Statistical mechanics of homogeneous partly pinned fluid systems

The homogeneous partly pinned fluid systems are simple models of a fluid confined in a disordered porous matrix obtained by arresting randomly chosen particles in a one-component bulk fluid or one of the two components of a binary mixture. In this paper, their configurational properties are investigated. It is shown that a peculiar complementarity exists between the mobile and immobile phases, which originates from the fact that the solid is prepared in presence of and in equilibrium with the adsorbed fluid. Simple identities follow, which connect different types of configurational averages, either relative to the fluid-matrix system or to the bulk fluid from which it is prepared. Crucial simplifications result for the computation of important structural quantities, both in computer simulations and in theoretical approaches. Finally, possible applications of the model in the field of dynamics in confinement or in strongly asymmetric mixtures are suggested.Comment: 12 pages, 2 figure

Comment on: "Static correlations functions and domain walls in glass-forming liquids: The case of a sandwich geometry" [J. Chem. Phys. 138, 12A509 (2013)]

In this Comment, we argue that the behavior of the overlap functions reported in the commented paper can be fully understood in terms of the physics of simple liquids in contact with disordered substrates, without appealing to any particular glassy phenomenology. This suggestion is further supported by an analytic study of the one-dimensional Ising model provided as Supplementary Material.Comment: 2+2 pages, 1+3 figure

What can be learned from the schematic mode-coupling approach to experimental data ?

We propose a detailed investigation of the schematic mode-coupling approach to experimental data, a method based on the use of simple mode-coupling equations to analyze the dynamics of supercooled liquids. Our aim here is to clarify different aspects of this approach that appeared so far uncontrolled or arbitrary, and to validate the results obtained from previous works. Analyzing the theoretical foundations of the approach, we first identify the parameters of the theory playing a key role and obtain simple requirements to be met by a schematic model for its use in this context. Then we compare the results obtained from the schematic analysis of a given set of experimental data with a variety of models and show that they are all perfectly consistent. A number of potential biases in the method are identified and ruled out by the choice of appropriate models. Finally, reference spectra computed from the mode-coupling theory for a model simple liquid are analyzed along the same lines as experimental data, allowing us to show that, despite the strong simplification in the description of the dynamics it involves, the method is free from spurious artifacts and provides accurate estimates of important parameters of the theory. The only exception is the exponent parameter, the evaluation of which is hindered, as for other methods, by corrections to the asymptotic laws of the theory present when the dynamics is known only in a limited time or frequency range.Comment: 13 pages, 5 figures, revtex4, to appear in J. Chem. Phy

Comment on ``Spherical 2 + p spin-glass model: An analytically solvable model with a glass-to-glass transition''

Guided by old results on simple mode-coupling models displaying glass-glass transitions, we demonstrate, through a crude analysis of the solution with one step of replica symmetry breaking (1RSB) derived by Crisanti and Leuzzi for the spherical $s+p$ mean-field spin glass [Phys. Rev. B 73, 014412 (2006)], that the phase behavior of these systems is not yet fully understood when $s$ and $p$ are well separated. First, there seems to be a possibility of glass-glass transition scenarios in these systems. Second, we find clear indications that the 1RSB solution cannot be correct in the full glassy phase. Therefore, while the proposed analysis is clearly naive and probably inexact, it definitely calls for a reassessment of the physics of these systems, with the promise of potentially interesting new developments in the theory of disordered and complex systems.Comment: 5 pages, third version (first version submitted to Phys. Rev. B on November 2006

Site-averaging in the integral equation theory of interaction site models of macromolecular fluids: An exact approach

A simple "trick" is proposed, which allows to perform exactly the site-averaging procedure required when developing integral equation theories of interaction site models of macromolecular fluids. It shows that no approximation is involved when the number of Ornstein-Zernike equations coupling the site-site correlation functions is reduced to one. Its potential practical interest for future theoretical developments is illustrated with a rederivation of the so-called molecular closures.Comment: 2 pages, revTeX

Influence of solvent quality on effective pair potentials between polymers in solution

