Temperature-dependent dielectric relaxation spectra of cross-linked styrene-butyl acrylate copolymers were measured at frequencies between 10 mHz and 1 MHz. The results were analyzed using the empirical Kohlrausch-Williams-Watts (KWW) and Havriliak-Negami (HN) formalisms. While the KWW and the HN formalisms were equally well able to fit the experimental data for the uncross-linked copolymer, the HN formalism provided superior fits at high levels of cross-linking. The fitting parameters obtained from the HN routine were used to interpret the data in terms of the model proposed by Schónhals and Schlosser that relates the molecular motion of the polymer with the HN parameters. In this model, = ß is correlated with the local intramolecular dynamics of the polymer and is not influenced by the level of cross-linking. On the other hand, the parameter m-a, which is related to the intermolecular correlations of the polymer chain segments, decreases with increasing level of cross-linking.However, in recent years there have been a number of papers published wherein researchers correlate the fitting parameters with molecular motions of the polymer chains.3-5The first successful attempt to treat permittivity was developed by Debye.6 However, the treatment developed by Debye predicted that a molecule would exhibit only a single relaxation time. For such a single relaxation process, the dielectric response can be described by eq 2 with a = 10=1 and as the Debye relaxation time.
Recently, a new multivariate analysis tool was developed to resolve mixture data sets, where the contributions ('concentrations') have an exponential profile. The new approach is called DECRA (direct exponential curve resolution algorithm). DECRA is based on the generalized rank annihilation method (GRAM). Examples will be given of resolving nuclear magnetic resonance spectra resulting from a diffusion experiment, spectra in the ultraviolet/visible region of a reaction and magnetic resonance images of the human brain.
The dielectric relaxation behavior of copolymers of styrene and butyl acrylate is investigated over a wide frequency range. The results are analyzed in terms of the free volume and configurational entropy theories. The calculated fractional free volume was nearly constant over the composition range studied while the volume expansion coefficient exhibits a maximum in the mid composition range. Even though the change in heat capacity at Tg varied linearly with composition, the free energy of activation calculated from the configurational entropy model reached a broad maximum in the mid composition range. In addition, the average dielectric relaxation time of the copolymers at Tg is not constant. In fact, the longest relaxation times were obtained for samples containing nearly equal amounts of styrene (S) and butyl acrylate (B). It is suggested that the SB diad has a relaxation time much longer than the relaxation times of the SS and BB diads.
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