Thermodiffusion of interacting colloids. II. A microscopic approach

A microscopic approach is presented to describe the contribution to the thermal diffusion coefficient of colloids due to intercolloidal particle interactions. An exact expression for the leading-order virial coefficient of the thermal diffusion coefficient of interacting colloidal spheres is derived in terms of the intercolloidal pair-interaction potential and hydrodynamic interaction functions. This general expression is explicitly evaluated for hard-core interactions and for spheres with a short-ranged attractive potential. The derivation is based on a Smoluchowski equation that is generalized to include temperature gradients. For short-ranged attractive potentials, a negative Soret coefficient is predicted under certain conditions, when the depth of the attraction increases with increasing temperature.     

Diffusion of spheres in isotropic and nematic networks of rods: electrostatic interactions and hydrodynamic screening

Translational diffusion of a small charged tracer sphere in isotropic and nematic suspensions of long and thin charged rods is investigated as a function of ionic strength and rod concentration. A theory for the diffusive properties of a small sphere is developed, where both (screened) hydrodynamic interactions and charge interactions between the tracer sphere and the rod network are analyzed. Hydrodynamic interactions are formulated in terms of the hydrodynamic screening length. As yet, there are no independent theoretical predictions for the hydrodynamic screening length for rod networks. Experimental tracer-diffusion data are presented for various ionic strengths as a function of the rod concentration, both in the isotropic and nematic states. Orientational order parameters are measured for the same ionic strengths as a function of the rod concentration. The hydrodynamic screening length is determined from these experimental data and scaling relations obtained from the above mentioned theory. For the isotropic networks, a master curve is found for the hydrodynamic screening length as a function of the rod concentration. For the nematic networks the screening length turns out to be a very sensitive function of the orientational order parameter.     

Dispersions and mixtures of particles with complex architectures in shear flow

We review the effect of shear flow on the phase behavior and structure of colloidal dispersions with increasing degree of complexity. We discuss dispersions of colloidal rods, stiff living polymers like wormlike micelles, and colloidal platelets. In addition, a review is presented on sheared binary dispersions. For all cases we discuss the interplay between thermodynamic instabilities and hydrodynamic instabilities.     

One-particle correlation function in evanescent wave dynamic light scattering

In order to interpret measured intensity autocorrelation functions obtained in evanescent wave scattering, their initial decay rates have been analyzed recently [P. Holmqvist, J. K. G. Dhont, and P. R. Lang, Phys. Rev. E 74, 021402 (2006); B. Cichocki, E. Wajnryb, J. Blawzdziewicz, J. K. G. Dhont, and P. R. Lang, J. Chem. Phys. 132, 074704 (2010); J. W. Swan and J. F. Brady, ibid. 135, 014701 (2011)]. A theoretical analysis of the longer time dependence of evanescent wave autocorrelation functions, beyond the initial decay, is still lacking. In this paper we present such an analysis for very dilute suspensions of spherical colloids. We present simulation results, a comparison to cumulant expansions, and experiments. An efficient simulation method is developed which takes advantage of the particular mathematical structure of the time-evolution equation of the probability density function of the position coordinate of the colloidal sphere. The computer simulation results are compared with analytic, first and second order cumulant expansions. The only available analytical result for the full time dependence of evanescent wave autocorrelation functions [K. H. Lan, N. Ostrowsky, and D. Sornette, Phys. Rev. Lett. 57, 17 (1986)], that neglects hydrodynamic interactions between the colloidal spheres and the wall, is shown to be quite inaccurate. Experimental results are presented and compared to the simulations and cumulant expansions.     

Dynamical manifestations of Hamiltonian monodromy

Monodromy is the simplest obstruction to the existence of global action–angle variables in integrable Hamiltonian dynamical systems. We consider one of the simplest possible systems with monodromy: a particle in a circular box containing a cylindrically symmetric potential-energy barrier. Systems with monodromy have nontrivial smooth connections between their regular Liouville tori. We consider a dynamical connection produced by an appropriate time-dependent perturbation of our system. This turns studying monodromy into studying a physical process. We explain what aspects of this process are to be looked upon in order to uncover the interesting and somewhat unexpected dynamical behavior resulting from the nontrivial properties of the connection. We compute and analyze this behavior.     

Thermodiffusion of interacting colloids. I. A statistical thermodynamics approach

The thermal diffusion coefficient of colloids consists of two additive contributions, one related to specific interactions between the surfaces of colloidal particles with solvent molecules, and a contribution due to interactions between the colloidal particles. In the present paper, the effect of intercolloidal particle interactions on their thermodiffusive behavior is discussed within a statistical thermodynamics framework. Transport coefficients are expressed in terms of the interaction potential between the colloidal spheres. A special feature of macromolecular systems is that this interaction potential is a potential of mean force, which is temperature dependent. It is shown that under certain conditions this implicit temperature dependence gives rise to negative Soret coefficients, that is, to diffusion of macromolecules to hot regions.     

Preparation and characterization of crosslinked PMMA latex particles stabilized by grafted copolymer

 The preparation of polymethyl methacrylate lattices stabilized by polyhydroxystearic acid and crosslinked with ethylene glycol dimethylmethacrylate (EGDM) has been studied. Crosslinking is a new development in the synthesis of PMMA latex. The particles are monodisperse when the concentration of EGDM ranges from 0.33 to 1.44%. The lattices are stable in aromatic and aliphatic solvents. Swelling occurs due to penetration of solvent molecules into the latex. The degree of swelling is calculated by viscosity and by dynamic light scattering measurements. Received: 30 January 1997 Accepted: 2 June 1997     

Brownian dynamics simulations of the self- and collective rotational diffusion coefficients of rigid long thin rods

Recently a microscopic theory for the dynamics of suspensions of long thin rigid rods was presented, confirming and expanding the well-known theory by Doi and Edwards [The Theory of Polymer Dynamics (Clarendon, Oxford, 1986)] and Kuzuu [J. Phys. Soc. Jpn. 52, 3486 (1983)]. Here this theory is put to the test by comparing it against computer simulations. A Brownian dynamics simulation program was developed to follow the dynamics of the rods, with a length over a diameter ratio of 60, on the Smoluchowski time scale. The model accounts for excluded volume interactions between rods, but neglects hydrodynamic interactions. The self-rotational diffusion coefficients D(r)(phi) of the rods were calculated by standard methods and by a new, more efficient method based on calculating average restoring torques. Collective decay of orientational order was calculated by means of equilibrium and nonequilibrium simulations. Our results show that, for the currently accessible volume fractions, the decay times in both cases are virtually identical. Moreover, the observed decay of diffusion coefficients with volume fraction is much quicker than predicted by the theory, which is attributed to an oversimplification of dynamic correlations in the theory.