Sorption, equilibrium data interpretation

Mechanisms of Sorption Processes. Kinetic studies are valuable for hypothesizing mechanisms of reactions in homogeneous solution, but the interpretation of kinetic data for sorption processes is more difficult. Recently it has been shown that the mechanisms of very fast adsorption reactions may be interpreted from the results of chemical relaxation studies (25-27). Yasunaga and Ikeda (Chapter 12) summarize recent studies that have utilized relaxation techniques to examine the adsorption of cations and anions on hydrous oxide and aluminosilicate surfaces. Hayes and Leckie (Chapter 7) present new interpretations for the mechanism of lead ion adsorption by goethite. In both papers it is concluded that the kinetic and equilibrium adsorption data are consistent with the rate relationships derived from an interfacial model in which metal ions are located nearer to the surface than adsorbed counterions. 

Figure 8. Example of apparent closed-system equilibrium fractionation, where Mo in solution is sorbed to Mn oxides (Barling and Anbar 2004). The 6 Mo values of the Mo remaining in solution during sorption follow die linear trends that are consistent widi closed-system equilibrium fractionation where isotopic equilibrium is continuously maintained between Mo in solution and diat sorbed to die Mn oxides. Three aqueous-solid pairs (shown widi tie lines) are consistent with this interpretation. The isotopic data cannot be ejqilained dirough a Rayleigh process, where die product of die reaction (sorbed Mo) is isolated from isotopic exchange widi aqueous Mo.

EQUILIBRIUM SORPTION VALUES. The equilibrium sorption values for the extracts at various pressures of benzene are shown in Table II. The results show that O-methylated extract sorbs the most benzene at the lower pressure and that the O-octylated extract sorbs the least. At the higher pressme, the order is reversed. We believe the data shown in Table II reflect changes in the relative amounts of adsorption and absorption (swelling) with increasing size of the added alkyl groups. This interpretation is based on surface area and solubility measurements described below. 

Kinetic and equilibrium studies of the sorption of methanol on various coals and on partially acety-lated samples of these coals have been used to elucidate a mechanism for this process. The data are interpreted in terms of partial acetylation blocking surface sites and perhaps interfering with intermolecular hydrogen bonding. It is proposed that the rate-determining step is a set of parallel, competing, second-order reactions involving transfer of methanol from the surface to the interior of the coal. All types of surface sites appear to participate, and the pressure-independent rate constant is considered to be the sum of the rate constants for each type of surface site. The dependence of the experimental rate constant on methanol pressure is a characteristic of the coal rank. 

The results of experimental studies of the sorption and diffusion of light hydrocarbons and some other simple nonpolar molecules in type-A zeolites are summarized and compared with reported data for similar molecules in H-chabazite. Henry s law constants and equilibrium isotherms for both zeolites are interpreted in terms of a simple theoretical model. Zeolitic diffusivitiesy measured over small differential concentration steps, show a pronounced increase with sorbate concentration. This effect can be accounted for by the nonlinearity of the isotherms and the intrinsic mobilities are essentially independent of concentration. Activation energies for diffusion, calculated from the temperature dependence of the intrinsic mobilitieSy show a clear correlation with critical diameter. For the simpler moleculeSy transition state theory gives a quantitative prediction of the experimental diffusivity. 

In this chapter we will mostly focus on the application of molecular dynamics simulation technique to understand solvation process in polymers. The organization of this chapter is as follow. In the first few sections the thermodynamics and statistical mechanics of solvation are introduced. In this regards, Flory s theory of polymer solutions has been compared with the classical solution methods for interpretation of experimental data. Very dilute solution of gases in polymers and the methods of calculation of chemical potentials, and hence calculation of Henry s law constants and sorption isotherms of gases in polymers are discussed in Section 11.6.1. The solution of polymers in solvents, solvent effect on equilibrium and dynamics of polymer-size change in solutions, and the solvation structures are described, with the main emphasis on molecular dynamics simulation method to obtain understanding of solvation of nonpolar polymers in nonpolar solvents and that of polar polymers in polar solvents, in Section 11.6.2. Finally, the dynamics of solvation with a short review of the experimental, theoretical, and simulation methods are explained in Section 11.7. 

Equation 6 can be shown to correspond in mathematical form to a model predicated on a continuous spectrum of sorption interaction energies. If this interpretation is imposed on equation 6, the variable n can be said to reflect both the level and distribution of sorption energies, and KF the sorption capacity. For most natural solids, n generally ranges in value between 0.5 and 1.0, the upper limit characterizing a linear isotherm. As defined, KF would logically incorporate the specific reactive surface area, SH, of the sorbent, which can be abstracted to yield a capacity term, KFh, expressed per unit surface area (KFh = KF/SH). A logarithmic transform of equation 6 can be used to facilitate evaluation of both KVu and n from observed equilibrium sorption data. 

While a number of established characterization methods exist for mesopores and macropores, the assessment of microporosity is much less advanced, due to experimental difficulties and the lack of a suitable model for the interpretation of the isotherm data. Obtaining accurate experimental isotherms is hampered by the long equilibration times required at the low liquid nitrogen temperatures. In order to overcome this limitation the micropore structure evaluation can be based on isotherms of carbon dioxide or other vapors obtained at higher temperatures, provided that a suitable equilibrium model for the sorption of non spherical molecules is available. 

Polymers are often polydisperse with respect to molecular weight. Whereas this is of minor importance for the solvent sorption in polymers (vapor-hquid equilibrium), this fact usually remarkably influences the polymer solubility (liquid-hquid equilibrium). Therefore, polydispersity needs to be accounted for in interpretation and modeling of experimental data. This can be done by applying continuous thermodynamics as well as by choosing a representative set of pseudocomponents. It was shown that a meaningful estimation of the phase boundary is possible when using only two or three pseudocomponents as soon as they reflect the important moments (Mn, Mw, Mz) of the molecular weight distribution. 

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