Mode-coupling Theory Results Research Articles

Short- and long-time diffusion and dynamic scaling in suspensions of charged colloidal particles.

We report on a comprehensive theory-simulation-experimental study of collective and self-diffusion in concentrated suspensions of charge-stabilized colloidal spheres. In theory and simulation, the spheres are assumed to interact directly by a hard-core plus screened Coulomb effective pair potential. The intermediate scattering function, fc(q, t), is calculated by elaborate accelerated Stokesian dynamics (ASD) simulations for Brownian systems where many-particle hydrodynamic interactions (HIs) are fully accounted for, using a novel extrapolation scheme to a macroscopically large system size valid for all correlation times. The study spans the correlation time range from the colloidal short-time to the long-time regime. Additionally, Brownian Dynamics (BD) simulation and mode-coupling theory (MCT) results of fc(q, t) are generated where HIs are neglected. Using these results, the influence of HIs on collective and self-diffusion and the accuracy of the MCT method are quantified. It is shown that HIs enhance collective and self-diffusion at intermediate and long times. At short times self-diffusion, and for wavenumbers outside the structure factor peak region also collective diffusion, are slowed down by HIs. MCT significantly overestimates the slowing influence of dynamic particle caging. The dynamic scattering functions obtained in the ASD simulations are in overall good agreement with our dynamic light scattering (DLS) results for a concentration series of charged silica spheres in an organic solvent mixture, in the experimental time window and wavenumber range. From the simulation data for the time derivative of the width function associated with fc(q, t), there is indication of long-time exponential decay of fc(q, t), for wavenumbers around the location of the static structure factor principal peak. The experimental scattering functions in the probed time range are consistent with a time-wavenumber factorization scaling behavior of fc(q, t) that was first reported by Segrè and Pusey [Phys. Rev. Lett. 77, 771 (1996)] for suspensions of hard spheres. Our BD simulation and MCT results predict a significant violation of exact factorization scaling which, however, is approximately restored according to the ASD results when HIs are accounted for, consistent with the experimental findings for fc(q, t). Our study of collective diffusion is amended by simulation and theoretical results for the self-intermediate scattering function, fs(q, t), and its non-Gaussian parameter α2(t) and for the particle mean squared displacement W(t) and its time derivative. Since self-diffusion properties are not assessed in standard DLS measurements, a method to deduce W(t) approximately from fc(q, t) is theoretically validated.

The dynamics of silica melts under high pressure: mode-coupling theory results

The high-pressure dynamics of a computer-modelled silica melt is studied in the frameworkof the mode-coupling theory of the glass transition using static structure input frommolecular dynamics computer simulation. The theory reproduces the experimentally knownviscosity minimum (diffusivity maximum) as a function of density or pressure and explainsit in terms of a corresponding minimum in its critical temperature. This minimum arisesfrom a gradual change in the equilibrium static structure which shifts from beingdominated by tetrahedral ordering to showing the cageing known from high-densityliquids. The theory is in qualitative agreement with computer simulation results.

Dynamic glass transition in two dimensions

The question of the existence of a structural glass transition in two dimensions is studied using mode coupling theory (MCT). We determine the explicit d dependence of the memory functional of mode coupling for one-component systems. Applied to two dimensions we solve the MCT equations numerically for monodisperse hard disks. A dynamic glass transition is found at a critical packing fraction phi(c)d=2 approximately equal 0.697 which is above phi(c)d=3 approximately equal 0.516 by about 35%. Phi(c)d scales approximately with phi(rcp)d, the value for random close packing, at least for d=2, 3. Quantities characterizing the local, cooperative "cage motion" do not differ much for d=2 and d=3, and we, e.g., find the Lindemann criterion for the localization length at the glass transition. The final relaxation obeys the superposition principle, collapsing remarkably well onto a Kohlrausch law. The d=2 MCT results are in qualitative agreement with existing results from Monte Carlo and molecular dynamics simulations. The mean-squared displacements measured experimentally for a quasi-two-dimensional binary system of dipolar hard spheres can be described satisfactorily by MCT for monodisperse hard disks over four decades in time provided the experimental control parameter Gamma (which measures the strength of dipolar interactions) and the packing fraction phi are properly related to each other.

Multiple-point and multiple-time correlation functions in a hard-sphere fluid

A recent mode-coupling theory of higher-order correlation functions is tested on a simple hard-sphere fluid system at intermediate densities. Multiple-point and multiple-time correlation functions of the densities of conserved variables are calculated in the hydrodynamic limit and compared to results obtained from event-based molecular dynamics simulations. It is demonstrated that the mode-coupling theory results are in excellent agreement with the simulation results provided that dissipative couplings are included in the vertices appearing in the theory. In contrast, simplified mode-coupling theories in which the densities obey Gaussian statistics neglect important contributions to both the multiple point and multiple-time correlation functions on all time scales.

