Adsorption entropy diffusion

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. 

The two contrasting approaches, the macroscopic viewpoint which describes the bulk concentration behavior (last chapter) versus the microscopic viewpoint dealing with molecular statistics (this chapter), are not unique to chromatography. Both approaches offer their own special insights in the study of reaction rates, diffusion (Brownian motion), adsorption, entropy, and other physicochemical phenomena [2]. 

Adsorption Entropy on Heterogeneous Surfaces with Surface Diffusion... 

These theoretical considerations of the thermochromatographic process presume that the adsorption entropy and enthalpy do not depend on the temperature. It was also postulated that the adsorbent was homogeneous, its surface was not saturated with the adsorbate (monolayer or less), and the carrier (reagent) gas was unsorbable. Diffusion in the solid phase (adsorbent) and surface diffusion were ignored. Furthermore, in the theoretical considerations the effect of the carrier (reagent) gas pressure on the substance transport was not taken into account, which, however, should be considered in the case of TC at reduced reactant gas pressures and vacuum TC or with densely filled columns. 

In the case of nonionic compounds, the driving forces for adsorption consist of entropy changes and weak enthalpic (bonding) forces. The sorption of these compounds is characterized by an initial rapid rate followed by a much slower approach to an apparent equilibrium. The faster rate is associated with diffusion on the surface, while slower reactions have been related to particle diffusion into micropores. 

Vq is the frequency of the small oscillation, and AG and AS are, respectively, the difference in Gibbs free energy and entropy of the adatom at the saddle point and the equilibrium adsorption site. Ed is the activation energy of surface diffusion, or the barrier height of the atomic jumps. 

The thermodynamic functions of fc-mers adsorbed in a simple model of quasi-one-dimensional nanotubes s adsorption potential are exactly evaluated. The adsorption sites are assumed to lie in a regular one-dimensional space, and calculations are carried out in the lattice-gas approximation. The coverage and temperature dependance of the free energy, chemical potential and entropy are given. The collective relaxation of density fluctuations is addressed the dependence of chemical diffusion coefficient on coverage and adsorbate size is calculated rigorously and related to features of the configurational entropy. 

Here A//adS is the enthalpy of adsorption, T is the temperature, and AAads is the entropy change associated with the adsorption of the protein onto the surface. Protein adsorption will take place if AGads < 0. Considering a complex system, where proteins are dissolved in an aqueous environment, and are brought into contact with an artificial interface, there are a vast number of parameters that impact AGads due to their small size (i.e., large diffusion coefficient), water molecules are the first to reach the surface when a solid substrate is placed in an aqueous biological environment. Hence, a hydrate layer is formed. With some delay, proteins diffuse to the interface and competition for a suitable spot for adsorption starts. This competition... 

As it can be seen from Fig. 5.22, when moving from the localized adsorption towards the mobile model, we can expect smooth decrease in the entropy of desorption. The entropy of the adsorbate which experiences lateral diffusion was discussed, in particular, by Patrikiejew, et al. [95]. They approached the problem by assuming that a fraction of the molecules is in completely mobile state, while the others are completely localized. Then they suggested that the canonical partition function (9ml... 

The dynamic surface tension studies of Tritons indicate that the surface tension decrease in the short time range is faster (as compared with the usual diffusion models) [60,61]. This fact supports the conclusion about the existence of a reorientation process for Tritons at the surface. Similarly to the CnEOm, in the homologous series of Tritons the b value also increases with the m (cf Fig. 3.38). This again supports the hydrophilic-hydrophobic character of the EO groups. From the temperature dependence of the adsorption equilibrium constant b (cf. Table 3.15), one can estimate the thermodynamic characteristics of Triton X-100 adsorption at the water/air interface. In particular, the AG values can be calculated at various temperatures using Eq. (3.11), and then estimate the standard enthalpy (AH ) and standard entropy of adsorption (AS ) via Eqs. (2.180) and (2.181). 

Adsorption is an entropically driven process by which molecules diffuse preferentially from a bulk phase to an interface. Due to the affinity that a surfactant molecule encounters towards both polar and non-polar phases, thermodynamic stability (i.e. a minimum in free energy or maximum in entropy of the system) occurs when these surfactants are adsorbed at a polar/non-polar (e.g. oil/water or air/water) interface. The difference between solute concentration in the bulk and that at the interface is the surface excess concentration. The latter... 

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