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Applications of commodity polymers are often hindered by their low thermal conductivity. In these systems, going from the standard polymers dictated by weak van der Waals interactions to biocompatible hydrogen bonded smart polymers, the thermal transport coefficient k varies between 0.1 - 0.4 W/Km. Combining all-atom molecular dynamics simulations with some experiments, we study thermal transport and its link to the elastic response of commodity plastics. We find that there exists a maximum attainable stiffness (or sound wave velocity), thus providing an upper bound of k for these solid polymers. The specific chemical structure and the glass transition temperature play no role in controlling k, especially when the microscopic interactions are hydrogen bonding based. Our results are consistent with the minimum thermal conductivity model and existing experiments. The effect of polymer stretching on k is also discussed.
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We study the phenomenon of migration of the small molecular weight component of a binary polymer mixture to the free surface using mean field and self-consistent field theories. By proposing a free energy functional that incorporates polymer-matrix elasticity explicitly, we compute the migrant volume fraction and show that it decreases significantly as the sample rigidity is increased. Estimated values of the bulk modulus suggest that the effect should be observable experimentally for rubber-like materials. This provides a simple way of controlling surface migration in polymer mixtures and can play an important role in industrial formulations, where surface migration often leads to decreased product functionality.
Descriptors that characterize the geometry and topology of the pore space of porous media are intimately linked to their transport properties. We quantify such descriptors, including pore-size functions and the critical pore radius $delta_c$, for four different models: maximally random jammed sphere packings, overlapping spheres, equilibrium hard spheres, and inherent structures of the quantizer energy. For precise estimates of the percolation thresholds, we use a strict relation of the void percolation around sphere configurations to weighted bond percolation on the corresponding Voronoi networks. We use the Newman-Ziff algorithm to determine the percolation threshold using universal properties of the cluster size distribution. Often, $delta_c$ is used as the key characteristic length scale that determines the fluid permeability $k$. A recent study [Torquato. Adv. Wat. Resour. 140, 103565 (2020)] suggested for porous media with a well-connected pore space an alternative estimate of $k$ based on the second moment of the pore size $langledelta^2rangle$. Here, we confirm that, for all porosities and all models considered, $delta_c^2$ is to a good approximation proportional to $langledelta^2rangle$. However, unlike $langledelta^2rangle$, the permeability estimate based on $delta_c^2$ does not predict the correct ranking of $k$ for our models. Thus, we confirm $langledelta^2rangle$ to be a promising candidate for convenient and reliable estimates of $k$ for porous media with a well-connected pore space. Moreover, we compare the fluid permeability of our models with varying degrees of order, as measured by the $tau$ order metric. We find that (effectively) hyperuniform models tend to have lower values of $k$ than their nonhyperuniform counterparts. Our findings could facilitate the design of porous media with desirable transport properties via targeted pore statistics.
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.
Thermal and other transport coefficients were recently shown to be largely independent of the microscopic representation of the energy (current) densities or, more generally, of the relevant conserved densities/currents. In this paper we show how this gauge invariance, which is intimately related to the intrinsic indeterminacy of the energy of isolated atoms, can be exploited to optimize the statistical properties of the current time series from which the transport coefficients can be evaluated. To this end, we make use of a variational principle that relies on the metric properties of the conserved currents, treated as elements of an abstract linear space. Different metrics would result in different variational principles. We finally show how a recently proposed data-analysis methodology based on the theory of transport in multi-component systems can be recovered by a suitable choice of this metric.
The holographic principle has proven successful in linking seemingly unrelated problems in physics; a famous example is the gauge-gravity duality. Recently, intriguing correspondences between the physics of soft matter and gravity are emerging, including strong similarities between the rheology of amorphous solids, effective field theories for elasticity and the physics of black holes. However, direct comparisons between theoretical predictions and experimental/simulation observations remain limited. Here, we study the effects of non-linear elasticity on the mechanical and thermodynamic properties of amorphous materials responding to shear, using effective field and gravitational theories. The predicted correlations among the non-linear elastic exponent, the yielding strain/stress and the entropy change due to shear are supported qualitatively by simulations of granular matter models. Our approach opens a path towards understanding complex mechanical responses of amorphous solids, such as mixed effects of shear softening and shear hardening, and offers the possibility to study the rheology of solid states and black holes in a unified framework.
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