Reorientational relaxation of a linear probe molecule in a simple glassy liquid.

Within the mode-coupling theory (MCT) for the evolution of structural relaxation in glass-forming liquids, correlation functions and susceptibility spectra are calculated characterizing the rotational dynamics of a top-down symmetric dumbbell molecule, consisting of two fused hard spheres immersed in a hard-sphere system. It is found that for sufficiently large dumbbell elongations, the dynamics of the probe molecule follows the same universal glass-transition scenario as known from the MCT results of simple liquids. The alpha-relaxation process of the angular-index j=1 response is stronger, slower, and less stretched than the one for j=2, in qualitative agreement with results found by dielectric-loss and depolarized-light-scattering spectroscopy for some supercooled liquids. For sufficiently small elongations, the reorientational relaxation occurs via large-angle flips, and the standard scenario for the glass-transition dynamics is modified for odd-j responses due to precursor phenomena of a nearby type-A MCT transition. In this case, a major part of the relaxation outside the transient regime is described qualitatively by the beta-relaxation scaling laws, while the alpha-relaxation scaling law is strongly disturbed.

Viscoelasticity and generalized Stokes–Einstein relations of colloidal dispersions

The linear viscoelastic and diffusional properties of colloidal model dispersions are investigated and possible relations between the (dynamic) shear viscosity and various diffusion coefficients are analyzed. Results are presented for hard sphere and charge-stabilized dispersions with long-range screened Coulomb interactions. Calculations of the dynamic long-time properties are based on a (rescaled) mode coupling theory (MCT). For hard sphere suspensions a simple hydrodynamic rescaling of the MCT results is proposed which leads to good agreement between the theory and experimental data and Brownian dynamics simulation results. The rescaled MCT predicts that the zero-shear limiting viscosity of hard sphere dispersions obeys nearly quantitative generalized Stokes–Einstein (GSE) relations both with regard to the long-time self-diffusion coefficient and the long-time collective diffusion coefficient measured at the principal peak of the static structure factor. In contrast, the MCT predicts that the same GSEs are violated in the case of dispersions of highly charged particles. The corresponding short-time GSEs are found to be partially violated both for charged and uncharged colloidal spheres. A frequency dependent GSE, relating the elastic storage and viscous loss moduli to the particle mean squared displacement, is also investigated, According to MCT, this GSE holds fairly well for concentrated hard spheres, but not for charge-stabilized systems. Remarkably good agreement is obtained, however, with regard to the frequency dependence of the Laplace-transformed reduced shear stress relaxation function and the Laplace-transformed reduced time-dependent self-diffusion coefficient for both charged and uncharged particle dispersions.

MCT Results for a simple liquid at the glass transition

Abstract The results of the mode coupling theory (MCT) for the slow relaxation processes in a liquid of hard spheres close to the liquid to glass transition are discussed. It is also shown that the MCT makes quantitative statements about the glassy structure, the relaxation processes in an intermediate time window and the final relaxation in the liquid phase. These results demonstrate the physical mechanism described by the idealized MCT and can be used to test the approximations of the theory experimentally.

Molecular-dynamics study of the glass transition in Ni80P20

Abstract A detailed molecular-dynamics investigation of the liquid-glass transition is carried out for a realistic model of the metal-metalloid glass-former Ni 80 P 20 , with a view to assessing some of the predictions of the recent mode-coupling theory. This theory suggests that relaxation in glasses proceeds in two steps: fast relaxation at short times, corresponding to local atomic rearrangements and described by a power law, and slow relaxation at long times, corresponding to atomic transport ( i.e. diffusion) and described by a stretched exponential (Kohlrausch law). The latter essentially disappears at the transition when the liquid becomes “structurally arrested”, i.e. glassy. The transition is therefore characterized by the passage from a state of ergodicity (the liquid) to a state of non-ergodicity (the glass). Our simulations agree with the results of mode-coupling theory for the existence of two scaling regimes, but do not lead to critical exponents consistent with the predicted behaviour.

Spectrum of electric field-gradient fluctuations in liquid rubidium

Abstract Mode-coupling theory results of the spectrum of electric field-gradient (Efg) fluctuations in liquid rubidium are presented. The small-frequency limit of the spectrum determines quadrupolar contributions to NMR-line-widths. We used the Price, Singwi, Tosi pair-potential and an Efg-potential which takes account of r-dependent Sternheimer antishielding effects. The theoretical results show very good agreement with computer simulations which use the same potential functions.