Alan R. Denton

Counterion penetration and effective electrostatic interactions in solutions of polyelectrolyte stars and microgels

Counterion distributions and effective electrostatic interactions between spherical macroions in polyelectrolyte solutions are calculated via second-order perturbation (linear response) theory. By modeling the macroions as continuous charge distributions that are permeable to counterions, analytical expressions are obtained for counterion profiles and effective pair interactions in solutions of star-branched and microgel macroions. The counterions are found to penetrate stars more easily than microgels, with important implications for screening of bare macroion interactions. The effective pair interactions are Yukawa in form for separated macroions, but are softly repulsive and bounded for overlapping macroions. A one-body volume energy, which depends on the average macroion concentration, emerges naturally in the theory and contributes to the total free energy.

Solid-phase structures of the dzugutov pair potential.

In recent computer simulations of a simple monatomic system interacting via the Dzugutov pair potential, freezing of the fluid into an equilibrium dodecagonal quasicrystal has been reported [M. Dzugutov, Phys. Rev. Lett. 70, 2924 (1993)]. Here, using a combination of molecular dynamics simulation and thermodynamic perturbation theory, we conduct a detailed analysis of the relative stabilities of solid-phase structures of the Dzugutov-potential system. At low pressures, the most stable structure is found to be a bcc crystal, which gives way at higher pressures to a fcc crystal. Although a dodecagonal quasicrystal and a sigma-phase crystal compete with the bcc crystal for stability, they always remain metastable.

Effective interactions and volume energies in charged colloids: linear response theory

Interparticle interactions in charge-stabilized colloidal suspensions, of arbitrary salt concentration, are described at the level of effective interactions in an equivalent one-component system. Integrating out the degrees of freedom of all microions from the partition function, and assuming a linear response to the macroion charges, general expressions are obtained for both an effective electrostatic pair interaction and an associated microion volume energy. For macroions with hard-sphere cores, the effective interaction is of the Derjaguin-Landau-Verwey-Overbeek screened-Coulomb form, but with a modified screening constant that incorporates excluded volume effects. The volume energy-a natural consequence of the one-component reduction-contributes to the total free energy, and can significantly influence thermodynamic properties in the limit of low-salt concentration. As illustrations, the osmotic pressure and bulk modulus are computed and compared with recent experimental measurements for deionized suspensions. For macroions of sufficient charge and concentration, it is shown that the counterions can act to soften or destabilize colloidal crystals.

Poisson–Boltzmann theory of charged colloids: limits of the cell model for salty suspensions

Thermodynamic properties of charge-stabilized colloidal suspensions and polyelectrolyte solutions are commonly modelled by implementing the mean-field Poisson-Boltzmann (PB) theory within a cell model. This approach models a bulk system by a single macroion, together with counterions and salt ions, confined to a symmetrically shaped, electroneutral cell. While easing numerical solution of the nonlinear PB equation, the cell model neglects microion-induced interactions and correlations between macroions, precluding modelling of macroion ordering phenomena. An alternative approach, which avoids the artificial constraints of cell geometry, exploits the mapping of a macroion-microion mixture onto a one-component model of pseudo-macroions governed by effective interparticle interactions. In practice, effective-interaction models are usually based on linear-screening approximations, which can accurately describe strong nonlinear screening only by incorporating an effective (renormalized) macroion charge. Combining charge renormalization and linearized PB theories, in both the cell model and an effective-interaction (cell-free) model, we compute osmotic pressures of highly charged colloids and monovalent microions, in Donnan equilibrium with a salt reservoir, over a range of concentrations. By comparing predictions with primitive model simulation data for salt-free suspensions, and with predictions from nonlinear PB theory for salty suspensions, we chart the limits of both the cell model and linear-screening approximations in modelling bulk thermodynamic properties. Up to moderately strong electrostatic couplings, the cell model proves accurate for predicting osmotic pressures of deionized (counterion-dominated) suspensions. With increasing salt concentration, however, the relative contribution of macroion interactions to the osmotic pressure grows, leading predictions from the cell and effective-interaction models to deviate. No evidence is found for a liquid-vapour phase instability driven by monovalent microions. These results may guide applications of PB theory to colloidal suspensions and other soft materials.

Fluid demixing in colloid–polymer mixtures: Influence of polymer interactions

We consider a binary mixture of hard colloidal spheres and nonadsorbing polymer coils. The polymers are regarded as effective spheres that interact with one another via a repulsive step-function pair potential and with colloids solely via excluded volume. The system is treated with a geometry-based density functional theory based on the exact zero-dimensional limit of the model. For bulk fluid phases, we calculate demixing binodals and find that with increasing strength of polymer–polymer interaction the coexisting colloidal liquid (vapor) phase becomes more concentrated (dilute) in polymer. In contrast to a simple mean-fieldlike perturbative density functional, our approach yields good agreement with an experimental demixing phase diagram.

