2016/06/20 by J. P. Wittmer, Ivan Kriuchevskyi, I. Kriuchevskyi +5
Materials Science · Mathematics · Physics and Astronomy · #Combinatorics #Dimensionless quantity #Material Dynamics and Properties #Mathematical physics #Mathematics #Physics #Polymer Nanocomposites and Properties #Polymer composites and self-healing #Quantum mechanics #Shear modulus #Thermodynamics #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.93.062611
published as PRE 93, 062611 (2016) · 12 pages, 11 figures
openalex publication_date 2016/06/20 · arxiv created 2016/06/21 · arxiv updated 2016/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 \mathrm\ensuremathΔt being the sampling time and t_\ensuremath⋆(f)\ensuremath∼1/f the Maxwell relaxation time (set by the spring recombination frequency f), the dimensionless parameter \mathrm\ensuremathΔx=\mathrm\ensuremathΔt/t_\ensuremath⋆(f) is systematically scanned from the liquid limit (\mathrm\ensuremathΔx\ensuremath≫1) to the solid limit (\mathrm\ensuremathΔx\ensuremath≪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 \mathrm\ensuremathΔx using the simple-average expression G(t)=\ensuremathμA\ensuremath-h(t) with \ensuremathμA=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)=\stackrel\ifmmode \else \~\fic(t) using the (rescaled) shear-stress autocorrelation function \stackrel\ifmmode \else \~\fic(t). Lower bounds for the m configurations required by both relations are given.