ADVISORY BOARDM. CHEParis, France

A. CORMA CANSValencia, Spain

D.D. ELEYNottingham, England

G. ERTLBerlin/Dahlem, Germany

G. HUTCHINGSCardiff, UK

E. IGLESIABerkeley, California, USA

H. KNZINGERMunich, Germany

P.W.N.M. VAN LEEUWENTarragona, Spain

J. ROSTRUP-NIELSENLyngby, Denmark

R.A. VAN SANTENEindhoven, The Netherlands

F. SCHTHMlheim, Germany

J.M. THOMASLondon/Cambridge, England

H. TOPSELyngby, Denmark

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CONTRIBUTORS

Tracy J. Benson

Center for Chemical Energy Engineering, Dan F. Smith Department of Chemical

Engineering, Lamar University, Beaumont, TX, USA

Wm. Curtis Conner Jr.

Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts,

USA

Prashant R. Daggolu

Dave C. Swalm School of Chemical Engineering, Mississippi State University, Mississippi

State, Mississippi, USA

Karl D. Hammond

Department of Nuclear Engineering, University of Tennessee, Knoxville, Tennessee, USA

Rafael A. Hernandez

Department of Chemical Engineering, University of Louisiana at Lafayette, Lafayette,

Louisiana, USA

Shetian Liu

Coal Chemical Catalysis Center, National Institute of Clean-and-Low-Carbon Energy,

Beijing, China

Robert Schlogl

Department of Inorganic Chemistry, Fritz Haber Institute of the Max Planck Society,

Berlin, Germany

Mark G. White

Dave C. Swalm School of Chemical Engineering, Mississippi State University, Mississippi

State, Mississippi, USA

vii

PREFACE

The obituaries of two giants in catalysis anchor this volume.

Paul Weisz created the field of shape-selective catalysis and was at the

core of the research that gave birth to the science and technology of

zeolite-catalyzed hydrocarbon conversion. He graced these volumes as

the author of three chapters, as Associate Editor from 1956 to 1959, and

as Editor from 1959 to 1993. No one did more for Advances in Catalysis.

Haldor Topse created one of the most influential and consistently inno-

vative industrial organizations in our field, leaving a legacy of robust new

technology, a commitment to basic research as the wellspring of industrial

innovation, and a dedication to serving mankind. Researchers in the com-

pany that bears his name have made numerous lasting contributions to these

Advances as authors and editorial board members.

Our first chapter, by Hammond and Conner, will serve both as a tutorial

and as an insightful review of the characterization of porous materials by

physical sorption techniques. This field has been spurred not only by the

widespread availability of automated equipment to facilitate the measure-

ments but also by advances in data interpretation including those guided

by density functional theory. As interest in porous materials grows, the chal-

lenges of using surface areapore volumemeasurements continue to expand.

The field is being stimulated with continuing discoveries in zeolites and

related materials; in materials with ordered mesopores; and in materials

with extremely high internal areas (such as metalorganic frameworks)

there is a flood of innovations in the design of complex pore networks

and tailored pore hierarchies. As the authors point out, good practice in

the use of physical sorption techniques requires an understanding of the

fundamentalswhich they set outand attention to details that are often

overlookedwhich they highlight. This chapter is a readable, practical

how-to guide that we believe may become required reading for many

who work with porous materials.

Carbon is widely used as a (rather inert) support in catalysis, but its own

catalytic properties have gone largely overlooked. Schlogl explains the

fascinating chemistries of inorganic carbons, including nanocarbons such

as fullerenes, nanotubes, nanofibers, and graphenes. He provides deep

insight into the electronic properties of carbon, including the effects of var-

ious structural elements on local, bulk, and topological levels. For example,

ix

on an atomistic level, carbon hybridization, defects in graphene sheets, and

surface functional groups are all significant. The author compares the prop-

erties of basal and prismatic carbon faces and explains the influences of

topologyand hence of curvature. This discussion demonstrates that car-

bon has it allmetal-like properties; olefinic properties associated with

localized double bonds; and acidbase properties stemming from the surface

functional groups. This combination offers rich opportunities for catalysis

but also presents a daunting challenge for characterization and synthesis. The

analysis of the electronic properties of a particular type of sitespresent

among a multiplicity of other sitesturns out to be quite involved. Schlogl

assesses the characterization techniques and provides guidance for controlled

syntheses of nanocarbons. He also reports on the inadvertent formation of

carbons as surface deposits during catalysis and their detrimental effects

and contrasts them with the perhaps surprising beneficial catalytic effects

of some such deposits. Case studies (oxidative dehydrogenation of ethylben-

zene and of alkanes) highlight the catalytic properties of nanocarbons and

demonstrate the success of the authors rigorous approach to synthesis and

characterization.

Addressing the rapid growth in research motivated by the need for sus-

tainable fuels and chemicals, and the corresponding focus on biomass con-

version, Benson, Daggolu, Hernandez, Liu, and White have taken on the

substantial task of organizing the literature of the surface and catalytic reac-

tions of oxygen-containing organic compounds. The authors start with a

foundation in reaction thermodynamics and present an extensive summary

of the adsorption chemistry of oxygenates on a wide range of surfaces. Most

of the knowledge in this area has emerged from surface science and compu-

tations, and the presentation illustrates the difficulty of analyzing the behav-

ior of oxygenates on more complex surfaces. The authors address various

classes of catalytic reactions that lead to removal of oxygen from organic

compoundsas products including water, CO2, CO, and others.

A reaction class considered in detail is hydrodeoxygenation, seemingly of

great potential for production of fuels from bio-oils but hindered by a lack

of fundamental understanding and a clear path forward for choosing viable

catalysts and processes. After presenting candidate processing steps for bio-

mass upgrading, the authors wrap up with some thoughtful concepts for

integrated process designs. This chapter will be a stimulus and a valuable

resource for researchers working on biomass conversion.

BRUCE C. GATES

FRIEDERIKE C. JENTOFT

x Preface

PAUL B. WEISZ19192012

Paul B. Weisz, 93, an internationally recognized expert in the areas of

zeolite catalysts and diffusion died on Tuesday, September 25, 2012, in State

College, PA.

In the 1960s and 1970s, working with several collaborators atMobil Oils

New Jersey research laboratories, Weisz pioneered the use of natural and

synthetic zeolites as catalysts for petroleum refining and petrochemical man-

ufacture. These zeolite catalysts eventually revolutionized many refining and

petrochemical conversion processes because they facilitated only certain

reactions between molecules having specific dimensions. To describe this

class of chemical reaction, Weisz coined the phrase shape-selective cataly-

sis. In 1960, he first published his concept of acid-catalyzed zeolitic reac-

tions and shape selectivity in a seminal article entitled Intracrystalline and

Molecular-Shape Selective Catalysis by Zeolite Salts ( J. Phys. Chem. 64,

382 (1960)) and in a 1962 article recognized the importance of acid catalysis

in zeolites ( J. Catal. 1, 301 (1962)).

Weiszs vision of shape selectivity, initially probed using natural zeolites

including erionite and chabazite, ultimately led to the discovery of the zeo-

lite ZSM-5 and at least 15 significant and distinct petrochemical and

xi

petroleum refining processes. His early work in multifunctional heteroge-

neous catalysis (Adv. Catal. 13, 137 (1962)) was fundamental to the

understanding and progress of multifunctional aromatic reforming catalysts.

Similarly, his work with Dwight Prater in the interpretation of measure-

ments in experimental catalysis (Adv. Catal. 6, 143 (1954)), which drew

heavily from the work of giants in diffusion with chemical reaction,

including Thiele and Damkohler, significantly advanced the understanding

of how practical catalysts function. His work in experimental measurements

in catalysis became essential reading for all who entered the field.

His 1962 article with J. S. Hicks, entitled The Behavior of Porous

Catalyst Particles in View of Internal Mass and Heat Diffusion Effects,

Chem. Eng. Sci. 17, 265 (1962) was selected as one of the 50 most influential

articles in Chemical Engineering Science in the publications 1995 Frontiers in

Chemical Engineering Science commemorative edition.

One of Pauls formidable strengths was his ability to communicate com-

plex theories succinctly. He was a constant contributor to the ACS publi-

cation ChemTech throughout the 1970s and 1980s, where he continued

to enlighten and delight readers with his insightful observations of how phe-

nomena like diffusion and kinetics applied to everyday life. His views of

catalysis were succinctly stated in numerous prefaces of Advances in Catalysis,

which he edited from 1956 until 1993.

Processes based on Weiszs concept of shape-selective catalysis were

first commercialized in the early 1960s. In displacing the more conven-

tional amorphous catalysts in gasoline production, the zeolite catalysts

were found to greatly increase the amount of gasoline produced from a

barrel of oil as well as the octane number of the gasoline at a time of dra-

matically increased demand for more and higher-octane-number gasoline.

