Adsorption model mobile

Introducing the mobile adsorption model into this derivation [16] ki changes to ... 

The above equations, especially Eq. 5.54 (and so the mobile adsorption model) obtained wide use in radiochemistry of TAEs. The adsorption entropy was calculated from Eq. 5.33 accepting A/V = 1. Several authors proposed approximate... 

The formula 5.32 for the standard entropy of the adsorbate in the mobile adsorption model can be rewritten as ... 

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. 

The generally accepted theoretical value of AS is the one obtained for the mobile adsorption model and the standard state V7A = 1 cm (B. Eichler and Zvara 1982)... 

The state of an adsorbate is often described as mobile or localized, usually in connection with adsorption models and analyses of adsorption entropies (see Section XVII-3C). A more direct criterion is, in analogy to that of the fluidity of a bulk phase, the degree of mobility as reflected by the surface diffusion coefficient. This may be estimated from the dielectric relaxation time Resing [115] gives values of the diffusion coefficient for adsorbed water ranging from near bulk liquids values (lO cm /sec) to as low as 10 cm /sec. 

One important direetion of study has been to use empirieal adsorption data, together with the preassumed model for loeal adsorption, and attempt to extraet information about the form of x(e) [13,14]. The ehoiee of the model for loeal adsorption, whieh is an important input here, has been eustomarily treated quite easually, assuming that it has rather limited influenee on the form and properties of the evaluated EADFs. Usually, one of so many existing equations developed for adsorption on uniform surfaees is used as the loeal adsorption isotherm. The most often used forms of 0 p, T,e) are the Langmuir [6] and the Fowler-Guggenheim [15] equations for loealized adsorption. Ross and Olivier [4] extensively used the equation for mobile adsorption, whieh results from the two-dimensional version of the van der Waals theory of fluids. The most radieal solution has been... 

The values of — AH for benzene are in the range 10-12 kcal/mole,15,19-20 being intermediate between values attributed to pure dispersion forces for saturated hydrocarbons and those in which more specific forces are involved. Furthermore, Ron and coworkers calculated the entropies of adsorption for benzene and concluded that the mobile gas model of adsorption was applicable, and Whalen18 found no simple relationship between the hydroxy site content and benzene adsorption. These results confirm the conclusions reached from the infrared data that benzene adsorption is essentially due to dispersion forces which should be greater than with saturated compounds, and that no hydrogen bonding is involved. 

The entropy of a mobile adsorption process can be determined from the model given in [4], It is based on the assumption that during the adsorption process a species in the gas phase, where it has three degrees of freedom (translation), is transferred into the adsorbed state with two translational degrees of freedom parallel to the surface and one vibration degree of freedom vertical to the surface. From statistical thermodynamics the following equation for the calculation of the adsorption entropy is derived ... 

The adsorption behavior of atoms and compounds for most of the experiments used in the described correlations were evaluated using differently defined standard adsorption entropies [28,52-57], Adsorption data from more recent experimental results were evaluated applying the model of mobile adsorption [4], In addition, data from previous experiments were reevaluated using this model. 

Fig. 23. Thermochromatography of 106Ru in 02 gas (20 ml/min) in an empty quartz column. The solid line represents the temperature profile in the column. Two different Ru zones were observed after completion of the experiment (for details see text). Some of the Ru was not volatilized at the starting position. The dashed lines indicates the modeled deposition zone of a species transported by mobile adsorption with -Af/a0(RuO4)=54 kJ/mol. Figure reproduced from [92].

So far the solution of the mass-balance equation for models with a single dominating process (partitioning or adsorption) was discussed in Sections 2.8 and 2.9. In both cases the solutions have similar form, with the difference in the definition of the parameters (volumes of the mobile and stationary phases in the case of partitioning total volume of the liquid phase and adsorbent surface area in the case of adsorption model). 

Hill ) idealized lateral transitions by considering the surface as "homogeneous" but with a sinusoidally varying potential energy. At low temperature, the adsorbed molecules can only vibrate in the minima, but with increasing temperature the fraction that can pass the maxima increases. In this model there is a gradual transition between localized and mobile adsorption over the entire (homogeneous) surface. 

From the contents of Chapter 5 it follows that the original evaluation of the VTC data in terms of the energy of desorption presented in Refs. [29, 31, 35] should be revised. The value of ed was deduced implying the model of mobile adsorption. Meanwhile, if the model were valid, the unhindered movement of the adsorbed molecules across the surface would result in the column, independently of... 

Thus treatment of the data with this alternative adsorption model yields a more negative enthalpy change by RT than the mobile model. 

Comparing the latter with Eq. 5.48 we see that the values - Aads7/mb and Naea coincide, except for the small term RTc/2. The latter is the difference between the mean kinetic energy of the molecules in three-dimensional and two-dimensional gas. Thus, the molecular kinetic approach is equivalent to the model of mobile adsorption. 

The adsorption potential is never flat, which would be the rationale for the model of ideal mobile adsorption there invariably occur distinct potential wells. 

The proposed competitive adsorption model was implemented and used to calculate the band profiles of cyclopentanone with mobile phases of different compositions. One more adjustable parameter, an equilibrium constant for additional interactions, was introduced in order to match calculated and experimental retention of cyclopentanone. Figure 15.3 compares some calculated and experimental band profiles of cyclopentanone for mobile phases containing different concentrations of methanol in the mobile phase. In general, the agreement observed with either methanol or acetonitrile is good. However, like as any other complicated model, there are many parameters which must be determined by fitting the experimental data to the model and stiU, at the end, the calculated retention times of the solute(s) must be adjusted using a last empirical parameter in order to match the experimental retention times. There are no independent ways to verify that these parameters are correct. Therefore, in practice, the use of a more simplified model remains preferable. 

It is then of great importance to develop simple models capable of describing the energetic topography on the basis of a few parameters and to study the effects of these parameters on several surface processes, with the hope that, in such a process, methods to obtain the relevant parameters from experimental data will be envisaged. These models can be of two kinds continuum models or lattice-gas models. The former are more suited to mobile adsorption, generally physisorption, and then more closely related to the surface energetic characterization problem, whereas the latter are more suited to locaHzed adsorption (e.g., chemisorption). 

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