Abstract." Two experimental techniques are described for the determination of the change of specific volume of polymers with temperature and aging time, which allow measurements between -160 °C and + 200 °C. Four technical amorphous polymers, PS, PVC, PMMA and PC have been investigated. Volume-temperature curves under constant rate of cooling are presented and interpreted with respect to relaxation processes known from other physical investigations. The rate dependence of dilatometric glass transition temperatures is compared with the time dependence of rheometric glass transition temperatures from shear creep data. Volume relaxation data at constant aging temperature are presented. Aging is found to proceed until very low temperatures in the glassy state for e.g. PMMA.For polystyrene, a comparison is made between the predictions of a very simple theory of volume relaxation due to Kovacs with experimental data, using additional information from volume temperature curves and the time temperature shift of the shear creep transition. The theory predicts a rate of volume relaxation which is much lower than that found by experiment.

The question is treated whether in the study of linear visco-elastic behavior of a material change of temperature is completely equivalent to a shift of the logarithmic time scale or not. If it is, the material is termed ``thermo-rheologically simple'' (class A). It is shown that, by plotting the results of a similar rheological experiment (for instance, a creep experiment) performed at different temperatures and comparing the curves obtained, one can decide whether the materials considered belongs to class A or not, by seeing whether the curves can be made to fit by shifting them along the axis of logarithmic time. Once the material has been decided to behave thermo-rheologically simple, one can plot the function describing the time-shift as function of the temperature. Some examples of thermo-rheologically simple materials are quoted from the literature. The micro-rheological conditions for thermo-rheologically simple behavior are discussed. It turns out that this behavior implies that in similar deformations at different temperatures always the same sequence of molecular events follows, whereas in materials not belonging to class A, not only the speed, but also the sequence of molecular processes changes when the temperature of the experiment changes. This implies, that materials of class A cannot from a heat treatment assume a special structure which could not be obtained by one temperature, whereas for materials of class B a heat treatment can indeed result in a special structure. It is reasonable to expect that thermo-rheologically simple materials will be found only among polymers containing no crystallites and no pronounced polar groups.

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Approximation methods for the calculation of relaxation spectra. from experimental data from dynamic measurements are given. It appears that better approximations are obtained when higher tirne-derivates of the moduli are measured. A chart showing quantitative relations between the accuracy of an approximation and the accuracy of various static a.nd dynamic experiments is given. § 1. Introduction. A well known problem 1) 2) 7) in the study of linear visco-elastic behaviour is the calculation of the so-called spectra from experimental data on relaxation or dynamic behaviour.Calling the relaxation spectrum L(7:) and the experimentally accessible relaxation function 1p(t), the dynamic modulus E'{oo) and the dynamic viscosity 1]'(00) = ooE"(oo) *), we have ce !jJ(t) = Je-tj~L(T)d In 7:, ce • 2-.2 E'(oo) = I 00 2-.2 L(r)d In 7:, .; 1 + w -00 00 " f W7:*) Instead of dynamic viscosity the quantity E"(w), which is of the dimension of a modulus. is frequently used in considering high polymers. We shall deal ill the following only with E"(w), the "imaginary part of rigidit v". The corresponding formulae involving 'Inoo) can be written down at once.-127-

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