Crystal nucleation mechanism in melts of short polymer chains under quiescent conditions and under shear flow

We present a molecular dynamics simulation study of crystal nucleation from undercooled melts of n-alkanes, and we identify the molecular mechanism of homogeneous crystal nucleation under quiescent conditions and under shear flow. We compare results for n-eicosane(C20) and n-pentacontahectane(C150), i.e. one system below the entanglement length and one above. Under quiescent conditions, we observe that entanglement does not have an effect on the nucleation mechanism. For both chain lengths, the chains first align and then straighten locally. Then the local density increases and finally positional ordering sets in. At low shear rates the nucleation mechanism is the same as under quiescent conditions, while at high shear rates the chains align and straighten at the same time. We report on the effects of shear rate and temperature on the nucleation rates and estimate the critical shear rates, beyond which the nucleation rates increase with the shear rate. We show that the viscosity of the system is not affected by the crystalline nuclei.Comment: 9 page

Flow-History-Dependent Behavior in Entangled Polymer Melt Flow with Multiscale Simulation

Polymer melts represent the flow-history-dependent behavior. To clearly show this behavior, we have investigated flow behavior of an entangled polymer melt around two cylinders placed in tandem along the flow direction in a two dimensional periodic system. In this system, the polymer states around a cylinder in downstream side are different from the ones around another cylinder in upstream side because the former ones have a memory of a strain experienced when passing around the cylinder in upstream side but the latter ones do not have the memory. Therefore, the shear stress distributions around two cylinders are found to be different from each other. Moreover, we have found that the averaged flow velocity decreases accordingly with increasing the distance between two cylinders while the applied external force is constant. While this behavior is consistent with that of the Newtonian fluid, the flow-history-dependent behavior enhances the reduction of the flow resistance.Comment: 6 pages, 3 figures, Proceedings of 5th International Mini-Symposium on Liquid

Dynamics and interactions of active rotors

We consider a simple model of an internally driven self-rotating object; a rotor, confined to two dimensions by a thin film of low Reynolds number fluid. We undertake a detailed study of the hydrodynamic interactions between a pair of rotors and find that their effect on the resulting dynamics is a combination of fast and slow motions. We analyse the slow dynamics using an averaging procedure to take account of the fast degrees of freedom. Analytical results are compared with numerical simulations. Hydrodynamic interactions mean that while isolated rotors do not translate, bringing together a pair of rotors leads to motion of their centres. Two rotors spinning in the same sense rotate with an approximately constant angular velocity around each other, while two rotors of opposite sense, both translate with the same constant velocity, which depends on the separation of the pair. As a result a pair of counter-rotating rotors are a promising model for controlled self-propulsion.Comment: 6 pages, 6 figure

Conformational transformations induced by the charge-curvature interaction at finite temperature

The role of thermal fluctuations on the conformational dynamics of a single closed filament is studied. It is shown that, due to the interaction between charges and bending degrees of freedom, initially circular aggregates may undergo transformation to polygonal shape. The transition occurs both in the case of hardening and softening charge-bending interaction. In the former case the charge and curvature are smoothly distributed along the chain while in the latter spontaneous kink formation is initiated. The transition to a non-circular conformation is analogous to the phase transition of the second kind.Comment: 23 pages (Latex), 10 figures (Postscript), 2 biblio file (bib-file and bbl-file

Dense colloidal suspensions under time-dependent shear

We consider the nonlinear rheology of dense colloidal suspensions under a time-dependent simple shear flow. Starting from the Smoluchowski equation for interacting Brownian particles advected by shearing (ignoring fluctuations in fluid velocity) we develop a formalism which enables the calculation of time-dependent, far-from-equilibrium averages. Taking shear-stress as an example we derive exactly a generalized Green-Kubo relation, and an equation of motion for the transient density correlator, involving a three-time memory function. Mode coupling approximations give a closed constitutive equation yielding the time-dependent stress for arbitrary shear rate history. We solve this equation numerically for the special case of a hard sphere glass subject to step-strain.Comment: 4 page

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

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

Strain Hardening of Polymer Glasses: Entanglements, Energetics, and Plasticity

Simulations are used to examine the microscopic origins of strain hardening in polymer glasses. While stress-strain curves for a wide range of temperature can be fit to the functional form predicted by entropic network models, many other results are fundamentally inconsistent with the physical picture underlying these models. Stresses are too large to be entropic and have the wrong trend with temperature. The most dramatic hardening at large strains reflects increases in energy as chains are pulled taut between entanglements rather than a change in entropy. A weak entropic stress is only observed in shape recovery of deformed samples when heated above the glass transition. While short chains do not form an entangled network, they exhibit partial shape recovery, orientation, and strain hardening. Stresses for all chain lengths collapse when plotted against a microscopic measure of chain stretching rather than the macroscopic stretch. The thermal contribution to the stress is directly proportional to the rate of plasticity as measured by breaking and reforming of interchain bonds. These observations suggest that the correct microscopic theory of strain hardening should be based on glassy state physics rather than rubber elasticity.Comment: 15 pages, 12 figures: significant revision

Crossover behavior for long reptating polymers

We analyze the Rubinstein-Duke model for polymer reptation by means of density matrix renormalization techniques. We find a crossover behavior for a series of quantities as function of the polymer length. The crossover length may become very large if the mobility of end groups is small compared to that of the internal reptons. Our results offer an explanation to a controversy between theory, experiments and simulations on the leading and subleading scaling behavior of the polymer renewal time and diffusion constant.Comment: 4 Pages, RevTeX, and 4 PostScript figures include

Additive Equivalence in Turbulent Drag Reduction by Flexible and Rodlike Polymers

We address the "Additive Equivalence" discovered by Virk and coworkers: drag reduction affected by flexible and rigid rodlike polymers added to turbulent wall-bounded flows is limited from above by a very similar Maximum Drag Reduction (MDR) asymptote. Considering the equations of motion of rodlike polymers in wall-bounded turbulent ensembles, we show that although the microscopic mechanism of attaining the MDR is very different, the macroscopic theory is isomorphic, rationalizing the interesting experimental observations.Comment: 8 pages, PRE, submitte