Adsorption from solution thermodynamics

Although we started out this chapter by discussing insoluble monolayers, it is evident that we have slipped into examples for which soluble amphipathics are being considered. In the next section we examine the thermodynamics of adsorption from solution. 

Until now we have discussed only insoluble monolayers. Although their behavior is complex, they have the conceptual simplicity of being localized in the interface. It has been noted, however, that even in the case of insoluble monolayers, the substrate should not be overlooked. The importance of the adjoining bulk phases is thrust into even more prominent view when soluble monolayers are discussed. In this case the adsorbed material has appreciable solubility in one or both of the bulk phases that define the interface. 

Gibbs treated this situation as part of his investigations into phase equilibria. Suppose we consider two phases a and /3 in equilibrium with a surface s dividing them. For the system so constituted, we may write 

Substituting this result into Equation (33) gives 

As we saw in Chapter 6 (Equation (6.16)), the quantity ydA may be equated to nonpressure-volume work when surface energy is being considered. With this consideration, Equation (35) simplifies still further to become 

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SCHAY,G., Adsorption of solutions of nonelectrolytes , in reference 9 2,155-211 (1969) Thermodynamics of adsorption from solution , in reference 15 ... 

Major advances in the thermodynamic treatment have been made by Defay and Prigogine (1951), Schay (1970), Schay and Nagy (1961, 1972), Schay et al. (1972), Nagy and Schay (1963), Kipling, (1965) and Everett (1972, 1973,1986). These and other authors have given considerable thought to the presentation and utilization of an experimental data adsorption from solution. 

For further reading on the thermodynamics of adsorption from solution see ) and the general references at the end of this chapter. 

Adsorption from solution is an exchange process. Consequences of this "first law" pervade all attempts to define individual (or partial) isotherms. Any assumption made on the adsorption of component 1 involves an assumption regarding component 2 deriving an equation for 1 implies deriving an equation for 2. This is (or should be) reflected in all models, and all thermodynamics and statistical thermodynamics should be consistent with this principle. 

Everett, D. H. Thermodynamics of adsorption from solutions, in Fundamentals of Adsorption Processes, Meyers, A. L., Belfort G. (Eds.), Eng. Found., New York, 1984. 

Determination of thermodynamic characteristics of adsorption from solutions... 

The thermodynamic characteristic of adsorption from solutions can be determined from the dependence of adsorption on temperature. But the determination of adsorption isotherms from solution at different temperatures is the rather complicate problems. Liquid chromatography may be very useful method for the determination of thermodynamic characteristics of adsorption at small coverage [11] because of the measurement of retention volume (the Henry constant) at different temperatures of the chromatographic columns makes it possible to calculate the heats of adsorption and the differential standard change entropy of adsorption from ... 

Denoyel, R., Rouquerol, F., and Rouquerol, J. (1990). Thermodynamics of adsorption from solution Experimental and formal assessment of the enthalpies of displacement. J. Colloid Inteface Sci., 136, 375—84. 

We now derive Eqs. (59) and (60) from adsorption thermodynamics (83). This can be done by using the completely general approach of solution thermodynamics as a starting point, the value of which would be to emphasize that adsorption and solution thermodynamics are completely equivalent, are derivable from each other, have the same starting point, and apply to the same systems (regardless of adsorbent perturbations, swelling, etc.). However, this point of view has been stressed elsewhere (83) and we confine ourselves here, except for a few further remarks later, to the special case of an inert adsorbent, this being the case for which adsorption thermodynamics is particularly useful and natural. 

Kohler, H.H., "Thermodynamics of Adsorption from Solution" in "Coagulation and... 

The adsorption from solution of larger [2]catenanes consisting of two 87-membered rings was studied on HOPG. The STM image shows with submolecular resolution that the [2]catenane adsorb on the HOPG forming domains. The authors discuss the thermodynamics reasons for adsorption and the dynamics of the adsorbed layer. 

The second contribution influencing polymer adsorption from solution is the Flory-Huggins interaction parameter between poljnner and solvent. Such an enthalpy of mixing term adds a contribution of X (t)2 z) — 4> ) to the interaction energy contribution, where 4) is the bulk solution concentration of the polymer (2) and, when approaches thermodynamically poor values, then the adsorbed amoimt of pol3mier increases significantly. Figure 5.13 shows experi-... 

Adsorption from solutions was fully studied by G. C. Schmidt. He first showed that the adsorbed amount reaches a maximum, when the surface is saturated, and does not then increase if the concentration of the solution is increased (1910). He proposed an adsorption formula (1911) taking this into account, which he later modified (1916). Extensive researches carried out from 1906 by Freundlich showed that a thermodynamic theory given by J. W. Gibbs (1877, see p. 742) could be used as a guide. A modification of the adsorption equation (5), viz. xlm=kc f (6), applies to solutions, where adsorbed amount, m=mass of adsorbent, equilibrium concentration of solution, k and n are constants (i/n varies from o i to o-8). It was apparently first used by C. H. D. Bodeker, then by W. Biltz, and Freundlich. 

Freundlich adsorption equation, although successful to explain many solution adsorption data, has failed to explain the data at very high and low concentrations. This is perhaps due to the fact that the Freundlich equation is empirical in nature and thermodynamically inconsistent at high and low concentrations. Thus, a theoretical analysis of adsorption from solution and the derivation of a suitable equation have been comparatively difQcult as both the components of the solution compete with each other for the available surface. Moreover, the thermal motion of the molecules in the liquid phase and their mutual interactions are much less well understood. It is, therefore, difQcult to correctly assess the nature of the adsorbed phase, whether monomo-lecular or multimolecular. The nature of the phase is usually determined by the nature of the carbon as well as by the nature of the components of the solution, the concentration of the solution, and the mutual solubility of the components. 