Weiszs work and its significant impact inspired efforts to look for new,

synthetic zeolites, which continue to this day. Several zeolites developed

under his guidance proved applicable for many other petroleum and pet-

rochemical processes, including those that produced precursors for poly-

ester (p-xylene) and high-quality lubricants. One of these zeolites (ZSM-5)

was the basis for Mobils methanol-to-gasoline process, the first new syn-

fuels process since the World War I development of the FischerTropsch

process. Throughout the 1970s and 1980s, Paul was intimately associated

with Mobils discovery of new catalytic materials and the processes that

were developed around them.

While working at Mobil, Paul Weisz took a sabbatical leave to earn his

doctoral degree from the Eidgenossische Technische Hochschule (ETH) in

xii Thomas F. Degnan

Zurich, Switzerland, in 1966. His thesis was based on an analysis of the per-

meation of dyes into fibers. His analysis was the basis for some of the fun-

damental laws associated with diffusing molecules in fibers based on the

molecular dimensions and chemical properties of the molecules.

Born in Pilsen, Czechoslovakia, Paul Weisz grew up with an innate

desire to become a scientist. He published his first article in a ham radio jour-

nal at the age of 16. Paul emigrated to the United States in 1939 from Berlin,

interrupting his graduate studies in Germany to attend Auburn University,

where he completed his B.S. degree in less than one year. Following his

graduation, he worked as a researcher at the Bartol Research Foundation

of the Franklin Institute in Swarthmore, PA. He later moved to the

Massachusetts Institute of Technology, where, as an electronics engineer,

he participated in the development of LORAN, a long-range radio

signal-based aid to navigation.

Weisz joined Mobil Research and Development Corporation in 1946 as

a Research Associate at Mobils Paulsboro, NJ, research laboratory. He

progressed through a number of technical assignments, in 1961 reaching

the position of Senior Scientist, the highest technical position in Mobil.

He managed Mobils Exploratory Process Research organization from

1967 until 1969 and its Central Research Laboratory in Princeton, NJ, from

1969 through 1982. He retired from Mobil in 1984.

He then began a third, highly productive career, applying chemical and

physical principles to biomedical research, first at the University of Pennsyl-

vania and then at the Pennsylvania State University. Working with Made-

leine Jouille at the University of Pennsylvania, he synthesized molecules that

mimic some of the healing properties of heparin while not exhibiting hep-

arins potentially dangerous side effects.

For his numerous industrial research accomplishments and contribu-

tions to the science of catalysis, Paul Weisz earned many awards, including

the E. V. Murphree Award in Industrial Chemistry from the American

Chemical Society (ACS) (1972), the Pioneer Award from the American

Institute of Chemists (1974), the Leo Friend Award from the ACS

(1977), the R. H. Wilhelm Award from the American Institute of Chem-

ical Engineers (1978), the Lavoisier Medal from the Societe Chemique de

France (1983), the Langmuir Distinguished Lecturer Award from the ACS

(1983), the Perkin Medal, the ACSs highest award (1985), the Carouthers

Award from the ACS (1987), and the National Medal of Technology,

awarded by President George H.W. Bush in 1992. Paul Weisz was elected

to the U.S. National Academy of Engineering in 1977 and received an

xiiiObituary Paul B. Weisz

Honorary Doctorate (Sc.D. in technological science) from the Swiss Fed-

eral Institute of Technology in 1980.

The catalysis community will miss one of its most original and influential

members.

Thomas F. Degnan

xiv Thomas F. Degnan

HALDOR TOPSE19132013

Dr. Haldor Topse, founder and Chairman of the Board of Haldor

Topse A/S, passed away on May 21, 2013, only 4 days before his 100th

birthday. His passing away was a great loss to his family, the company,

the catalysis communityand the world at large.

Dr. Topse was a researcher, an entrepreneur, and a businessman. He

was also an idealist and a humanist, deeply engaged in the global community.

In his words: The corporate world in itself means nothing unless it

improves the lives of people and the conditions in poor countries. He cre-

ated a unique company that today is world-leading in catalysis. His achieve-

ments have reached much further: he contributed significantly to the global

community through perseverance and dedication, leading to technological

and scientific contributions to solve key global challenges related to energy,

food, and the environment. Dr. Topse set high standards within the indus-

try; he never stopped pushing the technological boundaries. His vision

inspired and enabled progress that made the chemical industry more sustain-

able, profitable, and competitive.

xv

Haldor Topses leadership of the company led to accomplishments

ranging from fundamental understanding to technological advancements.

One of the first business areas of the companyand to this day one of

the most significantwas ammonia synthesis, in which Topse established

a dominant position based on innovations in the catalyst and the synthesis

process. Other achievements include environmental technologies and

ground-breaking catalytic process equipment. One of Haldor Topses last

efforts was the development of solid oxide fuel cells, and his persistence led

to the establishment of the subsidiary Topse Fuel Cell and a dedicated effort

to develop and commercialize this energy-efficient technology.

Haldor Topse was born in 1913, into a world recovering from a world

war and descending into recession. As a young man studying in Copenha-

gen, he saw the lines of people queuing for jobs, queuing for a free meal

and he vowed to himself that he would make a difference, that he would use

his knowledge and privileged position to contribute to making the world a

better place.

Topse continued his studies with, among others, Niels Bohr, the

Danish physicist and Nobel Laureate. By 1940, he had already made a name

for himself, but on the 9th of April of that year, Hitlers troops invaded Den-

mark. Topse had been offered a job in the United States. A plane was ready

to take him and his family from Denmark, but his departure was impossible,

because two of his children were hospitalized. His wife, Inger Topse,

turned to him and said, Now that we cannot leave, you must make some-

thing which will be useful after the war. And early on, Topse saw the

potential of catalysis, which today is the basis for most of the worlds chem-

ical production.

Topses base was the natural sciences; his years with Bohr were forma-

tive. He based his company on the strong belief that fundamental under-

standing of the chemistry and engineering of the processes in the

companys portfolio would provide a competitive edge. His policy was

always to invest significantly in researchin manpower and research instru-

ments, bench-scale test units, and pilot-scale units. This visionary approach

serves as a model for industrial as well as academic research institutions

worldwide.

Topses conviction was that research and new ideas are vital to staying

competitiveeven research that may not contribute directly to the bottom

line. Ideas that seemed unrealistic 20 or 30 years ago have developed into

xvi Bjerne S. Clausen and James Dumesic

technologies that contribute significantly today. Topse encouraged these

ideas to grow. Through his own scientific understanding and visionary

insights, he inspired the people around him, acting as a catalyst for the com-

pany he created and for the catalysis community as a whole.

Haldor Topses vision and his dedication to fundamental science fos-

tered the development of new catalysts and processes, allowing the company

to grow into new business areas: early on, he identified the business potential

of the refining industry, and thanks to his commitment, significant efforts

were made to develop hydroprocessing catalysts based on cutting-edge

research, resulting in the BRIM catalysts and technology. The develop-

ment of Topses WSA technology (wet gas sulfuric acid) started as the

side-project of one of Topses brightest researchers, and although Haldor

Topse doubted the potential of this technology, he encouraged the

research to continue. Today, Topses WSA technology contributes

significantly to a more sustainable world.

Dr. Topse was driven by a determination to make a difference. The

roots of this determination lie in the depression of the 1930sand his

opportunity to contribute to change. Today, seemingly everyone who

has known Haldor Topse is familiar with his stance that if you have

the ability and the means to contribute to the world, you also have the obli-

gation. Thus, beyond his contributions to science and engineering, Topse

contributed funds for schools, programs for street children, and other wor-

thy causes.

Topse held many influential posts. His knowledge and insight about

sociopolitical megatrends served the globe, exemplified by his work in

the Population Council in the 1970s. He had a knack for networking that

brought him into contact with people of influence: politicians, world

leaders, kings and queensfrom Nelson Mandela to Mahatma Gandhi.

Topse never sat back in awe; rather, he used his talent for dialogue and per-

suasion to express his sociopolitical views, to the benefit of mankind. These

views have been publicized in several books dealing with the global social

and economic situation.

Haldor Topse was honored with numerous awards and medals, among

them the Hoover Medal, in 1991. To Dr. Topse, one recognition espe-

cially stood out: in 1999, the Association of Danish Engineers named him

the Engineer of the century. The honor was given in recognition of both

his technical achievements in catalysis and his commitment to social issues.

xviiObituary Haldor Topse

Dr. Topses social engagement, passion for science, ambition, and

determination created a legacy that continues to exert an enormous world-

wide impact.We and our community will long remember him for his strong

commitment to the world around himand his belief that we all have an

obligation to contribute.

