Crowding of polymer coils and demixing in nanoparticle-polymer mixtures

Influence of solvent quality on depletion potentials in colloid-polymer mixtures

As first explained by the classic Asakura-Oosawa (AO) model, effective attractive forces between colloidal particles induced by depletion of nonadsorbing polymers can drive demixing of colloid-polymer mixtures into colloid-rich and colloid-poor phases, with practical relevance for purification of water, stability of foods and pharmaceuticals, and macromolecular crowding in biological cells. By idealizing polymer coils as effective penetrable spheres, the AO model qualitatively captures the influence of polymer depletion on thermodynamic phase behavior of colloidal suspensions. In previous work, we extended the AO model to incorporate aspherical polymer conformations and showed that fluctuating shapes of random-walk coils can significantly modify depletion potentials [W. K. Lim and A. R. Denton, Soft Matter 12, 2247 (2016); J. Chem. Phys. 144, 024904 (2016)]. We further demonstrated that the shapes of polymers in crowded environments sensitively depend on solvent quality [W. J. Davis and A. R. Denton, J. Chem. Phys. 149, 124901 (2018)]. Here, we apply Monte Carlo simulation to analyze the influence of solvent quality on depletion potentials in mixtures of hard-sphere colloids and nonadsorbing polymer coils, modeled as ellipsoids whose principal radii fluctuate according to random-walk statistics. We consider both self-avoiding and non-self-avoiding random walks, corresponding to polymers in good and theta solvents, respectively. Our simulation results demonstrate that depletion of polymers of equal molecular weight induces much stronger attraction between colloids in good solvents than in theta solvents and confirm that depletion interactions are significantly influenced by aspherical polymer conformations.

Influence of solvent quality on conformations of crowded polymers

The structure and function of polymers in confined environments, e.g., biopolymers in the cytoplasm of a cell, are strongly affected by macromolecular crowding. To explore the influence of solvent quality on conformations of crowded polymers, we model polymers as penetrable ellipsoids, whose shape fluctuations are governed by the statistics of self-avoiding walks, appropriate for a polymer in a good solvent. Within this coarse-grained model, we perform Monte Carlo simulations of mixtures of polymers and hard-nanosphere crowders, including trial changes in polymer size and shape. Penetration of polymers by crowders is incorporated via a free energy cost predicted by polymer field theory. To analyze the impact of crowding on polymer conformations in different solvents, we compute the average polymer shape distributions, radius of gyration, volume, and asphericity over ranges of the polymer-to-crowder size ratio and crowder volume fraction. The simulation results are accurately predicted by a free-volume theory of polymer crowding. Comparison of results for polymers in good and theta solvents indicates that excluded-volume interactions between polymer segments significantly affect crowding, especially in the limit of crowders much smaller than polymers. Our approach may help to motivate future experimental studies of polymers in crowded environments, with possible relevance for drug delivery and gene therapy.

Ionic size effects on the Poisson-Boltzmann theory

In this paper, we develop a simple theory to study the effects of ionic size on ionic distributions around a charged spherical particle. We include a correction to the regular Poisson-Boltzmann equation in order to take into account the size of ions in a mean-field regime. The results are compared with Monte Carlo simulations and a density functional theory based on the fundamental measure approach and a second-order bulk expansion which accounts for electrostatic correlations. The agreement is very good even for multivalent ions. Our results show that the theory can be applied with very good accuracy in the description of ions with highly effective ionic radii and low concentration, interacting with a colloid or a nanoparticle in an electrolyte solution.

