147 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
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
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
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
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
Polymer chain scission at constant tension - an example of force-induced collective behaviour
The breakage of a polymer chain of segments, coupled by anharmonic bonds with
applied constant external tensile force is studied by means of Molecular
Dynamics simulation. We show that the mean life time of the chain becomes
progressively independent of the number of bonds as the pulling force grows.
The latter affects also the rupture rates of individual bonds along the polymer
backbone manifesting the essential role of inertial effects in the
fragmentation process. The role of local defects, temperature and friction in
the scission kinetics is also examined.Comment: 6 pages, 7 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
Field - Driven Translocation of Regular Block Copolymers through a Selective Liquid - Liquid Interface
We propose a simple scaling theory describing the variation of the mean first
passage time (MFPT) of a regular block copolymer of chain length
and block size which is dragged through a selective liquid-liquid
interface by an external field . The theory predicts a non-Arrhenian
vs. relationship which depends strongly on the size of the blocks, , and
rather weakly on the total polymer length, . The overall behavior is
strongly influenced by the degree of selectivity between the two solvents
.
The variation of with and in the regimes of weak and
strong selectivity of the interface is also studied by means of computer
simulations using a dynamic Monte Carlo coarse-grained model. Good qualitative
agreement with theoretical predictions is found. The MFPT distribution is found
to be well described by a - distribution. Transition dynamics of ring-
and telechelic polymers is also examined and compared to that of the linear
chains.
The strong sensitivity of the ``capture'' time with respect to
block length suggests a possible application as a new type of
chromatography designed to separate and purify complex mixtures with different
block sizes of the individual macromolecules.Comment: 20 pages, 10 figure
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