Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userScaling of dynamical susceptibility at the onset of rigidity for disordered viscoelastic matter
152
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The onset of rigidity in interacting liquids, as they undergo a transition to a disordered solid, is associated with a dramatic rearrangement of the low-frequency vibrational spectrum. In this letter, we derive scaling forms for the singular dynamical response of disordered viscoelastic networks near both jamming and rigidity percolation. Using effective-medium theory, we extract critical exponents, invariant scaling combinations and analytical formulas for universal scaling functions near these transitions. Our scaling forms describe the behavior in space and time near the various onsets of rigidity, for rigid and floppy phases and the crossover region, including diverging length and time scales at the transitions. We expect that these behaviors can be measured in systems ranging from colloidal suspensions to anomalous charge-density fluctuations of strange metals.
rate research
Read More
Due to their unique structural and mechanical properties, randomly-crosslinked polymer networks play an important role in many different fields, ranging from cellular biology to industrial processes. In order to elucidate how these properties are controlled by the physical details of the network (textit{e.g.} chain-length and end-to-end distributions), we generate disordered phantom networks with different crosslinker concentrations $C$ and initial density $rho_{rm init}$ and evaluate their elastic properties. We find that the shear modulus computed at the same strand concentration for networks with the same $C$, which determines the number of chains and the chain-length distribution, depends strongly on the preparation protocol of the network, here controlled by $rho_{rm init}$. We rationalise this dependence by employing a generic stress-strain relation for polymer networks that does not rely on the specific form of the polymer end-to-end distance distribution. We find that the shear modulus of the networks is a non-monotonic function of the density of elastically-active strands, and that this behaviour has a purely entropic origin. Our results show that if short chains are abundant, as it is always the case for randomly-crosslinked polymer networks, the knowledge of the exact chain conformation distribution is essential for predicting correctly the elastic properties. Finally, we apply our theoretical approach to published experimental data, qualitatively confirming our interpretations.
Disordered biopolymer gels have striking mechanical properties including strong nonlinearities. In the case of athermal gels (such as collagen-I) the nonlinearity has long been associated with a crossover from a bending dominated to a stretching dominated regime of elasticity. The physics of this crossover is related to the existence of a central-force isostatic point and to the fact that for most gels the bending modulus is small. This crossover induces scaling behavior for the elastic moduli. In particular, for linear elasticity such a scaling law has been demonstrated [Broedersz et al. Nature Physics, 2011 7, 983]. In this work we generalize the scaling to the nonlinear regime with a two-parameter scaling law involving three critical exponents. We test the scaling law numerically for two disordered lattice models, and find a good scaling collapse for the shear modulus in both the linear and nonlinear regimes. We compute all the critical exponents for the two lattice models and discuss the applicability of our results to real systems.
The disordered microphases that develop in the high-temperature phase of systems with competing short-range attractive and long-range repulsive (SALR) interactions result in a rich array of distinct morphologies, such as cluster, void cluster and percolated (gel-like) fluids. These different structural regimes exhibit complex relaxation dynamics with significant relaxation heterogeneity and slowdown. The overall relationship between structure and configurational sampling schemes, however, remains largely uncharted. In this article, the disordered microphases of a schematic SALR model are thoroughly characterized, and structural relaxation functions adapted to each regime are devised. The sampling efficiency of various advanced Monte Carlo (MC) sampling schemes--Virtual-Move (VMMC), Aggregation-Volume-Bias (AVBMC) and Event-Chain (ECMC)--is then assessed. A combination of VMMC and AVBMC is found to be computationally most efficient for cluster fluids and ECMC to become relatively more efficient as density increases. These results offer a complete description of the equilibrium disordered phase of a simple microphase former as well as dynamical benchmarks for other sampling schemes.
Athermal systems across a large range of length scales, ranging from foams and granular bead packings to crumpled metallic sheets, exhibit slow stress relaxation when compressed. Experimentally they show a non-monotonic stress response when decompressed somewhat after an initial compression, i.e. under a two-step, Kovacs-like protocol. It turns out that from this response one can tell the age of the system, suggesting an interpretation as a memory effect. In this work we use a model of an athermal jammed solid, specifically a binary mixture of soft harmonic spheres, to explore this phenomenon through in-silico experiments. Using extensive simulations under conditions analogous to those in experiment, we observe identical phenomenology in the stress response under a two--step protocol. Our model system also recovers the behaviour under a more recently studied three-step protocol, which consists of a compression followed by a decompression and then a final compression. We show that the observed response in both two-step and three-step protocols can be understood using Linear Response Theory. In particular, a linear scaling with age for the two-step protocol arises generically for slow linear responses with power law or logarithmic decay and does not in itself point to any underlying aging dynamics.
Dynamical heterogeneities -- strong fluctuations near the glass transition -- are believed to be crucial to explain much of the glass transition phenomenology. One possible hypothesis for their origin is that they emerge from soft (Goldstone) modes associated with a broken continuous symmetry under time reparametrizations. To test this hypothesis, we use numerical simulation data from four glass-forming models to construct coarse grained observables that probe the dynamical heterogeneity, and decompose the fluctuations of these observables into two transverse components associated with the postulated time-fluctuation soft modes and a longitudinal component unrelated to them. We find that as temperature is lowered and timescales are increased, the time reparametrization fluctuations become increasingly dominant, and that their correlation volumes grow together with the correlation volumes of the dynamical heterogeneities, while the correlation volumes for longitudinal fluctuations remain small.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
