The bond rupture force for sulfur chains calculated from quantum chemistry simulations and its relevance to the tensile strength of vulcanized rubber.

From quantum chemistry simulations using density functional theory, we obtain the total electronic energy of an eight-atom sulfur chain as its end-to-end distance is extended until S-S bond rupture occurs. We find that a sulfur chain can be extended by about 40% beyond its nominally straight conformation, where it experiences rupture at an end-to-end tension of about 1.5 nN. Using this rupture force as the chain failure limit in an explicit polymer network simulation model (EPnet), we predict the tensile failure stress for sulfur crosslinked (vulcanized) natural rubber. Quantitative agreement with published experimental data for the failure stress is obtained in these simulations if we assume that only about 30% of the sulfur chains produce viable network crosslinks. Surprisingly, we also find that the failure stress of a rubber network does not scale linearly with the chain failure force limit.

The entropy of the rotational conformations of (poly)isoprene molecules and its relationship to rubber elasticity and temperature increase for moderate tensile or compressive strains.

Molecular networks comprised of crosslinked cis-1,4 polyisoprene, often referred to as "natural rubber," are one of the most common systems for the study of rubber elasticity. Under moderate tensile or compressive strain, network chains begin to assume straighter paths, as local molecular kinks are removed. Isoprene units along the chain backbone are mechanically forced from their equilibrium distributions of 18 possible rotational states into a smaller subset of states, restricted to more linear conformations with the greatest end-to-end distances. There are two consequences to this change: both the configurational entropy and average internal energy decrease. We find that the change in entropy, and resulting change in free energy, gives rise to an elastic force. We derive an expression for a chain extension force constant that we have incorporated in an explicit, three-dimensional meso-scale network simulation code. Using this force model, our simulations predict a macroscopic stress-strain relationship that closely matches published experimental values. We also predict a slight increase in temperature resulting from the change in average internal energy in the affected isoprene units that is consistent with experiments.

Atomistic methods in fluid simulation.

Atomistic methods, such as molecular dynamics and direct simulation Monte Carlo, constitute a powerful and growing set of techniques for fluid-dynamics simulation. The more fundamental nature of such methods, which exhibit nonlinear transport effects and small-scale fluctuations, extends their modelling accuracy to a significantly wider range of scales and regimes than the more traditional Navier-Stokes-based continuum fluid-simulation techniques. In this paper, we describe the current state of the art in atomistic fluid simulation, from both a theoretical and a computational standpoint, and outline the advantages and limitations of such methods. In addition, we present an overview of some recent atomistic-simulation results on fluid instabilities and on the physical scaling of atomistic techniques. Finally, we suggest possible avenues of future research in the field.

Scaling of atomistic fluid dynamics simulations.

We have performed a series of large-scale atomistic simulations of the Rayleigh-Taylor instability including up to 5.7 x 10(9) particles and spanning time and length scales of up to 170 ns and 45 microm , respectively. The results suggest that atomistic fluid dynamics simulations exhibit the same scaling as solutions of the continuum Navier-Stokes equations. Furthermore, a comparison with macroscopic Rayleigh-Taylor experiments suggests that the results of such atomistic simulations can, in fact, be scaled up to macroscopic dimensions, even for complex, nonstationary flows.

The importance of fluctuations in fluid mixing.

A ubiquitous example of fluid mixing is the Rayleigh-Taylor instability, in which a heavy fluid initially sits atop a light fluid in a gravitational field. The subsequent development of the unstable interface between the two fluids is marked by several stages. At first, each interface mode grows exponentially with time before transitioning to a nonlinear regime characterized by more complex hydrodynamic mixing. Unfortunately, traditional continuum modeling of this process has generally been in poor agreement with experiment. Here, we indicate that the natural, random fluctuations of the flow field present in any fluid, which are neglected in continuum models, can lead to qualitatively and quantitatively better agreement with experiment. We performed billion-particle atomistic simulations and magnetic levitation experiments with unprecedented control of initial interface conditions. A comparison between our simulations and experiments reveals good agreement in terms of the growth rate of the mixing front as well as the new observation of droplet breakup at later times. These results improve our understanding of many fluid processes, including interface phenomena that occur, for example, in supernovae, the detachment of droplets from a faucet, and ink jet printing. Such instabilities are also relevant to the possible energy source of inertial confinement fusion, in which a millimeter-sized capsule is imploded to initiate nuclear fusion reactions between deuterium and tritium. Our results suggest that the applicability of continuum models would be greatly enhanced by explicitly including the effects of random fluctuations.