Ideal solution theory

Gee and Orr have pointed out that the deviations from theory of the heat of dilution and of the entropy of dilution are to some extent mutually compensating. Hence the theoretical expression for the free energy affords a considerably better working approximation than either Eq. (29) for the heat of dilution or Eq. (28) for the configurational entropy of dilution. One must not overlook the fact that, in spite of its shortcomings, the theory as given here is a vast improvement over classical ideal solution theory in applications to polymer solutions. 

For a binary system of surfactants A and B, the mixed micelle formation can be modeled by assuming that the thermodynamics of mixing in the micelle obeys ideal solution theory. When monomer and micelles are in equilibrium in the system, this results in ... 

The mixture CMC is plotted as a function of monomer composition in Figure 1 for an ideal system. Equation 1 can be seen to provide an excellent description of the mixture CMC (equal to Cm for this case). Ideal solution theory as described here has been widely used for ideal surfactant systems (4.6—18). Equation 2 can be used to predict the micellar surfactant composition at any monomer surfactant composition, as illustrated in Figure 2. This relation has been experimentally confirmed (ISIS) As seen in Figure 2, for an ideal system, if the ratio XA/yA < 1 at any composition, it will be so over the entire composition range. In classical phase equilibrium thermodynamic terms, the distribution coefficient between the micellar and monomer phases is independent of composition. 

Below the CMC, the surfactant mixing in monolayers composed of similarly structured surfactants approximately obeys ideal solution theory. This means that the total surfactant concentration required to attain a specified surface tension for a mixture is intermediate between those concentrations for the pure surfactants involved. For mixtures of ionic/nonionic or anionic/cationic surfactants, below the CMC, the surfactant mixing in the monolayer exhibits negative deviation from ideality (i.e., the surfactant concentration required to attain a specified surface tension is less than that predicted from ideal solution theory). The same guidelines already discussed to select surfactant mixtures which have low monomer concentrations when micelles are present would also apply to the selection of surfactants which would reduce surface tension below the CMC. 

When two similarly structured anionic surfactants adsorb on minerals, the mixed admicelle approximately obeys ideal solution theory (jUL - Below the CMC, the total adsorption at any total surfactant concentration is intermediate between the pure component adsorption levels. Adsorption of each surfactant component in these systems can be easily predicted from pure component adsorption isotherms by combining ideal solution theory with an empirical correspond ng states theory approach (Z3). ... 

Recently, some studies on the mixture of fluorocarbon and hydrocarbon materials have been carried out by surface tension, interfacial tension, differential conductance, NMR and solubilization methods(1-9). Mukerjee( ) and Funasaki( ) reported that fluorocarbon and hydrocarbon mixtures exhibit departure from ideal solution theory. 

Non-ideal solution theory is used to calculate the value of a parameter, S, that measures the interaction between two surfactants in mixed monolayer or mixed micelle formation. The value of this parameter, together with the values of relevant properties of the individual, pure surfactants, determines whether synergism will exist in a mixture of two surfactants in aqueous solution. 

The nature of surface adsorption and micelle formation of various mixed FC- and HC-surfactants systems can be conveniently and well investigated by the non-ideal solution theory semi-emplrlcally applied in the surface layer and micelles. The weak "mutual phobic" interaction between FC- and HC-chains has been clearly revealed in the anionic-anionic and nonlonic-nonionic systems as Indicated by the positive values. value cannot be obtained... 

It is evident that the non-ideal solution theory of surface adsorption and micellization is a convenient and useful tool for obtaining the surface and the micelle compositions and for studing the molecular interaction in the binary surfactant system. 

The thermodynamics of mixing upon formation of the bilayered surface aggregates (admicelles) was studied as well as that associated with mixed micelle formation for the system. Ideal solution theory was obeyed upon formation of mixed micelles, but positive deviation from ideal solution theory was found at all mixture... 

Scamehorn et. al. (20) also presented a simple, semi—empirical method based on ideal solution theory and the concept of reduced adsorption isotherms to predict the mixed adsorption isotherm and admicellar composition from the pure component isotherms. In this work, we present a more general theory, based only on ideal solution theory, and present detailed mixed system data for a binary mixed surfactant system (two members of a homologous series) and use it to test this model. The thermodynamics of admicelle formation is also compared to that of micelle formation for this same system. 

The mixed admicelle is very analogous to mixed micelles, the thermodynamics of formation of which has been widely studied. If the surfactant mixing in the micelle can be described by ideal solution theory, the Critical Micelle Concentration (CMC) or minimum concentration at which micelles first form can be described by (21) ... 

A previously proposed theory to describe mixed adsorption in these systems (20) depended not only on ideal solution theory, but also on the correspond ng states theory to apply to surfactant mixtures. In that model, it was assumed that the adsorption isotherms for the pure components coincided when plotted against a reduced concentration. This occurs when the ratio CACB E/CACrt is the same at any adsorption level. When true, this simplifies the prediction of mixed adsorption isotherms somewhat, but that model is really a special case of the model presented here. 

Mixed Micelles. The CMC values -for the two pure sur-factants and well de-fined mixtures thereo-f are shown in Figure 2. The experiments were run at a high added salt level (swamping electrolyte) so the counterion contributed by the dissolved sur-factant is negligible. Predicted mixture CMC values -for ideal mixing -from Equation 1 are also shown. Ideal solution theory describes mixed micelle -formation very well, as is usually the case -for similarly structured sur-factant mixtures (12.19.21—2A) ... 

The predicted adsorption isotherms From ideal solution theory (Equations 6—9) are also shown in Figures 3—5. Since it is diFFicult to see degree oF Fit on a log-log plot, the ability to describe the data is better illustrated in Figures 6-9, where the CACm is plotted For several adsorption levels as a Function oF monomer composition along with predictions From Equation 6. 

This effect does not occur with the mixed micelles, where the spherical geometry of the hydrophobic core permits intimate contact between hydrocarbon chains of different lengths, so that the environment for hydrophobic groups is similar in the pure micelles as in the mixed micelles. As a result, ideal solution theory is obeyed. 

We will study three different applications of ideal solution theory to the calculation of density of a liquid. Each application will depend on the amount of information available. The first applies when the composition of the reservoir liquid is known. The second applies when solution gasoil ratio, gas composition, and stock-tank oil gravity are known. The third is used when solution gas-oil ratio, gas specific gravity, and stock-tank oil gravity are known. 

There are many measurement techniques for activity coefficients. These include measuring the colligative property (osmotic coefficients) relationship, the junction potentials, the freezing point depression, or deviations from ideal solution theory of only one electrolyte. The osmotic coefficient method presented here can be used to determine activity coefficients of a 1 1 electrolyte in water. A vapor pressure osmometer (i.e., dew point osmometer) measures vapor pressure depression. 

Scamehorn et. al. expanded a single component adsorption equation ( ) to describe the adsorption of binary mixtures of anionic surfactants of a homologous series (1 1). Ideal solution theory was found to describe the system fairly well. The mixed adsorption equations worked very well in predicting the mixture adsorption, but the equations were complex and would be difficult to extend beyond a binary system. 

Scamehorn et. al. ( ) also developed a reduced adsorption equation to describe the adsorption of mixtures of anionic surfactants, which are members of homologous series. The equations were semi-empirical and were based on ideal solution theory and the theory of corresponding states. To apply these equations, a critical concentration for each pure component in the mixture is chosen, so that when the equilibrium concentrations of the pure component adsorption isotherms are divided by their critical concentrations, the adsorption isotherms would coincide. The advantage of... 

The adsorption of binary mixtures of anionic surfactants in the bilayer region has also been modeled by using just the pure component adsorption isotherms and ideal solution theory to describe the formation of mixed admicelles (3 ). Positive deviation from ideality in the mixed admicelle phase was reported, and the non-ideality was attributed to the planar shape of the admicelle. However, a computational error was made in comparison of the ideal solution theory equations to the experimental data, even though the theoretical equations presented were correct. Thus, the positive deviation from ideal mixed admicelle formation was in error. 

If ideal solution, theory for mixed admicelle formation is assumed (/. = 1.0), six independant equations can be written tor a binary system. The set of equations consists of Equation 3 written for components 1... 

The adsorption isotherms of CgSO. and mixtures thereof, on alpha aluminum oxiae are illustrated in Figure 4. Also shown in Figure 4 is the extrapolation of the C SO. pure component adsorption isotherm down to its CAC and the ideal solution theory predictions. 

The agreement between the mixture adsorption data and ideal solution theory is excellent. It is important to remember that while looking at various constant leyels of adsorption in Region II, we are looking at the CAC of the mixed admicelle that has just formed on a particular patch. By looking at different adsorption levels, we are looking at how the two surfactants interact on different energy level patches on the surface. 

Micelles and monolayers composed of homologous mixtures of anionic surfactants can be approximately described by ideal solution theory to model the mixed surfactant aggregate (35). Therefore, surprising that mixed admicelles composed surfactants also obey ideal solution theory, important to note that this is true at all levels within Region II, as seen by the... 

When the absolute concentrations of the surfactants at the interface are not required, but only their relative concentrations, i.e., their relative effectiveness of adsorption, then these can be obtained in convenient fashion by use of non-ideal solution theory. 

Recalling, first, ideal solution theory, the solubility of a solid in a liquid is related to the heat of fusion of the solid and the temperature of the solution, ignoring ACp and AK terms. 

Ideal solution theory, which forms the basis of the method, involves a number of assumptions. In particular it applies only to weak solutions which in the context of the determination means nearly pure substances. Furthermore the impurity should not dissolve in the solid phase. The... 

It is evident that the first postulate is far from being followed by any real system. Moreover a lot of work has been done demonstrating severe effects due to surface heterogeneity. With respect to the ideal behavior of the solution it has been demonstrated that the ideal solution theory is a good approximation [138]. 

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