93 research outputs found
How to break the replica symmetry in structural glasses
The variational principle (VP) has been used to capture the metastable states
of a glass-forming molecular system without quenched disorder. It has been
shown that VP naturally leads to a self-consistent random field Ginzburg-Landau
model (RFGLM). In the framework of one-step replica symmetry breaking (1-RSB)
the general solution of RFGLM is discussed in the vicinity of the spinodal
temperature T_{A} in terms of ``hidden'' formfactors , g_{0}(k)
and . The self-generated disorder spontaneously arises. It is argued
that at T < T_{A} the activated dynamics is dominant.Comment: 11 pages, no figures, accepted by Europhys. Let
Langevin dynamics of the glass forming polymer melt: fluctuations around the random phase approximation
In this paper the Martin-Siggia-Rose (MSR) functional integral representation
is used for the study of the Langevin dynamics of a polymer melt in terms of
collective variables: mass density and response field density. The resulting
generating functional (GF) takes into account fluctuations around the random
phase approximation (RPA) up to an arbitrary order. The set of equations for
the correlation and response functions is derived. It is generally shown that
for cases whenever the fluctuation-dissipation theorem (FDT) holds we arrive at
equations similar to those derived by Mori-Zwanzig. The case when FDT in the
glassy phase is violated is also qualitatively considered and it is shown that
this results in a smearing out of the ideal glass transition. The memory kernel
is specified for the ideal glass transition as a sum of all water-melon
diagrams. For the Gaussian chain model the explicit expression for the memory
kernel was obtained and discussed in a qualitative link to the mode-coupling
equation.Comment: 30 pages, 5 figure
Dynamics of polymeric manifolds in melts: Hartree approximation
The Martin-Siggia-Rose functional technique and the self-consistent Hartree
approximation is applied to the dynamics of a D-dimensional manifold in a melt
of similar manifolds.The generalized Rouse equation is derived and its static
and dynamic properties are studied. The static upper critical dimension
discriminate between Gaussian and non-Gaussian regimes, whereas its dynamic
counterpart discriminates between Rouse- and renormalized-Rouse behavior. The
dynamic exponents are calculated explicitly. The special case of linear chains
shows agreement with MD- and MC-simulations.Comment: 4 pages,1 figures, accepted by EPJB as a Rapid Not
Dynamics of a polymer test chain in a glass forming matrix: The Hartree Approximation
In this paper the Martin-Siggia-Rose formalism is used to derive a
generalized Rouse equation for a test chain in a matrix which can undergo the
glass transition. It is shown that the surrounding matrix renormalizes the
static properties of the test chain. Furthermore the freezing of the different
Rouse modes is investigated. This yields freezing temperatures which depend
from the Rouse mode index.Comment: to be published in Journal de Physique I
Weak violation of universality for Polyelectrolyte Chains: Variational Theory and Simulations
A variational approach is considered to calculate the free energy and the
conformational properties of a polyelectrolyte chain in dimensions. We
consider in detail the case of pure Coulombic interactions between the
monomers, when screening is not present, in order to compute the end-to-end
distance and the asymptotic properties of the chain as a function of the
polymer chain length . We find where
and is the exponent which characterize
the long-range interaction . The exponent is
shown to be non-universal, depending on the strength of the Coulomb
interaction. We check our findings, by a direct numerical minimization of the
variational energy for chains of increasing size . The
electrostatic blob picture, expected for small enough values of the interaction
strength, is quantitatively described by the variational approach. We perform a
Monte Carlo simulation for chains of length . The non universal
behavior of the exponent previously derived within the variational
method, is also confirmed by the simulation results. Non-universal behavior is
found for a polyelectrolyte chain in dimension. Particular attention is
devoted to the homopolymer chain problem, when short range contact interactions
are present.Comment: to appear in European Phys. Journal E (soft matter
Detachment of semiflexible polymer chains from a substrate - a Molecular Dynamics investigation
Using Molecular Dynamics simulations, we study the force-induced detachment
of a coarse-grained model polymer chain from an adhesive substrate. One of the
chain ends is thereby pulled at constant speed off the attractive substrate and
the resulting saw-tooth profile of the measured mean force vs height
$D$ of the end-segment over the plane is analyzed for a broad variety of
parameters. It is shown that the observed characteristic oscillations in the $<
f >$-$D$ profile depend on the bending and not on the torsional stiffness of
the detached chains. Allowing for the presence of hydrodynamic interactions
(HI) in a setup with explicit solvent and DPD-thermostat, rather than the case
of Langevin thermostat, one finds that HI have little effect on the -
profile. Also the change of substrate affinity with respect to the solvent from
solvophilic to solvophobic is found to play negligible role in the desorption
process. In contrast, a changing ratio of the
binding energies of - and -segments in the detachment of an
-copolymer from adhesive surface strongly changes the - profile
whereby the -spikes vanish when .
