thermal contact with the cell wall and the thermopiles.
Similar difficulties were encountered by Handy et al. [1993]: the voltage to power ratio
for aresistorinside the cell was 9% lower than that for an externally wrapped resistance
wire. The difference was attributed to heat losses. We chose the Clapeyron equation as
the more reliable method of calibration.
47

3.6 Spurious Heat of Compression in Sample Cell
Before taking a measurement, the dosing loop and the sample cell are both at the tem-
perature T0 of the experiment; the pressure inside the sample cell is Pe, and the pressure
in the dosing loop is some higher pressure Pi. Increments of gas are added to the sample
cell by opening the valve between the dosing loop and the cell. The temperature of the
gas inside the dosing loop falls because of the expansion while the temperature of the gas
inside the sample cell rises as it is compressed by the incoming gas. The calorimeter
measures both the latent heat of adsorption and the sensible heat liberated by the com-
pressed gas as it cools to the temperature of the calorimeter. This sensible heat must be
subtractedfromthe heatregisteredby the thermopiles to obtain the heat of adsorption.
The spurious heat term generated by compression of the gas inside the cell was deter-
mined by expanding gas from the dosing loop into a sample cell containing no adsorbent.
For a 10 cm3
dosing loop and for a dead space of 18 cm3
in the sample cell, the linear
correlation
ß = aAP (3.12)
for the experimental data shown in Figure 3.3, a=3.94xl0-4 J/Torr. AP is the driving
force for the irreversible expansion: the pressure difference between the dosing loop and
the sample cell.
48

1 I 1 i i J
1111/
t * *
t * I
1 ! i /
1
1 x
t '" * • w
:
/i• / i
' i
I
t
i
i
t
1
Ï
Vt í ! 1 1
y / i ! ! | í
. £. 1 j 1 j í •^^^—
O 100 200 300 400 500 600 700
Pressure difference, ton-
Figure 33 Linear correlation of a spurious sensible heat
term for adding a dose of gas. The difference
in pressure is the pressure in the dosing loop
minus the pressure in the sample cell before
opening the valve.
The correlation ignores the effect of adsorption as gas enters the sample cell. For the case
of weak adsorption, when only a smallfractionof the gas entering the sample cell actu-
ally adsorbs, the neglect of adsorption is justified. For the case of strong adsorption, when
most of the gas entering the sample cell adsorbs, the spurious heat of compression is neg-
ligible compared to the heat of adsorption. Thus, for strong adsorption (95% of gas dose
adsorbs) or weak adsorption (5% of gas does adsorbs), the approximation that the heat of
compression is independent of adsorption is acceptable. We have no proof that the cor-
rection for the spurious heat of compression is negligible in the intermediate case when
about 50% of the gas dose adsorbs, but the excellent agreement of both strong and
49

weakly adsorbing gases with the Clapeyron equation is indirect evidence that Eq. 3.12 is
adequate for both strongly and weakly adsorbing gases.
Other calorimeters [Sircar et al. 1999] are designed for isothermal introduction of gas to
the sample cell. This is accomplished by adding increments of gas slowly through a nee-
dle valve so that the temperature of the gas in the dosing loop is equal to the temperature
in the sample cell (To). In the absence of adsorption, the reversible, isothermal introduc-
tion of a gas sample generates an exothermic heat inside the sample cell equal to RT0 per
mole of gas added; the signal for this spurious heat term can be nullified by adding the
same amount of gas to a reference cell wired in reverse polarity. Isothermal dosing is
effective for the measurement of heats of adsorption of pure gases. For mixtures, the fast,
irreversible addition of increments of gas shortens the time required for mixing and
equilibration.
3.7 RGA calibration
The gas phase composition is determined with aresidualgas analyzer (RGA), which is
based on mass spectrometry. When a gas is admitted to the RGA, bombardment by elec-
trons causes the molecules tofragmentinto positive ions of a whole series of masses. The
relative abundance of ions of various masses is characteristic of the particular molecule.
Compositions of gaseous mixtures can be determined by comparing their spectra with
that of the pure compounds determined under the same conditions.
50

