Heterogeneous Dynamics and Polymer Plasticity

St. Petersburg Paradox and Failure Probability

The St. Petersburg paradox provides a simple paradigm for systems that show sensitivity to rare events. Here, we demonstrate a physical realization of this paradox using tensile fracture, experimentally verifying for six decades of spatial and temporal data and two different materials that the fracture force depends logarithmically on the length of the fiber. The St. Petersburg model may be useful in a variety fields where failure and reliability are critical.

Natural rubber-SiO2 nanohybrids: interface structures and dynamics

Homogeneous dispersion of silica nanoparticles (SiO₂ NPs) in natural rubber (NR) is a key challenge for engineering high-performance nanocomposites and elucidation of their structure on a molecular basis. Towards this, the present work devised a novel route for obtaining 3D self-assembled SiO₂ NP-NR nanocomposites under aqueous conditions and in the presence of Mg²⁺, by establishing a molecular bridge that clamped the negatively charged NR and SiO₂ colloidal particles with a favoured NR-SiO₂ NP hetero-aggregation. The characteristic NR-SiO₂ NP hetero-aggregates displayed a decreased heat capacity with increase in the SiO₂ mass-fraction, implying a restricted NR chain mobility. Such changes in the interfacial layers were tapped by ²⁹Si NMR, DFT calculations and molecular dynamics simulations towards a mechanistic understanding of the structure and dynamics of the NR/SiO₂ NP hybrid. Simple models were used to illustrate basic ideas; specific electrostatic interactions such as ion-dipole and H-bonding interactions proved to be the driving forces for the organized assembly leading to the NR-SiO₂ hetero-aggregate over the NR-NR or SiO₂ NP-SiO₂ NP homo-aggregate. Molecular dynamics simulation of the aqueous canonical ensemble of the hybrid showed the stable molecular conformation to reveal a SiO₂ NP spherical core encapsulated by a hydrophobically interconnected NR polymer layer as the outer shell, as a unique structural model. Specifically, the lipid end of the NR was involved electrostatically while the lysine end (the protein part of NR) H-bonded to the core silica cluster thereby restricting random aggregation. The calculated negative free energy changes for the hetero-aggregate composites via their vibrational and rotational spectra proved the spontaneity of composite formation.

Thermalization of plastic flow versus stationarity of thermomechanical equilibrium in SGR theory

We discuss issues related to thermalization of plastic flow in the context of soft glassy rheology (SGR) theory. An apparent problem with the theory in its current form is that the stationarity of thermomechanical equilibrium obtained by requiring that its flow rule satisfy detailed balance in the absence of applied deformation requires plastic flow to be athermal. This prevents proper application of SGR to small-molecule and polymer glasses where plastic flow is often well thermalized. Clearly, one would like to have a SGR-like theory of thermalized plastic flow that satisfies stationarity. We discuss reasons why such a theory could prove very useful and clarify obstacles that must be overcome in order to develop it.

Thermalized formulation of soft glassy rheology

We present a version of soft glassy rheology that includes thermalized strain degrees of freedom. It fully specifies systems' strain-history-dependent positions on their energy landscapes and therefore allows for quantitative analysis of their heterogeneous yielding dynamics and nonequilibrium deformation thermodynamics. As a demonstration of the method, we illustrate the very different characteristics of fully thermal and nearly athermal plasticity by comparing results for thermalized and nonthermalized plastic flow.

Dynamical heterogeneities and mechanical non-linearities: Modeling the onset of plasticity in polymer in the glass transition

In this paper we focus on the role of dynamical heterogeneities on the non-linear response of polymers in the glass transition domain. We start from a simple coarse-grained model that assumes a random distribution of the initial local relaxation times and that quantitatively describes the linear viscoelasticity of a polymer in the glass transition regime. We extend this model to non-linear mechanics assuming a local Eyring stress dependence of the relaxation times. Implementing the model in a finite element mechanics code, we derive the mechanical properties and the local mechanical fields at the beginning of the non-linear regime. The model predicts a narrowing of distribution of relaxation times and the storage of a part of the mechanical energy --internal stress-- transferred to the material during stretching in this temperature range. We show that the stress field is not spatially correlated under and after loading and follows a Gaussian distribution. In addition the strain field exhibits shear bands, but the strain distribution is narrow. Hence, most of the mechanical quantities can be calculated analytically, in a very good approximation, with the simple assumption that the strain rate is constant.