Theory and Measurements of the Glass-Transformation Interval of Polystyrene

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Abstract
Equations for the apparent heat capacity in the glass‐transition interval as functions of temperature, heating rate, and thermal history have been developed and programmed for computation. The hole theory of liquids was used as basis for the analysis of the glass transition. Experimental information was derived from dynamic differential thermal analysis, DDTA, on polystyrene. The maximum of the apparent heat capacities found experimentally agrees with the theory. The peak temperatures Tm can be expressed over four decades of heating rates by logq = A′ − B/Tm, where q is the heating rate, A′ is an approximate constant, and B is the activation energy for hole formation. Higher cooling rates lead to higher activation energies on subsequent heating, indicating the need to recognize a hole size distribution. The minimum in the heat capacity that precedes the maximum on heating through the glass‐transition interval could be detected on quenched samples. Mathematical expressions for the minimum temperature and magnitude were developed. The temperature of ``half‐freezing'' on cooling, equivalent to Tool's ``fictive temperature,'' was found experimentally to occur at constant q·τ, where τ is the relaxation time (q·τ = 6.6° for polystyrene). From the ``half‐freezing'' temperatures as a function of cooling rate one can determine the properties of a ``mean hole.'' For polystyrene the activation energy of the mean hole is 157 600 cal/mole of holes.

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