STABILITY OF COLLOIDAL QUASICRYSTALS

Freezing of charge-stabilized colloidal suspensions and relative stabilities of crystals and quasicrystals are studied using thermodynamic perturbation theory. Macroion interactions are modelled by effective pair potentials combining electrostatic repulsion with polymer-depletion or van der Waals attraction. Comparing free energies -- counterion terms included -- for elementary crystals and rational approximants to icosahedral quasicrystals, parameters are identified for which one-component quasicrystals are stabilized by a compromise between packing entropy and cohesive energy.

Effective interactions and volume energies in charge-stabilized colloidal suspensions

Charge-stabilized colloidal suspensions can be conveniently described by formally reducing the macroion-microion mixture to an equivalent one-component system of pseudo-particles. Within this scheme, the utility of a linear response approximation for deriving effective interparticle interactions has been demonstrated (Grimson M J and Silbert M 1991 Mol. Phys. 74 397). Here the response approach is extended to suspensions of finite-sized macroions and used to derive explicit expressions for (1) an effective electrostatic pair interaction between pseudo-macroions and (2) an associated volume energy that contributes to the total free energy. The derivation recovers precisely the form of the DLVO (Derjaguin, Landau, Verwey, and Overbeek) screened Coulomb effective pair interaction for spherical macroions and makes manifest the important influence of the volume energy on thermodynamic properties of deionized suspensions. Excluded-volume corrections are implicitly incorporated through a natural modification of the inverse screening length. By including the nonlinear response of counterions to macroions, the theory may be generalized to systematically investigate effective many-body interactions.

Crowding of polymer coils and demixing in nanoparticle–polymer mixtures

The Asakura-Oosawa-Vrij (AOV) model of colloid-polymer mixtures idealises nonadsorbing polymers as effective spheres that are fixed in size and impenetrable to hard particles. Real polymer coils, however, are intrinsically polydisperse in size (radius of gyration) and may be penetrated by smaller particles. Crowding by nanoparticles can affect the size distribution of polymer coils, thereby modifying effective depletion interactions and thermodynamic stability. To analyse the influence of crowding on polymer conformations and demixing phase behaviour, we adapt the AOV model to mixtures of nanoparticles and ideal, penetrable polymer coils that can vary in size. We perform Gibbs ensemble Monte Carlo simulations, including trial nanoparticle-polymer overlaps and variations in the radius of gyration. Results are compared with predictions of free-volume theory. Simulation and theory consistently predict that ideal polymers are compressed by nanoparticles, and that compressibility and penetrability stabilise nanoparticle-polymer mixtures.

Mixtures of charged colloid and neutral polymer: Influence of electrostatic interactions on demixing and interfacial tension

The equilibrium phase behavior of a binary mixture of charged colloids and neutral, nonadsorbing polymers is studied within free-volume theory. A model mixture of charged hard-sphere macroions and ideal, coarse-grained, effective-sphere polymers is mapped first onto a binary hard-sphere mixture with nonadditive diameters and then onto an effective Asakura-Oosawa model [S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954)]. The effective model is defined by a single dimensionless parameter-the ratio of the polymer diameter to the effective colloid diameter. For high salt-to-counterion concentration ratios, a free-volume approximation for the free energy is used to compute the fluid phase diagram, which describes demixing into colloid-rich (liquid) and colloid-poor (vapor) phases. Increasing the range of electrostatic interactions shifts the demixing binodal toward higher polymer concentration, stabilizing the mixture. The enhanced stability is attributed to a weakening of polymer depletion-induced attraction between electrostatically repelling macroions. Comparison with predictions of density-functional theory reveals a corresponding increase in the liquid-vapor interfacial tension. The predicted trends in phase stability are consistent with observed behavior of protein-polysaccharide mixtures in food colloids.

Colloid-induced polymer compression

We consider a model mixture of hard colloidal spheres and nonadsorbing polymer chains in a theta solvent. The polymer component is modelled as a polydisperse mixture of effective spheres, mutually noninteracting but excluded from the colloids, with radii that are free to adjust to allow for colloid-induced compression. We investigate the bulk fluid demixing behaviour of this model system using a geometry-based density functional theory that includes the polymer size polydispersity and configurational free energy, obtained from the exact radius-of-gyration distribution for an ideal (random-walk) chain. Free energies are computed by minimizing the free energy functional with respect to the polymer size distribution. With increasing colloid concentration and polymer-to-colloid size ratio, colloidal confinement is found to increasingly compress the polymers. Correspondingly, the demixing fluid binodal shifts, compared to the incompressible-polymer binodal, to higher polymer densities on the colloid-rich branch, stabilizing the mixed phase.