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 $\tilde g(k)$, g_{0}(k) and $\Delta(k)$. 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 $d$ 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 $N$. We find $R \simeq N^{\nu}(\log N)^{\gamma}$ where $\nu = \frac{3}{\lambda+2}$ and $\lambda$ is the exponent which characterize the long-range interaction $U \propto 1/r^{\lambda}$. The exponent $\gamma$ 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 $2^4<N<2^{15}$. 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 $2^4<N<2^{10}$. The non universal behavior of the exponent $\gamma$ previously derived within the variational method, is also confirmed by the simulation results. Non-universal behavior is found for a polyelectrolyte chain in $d=3$ 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, $d_{\rm uc}=2D/(2-D)$, discriminates between Gaussian (or screened) and non-Gaussian regimes, whereas its dynamical counterpart, ${\tilde d}_{uc}=2d_{\rm uc}$, 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 $N$ and block size $M$ 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 $M$ and chain length $N$ as $\tau_{\perp} \propto M^{1+2\nu}$ (here $\nu\approx 0.6$ is the Flory exponent) and as $\tau_{\parallel} \propto N^2$, although initially the characteristic coil flattening time is predicted to scale with block size as $\propto M$. Since typically $N\gg M$ 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) $\tau(N,M)$ of a regular block copolymer of chain length $N$ and block size $M$ which is dragged through a selective liquid-liquid interface by an external field $B$. The theory predicts a non-Arrhenian $\tau$ vs. $B$ relationship which depends strongly on the size of the blocks, $M$, and rather weakly on the total polymer length, $N$. The overall behavior is strongly influenced by the degree of selectivity between the two solvents $\chi$. The variation of $\tau(N,M)$ with $N$ and $M$ 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 $\Gamma$ - 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 $\tau(N,M)$ with respect to block length $M$ 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