TITLE

Note: A simple picture of subdiffusive polymer motion from stochastic simulations

AUTHOR(S)
Gniewek, Pawel; Kolinski, Andrzej
PUB. DATE
February 2011
SOURCE
Journal of Chemical Physics;2/7/2011, Vol. 134 Issue 5, p056101
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Entangled polymer solutions and melts exhibit unusual frictional properties. In the entanglement limit self-diffusion coefficient of long flexible polymers decays with the second power of chain length and viscosity increases with 3-3.5 power of chain length.1 It is very difficult to provide detailed molecular-level explanation of the entanglement effect.2 Perhaps, the problem of many entangled polymer chains is the most complex multibody issue of classical physics. There are different approaches to polymer melt dynamics. Some of these recognize hydrodynamic interactions as a dominant term, while topological constraints for polymer chains are assumed as a secondary factor.3,4 Other theories consider the topological constraints as the most important factors controlling polymer dynamics. Herman and co-workers describe polymer dynamics in melts, as a lateral sliding of a chain along other5,6 chains until complete mutual disentanglement. Despite the success in explaining the power-laws for viscosity, the model has some limitations. First of all, memory effects are ignored, that is, polymer segments are treated independently. Also, each entanglement/obstacle is treated as a separate entity, which is certainly a simplification of the memory effect problem. In addition to that, correlated motions of segments are addressed within the framework of renormalized Rouse-chain theory,7 without calling any topological entanglements in advance. This approach leads to the generalized Langevin equation characterized by distinct memory kernels describing local and nonlocal segment correlations8,9,10 or to the Smoluchowski equation in which the segments' mobility is treated as a stochastic variable.11 Both models describe the polymer segments motion at a microscopic level. An interesting alternative is to solve the integrodifferential equation for the chain relaxation with a sophisticated kernel function.12 The design of the kernel function is based on a mesoscopic description of the polymer melt. These theories explain some experimental data, although the description of the crossover between the Rouse and non-Rouse behavior is not satisfactory. Obviously, within the scope of a short note we cannot review all theoretical concepts of the polymer melt dynamics. Here we focus just on the interpretation of the observed single segment autocorrelation function.
ACCESSION #
57854926

 

Related Articles

  • Limiting Dynamics for Spherical Models of Spin Glasses at High Temperature. Dembo, Amir; Guionnet, Alice; Mazza, Christian // Journal of Statistical Physics;Aug2007, Vol. 128 Issue 4, p847 

    We analyze the coupled non-linear integro-differential equations whose solution is the thermodynamical limit of the empirical correlation and response functions in the Langevin dynamics for spherical p-spin disordered mean-field models. We provide a mathematically rigorous derivation of their...

  • Langevin dynamics of Rouse chains under flow. Wang, Shi-Qing; Freed, Karl F. // Journal of Chemical Physics;3/15/1988, Vol. 88 Issue 6, p3944 

    A systematic approach is developed for describing the hydrodynamics of flowing polymer solutions by using a microscopic Langevin model for which the inertial nonlinearities and solvent advection are ignored. The influence of polymer motion on the solution velocity field is evaluated by averaging...

  • Oblique entry of a wedge into an ideal incompressible fluid. Goman, O.; Semenov, Yu. // Fluid Dynamics;Jul2007, Vol. 42 Issue 4, p581 

    A new approach to the solution of the self-similar problem of the entry of a wedge into an ideal fluid at an arbitrary angle to the free surface is proposed. The method is based on the construction of the expressions for the complex velocity and the derivative of the complex potential in a...

  • Aleksandrov-Bakelman-Pucci Type Estimates for Integro-Differential Equations. Guillen, Nestor; Schwab, Russell // Archive for Rational Mechanics & Analysis;Oct2012, Vol. 206 Issue 1, p111 

    In this work we provide an Aleksandrov-Bakelman-Pucci type estimate for a certain class of fully nonlinear elliptic integro-differential equations, the proof of which relies on an appropriate generalization of the convex envelope to a nonlocal, fractional-order setting and on the use of Riesz...

  • Beyond the linear approximations of the conventional approaches to the theory of chemical relaxation. Bianucci, Marco; Grigolini, Paolo; Palleschi, Vincenzo // Journal of Chemical Physics;3/15/1990, Vol. 92 Issue 6, p3427 

    The nonlinear coupling between the reacting system and its molecular bath results in a generalized Langevin equation with a memory kernel which is nonstationary as well as dependent on the reaction coordinate. In a preceding paper by Grigolini [J. Chem. Phys. 89, 4300 (1988)] a theory was...

  • Singular risk-neutral valuation equations. Costantini, Cristina; Papi, Marco; D'Ippoliti, Fernanda // Finance & Stochastics;2012, Vol. 16 Issue 2, p249 

    Many risk-neutral pricing problems proposed in the finance literature do not admit closed-form expressions and have to be dealt with by solving the corresponding partial integro-differential equation. Often, these PIDEs have singular diffusion matrices and coefficients that are not...

  • Criteria for the well-posedness of a linear two-point boundary value problem for systems of integro-differential equations. Dzhumabaev, D. S; Bakirova, E. A. // Differential Equations;Apr2010, Vol. 46 Issue 4, p553 

    We consider a linear two-point boundary value problem for systems of integro-differential equations. By using the parametrization method and an approximation of the integro-differential equation by a loaded differential equation, we establish coefficient tests for the well-posedness of the...

  • Entropy Production for Mechanically or Chemically Driven Biomolecules. Schmiedl, Tim; Speck, Thomas; Seifert, Udo // Journal of Statistical Physics;Jul2007, Vol. 128 Issue 1/2, p77 

    Entropy production along a single stochastic trajectory of a biomolecule is discussed for two different sources of non-equilibrium. For a molecule manipulated mechanically by an AFM or an optical tweezer, entropy production (or annihilation) occurs in the molecular conformation proper or in the...

  • Limiting Dynamics for Spherical Models of Spin Glasses at High Temperature. Dembo, Amir; Guionnet, Alice; Mazza, Christian // Journal of Statistical Physics;Feb2007, Vol. 126 Issue 4/5, p781 

    We analyze the coupled non-linear integro-differential equations whose solution is the thermodynamical limit of the empirical correlation and response functions in the Langevin dynamics for spherical p−spin disordered mean-field models. We provide a mathematically rigorous derivation of...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics