Introduction to Chemical Adsorption Analytical Techniques and Their Applications to Catalysis Paul A

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MIC Technical Publications January 2003

Introduction to Chemical Adsorption Analytical Techniques and their Applications to Catalysis Paul A. Webb

Micromeritics Instrument Corp., Norcross, Georgia 30093

Abstract The chemical adsorption isotherm reveals information about the active surface of a material and has been employed for many years as a standard analytical tool for the evaluation of catalysts. Temperature-programmed reaction techniques have emerged from the 1950’s as an indispensable companion to chemisorption isotherm analyses in many areas of industry and research. This paper provides an introduction to these analytical techniques.

Keywords: chemical adsorption, temperature programmed reactions, TPD, TPR, TPO, catalyst

1. Introduction and 800 kJ/mole for chemical bonds. A chemical Optimum design and efficient utilization of cata- bond involves sharing of electrons between the ad- lysts require a thorough understanding of the surface sorbate and the adsorbent and may be regarded as the structure and surface chemistry of the catalytic mate- formation of a surface compound. Due to the bond rial. Chemical adsorption (chemisorption) analyses strength, chemical adsorption is difficult to reverse. can provide much of the information needed to Physical adsorption takes place on all surfaces evaluate catalyst materials in the design and produc- provided that temperature and pressure conditions are tion phases, as well as after a period of use. The re- favorable. Chemisorption, however, is highly selec- quired analytical equipment can be relatively inex- tive and occurs only between certain adsorptive and pensive, simple to operate, and fast compared to al- adsorbent species and only if the chemically active ternate equipment capable of obtaining the same in- surface is cleaned of previously adsorbed molecules. formation. Under proper conditions, physical adsorption can 2. Differentiating physical and chemical adsorp- result in adsorbed molecules forming multiple layers. tion Chemisorption, in the typical case, only proceeds as A solid material usually exhibits a heterogeneous long as the adsorptive can make direct contact with distribution of surface energy. Gas, vapor, or liquid the surface; it is therefore a single-layer process. molecules may become bound to the surface if they Exceptions can exist if the adsorptive is highly polar approach sufficiently close to interact. The discus- such, NH3 being an example. Both physical and sions in this paper are confined to the adsorption (and chemical adsorption may occur on the surface at the desorption) of gases or vapors on (or from) solid sur- same time; a layer of molecules may be physically faces. The solid is called the adsorbent; the gas or adsorbed on top of an underlying chemisorbed layer. vapor molecule prior to being adsorbed is called the The same surface can display physisorption at one adsorptive and while bound to the solid surface, the temperature and chemisorption at a higher tempera- adsorbate. ture. For example, at liquid nitrogen temperature (77 K) nitrogen gas is adsorbed physically on iron Physical adsorption is the result of a relatively but at 800 K, an energy level too high for physical weak solid-gas interaction. It is a physical attraction adsorption bonds, nitrogen is adsorbed chemically to resulting from nonspecific, relatively weak Van der form iron nitride (Moore). Waal's forces and adsorption energy usually not ex- ceeding 80 kJ/mole, with typical energies being con- 3. General applications of gas sorption as analyti- siderably less. Physically adsorbed molecules may cal tools diffuse along the surface of the adsorbent and typi- A variety of surface features can be determined cally are not bound to a specific location on the sur- from observations of the adsorption process. The face. Being only weakly bound, physical adsorption quantity of molecules taken up by a surface depends is easily reversed. on several variables including temperature, pressure, Adsorption also can result in a surface complex, a surface energy distribution, and the surface area and union much stronger than a physical bond with heats porosity of the solid. The relationship between the of adsorption up to about 600 kJ/mole for C-N bonds quantity of molecules adsorbed and the pressure at

