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Register a new userShort- and long-time diffusion, and dynamic scaling in suspensions of charged colloidal particles
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We report on a comprehensive theory-simulation-experimental study of collective and self-diffusion in suspensions of charge-stabilized colloidal spheres. In simulation and theory, the spheres interact by a hard-core plus screened Coulomb pair potential. Intermediate and self-intermediate scattering functions are calculated by accelerated Stokesian Dynamics simulations where hydrodynamic interactions (HIs) are fully accounted for. The study spans the range from the short-time to the colloidal long-time regime. Additionally, Brownian Dynamics simulation and mode-coupling theory (MCT) results are generated where HIs are neglected. It is shown that HIs enhance collective and self-diffusion at intermediate and long times, whereas at short times self-diffusion, and for certain wavenumbers also collective diffusion, are slowed down. MCT significantly overestimate the slowing influence of dynamic particle caging. The simulated scattering functions are in decent agreement with our dynamic light scattering (DLS) results for suspensions of charged silica spheres. Simulation and theoretical results are indicative of a long-time exponential decay of the intermediate scattering function. The approximate validity of a far-reaching time-wavenumber factorization of the scattering function is shown to be a consequence of HIs. Our study of collective diffusion is amended by simulation and theoretical results for the self-intermediate scattering function and the particle mean squared displacement (MSD). Since self-diffusion is not assessed in DLS measurements, a method to deduce the MSD approximately in DLS is theoretically validated.
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For suspensions of permeable particles, the short-time translational and rotational self-diffusion coefficients, and collective diffusion and sedimentation coefficients are evaluated theoretically. An individual particle is modeled as a uniformly permeable sphere of a given permeability, with the internal solvent flow described by the Debye-Bueche-Brinkman equation. The particles are assumed to interact non-hydrodynamically by their excluded volumes. The virial expansion of the transport properties in powers of the volume fraction is performed up to the two-particle level. The first-order virial coefficients corresponding to two-body hydrodynamic interactions are evaluated with very high accuracy by the series expansion in inverse powers of the inter-particle distance. Results are obtained and discussed for a wide range of the ratio, x, of the particle radius to the hydrodynamic screening length inside a permeable sphere. It is shown that for x >= 10, the virial coefficients of the transport properties are well-approximated by the hydrodynamic radius (annulus) model developed by us earlier for the effective viscosity of porous-particle suspensions.
We investigate the combined effects of electrostatic interactions and hydrodynamic interactions on the short-time rotational self-diffusion coefficient in charge-stabilized suspensions. We calculate this coefficient as a function of volume fraction for various effective particle charges and amounts of added electrolyte. The influence of the hydrodynamic interactions on the rotational diffusion coefficient is less pronounced for charged particles than for uncharged ones. Salt-free suspensions are weakly influenced by hydrodynamic interactions. For these strongly correlated systems we obtain a quadratic volume fraction-dependence of the diffusion coefficient, which is well explained in terms of an effective hard sphere model.
Diffusion in bidisperse Brownian hard-sphere suspensions is studied by Stokesian Dynamics (SD) computer simulations and a semi-analytical theoretical scheme for colloidal short-time dynamics, based on Beenakker and Mazurs method [Physica 120A, 388 (1983) & 126A, 349 (1984)]. Two species of hard spheres are suspended in an overdamped viscous solvent that mediates the salient hydrodynamic interactions among all particles. In a comprehensive parameter scan that covers various packing fractions and suspension compositions, we employ numerically accurate SD simulations to compute the initial diffusive relaxation of density modulations at the Brownian time scale, quantified by the partial hydrodynamic functions. A revised version of Beenakker and Mazurs $deltagamma$-scheme for monodisperse suspensions is found to exhibit surprisingly good accuracy, when simple rescaling laws are invoked in its application to mixtures. The so-modified $deltagamma$ scheme predicts hydrodynamic functions in very good agreement with our SD simulation results, for all densities from the very dilute limit up to packing fractions as high as $40%$.
Thermally induced particle flow in a charged colloidal suspension is studied in a fluid-mechanical approach. The force density acting on the charged boundary layer is derived in detail. From Stokes equation with no-slip boundary conditions at the particle surface, we obtain the particle drift velocity and the thermophoretic transport coefficients. The results are discussed in view of previous work and available experimental data.
We discuss the peculiarities of the Seebeck effect in stabilized electrolytes containing the colloidal particles. Its unusual feature is the two-stage character, with the linear increase of differential thermopower as the function of colloidal particles concentration $n_{odot}$ during the first stage and dramatic drop of it at small $n_{odot}$ during the second one (steady state). We show that the properties of the initial state are governed by the thermo-diffusion flows of the mobile ions of the stabilizing electrolyte medium itself and how the colloidal particles participate in formation of the electric field in the bulk of suspension. In its turn the specifics of the steady state in thermoelectric effect we attribute to considerable displacements of the massive colloidal particles in process of their slow thermal diffusion and break down of their electroneutrality in the vicinity of electrodes
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