Phase behavior of a colloid plus binary polymer mixture: Theory

The theory of depletion flocculation in colloid + nonadsorbing polymer mixtures is extended to cover size polydispersity of the polymer. The case of colloid + binary polymer mixture is studied in detail. The main conclusion is that phase separation is enhanced in a colloid + binary polymer mixture when compared with a nominally equivalent colloid + monodisperse polymer mixture, except for the case where the equivalent polymer has the mass average molecular weight of the mixture. This equivalent polymer though has the closest correspondence to the true binodal of the mixture. Alternatively, if it is possible to use total effective coil volume fraction as a measure of polymer concentration, then phase behavior becomes insensitive to polymer size polydispersity. Size fractionation is predicted to occur, with the larger species being concentrated in the polymer rich phase, although the extent is not great. The influence of an undetected small polymer species on the onset of phase separation in a colloid + monodisperse polymer mixture is also examined. It is found that a small amount of contaminant can significantly lower the phase boundary, corresponding to the introduction of an additional short range depletion well in the interparticle potential.