For a binary mixture, the calibration constant (K) of the RGA is based upon the relation:
^- = K^- (3.13)
n h
where v¡ is the molefractionof component i in the gas phase and l is the intensity of the
mass/charge ratio detected for a particular ion ofthat component. Eq. (3.13) assumes that
the contribution to the intensity l is only due to component I, and the intensity h is only
due to component 2. When both components of a binary mixture contribute to the inten-
sity of a peak, the composition of the gas phase can still be determined by solving a sys-
tem of equations for the intensity ratios.
The intensity detected by the mass spectrometer is proportional to the flow rate of the
gaseous molecules through the leak valve. At low pressure, the opening of the leak valve
is small compared with the free mean path of the molecules. Theresultingeffusive flow
of the gas is directly proportional to its partial pressure and inversely proportional to its
molecular weight, so:
iL^PyifMi) ( 3 1 4 )
51

The free mean path decreases with pressure; at « 100 torr the mean free path is the same
order of magnitude as the opening of the leak-valve. When the ratio of the opening to the
free mean path is in the range from unity to 100, the flow is intermediate between effu-
sive and viscous [Roth, 1982]. For viscous flow, the composition of the gas leaving the
cell and the intensity ratio obeys the simple relation:
JL=fK (3.15)
h Pyi
The transition from effusive to viscous flow is important for molecules having a large
ratio of molecular weights, e.g. SF6 (1) and CH« (2) with a molecular weight ratio of 9.
In this case the calibration "constant" AT is a function of the pressure in the cell, as shown
in Figure 4. For gases with smaller ratios of molecular weight, such as C2H4 and C2H6
with a ratio near unity, the calibration constant is effectively independent of pressure.
Figure 5 shows calibration data for C2H4 (component 1) and C2H6 (component 2). Both
molecules contribute to the intensity /2s at m=28 but only C2H6 contributes to the inten-
sity /30 peak at m=30 so
%L=K{—^— (3.16)
y lis-ho
The average error in composition using the mass spectrometer is less than 1% for mid-
range compositions. The lowest mole fraction that can measured is about 0.0005. The
52

background noise is between 2 and 4 orders of magnitude smaller than the intensity of the
peaks used to measure the compositions.
14
12 -
-r 10
0 °
u
1 6
5
.o
200 400 600 800
Calorimeter cell pressure, ton*
1000
Figure 3.4 Effect of pressure on RGA calibration AT of Eq. (3.15) for mixtures
ofSF6andCH4.
53

U 1.5
Figure 3.5 Calibration of the composition for mixtures of CjtU and CiHe
based on Eq. (3.16). The calibration is independent of pressure.
3.8 Verification of Adsorption Equilibrium
The mixing time required when a new dose of gas is added to the sample cell containing
a gaseous mixture but no adsorbent is about 15 minutes. [Dunne et al. 1997]. Sampling
the gas phase continuously to check for equilibrium is impracticable because the amount
of gas sampled over 30 min would affect the mass balance used to calculate the amount
adsorbed.
54

Two methods were used for verifying the attainment of equilibrium for mixture adsorp-
tion. The first method is to fit the experimental data to a model, which is thermodynami-
cally consistent; agreement of the model with the experimental data is an indirect but ro-
bust method of verifying equilibration. A second, direct method is to verify that a par-
ticular point is independent of the order of contacting the adsorbates. Figure 3.6 shows
an example for the adsorption of mixtures of SF* (1) and CH4 (2). The closed and open
circles indicate two paths from zero loading to point A; the arrows show the direction of
the paths. These two paths intersect (approximately) at /it = 0.78 and ri2 = 0.12, or a mole
fraction JCI = 0.87. Figure 3.7 shows the selectivity for the same two paths; the selectivity
curves intersect at xi = 0.88. Therefore, within an uncertainty of about 2%, the selectivity
is independent of the order of contacting the adsorbates.
0.30
0.25
0.20
£0.15
0.10-
0.05
0.00
0.0 0.2 0.4 0.6 0.8 1.0 1.2
n(
Figure 3.6 Loci of loading by alternate paths for mixtures of SF6 and CH4. Black circles
and open circles indicate different paths that intersect at point A.
55

