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44365-AC7
Demixing of Colloid-Polymer Mixtures: Influence of Electrostatic Interactions and Polymer Conformations
Suspensions of colloidal particles -- nanometers to microns in size, often charged, dispersed in a fluid -- are encountered throughout all stages of petroleum recovery and processing. Water-based drilling muds, for example, pumped down the drill pipe to lubricate the cutting bit and transport cuttings to the surface, are mixtures of clay (e.g., bentonite), polymer, and electrolyte. Waters injected into wells to recover crude oil from porous sedimentary rock are suspensions of formation particles (e.g., kaolinite) and other particulate matter. Deposition of suspended or aggregated particles can block rock pores, reducing the permeability of a formation.
Clays in drilling fluids and injection waters consist of charged colloidal platelets. Water-soluble, nonadsorbing polymers, such as polysaccharides, are commonly added to petroleum suspensions as dispersants and thickeners to control viscosity and to modify thermal and rheological properties. Petroleum suspensions are thus typically complex mixtures of charged colloids and polymers. While electrostatic repulsion between colloids tends to stabilize aqueous suspensions against coagulation, depletion of polymer from the space between neighboring colloids induces effective attraction that can drive bulk demixing into colloid-rich and -poor phases. The polymer depletion mechanism depends sensitively on the conformations (size and shape) of the polymer coils, which in turn depend on colloidal confinement.
This project aims to resolve several basic questions relevant to the stability of petroleum suspensions: How is the miscibility of colloid-polymer mixtures influenced by competition between repulsive electrostatic interactions and attractive depletion-induced interactions? How are polymer conformations in a suspension modified by colloidal confinement? How do polymer shape fluctuations affect depletion and thereby demixing of colloid-polymer mixtures? Our working hypothesis is that electrostatic interactions and polymer shape anisotropy can enhance stability of colloid-polymer mixtures. Testing this hypothesis will further the long-term goal of linking interparticle interactions to bulk materials properties, which may impact the rational design and control of petroleum suspensions.
To address these broad questions, we are developing and implementing a variety of theoretical and computational methods, including linear-response theory, classical density-functional theory, thermodynamic perturbation theory, and Monte Carlo simulation. These methods are being applied to mesoscale models of colloid-polymer mixtures, which coarse-grain (preaverage) molecular details of microion distributions and polymer conformations. In our approach, the colloids are modeled as hard, impenetrable spheres and the polymers as effective, penetrable spheres or ellipsoids, which can fluctuate in size and shape in response to colloidal confinement.
To model mixtures of charged colloids and neutral polymers, we have combined several well-established methods to develop a variational approximation for the free energy. Effective electrostatic interactions between colloidal macroions are described by linear-response theory and first-order perturbation theory (with hard-sphere reference system) and excluded-volume interactions between colloids and polymers by free-volume theory. Mapping the system onto an effective Asakura-Oosawa model with rescaled polymer/colloid size ratio, and minimizing the variational free energy with respect to size ratio, yields an upper bound on the thermodynamic free energy.
With our collaborator, Prof. Matthias Schmidt (University of Bristol), we have applied this theoretical approach to calculate demixing phase diagrams over a range of parameters. The main qualitative prediction is that demixing is suppressed by strengthening electrostatic interactions, achieved in practice by either increasing the macroion charge or decreasing the salt concentration (see nugget). Moreover, an unusual (and still controversial) counterion-driven spinodal instability in deionized suspensions of highly charged macroions is predicted to be enhanced by polymer-depletion-driven effective colloidal attraction.
With a doctoral student, Mr. Ben Lu, we are now testing these predictions by Monte Carlo simulations, working within the constant-NPT Gibbs ensemble, i.e., two simulation boxes at constant total particle number, pressure, and temperature. To confirm the accuracy of our numerical algorithms, we first computed phase diagrams for neutral mixtures. After successfully reproducing previously published results for the Asakura-Oosawa model (with fixed effective polymer radius), we have proceeded to examine richer models in which the polymers can fluctuate in size and (in the protein limit of large polymer/colloid size ratio) are penetrable to the colloids. Our preliminary results indicate that polymer compressibility and penetrability both enhance the stability of the mixture.
With a postdoctoral fellow, Dr. Emmanuel Mbamala, we are investigating polymer shape anisotropy via a multiscale approach, combining molecular simulations of polymers with mesoscale theory and simulation of colloid-polymer mixtures. By modeling a polymer as a segmented, freely-jointed chain, moving by a slithering-snake algorithm on a lattice, we have already computed -- for both ideal and self-avoiding chains -- the radius of gyration tensor, whose eigenvalues represent the squares of the principal radii of an effective ellipsoid. For polymers squeezed between parallel, flat, hard walls, we find, with decreasing wall separation, first a reduction and then (at very close confinement) an increase in both the radius of gyration and the asphericity. The next steps are to input the eigenvalue distributions into both free-volume theory and Monte Carlo simulations of a model of hard-sphere colloids and shape-fluctuating ellipsoidal polymers.
