63 research outputs found
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 mean-field spin glass [Phys. Rev. B 73, 014412 (2006)], that
the phase behavior of these systems is not yet fully understood when and
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
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