Phase diagram of star-shaped polystyrene/cyclohexane system: location of critical point and profile of coexistence curve

Abstract

Coexistence curves of cyclohexane solutions of star-shaped polystyrenes (PSs) having 6.3 and 11.1 arms (arm molecular weight 1.88 × 10 5) were measured to investigate the effects of molecular shape on the phase diagram near the critical point. The reduced coexistence curve ф ф c versus τ τ c , where volume fraction ф and dimensionless temperature τ calculated from τ = (T − Θ) Θ with a usual temperature T and the theta temperature Θ were reduced by the values at the critical point, were compared with those of linear PSs. The reduced coexistence curves of star-shaped PSs do not superpose on the reduced universal curve of linear PS when the same Θ is assumed for linear and star-shaped PSs. The critical temperature T c and concentration ф c were compared with those of linear, randomly branched, and comb-shaped PSs. The location of the critical point of the star-shaped PS is very different from that of linear PS of the same molecular weight M w, indicating failure of the mean-field theory of polymer solutions. The same simple two-parameter scaling, which predicts the relations ф c ∼ ф∗ (= overlap concentration) and τ c ∼ (M w ф∗) −1 , does not hold for the star-shaped and linear PSs, when the same Θ is used for linear and star-shaped PSs. The scaling relations do not hold either even when we use different Θs for star-shaped PSs which were evaluated so that the reduced coexistence curves were superposed on the universal coexistence curve of linear PS. The ф c of star-shaped PS lies at a lower concentration than expected from its ф∗ and T c lies at a lower temperature than expected from ( M w ф∗) −1 .