60 -r
50-
40-
1 30-
<*>
20-
10-
0 -
0
Figure 3.7 Selectivity of SF6 relative to CH4 at 21.5°C. Symbols are the same as those in Figure
3.6 The selectivity at point A is independent of the order of contacting the components
3.9 Determination of Differential Heats from Finite Doses
The amount dosed an must be small enough to measure the differential heat but large
enough to generate an accurate signal Q. Because the differential heat is defined as the
ratio of ß/A/1 in the limit as An goes to zero, the error associated with finite increments
needs to be examined.
Assume that the differential heat q¿(n) is given exactly by the polynomial:
qd(n) = q0 + d|/i + d2/i2
+ d^n3
+ *" (3.17)
56

For a finite amount of gas adsorbed (An = /12 - «1), the approximate differential heat qs
measured experimentally is
I qd(n)dn
qS = -^ (3.18)
n2-nx
qs is the average value of the differential heat measured at the average loading (/ii+/i2)/2.
Comparison of qs with the exact differential heat at the same average loading gives the
error:
q6-qd=^x-n2)2
+^-(nx+n2)(nx-n2)2
^- (3.19)
12 s
The error is of order (n - mf. Because the leading term of the error is also proportional
to the second derivative of the heat curve, «75 = <7d for linear heat curves, independently of
the magnitude of the A/t.
Figure 3.8 shows hypothetical differential (solid line) and integral (dashed line) heats of
adsorption. The points show approximate heats qd calculated from Eq. (3.18) for finite
doses n - m =0.1,0.5, and 1.0 mol/kg. Only for finite doses as large as 1 mol/kg can the
difference between the exact differential q¿ and the approximate «75 be discerned. Typical
experimental values of An are of the order of 0.1 mol/kg. Except for abrupt changes of
the heat with coverage associated with phase transitions, the error associated with using
finite doses of gases to measure the differential heat is negligible.
57

It is convenient toreportdifferential heats of adsorption at the loading m instead of the
average loading («i + «2)/2. This introduces errors larger that that predicted by Eq. (3.19),
especially when the slope of the heat curve is large. Heats in Appendix 1 arereportedat
the final loading of m. Nevertheless, it is important to bear in mind that this approxima-
tion may not be valid for all cases.
55
— Isosteric heat
o An = 0.1 mol/kg
D An = 0.5 mol/kg
A An =1.0 mol/kg
" " Integral heat
1 2 3 4
Amount adsorbed, mol/kg
Figure 3.8 Comparison of the differential heat of adsorption (solid line) with
experimental heats determined with finite doses of gas. The dashed
line is the integral heat of adsorption. Heats determined experi-
mentally with small doses of order 0.1 mol/kg agree very well with
the exact differential heat.
58

3.10 Alternating Dosings of Each Component
Two independent dosings (A and B) arerequiredto measure the individual differential
heats of adsorption (q and qj) from a binary mixture.
ßA
= A/i,A
<jr,+An,A
<7i (3.20)
ßB
= A/i,B
(7,+A/i,B
<7i (3.21)
where QA
and QB
are the heats registered by the calorimeter and Ant and A/12 are the
amounts adsorbed, or desorbed, of components 1 and 2, respectively. When the system
of equation (3.20) and (3.21) is solved, the individual heats of adsorption are:
QA
ànB
-QB
AnA
^ ^
qi
~ánfto8
- Anfang
)B
*nA
-QA
AnB
Q°An?-Q"An[ f 3 2 3 .
Dosing of one component generates a positive incremental adsorption ofthat component
which is normally one or two orders of magnitude larger than the accompanying desorp-
tion of the other component. The solution of Eqs. (3.22) and (3.23) requires that the dos-
59

ing of the components be alternated; successive dosings of the same component generate
an indeterminate solution. A sample calculation is given in the following section
3.11 Sample calculation
The heat liberated by the adsorption of an increment An moles of gas is determined by
integrating the area under the response curve generated by the thermopiles. The noise
level on this signal is 1-2 fiV, which corresponds to aresolutionof 54 fiW. a typical re-
sponse curve is shown on Figure 3.9.
0.12
H 0.06
0.02-
ii r «^.y..,^. m , . , ,
•0.02
300 1000 1500
Time, i
2000 2300 3000
Figure 3.9 Thermopile response, voltage versus time.
60

