Microstructure and depletion forces in polymer-colloid mixtures from an interfacial statistical associating fluid theory

Abstract

By using a classical density functional theory (interfacial statistical associating fluid theory), we investigate the structure and effective forces in nonadsorbing polymer-colloid mixtures. The theory is tested under a wide range of conditions and performs very well in comparison to simulation data. A comprehensive study is conducted characterizing the role of polymer concentration, particle/polymer-segment size ratio, and polymer chain length on the structure, polymer induced depletion forces, and the colloid-colloid osmotic second virial coefficient. The theory correctly captures a depletion layer on two different length scales, one on the order of the segment diameter (semidilute regime) and the other on the order of the polymer radius of gyration (dilute regime). The particle/polymer-segment size ratio is demonstrated to play a significant role on the polymer structure near the particle surface at low polymer concentrations, but this effect diminishes at higher polymer concentrations. Results for the polymer-mediated mean force between colloidal particles show that increasing the concentration of the polymer solution encourages particle-particle attraction, while decreasing the range of depletion attraction. At intermediate to high concentrations, depletion attraction can be coupled to a midrange repulsion, especially for colloids in solutions of short chains. Colloid-colloid second virial coefficient calculations indicate that the net repulsion between colloids at low polymer densities gives way to net attraction at higher densities, in agreement with available simulation data. Furthermore, the results indicate a higher tendency toward colloidal aggregation for larger colloids in solutions of longer chains.

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

“…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.…”

“…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.…”

“…Thorough explanations of the depletion interaction are provided in, for example, references [1,[31][32][33][34][35]; depletion forces have been the focus of a number of studies, including [36][37][38][39][40][41][42][43]. In particular, Binder et al [35] have provided a detailed appraisal of the Asakura-Oosawa (AO) model, and its scope.…”

Mesoscopic structure prediction of nanoparticle assembly and coassembly: Theoretical foundation

“…Instead, since long-range contributions are very important in the formation of ordered nanostructure, 36 we introduce our approach to apply the Ewald summation technique in the context of the direct correlation function. The chemical potential from the Ewald summation is separately calculated and the direct correlation function is modified as (25) and…”

“…A combined approach of atomistic and field theoretic modeling as well as a novel MC approach have been suggested for simulation of BCP/NP self-assembly, 24 but they have the same or similar limitations found in atomistic simulations. Meanwhile, DFT approaches were suggested for different molecular systems, [25][26][27] but their applications were limited to local structure prediction. Thompson et al introduced a new numerical scheme of combining SCFT with DFT.…”