arXiv subjects

I. Kriuchevskyi

Publications and source records attributed to I. Kriuchevskyi.

6 recordsLinked to original sources

arXiv2022

Numerical determination of shear stress relaxation modulus of polymer glasses

Focusing on simulated polymer glasses well below the glass transition, we confirm the validity and the efficiency of the recently proposed simple-average expression $G(t) = μ_A - h(t)$ for the computational determination of the shear stress relaxation modulus $G(t)$. Here, $μ_A = G(0)$ characterizes the affine shear transformation of the system at $t=0$ and $h(t)$ the mean-square displacement of the instantaneous shear stress as a function of time $t$. This relation is seen to be particulary useful for systems with quenched or sluggish transient shear stresses which necessarily arise below the glass transition. The commonly accepted relation $G(t)=c(t)$ using the shear stress auto-correlation function $c(t)$ becomes incorrect in this limit.

cond-mat.soft↗

arXiv2018

Shear-stress fluctuations in free-standing polymer films

Using molecular dynamics simulation of a polymer glass model we investigate free-standing polymer films focusing on the in-plane shear modulus $μ$ and the corresponding shear-stress relaxation modulus $G(t)$ as functions of temperature $T$, film thickness $H$ (tuned by means of the lateral box size $L$) and sampling time $Δt$. Various observables are seen to vary linearly with $1/H$ demonstrating thus the (to leading order) linear superposition of bulk and surface properties. In agreement with recent studies on three-dimensional polymer glass-formers, $μ$ and $G(t)$ are found to decrease continuously with $T$. A jump-singularity is not observed. Confirming the time-translational invariance of our systems, the $Δt$-dependence of $μ$ is traced back to $G(t)$.

cond-mat.soft↗

arXiv2017

Shear-stress fluctuations and relaxation in polymer glasses

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 $Δt$. The linear response is characterized using (ensemble-averaged) expectation values of the contributions (time-averaged for each shear plane) to the stress-fluctuation relation $μ_{sf}$ 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 $μ_{sf}(T)$ decreases continuously with increasing T for all $Δt$ sampled, its standard deviation $δμ_{sf}(T)$ 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 $Δt$-dependence of $μ_{sf}$ and related quantities can be understood using a weighted integral over $G(t)$. This implies that the shear viscosity $η(T)$ may be readily obtained from the $1/Δt$-decay of $μ_{sf}$ above the glass transition.

cond-mat.soft↗

arXiv2017

Shear modulus and shear-stress fluctuations in polymer glasses

Using molecular dynamics simulation of a standard coarse-grained polymer glass model we investigate by means of the stress-fluctuation formalism the shear modulus $μ$ as a function of temperature $T$ and sampling time $Δt$. While the ensemble-averaged modulus $μ(T)$ is found to decrease continuously for all $Δt$ sampled, its standard deviation $δμ(T)$ is non-monotonous with a striking peak at the glass transition. Confirming the effective time-translational invariance of our systems, $μ(Δt)$ can be understood using a weighted integral over the shear-stress relaxation modulus $G(t)$. While the crossover of $μ(T)$ gets sharper with increasing $Δt$, the peak of $δμ(T)$ becomes more singular. % It is thus elusive to predict the modulus of a single configuration at the glass transition.

cond-mat.soft↗

arXiv2016

Shear-stress fluctuations in self-assembled transient elastic networks

Focusing on shear-stress fluctuations we investigate numerically a simple generic model for self-assembled transient networks formed by repulsive beads reversibly bridged by ideal springs. With $Δdt$ being the sampling time and $t_*(f) \sim 1/f$ the Maxwell relaxation time (set by the spring recombination frequency $f$) the dimensionless parameter $Δx = dt/t_*(f)$ is systematically scanned from the liquid limit ($Δdx \gg 1)$ to the solid limit ($Δx \ll 1$) where the network topology is quenched and an ensemble average over $m$ independent configurations is required. Generalizing previous work on permanent networks it is shown that the shear-stress relaxation modulus $G(t)$ may be efficiently determined for all $Δx$ using the simple-average expression $G(t) = μ_A - h(t)$ with $μ_A = G(0)$ characterizing the canonical-affine shear transformation of the system at $t=0$ and $h(t)$ the (rescaled) mean-square displacement of the instantaneous shear stress as a function of time $t$. This relation is compared to the standard expression $G(t) = C(t)$ using the (rescaled) shear-stress autocorrelation function $C(t)$. Lower bounds for the $m$ configurations required by both relations are given.

cond-mat.stat-mech↗

arXiv2015

Shear-strain and shear-stress fluctuations in generalized Gaussian ensemble simulations of isotropic elastic networks

Shear-strain and shear-stress correlations in isotropic elastic bodies are investigated both theoretically and numerically at either imposed mean shear-stress $τ$ ($λ=0$) or shear-strain $γ$ ($λ=1$) and for more general values of a dimensionless parameter $λ$ characterizing the generalized Gaussian ensemble. It allows to tune the strain fluctuations $μ_{γγ} \equiv βV \la δγ^2 \ra = (1-λ)/G_{eq}$ with $β$ being the inverse temperature, $V$ the volume, $γ$ the instantaneous strain and $G_{eq}$ the equilibrium shear modulus. Focusing on spring networks in two dimensions we show, e.g., for the stress fluctuations $μ_{ττ} \equiv βV \la δτ^2 \ra$ ($τ$ being the instantaneous stress) that $μ_{ττ} = μ_{A} - λG_{eq}$ with $μ_{A} = μ_{ττ}|_{λ=0}$ being the affine shear-elasticity. For the stress autocorrelation function $c_{ττ}(t) \equiv βV \la δτ(t) δτ(0) \ra$ this result is then seen (assuming a sufficiently slow shear-stress barostat) to generalize to $c_{ττ}(t) = G(t) - λ\Geq$ with $G(t)$ being the shear-stress relaxation modulus.

cond-mat.stat-mech↗