Multiphase Coexistences in Rod–Polymer Mixtures

Abstract

Using recently derived analytical equations of state for hard rod dispersions, we predict the phase behavior of athermal rod−polymer mixtures with free volume theory. The rods are modeled as hard spherocylinders, while the nonadsorbing polymer chains are described as penetrable hard spheres. It is demonstrated that all of the different types of phase states that are stable for pure colloidal rod dispersions can coexist with any combination of these phases if polymers are added, depending on the concentrations, rod aspect ratio, and polymer−rod size ratio. This includes novel two-, three-, and four-phase coexistences and isostructural coexistences between dilute and concentrated phases of the same kind, even for the more ordered (liquid) crystal phases. This work provides insight into the conditions at which particular multiphase coexistences are expected for well-defined model colloidal rod−polymer mixtures. We provide a quantitative map detailing the various types of isostructural coexistences, which confirms an early qualitative hypothesis by Bolhuis et al. (J. Chem. Phys. 107, 1997 1551.

Effects of polymer nonideality on depletion-induced phase behaviour of colloidal disks and rods

“…For rod-PHS mixtures a similar phase behaviour overview was predicted by calculating the different critical endpoints and four-phase coexistences [24]. In this case additional fourphase coexistences and a five phase coexistence are obtained which do not include isostructural coexistence.…”

“…Whenever two colloidal particles get closer and these depletion zones overlap, there is an effective (depletion) attraction mediated by the osmotic pressure of the polymers. The effect of this depletion attraction has also been modelled by theory and simulations for mixtures of hard disks or rods and polymers [14][15][16][17][18][19][20][21][22][23][24].…”

“…To quantify relevant physical properties of these systems the polymers are often described as (penetrable) hard spheres [8,[14][15][16][17][18][19][20][21][22][23][24]. Within a penetrable hard spheres (PHS) description the polymers are considered spherical particles that cannot overlap with the colloidal particles but can freely overlap with eachother.…”

“…While it might still be expected that, based upon the results for spherical colloids, deviations occur for large polymer sizes, it is difficult beforehand to predict the magnitude of the deviations due to the different colloid shape. Additionally, it is unknown whether the topology of the phase diagrams changes or the same multi-phase coexistences occur upon accounting for (self-)interacting polymers instead of using the penetrable hard sphere description of depletants [21][22][23][24]. In order to examine this we will apply free volume theory similarly as in previous work for mixtures of PHS and hard disks [22] or spherocylinders [23], but incorporate excluded volume interactions between the polymer segments.…”

Sedimentation of colloidal plate-sphere mixtures and inference of particle characteristics from stacking sequences

“…with n b the number of bulk binodals and n i the total number of inflection points in all the binodals. The occurrence of several layers in sedimentation-diffusion-equilibrium is unrelated to bulk coexistence in which the Gibbs phase rule dictates the maximum number of phases that can coexist simultaneously (with the notable exceptions found recently in colloid-polymer mixtures [41][42][43] in which by fine-tuning the interparticle interactions it is possible to find bulk multiphase coexistence involving more than three different phases). Under gravity, the maximum number of layers in a sequence, Eq.…”