Table 3.2 shows a sample calculation of loading and heats of adsorption, for mixtures of
SF6 (1) and CH4 (2), derived from the two points A and B. The incremental loading of
component i for measurementy is calculated by the mass balance equation:
An/=-L
1
RT
Vd
yf
fpd pd.f
M
+ Vl
r
pC.j-lyCj- pC.jyC.P
*c,j-l 7C
>J
(3.24)
The total loading of component i is ni = nfl
+Anî/w, where w is the mass of adsorbent.
The spurious heat term Qsp calculated from Eqs. (3.13) is subtracted from ßA
and QB
be-
fore calculating the differential heats from Eqs. (3.19) and (3.20). The thermopile cali-
bration constant is K = 0.0540 W/mV.
3.12 Conclusion
A calorimeter that can be used to measure multicomponent adsorption equilibria and in-
dividual heats of adsorption simultaneously was described in this chapter. Important con-
siderations when a mixture calorimeter, such as time of mixing, spurious heat of com-
pression, calibration of the residual gas analyzer and errors associated with considering
finite dosings to measure differential enthalpies are addressed.
61

Table 3.2 Sample calculation of heats of adsorption from alternating dosings A and B of the pure
components.
Variables Description A B_
~ ? Initial pressure in the dosing loop, torr
P* Pressure in the dosing loop after 2 min, torr
/^•J
*' Pressure in the cell prior to dosing, torr
Pc
'i
Pressure in the cell after dosing, torr
yid
Composition of the gas in the dosing loop
yfj
"' Composition of the gas in the cell prior to dosing
yt0
*j
Composition of the gas in the cell after equilibration
A Area (response from the thermopiles), mV s
T Temperature, K
zd
Compressibility factor for the gas in the dosing loop prior to
dosing
z** Compressibility factor for the gas in the dosing loop after 2 min.
z^"1
Compressibility factor for the gas in the cell prior to dosing
z^ Compressibility factor for the gas in the cell after dosing
Va
Dosing loop volume, cm3
Ve
' Cell volume, cm3
w Mass of adsorbent, g
K Thermopiles calibration constant, W/mV
Q Correction for compression effect, J
Ani Incremental amount adsorbed of component 1, mmol
A/12 Incremental amount adsorbed of component 2, mmol
nij
Loading of component 1, mol/kg
n2j Loading of component 2, mol/kg
q Isosteric heat of component 1, kJ/mol
_c¿ Isosteric heat of component 2, kJ/mol
352.6
84.90
15.58
85.08
0.000
1.000
0.201
31.31
294.2
0.9992
0.9998
0.9997
0.9996
10.0
303.0
97.39
85.08
91.41
1.000
0.201
0.225
69.98
294.36
0.9950
0.9984
0.9996
0.9996
17.853
1.1406
0.0540
0.000394
•0.0015
0.0798
0.6501
0.0700
36.7
22.6
0.1093
-0.0028
0.7460
0.0675
The ability of reaching equilibrium is tested by using different paths to meet some given
conditions and evaluating state properties at these conditions. State properties are path
independent, and this test provides a proof that equilibrium was achieved.
For presenting experimental results, it would be helpful if one of the variables such as the
total pressure or fugacity of one of the components could be held constant. However, the
62

necessary procedure for alternating doses generates a locus similar to the closed circles
shown on Fig. 3.6. The inability to obtain data along some locus such as an isobar is an-
noying but does not affect the analysis of the experimental data for activity coefficients
and excess functions. After covering the entire phase diagram for a binary mixture by
varying the preloading of the pure components, a model that fits the experimental data
can be used to generate loci such as isobars or constant loading of one component.
63

Chapter4
Experimental measurements of adsorption equilibria and heats
of adsorption
The ability of porous materials to adsorb fluids selectively is the basis of many industrial
applications, especially catalysis and the separation and purification of gases and liquids.
Industrial applications of adsorption include the recovery of organic solvent vapors, de-
hydration of gases, separation and purification of hydrogen from steam-methane reform-
ers, separation and purification of air, separation of normal paraffins from branch and cy-
clic paraffins, production of olefins from olefin and paraffin mixtures, etc. [Tien, 1994;
Crittenden and Thomas, 1998; Yang, 1987]. Even though adsorption plays an important
role in the gas separation and purification industry, the prediction of multicomponent
equilibria is still one of the most challenging problems in the adsorption field fTalu,
1998].
The main problem is a lack of accurate and consistent experimental data for testing theo-
ries. Almost no data is available on enthalpy of adsorbed mixtures although such infor-
mation is necessary for the modeling of fixed bed adsorbers. Indirect measurements of
mixture heats of adsorption using volumetric or gravimetric methods are possible in prin-
64

