Probability factor adsorption

In contrast, if adsorption requires two sites and the adsorbed monolayer is mobile, then/(0) = (1 — 9)2, which is the probability of finding two free adjacent sites. Integrating Equation (4.2) with this probability factor yields the following second-order expression ... 

The question still in doubt concerns the nature of the activation barrier. In the classical treatment, the only one described in Trapnell s monograph (11), a gas molecule diving to an adsorption site must surmount an activation barrier. As pointed out previously by Taylor in his 1932 paper introducing the concept of activated adsorption, this simple picture immediately raises the question of a very small probability factor for adsorption, of the order of 10"6. Of course this small probability factor may be explained away if it is identified with the small fraction of active sites available at the surface. Another possibility is the relatively large negative value of the activation entropy that can be obtained for certain models of the activated complex. A treatment of chemisorption by absolute rate theory was first given in 1940 (16), but the use of the... 

Parameter Calculation and Establishment of Relationships. The use of molecular modeling tools not being evident for nonexperts in the field, alternative tools can be applied for the assessment of values for rate coefficients, preexponential factors, and/or activation energies (22). Collision rate theory provides a simple description of a kinetic process. It counts the number of collisions, Zab, between the reacting species A and B in a bimolecular reaction or between the reacting species and the surface in the case of an adsorption step and applies a reaction probability factor, Prxn, to account for the fact that not every collision leads to a chemical reaction. 

The product f-F is usually referred to in chromatography of column flow as the retardation factor, Fr (Giddings, 1965). In a polymer flood, there are therefore two competing effects on the retardation factor adsorption, tending to make Fr> 1, and velocity enhancement, which tends to make Fr< 1. Note that if Fr = 1, then it is probable that there are no adsorption or excluded-volume effects however, it could be that they fortuitously cancel. 

Adsorption of macromolecules has been widely investigated both theoretically [9—12] and experimentally [13 -17]. In this paper our purpose was to analyze the probable structures of polymeric stationary phases, so we shall not go into complicated mathematical models but instead consider the main features of the phenomenon. The current state of the art was comprehensively summarized by Fleer and Lyklema [18]. According to them, the reversible adsorption of macromolecules and the structure of adsorbed layers is governed by a subtle balance between energetic and entropic factors. For neutral polymers, the simplest situation, already four contributor factors must be distinguished ... 

Comparison of entries 4 and 8 of Table 16 shows that linear IOS 2024 and AOS 2024 adsorption values were the same within a modest experimental error. The major chemical structure difference between them is the position of the sulfonate group on the carbon chain and perhaps the position of the carbon-carbon double bond. These two factors do not appear to have an appreciable effect on adsorption. Therefore, the lower adsorption of IOS 1518 relative to AOS 1618 is probably due to the greater hydrophobe branching of the internal olefin sulfonate or the lower di.monosulfonate ratio. 

Actually, it is recognized that two different mechanisms may be involved in the above process. One is related to the reaction of a first deposited metal layer with chalcogen molecules diffusing through the double layer at the interface. The other is related to the precipitation of metal ions on the electrode during the reduction of sulfur. In the first case, after a monolayer of the compound has been plated, the deposition proceeds further according to the second mechanism. However, several factors affect the mechanism of the process, hence the corresponding composition and quality of the produced films. These factors are associated mainly to the com-plexation effect of the metal ions by the solvent, probable adsorption of electrolyte anions on the electrode surface, and solvent electrolysis. 

The critical parameters for separation by displacement are the displacer concentration, the loading factor (ratio of the sample size to the column saturation capacity) and the column efficiency. The choice of displacer is probably the most critical step. For correct development to occur the adsorption isotherm of the displacer must overlie those of the feed components. The concentration of the i PlAcer controls the separation time and... 

Adsorption-desorption Partly Mechanisms for adsorption on similar materials will be similar. Soil adsorption data generally do not reflect the saturated conditions of the deep-well environment. Organic-matter content is a major factor affecting adsorption in the near-surface its significance in the deep-well environment is less clear. Fate studies involving artificial recharge are probably useful, but differences between fresh waters and deep brines may reduce relevance. 

The results of these studies are tabulated in Table IV. This table lists the surfaces studied, the intermediates observed, the products, the adsorption temperature (T ds). the initial sticking probability of HCOOH (Sq), the peak temperature for product evolution (7J,), and the activation energy (E i) and the preexponential factor (v) determined by methods discussed earlier (see Section I,D). Data for HCOOD is given where available in order to distinguish the two hydrogens in the acid. 

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