Journal of physical chemistry b vol:108 issue:41 pages:16168-16173
Several years ago Utracki and Simha reported a remarkable independence of molar mass of the ratio of the thermodynamic critical (consolute) concentration and the concentration of incipient coil overlap, also known as "critical" concentration. They investigated solutions of polystyrene in cyclohexane and also found the consolute concentration at the critical temperature to be approximately equal to the average segmental concentration within the coils. Here we supply an explanation for these indisputable experimental findings. To this end we examine three systems for which experimental information about the true consolute state and coil dimensions is available in the literature, viz. cyclohexane/polystyrene, methylcyclohexane/polystyrene, and diphenyl ether/polyethylene. The conclusion is that the two concentration ratios will usually vary with molar mass. The constancy observed by Utracki and Simha can be explained if it is assumed that their anionic polystyrene samples, though having narrow molar-mass distributions as expressed in M-w/M-n, were contaminated with small amounts of high molar-mass material responsible for considerable deviations between maximum-demixing and consolute concentrations. This conclusion is independent of whether the temperature- and concentration dependence of the coil dimensions are taken into account. For the concentration dependence we made use of an expression not published hitherto. Light-scattering data published earlier by Borchard and Rehage clearly demonstrate that the maximum in the 45/135 angular dissymmetry does not occur at the consolute concentration but close to, or at, the concentration at which the spinodal exhibits an extremum. Here we prove the latter point theoretically. The extremum of the spinodal is a consolute point in strictly binary systems only. Hence, the term "spinodal", rather than "critical", opalescence appears to be appropriate to indicate the phenomenon.