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Register a new userStructure, molecular dynamics, and stress in a linear polymer under dynamic strain
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Added by
Kartik Venkatraman Prof.
Publication date
2010
fields
Physics
and research's language is
English
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The structural properties of a linear polymer and its evolution in time have a strong bearing on its anisotropic stress response. The mean-square bond length and mean bond angle are the critical parameters that influence the time-varying stress developed in the polymer. The bond length distribution along the chain is uniform without any abrupt changes at the ends. Among the externally set parameters such as density, temperature, strain rate, and chain length, the density as well as the chain length of the polymer have a significant effect on the stress. At high density values, changes in mean-square bond length dominates over changes in radius of gyration and end-to-end length. In other words, bond deformations dominate as opposed to changes in size and shape. Also, there is a large change in the mean-square bond length that is reflected as a jump in the stress. Beyond a particular value of the chain length, $n = 50$, called the entanglement length, stress-response is found to have distinctly different behavior which we attribute to the entanglement effects. Short chain polymers more or less behave like rigid molecules. There is no significant change in their internal structure when loaded. Further, temperature and rate of loading have a very mild effect on the stress. Besides these new results, we can now explain well known polymeric mechanical behavior under dynamic loading from the point of view of the evolution of the molecular dynamics and the derived structural properties. This could possibly lead to polymer synthesis with desired mechanical behavior.
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Molecular dynamic simulation enables one to correlate the evolution of the micro-structure with anisotropic stress when a material is subject to strain. The anisotropic stress due to a constant strain-rate load in a cross-linked polymer is primarily dependent on the mean-square bond length and mean-square bond angle. Excluded volume interactions due to chain stacking and spatial distribution also has a bearing on the stress response. The bond length distribution along the chain is not uniform. Rather, the bond lengths at the end of the chains are larger and uniformly decrease towards the middle of the chain from both ends. The effect is due to the presence of cross-linkers. As with linear polymers, at high density values, changes in mean-square bond length dominates over changes in radius of gyration and end-to-end length. That is, bond deformations dominate over changes in size and shape. A large change in the mean-square bond length reflects in a jump in the stress response. Short-chain polymers more or less behave like rigid molecules. Temperature has a peculiar effect on the response in the sense that even though bond lengths increase with temperature, stress response decreases with increasing temperature. This is due to the dominance of excluded volume effects which result in lower stresses at higher temperatures. At low strain rates, some relaxation in the bond stretch is observed from $epsilon=0.2$ to $epsilon=0.5$. At high strain rates, internal deformation of the chains dominate over their uncoiling leading to a rise in the stress levels.
The effect of excluded volume interactions on the structure of a polymer in shear flow is investigated by Brownian Dynamics simulations for chains with size $30leq Nleq 300$. The main results concern the structure factor $S({bf q})$ of chains of N=300 Kuhn segments, observed at a reduced shear rate $beta=dot{gamma}tau=3.2$, where $dot{gamma}$ is the bare shear rate and $tau$ is the longest relaxation time of the chain. At low q, where anisotropic global deformation is probed, the chain form factor is shown to match the form factor of the continuous Rouse model under shear at the same reduced shear rate, computed here for the first time in a wide range of wave vectors. At high q, the chain structure factor evolves towards the isotropic equilibrium power law $q^{-1/ u}$ typical of self-avoiding walk statistics. The matching between excluded volume and ideal chains at small q, and the excluded volume power law behavior at large q are observed for ${bf q}$ orthogonal to the main elongation axis but not yet for ${bf q}$ along the elongation direction itself, as a result of interferences with finite extensibility effects. Our simulations support the existence of anisotropic shear blobs for polymers in good solvent under shear flow for $beta>1$ provided chains are sufficiently long.
We investigate by means of molecular dynamics simulation a coarse-grained polymer glass model focusing on (quasi-static and dynamical) shear-stress fluctuations as a function of temperature T and sampling time $Delta t$. The linear response is characterized using (ensemble-averaged) expectation values of the contributions (time-averaged for each shear plane) to the stress-fluctuation relation $mu_{sf}$ for the shear modulus and the shear-stress relaxation modulus $G(t)$. Using 100 independent configurations we pay attention to the respective standard deviations. While the ensemble-averaged modulus $mu_{sf}(T)$ decreases continuously with increasing T for all $Delta t$ sampled, its standard deviation $delta mu_{sf}(T)$ is non-monotonous with a striking peak at the glass transition. The question of whether the shear modulus is continuous or has a jump-singularity at the glass transition is thus ill-posed. Confirming the effective time-translational invariance of our systems, the $Delta t$-dependence of $mu_{sf}$ and related quantities can be understood using a weighted integral over $G(t)$. This implies that the shear viscosity $eta(T)$ may be readily obtained from the $1/Delta t$-decay of $mu_{sf}$ above the glass transition.
Molecular Dynamics simulations of a coarse-grained bead-spring model of flexible macromolecules tethered with one end to the surface of a cylindrical pore are presented. Chain length $N$ and grafting density $sigma$ are varied over a wide range and the crossover from ``mushroom to ``brush behavior is studied for three pore diameters. The monomer density profile and the distribution of the free chain ends are computed and compared to the corresponding model of polymer brushes at flat substrates. It is found that there exists a regime of $N$ and $sigma$ for large enough pore diameter where the brush height in the pore exceeds the brush height on the flat substrate, while for large enough $N$ and $sigma$ (and small enough pore diameters) the opposite behavior occurs, i.e. the brush is compressed by confinement. These findings are used to discuss the corresponding theories on polymer brushes at concave substrates.
We study the relaxation dynamics of a coarse-grained polymer chain at different degrees of stretching by both analytical means and numerical simulations. The macromolecule is modelled as a string of beads, connected by anharmonic springs, subject to a tensile force applied at the end monomer of the chain while the other end is fixed at the origin of coordinates. The impact of bond non-linearity on the relaxation dynamics of the polymer at different degrees of stretching is treated analytically within the Gaussian self-consistent approach (GSC) and then compared to simulation results derived from two different methods: Monte-Carlo (MC) and Molecular Dynamics (MD). At low and medium degrees of chain elongation we find good agreement between GSC predictions and the Monte-Carlo simulations. However, for strongly stretched chains the MD method, which takes into account inertial effects, reveals two important aspects of the nonlinear interaction between monomers: (i) a coupling and energy transfer between the damped, oscillatory normal modes of the chain, and (ii) the appearance of non-vanishing contributions of a continuum of frequencies around the characteristic modes in the power spectrum of the normal mode correlation functions.
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