Over the past decade a general consensus has developed concerning the formulation of the thermodynamics of adsorption from solution, and although the various treatments differ in detail there are no major areas of controversy.Several papers have, however, appeared recently presenting variations on earlier formulations and these are discussed below. 

For all kinds of transitions, the system tends to hesitate between order and disorder and is prone to exhibit thermodynamic fluctuations which reflect the search for a compromise between the simultaneous requirements for minimum energy and maximum entropy. As the conducting polymers are pseudo-one-dimensional/two-dimensional systems, the probability of thermodynamic fluctuation increases significantly, resulting in a decrease in the ordered phase. The basic concept is that all electrochemical reactions proceed by adsorption from solution. This amounts to the replacement of solvent molecules by substrate, a process which is simultaneously governed by solvent-electrode, solvent-solute and solute-electrode interactions. Water, which is the most common solvent, possesses a high dielectric constant and, as such, tends to reject at its bulk periphery all molecules with a low dielectric constant. 

Studying adsorption from solution of polymer mixtimes is of great interest for the theory of PCM because many binders for composites are two-and more-component systems. The presence of two components determines the specificity of the properties of the boundary layers formed by two different polymeric molecules. From another point of view, as the large majority of polymer pairs is thermodynamically immiscible,there may arise interphase layers between two components in the border layer at the interface. The selectivity of adsorption of various components, which is a typical feature of adsorption from mixture, leads to the change in composition of the border layer as compared with composition in the equilibrium solution. This fact, in turn, determines the non-homogeneity in distribution of components in the direction normal to the solid surface, i.e., creates some compositional profile. As compared with stud3ung adsorption from solution of individual polymers, adsorption from mixture is studied insufficiently. The first investigations in this field were done " for immiscible pair PS-PMMA on silica surface, in conditions remote from the phase separation. It... 

No other readily available method can offer the same scope, reliability and accuracy as gas adsorption. Adsorption from solution measurements are relatively easy to carry out, but often difficult to interpret they cannot be recommended for general use, but are essential for some applications involving treatment of liquid media. Although enthalpies of immersion are more difficult to determine, they can provide useful information provided that isotherm data are also available. Liquid flow calorimetry is becoming popular for the characterization of powders and porous solids, but the technique requires refinement if it is to be used to obtain thermodynamic data. 

The English translation of this book by D. Smith and N. G. Adams provides a detailed account of theoretical approaches and experimental techniques of adsorption. The subject matter, essentially comprising physical chemistry, includes defined substances, defined surfaces and their preparation, methods for studying the texture of adsorbents, methods of studying adsorption, the surface structure of solids, theories of adsorption forces, adsorption kinetics and thermodynamics, theories of adsorption equilibria, the mechanisms of physical adsorption and chemisorption, adsorption from flowing gases and liquids, practical applications of adsorption, adsorption from solutions and the relationship between adsorption and catalysis. 

As to the unreal limiting values of enthalpies [see Eq. (18)], in the past 10-15 years it has been proven both theoretically and experimentally that the enthalpies and entropies have finite values at total monolayer coverage. For example, in adsorption from solutions a total excess coverage is always formed, and, evidently, the changes in enthalpies (entropies) can be measured exactly. The experimental data prove [9] that the enthalpy of a total monolayer coverage can never become infinite. Since the infinite or finite character of thermodynamic functions is independent of the nature of the adsorptive system (gas/solid, vapor/solid, liquid/solid) the supposition of the classical isotherm equation concerning limiting values [Eqs (17) and (18)] should be rejected. 

The Gibbs adsorption equation for the adsorption of an ion / from solution can be written in the form of the thermodynamic equation... 

The papers in this volume deal with many of the foregoing questions and problems relating to adsorption from aqueous solution. In addition to general discussions of thermodynamic and kinetic aspects of adsorption phenomena, the papers include description of the results of studies on a variety of adsorbate-adsorbent systems. Among the adsorbates studied are (1) strong electrolytes (2) unhydrolyzed multi-valent cations ... 

The primary mechanism for energy conservation is adsorption of surfactant molecules at various available interfaces. However, when, for instance, the water-air interface is saturated conservator may continue through other means (Figure 12.3). One such example is the crystallization or precipitation of the surfactant from solution, in other words, bulk phase separation. Another example is the formation of molecular aggregates or micelles that remain in solution as thermodynamically stable, dispersed species with properties distinct from those of an isotropic solution containing monomeric surfactant molecules (Myers, 1992). 

Elements 108 - 116 are homologues of Os through Po and are expected to be partially very noble metals. Thus it is obvious that their electrochemical deposition could be an attractive method for their separation from aqueous solutions. It is known that the potential associated with the electrochemical deposition of radionuclides in metallic form from solutions of extremely small concentration is strongly influenced by the electrode material. This is reproduced in a macroscopic model [70], in which the interaction between the microcomponent A and the electrode material B is described by the partial molar adsorption enthalpy and adsorption entropy. By combination with the thermodynamic description of the electrode process, a potential is calculated that characterizes the process at 50% deposition ... 

Our approach to the thermodynamics of adsorption and immersion remains simple, although rigorous, and close to the experiment. This is why the thermodynamic treatment of the energetics of immersion in Section 5.2 is confined to the simple system of a solid immersed in a pure liquid. Similarly, in Section 5.3 consideration is given only to the adsorption from binary solutions. The thermodynamic nomenclature and definitions proposed here are consistent with the recommendations of IUPAC (Everett, 1972, 1986). 

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