Viscoelastic Effects on the Response of Electroelastic Materials.

Electroelastic materials, as for example, 3M VHB 4910, are attracting attention as actuators or generators in some developments and applications. This is due to their capacity of being deformed when submitted to an electric field. Some models of their actuation are available, but recently, viscoelastic models have been proposed to give an account of the dissipative behaviour of these materials. Their response to an external mechanical or electrical force field implies a relaxation process towards a new state of thermodynamic equilibrium, which can be described by a relaxation time. However, it is well known that viscoelastic and dielectric materials, as for example, polymers, exhibit a distribution of relaxation times instead of a single relaxation time. In the present approach, a continuous distribution of relaxation times is proposed via the introduction of fractional derivatives of the stress and strain, which gives a better account of the material behaviour. The application of fractional derivatives is described and a comparison with former results is made. Then, a double generalisation is carried out: the first one is referred to the viscoelastic or dielectric models and is addressed to obtain a nonsymmetric spectrum of relaxation times, and the second one is the adoption of the more realistic Mooney-Rivlin equation for the stress-strain relationship of the elastomeric material. A modified Mooney-Rivlin model for the free energy density of a hyperelastic material, VHB 4910 has been used based on experimental results of previous authors. This last proposal ensures the appearance of the bifurcation phenomena which is analysed for equibiaxial dead loads; time-dependent bifurcation phenomena are predicted by the extended Mooney-Rivlin equations.

On the nonlinear behaviour of nematic single crystal elastomers under biaxial mechanic and electrical force fields.

A slab of nematic-side-chain-liquid-single-crystal elastomer (NSCLSCE), with the director initially oriented in the z -direction, is subjected to a pair of equal mechanical loads and electrical force fields in the x , y directions. The electric fields tend to make easier the rotation of the director after the application of the mechanical force field. A nonlinear expression for the free energy density is used to obtain the interval of stretching for which the system becomes unstable. However, the elastic energy of the network is assumed to be linear. The stress-strain curves predicted by the model show an unstable zone between two linearly increasing segments. The possibility of bifurcation phenomena has been examined.

Retardation time spectra computed from complex compliance functions.

This work describes the calculation of retardation time spectra by minimization of the square of the differences between experimental compliance results and those recalculated from the spectra. Spectra were computed taking analytical complex dielectric results as the basis of the minimization process. Comparison of the spectra computed from both the complex dielectric permittivity and the dielectric loss with those calculated analytically shows that minimization methods based on complex dielectric permittivity data are more accurate than those based only on loss dielectric results.

Influence of structural chemical characteristics on polymer chain dynamics.

A comparative study of the dielectric relaxation behavior of two structurally close polymers containing aliphatic-aromatic side groups was carried out in order to get a better understanding on how slight differences in chemical structure affect the molecular responses to perturbation fields. Specifically, chain dynamics of poly(2-acryloyloxyethyl-2-naphthalene-2-ylacetate) and poly(2-methacryloyloxyethyl-2-naphthalene-2-ylacetate) were studied by broadband dielectric spectroscopy in the frequency range of 10(-2)-10(8) Hz and temperature window of 298-403 K. Also, the relaxation behavior of (2-acetyloxyethyl-2-naphthalene-2-ylacetate), model compound of the polymer side groups, was analyzed. The isotherms representing the dielectric loss in the frequency domain show important conductive contributions, especially at high temperature, which hide the low frequency side of the alpha relaxation. Conductivity also increases the real component of the complex permittivity in the low frequencies region. Retardation spectra were obtained by minimizing the sum of the squares of the difference between the experimental values of the complex permittivity for each frequency and the analytical ones, predicted by the linear phenomenological theory, using a Tikhonov regularization technique. The spectra present an apparent alpha peak with an excess wing at short time side resulting from the overlapping of the true alpha relaxation and a beta process. Three absorptions, named in increasing order of time gamma, beta, and alpha relaxations, are separated by deconvolution methods. The activation energies associated with the gamma process are 70.0+/-1.8, 68.0+/-1.4, and 74.8+/-0.8 kJ mol(-1) for (2-acetyloxyethyl-2-naphthalene-2-yl acetate), poly(2-acryloyloxyethyl-2-naphthalene-2-yl acetate) and poly(2-methacryloyloxyethyl-2-naphthalene-2-yl acetate), respectively. The respective activation energies associated with the beta relaxation are 121.7+/-2.4, 135.3+/-1.4, and 141.6+/-1.3 kJ mol(-1). Values of the shape parameters and the strengths of the relaxation processes were obtained as a function of temperature. The dynamic fragility of the polymers and the model compound was studied and compared with that reported for macromolecular and monomeric systems. Also, the evolution of the size of the correlated domains associated with the alpha relaxation was estimated. Finally, the gamma relaxation rather than the beta absorption obeys the criteria apparently held by the Johari-Goldstein beta processes.

Secondary and primary relaxations in hyperbranched polyglycerol: a comparative study in the frequency and time domains.

The non-Debye relaxation behavior of hyperbranched polyglycerol was investigated by broadband dielectric spectroscopy. A thorough study of the relaxations was carried out paying special attention to truncation effects on deconvolutions of overlapping processes. Hyperbranched polyglycerol exhibits two relaxations in the glassy state named in increasing order of frequency beta and gamma processes. The study of the evolution of these two fast processes with temperature in the time retardation spectra shows that the beta absorption is swallowed by the alpha in the glass-liquid transition, the gamma absorption being the only relaxation that remains operative in the liquid state. In heating, a temperature is reached at which the alpha absorption vanishes appearing the alphagamma relaxation. Two characteristics of alpha absorptions, decrease of the dielectric strength with increasing temperature and rather high activation energy, are displayed by the alphagamma process. Williams' ansatz seems to hold for these topologically complex macromolecules.

Deconvolution of the relaxations associated with local and segmental motions in poly(methacrylate)s containing dichlorinated benzyl moieties in the ester residue.

The relaxation behavior of poly(2,3-dichlorobenzyl methacrylate) is studied by broadband dielectric spectroscopy in the frequency range of 10(-1)-10(9) Hz and temperature interval of 303-423 K. The isotherms representing the dielectric loss of the glassy polymer in the frequency domain present a single absorption, called beta process. At temperatures close to Tg, the dynamical alpha relaxation already overlaps with the beta process, the degree of overlapping increasing with temperature. The deconvolution of the alpha and beta relaxations is facilitated using the retardation spectra calculated from the isotherms utilizing linear programming regularization parameter techniques. The temperature dependence of the beta relaxation presents a crossover associated with a change in activation energy of the local processes. The distance between the alpha and beta peaks, expressed as log(fmax;beta/fmax;alpha) where fmax is the frequency at the peak maximum, follows Arrhenius behavior in the temperature range of 310-384 K. Above 384 K, the distance between the peaks remains nearly constant and, as a result, the a onset temperature exhibited for many polymers is not reached in this system. The fraction of relaxation carried out through the alpha process, without beta assistance, is larger than 60% in the temperature range of 310-384 K where the so-called Williams ansatz holds.