Polydispersity Effects on the Demixing Behavior of Poly(Vinyl Methyl Ether)/Polystyrene Blends

Abstract

Phase equilibrium calculations for solutions or mixtures of synthetic polymers become considerably more difficult when there is polydispersity of the polymers. To simplify the calculations, polydispersity is often neglected in the calculations or accounted for in a summary way only, and often only relatively simple free energy relations are applied. For example, Halary et al. published experimental demixing data on poly(viny1 methyl ether)/polystyrene blends. In evaluating the data the following assumptions were made: 1) the minimum of the demixing curve equals the critical point, 2 ) the X-parameter is independent of concentration and molecular weight, 3) the polydispersity may be roughly taken into account by using the formulas for monodisperse polymers and using the weight-average molecular weight. Continuous thermodynamics proves to be a suitable method to overcome the difficulties caused by polydispersity. Therefore, this method permits one to obtain detailed information on the phase equilibria in polymer sohtions and in polymer blends in a relatively easy way. To show this, the data of Halary et al. are reanalyzed by means of continuous thermodynamics. In this way, more profound knowledge may be obtained from the experimental material, e.g., a more precise determination of the critical point and a more correct location of the spinodal. 1055

Polymer‐Polymer Interaction: Consistent Modeling in Terms of Chain Connectivity and Conformational Response

“…Table 1. True critical temperatures and critical compositions [5] for blends of PVME and PS taken from the literature. For the calculation of the number of polymer segments, the molecular weights stated in terms of number average values were converted into weight average molecular weights by means of the also reported polydispersity indices k of the samples according to M w ¼ M n (1þk)/k.…”

“…Critical temperatures as a function of blend composition measured for different representatives of the system PVME/ PS. [5] In one set of experiments the number of PVME segments was kept constant (full symbols) and in the other that of PS (open symbols). To calculate the numbers m of segments of PVME and n, that of PS, the molar volume of a segment was set 100 mL.…”

“…pairs of m and n values leading to the concurrence of two critical points. Also indicated are the combinations of m and n values that were studied experimentally [5] (open circles) and the combinations (full circles) for which spinodal lines and a complete phase diagram (full triangle) will be presented. (12) and (13) using the system specific parameters given in row two of Table 2, and its projections into the different planes.…”

“…The influences of polydispersity on the deviations of critical temperatures and critical compositions from the extrema of the cloud point curve may be complicated and become very large as can be seen from Figure 2 (T c ) and Table 2 (j c ) of ref. [5] Further sources of experimental errors cannot be excluded. Figure 12.…”

“…After that extensive demixing data, [1][2][3][4] measured for the standard polymer blend poly(vinyl methyl ether)/ polystyrene (PVME/PS) and evaluated with respect to critical temperatures and compositions, [5] are used to check the suitability of the proposed relations and procedures. Unfortunately the validity of the approach can be presently only tested by means of the information available for that system.…”