Bjerne S. Clausen*

James Dumesic*

*Parts of this text appeared in Angew. Chem. Int. Ed. 2013. Angewandte Chemie by Gesellschaft

Deutscher Chemiker Reproduced with permission of WILEY - V C H VERLAG GMBH & CO.

xviii Bjerne S. Clausen and James Dumesic

CHAPTER ONE

Analysis of Catalyst SurfaceStructure by Physical SorptionKarl D. Hammond*, Wm. Curtis Conner Jr.*Department of Nuclear Engineering, University of Tennessee, Knoxville, Tennessee, USADepartment of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts, USA

Contents

1. Introduction 72. The Phenomenon of Physical Adsorption 8

2.1 History of adsorption in catalyst characterization 82.2 Choice of adsorbate 92.3 Presentation of adsorption data 122.4 The Langmuir isotherm 142.5 Monolayers to multilayers 162.6 BET theory 18

3. A Tour of the Adsorption Isotherm: From Vacuum to Saturation and Back 273.1 The micropore-filling region: 108

7.2 Sorption analysis techniques derived from simulations 698. Details of Adsorption Apparatus 72

8.1 Volumetric adsorption systems 728.2 Start to finish: Acquiring an adsorption isotherm 75

9. Common Pitfalls in Adsorption Experiments and Analyses 859.1 Definitions of standard temperature and pressure 869.2 Measurement of the saturation pressure 869.3 Drift in bath temperatures/compositions and equipment calibration 889.4 Reference state for argon at 77 K 889.5 Misuse of the BET equation 899.6 Failure to degas properly 919.7 Inaccurate or nonequilibrium pressure readings 919.8 Correcting (incorrectly) for thermal transpiration 929.9 Interpreting hysteresis at low pressures to be porosity 949.10 Reporting 1720 pores 94

10. Summary 95References 97

Abstract

Heterogeneous catalysis usually takes place by sequences of reactions involving fluid-phase reagents and the exposed layer of the solid catalyst surface. Estimation of the totalcatalyst surface area, its potential accessibility to gas- or liquid-phase reactants, and gen-eral catalytic activity are initially based on themorphology of the catalyst. Universally, mea-surements of adsorption and their interpretation are used to estimate the surface area andporosity relevant to catalytic reactions. We provide here a description of many traditionaland recent techniques in adsorption-based catalyst characterization intended for exper-imental practitioners of adsorption. Our chapter includes descriptions of which regions ofthe isotherm correspond to micropore filling, mesopore filling, surface coverage, and sat-uration, supplemented by discussions of model isotherms, from the Langmuir isothermand the BrunauerEmmettTeller theory to the Halsey equation. Pore size distributionmethods include the BarrettJoynerHalenda and relatedmethods for mesopores, empir-ical methods developed for micropores, and simulation-based methods that have finallyresolved the differences between adsorption (increasing loading) and desorption(decreasing loading). This chapter also includes a discussion of hysteresis and metastabil-ity, both of which trip up experimentalists from time to time. We finish with a descriptionof data acquisitionmethods and equipment, which are often obscured behind the facadeof automation, and a discussion ofwhat users should be aware of andwhat can gowrong.

NOMENCLATURE[A] activity of species A

as normalized adsorption isotherm on a standard, nonporous material such as silica orcarbon; asVads/Vads(P/P 0.4)

g surface tension

2 Karl D. Hammond and Wm. Curtis Conner Jr.

u loading: yn/nm, interpreted as the fraction of unoccupied sites in the first layerui loading in layer ik proportionality constant between flux and pressure for an ideal gas; k (2pMakT)1/2m chemical potential ((partial) molar Gibbs free energy)n vibrational frequency along the normal mode that results in desorption from a layerr density of adsorbates atomic/molecular diameterV grand potential, OPVgAA surface area

AAA force constant between the adsorbate and itself in the HK and ChengYang models

AAE force constant between the adsorbate and the adsorbent in the HK and ChengYang

models

Adsorbate the atom/molecule that is adsorbing onto a surface

Adsorbent the solid species onto which the adsorbate adsorbs

Adsorptive a synonym for adsorbate

Am area of one molecule, typically reported in nm2 or A2 per molecule or atom but can also

be in m2/mol or m2/cm3 STP (i.e., surface area per unit volume adsorbed)

Ap surface area of a pore

ai sticking coefficient: probability of adsorbing given a collision with the surface

b Langmuirs parameter, which has units of inverse pressure

AEI International Zeolite Association framework code for materials such as AlPO-18,

SAPO-18, SIZ-8, and SSZ-39 (the code is derived from AlPO EIghteen)

ATS International Zeolite Association framework code for materials such as

AlPO-36, MAPO-36, FAPO-36, and SSZ-55 (the code comes from AlPO Thirty-Six)

BET BrunauerEmmettTeller theory

BJH the BarrettJoynerHalenda method of pore size distribution analysis for mesopores

CBET or C second BET fitting parameter (the other being the monolayer capacity), a

positive number related to the difference in the heat of adsorption between layers

Chemisorption chemical adsorption, the process of atoms ormolecules chemically reacting

with a solid surface, in contrast to physisorption

CH empirical Halsey constant in the FrenkelHalseyHill equation

CK constant of proportionality between inverse pore size and the base-10 logarithm of

relative pressure: CK 2gVl = RT log10 CPDFT classical potential density functional theory

D inner diameter of the glass tube used in physical adsorption experiments

d0 arithmetic mean diameter of adsorbate and adsorbent atoms/molecules in the HK model

Degassing the process of heating a sample to remove adsorbed gases, such as water, from the

surface in preparation for an adsorption experiment; also called outgassing

DFT density functional theory

DH the DollimoreHeal method of pore size distribution analysis for mesopores

Dp pore diameter, Dp2rpf fugacity

F Helmholtz free energy

Fr density functional

FAU International Zeolite Association framework code for materials such as faujasite,

zeolite X, zeolite Y, ECR-30, LZ-210, and SAPO-37 (the code comes from FAUjasite)

G Gibbs free energy of adsorption

3Analysis of Catalyst Surface Structure by Physical Sorption

h height of the bath

H enthalpy of adsorption

H1 hysteresis hysteresis classification in which the loop has similar shape on adsorption as it

does on desorption

H2 hysteresis hysteresis classification in which the loop has a different shape on adsorption

than it does on desorption; the adsorption process is gradual, whereas desorption is

sudden

HEU International Zeolite Association framework code for materials such as heulandite,

clinoptilolite, and LZ-219 (the code is derived from HEUlandite)

HK HorvathKawazoe model for adsorption in slit-like micropores

HRADS high-resolution adsorption, a term applied to techniques that measure adsorption

below about 1 Torr (103 atm)IBET intercept of the BET plot

Jm molecular flux hitting the surface

k Boltzmanns constant

ka rate coefficient for adsorption

kd rate coefficient for desorption

K equilibrium constant

length of the neck of the sample tubeLTA International Zeolite Association framework code for materials such as zeolite A, ITQ-29,

SZ-215,SAPO-42, andZK-21,ZK-22, andZK-4 (thecode isderived fromLindeTypeA, the

original name for zeolite A as synthesized by the Linde group at Union Carbide)

log natural logarithm (note that common (base 10) logarithms are written explicitly (e.g.,

log10(x)))

m mass of the adsorbent

Macropore pore with a radius larger than 50 nm (such pores fill near the saturation pressure

and are generally not resolvable on adsorption isotherms)

Manifold the chamber directly above a valve that connects it to the sample tube in a

volumetric adsorption system

Ma molecular (or atomic) mass of the adsorbate

MEL International Zeolite Association framework code for materials such as ZSM-11, SSZ-

46, silicalite-2, and TS-2 (the code is derived from Mobil ELeven)

Mesopore pore with a radius between 2 and 50 nm

MFI International Zeolite Association framework code for materials such as ZSM-5,

silicalite-1, EU-13, ISI-4, mutinaite, and KZ-1 (the code is derived from

Mobil FIve)

Micropore pore with a radius of 2 nm or less (important: the word micropore has

nothing to do with the word micrometer)

MTT International Zeolite Association framework code for materials such as ZSM-23,

EU-13, ISI-4, and KZ-1 (the code is derived from Mobil Twenty-Three)

MTW International Zeolite Association framework code for materials such as ZSM-12,

CZH-5, NU-13, TPZ-12, and VS-12 (the code derives from Mobil TWelve)

NA areal density of adsorbate atoms/molecules

Nanopore name sometimes used in place of the word pore, especially by authors

attempting to draw analogies to nanotechnology (all micropores, mesopores, and

macropores are nanopores, despite the illogic of the prefixes)

4 Karl D. Hammond and Wm. Curtis Conner Jr.

NE areal density of adsorbent atoms/molecules

nads or n number of molecules (or moles) adsorbed, usually per gram adsorbent

NamA number of moles in the adsorption manifold before the sample valve is opened

NamB number of moles in the adsorption manifold after the sample valve is opened

Ngas number of moles currently in the gas phase inside the adsorption manifold and over the

sample

Nin total number of moles added to the adsorption manifold since the start of the

experiment

NLDFT nonlocal density functional theory, a type of CPDFT in which the functional

includes the contributions of density gradients to the free energies

nm monolayer capacity: the number of molecules or moles of adsorbate in one layer on the

surface, typically normalized per unit mass of adsorbent

NMR nuclear magnetic resonance spectroscopy

Outgassing synonym for degassing

P absolute pressure

PA pressure in the adsorption manifold before the sample valve is opened

PB pressure in the adsorption manifold after the sample valve is opened

P/P relative pressureP saturation pressurePg pressure on the vapor side of a vaporliquid meniscus

