1/d1/d Expansion for kk-Core Percolation

The physics of $k$-core percolation pertains to those systems whose constituents require a minimum number of $k$ connections to each other in order to participate in any clustering phenomenon. Examples of such a phenomenon range from orientational ordering in solid ortho-para ${\rm H}_2$ mixtures to the onset of rigidity in bar-joint networks to dynamical arrest in glass-forming liquids. Unlike ordinary ($k=1$) and biconnected ($k=2$) percolation, the mean field $k\ge3$-core percolation transition is both continuous and discontinuous, i.e. there is a jump in the order parameter accompanied with a diverging length scale. To determine whether or not this hybrid transition survives in finite dimensions, we present a $1/d$ expansion for $k$-core percolation on the $d$-dimensional hypercubic lattice. We show that to order $1/d^3$ the singularity in the order parameter and in the susceptibility occur at the same value of the occupation probability. This result suggests that the unusual hybrid nature of the mean field $k$-core transition survives in high dimensions.Comment: 47 pages, 26 figures, revtex

Ergodicity and Slowing Down in Glass-Forming Systems with Soft Potentials: No Finite-Temperature Singularities

The aim of this paper is to discuss some basic notions regarding generic glass forming systems composed of particles interacting via soft potentials. Excluding explicitly hard-core interaction we discuss the so called `glass transition' in which super-cooled amorphous state is formed, accompanied with a spectacular slowing down of relaxation to equilibrium, when the temperature is changed over a relatively small interval. Using the classical example of a 50-50 binary liquid of N particles with different interaction length-scales we show that (i) the system remains ergodic at all temperatures. (ii) the number of topologically distinct configurations can be computed, is temperature independent, and is exponential in N. (iii) Any two configurations in phase space can be connected using elementary moves whose number is polynomially bounded in N, showing that the graph of configurations has the `small world' property. (iv) The entropy of the system can be estimated at any temperature (or energy), and there is no Kauzmann crisis at any positive temperature. (v) The mechanism for the super-Arrhenius temperature dependence of the relaxation time is explained, connecting it to an entropic squeeze at the glass transition. (vi) There is no Vogel-Fulcher crisis at any finite temperature T>0Comment: 10 pages, 9 figures, submitted to PR

Confinement effects on glass forming liquids probed by DMA

Many molecular glass forming liquids show a shift of the glass transition T-g to lower temperatures when the liquid is confined into mesoporous host matrices. Two contrary explanations for this effect are given in literature: First, confinement induced acceleration of the dynamics of the molecules leads to an effective downshift of T-g increasing with decreasing pore size. Second, due to thermal mismatch between the liquid and the surrounding host matrix, negative pressure develops inside the pores with decreasing temperature, which also shifts T-g to lower temperatures. Here we present dynamic mechanical analysis measurements of the glass forming liquid salol in Vycor and Gelsil with pore sizes of d=2.6, 5.0 and 7.5 nm. The dynamic complex elastic susceptibility data can be consistently described with the assumption of two relaxation processes inside the pores: A surface induced slowed down relaxation due to interaction with rough pore interfaces and a second relaxation within the core of the pores. This core relaxation time is reduced with decreasing pore size d, leading to a downshift of T-g proportional to 1/d in perfect agreement with recent differential scanning calorimetry (DSC) measurements. Thermal expansion measurements of empty and salol filled mesoporous samples revealed that the contribution of negative pressure to the downshift of T-g is small (<30%) and the main effect is due to the suppression of dynamically correlated regions of size xi when the pore size xi approaches

Feasibility of single-order parameter description of equilibrium viscous liquid dynamics

Molecular dynamics results for the dynamic Prigogine-Defay ratio are presented for two glass-forming liquids, thus evaluating the experimentally relevant quantity for testing whether metastable-equilibrium liquid dynamics to a good approximation are described by a single parameter. For the Kob-Andersen binary Lennard-Jones mixture as well as for an asymmetric dumbbell model liquid a single-parameter description works quite well. This is confirmed by time-domain results where it is found that energy and pressure fluctuations are strongly correlated on the alpha-time scale in the NVT ensemble; in the NpT ensemble energy and volume fluctuations similarly correlate strongly.Comment: Phys. Rev. E, in pres

