Demixing in athermal mixtures of colloids and excluded-volume polymers from density functional theory

Abstract

We study the structure and interfacial properties of model athermal mixtures of colloids and excluded volume polymers. The colloid particles are modeled as hard spheres whereas the polymer coils are modeled as chains formed from tangentially bonded hard spheres. Within the framework of the nonlocal density functional theory we study the influence of the chain length on the surface tension and the interfacial width. We find that the interfacial tension of the colloid-interacting polymer mixtures increases with the chain length and is significantly smaller than that of the ideal polymers. For certain parameters we find oscillations on the colloid-rich parts of the density profiles of both colloids and polymers with the oscillation period of the order of the colloid diameter. The interfacial width is few colloid diameters wide and also increases with the chain length. We find the interfacial width for the end segments to be larger than that for the middle segments and this effect is more pronounced for longer chains.

Fluid–fluid coexistence in an athermal colloid–polymer mixture: thermodynamic perturbation theory and continuum molecular-dynamics simulation

“…For interfacial widths of ∼5σ c then even the relatively large system size chosen in our current work will be insufficient to stabilise two phase-separated regions with two corresponding interfaces because the longest side of the simulation cell, 10σ c , would be no greater than the width of two adjacent interfaces. Moreover, due to the low interfacial tension of colloid-polymer systems, the interfaces are characterised by large local fluctuations not only in width [79] but also in composition [55,79,116]. Accordingly, even when phase separation has occurred, a clear profile of bulk regions separated by an interface is unlikely to be seen for all but the largest systems.…”

“…Further, there is no explicit description of the end-to-end distance or the radius of gyration of the chain. The second virial coefficient obtained with the TPT1 treatment scales linearly with the chain length m p [111,112] instead of the expected m 3ν p , where ν is the Flory exponent; [55] moreover, the use of TPT1 leads to ν = 1/2 [55], the ideal-chain value, whereas for self-avoiding chains the Flory exponent takes the value ν ∼ 3/5 in the dilute regime. As a result the swollen or dilute regime is not described accurately with the TPT1 approach [110].…”

“…To date, the phase behaviour of colloid-polymer mixtures has been addressed in a number of theoretical studies, in addition to those already mentioned; see, for example, references [34,43,[47][48][49][50][51][52][53][54][55][56][57]. Among these, we highlight the studies [43,[53][54][55]58] based on Wertheim's first-order thermodynamic perturbation theory (TPT1) [59,60]; these deal with the polymer at the monomer segment level [61], in contrast to studies based on the AO model or the AO approximation.…”

“…Estimates have been made of the interfacial width of AO colloidpolymer mixtures. Using density-functional theory, Brader et al [116] estimated the width to be ∼σ c close to the triple point while Bryk [55] suggested the width to be a few colloidal diameters wide, and increasing with increasing chain length of the polymer. Vink et al [79] obtained interfacial widths ∼7-9σ c using grand canonical Monte Carlo simulation (see figure 3 of reference [79]).…”

“…Among these, we highlight the studies [43,[53][54][55]58] based on Wertheim's first-order thermodynamic perturbation theory (TPT1) [59,60]; these deal with the polymer at the monomer segment level [61], in contrast to studies based on the AO model or the AO approximation. While it is gratifying that theoretical studies can be used to explain the phase separation seen experimentally, to assess the quality of the underlying models one still requires accurate verification of theories by direct molecular simulation.…”