INTRODUCTION TO CHEMICAL ADSORPTION ANALYTICAL TECHNIQUES AND THEIR APPLICATIONS TO CATALYSIS

constant temperature is called the adsorption iso- aluminum component. The end product is a highly therm. porous active metal ‘sponge’, all other scaffolding materials having been removed. Another unsup- Physical adsorption and desorption isotherms are ported metal catalyst is produced by fusing or sinter- important in characterizing the overall surface. The ing metal oxides with promoters, thus forming a net- slightest change in the shape of the plotted isotherm work of pores throughout the metal mass (van der is indicative of a particular surface feature. Analyses Laan). An example of this is a fused iron ammonia of physical adsorption isotherm data reveal the total synthesis catalyst. surface area, mesopore and micropore volume and area, total pore volume, the distribution of pore vol- Zeolitic catalysts form another group. Zeolites are ume and area by pore size, and surface energy distri- hydrated aluminosilicates and are used widely in the bution. Thus, physical adsorption is an important tool chemical industry and refining operations. Their ac- in the study of catalysts, particularly in evaluating the tivity is influenced by the silica to alumina ratio. support structure. Amorphous silica-alumina catalysts have a lower activity than zeolitic catalysts and are applied in mild The chemical adsorption isotherm also evaluates hydrocracking operations. An acidic surface is re- the surface, but is selective in that it only probes the quired for cracking and the acidity is associated with active areas—those capable of forming a chemical the oxygen atoms attached to aluminum atoms. bond with the adsorptive gas or vapor. This selectivity involves both the probe molecule and the molecu- 5. Chemisorption and catalysis lar or atomic composition of the active material, so The catalytic process can be generalized by a the choice of probe molecules is much more impor- short sequence of steps as follows. Consider reactant tant in chemisorption tests. Although isothermal molecules A and B in the gaseous bulk above a solid chemisorption tests are important in characterizing surface that supports an ensemble of active metal active surfaces, temperature-programmed tests are sites S. If molecule A is chemically adsorbed on one even more so. The basic form of data produced by of the active sites, a surface complex A is formed. these tests resembles a chromatogram of temperature Next, A reacts with B forming molecule A+B, which versus quantity desorbed. escapes the site, thus regenerating site S. 4. Catalyst Basics Sorption of at least one of the reactant molecules A catalyst affects the rate of a chemical reaction. is required for catalysis to occur. If the accelerated ‘Rate' is the most important word in this description rate of reaction simply was due to the concentration because a catalyst cannot induce a reaction that is not of molecules at the surface, catalysis would result permissible under the laws of thermodynamics. A from physical adsorption of the reactants. Chemi- catalyst only can increase the rate at which the reac- sorption is a essential step, the adsorbed molecule tion approaches equilibrium. forming an intermediate surface complex that is more receptive to chemical reaction. The dependence of Heterogeneous catalysts include metals, metal catalysis on chemisorption is one reason why chemi- oxides and solid acids. Pure metals may be employed sorption is such an informative analytical technique as solid catalysts, or may be dispersed as small grains in the study of catalysis—the chemistry occurring in on the surface of a supporting material such as TiO2, the application of the catalyst is being observed di- ZrO2, Al2O3, or SiO2. The preparation of a sup- rectly in the laboratory. ported catalyst involves selecting precursors of the active components and any necessary promoters and The performance of a catalyst depends on several mixing them in a solvent. The mixture forms a pre- variables. First, adsorption sites must be both nu- cipitant, or is used to coat an inert carrier, or is used merous and available to the reactant molecules. In to impregnate a carrier. Ultimately, the active metal some cases, grains of active metal are at the surface, or precursor is dispersed on the carrier. The product but there also are grains located below the surface is dried, mixed with a binder or forming agent, then and unavailable to the reactants. Adsorption sites ground, pelletized, extruded, or otherwise shaped. simply being located on the surface is insufficient to Finally, the material is calcined and activated by oxi- assure optimum performance. For example, some dation, reduction, or other means. potential adsorption sites may be located deep within a micropore that is too narrow for the reactant mole- One type of unsupported catalyst is composed of pure cule to enter or for the reaction product to exit; in this metal. Raney metal catalysts, for example, are pre- case the surface site cannot be an active participant in pared by dissolving an aluminum-nickel alloy in a chemisorption. A site could be located along a tortu- solution of sodium hydroxide, which dissolves the

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ous path that impedes the efficient flow of reactants from the injected quantity yielding the quantity ad- toward the active site and products away from the sorbed from each injection. These are summed to site. Since many active metals are very expensive, an determine the capacity of the sample mass. Injections important design criterion is to maximize the number may be made by syringe or by a manual or automated of active sites per unit of metal. HPLC-type, loop injection valve. Since the end- point (saturation) is the only point measured, the Catalytic activity depends on how rapidly number of injections may be only a few and there are chemisorption occurs and the strength (energy) of the no pressure changes. Thus, the flowing-gas tech- chemisorption bond. If the bond is too weak, the nique is often performed manually, although auto- molecule may desorb prior to reacting; if too strong, mated instruments also are available. the release of the product and regeneration of the site may be retarded. Isothermal chemisorption methods Over the past few decades, temperature- as well as temperature-programmed chemisorpiton programmed chemisorption analyzers have become methods can be used to study surface energy distribu- recognized as extremely valuable tools for character- tion. izing catalysts. The method is sometimes simply referred to as temperature-programmed reactions, and Chemisorption as described above pertains to the use includes Temperature-Programmed Desorption of catalysts in various applications. The same reac- (TPD), Temperature Programmed Reduction (TPR) tions, only on a smaller scale, also can occur in a and Temperature Programmed Oxidation (TPO). The sample tube under controlled conditions allowing the dynamic chemisorption method is particularly suit- process to be studied. This is chemisorption used as able to performing temperature program analyses. an analytical technique. Chemisorption analyses are applied to physically characterize a catalyst material, 6.2 Chemisorption Analyses to determine a catalyst’s relative efficiency in pro- The versatility of the chemisorption technique is il- moting a particular reaction, to study catalyst poison- lustrated by the extent of information about a mate- ing, and in monitoring the degradation of catalytic rial that can be acquired. Some of its versatility has activity over time of use. Among the various instru- been revealed in the discussion above. In the follow- ment techniques used in analyzing catalysts, chemi- ing sections, additional capabilities are explored. sorption techniques are the most universally employed. In the examples that follow, only catalysts composed of a single active species are considered to simplify 5. Chemisorption instruments the math. In the case of mixed metal catalysts, many Isothermal chemisorption analyses are obtained of the equations below would require summing a by two chemisorption techniques: a) static volumetric series of terms, one for each adsorbing species and chemisorption, and b) dynamic (flowing gas) chemi- each term weighted by the fractional contribution of sorption. the species to the whole. The volumetric technique is convenient for ob- 6.2.1 The chemisorption isotherm taining a high-resolution measurement of the chemi- An isotherm is a set of quantity-adsorbed versus pres- sorption isotherm from very low pressure to atmos- sure data points that characterize the adsorption proc- pheric pressure at essentially any temperature from ess at a constant temperature. To understand this bet- near ambient to 1000+ oC. Commercial embodi- ter, consider a reactor of constant volume V that ments of this technique are almost exclusively auto- contains a sample and a quantity of gas molecules N. mated. Obtaining a high-resolution isotherm requires Chemisorption theory assumes that the active surface many, precise dosing steps in pursuit of the equilib- of a solid contains a fixed number N of adsorption rium point, and many pressure steps which, without s sites and only one molecule at a time can occupy a automation, would be a time-consuming and error site. The molecules in the sample tube that are com- prone procedure. peting for an adsorption site represent a concentration The flowing gas (dynamic) technique operates at C that can be expressed in general by solving the gas ambient pressure. After the sample has been cleaned, law , or small injections (doses) of accurately known quanti- N/V = P/RT (1) ties of adsorptive are administered in pulses until the sample is saturated, thus the name, ‘pulse chemisorp- where N and V have previously been defined, P is tion’. A calibrated thermal conductivity detector pressure, T temperature, and R the gas constant (TCD) monitors the quantity of adsorptive that is not taken up by active metals. This quantity is subtracted

