Liquid-Liquid Phase Separation in Multicomponent Systems 637 improvements in selectivity. Such increases in selectivity must reflect a consolidation of the membrane skin region.Coagulation behavior for the aromatic polyamides (polymers III and II) is similar. Rate of coagulation, as evidenced by the development of an opaqueness, occurs more rapidly for the aromatic polyamides than for the polyamide-hydrazide. ConclusionsTypical flux-rejection data for the membrane systems described, with various feed solutions, are summarized in Table V. These aromatic polyamide membranes are characterized by their good mechanical strength, as illustrated in Figure 7.Here a comparison of flux-pressure response between polymer I and cellulose acetate is made. A straight line plot for flux is observed up to pressures of 1800 psi, with some departure from linearity evident after 1 hr. The deflection in the flux line for cellulose acetate is seen to coincide with a decrease in rejection, indicating development of a membrane defect.Typical mechanical properties for asymmetric membranes prepared from these polymers are shown in Table VI. In addition to their good mechanical properties, these aromatic polyamides show remarkable chemical resistance, especially in the high-pH range. This is in marked contrast to the cellulose acetate systems.1 23456789 Membrane reverse osmosis performance for aqueous salt rejections appears unaltered after 1 week of storage in 1 A solutions of H2S04, HC1, HNOs, CHsCOOH, NaOH, andNH4OH.Selectivity of these membranes to solutes other than NaCl is quite good, as illustrated by results for polymer III in Table VII.

Abstract

Critical miscibility data obtained from measurements of phase‐volume ratios have been used to calculate the concentration dependence of the pair interaction parameter for the system polystyrene–cyclohexane. The measured temperature and concentration ranges are 11–30°C and 4–18% polymer by weight, respectively. With the Gibbs free energy of mixing expressed in polymer segment mole fractions, x*, the pair interaction parameter is g(x*, T) = 0.4961 + 71.92/T + 0.2312x* + 0.0750x*2. In a polymer volume fraction formulation the parameter is g(φ, T) = 0.4099 + 90.65/T + 0.2064 φ + 0.0518 φ2, which approximates to χ(φ, T) = 0.2035 + 90.65/T + 0.3092 φ + 0.1554 φ2. Comparison of the temperature and concentration dependence with that obtained by other authors shows very good agreement, even when extensive extrapolations in temperature and concentration are applied. The present function is believed to be the most accurate. Solutions of mixtures of two narrow‐distribution polystyrenes in cyclohexane show separation into three liquid phases under the exact conditions predicted by theoretical calculation with the present pair‐interaction function.

41) Di Paola-Baranyi, G.; Fletcher, S. J.; Degre, P. Macromolecules (42) McMaster, L. P. Macromolecules 1976, 6, 760. (43) Stein, R. S.; Hadziioannou, G.; accepted for publication in (44) Herkt-Maetzky, C.; Schelten, J., private communication. (45) The Rayleigh factor is defined as 1982, 15, 885. Macromolecules.where d is the sample-to-detector distance, I,(g) is the scattered intensity, Io is the incident beam intensity, and V, is the scattering volume. The R(q') used in light scattering is equivalent to the differential scattering cross section d2/dQ used in neutron scattering.ABSTRACT The cloud-point curve equation is derived for a solution of a polydisperse polymer with a concentration-dependent interaction parameter g( TA), and a method for its numerical solution is devised.Also, a classification scheme is proposed for critical points based on their multiplicity, and the relationship between our and the previously devised categories is probed (particularly between our triple critical point and the tricritid point). Criteria for the existence of critical points of multiplicity m = 2-6 are given in terms of chain-length averages, concentration derivatives of g( T,4), and the overall polymer concentration 4. The significance of multiple critical points lies in their close association with multiphase equilibria. Such points may arise because of the asymmetry of the chain-length distribution and/or because of a strong concentration dependence of g(T,4). Two specific cases are analyzed a polydisperse polymer solution with a concentration-independent parameter g( T ) , and a monodisperse polymer solution with a concentration-dependent parameter g(T,&). In the first instance, multiple critical points may appear even in systems with only a few components if their characteristics are properly chosen. At most, an s-component system at constant pressure may display a critical point of multiplicity 2s -3, and it may separate into s phases. In the latter case, double and triple critical points may appear if the concentration dependence of g(T,$) is at least quadratic. The pattern of cloud-point curves for the two analyzed cases is distinctly different.

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