Which is the Dynamics of Stretched Biomolecular Chains? (original) (raw)
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Elasticity of polymer networks
We develop and solve a new molecular model for nonlinear elasticity of entangled polymer networks. This model combines and generalizes several succeseful ideas introduced over the years in the field of the rubber elasticity. The topological constraints imposed by the neighboring network chains on a given network are represented by the confining potential that changes upon network deformation. This topological potential restricts fluctuations of the network chain to the nonaffinely deformed confining tube. Network chains are allowed to fluctuate and redistribute their length along the contour of their confining tubes. The dependence of the stress σ on the elongation coefficient λ for the uniaxially deformed network is usially represented in the form of the Mooney stress, f*(1/λ) ) σ/(λ -1/λ 2 ). We find a simple expression for the Mooney stress, f*(1/λ) ) Gc + Ge/(0.74λ + 0.61λ -1/2 -0.35), where Gc and Ge are phantom and entangled network moduli. This allows one to analyze the experimental data in the form of the universal plot and to obtain the two moduli G c and Ge related to the densities of cross-links and entanglements of the individual networks. The predictions of our new model are in good agreement with experimental data for uniaxially deformed polybutadiene, poly(dimethylsiloxane), and natural rubber networks, as well as with recent computer simulations.
Entropic elasticity of polymers and their networks
2011
The elastic energy for many biopolymer systems is comparable to the thermal energy at room temperature. Therefore, biopolymers and their networks are constantly under thermal fluctuations. From the point of view of thermodynamics, this suggests that entropy plays a crucial role in determining the mechanical behaviors of these filamentous biopolymers. One of the main goals of this thesis is to understand how thermal fluctuations affect the mechanical properties and behaviors of filamentous networks, and also how stress affects the thermal fluctuations.
Two tube models of rubber elasticity
Journal of Polymer Science Part B: Polymer Physics, 2006
Polymer entanglements lead to complicated topological constraints and interactions between neighboring chains in a dense solution or melt. Entanglements can be treated in a mean field approach, within the famous reptation model, since they effectively confine each individual chain in a tube-like geometry. In polymer networks, due to crosslinks preventing the global reptation and constraint release, entanglements acquire a different topological meaning and have a much stronger effect on the resulting mechanical response. In this article we discuss two different models of rubber elasticity, both utilizing the reptation ideas. First, we apply the classical ideas of reptation statistics to calculate the effective rubber-elastic free energy of an entangled rubbery network. In the second approach, we examine the classical Rouse dynamics of chains with quenched constraints at their ends by crosslinks, and along the primitive path by entanglements. We then proceed to average a microscopic stress tensor for the network system and present it in a manageable form in the equilibrium t → ∞ limit. Particular attention is paid to the treatment of compressibility and hydrostatic pressure in a sample with open boundaries.
A Tube Model of Rubber Elasticity
2001
Polymer entanglements lead to complicated topological constraints and interactions between neighbouring chains in a dense solution or melt. Entanglements can be treated in a mean field approach, within the famous reptation model, since they effectively confine each individual chain in a tube-like geometry. In polymer networks, due to crosslinks preventing the reptation constraint release, entanglements acquire a different topological meaning and have a much stronger effect on the resulting mechanical response. We apply the classical ideas of reptation dynamics to calculate the effective rubber-elastic free energy of an entangled rubbery network. We then compare the results with other theoretical approaches and establish a particularly close mapping with the hoop-model, with equally good description of experimental data. The present consistent reptation theory allows further development of dynamic theory of stress relaxation.
Macromolecular Symposia, 2013
Classical network elasticity theories are based on the concept of flexible volumeless network chains fixed into a network in which there are no excluded volume, or even topological, interactions between the chains and where the chains explore accessible configurations by Brownian motion. In this type of 'classical' model of rubber elasticity, the elasticity of the deformed network derives from the entropic changes arising from a deformation of the network junction positions. The shortcoming of this approach is clear from the observation that unswollen rubbery materials are nearly incompressible, reflecting the existence of strong intermolecular interactions that restrict the polymer chains to an exploration of their local tube-like molecular environments. The imposition of a deformation of these solid rubbery materials then necessitates a consideration of how the local molecular packing constraints become modified under deformation and the impact of these changes on the macroscopic elasticity of the material as a whole. Many researchers have struggled with this difficult problem, in the present paper we focus on the simple 'localization model' of rubber elasticity of Gaylord and Douglas (GD), which provides a simple minimal model for the network elasticity of rubbers having strong intermolecular interactions in the dense polymer state. Particular emphasis is given in the implications of this model in describing how network elasticity changes with swelling by a solvent, a phenomenon where large deviations from classical elasticity have been observed and a situation relevant to numerous applications involving rubbery materials. We also discuss the nature of entanglement based on the same packing picture and deduce general relationships for entanglement in terms of molecular parameters and we find that our predictions accord with recent experimental correlations relating chain molecular structure to the entanglement molecular mass.
Stretching of a semiflexible chain composed of elastic bonds
Polymer Science Series A, 2010
We study the extension of semiflexible (persistent) polymer chains composed of elastic bonds under the action of forces applied to their ends. For a given discrete model of a chain, the effective potential energy includes three components: the energy of bonds in the external dipole field, the energy of elastic defor mation of bonds, and the energy of bending, which depends on the angles between neighboring bonds. The extension/contraction modulus of bonds is high but finite. To calculate the relative extension and its variance, the variational method for finding the maximum eigenvalue of the transfer operator in the space of orienta tions of bonds is used. For chains composed of more than ten bonds, the results appear to approach the data of simulation of chain extension by the collisional molecular dynamics method. Two proposed extensionforce dependences are compared with the computer experiment, and this comparison makes it possible to define the limits of their applicability.
A Constraint Dynamics Approach to Rubber Elasticity
Rubber Chemistry and Technology, 1993
The coupling model of relaxation is applied to crosslinked rubber, with a connection drawn between the dynamics of network junctions and statistical mechanics derived rubber elasticity theory. The suggestion that unifying concepts must underlie dynamical models and thermodynamic theories is shown to be supported by analyses of recent 31P NMR spectroscopy measurements by Shi, Dickinson, MacKnight and Chien on polytetrahydrofuran networks and of our mechanical relaxation data on stretched and unstretched polycarbonate.