The slope equations: a universal relationship between local structure and glass transition temperature

In this article, we present a universal relationship between the glass transition temperature $T_g$ and the local glass structure. The derivation of the simplest expression of this relationship and some comparisons with experimental $T_g$ values have already been reported in a recent letter. We give here the analytical expression of the parameter $\beta$ of the Gibbs-Di Marzio equation and also new experimental probes for the validity of the relationship, especially in low modified binary glasses.