A complex plane analysis of α‐dispersions in some polymer systems

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Abstract
The α‐dispersion in many polymer systems is the process to be associated with the glass transition temperature where many physical properties undergo drastic changes. We have measured and analyzed the complex dielectric behavior of the α‐dispersions for five polymers [i.e., polycarbonate and polyisophthalate esters of bisphenol A, isotactic poly‐(methyl methacrylate), poly(methyl acrylate), and a copolymer of phenyl methacrylate and acrylonitrile] and have found that the usual methods of analysis cannot be used to represent the data. However, it is possible to represent the relaxation process as the sum of two dispersions but there is no evidence to support this contention. An empirical expression is proposed to represent the data. This expression which takes the form of appears to be a general representation for the three known dispersions, i.e., Debye, circular arc, and skewed semicircle. The complex dielectric constants calculated with the aid of this expression and the parameters for each polymer system which was determined graphically were found to be in excellent agreement with the experimental complex dielectric constants. This method of representation was extended to sixteen α‐dispersions reported in the literature always with excellent results.

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