Quantitative expression of adsorption

It follows from the discussion of the quantitative expression of adsorption in Chapter 2 that the most appropriate demarcation between the gas and the adsorbed phase is the Gibbs dividing surface (GDS). This enables us to express the adsorption data in terms of the surface excess and avoids having to determine (or assume) the absolute thickness of the adsorbed layer. 

Quantitative expression of the energies involved in adsorption from solution... 

This expression can be used to describe both pore and solid diffusion so long as the driving force is expressed in terms of the appropriate concentrations. Although the driving force should be more correctly expressed in terms of chemical potentials, Eq. (16-63) provides a qualitatively and quantitatively correct representation of adsorption systems so long as the diffusivity is allowed to be a function of the adsorbate concentration. The diffusivity will be constant only for a thermodynamically ideal system, which is only an adequate approximation for a limited number of adsorption systems. 

While all rates of these unimolecular reactions can be fit quantitatively by LH expressions. Equation 11, the heats of adsorption determined from the temperature dependence of the adsorption equillb-rium constant. Equation 14, do not agree with the measured reaction activation energy except for NH3 where = 16 2 kcal/mole. NO... 

Weisz (22) derives quantitative expressions for the heat of adsorption, the rate of adsorption, and the amount of adsorption, for a simple model. The model used involves a simple surface barrier of the type in Fig. 5, with adsorption traps as the only surface traps, and where, if the system reaches equilibrium, adsorption occurs until the adsorption traps are at the energy of the Fermi level. Weisz shows that the surface cannot become... 

The last term in Equation 1 represents the global kinetics, expressed as the rate of adsorption per unit volume of bed. It cannot be written in terms of concentrations in the fluid phase—the equations must be solved to do this—but it may be expressed quantitatively in terms of Ci by writing an expression for the diffusion rate ... 

A possible way to increase the accuracy of this immersion approach is to use the slurry method and to analyse a weighed sample of the slurry in the bottom of the test-tube, instead of analysing the supernatant (Nunn etal., 1981). One then simply makes use of Equation (5.49), the operational expression of the relative surface excess of the solute with respect to the solvent. Here n1 and n2 are the total amounts of solute and solvent in the sample of slurry (either adsorbed or in solution) and c[ and c their concentrations in the solution. If one uses a liquid-solid ratio large enough to avoid any measurable change in concentration on adsorption, then c and c are simply the concentrations in the starting solution. The measurement is accurate provided the quantitative analysis of the slurry, which involves measuring the total amounts of 2 and 1... 

DNOSBP, was varied from 1.1 to 96.9 /unoles/liter. Relative rate constants, expressed in units of (/xmoles/gram)2/hr., derived from the present experiments are plotted in Figure 4 vs. initial concentration of solute. The linearity of the trace so obtained indicates good agreement with the concentration dependence of adsorption rate noted previously for sul-fonated alkylbenzenes (8). Thus, the previous and present experiments suggest that the nature of the effect of concentration may well be general and quantitatively as well as qualitatively predictable. 

Physical adsorption is a universal phenomena, producing some, if not the major, contribution to almost every adhesive contact. It is dependent for its strength upon the van der Waals attraction between individual molecules of the adhesive and those of the substrate. Van der Waals attraction quantitatively expresses the London dispersion force between molecules that is brought about by the rapidly fluctuating dipole moment within an individual molecule polarizing, and thus attracting, other molecules. Grimley (1973) has treated the current quantum mechanical theories involved in simplified mathematical terms as they apply to adhesive interactions. 

A phenomenon of concentration of a substance on the interface is called adsorption. Surface activity is due to the unequal distribution of a solute between the surface and the bulk solution. Quantitative description of the adsorption of a solute at gas-liquid interfaces, under an equilibrium condition, is expressed by the Gibbs adsorption equation as... 

It is an interesting and significant fact that the author in 1926 found that the quantitative relations between the concentration of acetylcholine and its action on muscle cells, an action the nature of which is wholly unknown, could be most accurately expressed by the formulae devised by Langmuir to express the adsorption of gases on metal filaments. 

Equilibrium of adsorption on a solid is characterized by an adsorption isotherm, which shows the concentration on the solid as a function of the concentration in the contacting fluid. A quantitative measure of uptake of a gaseous species by a liquid is the distribution coefficient, defined as the ratio of the concentration on the solid to that in the contacting fluid. If concentration-independent, the coefficient is also called Henry coefficient. Diffusion of a species in a porous solid is expressed in terms of an effective diffusion coefficient, whose value accounts for the retardation by the solid matrix. Mass transfer to or from a solid is expressed in terms of a mass-transfer coefficient, the flux being the product of that coefficient and a concentration difference as "driving force."... 

Any type of specific barriers hinder the adsorption/desorption exchange of ionic and nonionic surfactants between the subsurface and the adsorption layer. In contrast to these specific barriers the electrostatic retardation influences the exchange at the boundary between diffuse and diffusion layer. Thus, the effects of specific and electrostatic retardation do not overlap but multiply each other. This means, that the collective effect of both can be measurable even when the separate effects are insignificant. The amplification of one retardation by the other is quantitatively expressed in the present theory. Varying the electrostatic conditions by electrolyte concentration and pH changes systematic studies of specific barriers and electrostatic retardations can be performed. 

We therefore believe that the Elovich equation may be used as a basis for a quantitative interpretation of rates of adsorption and desorption both from the single-gas phase, and from binary mixtures, and that it is a useful expression, like that for a Freundlich isotherm in equilibrium adsorption studies, as a means of describing the heterogeneous nature of many rate processes. We have not attempted to describe, in detail, the extensive experimental data that are available in the literature since this has been thoroughly and critically assessed up to 1960 by Low (5) who has written an excellent and comprehensive review in which he provides references to the original papers. 

The thermodynamics and dynamics of interfacial layers have gained large interest in interfacial research. An accurate description of the thermodynamics of adsorption layers at liquid interfaces is the vital prerequisite for a quantitative understandings of the equilibrium or any non-equilibrium processes going on at the surface of liquids or at the interface between two liquids. The thermodynamic analysis of adsorption layers at liquid/fluid interfaces can provide the equation of state which expresses the surface pressure as the function of surface layer composition, and the adsorption isotherm, which determines the dependence of the adsorption of each dissolved component on their bulk concentrations. From these equations, the surface tension (pressure) isotherm can also be calculated and compared with experimental data. The description of experimental data by the Langmuir adsorption isotherm or the corresponding von Szyszkowski surface tension equation often shows significant deviations. These equations can be derived for a surface layer model where the molecules of the surfactant and the solvent from which the molecules adsorb obey two conditions ... 

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