Statistical thermodynamics of adsorption

D. Nicholson, N. D. Parsonage. Computer Simulation and the Statistical Thermodynamics of Adsorption. New York Academic Press, 1983. 

Tompkins (1978) concentrates on the fundamental and experimental aspects of the chemisorption of gases on metals. The book covers techniques for the preparation and maintenance of clean metal surfaces, the basic principles of the adsorption process, thermal accommodation and molecular beam scattering, desorption phenomena, adsorption isotherms, heats of chemisorption, thermodynamics of chemisorption, statistical thermodynamics of adsorption, electronic theory of metals, electronic theory of metal surfaces, perturbation of surface electronic properties by chemisorption, low energy electron diffraction (LEED), infra-red spectroscopy of chemisorbed molecules, field emmission microscopy, field ion microscopy, mobility of species, electron impact auger spectroscopy. X-ray and ultra-violet photoelectron spectroscopy, ion neutralization spectroscopy, electron energy loss spectroscopy, appearance potential spectroscopy, electronic properties of adsorbed layers. 

Statistical thermodynamics of adsorption dictate that the pure gas adsorption isotherm of component i be linear at the limit of F - > 0 ... 

Statistical thermodynamics of adsorption dictates that the adsorption isotherm of component i from a mixture be a linear function of the partial pressure of that component (pi = Py,) in the Henry s law region (pj 0) ... 

Statistical Thermodynamics of Adsorbates. First, from a thermodynamic or statistical mechanical point of view, the internal energy and entropy of a molecule should be different in the adsorbed state from that in the gaseous state. This is quite apart from the energy of the adsorption bond itself or the entropy associated with confining a molecule to the interfacial region. It is clear, for example, that the adsorbed molecule may lose part or all of its freedom to rotate. 

The preceding derivation, being based on a definite mechanical picture, is easy to follow intuitively kinetic derivations of an equilibrium relationship suffer from a common disadvantage, namely, that they usually assume more than is necessary. It is quite possible to obtain the Langmuir equation (as well as other adsorption isotherm equations) from examination of the statistical thermodynamics of the two states involved. 

In general, it seems more reasonable to suppose that in chemisorption specific sites are involved and that therefore definite potential barriers to lateral motion should be present. The adsorption should therefore obey the statistical thermodynamics of a localized state. On the other hand, the kinetics of adsorption and of catalytic processes will depend greatly on the frequency and nature of such surface jumps as do occur. A film can be fairly mobile in this kinetic sense and yet not be expected to show any significant deviation from the configurational entropy of a localized state. 

The increasing industrial applications for adsorption have stimulated a growing interest in research. The research has been advancing on several fronts thermodynamics of adsorption (particularly statistical mechanics), diffusion of pores, PSA simulation, new process and cycle development, sorbent characterization, and development of new sorbents. Significant advances have been made on all fronts during the last decade. 

Theoretical molecular statistic calculations of adsorption thermodynamic properties for colloid systems are generally believed to be a quite cumbersome problem. This is mainly... 

Ramirez-Pastor, A.J., Pereyra, V.D., and Riccardo, J.L. (1999). Statistical thermodynamics of linear adsorbates in low dimensions application to adsorption on heterogeneous surfaces. Langmuir, 15, 5707—12. 

The statistical thermodynamics of block copolymer adsorption was considered elsewhere.Many theories attempt to characterize adsorption by smface density, block segment distribution profile, and the thickness of adsorbed layer. As a rule, an adsorbed diblock copolymer has one block adsorbed on the surface in a rather flat conformation, whereas the other block, having a lower surface activity, forms dangling tails. Because of their freely dangling blocks, adsorbed diblock copolymers are often interpenetrated. The adsorption of block copolymers leads to the segregation of blocks in the adsorption layer. It was found that both kinetic and equilibrium features of the block copolymer adsorption are intimately related to the phase behavior of the block copolymer solution. In particular, a very strong increase in the adsorbed amount is observed when the system approaches the phase boundary. As a consequence, a partial phase separation phenomenon may proceed in the surface zone. 

Stoltze and Norskov proceed by applying statistical mechanical methods to this sequence, essentially expressing the thermodynamic properties of reactants and intermediates in terms of spectroscopic properties. Further they treat within the same model, the kinetics of adsorption of N2 as well as the thermodynamics of adsorption for H2 and NH3. 

One of the simplest quantitative models was proposed by Horvath and Kawazoe (ref. 12) developed for adsorption in active carbons. It is employed in these studies to compare different zeolites, but, recognizing the differences between active carbons and zeolites, it is only a qualitative measure of pore dimensions. This method (denoted "H-K ) is based on statistical thermodynamics of the adsorbed gas molecules on surfaces. They use a 10-6 Lennard-Jones potential model to relate the free energy of a sorbed gas molecule to the distance between the gas molecule and solid surface. The smallest pore size is constrained by the diameter of the sorbent molecule (e.g., for nitrogen 3.65 A). Sensitivity increases with decreasing pore size. The comparison between the pore size predicted by the Kelvin and H-K theories is shown below in figure 1. 

Hill, T. L., 1949. Statistical mechanics of adsorption. V. Thermodynamics and heat of adsorption. 

Statistical mechanics of adsorption, IX. Adsorption thermodynamics and solution... 

Thus from an adsorption isotherm and its temperature variation, one can calculate either the differential or the integral entropy of adsorption as a function of surface coverage. The former probably has the greater direct physical meaning, but the latter is the quantity usually first obtained in a statistical thermodynamic adsorption model. 

Thermodynamically Consistent Isotherm Models. These models include both the statistical thermodynamic models and the models that can be derived from an assumed equation of state for the adsorbed phase plus the thermodynamics of the adsorbed phase, ie, the Gibbs adsorption isotherm,... 

Statistical Thermodynamic Isotherm Models. These approaches were pioneered by Fowler and Guggenheim (21) and Hill (22). Examples of the appHcation of this approach to modeling of adsorption in microporous adsorbents are given in references 3, 23—27. Excellent reviews have been written (4,28). 

Many simple systems that could be expected to form ideal Hquid mixtures are reasonably predicted by extending pure-species adsorption equiUbrium data to a multicomponent equation. The potential theory has been extended to binary mixtures of several hydrocarbons on activated carbon by assuming an ideal mixture (99) and to hydrocarbons on activated carbon and carbon molecular sieves, and to O2 and N2 on 5A and lOX zeoHtes (100). Mixture isotherms predicted by lAST agree with experimental data for methane + ethane and for ethylene + CO2 on activated carbon, and for CO + O2 and for propane + propylene on siUca gel (36). A statistical thermodynamic model has been successfully appHed to equiUbrium isotherms of several nonpolar species on 5A zeoHte, to predict multicomponent sorption equiUbria from the Henry constants for the pure components (26). A set of equations that incorporate surface heterogeneity into the lAST model provides a means for predicting multicomponent equiUbria, but the agreement is only good up to 50% surface saturation (9). 

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