Polymer–particle mixtures: Depletion and packing effects (original) (raw)
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Polymer depletion interaction between a colloid particle and a wall: A Monte Carlo study
The Journal of Chemical Physics, 2002
An off-lattice bead-spring model of a polymer solution in a container with impenetrable walls is used to study the depletion interaction of a colloid particle with the planar wall by means of a Monte Carlo simulation. As expected, this interaction is found to depend essentially on the ratio ϭR/R g of the particle radius R to the mean radius of gyration R g of the polymer chains in the case of dilute and semidilute solutions. For large particle to polymer size ratio Ͼ1 this effective force is attractive and decreases steadily with growing distance D of the colloid from the wall. It is found to scale linearly with in agreement with recent theoretical predictions. In the opposite case of Ͻ1 the depletion force is found to change nonmonotonically with D and go through a maximum at a particular distance D max рR g . In both cases, however, local variations of the polymer density profile, which we detect at higher polymer concentrations, are found to influence the depletion force and even to change it locally from attraction to repulsion. The monomer density distribution far away from/or around the colloid in the vicinity of the wall is also investigated and related to the observed behavior of the depletion force.
The Journal of Chemical Physics, 2013
In this work, we study the influence of polymer chain length (m), based on Lennard-Jones potential, and nanoparticle (NP)-polymer interaction strength (ɛnp) on aggregation and dispersion of soft repulsive spherically structured NPs in polymer melt using coarse-grain molecular dynamics simulations. A phase diagram is proposed where transitions between different structures in the NP-polymer system are shown to depend on m and ɛnp. At a very weak interaction strength ɛnp = 0.1, a transition from dispersed state to collapsed state of NPs is found with increasing m, due to the polymer's excluded volume effect. NPs are well dispersed at intermediate interaction strengths (0.5 ⩽ ɛnp ⩽ 2.0), independent of m. A transition from dispersion to agglomeration of NPs, at a moderately high NP-polymer interaction strength ɛnp = 5.0, for m = 1–30, is identified by a significant decrease in the second virial coefficient, excess entropy, and potential energy, and a sharp increase in the Kirkwood-B...
Computer simulations of phase transitions of bulk and confined colloid–polymer systems
Physica A: Statistical Mechanics and its Applications, 2006
Grand canonical Monte Carlo, histogram reweighting and finite-size scaling methods are used to determine the phase transitions of bulk (three-dimensional) and confined (quasi-two-dimensional) neutral colloid-polymer systems. The colloids are modeled as hard spheres and the polymer molecules as hard chains, and the only attractive forces are effective ones induced by depletion effects. In contrast to the predictions of mean field and other approximate theories, the nature of the coexistence phases is found to not depend solely on the polymer-to-colloid size ratio, q, but on the colloid diameter, the polymer radius of gyration, and the polymer monomer size. The threshold values of q for the onset of liquid-liquid phase separation differ significantly from earlier predictions, and depend strongly on the dimensionality of space. Extrapolation to the ''protein limit'' of very small colloid and very long polymer indicates that immiscibility persists at this limit in three dimensions, while it does not always do so for confined systems. r
Effects of polymer polydispersity on the phase behaviour of colloid–polymer mixtures
Journal of Physics: Condensed Matter, 2005
We study the equilibrium behaviour of a mixture of monodisperse hard sphere colloids and polydisperse non-adsorbing polymers at their θ-point, using the Asakura-Oosawa model treated within the free-volume approximation. Our focus is the experimentally relevant scenario where the distribution of polymer chain lengths across the system is fixed. Phase diagrams are calculated using the moment free energy method, and we show that the mean polymer size ξc at which gas-liquid phase separation first occurs decreases with increasing polymer polydispersity δ. Correspondingly, at fixed mean polymer size, polydispersity favours gas-liquid coexistence but delays the onset of fluid-solid separation. On the other hand, we find that systems with different δ but the same mass-averaged polymer chain length have nearly polydispersity-independent phase diagrams. We conclude with a comparison to previous calculations for a semi-grandcanonical scenario, where the polymer chemical potentials are imposed; there it was found that fluid-solid coexistence was favoured over gas-liquid in some areas of the phase diagram. Our results show that this somewhat counter-intuitive result arose because the actual polymer size distribution in the system is shifted to smaller sizes relative to the polymer reservoir distribution.
