Experimental Data to Provide Information over Wide Ranges of Time Scale

Correlation of Experimental Data to Provide Information over Wide Ranges of Time Scale 

To cover a wide enough time scale to reflect the variety of molecular motions in polymeric systems, often 10 to 15 logarithmic decades, one must usually combine information from transient and sinusoidal experiments. It is then necessary to calculate from the results of one type of measurement what would have been observed in the other, in the same range of time (or inverse radian frequency). Fortunately, this is possible, provided the viscoelastic behavior is linear. In principle, knowledge of any one of the functions J(t), G(t), G (to), G (o)), J (to), / ( ) over the entire range of time or frequency (plus in certain cases one or two additional constants) permits calculation of all the others. Even if the values are not available over the entire range of the argument, approximation methods can be applied. These calculations are treated in detail in Chapters 3 and 4. 

Since each of the preceding functions can be calculated from any other, it is an arbitrary matter which is chosen to depict the behavior of a system and to correlate with theoretical formulations on a molecular basis. In fact, two other derived functions are sometimes used for the latter purpose—the relaxation and retardation spectra, H and L, which will be defined in Chapter 3. Actually, different aspects of the viscoelastic behavior, and the molecular phenomena which underlie them, have different degrees of prominence in the various functions enumerated above, so it is worthwhile to examine the form of several of these functions even when all are calculated from the same experimental data. A qualitative survey of their appearance will be presented in Chapter 2. 

Even when only one experimental method is available, covering perhaps two or three decades of logarithmic time or frequency scale, the viscoelastic functions can 

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