Charge-stabilized Colloidal Suspensions Research Articles

Brownian-dynamics simulation studies of a charge-stabilized colloidal suspension under shear flow.

We have carried out Brownian-dynamics simulations of a charged colloidal suspension under oscillatory shear flow with both Couette and Poiseuille velocity profiles. We show that in the steady-shear limit, for both of the velocity profiles, the enhancement of the self-diffusion coefficient in directions transverse to the flow shows a crossover from a $\dot\gamma^2$ dependence to a $\dot\gamma^{1/2}$ dependence as the shear rate $\dot\gamma$ increases. The magnitude of the enhancement is a function of the interparticle interaction strength. There is a layering tendency in the direction of the velocity gradient for Couette flow, while such a tendency is not that prominent for Poiseuille flow.

Dynamics and sedimentation velocity in charge-stabilized colloidal suspensions

Charge-stabilized suspensions are characterized by the strong electrostatic interactions between the particles so that rather dilute systems may exhibit strong correlation resulting in a well-developed short-range order. This microstructure, quantitatively described by the pair distribution functiong(r), is rather different from that of (uncharged) hard spheres. It is shown how this difference affects the «hydrodynamic function»H(k), which appears in the expression for the first cumulant Γ(k)=k2Deff(k)=k2H(k)/S(k) of the dynamic autocorrelation function. Without hydrodynamic interaction,H(k)=D0, which is the free-diffusion coefficient. Using pairwise additive hydrodynamic interaction and the lowest-order many-body theory of hydrodynamic interaction, it is found thatH(k) can deviate considerably fromD0 even for systems of volume fractions ϕ as low as 10−3. These effects are more pronounced for collective diffusion than for self-diffusion. SinceH(k=0) is closely related to the sedimentation velocity, we have studied this quantity as a function of volume fraction. It is found that (H(0)/D0) −1 scales asφ1/3 at low ϕ in salt-free suspensions.

Sedimentation equilibrium in concentrated charge-stabilized colloidal suspensions

Preliminary results are reported for the density and charge density profiles of a charged colloidal suspension in sedimentation equilibrium. Calculations are based on a simple free energy functional, which includes excluded volume and Coulomb contributions. The suspension is shown to behave like a condenser.

Short-time dynamics of charge-stabilized colloidal suspensions

We have calculated the combined effects of the electrostatic and hydrodynamic interactions on the short-time dynamics of charge-stabilized colloidal suspensions, which can be investigated experimentally from the first cumulant of the dynamic scattering function. The first cumulant is obtained using two methods, a pairwise-additivity approximation for the many-body hydrodynamic interaction combined with a far-field expansion of the mobility tensors, and a renormalized density fluctuation expansion due to Beenakker and Mazur. An effective hard-sphere model is employed to provide a simple physical interpretation of the results derived from both methods. It is shown that even for moderately charged colloidal particles the hydrodynamic interaction cannot be neglected, and that its effects are more pronounced for collective diffusion than for self-diffusion. Moreover, our calculations predict a non-analytic volume fraction dependence of the sedimentation velocity, with an exponent whose numerical value is sensitive to the amount of added electrolyte.

Dynamical criterion for freezing of colloidal liquids.

A simple dynamical criterion for crystallization of a colloidal fluid which undergoes Brownian motion is proposed, similar in spirit to the classic Lindemann melting rule. It states that the ratio of the long-time and short-time self-diffusion coefficients is a universal number very close to 0.1 along the freezing line. This phenomenological crystallization rule is confirmed both by Brownian dynamics simulations of a Yukawa liquid and by forced Rayleigh scattering experiments on charge-stabilized colloidal suspensions.