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For a specific gas-solid system at equilibrium under involving fragmenting (dissociation) of the adsorp- specific conditions of temperature and pressure, a tive molecule. The isotherm is asymptotic to q = 1, certain fraction q of the total number of available which is full coverage, or completion of the sites Ns will be occupied by nads adsorbed molecules. monolayer. This is described by Several Langmuir isotherms are illustrated in Figure

q = nads/Ns (2) 1, the only difference being the magnitude of b. The b parameter is directly related to surface energy; in- The rate at which equilibrium is achieved depends on creasing surface energy increases the probability of the concentration of molecules involved as well as adsorption at a given pressure. The b parameter is other considerations, the latter being grouped into a inversely related to temperature, which, when in- parameter referred to as the ‘rate constant’ k. creased, increases molecular energy and decreases the For the adsorption process, the concentration of un- probability of adsorption at a given pressure. adsorbed molecules competing for the remaining sites In the illustration, b1 is less than b2, which is less is C-qC and the rate of adsorption is kads(C-qC) or than b3, and so on, b5 being 50 times greater than b1. kadsC (1-q). For desorption the fraction of molecules From this one it may be inferred that the same sample desorbed is ? and the rate of desorption is kdesq. being analyzed at five different temperatures would When equilibrium is achieved, the rate of adsorption produce a similar set of isotherms, as would five dif- and desorption are equal, that is, ferent samples of different surface energy measured at the same analytical temperature. kadsC (1-q) = kdesq (3a) or Obtaining a chemisorption isotherm is not necessarily a direct measurement as illustrated in Figures 2. In q/ (1-q) = kadsC/ kdes (3b) the typical case indicated by these illustrations, there Using K to represent kads/k and solving for will be molecules (indicated by R) weakly adsorbed des to the surface of the support and there also will be a q yields chemisorbed monolayer of molecules (indicated by I) q = KC/ (1+KC) (4) on the active surface. Depending on the pressure and temperature, there also can be molecules physically Recalling that the environment is of constant volume adsorbed on top of the chemisorbed monolayer. V and constant temperature T, changing pressure is the only remaining way to change concentration C. Weak adsorption is termed reversible adsorption and Eq. 1 establishes that concentration is directly pro- strong chemisorption, irreversible, thus the R and I portional to pressure, therefore if concentration- labels in the illustration. The initial isotherm will be a pressure proportionality constant is combined with K combination of reversible and irreversible adsorption. and represented by b, Eq.4 can be written Active metal

q = bP/ (1+bP) (5) Sample, after initial This is the famous Langmuir isotherm, which accu- cleaning by heat and vacuum. rately describes most chemisorption isotherms not After first adsorption R R I I I I R R test. Langmuir Isotherms 1 0.9 b5 After vacuum de- b4 I I I I 0.8 b3 gassing prior to second 0.7 adsorption test. 0.6 0.5 b2 0.4 After second adsorption b1 R R I I I I R R 0.3 test. 0.2

Degre e of Cov er age 0.1 0 0 200 400 600 800 1000 Figure 2. Four steps in determining the isotherm PressurePressure (arbitrary units) for only irreversible adsorption.

Figure 1. A family of calculated Langmuir iso- The reversible and irreversible contributions to a therms, each with a different value of b. combined isotherm can be distinguished by running a

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6 Example of Analytical Data

5 Test 1

4 sorbed

d 3 Differ- ence

tity A 2 n Test 2 1 Qua

0 0 100 200 300 400 500 600 700 Pressure (arbitrary units)

