The properties and applications of liquid-crystal polymers

The fibre that best combines both high specific modulus and high specific stress at breakage is a particular type made from PRO, the formula for which is shown in fig. 12.18(a). It is clear that this molecule must be very stilf, because the only bonds about which rotation can occur are collinear with the molecular axis and there is also a relatively large number of bonds nearly parallel to the axis. Fibres of the Kevlar or Vectra type have significantly lower values both for stilfness and for strength, which is due at least in part to the fact that they have some backbone bonds that are not collinear with the molecular axis and they 

So far it has tacitly been assumed that the molecular chains are highly aligned parallel to the fibre axis, but there must in reality be a distribution of orientations. If the degree of orientation is very high, (cos 0) = ((l — sin 0) ) 1—2 sin 0, sin 0cos 0) = sin 0(l —sin 0)) (sin 0) and (sin 0) 0, where 6 is the angle between the axis of a typical 

This equation with fixed values of max and (sin 0 has often been found to fit experimental data for the temperature dependences of E and G well, although slightly different models have sometimes been used. In this simple model the oriented units are assumed to be aggregates of fully aligned chains and it is the low value of G for these units and its temperature dependence that cause the modulus of the fibre to be lower than max and to be temperature-dependent. 

The following values of the tensile modulus E and rigidity modulus G, expressed in gigapascals, were found for a random co-polyester fibre at two different temperatures E = 125, G = 1.1 and E = 62, G = 0.28. Assuming that equation (12.19) applies, calculate the value of Ej ax and the order parameter S for the fibre. 

Inserting values Ei, G and E2, G2 for the two temperatures into this equation and dividing one resulting equation by the other leads immediately 

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