ciple but require voluminous data on isobars, isotherms, and loci of constant composition
[Sircar, 1985, 1992].
Recently, different techniques have been used to measure enthalpies of adsorbed mix-
tures: Bajusz et al. (1998a, 1998b) used a steady state isotopic transient kinetic analysis
technique, other studies have used the isosteric method [Bulow, 1994; Bulow and Shen
1998; Hampson and Rees, 1993; Rees. et al. 1991], and lately calorimetric studies have
been reported [Dunne et al. 1997; Siperstein et al. 1999b; Sircar et. al 1999].
The objective of this work is to understand the basis for deviations from ideality of ad-
sorbed mixtures and attempt to predict them on the basis of single-gas properties. Devia-
tions from ideal mixing are expressed as excess functions: excess chemical potential (ac-
tivity coefficients) and excess enthalpy (deviations from ideal enthalpy of mixing). This
excess function approach is analogous to standard methods for expressing nonideal be-
havior in liquid mixtures [Prausnitz et al. 1999].
However, the use of excess functions for describing deviations from ideal mixing in the
adsorbed phase differs from liquid solutions is several subtle but important ways, espe-
cially in how these excess functions are measured experimentally. In the case of bulk liq-
uids, excess functions are measured at constant pressure and temperature. In the case of
adsorbed mixtures, excess properties are referred to the pure component adsorption at the
same temperature and surface potential (Chapter 2).
65

A custom-made calorimeter was used to measure the enthalpy of mixing, which in com-
bination with the adsorption isotherm provides a complete thermodynamic description of
the effect of temperature, pressure, and composition variables. We studied seven binaries
and one ternary system on two types of zeolites, silicalite and faujasite. The nonidealities
in loading, selectivity, and enthalpies (heats) are described within experimental error by a
three-constant equation which is thermodynamically consistent and has the correct as-
ymptotes at high and low coverage. Multicomponent equilibria can be predicted accu-
rately from binary constants without using any additional parameters.
A correlation of binary excess functions with pure-component properties enables multi-
component adsorption to be predicted from single-gas adsorption isotherms and thus rep-
resents a major improvement over the theory of ideal adsorbed solutions (IAS) [Myers
and Prausnitz, 1965].
4.1 Materials
Two types of zeolites were studied, silicalite (MFI) and NaX (FAU) arrangement [Meier
and Olson, 1992]. The structures and compositions of these materials are very different.
Silicalite has a unit cell composition of SfeOm and contains straight and sinusoidal
channels with pore openings of 5.3x5.6 and 5.1x5.5 A, respectively [Flanigen, et al.
1978; Olson, et al. 1981].
66

Figure 4.1 MFI structure (view along 010)
NaX has a unit cell composition of NagôAIsôSiioôOsM and contains 15 A-diameter super-
cages interconnected by 7.4 A-diameter windows in a tetrahedral arrangement [Meier and
Olson, 1992].
Non-framework cations in NaX are mainly located in three different sites [Olson, 1995].
Ions in Site I (SI) are inside the hexagonal prism connecting the sodalite cages; ions in
Site I1
are in a six member ring that connects an hexagonal prism with a sodalite cage.
Ions in Site II (Sil) and Site III (SIII) are accessible to the adsorbed molecules. Su ions
are in a six-member ring facing the supercage and SIII in a four-member ring also facing
the supercage. Figure 4.2 shows these locations. The distribution of the tons in these lo-
cations depends on the nature of the cation [Olson, 1995; Godber, et al. 1989]. For dehy-
67