Figure 3. The isotherm resulting from Test 1 is a Figure 4. A series of detector signals following injec- combination of reversible and irreversible adsorp- tions of X ml of adsorptive; the integrated area of each tion. The isotherm from Test 2 corresponds only to peak is indicated. None of injections 5, 6, and 7 was reversible adsorption. The difference is the isotherm from only irreversible adsorption. adsorbed. second adsorption test. After the initial adsorption The partial pressure of the adsorptive momentarily test and prior to the second test, the sample is sub- increases over the sample as the pulse passes and jected to vacuum only, causing the weakly adsorbed some or all of the injected quantity of gas is ad- molecules to desorb, leaving only those molecules sorbed. Any unadsorbed gas is swept through the that have formed a strong chemisorption bond with detector where it is registered. Note that, unlike the the active surface. static method (described above), the net adsorption is only irreversible adsorption because, after the pulse The second adsorption test is performed under the of adsorptive passes, the partial pressure of the ad- same conditions as the initial test, but this time the sorptive in the bulk gas is essentially zero and escap- active surface is already covered with a chemisorbed ing weakly adsorbed molecules are swept to the de- monolayer. The uptake of adsorbate will be only that tector by the carrier stream. associated with reversible adsorption. Subtracting the quantity reversibly adsorbed from the combined iso- As the monolayer forms on the active surface, less therm at each pressure value yields an isotherm of and less of the injected adsorptive is taken up by the ireversible adsorption. The analytical results are illus- sample. Injections continue until the sample is satu- trated in Figure 3. rated, as indicated when all subsequent detector peaks remain the same size. The results of such a 6.2.2 Number of accessible active sites test are shown in Figure 4, which illustrates the out- Both static volumetric and dynamic chemisorption put of the detector. The area of each peak is propor- techniques can be used to measure the quantity of gas tional to the quantity of the injection that was not required to form a monolayer of chemisorbate on an adsorbed. active surface. The dynamic method yields only a In Figure 4, the integrated area of peaks associated single data point, which corresponds to the quantity with injections 5, 6, and 7 indicate that no adsorp- of adsorptive required to saturate the active surface tion occurred, so the active area is saturated. All of with a monolayer. The monolayer capacity of the the first injection was adsorbed, as was 88% of injec- active surface is calculated from the derived irre- tion 2, 20% of injection 4, and 2% of injection 3. versible adsorption isotherm illustrated in Figure 3. From the known quantity of each injection, the frac- Since the irreversible adsorption isotherm is asymp- tion of each injection that was adsorbed, and the mass totic to the value of total coverage (of the active sur- of sample material, the number of moles of adsorp- face), the plateau of the isotherm is extrapolated back tive gas taken up by each gram of sample is deter- to the y-axis to yield the monolayer capacity value. mined. Extrapolating to the y-axis the linear section of the combined reversible-irreversible isotherms also pro- The adsorption process can involve the separation of vides a reasonable value for the monolayer coverage a molecular adsorptive into two or more molecular or quantity. atomic entities (ions or radicals), each entity forming a bond with individual active surface sites. This is The dynamic chemisorption method requires called dissociative or second-order adsorption in (manually or automatically) injecting small, pre- contrast to first-order or non-dissociative adsorption cisely-known quantities of adsorptive into a stream of in which the adsorptive molecule remains intact dur- inert carrier gas that flows through the sample bed.

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ing adsorption. The result of dissociative adsorption g% = (Ns/NT) x 100% (7) is that the number of adsorptive molecules N deter- m Dispersion is expressed as a ratio of available metal mined to have been taken up per gram of sample does to total metal. Another fraction that is determined not equal the number of active surface atoms that from the manufacturing procedure is the ratio of the participated in chemisorption. weight of metal to the mass of the bulk catalyst mate- To determine the number of surface atoms involved, rial, expressed as a decimal fraction or as a percent- the stoichiometry of the surface reaction must be con- age. sidered. Stoichiometry refers to the relationship between the amounts of substances that react together 6.2.5 Active particle (crystallite) size in a particular chemical reaction, and the amounts of This estimation of active particle size is a geometrical products that are formed. For example, a hydrogen calculation based on the assumption that the crystal- molecule (H2) may dissociate into two hydrogen at- lite shape is of regular geometry, a sphere typically oms and react with two active surface atoms, as is the being the geometry of choice. What is known from case with Pt. So, the number of adsorptive molecules previous calculations is the active surface area per taken up by the active surface must be multiplied by a gram of sample material AA and, from the catalyst stoichiometry factor Fs (where Fs = 2 in the example manufacturing procedure, the fractional proportion of case) to arrive at the number of surface atoms Ns or metal in the catalyst bulk. ‘sites’. Mathematically, N = F x N (6) The calculation employs an expression of the geome- s s m try of the grain. From the assumed regular geometry, where Ns and Nm are determined per gram of sample. the diameter can be expressed in terms of the area and volume. The volume of active metal is not The adsorptive molecule may be able to bond in more than one configuration with the active surface. The known, although the atomic or molecular density rm proportion of molecules bonding in each possible is; therefore the volume can be expressed in terms of way must be taken into consideration, often yielding density. The area of active metal per gram of sample was previously measured, providing a value for a non-integer stoichiometry factor. 2 area per unit mass of metal Am (m /g). Substituting 6.2.3 Active surface area these expressions into the general relationship for D The specific active surface area follows from the = f(A,V) yields number of molecules Ns adsorbed on the active sur- D = 5/rmAm (8) face of one gram of sample. Specific active surface for a cubic grain on the surface (five of six faces ex- area AA is determined by multiplying the area Am occupied by one surface molecule by the number of posed) and adsorbed molecules per gram N . The area occupied s D = 6/rmAm (9) by a single atom originating from the adsorptive usually can be located in the literature. It also can be for a hemisphericaly shaped particle. determined experimentally, if necessary, by determin- The diameter calculated by the above equation repre- ing the BET surface area of a sample of pure active sents the average diameter of the active metal grains material using N2, then determining the molar uptake onto which adsorption occurred. of the active adsorptive on the same sample. 6.2.6 Temperature programmed chemisorption 6.2.4 Metal dispersion and percent metal As the name of the method implies, temperature Metal dispersion describes the ratio of the number of programmed chemisorption is a method that involves active metal atoms available for reaction to the total the effects of temperature on surface reactions. There number of metal atoms in the catalyst material. The are three principal reactions that are studied as a quantity of active metal incorporated per unit mass of function of temperature: 1) desorption, 2) reduction, support material is available from the manufacturing and 3) oxidation. formula; this will yield the quantity of active metal atoms NT per unit mass of catalyst. Chemisorption Temperature-programmed desorption by the dy- analysis as described above is used to determine the namic method involves placing a sample in a sample quantity of active metal per gram that is available for cell and pre-treating it to remove any adsorbed spe- reaction. The percent dispersion is the ratio of the cies from the active surface. Next, a selected gas or available quantity to total quantity of active mole- vapor is chemisorbed onto the active sites until satu- cules times 100%, or ration is achieved, after which the remaining adsorp-