Effect of excluded volume interactions on the interfacial properties of colloid-polymer mixtures
The Journal of Chemical Physics, 2008
We report a numerical study of equilibrium phase diagrams and interfacial properties of bulk and confined colloid-polymer mixtures using grand canonical Monte Carlo simulations. Colloidal particles are treated as hard spheres, while the polymer chains are described as soft repulsive spheres. The polymer-polymer, colloid-polymer, and wall-polymer interactions are described by density-dependent potentials derived by Bolhuis and Louis ͓Macromolecules 35, 1860 ͑2002͔͒. We compared our results with those of the Asakura-Oosawa-Vrij model ͓J. Chem. Phys. 22, 1255 ͑1954͒; J. Polym Sci 33, 183 ͑1958͒; Pure Appl. Chem. 48, 471 ͑1976͔͒ that treats the polymers as ideal particles. We find that the number of polymers needed to drive the demixing transition is larger for the interacting polymers, and that the gas-liquid interfacial tension is smaller. When the system is confined between two parallel hard plates, we find capillary condensation. Compared with the Asakura-Oosawa-Vrij model, we find that the excluded volume interactions between the polymers suppress the capillary condensation. In order to induce capillary condensation, smaller undersaturations and smaller plate separations are needed in comparison with ideal polymers.
Depletion interactions in colloid-polymer mixtures
Physical Review E, 1996
We present a neutron-scattering study of depletion interactions in a mixture of a hard-sphere-like colloid and a nonadsorbing polymer. By matching the scattering length density of the solvent with that of the polymer, we measured the partial structure factor S c (Q) for the colloidal particles. It is found that the measured S c (Q) for different colloid and polymer concentrations can be well described by an effective interaction potential U(r) for the polymer-induced depletion attraction between the colloidal particles. The magnitude of the attraction is found to increase linearly with the polymer concentration, but it levels off at higher polymer concentrations. This reduction in the depletion attraction presumably arises from the polymer-polymer interactions. The experiment demonstrates the effectiveness of using a nonadsorbing polymer to control the magnitude as well as the range of the interaction between the colloidal particles. ͓S1063-651X͑96͒10911-9͔
Phase behaviour of mixtures of colloidal spheres and excluded-volume polymer chains
Journal of Physics: Condensed Matter, 2002
We study the phase behaviour of mixtures of colloidal spheres and polymers that have an excluded-volume interaction dispersed in a (background) solvent using the concept of free volume theory. The depletion layer thickness is calculated from the negative adsorption of polymer segments around a sphere. The correlation length and thermodynamic properties of the excluded-volume interacting polymer chains in solution are taken into account by using results from the renormalization group theory. For small polymer-colloid size ratios the difference from an ideal description of the polymers is small, while for larger size ratios the gas-liquid coexistence region shifts in the direction of higher polymer concentrations and at the same time the liquid-crystal coexistence region becomes more extended. Both the gas-liquid region and the gasliquid-crystal region become less extended. These features are compared to experiment.
The Journal of Chemical Physics, 2021
Polymer-mediated colloidal interactions control the stability and phase properties of colloid-polymer mixtures that are critical for a wide range of important applications. In this work, we develop a versatile self-consistent field theory (SCFT) approach to study this type of interaction, based on a continuum confined polymer solution model with explicit solvent and confining walls. The model is formulated in the grand canonical ensemble, and the potential of mean force for the polymer-mediated interaction is computed from grand potentials. We focus on the case of non-adsorbing linear polymers and present a systematic investigation on depletion effects using SCFT. The properties of confined polymer solutions are probed, and mean-field profiles of induced interactions are shown across different physical regimes. We expose a detailed parametric dependence of the interaction, concerning both attractive and repulsive parts, on polymer concentration, chain length, and solvent quality, and explore the effect of wall surface roughness, demonstrating the versatility of the proposed approach. Our findings show good agreement with previous numerical studies and experiments, yet extend prior work to new regimes. Moreover, the mechanisms of depletion attraction and repulsion, along with the influence of individual control factors, are further discussed. We anticipate that this study will provide useful insight into depletion forces and can be readily extended to examine more complex colloid-polymer mixtures. I. INTRODUCTION Colloids, consisting of colloidal particles (of a linear dimension approximately between 1 nm and 1 µm) in dispersed phases, are ubiquitous in nature and daily life. Among colloidal systems, colloid-polymer mixtures are commonly presented in biological systems and find broad applications in chemicals, pharmaceuticals, food, and personal-care products. 1,2 Being a widely used model system for both experimental and theoretical studies, the colloid-polymer mixture exhibits a rich phase behavior, which is mainly dictated by the polymer-mediated colloidal interaction in addition to other interactions, including van der Waals, electrostatic, 2
Molecular Physics, 2004
We use thermodynamic perturbation theory to calculate the free energies and resulting phase diagrams of binary systems of spherical colloidal particles and interacting polymer coils in good solvent within an effective one-component representation of such mixtures, whereby the colloidal particles interact via a polymer-induced depletion potential. MC simulations are used to test the convergence of the high temperature expansion of the free energy. The phase diagrams calculated for several polymer to colloid size ratios differ considerably from the results of similar calculations for mixtures of colloids and ideal (non-interacting) polymers, and are in good overall agreement with the results of an explicit two-component representation of the same system, which includes more than two-body depletion forces.