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

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

Adsorption of a fluid in an aerogel: integral equation approach

We present a theoretical study of the phase diagram and the structure of a fluid adsorbed in high-porosity aerogels by means of an integral-equation approach combined with the replica formalism. To simulate a realistic gel environment, we use an aerogel structure factor obtained from an off-lattice diffusion-limited cluster-cluster aggregation process. The predictions of the theory are in qualitative agreement with the experimental results, showing a substantial narrowing of the gas-liquid coexistence curve (compared to that of the bulk fluid), associated with weak changes in the critical density and temperature. The influence of the aerogel structure (nontrivial short-range correlations due to connectedness, long-range fractal behavior of the silica strands) is shown to be important at low fluid densities.Comment: 24 pages, 9 figure

Coarse-graining polymers as soft colloids

We show how to coarse grain polymers in a good solvent as single particles, interacting with density-independent or density-dependent interactions. These interactions can be between the centres of mass, the mid-points or end-points of the polymers. We also show how to extend these methods to polymers in poor solvents and mixtures of polymers. Treating polymers as soft colloids can greatly speed up the simulation of complex many-polymer systems, including polymer-colloid mixtures.Comment: to appear in Physica A, special STATPHYS 2001 edition. Content of invited talk by AA

Coarse-graining diblock copolymer solutions: a macromolecular version of the Widom-Rowlinson model

We propose a systematic coarse-grained representation of block copolymers, whereby each block is reduced to a single ``soft blob'' and effective intra- as well as intermolecular interactions act between centres of mass of the blocks. The coarse-graining approach is applied to simple athermal lattice models of symmetric AB diblock copolymers, in particular to a Widom-Rowlinson-like model where blocks of the same species behave as ideal polymers (i.e. freely interpenetrate), while blocks of opposite species are mutually avoiding walks. This incompatibility drives microphase separation for copolymer solutions in the semi-dilute regime. An appropriate, consistent inversion procedure is used to extract effective inter- and intramolecular potentials from Monte Carlo results for the pair distribution functions of the block centres of mass in the infinite dilution limit.Comment: To be published in mol.phys(2005

The Localization Transition of the Two-Dimensional Lorentz Model

We investigate the dynamics of a single tracer particle performing Brownian motion in a two-dimensional course of randomly distributed hard obstacles. At a certain critical obstacle density, the motion of the tracer becomes anomalous over many decades in time, which is rationalized in terms of an underlying percolation transition of the void space. In the vicinity of this critical density the dynamics follows the anomalous one up to a crossover time scale where the motion becomes either diffusive or localized. We analyze the scaling behavior of the time-dependent diffusion coefficient D(t) including corrections to scaling. Away from the critical density, D(t) exhibits universal hydrodynamic long-time tails both in the diffusive as well as in the localized phase.Comment: 13 pages, 7 figures