A simple statistical approach to model the time-dependent response of polymers with reversible cross-links

Abstract

A new class of polymers characterized by dynamic cross-links is analyzed from a mechanical point of view. A thermodynamically consistent model is developed within the Lagrangian framework for polymers that can rearrange their internal cross-links. Such a class of polymers has the capability to reset their internal microstructure and the microscopic remodeling mechanism leads to a behavior similar to that of an elastic fluid. These materials can potentially be used in several fields, such as in biomechanics, smart materials, morphing materials to cite e few. However, a comprehensive understanding is necessary before we can predict their behavior and perform material design for advanced technologies. The proposed formulation–following a statistical approach adapted from classical rubber elasticitye is based on the evolution of the molecular chains’ end-to-end distance distribution function. This distribution is allowed here to evolve with time, starting from an initial stress-free state and depending on the deformation history and the cross-link attachment/detachment kinetics. Some simple examples are finally presented and discussed to illustrate the capability and generality of the developed approach.

Modeling cells spreading, motility, and receptors dynamics: a general framework

“…Homogenized models for the mechanical response of a cell shall condense in effective properties the: i) polymerisation/depolimerisation of filaments; ii) the process of cross-linking that determine the architecture of cytoskeletal filaments; iii) the passive mechanical properties of the cytosol. The thermodynamics of statistically-based continuum theories for polymers with transient networks [76][77][78][79][80] appear to be a valuable candidate for the selection of free energies ψ el R (c F R , C) and ψ in R (c F R , E, ξ ). At present however, such a comprehensive model has not yet been proposed for the pseudopodia driven cell motion.…”

“…At present, research on the identification of suitable free energies ψ el,iso R (c F R , C e i ) + ψ in R (c F R , E e − ξ ) for the active stress S active is on going, based on statistical mechanics of cytoskeletal reorganization in stress fibers and pseudopodia. We thus accounted only for the passive stress S passive by means of rubber visco-elasticity (76). Such a multi-physics initial boundary value problem in the bulk and on the membrane of the cell, rephrased in a weak form and further discretized via finite elements, has been implemented in a high performance computing code with a staggered Newton-Raphson solver, in the deal.ii framework ( http://www.dealii.org ).…”

Fluidization of Transient Filament Networks

“…By assuming that the material is incompressible, we can obtain the constitutive stress-strain relation of the transient filament network, as the derivative σ ela ij = ∂F t.n /∂E ij , since there is no difference between the Gibbs free energy G t.n = F t.n (t) + p det[E], and the Helmholtz F t.n , when we use the rigid constraint I 3 = det[E] = 1. Note that there are also various microscopic models16,43 for the transient network, especially transient rubber, which deal with the mechanical properties from the statistical viewpoint.…”

Adjustable viscoelasticity allows for efficient collective cell migration

“…Mechanical strain of cytoskeletal network has also been measured in epithelial cells by using flow analysis, and mechanisms controlling cytoskeletal stiffening have been proposed [113,114]. Not only polymerisation and the passive mechanical properties of its components determine the mechanical state of the cytoskeleton, cross-linking factors have also been proposed to play a role in determining the architecture of cytoskeletal filaments and consequently their elastic state [[115], [116], [117], [118]]. The activity of molecular motors such myosin-II in combination with cross-linkers is also related to the viscoelastic properties of the cytoskeleton [89,119].…”