Molecular interaction parameter

A variety of equations-of-state have been applied to supercritical fluids, ranging from simple cubic equations like the Peng-Robinson equation-of-state to the Statistical Associating Fluid Theoiy. All are able to model nonpolar systems fairly successfully, but most are increasingly chaUenged as the polarity of the components increases. The key is to calculate the solute-fluid molecular interaction parameter from the pure-component properties. Often the standard approach (i.e. corresponding states based on critical properties) is of limited accuracy due to the vastly different critical temperatures of the solutes (if known) and the solvents other properties of the solute... 

The interdependence of the Gibbs energy of adsorption and the molecular interaction parameter was recently discussed in detail by Karol-czak, who used a six-parameter model. Contrary to the rather general Damaskin model, no relation between the molecular interaction parameter A and AGads was assumed. It was suggested that this is an arbitrary relation dependent on the theoretical model used in fitting experimental data within acceptable experimental errors. 

It is noted that the molecular interaction parameter described by Eq. 52 of the improved model is a function of the surfactant concentration. Surprisingly, the dependence is rather significant (Eig. 9) and has been neglected in the conventional theories that use as a fitting parameter independent of the surfactant concentration. Obviously, the resultant force acting in the inner Helmholtz plane of the double layer is attractive and strongly influences the adsorption of the surfactants and binding of the counterions. Note that surface potential f s is the contribution due to the adsorption only, while the experimentally measured surface potential also includes the surface potential of the solvent (water). The effect of the electrical potential of the solvent on adsorption is included in the adsorption constants Ki and K2. 

In order to elucidate the effect of alkyl alcohol on the surface adsorption of CyFNa and C,oSNa, it is useful to calculate the surface molecular interaction parameters of the binary surface active mixtures (y8,) according to the equation at constant surface tension and constant ionic strength (13,14,10) ... 

By extending regular solution theory for binary mixtures of AEg in aqueous solution to the adsorption of mixture components on the surface (3,4), it is possible to calculate the mole fraction of AEg, Xg, on the mixed surface layer at tt=20, the molecular interaction parameter, 6, the activity coefficients of AEg on the mixed surface layer, fqg and f2s and mole concentration of surfactant solution, CTf=20 3t surface pressure tt=20 mn-m l (254p.l°C). The results from the following equations are shown in Table I and Table II. 

The most reliable method of obtaining the molecular interaction parameters is by fitting measured temperature-dependent transport data to the rigorous kinetic gas theory expressions, and extracting e and a. 

The molecular-interaction parameter can give rise to either positive or negative contributions to the term In y,. If the solvent tends to be self-associated, then the addition of a nonpolar solute disrupts solvent structure. Figure 2-5 indicates that n-decane in water has an activity coefficient of about 100,000. This high activity coefficient in solution is typical of the weak interaction of solute and solvent. On the other hand, where the molecular interaction between solute and solvent is strong, the activity coefficient would be expected to be low, and solute-solvent interactions and association constants may be measurable. ... 

The two fundamental properties of surfactants are monolayer formation at interfaces and micelle formation in solution for surfactant mixtures, the characteristic phenomena are mixed monolayer formation at interfaces (Chapter 2, Section RIG) and mixed micelle formation in solution (Chapter 3, Section VIII). The molecular interaction parameters for mixed monolayer formation by two different surfactants at an interface can be evaluated using equations 11.1 and 11.2 which are based upon the application of nonideal solution theory to the thermodynamics of the system (Rosen, 1982) ... 

For evaluating the molecular interaction parameters for mixed micelle formation by two different surfactants, equations 11.3 and 11.4 (Rubingh, 1979) are used. 

The determination of and pM experimentally is shown in Figure 11-1. Surface tension-log surfactant concentration curves for each of the two individual suractants in the system and at least one mixture of them at a fixed value of a must be determined. For calculating (the molecular interaction parameter for mixed monolayer formation at the aqueous solution-air interface), Cj, C2 and C°2 are required for pM, the CMCs, Cf, C2, and Cf2, are needed. 

The molecular interaction parameters evaluated using equations 11.1-11.4, together with the properties of the individual surfactants (see Section III below), are used to predict whether synergism of a particular type will occur when the two surfactants are mixed and, if so, the molar ratio of the two surfactants at which maximum synergism will exist and the relevant property of the mixture at that point. The particular interaction parameters used depend upon the nature of the interfacial phenomenon involved as described below. 

II. EFFECT OF CHEMICAL STRUCTURE AND MOLECULAR ENVIRONMENT ON MOLECULAR INTERACTION PARAMETERS... 

A considerable number of molecular interaction parameters on well-characterized surfactant pairs have been measured during the past two decades. In addition, information on how the parameters change with variation in the chemical structures of the two surfactants and in their molecular environment (pH, temperature, ionic... 

Based upon the same nonideal solution theory used in the evaluation of molecular interaction parameters above, the conditions for the existence of synergism in... 

However, it should be understood that, because of the assumptions and approximations used in the nonideal solution theory upon which these relations are based, the calculated values for conditions at the point of maximum synergism may only approximate the values found under experimental conditions and should be used mainly for estimation purposes. This is especially true when commercial surfactants are used that may contain surface-active materials (impurities) of a type different from that of the nominal surfactant. These may cause the molecular interaction parameters to have values somewhat different from those listed in Table 11-1 for the nominal surfactant. When such impurities are suspected, it is advisable to determine experimentally the values of the interaction parameters. 

Equation (4.419) is identical to Equation (4.379) except for the replacement of mole fraction x by group fraction X, and molecular-interaction parameters A by group-interaction parameters a. 

The dependence of ip on the ratio of particle radii k = R2/R1 for various values of molecular interaction parameter Sa obtained by numerical integration of the expression (13.87) is shown in Fig. 13.24. Dashed lines indicate the asymptotics (13.95) for i 2 Ri-... 

These three theories predict the global phase behavior of microemulsion systems in terms of bending elastic properties (first approach), molecular interaction parameters (second approach), and expansion coefficients of order parameter fields (third approach). In this review, we try to fill the gap between the early years approach and item 1, above. 

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