Types of Deviations from Gaussian Behaviour

Various Types of Deviations from Gaussian Behaviour 

All dry networks and many swollen networks exhibit deviations from the Gaussian network behaviour discussed in the previous chapter. These deviations may have various causes  

Theories based on these concepts all have to take into account the phenomenology of the stress-strain behaviour of networks. In unilateral extension as well as compression one observes, even at moderate extension (1.1 AX 2), deviations from the Gaussian behaviour, which can be empirically described by the so-called Mooney-Rivlin equation  

This equation can be derived from a postulated elastic free energy expression  

Again it has been found experimentally that (Cx + C2) does not correspond with the Mooney-Rivlin constants in extension and compression. One is thus faced with the problem of deciding which Cx to identify with the Gaussian constant. Several authors consider Ct in extension to be the Gaussian constant, but in view of the above this position cannot be maintained. One could instead identify the compression modulus with the Gaussian constant 3(AvkT/Lt) Kr2)4/(r2 0) because in compression Cg is always found to be very small or zero. There is, however, no theoretical justification for this procedure either. 

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