Nanometer Scale Dielectric Fluctuations at the Glass Transition

Using non-contact scanning probe microscopy (SPM) techniques, dielectric properties were studied on 50 nanometer length scales in poly-vinyl-acetate (PVAc) films in the vicinity of the glass transition. Low frequency (1/f) noise observed in the measurements, was shown to arise from thermal fluctuations of the electric polarization. Anomalous variations observed in the noise spectrum provide direct evidence for cooperative nano-regions with heterogeneous kinetics. The cooperative length scale was determined. Heterogeneity was long-lived only well below the glass transition for faster than average processes.Comment: 4 pages, 4 embedded PS figures, RevTeX - To appear in Phys. Rev. Let

Energy landscape - a key concept for the dynamics of glasses and liquids

There is a growing belief that the mode coupling theory is the proper microscopic theory for the dynamics of the undercooled liquid above a critical temperature T_c. In addition, there is some evidence that the system leaves the saddlepoints of the energy landscape to settle in the valleys at this critical temperature. Finally, there is a microscopic theory for the entropy at the calorimetric glass transition T_g by Mezard and Parisi, which allows to calculate the Kauzmann temperature from the atomic pair potentials. The dynamics of the frozen glass phase is at present limited to phenomenological models. In the spirit of the energy landscape concept, one considers an ensemble of independent asymmetric double-well potentials with a wide distribution of barrier heights and asymmetries (ADWP or Gilroy-Phillips model). The model gives an excellent description of the relaxation of glasses up to about T_g/4. Above this temperature, the interaction between different relaxation centers begins to play a role. One can show that the interaction reduces the number of relaxation centers needed to bring the shear modulus down to zero by a factor of three.Comment: Contribution to the III Workshop on Nonequilibrium Phenomena in Supercooled Fluids, Glasses and Amorphous Materials, 22-27 September 2002, Pisa; 14 pages, 3 figures; Version 3 takes criticque at Pisa into account; final version 4 will be published in J.Phys.: Condens.Matte

Classical, non-linear, internal dynamics of large, isolated, vibrationally excited molecules

This work reports numerical experiments intended to clarify the internal equilibration process in large molecules, following vibrational excitation. A model of amorphous and oxygenated hydrocarbon macromolecule (about 500 atoms)--simulating interstellar dust-- is built up by means of a chemical simulation code. Its structure is optimized, and its normal modes determined. About 4.5 eV of potential energy is then deposited locally by perturbing one of the C-H peripheral bonds, thus simulating the capture of a free H atom by a dangling C bond. The ensuing relaxation of the system is followed for up to 300 ps, using a molecular mechanics code. When steady state is reached, spectra and time correlation functions of kinetic energy and bond length fluctuations indicate that most normal modes have been activated, but the motion remains quasi-periodic or regular. By contrast, when the molecule is violently excited or embedded in a thermal bath (modelled by Langevin dynamics), the same markers clearly depict chaotic motions. Thus it appears that even such a large system of oscillators is unable to provide the equivalent of a thermal bath to any one of these, unless there are strong resonances between some of them. In general, therefore, an energy of a few eV's deposited in an isolated molecule will not be immediately thermalized. This conclusion is of consequence for the interpretation of astronomical UIB spectra. Key Words:IS dust--UIBs--Excitation, relaxation processes.Comment: 19 pages, 9 figures, J. of Phys. B 2002, vol 35(17

Time-temperature superposition in viscous liquids

Dielectric relaxation measurements on supercooled triphenyl phosphite show that at low temperatures time-temperature superposition (TTS) is accurately obeyed for the primary (alpha) relaxation process. Measurements on 6 other molecular liquids close to the calorimetric glass transition indicate that TTS is linked to an $\omega^{-1/2}$ high-frequency decay of the alpha loss, while the loss peak width is nonuniversal.Comment: 4 page

Superdipole Liquid Scenario for the Dielectric Primary Relaxation in Supercooled Polar liquids

We propose a dynamic structure of coupled dynamic molecular strings for supercooled small polar molecule liquids and accordingly we obtain the Hamiltonian of the rotational degrees of freedom of the system. From the Hamiltonian, the strongly correlated supercooled polar liquid state is renormalized to a normal superdipole (SD) liquid state. This scenario describes the following main features of the primary or a-relaxation dynamics in supercooled polar liquids: (1) the average relaxation time evolves from a high temperature Arrhenius to a low temperature non-Arrhenius or super-Arrhenius behavior; (2) the relaxation function crosses over from the high temperature exponential to low temperature non-exponential form; and (3) the temperature dependence of the relaxation strength shows non-Curie features. According to the present model, the crossover phenomena of the first two characteristics arise from the transition between the superdipole gas and the superdipole liquid. The model predictions are quantitatively compared with the experimental results of glycerol, a typical glass-former.Comment: 40 pages, 3 figure