Gibbs-Di Marzio equation

Gordon-Taylor equation) (Gibbs-Di Marzio equation) (Fox equation)... 

In Fig. 7.70 the Barton equation for copolymer glass transitions is listed. It is based on the assumption that the four possible dyads in a copolymer, poly(A-co-B), have the following glass ttansitions AA (Tj = T aa). BB (T = T bb), AB, and BA (Tg = TgAB = T ba)- Inserting these three different glass transitions into the Gibbs-Di Marzio equation for the intermolecular effects, leads to ... 

Both expressions have been linked to the conformational entropy at the glass transition (126,127). A number of additional equations have been compared to the experimental data as illustrated in Figure 15. The Gibbs-Di Marzio equation. 

A different equation results if one assumes that the product of the change in expansivity with the glass transition temperature, AaT, is a constant, known as the empirical Simha-Boyer rule AaT = 0.113. The well-known and simple Fox expression for the glass transition temperature results on insertion of the Simha-Boyer rule into the Gordon-Taylor equation. The Gibbs-Di Marzio and the Fox equations are easily generalized to SVT or pVT equations of state when assuming that the solution can be based on simple additivity of the homopolymer properties. 

Equation (C.4) is applicable for the Di Marzio-Gibbs [6] flexible bond additivity model, where p refers to the component density, p and y refers to the masses and the numbers of flexible bonds of the monomers, and Aa = o eit f giass the increments of thermal expansion coefficient at the glass transition temperature. Equation (C.2) reverts to Equation (C.l) when the densities of the two commoners are equal and the constant Kq x for volume additivity can be approximated as Kp= T aIT b- Equations (C.l) and (C.2) have also been used to predict glass transition temperatures of binary polymer blends as well. 

Gibbs and Di Marzio [23,24] proposed that the dilatometric Tg is a manifestation of a true equilibrium second-order transition at the temperature T2. In a further development, Adams and Gibbs [21] have shown how the WLF equation can then be derived. On their theory, the frequency of molecular jumps is given by... 

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