arXiv subjects

O. Benzerara

Publications and source records attributed to O. Benzerara.

4 recordsLinked to original sources

arXiv2022

Marginally compact hyperbranched polymer trees

Assuming Gaussian chain statistics along the chain contour, we generate by means of a proper fractal generator hyperbranched polymer trees which are marginally compact. Static and dynamical properties, such as the radial intrachain pair density distribution or the shear-stress relaxation modulus, are investigated theoretically and by means of computer simulations. We emphasize that albeit the self-contact density diverges logarithmically with the total mass $N$, this effect becomes rapidly irrelevant with increasing spacer length $S$. In addition to this it is seen that the standard Rouse analysis must necessarily become inappropriate for compact objects for which the relaxation time $τ_p$ of mode $p$ must scale as $τ_p \sim (N/p)^{5/3}$ rather than the usual square power law for linear chains.

cond-mat.soft↗

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↗

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↗

arXiv2015

Fluctuation-dissipation relation between shear stress relaxation modulus and shear stress autocorrelation function revisited

The shear stress relaxation modulus $G(t)$ may be determined from the shear stress $τ(t)$ after switching on a tiny step strain $γ$ or by inverse Fourier transformation of the storage modulus $G^{\prime}(ω)$ or the loss modulus $G^{\prime\prime}(ω)$ obtained in a standard oscillatory shear experiment at angular frequency $ω$. It is widely assumed that $G(t)$ is equivalent in general to the equilibrium stress autocorrelation function $C(t) = βV \langle δτ(t) δτ(0)\rangle$ which may be readily computed in computer simulations ($β$ being the inverse temperature and $V$ the volume). Focusing on isotropic solids formed by permanent spring networks we show theoretically by means of the fluctuation-dissipation theorem and computationally by molecular dynamics simulation that in general $G(t) = G_{eq} + C(t)$ for $t > 0$ with $G_{eq}$ being the static equilibrium shear modulus. A similar relation holds for $G^{\prime}(ω)$. $G(t)$ and $C(t)$ must thus become different for a solid body and it is impossible to obtain $G_{eq}$ directly from $C(t)$.

cond-mat.stat-mech↗