Dynamics of an active crosslinker on a chain and aspects of the dynamics of polymer networks

[摘要] ENGLISH ABSTRACT: Active materials are a subset of soft matter that is constantly being driven out ofan equilibrium state due to the energy input from internal processes such as thehydrolysis of adenosine triphosphate (ATP) to adenosine diphosphate (ADP), asfound in biological systems.Firstly, we construct and study a simple model of a flexible filament with anactive crosslinker/molecular motor. We treat the system on a mesoscopic scale usinga Langevin equation approach, which we analyse via a functional integral approachusing the Martin-Siggia-Rose formalism. We characterise the steady state behaviourof the system up to first order in the motor force and also the autocorrelation offluctuations of the position of the active crosslink on the filament. We find that thisautocorrelation function does not depend on the motor force up to first order forthe case where the crosslinker is located in the middle of the contour length of thefilament. Properties that characterise the elastic response of the system are studiedand found to scale with the autocorrelation of fluctuations of the active crosslinkposition.Secondly, we give a brief overview of the current state of dynamical polymernetwork theory and then propose two dynamical network models based on aCayley-tree topology. Our first model takes a renormalisation approach and deriverecurrence relations for the coupling constants of the system. The second modelbuilds on the ideas of an Edwards type network theory where Wick's theorem isemployed to enforce the constraint conditions. Both models are examined using afunctional integral approach.

[发布机构] Stellenbosch University