Critical demixing concentration

Comments. The solvent mixture is used at its binary critical demixing concentration, i.e.,... 

Recently, renormalization group calculations have been used to derive new scaling laws for the molecular weight dependence of the interaction parameter, Xab between unlike polymers (A and B) in a good solvent and the critical demixing concentration. The purpose of this paper is to present some experimental results which verify this theory for several mixtures of two polymers polystyrene (PS) - poly(dimethyl-siloxane) (PDMS), poly(methyl-methacrylate) (PMMA)-PDMS, PS-PMMA and PS-poly (vinylacetate) (PVAc). 

Fig. 7.6 Critical micelle concentrations for mixtures of sodium perfluorooctanoate with sodium decyl sulfate (A) and sodium laurate (O). Dashed lines represent expected values for Ideal mixing, assuming B = 0.645 [Eq. (6)]. Curves 1, 2, 3, and 4 show expected values for complete demixing of micelles [Eq. (7)]. Curve 1 was calculated for B = 0.53 curves 2, 3, and 4 were calculated assuming B = 0.645. (From Ref. 68. Reproduced by permission of the American Chemical Society.)...

Lake [117] used kinetic dialysis to examine the existence of cdc. The cdc of the sodium decanoate-sodium perfluorooctanoate mixed-micelle system was found to occur at a specific surfactant concentration and mole fraction. Ben Ghoulam et al. [118] determined the demixing diagram of the Neos Ftergent (a branched alkylbenzenesulfonate by surface tensiometry) and measured second critical micelle concentrations. However, a critical demicellization concentration was not observed. 

Fig. 17 B/E-p dependence of the critical temperatures of liquid-liquid demixing (dashed line) and the equilibrium melting temperatures of polymer crystals (solid line) for 512-mers at the critical concentrations, predicted by the mean-field lattice theory of polymer solutions. The triangles denote Tcol and the circles denote T cry both are obtained from the onset of phase transitions in the simulations of the dynamic cooling processes of a single 512-mer. The segments are drawn as a guide for the eye (Hu and Frenkel, unpublished results)...

Taking into account changes in concentration of four layers, Williams and Mason (50) have shown that if a > 0, enrichment in the component with the lower heat of sublimation is enhanced compared to that found for ideal solutions. Near the critical temperature of demixing, the dependence of surface concentration on bulk would be highly reminiscent of this dependence for temperatures lower than the critical temperature. 

Apart from liquid-liquid transitions, liquid-vapor transitions in aqueous electrolyte solutions have played a crucial role in debates on ionic criticality [142-144], The liquid-vapor transition is usually associated with a mechanical instability with diverging density fluctuations, while liquid-liquid transitions are associated with a material instability with diverging concentration fluctuations. This requires, however, that both regimes are well-separated. Their interference can lead to complex phase behavior with continuous transitions from liquid-liquid demixing to liquid-gas condensation [9, 145, 146]. It is then not trivial to define the order parameter [147-149]. 

Ternary solutions of immiscible polymers in a low-molecular solvent display wide miscibility gaps. Consequently, they invariably involve demixing above a critical concentration of total polymer by spinodal decomposition and subsequent coarsening processes. When solvent evaporation progresses the enhanced viscosity will slow down the rate of phase separation to a level at which no further phase changes can be observed. 

There is, however, a mass transfer problem of demixing at lower temperatures caused by high viscosities. Concentrated polymer solutions tend to take hours to form two distinct liquid phases. A solution to this problem is the use of the lower critical solution temperature. Because of their thermodynamic nature, all polymer-solvent mixtures tend to form two liquid phases ( LL ) with low viscosities, at higher temperatures (LCST) as depicted in Figure 3. 

Figure 4. Demixing temperatures for Lennard-Jones polymer in Lennard-Jones solvent at P, = 2 as a function of polymer concentration for 16-mers (circles) and 64-mers (triangles). Temperature and pressure units are relative to the critical solvent properties. The Lennard-Jones interaction potential energy is cut at 2.5a and shifted [80].

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