Adsorption isotherm exponential

This is simply a collection of constants in an exponential function format. The constants cannot be related to the interactions at a molecular level. In contrast, the refit of the data to the Langmuir adsorption isotherm... 

However, with an inhomogeneous electrode surface and adsorption energies that are different at different sites, the reaction rate constant and the related parameter will also assume different values for different sites. In this case the idea that the reaction rate might be proportional to surface concentration is no longer correct. It was shown by M. Temkin that when the logarithmic adsorption isotherm (10.15) is obeyed, the reaction rate will be an exponential function of the degree of surface coverage by the reactant ... 

For different acceptor particle adsorption isotherms expressions (1.85) - (1.89) provide various dependencies of equilibrium values of <7s for a partial pressure P (ranging from power indexes up to exponential). Thus, in case when the logarithmic isotherm Nt InP is valid the expression (1.85 ) leads to dependence <75 P" often observed in experiments [20, 83, 155]. In case of the Freundlich isotherm we arrive to the same type of dependence of - P" observed in the limit case described by expression (1.87). 

Equation (135) is the well-known Freundlich adsorption isotherm. In a number of instances this isotherm accurately describes experimental data. The interpretation of the Freundlich adsorption isotherm as resulting from exponential nonuniformity of surface is due to Zel dovich 43). 

There are several theoretical derivations of adsorption isotherms. The simple Langmuir equation [Eq. (4.2), named after the American chemist and 1932 Nobel laureate Irving Langmuir], describes the formation of a monolayer on a surface [81]. This corresponds to the type I isotherm shown in Figure 4.15. Here Vis the amount adsorbed, Vm is the amount adsorbed in one monolayer, p is the pressure and b is the adsorption coefficient, which depends exponentially on the heat of adsorption. 

A pronounced contribution of surface heterogeneity may result in a more or less exponential decrease of Qe with 0, leading to the exponential adsorption isotherm (76). 

An exaggerated emphasis on heats of chemisorption has probably been harmful in the proper understanding of the role of chemisorption in surface phenomena. Thus the marked nonuniformity of all surfaces with respect to heats of chemisorption has led to rather elaborate treatments where models of surface heterogeneity (statistical distribution of energy sites) or, less successfully, specific forces of interaction between adsorbed species have been invoked to explain the non-Langmuirian adsorption isotherms. For instance the Frumkin isotherm can be obtained with a linear variation of heats of adsorption with coverage, and the Freundlich isotherm is attributed to an exponential variation of heats of adsorption. 

Adsorption at a charged sur u% where both electrostatic and specific chemical interactions are involved can be discussed in terms of the Langmuir adsorption isotherm, where the distribution coefficient b is given by the exponential of a sum of the electrochemical and electrostatic forces. In this treatment the fractional surface coverage, 6, is given by [43]... 

Having measured for a certain system the experimental adsorption isotherm ( ), one may draw Qs as the function of 0, assuming various values of k (0,1) and C. In this way, one obtains a family of exponentially decreasing curves, the shape of which is similar to that of the experimentally observed heats of adsorption curves. 

In contrast to localized adsorption, mobile adsorption models assume that molecules can diffuse freely on the surface. One of the most popular equations used to describe mobile adsorption is that proposed by Hill and de Boer [105] as an analogue of the FG isotherm. This equation can be obtained by combining the two-dimensional form of van der Waals equation with the Gibbs adsorption isotherm. Note that the pre-exponential factors for localized and mobile adsorption are different. In the case of localized adsorption, the pre-exponential factor Kq takes into account the vibrations of adsorbing molecules in X, y and z direction, whereas the factor for the mobile adsorption contains only the partition functions for vibration in the z-direction and the transnational partition function describing mobility of adsorbing molecules in the (x,y)-plane. 

In this work the independent method for determining the parameter n is presented. The main idea of this method is supported by a new form of the so - called exponential adsorption isotherm [2] and takes into account both heterogeneity of the solids and the nonideality of the liquid mixtures. One ought stress that this method in contrast to aforementioned is suitable for analyzing all types of the excess adsorption isotherms. 

A general exponential adsorption isotherm for describing adsorption data on heterogeneous solid surfaces converges with Eq.(5) and has the following form [7] ... 

It should be remarked here that except perhaps for OH and O species on noble metals, the adsorption energy of an intermediate is rarely distributed in a linear way with coverage thus for submonolayer chemisorption, states with discretely different adsorption energies are the rule rather than the exception, so that a continuous exponential function in g is usually less than realistic as a basis for writing an electrochemical adsorption isotherm equation. When terms such as exp(g0) are included, this introduces a further implicit T-dependent quantity since really exp(g0) = exp(r0/RT), i.e., g is a/(T- ). 

For derivation of adsorption isotherms in the case of exponential nonuniformity, the desorption exponent q=ln b = -lna should be preferably used as an integration variable. 

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