Physisorption physical adsorption, the process of atoms or molecules adhering to a surface

without forming chemical bonds, in contrast to chemisorption

P pressure on the liquid side of a vaporliquid meniscus

Ps standard pressure (usually 1 atm.101,325 Pa760 Torr)Q heat of adsorption (negative enthalpy change of adsorption); subscript i indicates

adsorption on the ith molecular layer

QL heat of condensation

QSDFT quenched solid density functional theory, a type of CPDFT in which gradients in

both the adsorbate and adsorbent densities are factored into the free energy calculation;

the net effect is more flexible pore walls than NLDFT

R universal gas constant (in J mol1 K1)RHO International Zeolite Association framework code for materials such as zeolite Rho,

ECR-10, LZ-214, and pahaspaite

rc rate of condensation

re rate of evaporation

rK or hri mean radius of curvature of the meniscus inside a filled or filling pore, often calledthe Kelvin radius

Re ratio of the volume of the empty tube to the manifold volume

Rf ratio of the volume of the filled tube to the manifold volume

Rn square of the ratio of the volume of a cylinder representing the pore and another

cylinder representing the fluid added to/removed from the pore; used in BJH

analysis

rp mean pore radius

S entropy

SBET slope of the BET plot

SABET surface area as extracted from the BET equation

5Analysis of Catalyst Surface Structure by Physical Sorption

SANS small-angle neutron scattering

SBA material code designating unique materials first made at the University of California,

Santa Barbara, such as SBA-15

SEM scanning electron microscopy

SF SaitoFoley model of adsorption in cylindrical micropores

STP standard temperature and pressure, typically defined as 273.15 K and 1 atm

t statistical thickness of the adsorbed layer

T absolute temperature (in Kelvins)

Tb temperature of the bath

TEM transmission electron microscopy

TON International Zeolite Association framework code for materials such as zeolite Theta-1,

ISI-1, KZ-2, NU-10, and ZSM-22 (the code comes from Theta-ONe)

Tr room temperature, typically about 2025C

Ts standard temperature (usually 273.15 K0 C, but others are also commonly used)Tt triple-point temperature (in Kelvins)

Type I isotherm an isotherm, such as the Langmuir isotherm, that is concave and has no

apparent multilayer adsorption

Type II isotherm an isotherm, such as the BET isotherm, that has an inflection point and

shows multilayer adsorption but no hysteresis

Type IV isotherm an isotherm that begins like a Type II isotherm but exhibits hysteresis

Vads or V standard volume adsorbed, in cm3 STP/g adsorbent. VadsnadsRTs/Ps

Vam volume of the adsorption manifold, typically in cm3

Vbulb volume of the bulb at the bottom of a typical glass adsorption cell

VDS apparent volume of the chamber containing the sample from the sample valve onward,

including effects due to temperature gradients, typically in cm3

Ve volume of the empty calibration tube, typically in cm3

Vf volume of the calibration tube after the known-volume insert is in place, typically

in cm3

Vg molecular or molar volume of the vapor phase

Vgas volume, at STP, of adsorbate currently in the gas phase inside the sample and manifold

volumes

Vin total volume, at STP, of adsorbate added to the adsorption manifold since the start of the

experiment

VET International Zeolite Association framework code for the zeolite VPI-8 (the code is

derived from Virginia Polytechnic Institute EighT)

VFI International Zeolite Association framework code for materials such as VPI-5,

AlPO-54, H1, and MCM-9 (the code is derived from Virginia Polytechnic Institute FIve)

V liquid molar or molecular volume

Vm monolayer volume, or the volume all adsorbed molecules would take up if desorbed and

returned to STP; VmnmRTs/PsVp pore volume

Vstd volume of a known standard, such as a cylindrical tube of precision-bore glass

w width of slit-like pores in the HK model

W weighting function for each isotherm in the simulated kernel of isotherms; this

becomes the pore size distribution function when fit to an experimental isotherm

xm areal density of surface sites

6 Karl D. Hammond and Wm. Curtis Conner Jr.

1. INTRODUCTION

Physical adsorption results from interactions between subcritical fluid

species and nearly any solid surface. The measurements are made by a variety

of well-developed techniques and interpreted by using ever more sophisti-

cated models. Physical adsorption experiments probe thermodynamic phase

equilibria between bulk fluid phases and adsorbed phases, which progress

from single, isolated molecules to a single layer of molecules on the surface

(a monolayer) to multilayers to condensation (or sublimation). Analyses of

equilibrium data characterizing the adsorption of physisorbing gases are

commonly employed to estimate the morphology of the sample, including

the total surface area, the distribution of the dimensions of any pores (ranging

in diameter from about 0.1 to 50 nm), and the total pore volume/void frac-

tion. These analyses are employed to guide understanding of the influence of

morphology on sorption, separations, and catalysis.

Considerable progress has been made in the last several decades in inves-

tigations of physical adsorption on high-surface-area solids, both experimen-

tally and theoretically (18), such that we now understand the phenomena

associated with sorption far better than we ever have. Furthermore, materials

synthesis has developed to such an extent that we can now produce materials

possessing very high surface areas (>1000 m2 g1 of solid) or with uniformpores in the range 120 nm, or even solids with multiscale porosity compris-

ing a network of pores of one size embedded within a network of pores of

another dimension and/or connectivity. Physical adsorption (physisorption)

is then employed to characterize, design, and optimize the morphology of

the material for specific applications.

The purpose of this chapter is to provide an understanding of what is

known about physisorption with respect to analyses and interpretation as

these relate to the morphology of high-surface-area solids. To these ends,

we begin by describing the sequence of phenomena associated with phy-

sisorption, its history, and simple modes of adsorption on relatively flat sur-

faces. We then begin our tour, considering the adsorption isotherm, region

by region (Section 3). Adsorption onmaterials having pores less than 2 nm in

fundamental dimensions (called micropores) exhibits unique challenges,

as their pores fill at extremely low pressures, before the surface is completely

covered; these challenges are discussed in Section 4. For larger pores, called

mesopores and macropores, there is often hysteresis between the adsorbing

7Analysis of Catalyst Surface Structure by Physical Sorption

and desorbing trajectories along an adsorption isotherm; the phenomenon of

adsorption hysteresis is discussed in Section 5. We also discuss methodolo-

gies involved in determining porosity and pore size distributions and close

the chapter with discussions of the experimental aspects of adsorption: how

adsorption apparatus works and how to avoid some common mistakes in

measuring and interpreting adsorption data.

2. THE PHENOMENON OF PHYSICAL ADSORPTION

2.1. History of adsorption in catalyst characterizationIt was recognized well over a century ago that solid surfaces could enable

gases or liquids to react under conditions in which they would not react

in the absence of the surface. These observations were quickly understood

to occur when molecules or atoms stuck to the surface, changing both

their relative reaction energies and their local concentrations. This

processatoms and molecules adhering to a surfacewas termed adsorp-

tion by Kayser in 1881 (9). Irving Langmuir (10,11) later expressed the

kinetics of steps associated with the individual adsorption and desorption

processes by assuming that each atom/molecule reacted with an array of

sites on the surface,

AS !ka A S AS 1:1AS !kd AS AS, 1:2

where [A] represents the activity of an adsorbed molecule, the adsorbate, and

[S] the activity of a site on the solid, the adsorbent. The adsorbate can also be

called the adsorptive, especially in situations in which adsorbent and

adsorbate may be confused. At equilibrium, an equilibrium constant,

K, reflects the ratio of adsorption and desorption rate coefficients, ka/kd.

Langmuir was attempting to provide a quantitative analytical back-

ground for heterogeneous catalytic reactions, and the sorption processes

to which he was referring were generally exothermic and activatedwhat

we would now call chemical adsorption, or chemisorption. However, it was soon

understood that less exothermic processes could occur under the general

heading of adsorption, and indeed, adsorption could occur without for-

ming chemical bonds with the surface. Such nonchemical adsorption is

called physical adsorption, or physisorption.

8 Karl D. Hammond and Wm. Curtis Conner Jr.

2.2. Choice of adsorbateThe choice of adsorbate (vapor to be adsorbed) is largely dictated by the type

of information desired and the adsorbent that one wishes to characterize. For

physical adsorption, the adsorbatemust be chemically inert with respect to all

compounds present on the surface. Nitrogen and argon are common choices

for this reasonand several other (very important) considerations: they are

readily available, inexpensive, and relatively safe to handle. Nitrogen and

argon also have another distinct advantage when it comes to porous mate-

rials: they are very small molecules and can thus penetrate much smaller

pores and cover smaller surface features than larger molecules such as

cyclohexane.

Krypton has been employed as an adsorbate, particularly for materials

with very low surface areas. The reason for this application is that kryptons

vapor pressure at liquid nitrogen temperature is very low (2 Torr (12)),meaning that errors in the dead space (Section 8.2.1) are less important.

