The striking similarity of ac conduction in quite different disordered solids is discussed in terms of experimental results, modeling, and computer simulations. After giving an overview of experiment, a macroscopic and a microscopic model are reviewed. For both models the normalized ac conductivity as a function of a suitably scaled frequency becomes independent of details of the disorder in the extreme disorder limit, i.e., when the local randomly varying mobilities cover many orders of magnitude. The two universal ac conductivities are similar, but not identical; both are examples of unusual non-power-law universalities. It is argued that ac universality reflects an underlying percolation determining dc as well as ac conductivity in the extreme disorder limit. Three analytical approximations to the universal ac conductivities are presented and compared to computer simulations. Finally, model predictions are briefly compared to experiment. CONTENTS I. Introduction 873 II. Preliminaries 873 III. Ac Conduction in Disordered Solids: Facts 874 IV. Macroscopic Model 877 A. Definition 877 B. Ac universality in the extreme disorder limit 878 V. Symmetric Hopping Model 880 A. Definition 880 B. Ac universality in the extreme disorder limit 882 VI. Cause of Universality 883 A. Role of percolation 883 B. Percolation based approximations 885 VII. Discussion 887 A. Model predictions 887 B. Models versus experiment 888 C. Outlook 888 Acknowledgments 890 References 890

This paper is the fourth in a series devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids where virial and potential energy correlate better than 90% in their thermal equilibrium fluctuations in the NVT ensemble. For such liquids we here introduce the concept of "isomorphic" curves in the phase diagram. A number of thermodynamic, static, and dynamic isomorph invariants are identified. These include the excess entropy, the isochoric specific heat, reduced-unit static and dynamic correlation functions, as well as reduced-unit transport coefficients. The dynamic invariants apply for both Newtonian and Brownian dynamics. It is shown that after a jump between isomorphic state points the system is instantaneously in thermal equilibrium; consequences of this for generic aging experiments are discussed. Selected isomorph predictions are validated by computer simulations of the Kob-Andersen binary Lennard-Jones mixture, which is a strongly correlating liquid. The final section of the paper relates the isomorph concept to phenomenological melting rules, Rosenfeld's excess entropy scaling, Young and Andersen's approximate scaling principle, and the two-order parameter maps of Debenedetti and co-workers. This section also shows how the existence of isomorphs implies an "isomorph filter" for theories for the non-Arrhenius temperature dependence of viscous liquids' relaxation time, and it explains isochronal superposition for strongly correlating viscous liquids.

Relaxation in supercooled liquids above their glass transition and below the onset temperature of ''slow'' dynamics involves the correlated motion of neighboring particles. This correlated motion results in the appearance of spatially heterogeneous dynamics or ''dynamical heterogeneity.'' Traditional two-point time-dependent density correlation functions, while providing information about the transient ''caging'' of particles on cooling, are unable to provide sufficiently detailed information about correlated motion and dynamical heterogeneity. Here, we study a four-point, time-dependent density correlation function g 4 (r,t) and corresponding ''structure factor'' S 4 (q,t) which measure the spatial correlations between the local liquid density at two points in space, each at two different times, and so are sensitive to dynamical heterogeneity. We study g 4 (r,t) and S 4 (q,t) via molecular dynamics simulations of a binary Lennard-Jones mixture approaching the mode coupling temperature from above. We find that the correlations between particles measured by g 4 (r,t) and S 4 (q,t) become increasingly pronounced on cooling. The corresponding dynamical correlation length 4 (t) extracted from the small-q behavior of S 4 (q,t) provides an estimate of the range of correlated particle motion. We find that 4 (t) has a maximum as a function of time t, and that the value of the maximum of 4 (t) increases steadily from less than one particle diameter to a value exceeding nine particle diameters in the temperature range approaching the mode coupling temperature from above. At the maximum, 4 (t) and the ␣ relaxation time ␣ are related by a power law. We also examine the individual contributions to g 4 (r,t), S 4 (q,t), and 4 (t), as well as the corresponding order parameter Q(t) and generalized susceptibility 4 (t), arising from the self and distinct contributions to Q(t). These contributions elucidate key differences between domains of localized and delocalized particles.

We perform molecular dynamics simulations of a bead-spring polymer melt surrounding a nanoscopic particle. We explore the effect of the polymer/nanoparticle interactions, surface-to-volume ratio, and boundary conditions on both the structure and dynamics of the polymer melt. We find that the chains near the nanoparticle surface are elongated and flattened and that this effect is independent of the interaction for the range of interactions we study. We show that the glass transition temperature T g of the melt can be shifted to either higher or lower temperatures by tuning the interactions between polymer and nanoparticle. A gradual change of the polymer dynamics approaching the nanoparticle surface causes the change in the glass transition. The magnitude of the shift is exaggerated by increasing fraction of surface monomers in the system. These behaviors support a "many-layer"-based interpretation of the dynamics. Our findings appear applicable to systems in which surface interactions dominate, including both traditional and nanofilled polymer melts, as well as systems with markedly different geometries, such as ultrathin polymer films. In particular, we show how our results might be compared with those obtained from experimental studies of "bound" polymer.

An equilibrated model glass-forming liquid is studied by mapping successive configurations produced by molecular dynamics simulation onto a time series of inherent structures (local minima in the potential energy). Using this "inherent dynamics" approach we find direct numerical evidence for the long held view that below a crossover temperature, Tx, the liquid's dynamics can be separated into (i) vibrations around inherent structures and (ii) transitions between inherent structures (M. Goldstein, J. Chem. Phys. 51, 3728 (1969)), i.e., the dynamics become "dominated" by the potential energy landscape. In agreement with previous proposals, we find that Tx is within the vicinity of the mode-coupling critical temperature Tc. We further find that at the lowest temperature simulated (close to Tx), transitions between inherent structures involve cooperative, string like rearrangements of groups of particles moving distances substantially smaller than the average interparticle distance.