Excess free energy interaction parameter

With this command, all three parameters in the WS mixing mle, the two excess free-energy model parameters, and the binary interaction pai ametcv, kjj, are optimized.)... 

The mixed cmc behavior of these (and many other) mixed surfactant systems can be adequately described by a nonideal mixed micelle model based on the psuedo-phase separation approach and a regular solution approximation with a single net interaction parameter B. However, the heats of micellar mixing measured by calorimetry show that the assumptions of the regular solution approximation do not hold for the systems investigated in this paper. This suggests that in these cases the net interaction parameter in the nonideal mixed micelle model should be interpreted as an excess free energy parameter. 

Using an automated film balance the behavior of mixed monomolecular films exhibiting deviations from ideality was studied. Particular attention was paid to condensation effects obtained when cholesterol is mixed with a more expanded component. The deviations at various film pressures are discussed in terms of the partial molecular areas of the film components. Slope changes in these plots are caused by phase transitions of the expanded monolayer component and do not indicate the formation of surface complexes. In addition, the excess free energies, entropies, and enthalpies of mixing were evaluated, but these parameters could be interpreted only for systems involving pure expanded components, for which it is clear that the observed condensation effects must involve molecular interactions. 

The influence of size and shape on the diffusion of hydrophobic solutes was estimated by simulations involving artificial Lennard-Jones particles those intermolecu-lar interaction parameters were based on those for ammonia or oxygen, respectively. The results on the size dependence of diffusion confirmed that the membrane interior differs strongly from a bulk hydrocarbon. In the center of the bilayer, the excess free energy for hydrophobic Lennard-Jones particles remained low irrespective of the size of the particles. This can be explained by the large fraction of accessible volume in that region. 

Figure 2. The negative of the excess free energy (—f) vs the thicknesses of water (<5i) and oil (r)2) layers. The interaction parameters are given in the text.

In his classic paper, Flory predicted the phase behavior in solutions of rod-like particles (5). The resulting phase diagram related the solvent-solute interaction parameter %i ( -5) to the volume fraction, V2, for polymer rods with an axial ratio of 100. A positive Xi makes a positive or excess free energy contribution to mixing. Good solvents are characterized by small Xi values. Two of Flory s major predictions are that the minimum polymer concentration required for mesophase formation will increase as Xi decreases, sharply at first, then more gradually, and at certain Xi values two different anisotropic phases coexist. Our microscopical observations of conjugated phases may reflect the validity of the latter prediction. 

This equation introduces the binary interaction parameter in a manner similar to that of eqn. (3.3.6) of the van der Waais one-lluid mixing rule. Next, the following modified form of the NRTL equation was used for the excess free-energy term ... 

Solubilities. Extrapolation from Liquid Phase. Solubilities of various copper carboxylate salts in pure octane and hexadecane at 90 °C are shown in Figure 2. The solubility of the octanoate salt is quite high but cannot be measured accurately because of experimental difficulties (discussed above). If one applies regular solution theory (6) with the assumption that the excess free energies of mixing (or alternatively the solvent-solute interaction parameters) are equal for a particular salt in an alkane medium, then the following equation can be derived (7) ... 

For the binary pair //, Tg and Tg are adjustable parameters, and ag(— ug) is a third parameter that can be fixed or adjusted. Excess free energy for the liquid system is expressed by an extension of Scott s cell theory, wherein only two-molecule interactions are considered. 

To calculate the partial molal excess free energies gf and from this the activity coefficients and the excess enthalpy, size parameters for each functional group and binary interaction parameters for each pair of functional groups are required. Size parameters can be calculated from theory. Interaction parameters are back-calculated from existing phase equilibrium data and then used with the size parameters to predict phase equilibrium properties of mixtures for which no data are available. 

Here xi is the interaction parameter measured experimentally at volume fraction vj such that kTx represents the excess free energy associated with the transfer of one solvent molecule from pure polymer to a polymer solution at volume fraction V2. 

To evaluate JGsfj-j it is necessary to introduce the segmental interaction parameter Xij- This is defined such that kTxtj represents the excess free energy associated with the transfer of one (solvent sized) segment of type i (or one solvent molecule if /= 1) from pure / to pure j. If there are Srii segments of i in SV, and the volume fraction of j therein is Vy, then it follows that... 

The compact core of a micelle is characterized by a uniform polymer density, fiXBs), chemical potential per monomer unit, plb Xbs), and excess free energy per unit area of the core-water interface, kBTy xBs)- Here, Xbs T) is the Hory-Huggins parameter of monomer (B)-solvent (5) interaction, and Xbs T) > Xbs 0) = 1/2 under poor solvent conditions for the monomer units of block B. Although the solubility of polymers in organic solvents usually decreases with a decrease in temperature, dxiT)fdT < 0, the situation is more complex in aqueous solutions. In particular, it appears that the solubility of thermosensitive block B in water typically decreases with an increase in temperature [11], and hence dXBsiJ)/dT>0. In this case, the collapse of blocks B and the aggregation of the block copolymers into micelles occur at r > LCST, where LCST is the lower critical solution temperature. 

Interaction parameter does depend on T and P, and the excess Gibbs free energy of mixing is described as in the preceding model ... 

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