Asymmetric activity coefficient models

Polyzou, E.N. et ah. Assessment of activity coefficient models for predicting solid-liquid equilibria of asymmetric binary alkane systems, Ind Eng. Chem. Res., 38, 316-323, 1999. 

Voutsas, E.C., Kalospiros, N.S., and Tassios, D.P., A combinatorial activity coefficient model for symmetric and asymmetric mixtures, Eluid Phase Equilibria, 109, 1, 1995. 

For liquids and solids, determine the activity coefficients for binary and multicomponent mixtures through activity coefficient models, including the two-suffix Margules equation, the three-suffix Margules equation, the van Laar equation, and the Wilson equation. Identify when the symmetric activity coefficient model is appropriate and when you need to use an asymmetric model. 

Examination of Equation (7.57) [or Equations (7.55) and (7.56)] already shows one limitation in our model for g . It is completely symmetric that is, if we interchanged a and h in this equation, it would be no different. Accordingly, it could not be used to model systems in which the activity coefficients are not symmetric, such as that depicted in Example 7.7. Such asymmetric activity coefficient models will be presented in the next section. 

Since the value for A based on species a is close to that from species b, the system is reasonably symmetric and we can use the two-suffix Margules equation. Alternatively, we could use an asymmetric activity coefficient model the van Laar equation is commonly used for azeotropes. 

The case of binary solid-liquid equilibrium permits one to focus on liquid-phase nonidealities because the activity coefficient of solid component ij, Yjj, equals unity. Aselage et al. (148) investigated the liquid-solution behavior in the well-characterized Ga-Sb and In-Sb systems. The availability of a thermodynamically consistent data base (measurements of liquidus, component activity, and enthalpy of mixing) provided the opportunity to examine a variety of solution models. Little difference was found among seven models in their ability to fit the combined data base, although asymmetric models are expected to perform better in some systems. 

Some typical results are shown in Figure 16.2 (LLE for PS/acetone), Table 16.4 (infinite dilution activity coefficient for PBMA solutions in a variety of solvents). Tables 16.5 and 16.6 (activity coefficients of low- and heavy-molecular-weight alkanes in asymmetric athermal-alkane solutions). Table 16.7 (VLB for ternary polymer-solvent solutions). Figure 16.6 (VLB calculations for systems containing the commercial epoxy resin Araldit), and Table 16.8 (comparison of LLE results from various thermodynamic models). 

Depending on the type of the alloy, different models can be used to calculate the activity coefficient. For electrodeposited CoPt and FePt alloys which show strong negative departure from ideality,an asymmetric regular solution model is used to define XB (B = Fe or Co) ... 

The UNIFAC model diseussed in the previous section does suffer from a number of shortcomings, particularly for values of the activity coefficients in infinite dilution, the enthalpies of mixing and the values obtained for highly-asymmetrical systems. In order to improve the data, adjustments were made in three directions (1987) ... 

Eads, C.D., Robosky, L.C. NMR studies of binary surfactant mixture thermodynamics molecular size model for asymmetric activity coefficients. Langmuir 1999, 75(8), 2661-2668. 

The activity coefficients on the right of Figure 7.11 show asymmetric behavior. Ifwe wish to account for such asymmetric activity coefficients, we need to include more than one parameter in our model for g . One obvious way to break the symmetry is by adding a term with xa Xh) to the model as follows ... 

This equation is algebraically the simplest of the asymmetric models and also gives reasonable predictions of many binary systems it can even model systems whose activity coefficients show a maximum or a minimum. 

Membrane deterioration may be merely caused by decrease of acetyl content(C ) in the active surface layer as a result of hydrolysis or oxidation, not by structure change. Analysis was carried out based on solution-diffusion model proposed by Lonsdale etal( ), using their measured values of solute diffusivity and partition coefficient in homogeneous membrnaes of various degree of acetyl content and also using those values of asymmetric membranes heat treated at various temperatures measured by Glueckauf(x) ... 

The model active transport system described by Dr. Thomas is based on an asymmetric arrangement of two enzymes. A model active transport system was also described by Blumenthal et al. several years ago based on a single enzyme immobilized between asymmetric boundaries [Blumenthal, Caplan, and Kedem, Biophys. J., 7, 735 (1967)]. In the latter case the phenomenological coefficients were measured, and it was possible to demonstrate Onsager symmetry and the correlation between the thermodynamic coefficients and the kinetic constants. 

As in the case of poly-a-olefins, only in some poly-vinyl-ethers in which the asymmetric carbon atom of the lateral chains is in the ft position with respect to the principal chain and in which the optical activity is remarkably higher than in low molecular weight models, it was found that the optical activity and its temperature coefficient remarkably depend on the stereoregularity of the sample. 

Transport of molecules across the cell membrane occurs by passive and facilitated diffusion and active transport (Stein, 1986 Finkelstein, 1987). Passive transport is governed by a mass-transfer coefficient, surface area for exchange, transmembrane concentration difference, and a partition coefficient. The partition coefficient can be modified by charge, pH, temperature, and presence of other drugs. Facilitated transport may be most simply described by Michaelis-Menten kinetics. Depending upon the carrier system, symmetric or asymmetric models may be used. 

Again, differences between the optical activity of the polymers and their model compounds were found which depend on the distance of the asymmetric center from the main chain. The highest deviation was observed for the a position. The optical activity and its temperature coefficient depend on the stereoregularity of the polymer [2]. An enhancement of the optical activity was observed when poly-(iS )-2-methylbutylvinyl ether was com-plexed with strong Lewis acids such as Al(i-Bu)3 [11]. This was attributed both to a modification of the chromophore transitions and to a conformational effect due to the larger size of the side chain. 

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