The ability to separate enzymes, nucleic acids, cells, and viruses is an important asset in life sciences. This can be realised by using their spontaneous asymmetric partitioning over two macromolecular aqueous phases in equilibrium with one another. Such phases can already form while mixing two different types of macromolecules in water. We investigate the effect of polydispersity of the macromolecules on the two-phase formation. We study theoretically the phase behavior of a model polydisperse system: an asymmetric binary mixture of hard spheres, of which the smaller component is monodisperse and the larger component is polydisperse. The interactions are modelled in terms of the second virial coefficient and are assumed to be additive hard sphere interactions. The polydisperse component is subdivided into sub-components and has an average size ten times the size of the monodisperse component. We calculate the theoretical liquid–liquid phase separation boundary (the binodal), the critical point, and the spinodal. We vary the distribution of the polydisperse component in terms of skewness, modality, polydispersity, and number of sub-components. We compare the phase behavior of the polydisperse mixtures with their concomittant monodisperse mixtures. We find that the largest species in the larger (polydisperse) component causes the largest shift in the position of the phase boundary, critical point, and spinodal compared to the binary monodisperse binary mixtures. The polydisperse component also shows fractionation. The smaller species of the polydisperse component favor the phase enriched in the smaller component. This phase also has a higher-volume fraction compared to the monodisperse mixture.

The ability to separate enzymes, or cells or viruses, from a mixture is important and can be realized by the incorporation of the mixture into a macromolecular solution. This incorporation may lead to a spontaneous phase separation, with one phase containing the majority of one of the species of interest. Inspired by this phenomenon, we studied the theoretical phase behavior of a model system composed of an asymmetric binary mixture of hard spheres, of which the smaller component was monodisperse and the larger component was polydisperse. The interactions were modeled in terms of the second virial coefficient and could be additive hard sphere (HS) or nonadditive hard sphere (NAHS) interactions. The polydisperse component was subdivided into two subcomponents and had an average size ten or three times the size of the monodisperse component. We gave the set of equations that defined the phase diagram for mixtures with more than two components in a solvent. We calculated the theoretical liquid–liquid phase separation boundary for the two-phase separation (the binodal) and three-phase separation, the plait point, and the spinodal. We varied the distribution of the polydisperse component in skewness and polydispersity, and we varied the nonadditivity between the subcomponents as well as between the main components. We compared the phase behavior of the polydisperse mixtures with binary monodisperse mixtures for the same average size and binary monodisperse mixtures for the same effective interaction. We found that when the compatibility between the polydisperse subcomponents decreased, the three-phase separation became possible. The shape and position of the phase boundary was dependent on the nonadditivity between the subcomponents as well as their size distribution. We conclude that it is the phase enriched in the polydisperse component that demixes into an additional phase when the incompatibility between the subcomponents increases.

We study the theoretical phase behavior of an asymmetric binary mixture of hard spheres, of which the smaller component is monodisperse and the larger component is polydisperse. The interactions are modeled in terms of the second virial coefficient and can be additive hard sphere (HS) or nonadditive hard sphere (NAHS) interactions. The polydisperse component is subdivided into two sub-components and has an average size ten or three times the size of the monodisperse component. We give the set of equations that defines the phase diagram for mixtures with more than two components in a solvent. We calculate the theoretical liquid-liquid phase separation boundary for two phase separation (the binodal) and three phase separation, the plait point, and the spinodal. We vary the distribution of the polydisperse component in skewness and polydispersity, next to that we vary the non-additivity between the sub-components as well as between the main components. We compare the phase behavior of the polydisperse mixtures with binary monodisperse mixtures for the same average size and binary monodisperse mixtures for the same effective interaction. We find that when the compatibility between the polydisperse sub-components decreases, three-phase separation becomes possible. The shape and position of the phase boundary is dependent on the non-additivity between the subcomponents as well as their size distribution. We conclude that it is the phase enriched in the polydisperse component that demixes into an additional phase when the incompatibility between the sub-components increases.

This chapter is based on: Luka Sturtewagen and Erik van der Linden. Effect of polydispersity on the phase behavior of additive hard spheres in solution, part I. (submitted)