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Register a new userRelaxation time of a polymer glass stretched at very large strains
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Added by
Caroline Crauste-Thibierge
Publication date
2020
fields
Physics
and research's language is
English
Authors
R. Sahli
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The polymer relaxation dynamic of a sample, stretched up to the stress hardening regime, is measured, at room temperature, as a function of the strain $lambda$ for a wide range of the strain rate $dotgamma$, by an original dielectric spectroscopy set up. The mechanical stress modies the shape of the dielectric spectra mainly because it affects the dominant polymer relaxation time $tau$, which depends on $lambda$ and is a decreasing function of $dotgamma$. The fastest dynamics is not reached at yield but in the softening regime. The dynamics slows down during the hardening, with a progressive increase of $tau$. A small inuence of $dotgamma$ and $lambda$ on the dielectric strength cannot be excluded.
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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.
We report experimental evidence that a polymer stretched at constant strain rate $dotlambda$ presents complex memory effects after that $dotlambda$ is set to zero at a specific strain $lambda_w$ for a duration $t_w$, ranging from $100$s to $ 2.2times10^5$s. When the strain rate is resumed, both the stress and the dielectric constant relax to the unperturbed state non monotonically. The relaxations depend on the observable, on $lambda_w$ and on $t_w$. Relaxation master curves are obtained by scaling the relaxation time as $t/ln (t_w)$. The dielectric evolution also captures the distribution of the relaxation times, so the results impose strong constraints on the relaxation models of polymers under stress and they can be useful for a better understanding of memory effects in other disorder materials.
The relaxation of the specific heat and the entropy to their equilibrium values is investigated numerically for the three-dimensional Coulomb glass at very low temperatures. The long time relaxation follows a stretched exponential function, $f(t)=f_0exp[-(t/tau)^beta]$, with the exponent $beta$ increasing with the temperature. The relaxation time follows an Arrhenius behavior divergence when $Tto 0$. A relation between the specific heat and the entropy in the long time regime is found.
Low-frequency Raman and inelastic neutron scattering of amorphous bis-phenol A polycarbonate is measured at low temperature, and compared. The vibrational density of states and light-vibration coupling coefficient are determined. The frequency dependences of these parameters are explained by propagating vibration modes up to an energy of about 1 meV, and fracton-like modes in more cohesive domains at higher energies. The vibrational dynamics is in agreement with a disorder in the glass, which is principally of bonding or of elasticity instead of density.
We study random walks on the dilute hypercube using an exact enumeration Master equation technique, which is much more efficient than Monte Carlo methods for this problem. For each dilution $p$ the form of the relaxation of the memory function $q(t)$ can be accurately parametrized by a stretched exponential $q(t)=exp(-(t/tau)^beta)$ over several orders of magnitude in $q(t)$. As the critical dilution for percolation $p_c$ is approached, the time constant $tau(p)$ tends to diverge and the stretching exponent $beta(p)$ drops towards 1/3. As the same pattern of relaxation is observed in wide class of glass formers, the fractal like morphology of the giant cluster in the dilute hypercube is a good representation of the coarse grained phase space in these systems. For these glass formers the glass transition can be pictured as a percolation transition in phase space.
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