We perform systematic simulation experiments on model systems with soft-sphere repulsive interactions to test the predicted dynamic equivalence between soft-sphere liquids with similar static structure. For this we compare the simulated dynamics (mean squared displacement, intermediate scattering function, α-relaxation time, etc.) of different soft-sphere systems, between them and with the hard-sphere liquid. We then show that the referred dynamic equivalence does not depend on the (Newtonian or Brownian) nature of the microscopic laws of motion of the constituent particles, and hence, applies independently to colloidal and to atomic simple liquids. Finally, we verify another more recently proposed dynamic equivalence, this time between the long-time dynamics of an atomic liquid and its corresponding Brownian fluid (i.e., the Brownian system with the same interaction potential).
A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, F_{lm,lm}(k,t) and F_{lm,lm}^{S}(k,t), are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density n_{lm}(k,t) and the translational (α=T) and rotational (α=R) current densities j_{lm}^{α}(k,t). Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by S_{lm,lm}(k). Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, γ_{T} and γ_{R}, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters η (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.
In this work, the resealed mean spherical approximation (RMSA) for colloidal mixtures interacting via a DLVO-type potential is developed, and its application to suspensions of highly charged macroions is illustrated. For this purpose we introduce a simple scheme to solve the mean spherical approximation (MSA) for Yukawa mixtures with factorized coupling parameters. This scheme consists of the mapping of the Yukawa system onto a corresponding primitive model system. Such a correspondence is used as a device for the calculation of the static structure functions of the original Yukawa mixture. Within this scheme, a straightforward implementation of the resealing procedure is performed, which allows for the calculation of partial structure factors in strongly interacting mixtures. The resealing procedure we use is an extension of that introduced by Hansen and Hayter for monodisperse suspensions. The structure factors obtained with the resealed mean spherical approximation compare well with computer simulation results. The advantages and limitations of the RMSA are also discussed in some detail.
Long-time self-diffusion coefficients of ferrofluid suspensions are derived from an effective Langevin equation approach. The dependences of these transport properties on the volume fraction of particles and the strength of interparticle interaction are investigated. Strong reduction of the rotational and the translational Brownian motion of the particles is manifested upon increase of particle-particle interaction or ferrofluid concentration.
The structure factors S k for simple liquid metals are calculated using a model¯uid composed of hard spheres of Y ukawa-type in the mean spherical approximation. The solution of the Ornstein± Zernike equation f or the direct correlation f unction is exact and the analytic expressions are obtained f or the structure f actor. These expressions are then used to predict structure factors for a number of simple liquid metals, leading to good agreement with experimental data.
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