Small-Angle Neutron Scattering Study of Interplay of Attractive and Repulsive Interactions in Nanoparticle-Polymer System

The phase behavior of nanoparticle (silica)-polymer (polyethylene glycol) system without and with an electrolyte (NaCl) has been studied. It is observed that nanoparticle-polymer system behaves very differently in the presence of electrolyte. In the absence of electrolyte, the nanoparticle-polymer system remains in one-phase even at very high polymer concentrations. On the other hand, a re-entrant phase behavior is found in the presence of electrolyte, where one-phase (individual) system undergoes two-phase (nanoparticle aggregation) and then back to one-phase with increasing polymer concentration. The regime of two-phase system has been tuned by varying the electrolyte concentration. The polymer concentration range over which the two-phase system exists is significantly enhanced with the increase in the electrolyte concentration. These systems have been characterized by small-angle neutron scattering (SANS) experiments of contrast-marching the polymer to the solvent. The data are modeled using a two-Yukawa potential accounting for both attractive and repulsive parts of the interaction between nanoparticles. The phase behavior of nanoparticle-polymer system is explained by interplay of attractive (polymer-induced attractive depletion between nanoparticles) and repulsive (nanoparticle-nanoparticle electrostatic repulsion and polymer-polymer repulsion) interactions present in the system. In the absence of electrolyte, the strong electrostatic repulsion between nanoparticles dominates over the polymer-induced depletion attraction and the nanoparticle system remains in one-phase. With addition of electrolyte, depletion attraction overcomes electrostatic repulsion at some polymer concentration, resulting into nanoparticle aggregation and two-phase system. Further addition of polymer increases the polymer-polymer repulsion which eventually reduces the strength of depletion and hence re-entrant phase behavior. The effects of varying electrolyte concentration on the phase behavior of nanoparticle-polymer system are understood in terms of modifications in nanoparticle-nanoparticle and polymer-polymer interactions. The nanoparticle aggregates in two-phase systems are found to have surface fractal morphology.

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

Structural features of phase-separated athermal colloid-polymer mixtures in the so-called "protein limit," where polymer chain dimensions exceed those of the colloid, are investigated using grand canonical Monte Carlo simulations on a fine lattice. Previous work [N. A. Mahynski et al., Phys. Rev. E 85, 051402 (2012)] has shown that this model accurately captures the phase behavior of experimental systems, and that colloids with sufficiently small diameters, σ(c), relative to that of the monomeric segments, σ(s), phase separate more readily than their large-diameter counterparts. In the present study, we directly connect colloid and polymer structure with their phase behavior by investigating these solutions along their binodal curves; we also explore the role of colloid surface curvature in destabilizing such solutions. Our findings suggest that simple consideration of an additional depletion radius, on the order of the σ(s), leads to a quantitatively accurate prediction of the division between stable and unstable ranges of d=σ(s)/σ(c). We compare these results to continuum models with different bonding potentials between monomer segments in order to elucidate the significance of the lattice model's bond fluctuations and inherently coarse colloid surface. In a number of cases, the continuum models deviate both qualitatively and quantitatively from the lattice results, but the binodals of the continuum models are presently not known, making a strong conclusion about these differences impossible.

Pressure and density scaling for colloid-polymer systems in the protein limit

Grand canonical Monte Carlo and histogram reweighting techniques are used to study the fluid-phase behavior of an athermal system of colloids and nonadsorbing polymers on a fine lattice in the "protein limit," where polymer dimensions exceed those of the colloids. The main parameters are the chains' radius of gyration, R_{g}, the diameter of the colloids, σ_{c}, and the monomer diameter, σ_{s}. The phase behavior is controlled by the macroscopic size ratio, q_{r}=2R_{g}/σ_{c}, and the microscopic size ratio, d=σ_{s}/σ_{c}. The latter ratio is found to play a significant role in determining the critical monomer concentration for q_{r}≲4 and the critical colloid density for all chain lengths. However, the critical (osmotic) pressure is independent of the microscopic size ratio at all macroscopic size ratios studied. Quantitative agreement is observed between our simulation results and experimental data. We scale our results based on the polymer correlation length, which has previously been suggested to universally collapse these binodals [Bolhuis et al., Phys. Rev. Lett. 90, 068304 (2003); Fleer and Tuinier, Phys. Rev. E 76, 041802 (2007)]. While the density binodals exhibit universal characteristics along the low-colloid-density branch, such features are not present in the corresponding high-density phase. However, pressure binodals do collapse nicely under such a scaling, even far from the critical point, which allows us to produce a binodal curve whose shape is independent of either size ratio.