Demixing curve

Fig. 3 Liquid-liquid demixing curves (dashed lines denoted by T ) and liquid-solid transition curves (solid lines denoted by Tm) of polymer solutions with variable energy parameter sets [denoted by T(EV/EC, B/Ec)]. The solution system is made of 32-mers in a 32-sized cubic box. a Theoretical curves b simulation results in the optimized approach [14]...

Fig. 8 Theoretical liquid-liquid demixing curve (solid line) and the bulk melting temperature (dashed line) of a flexible-polymer blend with one component crystallizable and with athermal mixing. The chain lengths are uniform and are 128 units, the linear size of the cubic box is 64, and the occupation density is 0.9375 [86]...

The demixing curves in the W/S pseudoternary diagrams for the hexanol and pentanol systems have been calculated according to the above theoretical treatment. These lines have been determined in the following way. The calculation of the state equation is applied to a dilution line along such a line the inverse micelles have a constant radius R. The micelles contain the whole water (volume Vw), the surfactant (volume V ) and a part of the alcohol V. The rest of alcohol is in the oil continuous phase. We suppose that the alcohol-oil ratio in the continuous phase is constant and is equal to k. Besides, in the calculation of the micellar radius R one assumes that the surfactant and the alcohol molecules which are situated at the interface have a constant area per chain s. In mos of the previous studies s has been found constant and equal to 25 A2. This value is taken equal for the alcohol and surfactant chains. Consequently ... 

Figure 5. Comparison between experimental (full line) and calculated (dashed line) demixing curves in the oil rich region of the hexanol and pentanol systems. is the experimental critical point. P-E is the theoretical critical point.

Figure 1. Demixing diagrams for PS in 0-solvents and poor solvents (schematic). The variable X might be pressure, Mw D/H ratio in solvent or solute, etc. See text for a further discussion, (a, top left) PS in a 0-solvent (monodisperse approximation). For X=Mw - the X=0 intercepts of the upper and lower heavy lines drawn through the minima or maxima in the demixing curves define 0Land0u, respectively, (b, top right) PS in a poor solvent (monodisperse approximation). The heavy dot at thecenterlocates the hypercritical (homogeneous double critical) point. (c, bottom right) The effect of polydispersity. BIN=binoda] curve, CP=cloud point curve, SP=spinodal, SHDW=shadow curve. See text Modified from ref. 6 and used with permission.

With the aid of thermal analysis the limits of the metastable demixii region can indeed be established. These are represented by the dotted branches of the curves, which are the continuation of the (full line) demixing curve in the temperature region (56°—78°) in which the demixing is stable. The other two branches of the curves represent the equilibria saturated solution — anhydrous crystals. 

An interesting phase behavior was observed experimentally [38] for the system poly(ethylene-co-methyl acrylate) in the solvent ethylene (Figure 10.13). Starting from low-density polyethylene, an increasing content of methyl acrylate in the copolymer shifts the demixing curve to lower pressures up to 13 mol% of methyl acrylate in the copolymer, whereas with further addition of methyl acrylate the solubility again decreases. In this case, the binary parameter is a linear function of the copolymer composition [38]. Figure 10.13 demonstrates the performance of the PC-SAFT EOS. The model is able to describe the observed dependence on temperature and molar mass as well as the nonmonotonic dependence on copolymer composition. 

Fig. 4.10 Theoretical calculation (a) and Monte Carlo simulations (b) of liquid-liquid demixing curves dashed lines) and liquid-solid curves solid lines) of polymer solutions with different energy parameter combinations, denoted by T E IE, BIE ) (Hu et al. 2003a)...

Figure 13.5 shows the parallel results of liquid-liquid demixing curves and liquid-solid coexistence curves in polymer solutions with different energy parameter sets, obtained from the lattice mean-field theory and Monte Carlo simulations. Theoretical calculations and Monte Carlo simulations agree well with each other, validating the mean-field assumption in theoretical approaches. 

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