Nonlinear counterion screening in colloidal suspensions

A new ‘‘ab initio’’ method is presented which is designed to simulate highly asymmetric systems of charged particles such as micellar solutions and charge-stabilized colloidal suspensions. The hybrid description considers the macroion degrees of freedom explicitly, while the microscopic counterions are treated within the framework of density functional theory. The counterion density profile is treated as a dynamical variable which is coupled to the macroion positions; the corresponding equation of motions are derived from a Lagrangian which contains a fictitious kinetic energy term associated with the inhomogeneous counterion density, with a fictitious mass chosen so that the counterions stay as close as possible to the surface of lowest free energy (adiabatic condition). The discontinuous behavior of the counterion density profile at the macroion surfaces is suppressed by the use of a classical pseudopotential scheme without spoiling the rapid variation of the counterion density profile outside the macroion cores. The ab initio method is implemented in Molecular and Brownian Dynamics simulations of concentrated colloidal suspensions, and the results are compared to the predictions of much simpler simulations based on the pairwise additive effective Derjaguin–Landau–Verwey–Overbeek (DLVO) potential between macroions. The density profiles calculated from the DLVO model differ considerably from the predictions of the ab initio simulations, but the macroion pair structures are in reasonable agreement. Recent ‘‘improvements’’ of the standard DLVO theory are found to overestimate or underestimate the pair structure considerably. The density functional formalism may be used to derive systematic many-body corrections to the effective DLVO pair potential. The extension of the ab initio method to treat colloidal suspensions in the presence of added salt is briefly sketched.

Thermodynamic properties of the fluid, fcc, and bcc phases of monodisperse charge-stabilized colloidal suspensions within the Yukawa model.

The thermodynamic properties of the Yukawa model for colloidal suspensions are determined theoretically from the Rogers-Young integral equation for the fluid phase and from a recently introduced van der Waals-like theory for the solid phases. Very good agreement with the Monte Carlo simulations of Meijer and Frenkel [J. Chem. Phys. 94, 2269 (1991)] is found for both the fluid and the (fcc-bcc) solid phases. The location of the two-phase coexistences, however, is shown to involve such small free-energy and density changes that no definite statements about the phase diagram are possible within the present accuracy.

Self-diffusion in sheared suspensions: Violation of the Einstein relation.

Starting from the Smoluchowski equation we derive exact microscopic expressions for the self-diffusion and the self-mobility coefficients of a sheared suspension of interacting colloidal particles in a semidiluted regime. We find that the usual Einstein relation between the self-mobility and the self-diffusion matrices is no longer valid for this nonequilibrium situation. The self-mobility and self-diffusion matrices are explicitly calculated in a low-shear-rate regime for a charge-stabilized colloidal suspension.

Shear melting of colloids: A nonequilibrium phase diagram.

Experiments show that charge-stabilized colloidal suspensions form crystals which can melt by applied shear stress. We present a molecular-dynamics simulation study of shear melting in colloids. The nonequilibrium phase diagram is calculated for a volume fraction which has an equilibrium fcc structure. The mechanism for flow in the sheared solid is found to be planes sliding over planes. We find that weak equilibrium solids (high added salt) shear melt, but strong equilibrium solids do not. Instead, shear produces a crossover to a new solid structure. This appears in the phase diagram as a reentrant solid phase. Results for shear stress and phase diagram are consistent with existing experiments.

Phase diagram of Yukawa systems: Model for charge-stabilized colloids.

The phase diagram of particles interacting through a repulsive screened Coulomb (Yukawa) potential has been calculated. Such interactions describe charge-stabilized colloidal suspensions and provide a potential of variable shape which can be used to test general ideas about phase transitions, including the phenomenological Hansen-Verlet and Lindemann rules. Competition between bcc and fcc solid phases was explored through calculations of the free-energy difference. For a range of screening lengths we found a transition from a low-temperature fcc phase to a high-temperature bcc phase.

Validity of the high temperature approximation and influence of polydispersity on the phase separation in charged colloidal dispersions

A recent perturbation calculation predicting a ‘liquid-gas’ phase separation of charge-stabilized colloidal suspensions is tested against the thermodynamically self-consistent generalized mean spherical approximation. A comparison between the two calculations shows that the perturbation calculation predicts a reasonably accurate critical temperature, but overestimates the critical density. These critical parameters are moreover shown to be rather insensitive to moderate degrees of polydispersity.