Raman spectral studies of solutions of alkali metal perchlorates in dimethyl sulfoxide and water

Raman spectra of solutions of alkali metal perchlorates in dimethyl sulfoxide (DMSO) in the Cl-O, C-S, and S=O stretching regions, as well as of perchlorates in aqueous solutions in the Cl-O stretching region are reported. The results are discussed in terms of half-bandwidths, relative intensities, and depolarization ratios. For H2O the half-bandwidth of the Cl-O stretching band at ~935 cm-1 is almost double the value in DMSO solutions. Solutions of perchlorates in DMSO show two symmetric bands in the Cl-O stretching region, whereas in aqueous solutions only one band is observed. The half-bandwidths in perchlorate solutions in DMSO for the C-S stretching band increase with increase in concentration of perchlorate compared to that of liquid DMSO. The band contours in the S=O stretching region in DMSO solutions also show significant changes. These observations are explained on the basis of formation of ion pairs of metal perchlorates in solutions of DMSO and ion hydrates in the case of aqueous solutions

Raman spectral studies on the structure of acetonitrile and its solutions with electrolytes and nonelectrolytes

Raman spectra of acetonitrile is reported in its solutions with carbon tetrachloride, water, methanol, dimethyl sulphoxide (DMSO) and some electrolytes in C≡N stretching as well as in CH3 stretching regions. Vibrational correlation functions are computed for the CH3 stretching mode for varying concentrations of solutions. The vibrational relaxation times evaluated are also reported for these systems. It is found that association of acetonitrile through dipolar interactions is accompanied by an increase in intensity and a decrease in the frequency of C≡N band, whereas interactions through hydrogen bonding are accompanied by a decrease in intensity and increse in frequency. In the case of hydrogen bonding through methanol and also interactions through cations, new bands on the high frequency side appear, which are assigned to the complexed C≡N stretching bands. The CH3 vibrational relaxation times are found to decrease on dilution for aqueous solutions of acetonitrile, whereas an increase in the vibrational relaxation times is found in the solutions of acetonitrile in CCl4. In the case of solutions of electrolytes in acetonitrile, the vibrational relaxation times decrease with increasing concentration of electrolyte. The results are explained on the basis of the effect of complexation of C≡N on the CH3 group

Unstable Attractors: Existence and Robustness in Networks of Oscillators With Delayed Pulse Coupling

We consider unstable attractors; Milnor attractors $A$ such that, for some neighbourhood $U$ of $A$, almost all initial conditions leave $U$. Previous research strongly suggests that unstable attractors exist and even occur robustly (i.e. for open sets of parameter values) in a system modelling biological phenomena, namely in globally coupled oscillators with delayed pulse interactions. In the first part of this paper we give a rigorous definition of unstable attractors for general dynamical systems. We classify unstable attractors into two types, depending on whether or not there is a neighbourhood of the attractor that intersects the basin in a set of positive measure. We give examples of both types of unstable attractor; these examples have non-invertible dynamics that collapse certain open sets onto stable manifolds of saddle orbits. In the second part we give the first rigorous demonstration of existence and robust occurrence of unstable attractors in a network of oscillators with delayed pulse coupling. Although such systems are technically hybrid systems of delay differential equations with discontinuous `firing' events, we show that their dynamics reduces to a finite dimensional hybrid system system after a finite time and hence we can discuss Milnor attractors for this reduced finite dimensional system. We prove that for an open set of phase resetting functions there are saddle periodic orbits that are unstable attractors.Comment: 29 pages, 8 figures,submitted to Nonlinearit

The Glass Transition and Liquid-Gas Spinodal Boundaries of Metastable Liquids

A liquid can exist under conditions of thermodynamic stability or metastability within boundaries defined by the liquid-gas spinodal and the glass transition line. The relationship between these boundaries has been investigated previously using computer simulations, the energy landscape formalism, and simplified model calculations. We calculate these stability boundaries semi-analytically for a model glass forming liquid, employing accurate liquid state theory and a first-principles approach to the glass transition. These boundaries intersect at a finite temperature, consistent with previous simulation-based studies.Comment: Minor text revisions. Fig.s 4, 5 update

