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Register a new userGiant Casimir non-equilibrium forces drive coil to globule transition in polymers
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We develop a theory to probe the effect of non-equilibrium fluctuation-induced forces on the size of a polymer confined between two horizontal thermally conductive plates subject to a constant temperature gradient, $ abla T$. We assume that (a) the solvent is good and (b) the distance between the plates is large so that in the absence of a thermal gradient the polymer is a coil whose size scales with the number of monomers as $N^{ u}$, with $ u approx 0.6$. We predict that above a critical temperature gradient, $ abla T_c sim N^{-frac{5}{4}}$, favorable attractive monomer-monomer interaction due to Giant Casimir Force (GCF) overcomes the chain conformational entropy, resulting in a coil-globule transition. The long-ranged GCF-induced interactions between monomers, arising from thermal fluctuations in non-equilibrium steady state, depend on the thermodynamic properties of the fluid. Our predictions can be verified using light-scattering experiments with polymers, such as polystyrene or polyisoprene in organic solvents (neopentane) in which GCF is attractive.
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We perform numerical simulations of an active fully flexible self-avoiding polymer as a function of the quality of the embedding solvent described in terms of an effective monomer-monomer interaction. Specifically, by extracting the Flory exponent of the active polymer under different conditions, we are able to pin down the location of the coil-globule transition for different strength of the active forces. Remarkably, we find that a simple rescaling of the temperature is capable of qualitatively capture the dependence of the $Theta$-point of the polymer with the amplitude of the active fluctuations. We discuss the limits of this mapping, and suggest that a negative active pressure between the monomers, not unlike the one that has already been found in suspensions of active hard spheres, may also be present in active polymers.
We consider a free energy functional on the monomer density function that is suitable for the study of coil-globule transition. We demonstrate, with explicitly stated assumptions, why the entropic contribution is in the form of the Kullback-Leibler distance, and that the energy contribution is given by two-body and three-body terms. We then solve for the free energy analytically on a set of trial density functions, and reproduce de Gennes classical theory on polymer coil-globule transition. We then discuss how our formalism can be applied to study polymer dynamics from the perspective of dynamical density function theory.
Using general scaling arguments combined with mean-field theory we investigate the critical ($T simeq T_c$) and off-critical ($T e T_c$) behavior of the Casimir forces in fluid films of thickness $L$ governed by dispersion forces and exposed to long-ranged substrate potentials which are taken to be equal on both sides of the film. We study the resulting effective force acting on the confining substrates as a function of $T$ and of the chemical potential $mu$. We find that the total force is attractive both below and above $T_c$. If, however, the direct substrate-substrate contribution is subtracted, the force is repulsive everywhere except near the bulk critical point $(T_c,mu_c)$, where critical density fluctuations arise, or except at low temperatures and $(L/a) (betaDelta mu) =O(1)$, with $Delta mu=mu-mu_c <0$ and $a$ the characteristic distance between the molecules of the fluid, i.e., in the capillary condensation regime. While near the critical point the maximal amplitude of the attractive force if of order of $L^{-d}$ in the capillary condensation regime the force is much stronger with maximal amplitude decaying as $L^{-1}$. Essential deviations from the standard finite-size scaling behavior are observed within the finite-size critical region $L/xi=O(1)$ for films with thicknesses $L lesssim L_{rm crit}$, where $L_{rm crit}=xi_0^pm (16 |s|)^{ u/beta}$, with $ u$ and $beta$ as the standard bulk critical exponents and with $s=O(1)$ as the dimensionless parameter that characterizes the relative strength of the long-ranged tail of the substrate-fluid over the fluid-fluid interaction. We present the modified finite-size scaling pertinent for such a case and analyze in detail the finite-size behavior in this region.
We present a study of the parallel tempering (replica exchange) Monte Carlo method, with special focus on the feedback-optimized parallel tempering algorithm, used for generating an optimal set of simulation temperatures. This method is applied to a lattice simulation of a homopolymer chain undergoing a coil-to-globule transition upon cooling. We select the optimal number of replicas for different chain lengths, N = 25, 50 and 75, using replicas round-trip time in temperature space, in order to determine energy, specific heat, and squared end-to-end distance of the hopolymer chain for the selected temperatures. We also evaluate relative merits of this optimization method.
Effective Casimir forces induced by thermal fluctuations in the vicinity of bulk critical points are studied by means of Monte Carlo simulations in three-dimensional systems for film geometries and within the experimentally relevant Ising and XY universality classes. Several surface universality classes of the confining surfaces are considered, some of which are relevant for recent experiments. A novel approach introduced previously EPL 80, 60009 (2007), based inter alia on an integration scheme of free energy differences, is utilized to compute the universal scaling functions of the critical Casimir forces in the critical range of temperatures above and below the bulk critical temperature. The resulting predictions are compared with corresponding experimental data for wetting films of fluids and with available theoretical results.
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