Investigations concerning special critical points in multicomponent liquid mixtures

Abstract

The key results of the present investigations [4] can be summarized as follows:

Water behaves as a field variable and hence, as an effective substitute for pressure in exploring the coexistence surface of the system [polystyrene + acetone + water] in a highly controlled manner. A very close access to a CDP, as evidenced by a ?T as small as 0.194°C, has been achieved. The parabolic nature of the critical and extremum lines has been established. This issue had not been quantitatively addressed by earlier work on CDP in polymer solutions [2, 3]. The parabolicity of these lines permits one to rationalize the experimental results in terms of the Landau-Ginzburg theory and the geometrical picture of phase transitions [1, 33, 52, 54-57]. The unambiguous doubling of the critical exponents, ? and ?, in the vicinity of a CDP (i.e., as ?Tb ? 0) in terms of their 3-D Ising values has been demonstrated. The role of t_ui in restoring the universal value of ? (=0.325), over a wide range of ?Ts, has been validated. This finding is again in contrast to the analysis of Casielles et al. [3] that implies the inability of t_ui to restore the universality of the critical exponent. The analysis of the coexistence data with t as well as t_ui yielded a good fit only with the correction-to-scaling term. In fact, a satisfactory fit with a universal ? was obtained by Casielles et al. [3] (in terms of t_ui) when the correction-to-scaling term was invoked. It has been shown that the upper and lower coexistence curves (for a given ?T) display a similar shape in that they are consistent with the same value of ?. The amplitudes of the two curves are also reasonably similar (Tables 5.7 and 5.8). In our system [polystyrene + acetone + water], in so far as the order parameter is concerned, ?Tf represents the correct measure of the distance to a CDP and an effective CDP is realized when ?T = 0. The role of water in these complex systems remains to be understood from a microscopic viewpoint in the wake of the Patterson-Delmas theory of polymer solubility [5, 10, 11, 17, 62]. Finally, our results are in consonance with earlier investigations [3, 19, 21] in that they do not display (i) a distortion in the coexistence curves in the close vicinity of a CDP (Fig. 5.8), (ii) any evidence for a homogeneous, one-phase ‘hole’ inside the two-phase region of the hourglass phase diagram (Fig. 5.8). These two aspects, however, constitute the key outcomes of a series of recent investigations by Van Hook et al. [34].