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higher temperature (493 K) probably corresponds to TCD Signal (H2 Produced) hydrogen spillover due to the presence of Pt on alumina. The third and final peak obtained at 570 K corresponds to the hydrogen chemisorbed by Pt. This peak is quantified to estimate the quantity of Pt available for catalytic activity in a reactor. Binding energies can be quantified using the TPD method as will be discussed subsequently Temperature-programmed reduction is a method by which a reducing gas mixture such as hydrogen di- luted in an inert gas flows over a sample of an oxide. The initial temperature is usually below the reduction 393 493 570 Temperature (K) temperature. Next, sample temperature is increased at Figure 5. TPD chromatogram of Hydrogen desorbing a constant rate and, as reduction begins, hydrogen is from alumina supported platinum. Three distinct ad- consumed from the carrier mixture, which is detected sorption bond strengths are evident. by a TCD. When reduction ceases, no more hydrogen is consumed and the thermal conductivity of the gas from the sample tube returns to baseline. Several tive molecules are flushed out with an inert gas. Tem- reduction peaks may be detected over the course of perature (energy) is increased at a controlled rate the temperature ramp because reduction likely will be while a constant flow of inert gas is maintained over initiated at various thermal energy levels. Each peak the sample. The inert gas and any desorbed molecules then corresponds to a different oxide and the ampli- are monitored by a TCD. The TCD signal is propor- tude of each peak is proportional to the reaction rate. tional to the quantity of molecules desorbed as thermal energy, monitored by a thermocouple, overcomes Iron oxide in the form of hematite exhibits three the binding energy. Quantities desorbed at specific phases of reduction corresponding to the three oxides temperatures provide information about the number, of iron. A TPR analysis of hematite was performed strength and heterogeneity of the adsorption sites. using a reducing gas composed of 10% hydrogen in Analysis data are usually plotted as quantity desorbed argon and a temperature ramp rate of 10 °C/min. Fig- versus temperature, or as both temperature and quan- ure 6 shows the results. The first reduction peak ap- tity desorbed plotted over time. pears at 575 K, corresponding to the transition of Fe O to Fe O . The peak at 627 K corresponds to the Figure 5 is a typical TPD profile of hydrogen desorp- 2 3 3 4 transformation of Fe O to FeO. The final peak at tion from Pt supported on Al O . The first peak is 3 4 2 3 748 K corresponds to the transition of FeO to Fe. The obtained at a temperature of 393 K. This peak corre- positions of the maxima shown in Figure 6 may differ sponds to the weak adsorption of hydrogen and may somewhat from sample to sample depending on the relate to desorption from the support or from weak particle size of the Fe O and other parameters such chemisorption. The second peak obtained at the next 2 3 as temperature ramp rate.

Temperature Quantity of Temperature-programmed oxidation may be used to (oC) O2 determine the quantity of reduced species (also called 1000 Fe Temperature degree of reduction), but the difficulty with this type of analysis is in attaining total oxidation. More com- 800 FeO monly, TPO is used in applications such as the study Fe3O4 of the kinetics of coking, evaluation of catalyst 600 TCD Output carbon burn off, determination of the different forms of carbonaceous deposits present on the catalysts 400 after a CO decomposition reaction or, stated more generally, measurements of oxygen consumption and 200 product yields. Fe2O3 The sample is heated at a uniform rate as the reactant 30 40 50 60 70 80 Time (min) gas, typically 2% to 5% oxygen, is applied to the sample in pulses, or alternatively, as a steady stream. Figure 6 Temperature-programmed reduction of Fe2O3 The oxidation reaction occurs at a specific tempera- by hydrogen. ture resulting in an uptake of oxygen. The amount of

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oxygen consumed during the reaction is related to the physisorption as well as the net energy path taken by quantity of a species on the surface. the chemisorbed molecule. It should be understood while examining this diagram that it is a basic depic- 6.2.7 Surface energy and first order kinetics tion of a single molecule approaching a surface and Adsorption and desorption mechanisms are com- considers only energy as a function of distance from posed of some combination of elementary kinetic the surface, neglecting other variables. steps. For example, a diatomic molecule can be ad- One situation that would greatly change the shape of sorbed or, as it approaches the surface, it may frag- the chemisorption curve in Figure 7 would be if the ment into atoms that are adsorbed independently. adsorption process were to be dissociative. Dissocia- The former case is called non-dissociative chemisorp- tive chemisorption requires an expenditure of energy tion or first-order kinetics, the latter is dissociative (dissociation energy) to fracture the adsorptive mole- chemisorption or second-order kinetics. First-order cule. This would result in the net energy path having kinetics will be of primary focus in the following a positive peak just before the negative-going poten- discussions. tial energy well. This is illustrated in Figure 8. As in The interaction of a single, isolated molecule with a Figure 8, the physical adsorption path initially is surface can be depicted in a plot of potential energy more favorable (lower energy) as the molecule ap- versus distance from surface as in Figure 7. For proaches the surface, but to dissociate and chemisorb, comparison, Figure 7 also includes an energy plot for a positive energy step is required to make the transition to the chemisorption path. This energy is in ex- Potential Energy vs Distance from Surface 5 cess of the dissipated potential energy of the mole- 4 cule. 3 2 An important variable that changes the shape of the 1 non-dissociative chemisorption energy curve is the 0 number of molecules already adsorbed on the surface. -1 The most energetic sites (the deepest potential wells) -2 Chemisorptoni En e r g y ( a rb i t ar u n it s) are occupied first. This manner of coverage continues -3 Physisorption Net path to until, finally, those sites having the lowest energy are -4 chemisorption -5 occupied. The energy plotted as a function of surface 0 1 2 3 4 5 6 7 8 coverage (loading) characterizes the degree of het- DistanceD istfromance surface (Angstro m(Ans) g- stroms) erogeneity of surface energy. This plot provides valu- Figure 7. Potential energy wells associated with able information about catalyst activity under specific physical adsorption and non-dissociative chemical conditions. For some applications, rather than a plot adsorption. The equilibrium position for the adsorp- of surface energy distribution, a single value for the tive molecule is at the minimum energy position. The energy associated with the reaction may suffice. circle is a scale reference that depicts the approximate size of a hydrogen atom. Adsorption is an exothermic process, thus it ultimately yields energy (energy of adsorption) even if 12 Activation Energy some energy input (activation energy) is required to Dissociative chemsi orption 10 initiate the process. Reversing adsorption requires Physical adsorptoni the input of energy, the required quantity being the 8 Net path to chemisorPath top tion depth of the potential well. 6

