Adsorption internal energy

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. 

A MC study of adsorption of living polymers [28] at hard walls has been carried out in a grand canonical ensemble for semiflexible o- 0 polymer chains and adsorbing interaction e < 0 at the walls of a box of size C. A number of thermodynamic quantities, such as internal energy (per lattice site) U, bulk density (f), surface coverage (the fraction of the wall that is directly covered with segments) 9, specific heat C = C /[k T ]) U ) — U) ), bulk isothermal compressibility... 

We review Monte Carlo calculations of phase transitions and ordering behavior in lattice gas models of adsorbed layers on surfaces. The technical aspects of Monte Carlo methods are briefly summarized and results for a wide variety of models are described. Included are calculations of internal energies and order parameters for these models as a function of temperature and coverage along with adsorption isotherms and dynamic quantities such as self-diffusion constants. We also show results which are applicable to the interpretation of experimental data on physical systems such as H on Pd(lOO) and H on Fe(110). Other studies which are presented address fundamental theoretical questions about the nature of phase transitions in a two-dimensional geometry such as the existence of Kosterlitz-Thouless transitions or the nature of dynamic critical exponents. Lastly, we briefly mention multilayer adsorption and wetting phenomena and touch on the kinetics of domain growth at surfaces. 

The parameter determined from simulations that can be most readily compared to an experimentally observable quantity is the heat of sorption. The mean total internal energy determined by the simulations, (V), can be equated to the isosteric heat of adsorption, Qst, in the limit of low occupancy, as follows ... 

The use of statistical calculations of configuration integrals to determine thermodynamic adsorption characteristics of zeolites dates back to the late 1970s (49). Kiselev and Du (22) reported calculations based on atom-atom potentials for Ar, Kr, and Xe sorbed in NaX, NaY, and KX zeolites. Then-calculations, which included an electrostatic contribution, predicted changes in internal energy in excellent agreement with those determined experimentally. The largest deviation between calculated and experimental values, for any of the sorbates in any of the hosts, was a little over 1 kJ/mol. 

In adsorption of a species onto a surface, a bond is formed. When the binding is very weak, for example, through van der Waals interactions, the molecule is said to be physically adsorbed (physisorbed). Such species are typically bound by a few (< 10) kcal/mol. In other cases a chemical bond forms between the adsorbate and the surface, meaning the molecule is chemically adsorbed (chemisorbed). Thus chemisorbed molecules are typically bound to the surface by tens of kcal/mol. In either case, the net internal energy change in an adsorption process A Eads is always negative ... 

U9 is the total internal energy of the free gas. Since usually the amount adsorbed is small compared to the total amount of gas in the reservoir the properties of the free gas do not change significantly during adsorption. Thus, dU9/dNa = U which leads to... 

In the case of dissociative adsorption on surfaces there is an additional channel into which energy can be transfered, namely the conversion of the kinetic and internal energy of the molecule into translational energy of the fragments on the surface with respect to each other. In fact, in the dissociation of light molecules such as 1I2 on metal surfaces the dissociative adsorption probability is... 

It is usually assumed that the properties of the bulk of the adsorbent are not affected by physisorption and therefore that its internal energy and its entropy do not change on adsorption, so that ... 

The differential energy of adsorption can also be regarded as the change of internal energy of the complete adsorption system, produced by the adsorption of an infinitesimal surface excess amount dn°, when temperature, volume and surface area are held constant (and assuming the adsorbent to be inert and that its internal energy is not changed). Thus,... 

Integration of the differential energy of adsorption is quite straightforward from Equation (2.50). Since the gas is ideal, its molar internal energy does not vary with pressure so that ... 

The most common calorimetric technique is the discontinuous procedure where the adsorptive is introduced in successive steps. The calorimetric cell with its contents (adsorbent and adsorptive) must be considered as an open system (cf. Figure 3.15). It is only when the adsorptive is introduced reversibly and when the step is small enough (so that the amount introduced can be written d n and the pressure increase dp) that the derivation of a differential energy of adsorption (as defined by Equations (2.49) and (2.50)) is possible. Under these conditions, and taking into account the internal energy contributed by the gaseous adsorptive, we can write ... 

Different types of heats of adsorption can be defined based on the variables which are kept constant during the experiment (F, F, p,/I, etc.). Here we shall discuss three such heats. The first heat is usually called the differential heat of adsorption although it is, in fact, defined as a change in internal energy the second is the isosteric enthalpy of adsorption formerly called isosteric heat of adsorption and the third is the isothermal heat of adsorption (ijth). We shall develop expressions that allow these heats to be determined from experimental calorimetric data and show how these quantities are interrelated. 

By definition, the integral heat of adsorption is defined as the amount of heat evolved by the system when " or n are adsorbed at constant temperature and volume. Thus, since no volume work is done, the integral heat is obtained in accordance with the first law of thermodynamics as the final minus the initial internal energy of the system ... 

By convention Q " is positive. The molar integral heat of adsorption is defined as the molar change in internal energy during the adsorption process (A u")... 

It will be shown that the combined total internal energy of the modeled adsorbate leads directly to the integral heat of adsorption, from which the experimentally observable isosteric heat of adsorption can be calculated and a comparison made. 

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