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, 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. Our approach builds on the classic Asakura-Oosawa (AO) model, which treats the colloids as hard, impenetrable spheres, but goes beyond the AO model by modeling 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.
We have applied this theoretical approach to calculate demixing phase diagrams for relatively weakly charged colloids. 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. Moreover, an unusual (and still debated) counterion-driven spinodal instability in deionized suspensions of highly charged macroions is predicted to be enhanced by effective colloidal attraction driven by polymer depletion. Recently, we have incorporated charge renormalization into the model to account for nonlinear counterion screening, which can reduce the effective macroion charge, and demonstrated close agreement with simulations of the primitive model of charged colloids.
With Ben Lu (doctoral student), we are developing and performing Monte Carlo simulations of the above models within the Gibbs ensemble. In these studies, we have focused initially on the nanoparticle limit of large polymer/colloid size ratio. Our results (in preparation for publication) indicate that polymer compressibility and penetrability both enhance the stability of colloid-polymer mixtures (see nugget).
With Dr. Emmanuel Mbamala (postdoctoral fellow), we are investigating polymer shape anisotropy by combining molecular simulations of polymers with statistical mechanical theories of colloid-polymer mixtures. Modeling the polymers as freely-jointed, segmented chains that slither on a lattice, we have computed the radius of gyration tensor, whose eigenvalues represent the squares of the principal radii of an effective ellipsoid. Our results for polymers squeezed between parallel, hard walls (in preparation for publication) show that with increasing confinement, the radius of gyration and the asphericity of a polymer coil first decrease and then increase. We are now inputing the eigenvalue distributions into a free-volume theory of model hard-sphere colloids and shape-fluctuating ellipsoidal polymers, exploiting a scaled-particle approximation for the free volume accessible to an ellipsoid in a fluid of volume-excluding hard spheres. Our approach will lead to improved predictions of demixing phase diagrams.