4 Figures 7 and 8 pertain to the potential energy of a Atom A + Atom B 2 single, isolated molecule, however it is the energy Activation Dissociation 0 potential of all of the particles in the system that de- En er g y (a r bi t ra uni s) 0 5 10 15 20 25 termines if the system is in equilibrium. At equilib- -2 rium, a molecule at any location in the system should -4 Energy path of molecule AB if non-dissociative adsorption experience the same energy potential; this applies to -6 Distance from surface (Angstroms) molecules in the bulk gas or vapor surrounding the Figure 8. Potential energy wells associated with physi- solid and to the adsorbed molecules at the solid sur- cal adsorption and dissociative chemical adsorption. face. The net energy path for a molecule to chemically ad- sorb has a positive excursion called the activation en- For a specific adsorbate-adsorbent system, adsorption ergy. This input of energy is necessary for adsorption equilibrium is achieved by a delicate balance between and any subsequent catalytic reaction. the pressure P of the bulk gas phase, analytical tem-

-8- INTRODUCTION TO CHEMICAL ADSORPTION ANALYTICAL TECHNIQUES AND THEIR APPLICATIONS TO CATALYSIS

perature T, and the degree of surface coverage q. step-by-step derivation is presented here because it Experimentally, one of these parameters is held con- may be of interest to some readers and a detailed stant, the other is assigned a value, and the third is derivation is difficult to find in the literature. Por- observed to determine its value at equilibrium. An tions of what follows were gleaned from works of isotherm conveys the degree of surface coverage as a Schroeder and Gottfried, Houston, Nix, and Garrett. function of pressure at constant temperature (q = Desorption involves the time rate of change of the f(P)T), an adsorption isobar expresses the degree of number of adsorbed molecules N, algebraically ex- surface coverage as a function of temperature at con- pressed as DN/Dt. This also may be viewed as the stant pressure q = f(T)P), and an isostere shows the time rate of change in the number of available ad- relationship between pressure and the temperature for sorption sites Na. a constant degree of coverage. (P = f(T)q). (Note: Time-dependent and temperature-dependent changes The Clausius-Clapeyron equation expresses the heat are more conveniently dealt with mathematically by consider- of adsorption at a specific degree of surface coverage ing each step change in time or temperature to be infinitesi- mally small. Thereby, DN/Dt can be replaced by dN/dt and q in terms of pressure and temperature, thus it yields algebraic manipulation is replaced by differential calculus. the isosteric heat of adsorption qst. The equation in For readers not familiar with calculus, any expression of the partial differential form is form dX/dY can be considered to be the slope of a plot of X versus Y at a given value of X.) qst = R(dlnP /d(1/T)) (10) The kinetic expression for the rate of desorption Rd where T is temperature, P pressure, and R the gas is x constant. -dN/dt = Rd = k N (12) Obtaining related values of temperature and pressure where k is the rate constant, -N the instantaneous for a given degree of coverage is achieved by obtain- surface concentration (number) of the adsorbed spe- ing multiple isotherms of the same sample at different cies (negative indicating decreasing), and x the ki- temperatures and scaling the quantity adsorbed axis netic order. Only the simplest case, first order (non- in units of degrees of coverage. This provides a dissociative) kinetics, is considered here; therefore means for extracting from the set of isotherms, a set x=1. Note that the rate of desorption constantly of isobars plotted as degree of coverage versus tem- changes as the number of molecules remaining on the perature over the range of temperature used in the surface diminishes. analyses. From the set of isobars, a set of pressure versus temperature values for various values of val- Figures 8 and 9 illustrate that activation energy may ues of volume adsorbed can be extracted. These are or may not be required to cause adsorption to pro- plotted as ln(P) vs. 1/T. ceed. However, these figures also illustrate that there always is an activation barrier that must be overcome The Clausius-Clapeyron equation, above, can be re- for the molecule to desorb, that is, for the chemisorp- grouped in linear form, y = m(x), yielding tion surface reaction to reverse. The relationship between the rate constant and energy in energy- ln(P) = q (1/T) (11) V st V dependent reactions such as desorption can be ex- R being a scaling constant that does not affect the pressed in an Arrhenius form, specifically slope. For value of quantity adsorbed, there is a dif- k=Ae-Ed/RT (13) ferent slope, qst. Plotting the set of slopes as a function of quantity adsorbed provides the sought-after where Edes is the activation energy and the subscript graph of surface energy versus quantity adsorbed, ‘d’ identifying the particular case as that of desorp- which relates to surface coverage or loading. tion. The pre-exponential factor A can be considered Heat of adsorption also can be calculated from data the number of attempts by the molecule per unit time obtained by dynamic chemisorption by what is some- to escape from the potential well. T is temperature times called the ‘heating rate variation’ method. (degrees Kelvin) and R the universal gas constant. Since quantity adsorbed as a function of pressure is The product RT is thermal energy, so the exponent not monitored by the dynamic method, an expression E/RT is the ratio of activation energy to thermal en- of energy other than those of Eqs. 10 and 11 must be ergy. While E is larger than RT, there is little prob- sought. As an exercise, such an expression is derived ability of desorption. in the following paragraphs. The result (Equation Substituting the Arrhenius expression into Eq. 8 21) can be taken and used on faith and the drudgery gives of wading through the math avoided. However, the -Ed / RT Rd = NAe (14)

