The interfacial tension Q between the coexisting phases of the systems methylcyclohexane/polystyrene and cyclohexane/polystyrene was measured by means of the spinning drop and sessile drop methods as a function of (T, - T)/T, = z, the reduced distance from the critical temperature, for different relative molar masses M of the polymer (17 500-175 000). The minimum z value that could be realized amounted to 1.7 x 10e3 and the corresponding u value to 0.0007 mN m-l. The results were evaluated according to the relations (1) lna=A-[,lnM+plnz and (2) lnAcp=B-[,lnM+filnz in which Acp is the difference in the volume fraction of the polymer in the coexisting phases, A and B are constants for a given solvent, and [,,, is, p and fi are the critical exponents. With increasing M the exponent p is found to fall from values which are close to that predicted by the mean-field theory (1.50) to those resulting from the Ising model (1.26) ; p equals 0.35 in the entire region of M (mean-field : 0.50, Ising : 0.31). In contrast to the critical exponents, A and B are not universal constants but vary from solvent to solvent, i.e. the above relations are of little use for the prediction of 0. This deficiency can, however, be overcome by substituting z from (2) into (1) and replacing M by N, the number of monomeric units. The different parameters of the resulting relation (3) In Q = D + 6 In N + (pi/?) In Acp no longer depend on the particular chemical nature of the system. It therefore constitutes a useful master curve to obtain 0 from knowledge of the composition of the coexisting phases. The evaluation of the present measurements together with unpublished material yields D = ln[O.l53(mN m-l)], 6 = (lap/b) - 4, = 0.50 (identical with the mean-field value) and p//3 = 3.85 (mean-field : 3.00, Ising -4.00).
Посилання на статтю:
Interfacial tension between solutions of polystyrenes: establishment of a useful master curve / M. Heinrich and B. A. Wolf* // Polymer. – 1992. – Vol 33. – P. 1926-1931.