Xenon is also an inert probe for low-surface-area materials; like krypton, it is

typically used at liquid nitrogen temperatures. This choice is one of practi-

cality: liquid nitrogen is much cheaper than liquid krypton or xenon. It has

the drawback that 77 K is well below the triple points of both krypton and

xenon. XenonNMR spectroscopy has also been employed to probe the tex-

ture and chemistry of surfaces; see the many studies by Fraissard et al.

(1318).

Water can be used as an adsorbate, but its highly polar nature provides

some interesting analysis quirks. The most important of these is that inter-

actions between water molecules are sometimes stronger than interactions of

water with surface atoms/molecules, meaning that the isotherm (see next

section) is convex to the pressure axis. This is particularly true for graphite

and other carbonaceous (i.e., nonpolar) adsorbents. Water adsorption there-

fore holds its own niche in the adsorption community and requires

completely different interpretations than those characterizing more typical

adsorbateadsorbent interactions.We do not discuss water adsorption in this

chapter.

Carbon dioxide is an increasingly common choice as an adsorbate. How-

ever, it poses challenges in the interpretation of adsorption data: carbon

dioxide sublimes under the conditions of most adsorption experiments,

which implies that any concept of monolayer adsorption is complicated

by the differences between the surface phase, a supercooled liquid reference

phase, and the solid phase that actually occurs at saturation. It has also been

9Analysis of Catalyst Surface Structure by Physical Sorption

known to chemisorb on many materials (12), and it is also known to inter-

calate between layers of carbonaceous materials (19,20), a process that is

more akin to dissolution or absorption than adsorption.

Hydrocarbons such as methane or butane are commonly used as adsor-

bates, but only for the purpose of estimating adsorption capacities of that spe-

cific hydrocarbon, such as for interpretation of diffusion or catalytic activity

data.We emphasize, however, that the surface area and porosity accessible to

larger hydrocarbons such as benzene or nonane may be smaller than those

available to small molecules such as nitrogen or argon. Indeed, materials with

multiscale porosity may have many small pores connecting larger ones; if the

adsorbing molecule is too large to diffuse through the small pores at appre-

ciable rates, large fractions of the porosity may be inaccessible. Furthermore,

if the surface is atomically rough, the adsorbate might not adsorb on the

rougher areas, obscuring the surface area.

For the purpose of surface area determination and assessment of porosity,

which are the primary topics of this chapter, the use of nitrogen and argon is

nearly universal for the reasons discussed earlier in this section. Other inert

gases, such as krypton or xenon, are also used in specialized adsorption

experiments, such as determining occluded porosity (e.g., pores accessible

to nitrogen but not xenon), assessing surface roughness (21), or determining

surface areas of very low-surface-area materials.1 A list of common adsor-

bates and their properties is included in Table 1.1.

It might be noted that nitrogen, oxygen, and carbon dioxide have non-

zero quadrupole moments, whereas argon, krypton, and xenon do not.

Quadrupolar interactions between adsorbing species and a surface have been

invoked to explain several differences in adsorption phenomena (22). These

include smaller molecular surface areas for nitrogen as a consequence of

nitrogens ability to stand up on the surface because of interactions

between its quadrupole moment and ions or polar functional groups on

the surface, such as oxides or hydroxides. The coverage per molecule is less

when the nitrogen molecule is perpendicular to the surface than it is when

the molecule lies flat on the surface with its axis parallel to the surface.

Quadrupolar interactions have also been suggested as the reason why nitro-

gen adsorbs on zeolites and other microporous silicates at lower pressures

than argon (which lacks a quadrupole moment). However, we note that

silicalite-1 exhibits the same differences between nitrogen and argon

1 Krypton and xenon are often used in low-surface-area analyses because their vapor pressures at liquid

nitrogen temperatures are extremely low, minimizing errors in the dead volume (Section 8.2.4).

10 Karl D. Hammond and Wm. Curtis Conner Jr.

Table 1.1 Common adsorbates and their properties under the conditions of common adsorption experimentsVapor T (K) Am (

2) Am (m2/cm3 STP) g (N/m) V (cm

3/mol) P (Torr) CK () References

N2 77.36 16.2a 4.30 0.00888 34.7 760 4.16 (2325)

N2 87.30 0.00667 36.9 2130 2.95 (23,24)

N2 90.20 17.0 4.51 0.00606 37.7 2750 2.65 (2325)

Ar 77.36b 18.0c 4.78 27.5 230c (12,26)

Ar 87.30 16.6a 4.40 0.01242 28.6 760 4.25 (12,27)

Ar 90.20 14.4 3.82 0.01186 29.1 1020 4.00 (2426)

O2 90.20 14.1 3.74 0.0132 28.1 760 4.30 (25,28,29)

CO2 194.7b 14.1 3.74 28.1 1320d (28,30)

Kr 77.36b 20.8 5.52 1.78 (31,32)

Xe 77.36b 23.3 6.18 0.00187 (33,34)

aThere are two proposals (12): use 16.6 A2 for adsorption on both carbons and oxides, meaning Am(N2, 77 K)16.2 A2 for adsorption on carbons and 19.3 A2 foradsorption on oxides; or use 16.2 A2 for adsorption on everything for nitrogen and use 13.8 A2 for argon adsorption on carbons and 16.6 A2 for adsorption on oxides.Keeping the value for nitrogen constant and changing the value for argon is typical, although not necessarily motivated by any theoretical considerations.bTemperature is below the triple-point temperature.cThe value of 230 Torr refers to the supersaturated liquid; the sublimation pressure at 77.36 K is 200 Torr (26). The value Am18.0 A2 corresponds to BET plots usingthe sublimation pressure rather than the vapor pressure (12).dThe value of 1320 Torr refers to the supersaturated liquid; the sublimation pressure is of course 760 Torr (30).Symbols: T, temperature of bath; Am, area of one monolayer for use with Equation (1.22); g, surface tension; and V, molar volume for the Kelvin equation(Equation 1.23); CK 2gVl = RT log10 , the constant for the reduced Kelvin equation (Equation 1.35); and P, saturation pressure. Rows in boldface indicatethe most common and/or recommended bath temperature for the adsorbate in question.

adsorption as ZSM-5, even though the former has no aluminum or internal

hydroxyl groups. We are unaware of any independent spectroscopic evi-

dence of significant quadrupolar interactions giving rise to differences in ori-

entation or energetics under the conditions employed in physisorption

measurements, but we do not discount the possibility.

2.3. Presentation of adsorption dataAdsorption data are largely presented in two ways: isotherms, or plots of

quantity adsorbed against pressure or a similar abscissa at a fixed temperature;

and isobars, or plots of quantity adsorbed against temperature or inverse tem-

perature at constant pressure. Isotherms are muchmore common, as it is typ-

ically much more difficult to control pressure at non-atmospheric values than

it is to control temperatures. A list of common low-temperature baths is

given in Table 1.2. The vast majority of adsorption isotherms for the purpose

of catalyst characterization are nitrogen isotherms recorded at 77 K (liquid

nitrogen at its normal boiling point).

Adsorption isotherms are plots of quantity adsorbed against pressure,

fugacity, activity, or chemical potential. Pressure is nearly always the pre-

ferred abscissa in experiments: measuring the chemical potential is (unfortu-

nately) rather difficult. Theoretical or simulated isotherms, however, often

are based on chemical potential or activity instead. There is little difference

Table 1.2 Common (and not-so-common) low-temperature baths used in physical andchemical adsorptionBath Bath temperature Adsorbates typically used Tt (K)

d

Nitrogen 77.36 K (boiling) N2, Ar, Kr, Xe 63.1526

Argon 87.30 K (boiling) Ar, N2, Kr, Xe 83.8058

Oxygen 90.20 K (boiling) Ar, N2a 54.36

CO2b 194.7 K (subliming) Hydrocarbons, CO2 216.55

Ammonia 240 K (boiling) Ammonia 195.40

Water/ice 273.15 K (freezing) Hydrocarbons, carbohydrates, CO2 273.16

Ambient air 292300 K H2,c COc N/A

Boiling water 373.15 K (boiling) 273.16

aLiquid oxygen baths are typically used only in specialized experiments because of safety concerns.bCarbon dioxide baths are usually dry ice in a low-freezing liquid such as acetone or alcohol.cFor chemisorption.dThe symbol Tt indicates the triple-point temperature.

12 Karl D. Hammond and Wm. Curtis Conner Jr.

between these choices: the vapor phase obeys the ideal gas law at the pres-

sures involved in most adsorption experiments, and thus the pressure and

chemical potential are related via the following result, derived from the

GibbsDuhem equation:

m m kT log a m kT log f =f m kT log P=P 1:3

where P is the saturation pressure, the pressure at which the bulk liquid isin equilibrium with the vapor at this temperature, and the quantity P/P isa dimensionless quantity called the relative pressure. Strictly speaking,

the reference pressure is not necessarily equal to the saturation pressure,

but the difference in chemical potential between two points on the isotherm

will still be equivalent to a difference in the logarithm of the relative

pressure.

The quantity adsorbed is usually expressed inmoles or the equivalent (see

following paragraph) and normalized by the mass of the adsorbent. This nor-

malization is dubious in some cases: the quantity adsorbed per gram of a very

dense adsorbent may be quite high per unit volume of adsorbent, for exam-

ple, despite low values of the number of moles per gram on the isotherm.

