Time, rate and frequency

In the treatment above, we have dealt with time and its reciprocal, rate. The concept of rate of molecular rotation is clear enough. However, we were not specific about what we meant by rate of observation . We can look at this in two ways. 

The first is to consider the time over which observations are made, and then simply take its reciprocal. For example, in the volume contraction experiments of Kovacs, rate of cooling is measured as degrees per unit time. 

However, an alternative concept arises if the action on the polymer is carried out in a periodic, cyclical way. In this section we are concerned with mechanical properties, so we could apply a deforming stress in an alternating push-pull fashion. The resulting strain would also be periodic, being extension during the pull and contraction on the push. Then the most convenient measurement of the time or rate of the stress/strain observation is the frequency of the applied stress. High frequencies correspond to stress applied over short times, while low frequencies correspond to stress applied over long times. In this way the time of the experiment as experienced by the molecules is the time of one cycle of the periodic stress/strain, and not the total time over 

The modulus-logarithm frequency curve is a mirror image of the modulus-logarithm time curve. At higher temperatures, the molecules are moving faster, and so the transitions are moved to higher frequencies (broken 

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