Publisher Summary This chapter presents five common surface complexation models of the mineral–solution interface and their use in describing soil chemical systems. Common model characteristics and adjustable parameters are discussed. For each model, surface species, chemical reactions, equilibrium constant expressions, and surface activity coefficients are described. Applications of the model to ion adsorption on soil minerals and soils are presented. Incorporation of surface complexation models into computer codes is also discussed. All surface complexation models are based on a balance of surface charge expression. They contain at least one coulombic correction factor to account for the effect of surface charge on surface complexation and explicitly define equilibrium constant expressions for surface complexes. They contain mass balance equations for each type of surface site and charge balance equations for each surface plane of adsorption. Thus, all models contain adjustable parameters—the equilibrium constants, the capacitance density for the i th surface plane, and the total number of reactive surface hydroxyl groups.

Use of surface complexation models in soil chemical systems

A physicochemical model is proposed to describe sorption in proton-exchange membranes (PEMs), which can predict the complete isotherm as well as provide a plausible explanation for the long-unresolved phenomenon termed Schroeder's paradox, namely, the difference between the amounts sorbed from a liquid solvent vs. from its saturated vapor. The solvent uptake is governed by the swelling pressure caused within the membrane as a result of stretching of the polymer chains upon solvent uptake, Π M , as well as a surface pressure, Π σ , due to the curved vapor-liquid interface of pore liquid. Further, the solvent molecules in the membrane are divided into those that are chemically, or strongly, bound to the acid sites, λ C i, and others that are free to physically equilibrate between the fluid and the membrane phases, λ F i. The model predicts the isotherm over the whole range of humidities satisfactorily and also provides a rational explanation for the Schroeder's paradox.

https://iopscience.iop.org/article/10.1149/1.1623495/pdf

Sorption in Proton-Exchange Membranes An Explanation of Schroeder’s Paradox

The Soret coefficient ST and collective (mass) diffusion coefficient Dc of polystyrene dissolved in the good-solvent toluene has been measured over a range of concentrations and molecular masses with an optical beam-deflection method. Our measurements indicate that ST scales inversely with the polymer translational diffusion coefficient in dilute solutions, exhibits a power-law scaling with polymer concentration, and an independence of polymer molecular mass in semidilute solutions. These findings are consistent with the known scaling of 1/Dc in dilute and semidilute polymer solutions, the relative insensitivity of the thermal-diffusion coefficient Dth of polystyrene in toluene to polymer concentration, and the relation ST=Dth/Dc from irreversible thermodynamics. We are able to represent our ST and Dc data by theoretically motivated reduced-concentration master curves, but the concentration-molecular mass scaling variables are found to be different for each transport property, a result contrary to theoret...

Thermal and Mass Diffusion in a Semidilute Good Solvent-Polymer Solution

We have developed a sensitive interferometric technique for measuring the temperature derivative of the refractive index of liquids with an accuracy of 0.5% as illustrated by measurements with mixtures of liquid n‐hexane and toluene. In addition the concentration dependence of the refractive index of these mixtures has been measured with refractometry. The experimentally observed temperature dependence of the refractive index appears to be consistent with a modification of the Lorentz–Lorenz relation proposed by Looyenga.

William Norman Rae

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