Comparing the quantity adsorbed per gram of ceria (r7 g/cm3) wouldnot be a good comparison to the quantity adsorbed per gram of alumina

(r4 g/cm3), for example, because of the difference in density. Whencomparing quantity adsorbed across different materials, one should take care

to normalize the plots in such a way that the resulting comparison makes

logical sense.

When measuring adsorption isotherms, it is common to substitute the

number of molecules (or moles) adsorbed, n, for standard volumes adsorbed,

V. The standard volume is simply the volume that the molecules would take

up in an ideal gas at standard temperature and pressure (STP).What precisely

it means to be at STP is somewhat varied; we discuss this in Section 9.1.

Because these quantities differ by a constant, it makes very little difference

which one is chosen. Because using standard volumes typically requires one

fewer set of conversions (see Section 8), doing so is typical. From this point

on, we make no distinction between the number of molecules or moles and

standard volumes, and, in all instances when n appears in the equations in the

preceding text, it can be replaced byVwithout changing the meaning of the

equations.

The astute reader will note readily that it is the logarithm of pressure that is

proportional to changes in chemical potential, the driving force behind

13Analysis of Catalyst Surface Structure by Physical Sorption

adsorption. Using logarithmic pressure axes, however, is hindered by the

fact that taking the logarithm obscures most of the interesting parts of

the isotherm related to porosity (Section 3), which occur in the decade

between P/P101 and P/P1.Examples of adsorption isotherms can be found in figures throughout this

document. We consider some model isotherms in the remainder of this sec-

tion. We emphasize that none of these models predicts observed adsorption

isotherms in perfect detail in all regions of the isotherms. Indeed, they tend

to be good models of adsorption only for idealized systems or in relatively

narrow regions of the adsorption isotherm.

2.4. The Langmuir isothermThe Langmuir adsorption isotherm (11) is the simplest model of adsorption

that yields useful results. The Langmuir isotherm is based on the following

assumptions:

1. The surface consists of a uniform two-dimensional array of identical

adsorption sites.

2. The probability of adsorbing on or desorbing from a site is independent

of the number of nearby molecules (the loading, y).3. The activation energy for desorption is equal to the heat of adsorption,Q.

4. The vapor phase obeys the ideal gas law.

5. A site may not adsorb more than one adsorbate species at a time (no

layering).

With these assumptions, the number of molecules striking the surface per

unit area (the flux, Jm) is the following (35):

JmP1

2p1

MakT

rPk 1:4

where P is the pressure of the gas,Ma the molecular mass of the adsorbate, k

Boltzmanns constant, and T temperature. If we define the loading (fraction

of occupied sites) as y, then the fraction of empty sites is 1y. If we assumethat there is a probability, a, of a molecule sticking to the surface, then the

rate of condensation is

rc aJm 1y aPk 1y : 1:5By the third assumption, the rate of evaporation is

re xmneQ=kTy, 1:6

14 Karl D. Hammond and Wm. Curtis Conner Jr.

where xm is the number of surface sites per unit area and n is the frequency ofvibration along the reaction coordinate that results in desorption. At

equilibrium, rc re and, thus,aPk 1y xmneQ=kTy: 1:7

Solving for the loading, we obtain the Langmuir adsorption isotherm,

y akPxmneQ=kT aLP

bP

1 bP 1:8

where bak/(xmneQ/kT) has units of inverse pressure and is often a fittedparameter. If we define Ps as the standard-state pressure, then the quantity

KbPs is the equilibrium constant of the reaction, that is,

K T eDGads=kT eDSads=keDHads=kT eDSads=keQ=kT , 1:9

where G is Gibbs free energy, S entropy, and H enthalpy.

These results are summarized in Figure 1.1. The primary characteristic of

the Langmuir isotherm is the last assumption: only a single layer forms,

A + ka

A

A kd

A +

KineticskaP(1 q) = kdq q

1 q=

kakd

P = bP

q =bP

1 + bP

At equilibrium

1 2

0.25

0.5

0.75

1b = 10 atm1

b = 1 atm1

b = 0.1 atm1

P (atm)

q

Figure 1.1 The Langmuir (Type I) adsorption isotherm. In this model, a single layer, ormonolayer, forms when adsorbate particles adhere to specific sites on the surface,resulting in a horizontal asymptote at unit loading. The loading, y, is the quantityadsorbed divided by the quantity adsorbed at saturation (infinite pressure). Highervalues of b indicate stronger adsorbateadsorbent interactions.

15Analysis of Catalyst Surface Structure by Physical Sorption

meaning there is saturation (a horizontal asymptote) once monolayer capac-

ity is reached. Equation (1.8) is the basis for most theories of heterogeneous

catalysis and chemical adsorption.

2.5. Monolayers to multilayersThe Langmuir adsorption isotherm (Equation 1.8) is based on the

assumption that adsorption proceeds from zero up to saturation,

y!1. The adsorbate species in the gas or liquid phase are in equilibriumat a specific temperature and pressure with the species adsorbed on the

surface. All species adsorbed are presumed to have equal chemical

potentials, which do not depend on the presence of other adsorbed spe-

cies. Thus, it is assumed that the interactions of each adsorbing species

with the surface are identical and that interactions between adsorbate

atoms/molecules on the surface are much weaker than the interactions

with the surface.

When applied to reversible chemical adsorption (chemisorption),

the Langmuir adsorption isotherm applies to both uniformly distributed sites,

in which case the loading is proportional to the fractional coverage of

the surface, and sites distributed on only a (possibly small) fraction of the sur-

face. In the latter case, saturation of the Langmuir adsorption isotherm rep-

resents the covering of only a part of the surface.

In physical adsorption, in contrast to chemisorption, the entire surface

accessible to the adsorbate is involved. Thus, to a good approximation,

the surface is entirely composed of active sites, and saturation would be

achieved when the adsorbing species completely covers the surface. This

would represent a monolayer of adsorbed species. Intuitively, the maximum

coverage would reflect the closest packing of adsorbing species on the sur-

face. In physisorption, the forces between an adsorbed species and a surface

site are relatively weak, and the adsorbed species are relatively free to move

across the surface and to change the surface sites with which they primarily

interact. This facile, two-dimensional mobility also differentiates physical

from chemical adsorption.

Physisorption occurs as a consequence of the interactions between any

surface and molecules as the temperature approaches the boiling (or dew)

point of the molecules in the gas. It begins at a temperature or pressure

substantially below the actual pressure or temperature at which bulk

16 Karl D. Hammond and Wm. Curtis Conner Jr.

condensation would occur. As an analogy, we can feel the effects of

humidity even though it is not raining, or even damp, outside.

When an atom or molecule approaches any surface, it is influenced by

forces of attraction (e.g., van derWaals forces). A molecule is also influenced

by such forces when it approaches other adsorbed molecules. In physical

adsorption, whereby adsorbateadsorbent interactions are relatively weak,

a molecule that encounters a molecule already adsorbed will be influenced

by similar (albeit weaker) forces of attraction than those involving a surface

site. It will have a probability of adsorbing on top of a group of already

adsorbed molecules, which will probably be less than the probability of

adsorbing if it had encountered the uncovered surface. The difference in

the probabilities between adsorbing on top of already adsorbed species

and on exposed solid surface is directly related to the difference between

the energies of attraction between the surface and an adsorbing molecule

and between an adsorbed molecule and an adsorbing molecule. The surface

also contributes to the forces of attraction for adsorption of the molecules in

the second and higher layers, but the forces are reduced because the mole-

cules are at a larger distance from the surface.

Physical adsorption will therefore involve the formation of more than a

single layer of adsorbed molecules as the pressure increases. Thus, multilayer

adsorption is primarily a property of physical adsorption. It can, however, be

found for chemisorption if subsequent layers differ in composition, as in

atomic layer deposition (36).

If we wish to interpret the relationship between the quantity adsorbed

and pressure under isothermal conditions (or the quantity adsorbed

and temperature under isobaric conditions), it is necessary to understand

multilayer adsorptionspecifically, the relationship between adsorption

of the first layer (the monolayer) and adsorption of subsequent layers. Prob-

ability (and thus entropy) leads one to conclude that the second layer should

start to fill before the first layer is completed, provided there is not an

extremely large difference in the heat of adsorption between these layers.

As the number of adsorbed layers increases, it is also reasonable to assume

that the heat of adsorption will eventually approach the heat of condensation

of the adsorbate. Several relationships have been proposed to express the

changes in the amount adsorbed and the pressure and temperature for

adsorption up to and in excess of a monolayer. We discuss several of these

throughout this chapter.