Eventually, performing an atomistic simulation of a (bio)-polymer {\it
polyglycine}, we demonstrate that the simulation results, derived from our
coarse-grained model, comply favorably with those from the all-atom simulation.Comment: Latex, 12 pages, 8 figures, to appear in JC
The Hartree approximation in dynamics of polymeric manifolds in the melt
The Martin-Siggia-Rose (MSR) functional integral technique is applied to the
dynamics of a D - dimensional manifold in a melt of similar manifolds. The
integration over the collective variables of the melt can be simply implemented
in the framework of the dynamical random phase approximation (RPA). The
resulting effective action functional of the test manifold is treated by making
use of the selfconsistent Hartree approximation. As an outcome the generalized
Rouse equation (GRE) of the test manifold is derived and its static and dynamic
properties are studied. It was found that the static upper critical dimension,
, discriminates between Gaussian (or screened) and
non-Gaussian regimes, whereas its dynamical counterpart, , distinguishes between the simple Rouse and the
renormalized Rouse behavior. We have argued that the Rouse mode correlation
function has a stretched exponential form. The subdiffusional exponents for
this regime are calculated explicitly. The special case of linear chains, D=1,
shows good agreement with MD- and MC-simulations.Comment: 35 pages,3 figures, accepted by J.Chem.Phy
Driven translocation of a polymer: role of pore friction and crowding
Force-driven translocation of a macromolecule through a nanopore is
investigated by taking into account the monomer-pore friction as well as the
"crowding" of monomers on the {\it trans} - side of the membrane which
counterbalance the driving force acting in the pore. The set of governing
differential-algebraic equations for the translocation dynamics is derived and
solved numerically. The analysis of this solution shows that the crowding of
monomers on the trans side hardly affects the dynamics, but the monomer-pore
friction can substantially slow down the translocation process. Moreover, the
translocation exponent in the translocation time - vs. - chain length
scaling law, , becomes smaller when monomer-pore
friction coefficient increases. This is most noticeable for relatively strong
forces. Our findings may explain the variety of values which were
found in experiments and computer simulations.Comment: 12 page
Kinetics of copolymer localization at a selective liquid-liquid interface
The localization kinetics of a regular block-copolymer of total length
and block size at a selective liquid-liquid interface is studied in the
limit of strong segregation between hydrophobic and polar segments in the
chain. We propose a simple analytic theory based on scaling arguments which
describes the relaxation of the initial coil into a flat-shaped layer for the
cases of both Rouse and Zimm dynamics. For Rouse dynamics the characteristic
times for attaining equilibrium values of the gyration radius components
perpendicular and parallel to the interface are predicted to scale with block
length and chain length as (here
is the Flory exponent) and as ,
although initially the characteristic coil flattening time is predicted to
scale with block size as . Since typically for multiblock
copolymers, our results suggest that the flattening dynamics proceeds faster
perpendicular rather than parallel to the interface, in contrast to the case of
Zimm dynamics where the two components relax with comparable rate, and proceed
considerably slower than in the Rouse case.
We also demonstrate that, in the case of Rouse dynamics, these scaling
predictions agree well with the results of Monte Carlo simulations of the
localization dynamics. A comparison to the localization dynamics of {\em
random} copolymers is also carried out.Comment: 11 pages, 15 figure
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