Molecular stress and strain in an oriented extended-chain polymer of finite molecular length (original) (raw)
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Journal of Inorganic and Organometallic Polymers and Materials, 2011
The Monte-Carlo (MC) rotational-isomeric-state (RIS) method developed previously to model the stress-strain behaviour of poly(ethylene terephthalate) (PET) is now applied to short PET chains of between 42 and 84 skeletal bonds. The effects on the radial and probability density distribution functions of the long, flexible virtual bond used to represent the terephthaloyl unit are investigated. The distribution functions generated, based on finite samples of chains, are found to be discontinuous with subsidiary maxima in their tails. The discontinuities lead to uncertainties in the simulated network elasticity properties and, in order to reduce the uncertainty, it is necessary to truncate the distributions at the values of r where they first become discontinuous. The stressstrain properties calculated from the truncated distributions are shown to be consistent with those presented previously for longer PET chains, for which discontinuities in the sampled functions are not apparent.
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The viscoelasticity of stretched polymer chains has been studied by the method of collisional dynamics. To this end, time correlation functions of the fluctuations of the microscopic stress tensor are modeled and relaxation moduli are expressed. Before, for stretched polymer networks, correlation functions used to be calculated in terms of an approximate theory that allowed one to estimate the strain dependences of loss modulus. The calculated dependences are shown to agree qualitatively with the results of measurements performed over a wide interval of strains, including prefracture strains. This theory is verified by comparing the time correlation functions of stress tensor fluctuations for a single stretched chain; these functions are found by computer-aided simulation and calculated on the basis of the existing analytical theory. In this case, a simple theory is adopted according to which a polymer molecule represents a chain composed of N atoms connected by freely jointed elastic bonds. The first and N th atoms of this chain are attached by harmonic springs to immobile points located at a fixed distance. The decay of time correlation functions under study can be resolved into three stages. After a short initial interval provided by local motions, one can observe a region of power-law decay, which is followed by monoexponential decay at long times. The results of computer-aided simulation generally agree with the predictions of analytical theory. Certain discrepancies primarily concern the dependences of the exponent of power-law relaxation on the degree of chain stretching.
Dynamics of stretched polymer chains. 2
Macromolecules, 1985
We study the internal modes of an ideal polymer chain that is being stretched by an external force. The effects of the force on the hydrodynamic interaction are investigated by using a preaveraged Oseen tensor approach, for both Gaussian and freely jointed polymer chains.
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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.
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It has become clear in recent years that the simple uniform wormlike chain model needs to be modified in order to account for more complex behavior which has been observed experimentally in some important biopolymers. For example, the large flexibility of short ds-DNA has been attributed to kink or hinge defects. In this paper, we calculate analytically, within the weak bending approximation, the force-extension relation of a wormlike chain with a permanent hinge defect along its contour. The defect is characterized by its bending energy (which can be zero, in the completely flexible case) and its position along the polymer contour. Besides the bending rigidity of the chain, these are the only parameters which describe our model. We show that a hinge defect causes a significant increase in the differential tensile compliance of a prestressed chain. In the small force limit, a hinge defect significantly increases the entropic elasticity. Our results apply to any pair of semiflexible ...
The Journal of Chemical Physics, 2012
Recent developments of microscopic mechanical experiments allow the manipulation of individual polymer molecules in two main ways: uniform stretching by external forces and non-uniform stretching by external fields. Many results can be thereby obtained for specific kinds of polymers and specific geometries. In this work we describe the non-uniform stretching of a single, non-branched polymer molecule by an external field (e.g. fluid in uniform motion, or uniform electric field) by a universal physical framework which leads to general conclusions on different types of polymers. We derive analytical results both for the freely-jointed chain and the worm-like chain models based on classical statistical mechanics. Moreover, we provide a Monte Carlo numerical analysis of the mechanical properties of flexible and semi-flexible polymers anchored at one end. The simulations confirm the analytical achievements, and moreover allow to study the situations where the theory can not provide explicit and useful results. In all cases we evaluate the average conformation of the polymer and its fluctuation statistics as a function of the chain length, bending rigidity and field strength.
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stretching experiments on short polyethylenes or on other soft matter materials involving linear paraffinic chains. It is argued that the dual character of elastic response described by the conjugated force profiles is a universal feature of mechanochemistry of chain molecules whenever the chain length discontinuously increases at a transition.