Solutions of interacting linear polymers are mapped onto a system of ``soft'' spherical particles interacting via an effective pair potential. This coarse-graining reduces the individual monomer-level description to a problem involving only the centers of mass (CM) of the polymer coils. The effective pair potentials are derived by inverting the CM pair distribution function, generated in Monte Carlo simulations, using the hypernetted chain (HNC) closure. The method, previously devised for the self-avoiding walk model of polymers in good solvent, is extended to the case of polymers in solvents of variable quality by adding a finite nearest-neighbor monomer-monomer attraction to the previous model and varying the temperature. The resulting effective pair potential is found to depend strongly on temperature and polymer concentration. At low concentration the effective interaction becomes increasingly attractive as the temperature decreases, eventually violating thermodynamic stability criteria. However, as polymer concentration is increased at fixed temperature, the effective interaction reverts to mostly repulsive behavior. These issues help illustrate some fundamental difficulties encountered when coarse-graining complex systems via effective pair potentials.Comment: 15 pages, 12 figures (one added in revised version), revTeX

Relating monomer to centre-of-mass distribution functions in polymer solutions

A relationship between the measurable monomer-monomer structure factor, and the centre-of-mass (CM) structure factor of dilute or semi-dilute polymer solutions is derived from Ornstein-Zernike relations within the ``polymer reference interaction site model'' (PRISM) formalism, by considering the CM of each polymer as an auxiliary site and neglecting direct correlations between the latter and the CM and monomers of neighbouring polymers. The predictions agree well with Monte Carlo data for self-avoiding walk polymers, and are considerably more accurate than the predictions of simple factorization approximations.Comment: uses eps.cls, v2 is close to final published versio

Mode-coupling theory of the glass transition for confined fluids

We present a detailed derivation of a microscopic theory for the glass transition of a liquid enclosed between two parallel walls relying on a mode-coupling approximation. This geometry lacks translational invariance perpendicular to the walls, which implies that the density profile and the density-density correlation function depends explicitly on the distances to the walls. We discuss the residual symmetry properties in slab geometry and introduce a symmetry adapted complete set of two-point correlation functions. Since the currents naturally split into components parallel and perpendicular to the walls the mathematical structure of the theory differs from the established mode-coupling equations in bulk. We prove that the equations for the nonergodicity parameters still display a covariance property similar to bulk liquids.Comment: 16 pages; to be published in PR

Study of the Depolarized Light Scattering Spectra of Supercooled Liquids by a Simple Mode-Coupling Model

By using simple mode coupling equations, we investigate the depolarized light scattering spectra of two so-called "fragile" glassforming liquids, salol (phenylsalicylate) and CKN (Ca_{0.4}K_{0.6}(NO_3)_{1.4}), measured by Cummins and coworkers. Nonlinear integrodifferential equations for the time evolution of the density-fluctuations autocorrelation functions are the basic input of the mode coupling theory. Restricting ourselves to a small set of such equations, we fit the numerical solution to the experimental spectra. It leads to a good agreement between model and experiment, which allows us to determine how a real system explores the parameter space of the model, but it also leads to unrealistic effective vertices in a temperature range where the theory makes critical asymptotic predictions. We finally discuss the relevance and the range of validity of these universal asymptotic predictions when applied to experimental data on supercooled liquids.Comment: 31 LaTeX pages using overcite.sty, 10 postscript figures, accepted in J. Chem. Phy

Mode-coupling theory predictions for the dynamical transitions of the partly pinned fluid systems

The predictions of the mode-coupling theory (MCT) for the dynamical arrest scenarios in a partly pinned (PP) fluid system are reported. The corresponding dynamical phase diagram is found to be very similar to that of a related quenched-annealed (QA) system. The only significant qualitative difference lies in the shape of the diffusion-localization lines at high matrix densities, with a re-entry phenomenon for the PP system but not for the QA model, in full agreement with recent computer simulation results. This finding clearly lends support to the predictive power of the MCT for fluid-matrix systems. Finally, the predictions of the MCT are shown to be in stark contrast with those of the random first-order transition theory. The PP systems are thus confirmed as very promising models for tests of theories of the glass transition.Comment: 5 pages, 2 figure