Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userElasticity of highly cross-linked random networks
74
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Starting from a microscopic model of randomly cross-linked particles with quenched disorder, we calculate the Laudau-Wilson free energy S for arbitrary cross-link densities. Considering pure shear deformations, S takes the form of the elastic energy of an isotropic amorphous solid state, from which the shear modulus can be identified. It is found to be an universal quantity, not depending on any microscopic length-scales of the model.
rate research
Read More
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.
Assemblies of purely repulsive and frictionless particles, such as emulsions or hard spheres, display very curious properties near their jamming transition, which occurs at the random close packing for mono-disperse spheres. Although such systems do not contain the long and cross-linked polymeric chains characterizing a rubber, they behave macroscopically in a similar way: the shear modulus $G$ can become infinitely smaller than the bulk modulus $B$. After reviewing recent theoretical results on the structure of such packing (in particular their coordination) I will propose an explanation for the observed scaling of the elastic moduli, and explain why the arguments both apply to soft and hard particles.
We have made experimental observations of the force networks within a two-dimensional granular silo similar to the classical system of Janssen. Models like that of Janssen predict that pressure within a silo saturates with depth as the result of vertical forces being redirected to the walls of the silo where they can then be carried by friction. By averaging ensembles of experimentally-obtained force networks in different ways, we compare the observed behavior with various predictions for granular silos. We identify several differences between the mean behavior in our system and that predicted by Janssen-like models: We find that the redirection parameter describing how the force network transfers vertical forces to the walls varies with depth. We find that changes in the preparation of the material can cause the pressure within the silo to either saturate or to continue building with depth. Most strikingly, we observe a non-linear response to overloads applied to the top of the material in the silo. For larger overloads we observe the previously reported giant overshoot effect where overload pressure decays only after an initial increase [G. Ovarlez et al., Phys. Rev. E 67, 060302(R) (2003)]. For smaller overloads we find that additional pressure propagates to great depth. This effect depends on the particle stiffness, as given for instance by the Youngs modulus, E, of the material from which the particles are made. Important measures include E, the unscreened hydrostatic pressure, and the applied load. These experiments suggest that when the load and the particle weight are comparable, particle elasticity acts to stabilize the force network, allowing non-linear network effects to be seen in the mean behavior.
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.
We suggest a simple model for reversible cross-links, binding and unbinding to/from a network of semiflexible polymers. The resulting frequency dependent response of the network to an applied shear is calculated via Brownian dynamics simulations. It is shown to be rather complex with the timescale of the linkers competing with the excitations of the network. If the lifetime of the linkers is the longest timescale, as is indeed the case in most biological networks, then a distinct low frequency peak of the loss modulus develops. The storage modulus shows a corresponding decay from its plateau value, which for irreversible cross-linkers extends all the way to the static limit. This additional relaxation mechanism can be controlled by the relative weight of reversible and irreversible linkers.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