drated NaX, in one unit cell there are 2.9 ions in site I, 29.1 ions in site V, 31 ions in site
II, and 29.8 ions in site III' [Olson, 1995].
SI
SU
. SHI'
Figure 4.2 NaX structure indicating ion positions.
Silicalite provides a practically homogeneous environment for both polar and non-polar
molecules, whereas polar molecules exhibit energetic heterogeneity in NaX due to the
presence of non-framework sodium ions.
We used commercial powders of these zeolites: silicalite (Linde S115) manufactured by
Union Carbide Corp. and NaX (Linde 13X) with a Si/Al ratio of 1.23. Thermogra-
vimetric analysis of the samples yielded dehydrated weights of 99% and 76% of that in
air,respectively[Dunne etal. 1996a, 1996b].
We studied a variety of polar and non-polar gases. Gases used in the experiments were
from Air Products & Chemicals, Inc. (SF6, 99.99%; C2H4, 99.5%; C2H6, 99%; C3Hg,
68

99.5%) andfromAireo (CO2,99.99%; CH4,99.99%). Table 4.1 summarizes the proper-
ties of these gases.
Table 4.1 Properties of the gases studied*
Property
Critical temperature, 7c, K
Critical pressure, Pc, kPa
Critical volume, Vc, cm3
/mol
Ascentric factor, (0
Quadrupole moment, 0/10'26
esu
Polarizability, a/10*24
, cm3
"TakenfromSmith, et al. 1999;
CH4
190.6
45.99
98.6
0.012
0
2.5
leid et al.
CjH«,
305.3
48.72
145.5
0.100
<1
4.5
C,H,
369.8
42.48
300.0
0.153
C A
282.3
50.40
131.
0.087
xn-3.5
yr- 1.7
rr. 1.8
4.2
CO,
304.2
73.83
94.0
0.244
-4.5
2.6
986, and Gray and Gubbins, 1984.
SF<
318.7
37.6
198.8
0.286
0
4.5-6.5
4.2 Method
The multicomponent calorimeter and the experimental procedure were described in detail
in Chapter 3. Some particular details for the conditions of the experiment are presented in
this section.
The pretreatment procedure for the sample was heating in situ under vacuum from room
temperature to 110°C over 24 hours for afreshsample, or 12 hours when regenerating a
69

used sample; followed by heating over a period of 12 h from 110°C to 350°C and finally,
maintaining the temperature at 350°C for 12 h.
For binary and ternary mixture measurements, the components were dosed alternately in
order to measure the mixture enthalpies. The composition of the equilibrium gas was
measured with a mass spectrometer through a leak valve attached to the sample cell.
Loadings of both components were calculated from mass balances using standard volu-
metric procedures. The attainment of equilibrium was verified by reversing the order in
which the components were added to the sample cell as described in Chapter 3.
4.3 Results
4.3.1 Single-Gas Isotherms and Isosteric Heats
Calculations of mixture properties such as adsorbed-phase activity coefficients are ex-
tremely sensitive to the properties of the single adsorbates. For this reason, we devoted
special attention to the reproducibility of the experimental data. Reversibility was estab-
lished by comparing points obtained by adsorption and desorption. Single gas isotherms
are shown in Figures 4.3-4.4. The three experimental points for CH4 on silicalite at pres-
sures above 1 bar were taken from Golden and Sircar [1994] in order to avoid having to
extrapolate our data to high pressure for mixture calculations. The experimental data are
tabulated in Appendix 1.
70

In preparation for calculating thermodynamic properties, the single gas isotherms were
fitted with a modified virial equation:
HP = n—2Î—expjCi/i+C2n2
+ C3n3
+ C4n4
} (4.1)
Constants for Eq. (4.1) are given in Table 4.2. The virial equation extrapolates properly to
zero pressure: lim P- O (dn/dp) = H. The factor m/Qn-n) was added to enforce Lang-
muirian behavior at high pressure where the virial expansion used by itself diverges.
Thus Eq. (4.1) has the correct asymptotic behavior at high and low pressure plus suffi-
cient flexibility to fit all of the isotherms within experimental error. The average differ-
ence between the experimental pressure and the value that was calculated by Eq. (4.1) is
1.1%.
The differential enthalpies (heats) of adsorption shown in Figures 4.5 and 4.6 were fit by
a Maclaurin series:
ßa = Go + Dm + D2n2
+ Dm1
+ D*n* (42)
Constants for Eq. (4.2) are given in Table (4.3). The average error between the experi-
mental and calculated enthalpy is 1.3%.
71

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