-9- INTRODUCTION TO CHEMICAL ADSORPTION ANALYTICAL TECHNIQUES AND THEIR APPLICATIONS TO CATALYSIS

This is the Polanyi-Wigner equation for rate of first- During a temperature-programmed analysis test, the order desorption. One can experiment with this sample is heated linearly so that the temperature T at equation to better understand what it describes in any time t can be calculated by regard to desorption How desorption rate (Rd), cov- T(t) = To + bt (15a) erage (N) and the energy ratio (E /RT) change as a d or function of temperature are plotted in Figure 10, the values being normalized on the vertical axis for con- dT(t)/dt = b (15b) venience. During an actual experiment the detector output would correspond to the rate of desorption. where b is? the heating rate or ramp rate dT/dt in units of degrees K per unit time. As temperature is in- The temperature Tm at which the rate of desorption is maximum is easily observed in Figure 10 as it would creased, there is a change in the number of molecules be on a plot of detector signal (quantity of evolved being desorbed per unit time, expressed by dN/dT. molecular species) versus temperature. Multiplying the time-dependent heating rate (dT/dt) in degrees/min by the temperature dependent rate of desorption (-dN/dT) in molecules/degree) gives time- Coverage, Rate of Desorption, and Energy Ratio vs. Tempera- ture dependent rate of desorption, Rd. Mathematically, % Max. Value of -Rd (equivalent to absolute value of slope of coverage plot) 100Value -dN/dT * dT/dt = dN/dt = Rd (16) Coverage (N) 80 Heating rate b was defined in Eq. 15a as dT/dt, therefore, substitution into the left side of Eq. 12 gives 60 Ed/RT (energy ratio) -dN/dT * b = Rd (17) 40 Substitution of Eq. 17 into Eq. 14 yields 20

0 -Ed/RT 0 200 400 Temperature600 (K800) 1000 1200 1400 -dN/dT * b = N A e (18)

Figure 10. Parameters of Eq. 14 are plotted against and rearrangement yields the temperature-dependent temperature. The amplitude of each parameter is di- rate of desorption, vided by its maximum value x 100% as a means of nor- -dN/dT = (NA/b) e-Ed/RT (19) malizing the data. which describes the rate of desorption plot in Figure Note: Figure 10 was produced by Microsoft Excel® using 10. As temperature increases, the rate of desorption Eq. 14 and arbitrary values for the parameters. This allows maximizes at Tm and at that temperature the slope experimentation with the parameters and comparison of (first derivative) of Eq. 15 equals zero, that is, various plots predicted by the Polanyi-Wigner model. It can be observed that peaks are somewhat asymmetric around d[ (NA/b) e-Ed/RTm]/dT = 0 (20) Tm, increasing the initial coverage value causes the peak to increase in amplitude but with Tm remaining constant. For clarity and continuity, the reader is reminded that Increasing the value of A causes the peak to move towards Equation 20 has the form d(uv)/dT, where u = lower temperatures. Increasing Ed causes the peak to -Ed/RT broaden and the maximum value occur at higher tempera- (A/b)N, v = e , and N is a function of temperature tures. (T). Extracting the log of both sides of Equation 10 pro- Equation 20 yields duces 2 -Ed/RTm -Ed/RTm NA/b Ed/RTm e + A/b e dN/dT = 0 ln Rd = ln N + ln A - Ed / RT (21) Grouping this equation in linear form, y = (m)x +(b) yields Now, substitute the right side of Equation 19 for dN/dT (a negative value; see Equation 12) in Equa- ln Rd = (-Ed / R)1/T + (ln N + ln A) tion 13 and factor. This gives

2 -Ed/RTm -Ed/RTm -Ed/RTm Plotting ln Rd versus 1/T produces a straight line NA/b Ed/RTm e - A/b e (NA/b) e = 0 having slope -E /R and intercept (ln N + ln A). The d (22a) problem, here, is that numerical values for Rd are not available, so the derivation must be expanded. or

-10- INTRODUCTION TO CHEMICAL ADSORPTION ANALYTICAL TECHNIQUES AND THEIR APPLICATIONS TO CATALYSIS

2 -Ed/RTm -Ed/RTm - 2 NA/b Ed/RTm e = A/b e (NA/b) e Ed/RTm = ln Tm /b - ln Ed/AR (30a) Ed/RTm (22b) 2 Ed= RTm(ln Tm /b - ln Ed/AR) (30b) Eliminate common terms on left and right sides, and there is left Ed= RTm(ln ATm/b - ln Ed/RTm) (30c)

2 -Ed/RTm This equation is simplified by estimating the ln Ed/RTm = A/b e (23) Ed/RTm term on the right side to be 3.64, which in- The values of Tm, b, and R are known; A is unknown troduces an error of less than 1.5% for values of A/b 8 13 as is Ed, the value which is sought. One approach to between 10 /K and 10 /K, A typically being ap- determining the unknowns is to express the terms of proximated for first order kinetics to be 1013/s. Thus,