Potential Energy Landscape Equation of State

Depth, number, and shape of the basins of the potential energy landscape are the key ingredients of the inherent structure thermodynamic formalism introduced by Stillinger and Weber [F. H. Stillinger and T. A. Weber, Phys. Rev. A 25, 978 (1982)]. Within this formalism, an equation of state based only on the volume dependence of these landscape properties is derived. Vibrational and configurational contributions to pressure are sorted out in a transparent way. Predictions are successfully compared with data from extensive molecular dynamics simulations of a simple model for the fragile liquid orthoterphenyl.Comment: RevTeX4, 4 pages, 5 figure

Metastable configurations of spin models on random graphs

One-flip stable configurations of an Ising-model on a random graph with fluctuating connectivity are examined. In order to perform the quenched average of the number of stable configurations we introduce a global order-parameter function with two arguments. The analytical results are compared with numerical simulations.Comment: 11 pages Revtex, minor changes, to appear in Phys. Rev.

Thermodynamic and structural aspects of the potential energy surface of simulated water

Relations between the thermodynamics and dynamics of supercooled liquids approaching a glass transition have been proposed over many years. The potential energy surface of model liquids has been increasingly studied since it provides a connection between the configurational component of the partition function on one hand, and the system dynamics on the other. This connection is most obvious at low temperatures, where the motion of the system can be partitioned into vibrations within a basin of attraction and infrequent inter-basin transitions. In this work, we present a description of the potential energy surface properties of supercooled liquid water. The dynamics of this model has been studied in great details in the last years. Specifically, we locate the minima sampled by the liquid by ``quenches'' from equilibrium configurations generated via molecular dynamics simulations. We calculate the temperature and density dependence of the basin energy, degeneracy, and shape. The temperature dependence of the energy of the minima is qualitatively similar to simple liquids, but has anomalous density dependence. The unusual density dependence is also reflected in the configurational entropy, the thermodynamic measure of degeneracy. Finally, we study the structure of simulated water at the minima, which provides insight on the progressive tetrahedral ordering of the liquid on cooling

Inherent-Structure Dynamics and Diffusion in Liquids

The self-diffusion constant D is expressed in terms of transitions among the local minima of the potential (inherent structure, IS) and their correlations. The formulae are evaluated and tested against simulation in the supercooled, unit-density Lennard-Jones liquid. The approximation of uncorrelated IS-transition (IST) vectors, D_{0}, greatly exceeds D in the upper temperature range, but merges with simulation at reduced T ~ 0.50. Since uncorrelated IST are associated with a hopping mechanism, the condition D ~ D_{0} provides a new way to identify the crossover to hopping. The results suggest that theories of diffusion in deeply supercooled liquids may be based on weakly correlated IST.Comment: submitted to PR

Interplay Between Time-Temperature-Transformation and the Liquid-Liquid Phase Transition in Water

We study the TIP5P water model proposed by Mahoney and Jorgensen, which is closer to real water than previously-proposed classical pairwise additive potentials. We simulate the model in a wide range of deeply supercooled states and find (i) the existence of a non-monotonic ``nose-shaped'' temperature of maximum density line and a non-reentrant spinodal, (ii) the presence of a low temperature phase transition, (iii) the free evolution of bulk water to ice, and (iv) the time-temperature-transformation curves at different densities.Comment: RevTeX4, 4 pages, 4 eps figure

Potential Energy Landscape and Long Time Dynamics in a Simple Model Glass

We analyze the properties of a Lennard-Jones system at the level of the potential energy landscape. After an exhaustive investigation of the topological features of the landscape of the systems, obtained studying small size sample, we describe the dynamics of the systems in the multi-dimensional configurational space by a simple model. This consider the configurational space as a connected network of minima where the dynamics proceeds by jumps described by an appropriate master equation. Using this model we are able to reproduce the long time dynamics and the low temperature regime. We investigate both the equilibrium regime and the off-equilibrium one, finding those typical glassy behavior usually observed in the experiments such as: {\it i)} stretched exponential relaxation, {\it ii)} temperature-dependent stretching parameter, {\it iii)} breakdown of the Stokes-Einstein relation, and {\it iv)} appearance of a critical temperature below which one observes deviation from the fluctuation-dissipation relation as consequence of the lack of equilibrium in the system.Comment: 11 pages (Latex), 9 ps figure