On the One-Dimensional Transition State Theory and the Relation between Statistical and Deterministic Oscillation Frequencies of Anharmonic Energy Wells

The transition state theory allows the development of approximated models useful to study the non-equilibrium evolution of systems undergoing transformations between two states (e.g., chemical reactions). In a simplified 1D setting, the characteristic rate constants are typically written in terms of a temperature-dependent characteristic oscillation frequency ${\nu }_s$, describing the exploration of the phase space. As a particular case, this statistical oscillation frequency ${\nu }_s$ can be defined for an arbitrary convex potential energy well. This value is compared here with the deterministic oscillation frequency ${\nu }_d$ of the corresponding anharmonic oscillator. It is proved that there is a universal relationship between statistical and deterministic frequencies, which is the same for classical and relativistic mechanics. The independence of this relationship from the adopted physical laws gives it an interesting thermodynamic and pedagogical meaning. Several examples clarify the meaning of this relationship from both physical and mathematical viewpoints.     

Thermorheological Simplicity and Fragility of Azobenzene Nematogenic Side-Chain Polymers

Summary: The linear viscoelastic response of polymers from a nematogenic azobenzene methacrylate and its copolymers with nonmesogenic methyl methacrylate was studied. These samples showed thermorheological simplicity in the whole investigated temperature range, even across the nematic-isotropic transition. The temperature dependence of the zero-shear viscosity confirmed a thermorheologically simple behavior, which allowed interpretation of η(T) in the framework of free-volume theory. The way the relaxation mechanisms tended to their asymptotic behavior was described in terms of fragility parameters, and a comparison of fragilities of the samples was carried out. The analysis of fragility and temperature dependence of viscosity provided better understanding of the way the architecture of these nematic polymers influences free-volume quantities and determines relaxation mechanisms.