Two harmonically coupled Brownian particles in random media

We study the behaviour of two Brownian particles coupled by an elastic harmonic force in a quenched disordered medium. We found that to first order in disorder strength, the relative motion weakens (with respect to the reference state of a Brownian particle with the double mass) the effect of the quenched forces on the centre of mass motion of the Brownian particles, so that the motion will become less subdiffusive (superdiffusive) for potential (solenoidal) disorder. The mean-square relative distance between the particles behaves in a different way depending of whether the particles are free to move or one particle is anchored in the space. While the effect of nonpotential disorder consists in increasing the mean-square distance in both cases, the potential disorder decreases the mean-square distance, when the particles are free to move, and increases it when one particle is anchored in the space.Comment: 8 pages, 3 figure

Bimodal distribution function of a 3d wormlike chain with a fixed orientation of one end

We study the distribution function of the three dimensional wormlike chain with a fixed orientation of one chain end using the exact representation of the distribution function in terms of the Green's function of the quantum rigid rotator in a homogeneous external field. The transverse 1d distribution function of the free chain end displays a bimodal shape in the intermediate range of the chain lengths ($1.3L_{p},...,3.5L_{p}$). We present also analytical results for short and long chains, which are in complete agreement with the results of previous studies obtained using different methods.Comment: 6 pages, 3 figure

Localization and freezing of a Gaussian chain in a quenched random potential

The Gaussian chain in a quenched random potential (which is characterized by the disorder strength $\Delta$) is investigated in the $d$ - dimensional space by the replicated variational method. The general expression for the free energy within so called one - step - replica symmetry breaking (1 - RSB) scenario has been systematically derived. We have shown that the replica symmetrical (RS) limit of this expression can describe the chain center of mass localization and collapse. The critical disorder when the chain becomes localized scales as $\Delta_c \simeq b^d N^{-2 + d/2}$ (where $b$ is the length of the Kuhn segment length and $N$ is the chain length) whereas the chain gyration radius $R_{\rm g} \simeq b (b^d/\Delta)^{1/(4 - d)}$. The freezing of the internal degrees of freedom follows to the 1-RSB - scenario and is characterized by the beads localization length $\bar{{\cal D}^2}$. It was demonstrated that the solution for $\bar{{\cal D}^2}$ appears as a metastable state at $\Delta = \Delta_A$ and behaves similarly to the corresponding frozen states in heteropolymers or in $p$ - spin random spherical model.Comment: 18 pages, 6 figures, submitted to J. Chem. Phy

Drift of a polymer chain in disordered media

We consider the drift of a polymer chain in a disordered medium, which is caused by a constant force applied to the one end of the polymer, under neglecting the thermal fluctuations. In the lowest order of the perturbation theory we have computed the transversal fluctuations of the centre of mass of the polymer, the transversal and the longitudinal size of the polymer, and the average velocity of the polymer. The corrections to the quantities under consideration, which are due to the interplay between the motion and the quenched forces, are controlled by the driving force and the degree of polymerization. The transversal fluctuations of the Brownian particle and of the centre of mass of the polymer are obtained to be diffusive. The transversal fluctuations studied in the present Letter may also be of relevance for the related problem of the drift of a directed polymer in disordered media and its applications.Comment: 11 pages, RevTex, Accepted for publication in Europhysics Letter

Statistical mechanics of semiflexible polymers

We present the statistical-mechanical theory of semiflexible polymers based on the connection between the Kratky-Porod model and the quantum rigid rotator in an external homogeneous field, and treatment of the latter using the quantum mechanical propagator method. The expressions and relations existing for flexible polymers can be generalized to semiflexible ones, if one replaces the Fourier-Laplace transform of the end-to-end polymer distance, $1/(k^{2}/3+p)$, through the matrix $\tilde{P}(k,p)=(I+ikDM)^{-1}D$, where $D$ and $M$ are related to the spectrum of the quantum rigid rotator, and considers an appropriate matrix element of the expression under consideration. The present work provides also the framework to study polymers in external fields, and problems including the tangents of semiflexible polymers. We study the structure factor of the polymer, the transversal fluctuations of a free end of the polymer with fixed tangent of another end, and the localization of a semiflexible polymer onto an interface. We obtain the partition function of a semiflexible polymer in half space with Dirichlet boundary condition in terms of the end-to-end distribution function of the free semiflexible polymer, study the behaviour of a semiflexible polymer in the vicinity of a surface, and adsorption onto a surface.Comment: 30 pages, 7 figures, changed conten

Fluctuation effects in the theory of microphase separation of diblock copolymers in the presence of an electric field

We generalize the Fredrickson-Helfand theory of the microphase separation in symmetric diblock copolymer melts by taking into account the influence of a time-independent homogeneous electric field on the composition fluctuations within the self-consistent Hartree approximation. We predict that electric fields suppress composition fluctuations, and consequently weaken the first-order transition. In the presence of an electric field the critical temperature of the order-disorder transition is shifted towards its mean-field value. The collective structure factor in the disordered phase becomes anisotropic in the presence of the electric field. Fluctuational modulations of the order parameter along the field direction are strongest suppressed. The latter is in accordance with the parallel orientation of the lamellae in the ordered state.Comment: 16 page

Statistical mechanical description of liquid systems in electric field

We formulate the statistical mechanical description of liquid systems for both polarizable and polar systems in an electric field in the $\mathbf{E}$-ensemble, which is the pendant to the thermodynamic description in terms of the free energy at constant potential. The contribution of the electric field to the configurational integral $\tilde{Q}_{N}(\mathbf{E})$ in the $\mathbf{E}$-ensemble is given in an exact form as a factor in the integrand of $\tilde{Q}_{N}(\mathbf{E})$. We calculate the contribution of the electric field to the Ornstein-Zernike formula for the scattering function in the $\mathbf{E}$-ensemble. As an application we determine the field induced shift of the critical temperature for polarizable and polar liquids, and show that the shift is upward for polarizable liquids and downward for polar liquids.Comment: 6 page

Semiflexible polymers: Dependence on ensemble and boundary orientations

We show that the mechanical properties of a worm-like-chain (WLC) polymer, of contour length $L$ and persistence length \l such that t=L/\l\sim{\cal O}(1), depend both on the ensemble and the constraint on end-orientations. In the Helmholtz ensemble, multiple minima in free energy near $t=4$ persists for all kinds of orientational boundary conditions. The qualitative features of projected probability distribution of end to end vector depend crucially on the embedding dimensions. A mapping of the WLC model, to a quantum particle moving on the surface of an unit sphere, is used to obtain the statistical and mechanical properties of the polymer under various boundary conditions and ensembles. The results show excellent agreement with Monte-Carlo simulations.Comment: 15 pages, 15 figures; version accepted for publication in Phys. Rev. E; one new figure and discussions adde