17Analysis of Catalyst Surface Structure by Physical Sorption

2.6. BET theory2.6.1 The BET equationBy far, the best known model of multilayer adsorption is that developed

by Brunauer, Emmett, and Teller (37), universally known in the adsorp-

tion community as BET theory. This theory was developed to describe

the initial adsorption of a monolayer and the simultaneous adsorption of

multilayers. It starts with the premise that more than a single layer can be

formed on a surface. It is further based on the assumption that the energy

of interaction between the adsorbing species and the surface is strongest in

the first layer and decreases for subsequent layers. To simplify the ana-

lyses, Brunauer, Emmett, and Teller made a further assumption: the

energy of interaction (heat of adsorption) between Nth and N1st layersfor N2 and as N!1 is the same as the heat of condensation. The BETtheory is also based on the assumption that the corresponding sticking

coefficients and attempt frequencies for the second and higher layers

are the same as for the second layer. Only the forces of interaction

(and sticking coefficients and attempt frequencies) between the surface

and the first layer are different in the BET theory. Furthermore, it is

assumed that the volume of each adsorbed layer is identical. This is equiv-

alent to assuming that the surface is flat (smooth on an atomic scale).

Moreover, at PP, the saturation pressure, the number of layers is infi-nite, and the adsorbate density becomes identical to that of the

bulk liquid.

Just as in the Langmuir expression (Equation 1.8), it is possible to express

the formation of a monolayer by considering the rate of adsorption onto

empty sites and their rate of desorption. We express the fraction of empty

sites as y0 and the concentration of those sites covered in the first layer asy1 (and so on for higher layers). The heat of adsorption in the first layeris Q1, and xm is the number density of sites in the sample, as before.

By analogy to Equation (1.7), the rate of ad/desorption for each layer i at

equilibrium is as follows:

aiPk 1yi xmnieQi=kTyi: 1:10

The attempt frequency ni is, at the microscopic level, the vibrational fre-quency of the normal mode of the adsorbed complex that, if sufficiently

excited, will result in desorption of a molecule. It is never actually measured,

nor is it necessary to do so.

18 Karl D. Hammond and Wm. Curtis Conner Jr.

By definition,

X1i0

yi 1, 1:11

and the number of molecules adsorbed on the surface is nnmP

i01 iyi,

where nm is the monolayer capacity (total number of sites in the sample). From

Equation (1.10) and the assumption that the second and higher layers have

identical properties, we find the following set of equations:

y1 a1xmn1

PeQ1=kT y0

y2 a2xmn2

PeQL=kTy1 a1xmn1

a2

xmn2P2e Q1QL =kTy0

y3 a2xmn2

PeQL=kTy2 a1xmn1

PeQ1=kTa2

xmn2PeQL=kT

2y0

. . .

yi a2xmn2

PeQL=kTyi1 a1xmn1

PeQ1=kTa2

xmn2PeQL=kT

i1y0 1:12

These equations can be written more concisely if we define ay1/y0 andby2/y1. We define another constant, C, as their ratio,

C ab a1a2

n2n1exp

Q1QLkT

1:13

and write the fractional coverage of each layer as follows:

yi abi1y0 biCy0: 1:14C is positive and dimensionless. From Equation (1.11), we can write

y0 1X1i1

yi 1X1i1

bi" #

Cy0: 1:15

Because b

nnm Cb

1b 1bCb : 1:16

If we now factor in the assumption that n!1 as P!P, then we know,from the definition of b, that

limP!Pb 1

a2

xmn2PeQL=kT , 1:17

which means that bP/P and thusn

nm CP=P

1P=P 1 C1 P=P : 1:18

Equation (1.18) is the BET adsorption isotherm. To find the number of

molecules in one monolayer, which is proportional to the surface area, it is

convenient to rearrange this equation into something easily plotted, such as

P=P

n 1P=P 1

nmCC1

nmCP=P: 1:19

Equation (1.19) is called the BET equation. A plot of the left-hand term, P/

n(PP), versus P/P yields (if the model assumptions are accurate, at least) astraight line with slope (C1)/nmC and intercept 1/nmC. The surface area,SABET, and the value ofC (often writtenCBET) are therefore given in terms

of the slope, SBET, and the intercept, IBET, by the following:

SABET AmSBET IBET and CBET 1

SBET

IBET1:20

where Am is the area one molecule occupies on the surface. The general

approach employed in the BET theory is depicted in Figure 1.2.

2.6.2 The constant C in the BET equationThe value of C in Equation (1.19) reflects the differences between the for-

mation of the first layer and the formation of subsequent layers (i.e., a/b as inEquation (1.13)). In the BET formulation, this is viewed as the difference

between the first and second layers, with all layers from 2 to 1 regardedas being similar. Differences between the reflection coefficients and attempt

frequencies between the first and second layer are presumably small (of order

unity), so that the value ofC is most sensitive to the difference in interaction

energy (heat of adsorption) between the surface and the first layer and

20 Karl D. Hammond and Wm. Curtis Conner Jr.

between the second and subsequent layers (these latter differences tend to

the heat of condensation). That is,

C a1a2

n2n1exp

Q1Q2kT

exp Q1QL

kT

1SBET

IBET1:21

The value of C therefore reflects the difference in the heat of adsorption

for the first layer compared with the heat of condensation. The value of C is

thus sensitive to the enhancement resulting from adsorption in comparison

with bulk condensation. Large values of C reflect high adsorption energies

AdsorbentMonolayer

Liquid-like second and higher layers

kd,iqi = ka,iPqi1

Each layer is assumedLangmuir-like on top of prior

layers, but the first layer differsfrom all higher layers.

C = AeQ1Q2

kT > 0P/

Vads(1 P/P )=

1

CVm+

C 1

CVmP /P

BET Equation

P / P

P /P

Vads(1 P / P )

slope =C 1CVm

intercept =1

CVm

BET PlotVm =

1

slope + intercept

C = 1 +slope

intercept

P

Figure 1.2 Schematic representation of the BET adsorption isotherm and its assump-tions. Themonolayer volume, Vm, from the BET plot is often used to estimate the surfaceareas of catalysts, provided that the value of C is reasonable and the assumptions of themodel apply.

21Analysis of Catalyst Surface Structure by Physical Sorption

for the first layer, whereas small values of C reflect small differences in

adsorption compared with condensation.

The ability to calculate a monolayer volume from an adsorption iso-

therm depends on the nature of the isotherm and, thus, on the difference

in the energy for the interaction between the surface and the first layer and

the energy of interaction between the first and subsequent layers. Low

values of C calculated from the BET equation can mean that the first layer

is not significantly enhanced in adsorption compared with subsequent

layers, and it will therefore be difficult to determine a proper value of

the monolayer volume. A rule of thumb is that C must be greater than 50

for the BET theory to give rise to a reasonable calculation of the monolayer

volume and, thus, the surface area (38). A C value of 20 corresponds to a

difference of greater than 1.92 kJ/mol in the heat of adsorption of nitrogen

at 77 K, for example; the heat of condensation is 5.56 kJ/mol at this

temperature.

At the other extreme, large values of C reflect (in the BET theory) large

differences in the energy of interaction for the first layer compared with sub-

sequent layers. The theory was developed to represent physical adsorption

on a flat (or nearly flat) surface, not chemisorption or adsorption in micro-

pores (i.e., pores less than approximately 2 nm in radius, for which the

assumption of a flat surface is no longer valid). Thus, there is an upper limit

to the value of C for which BET analysis is reasonable to employ. Sing et al.

(12,38) suggested that values of C greater 200 found in BET analyses would

make the analysis questionable, and therefore the surface areas calculated

from such data should be used only with reservation. A C value of 200 cor-

responds to a difference in the heat of adsorption of 19.2 kJ/mol for nitrogen

adsorption at 77 K. The shape of the BET isotherm as a function of the C

parameter is shown in Figure 1.3.

It is apparent from Figure 1.3 that isotherms with low values of C do not

exhibit a definite transition between the first and subsequent layers (this tran-

sition occurs at a relative pressure of0.1), whereas isotherms characterizedby higher values of C (>200) exhibit a transition at much lower relativepressures. Intermediate values of C (and thus the difference between the

adsorption in the first layer and that in subsequent layers) give an easily dis-

tinguishable transition from monolayer to multilayer adsorption. Higher

values of C imply strong adsorption (i.e., more than simple physical adsorp-

tion onto a flat surface).

We emphasize that the calculation suggested earlier (C1 slope/inter-cept) can be extremely sensitive to the value of the intercept. This point is

22 Karl D. Hammond and Wm. Curtis Conner Jr.

0.1 0.2 0.3 0.4 0.5106 105 104 103 102 101

Relative pressure (P/P) Relative pressure (P/P)

0

0.5

1

1.5

2

L

o

a

d

i

n

g

(

n

/

n

m

)

C = 1

10

50

100

200

1000

10,000

1

10

50

2001000

10,000

Figure 1.3 The shape of the BET isotherm varies significantly as a function of the C parameter. Values of C between 50 and 200 (shadedregion) are generally considered reasonable; values outside this range are found in situations for which the assumptions underlying the BETtheory are likely invalid. The plot on the left is represented with the pressure on a logarithmic scale; such plots are typical for high-resolution(micropore) adsorption isotherms.

particularly problematic because the BET surface area parameter is often not

particularly sensitive to the intercept. The slope is always positive (unless

C

difference is smaller than the uncertainty in the measurement of Am. The

value of the area for a close-packed liquid is thus often used, meaning

Am13.8 A2 per atom. A value of 14.2 A2 per atom is used in some casesas well (39). In general, surface areas can be determined from argon iso-

therms, but the value of the specific surface area assumed in the calculation

should be specified along with the C constant in the BET equation. Values

for other temperatures and other adsorbates are presented in Table 1.1.