Equation 23 in linear form, y = mx + b. This can be 13 done by rearrangement to Ed= RTm(ln 10 Tm/b - 3.64) (31) T 2/b = E /AR eEd/RTm (24) Much like the single point method of determining m d BET surface area, this method introduces some error, Taking the log of each side yields but it allows Ed to be estimated from a single desorption chromatogram. (Schroeder and Gottfried). ln T 2/b = E /RT + ln E /AR (25a) m d m d Rather than estimating the value of A, a series of 2 a linear equation in which y = ln Tm /b, x = 1/Tm , m chromatograms could be obtained for different values = Ed/R, and b = ln Ed/AR. Plotting y versus x for a of b and the values of Ed and A determined from the series of b values allows the determination of Ed. linear plot. Another form of Equation 25a sometimes found in In using the Redhead method, it must be remembered the literature follows from expanding the logarithmic that it applies only to first order kinetics. In regard to terms to obtain higher order reactions, Stoltz admonishes (Stoltze),

2lnTm – lnb = Ed/RT + ln Ed/AR (25b) “To describe E obtained in this fashion as an ap- proximation is an understatement, completely wrong is a better description.” Another way to arrive at Equation 25 from Equation SUMMARY 22a is to factor and rearrange the latter equation, giv- ing Solid catalysts play a ‘behind the scenes role’ in making affordable and even making possible many of the -Ed/RTm 2 -Ed/RTm NA/b e [Ed/RTm - A/b e ] = 0 (26) benefits enjoyed in everyday life. Chemisorption is a Dividing both sides of this equation by the expres- fundamental step in catalytic reactions, so being able sion in the brackets gives to study the chemisorption process on a small scale in the laboratory is of great benefit. Modern analytical 2 -Ed/RTm Ed/RTm = A/b e (27) instruments capable of characterizing these reactions which is the same as Equation 23. are powerful tools for monitoring and controlling the manufacture and application of catalysts and predict- There also is the case ing performance characteristics of newly developed

2 -Ed/RTm catalyst materials. [Ed/RTm - A/b e ] = 0 (28a) or

2 -Ed/RTm Ed/RTm = A/b e (28b) established by dividing both sides of Equation 26 by the factors outside of the brackets or by logically de- ducing that since neither factor NA/b nor e-Ed/RT has a value of zero during the desorption process, the expression in the brackets of Equation 26 must equal zero. Rearranging yields

2 Ed/RTm Tm /b = Ed/AR e (29) which is the same as Equation 24 Following the method of Redhead, Equation 25 is rearranged as follows:

-11- INTRODUCTION TO CHEMICAL ADSORPTION ANALYTICAL TECHNIQUES AND THEIR APPLICATIONS TO CATALYSIS

Resources used in the development of this paper: James P. Olivier, Thermodynamic Properties of Con- Thomas H. Maugh, Industry Steps Up Quest for fined Fluids I: Experimental Measurements of Kryp- Catalysts, High Technology, August 1984. ton Adsorbed by Mesoporous Silica From 80K to Scholten, Pijpers and Hustings, Surface Characteri- 130K, The 2nd Pacific Basin Conference on Adsorp- zation of Supported and Nonsupported Hydrogena- tion Science and Technology, University of Queen- tion Catalysts, Catal. Rev.--Sci. Eng., Vol. 27, No. 1, sland, Brisbane, Australia, May 2000 (1985) Sven L.M. Schroeder and Michael Gottfried, Tem- A. Baiker, Experimental Methods for the Characteri- perature-Programmed Desorption (TPD) and Ther- zation of Catalysts. II. X-Ray Diffraction, Tempera- mal Desorption Spectroscopy (TDS), Freie Univer- ture-Programmed Desorption and Reduction, Ther- sity, Berlin (Internet http://userpage.chemie.fu- mogravimetry and Differential Thermoanalysis, In- berlin.de/~pcfp/V18/pdf/v18.pdf) ternational Chemical Engineering, Vol. 25, No. 1 (1985). Paul L. Houston, Cornell University Chemical Kine- matics and Reaction Dynamic, Ithaca Philip Moriarty, Atoms and Molecules at Surfaces, School of Physics & Astronomy, University of Not- Roger Nix, An Introduction to Surface Chemistry, tingham ( World Wide Web http:// Department of Chemistry, Queen Mary University of www.nottingham.ac.uk/~ppzpjm/sect4_2.htm) London (World Wide Web http:// www.chem.qmw.ac.uk/surfaces/scc/scat2_4.htm) M. B. Raschke, U. Ho, Chemisorption energy of hydrogen on silicon surfaces, Physical Review B, Simon J. Garrett, An Introduction to Surface Chemis- Volume 63 try (lecture notes) , Michigan State University.

W.J. Moore, Physical Chemistry, Prentice-Hall, Inc. (1972). P. A. Redhead, The Ultimate Vacuum, Vacuum 12, 203-211, 1962 J.H. de Boer, The Dynamical Character of Adsorp- tion, Oxford at the Clarendon Press (1953). Per Stoltze, Introduction to heterogeneous catalysis- Concepts and calculations, Department of Physics, G.C. Bond, Heterogeneous Catalysis- Principles and Applications, Claredon Press, Oxford (1987) Technical University of Denmark. John H. Sinfelt, Structure of Metal Catalysts, Review Gerard P. van der Laan, Kinetics, Selectivity and of Modern Physics, Vol. 51, No. 3 (1979) Scale Up of the Fischer-Tropsch Synthesis, Doctoral Thesis, University of Groningen, The Netherlands, 1999

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