Fox-Loshaek equation

These relationships show that (i) if the copolymer approach is considered as a correct model, this means that the Fox-Loshaek relationship is only valid at low crosslink densities (as effectively found experimentally) (ii) The Fox-Loshaek constant is an increasing function of Tgi, e.g., of the chain stiffness, as effectively found. KFl varies from 6-10 K kg mol-1 for fully aliphatic to 50-60 K kg mol-1 for highly aromatic systems. Thus, it appears that both chain stiffness and crosslinking effects cannot be considered independent. The effect of crosslinking, represented for instance by (Tg—Tgi) in the Fox-Loshaek equation, is an increasing function of the chain stiffness. This dependence is taken into account in the approach based on the theory of conformational entropy (Di Marzio, 1964) and leads to... 

Let us remark that Di Marzio s equation reduces to the Fox-Loshaek equation at low crosslink densities ... 

This equation is equivalent to the Fox Loshaek relationship, provided... 

Finally a quite empirical equation, proposed by Fox and Loshaek (1955), should be mentioned ... 

Figure 5-12. Glass transition change in the system poly(styrene-co-divinylbenzene) as a function of the crosslink density. No is the number density (e.g., mmol/cm3) crosslinks, whereas p is the bulk mass density (e.g., g/cm3). The dotted line is the fit of equation (5-29) with the result that kp is 130 10 g/mol. [Adapted from T. G Fox and S. Loshaek, J. Polym. Sci., 15, 371 (1955). Copyright 1955, Wiley Periodicals, Inc., a Wiley Company.]...

Crosslinking can increase the Tg above that of the infinite molecular weight linear polymer. This increase can be accounted for with the equation of Fox and Loshaek [74]. 

Equation (56) results in a linear dependence of Tg vs, p, and has been found to describe the change in Tg with crosslinking for many polymers. Figure 26 shows the results for poly(styrene-co-divinylbenzene) obtained by Fox and Loshaek. We note here that some workers claim that 71... 

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