Theoretical study of miscibility and glasshyphen;forming trends in mixtures of polystyrene spheres

摘要

We present a theoretical study of glasshyphen;forming trends and miscibility in mixtures of polystyrene spheres (lsquo;lsquo;polyballsrsquo;rsquo;) of different diameters, suspended in an aqueous solution. The polyballs are assumed to be charged and to interact via a Debyendash;Huuml;ckel screened Coulomb potential. The Helmholtz free energy is calculated from a variational principle based on the Gibbsndash;Bogolyubov inequality, in which a mixture of hard spheres of different diameters is chosen as the reference system. It is found that when the charges of the two types of polyballs are sufficiently different, the variationally determined ratio of hardhyphen;sphere diameters differs substantially, leading to packing difficulties characteristic of glass formation. The experimentally observed range of glass formation corresponds to a ratio of hardhyphen;sphere diameters of 0.8 or less. Calculations of the free energy as a function of concentration indicate that the liquid polyball mixture is stable against the phase separation, even for widely different polyball charges.