If the assumptions underlying the model hold, Vads(1P/P) is a strictlyincreasing function of relative pressure in the range in which the BET equa-

tion is applied, and if the value of C is reasonable, then measured values of

the BET surface area are typically repeatable within 5%.

2.6.4 Rough estimates: The single-point BET surface areaThe value of Am4.30 m2/cm3 STP for nitrogen at 77 K lends itself to aneasy estimate of the BET surface area of a non-microporous material. Pick a

point on the isotherm that is above monolayer coverage but below any

mesopore filling; P/P0.2 is usually a good choice, although values any-where in the range from 0.1 to 0.25 have been used by various authors,

depending on their guess of Point B defined by Brunauer et al. (37).

Now, multiply the volume adsorbed (in cm3/g) by 4.3 (or 4 for a rougher

estimate). The result is a very rough estimate of the surface area.

2.6.5 Weaknesses of the BET theoryThe BET theory was formulated on the basis of a series of assumptions

(Section 2.6.1) that may or may not be too restrictive for a particular system.

Fortunately, for a large fraction of solids, these assumptions are appropriate at

relative pressures below P/P0.3 (i.e., an average of approximately onemonolayer of adsorption on a smooth surface). One problem with the for-

mulation of the BET theory is that each individual molecule added on top of

another molecule in a partial layer is viewed as being adsorbed with the same

energy as found for bulk condensation. The interactions between molecules

in a given layer are also disregarded. Thus, the n1st and n2nd layers maybegin to form before the nth layer is complete. This picture also does not

fully account for the entropy of adsorption: it accounts for changes in con-

figurational entropy (ways of arranging molecules on the surface), but

neglects entropy arising from molecular mobility, as the molecules are fixed

in position in the BET model (12). It is also difficult to interpret rough sur-

faces in the context of BET theory, as such surfaces violate the assumption of

an array of nearly identical adsorption sites.

25Analysis of Catalyst Surface Structure by Physical Sorption

Halsey (40) observed that the BET theory includes the quite untenable

hypothesis that an isolated adsorbed molecule can adsorb a second mole-

cule on top, yielding the full energy of liquefaction, and that in turn the

second molecule can adsorb a third.... One would expect that the linear

picture of columns of molecules would not be formed, but instead layers

would more closely approximate close-packed layers, in which subsequent

adsorbing molecules can interact with more than one molecule in the

layer(s) below. These effects, if accounted for, would all add small correc-

tions to the BET equation, some of which become more important for

specific systems.

The assumption that the second and subsequent layers all have adsorption

energies that are equal to the energy of condensation neglects the possibility

that the second layer may be influenced by the solid surface, which is only a

few Angstroms distant. In many cases, the second layer will be influenced by

the presence of the surface below and thus interact with the surface. This net

interaction energy in the second layer will fall somewhere between that of

the first layer and the energy of condensation. As layers above the second

layer are formed, the differences between the first and the second and the

second and the third layers become evident.

The BET theory therefore overestimates the rate at which multilayers

form and does not account for the adsorption entropy. It also simplifies

the energy of interaction between layers. However, these problems occur

primarily at loadings above an average of one monolayer of adsorption.

At loadings up to onemonolayer average coverage, the BET theory has been

shown to provide the most consistent approach for the estimation of the

exposed surface area for surfaces for which appropriate values ofC are found

(12,38,41)that is, for C>50 (reasonably strong forces of adsorption) andC

3. A TOUR OF THE ADSORPTION ISOTHERM: FROMVACUUM TO SATURATION AND BACK

A physical adsorption isotherm can be analyzed to determine a variety

of morphological characteristics of a solid. No single theory is able to reflect

all physical interactions for sorption (adsorption and desorption): from the

first few sorbing molecules, to a monolayer, to multilayers, to condensation

of a liquid (or even a solid) throughout the system. Theories have been

developed to represent each of the sequential processes associated with

the measurement of sorption.

In this section, we offer a tour of the physical adsorption isotherm,

starting at the lowest pressures that can be obtained by conventional vacuum

equipment (typically P108 P or higher), progressing in order throughthe following regions: micropore filling, surface coverage (monolayer for-

mation), mesopore filling, macropore filling, saturation, macropore empty-

ing, and mesopore emptying. The astute reader will recognize that these

regions often overlapbecause the transition between them is often

unclearand thus analysis is typically restricted to ensure applicability of

the given model analyses. We use Figure 1.4 as a guide.

3.1. The micropore-filling region: 108

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

100

200

300

400

500

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

200

400

600

800

1000

Vol

ume

adso

rbed

(cm

3 S

TP

/g)

Vol

ume

adso

rbed

(cm

3 S

TP

/g)

Relative pressure (P/P)

Relative pressure (P/P)

Figure 1.4 Nitrogen isotherms at 77 K on SBA-15 silica samples that incorporate bothmicropores andmesopores, suggesting different regions of the isotherm as discussed inthe text. The top plot indicates a solid containing larger mesopores than the lower plot;the material represented in the lower plot has pores that lie right on the transitionbetween micropores and mesopores.

28 Karl D. Hammond and Wm. Curtis Conner Jr.

adsorption, or HRADS (a term coined by Venero and Chiou (42)), as dis-

cussed in Section 4.

A representation of the phenomena associated with this region of the

adsorption spectrum is shown in Figure 1.5. The pores fill at pressures well

below those required to give a monolayer on the exterior surface because of

Figure 1.5 Schematic representation of pore filling in micropores. The pores fill withadsorbate before the exterior surface is covered. Reprinted with permission from Ref. (43).Copyright 2005, American Chemical Society.

29Analysis of Catalyst Surface Structure by Physical Sorption

the three-dimensional interactions between the sorbing molecule and the

surface. It is not even clear what is the density of the sorbed species when

the pores are filled, as this depends on the molecule-to-surface and

molecule-to-molecule interactions, which can differ even for physisorption.

3.2. Monolayer region: 0.05

three-dimensional network), these void spaces will gradually fill with

condensing adsorbate as the pressure increases. The smaller pores fill

and empty at lower relative pressures. At the same time, more is

adsorbed as the exposed surface becomes thicker. The existence of

hysteresisa difference in quantity adsorbed at the same relative pres-

sure between the adsorption and desorption branches of the

isothermis discussed in Section 5. We stress that mesoporosity often

is present when a sample consists of an agglomerate of particles: such

porosity is created between the particles, and the voids created by the

agglomeration are often similar in size to the dimensions of the primary

particles (Figure 1.6).

Figure 1.6 Simplified representation of the process of adsorption and desorption inmesopores, showing surface coverage, pore filling, pore emptying (both by cavitationand otherwise), and saturation. Note that the surface is covered before the pores fill.Reprinted with permission from Ref. (43). Copyright 2005, American Chemical Society.

31Analysis of Catalyst Surface Structure by Physical Sorption

3.5. Adsorption on exterior surfaces: 0.45

range of pressures that can be measured with such transducers is four

decades at best, with accuracy increasing near the top of the range. Thus,

a 1000 Torr transducer (e.g., one that translates a pressure in the range

01000 Torr into a voltage in the range 010 V) is most accurate in

the range 1001000 Torr, is marginally accurate from 1 to 10 Torr,

and is not accurate at all below about 0.1 Torr (about 104 atm). Con-sequently, at least two transducers are required to cover the required

range of pressures, preferably a combination that includes a transducer

that is accurate (1%) at approximately 105 Torr. Not all adsorptioninstruments that claim to measure microporosity by HRADS employ

pressure measurement systems (transducers) with this precision, and in

the ones that do, the low-pressure transducer is often optional

equipment.

In addition to the required pressure measurement accuracy, the mea-

surements must be performed over a sufficiently long time that adsorp-

tion equilibrium is achieved. This concern is often not readily apparent:

if one watches the pressure drop, it may appear stable for several minutes

before dropping as little as 104 Torr, but over a longer period (say,30 min), the pressure will drop by more than two or three times that,

and neglect of the continuing change can lead to significant errors in

the determination of pore sizes. The experimental problem is that the

heats of adsorption in microporous solids are unusually high, often sig-

nificantly higher than the heat of vaporization. Furthermore, the rates of

heat and mass transfer to and from the micropores are low because of the

low pressures involved with samples that are essentially thermal insulators

and held in glass (a good thermal insulator itself ). It therefore takes a

considerable time for sorption equilibrium to be reached: as much as

an hour or more between points may be necessary at the lowest pressures

at which adsorption takes place. It is extremely important that the mea-

surements be performed properlyconsequences of not doing so range

from inaccurate determinations of pore sizes to nonphysical results (such

as oscillating isotherms (44)).

The measurem