Structure of colloid-polymer suspensions

Abstract

We discuss structural correlations in mixtures of free polymer and colloidal particles on the basis of a microscopic, two-component liquid-state integral equation theory. Whereas in the case of polymers much smaller than the spherical particles the relevant polymer degree of freedom is the centre of mass, for polymers larger than the (nano-) particles, conformational rearrangements need to be considered. They have the important consequence that the polymer depletion layer exhibits two widely different length scales, one of the order of the particle radius, the other of the order of the polymer radius or the polymerdensity screening length in dilute or semidilute concentrations, respectively. Because we find a spinodal instability (mostly) below the overlap concentration, the latter length is (mostly) set by the radius of gyration. As a consequence of the structure of the depletion layer, the particle-particle correlations depend on both length scales for large polymers. Because of the high local compressibility of large polymers, the local depletion layer is a strong function of particle density, but a weak function of polymer concentration. The amplitude of the long-ranged tail of the depletion layer also depends asymptotically only on the colloid concentration, while the range increases upon approaching the (meanfield) spinodal. The colloid correlations may be understood as characteristic for particles with a short-ranged potential when small polymers are added, and as characteristic for particles with a long-ranged, van der Waals-like attraction when the added free polymer coils are much larger. Small polymers fill the voids between the particles rather homogeneously, exhibiting correlations inside the mesh (which gets squeezed by the colloids) and Porod-like correlations for larger distances. The structure factor of large polymers, however, exhibits no ramified mesh and becomes a Lorentzian characterized by the mixture correlation length, which diverges at the spinodal.

Analytical phase diagrams for colloids and non-adsorbing polymer

“…In recent years, there have been significant theoretical developments which take into account the polymeric excluded-volume interactions [30][31][32][33][34][35][36][37][38][39][40][41]. As examples of methods that enable the prediction of the phase behavior of colloid-polymer mixtures we mention polymer-colloid liquid state theory [31][32][33][34], thermodynamic perturbation theories [12,35], density functional theory [36,37], a Gaussian-core model [14,38,39], and computer simulations of HS plus self-avoiding polymer chains [40,41].…”

“…As examples of methods that enable the prediction of the phase behavior of colloid-polymer mixtures we mention polymer-colloid liquid state theory [31][32][33][34], thermodynamic perturbation theories [12,35], density functional theory [36,37], a Gaussian-core model [14,38,39], and computer simulations of HS plus self-avoiding polymer chains [40,41]. To obtain phase lines these methods require a significant amount of numerical work.…”

Flory-Huggins theory for athermal mixtures of hard spheres and larger flexible polymers

“…[15,24] are for ideal polymers. Reference [18] is a review of recent work on colloid-polymer mixtures, focusing mainly on the structure and on the results of integral equations, but also discussing other approaches and the phase behaviour. Earlier work by the author [23] assumed that the phase separation would occur when the polymer was semidilute.…”

Structure of phase-separated athermal colloid-polymer systems in the protein limit

“…We find a range of diverse structural features that emerge on different sides of these binodals as q r is increased, illustrating the non-trivial contribution polymer internal degrees of freedom have on the overall free energy of the system. While there have been theoretical attempts to treat such systems at coexistence with liquid-state integral equation theory [24][25][26], such theories can only predict the spinodal curve, rather than the binodal. Due to computational limitations, previous simulations have also not been able to capture structural details of large many-body systems, nor have they been explicitly linked to phase behavior as they are often at the limit of either one or two colloids [27,28], or have restricted colloid translational degrees of freedom such as in quenched matrices [29].…”