L. L. Gonçalves

Relaxation in kinetic models on alternating linear chains.

A restricted dynamics, previously introduced in a kinetic model for relaxation phenomena in linear polymer chains, is used to study the dynamic critical exponent of one-dimensional Ising models. Both an alternating isotopic chain and an alternating-bond chain are considered. In contrast with what occurs for Glauber dynamics, in these two models the dynamic critical exponent turns out to be the same. The alternating isotopic chain with the restricted dynamics is shown to lead to Nagel scaling for temperatures above some critical value. Further support is given relating the Nagel scaling to the existence of multiple (simultaneous) relaxation processes, the dynamics apparently not playing the most important role in determining such scaling.

Nagel scaling and relaxation in the kinetic Ising model on an n-isotopic chain

The kinetic Ising model on an n-isotopic chain is considered in the framework of Glauber dynamics. The chain is composed of N segments with n sites, each one occupied by a different isotope. Due to the isotopic mass difference, the n spins in each segment have different relaxation times in the absence of interactions, and consequently the dynamics of the system is governed by multiple relaxation mechanisms. The solution is obtained in closed form for arbitrary n, by reducing the problem to a set of n coupled equations, and it is shown rigorously that the critical exponent z is equal to 2. Explicit results are obtained numerically for any temperature and it is also shown that the dynamic susceptibility satisfies the new scaling (Nagel scaling) proposed for glass-forming liquids. This is in agreement with our recent results (L. L. Goncalves, M. Lopez de Haro, J. Taguena-Martinez and R. B. Stinchcombe, Phys. Rev. Lett. 84 , 1507 (2000)), which relate this new scaling function to multiple relaxation processes.

A simple model for relaxation phenomena in linear polymer chains

A quasi one-dimensional kinetic Ising-like model is developed to study relaxation phenomena in linear polymer chains. In the case where the number N of bonds in the chain is very large, the model Hamiltonian reduces to the one giving the intramolecular energy of the Gibbs-di Marzio lattice model. The equations governing the dynamics of the different correlation functions are derived for this model and used to study relaxation phenomena in the system in the long-chain limit. First, the dielectric response where two cases are considered, namely, a single dipole placed in the middle of the chain and N non-interacting dipoles. In both cases a Debye behaviour is obtained. The effect of the temperature is introduced by considering a temperature-dependent relaxation time and surprisingly good agreement between the temperature dependence of the frequency of the maximum of the loss curve as computed with the model and experimental data of PMA and PVAC is obtained. Second, the relaxational heat capacity is analogously calculated; in this case, however, although the parameters used in the actual computations correspond to PMA and PVAC, respectively, no comparison with actual experimental results was feasible. One finds that here the behaviour is not Debye and no simple universality arises from the theoretical predictions.

RELAXATIONAL HEAT CAPACITY AND UNIVERSALITY IN LINEAR POLYMER CHAINS

The relaxational heat capacity of an infinite linear polymer chain is computed. The result is derived within a kinetic Ising-like model previously introduced to provide for a dynamical generalization of the Gibbs-di Marzio lattice model. The questions of universality of the dynamic responses of the chain and of the existence of more than one relaxation time if one considers different probes are discussed.

Relaxation in The Kinetic Ising Model on The Periodic Inhomogeneous Chain

The kinetic Ising model on an inhomogeneous periodic chain, which is composed of N segments with n different bonds, is considered. The model is studied within the Glauber dynamics and the restricted dynamics introduced by the authors for the description of relaxation phenomena in linear polymer chains, and it corresponds to an extension of the alternating bond model and the n-isotopic model. For both dynamics, the solution of the model may be obtained exactly for arbitrary