Attractors for multi-valued lattice dynamical systems with nonlinear diffusion terms

This paper is devoted to the long-term behavior of nonautonomous random lattice dynamical systems with nonlinear diffusion terms. The nonlinear drift and diffusion terms are not expected to be Lipschitz continuous but satisfy the continuity and growth conditions. We first prove the existence of solutions, and establish the existence of a multi-valued nonautonomous cocycle. We then show the existence and uniqueness of pullback attractors parameterized by sample parameters. Finally, we establish the measurability of this pullback attractor by the method based on the weak upper semicontinuity of the solutions.

Modelling Sorption Thermodynamics and Mass Transport of n-Hexane in a Propylene-Ethylene Elastomer

Optimization of post polymerization processes of polyolefin elastomers (POE) involving solvents is of considerable industrial interest. To this aim, experimental determination and theoretical interpretation of the thermodynamics and mass transport properties of POE-solvent mixtures is relevant. Sorption behavior of n-hexane vapor in a commercial propylene-ethylene elastomer (V8880 VistamaxxTM from ExxonMobil, Machelen, Belgium) is addressed here, determining experimentally the sorption isotherms at temperatures ranging from 115 to 140 °C and pressure values of n-hexane vapor up to 1 atm. Sorption isotherms have been interpreted using a Non Random Lattice Fluid (NRLF) Equation of State model retrieving, from data fitting, the value of the binary interaction parameter for the n-hexane/V8880 system. Both the cases of temperature-independent and of temperature-dependent binary interaction parameter have been considered. Sorption kinetics was also investigated at different pressures and has been interpreted using a Fick’s model determining values of the mutual diffusivity as a function of temperature and of n-hexane/V8880 mixture composition. From these values, n-hexane intra-diffusion coefficient has been calculated interpreting its dependence on mixture concentration and temperature by a semi-empiric model based on free volume arguments.

DNA thermal denaturation by polymer field theory approach: effects of the environment

We analyse the effects of the environment (solvent quality, presence of extended structures - crowded environment) that may have impact on the order of the transition between denaturated and bounded DNA states and lead to changes in the scaling laws that govern conformational properties of DNA strands. We find that the effects studied significantly influence the strength of the first order transition. To this end, we re-consider the Poland-Scheraga model and apply a polymer field theory to calculate entropic exponents associated with the denaturated loop distribution. For the d = 3 case, the corresponding diverging ε = 4-d expansions are evaluated by restoring their convergence via the resummation technique. For the space dimension d = 2, the exponents are deduced from mapping the polymer model onto a two-dimensional random lattice, i.e., in the presence of quantum gravity. We also show that the first order transition is further strengthened by the presence of extended impenetrable regions in a solvent that restrict the number of the macromolecule configurations.

A classical density functional theory model for fragility in the hard-sphere limit

We study, using the classical density functional theory (DFT), the fragility and short-time elastic constants of a soft-sphere liquid. For the amorphous state, the order parameter is the inhomogeneous density function $\rho({\bf r})$ which is described in terms of Gaussian density profiles centered on a set random lattice points $\{{\bf R}_i\}$. The latter is characterized in terms of the Bernel pair function $g_\mathrm{B}(r)$. Based on the Adam–Gibbs-type relation between the $\alpha$ relaxation time $\tau_\alpha$ and the configurational entropy $\mathcal{S}_{\rm c}$, a thermodynamic fragility $m_\mathrm{T}$ for the liquid is defined. The concentration or average density of the liquid is treated as the control parameter here instead of temperature. The configurational entropy of the liquid is calculated using the DFT model. Variations in the short-range structure of the amorphous state are made with different choices for the value of $g_\mathrm{B}(r)$ at short distances, and its implications on the correlation between fragility $m_\mathrm{T}$ and the softness index $n$ are studied. The dependence of Poisson’s ratio $\nu$ on the softness index $n$ of the interaction potential is also obtained from the density dependence of the metastable state free energy. The correlation between $m_\mathrm{T}$ and $\nu$ follows.