A relationship between the glass transition temperature (Tg) and fractional conversion for thermosetting systems

An equation, based on thermodynamic considerations to relate the glass transition temperature, T_g, to compositional variation of a polymer system, is adapted in this article for modeling the T_g vs. fractional conversion (x) relationship of reactive thermosetting systems. Agreement between the adapted equation and experimental T_g vs. x data is found for several thermosetting crosslinking systems (i.e., epoxies and cyanate ester/polycyanurate) as well as for reactive thermosetting linear polymer systems (i.e., polyamic acid and esters to polyimides). The equation models the experimentally obtained T_g vs. x behavior of thermosetting systems which include competing reactions. Agreement for widely varying molecular structures demonstrates the generality of the equation. The entire T_g vs. x relationship can be predicted for a thermosetting material by using the T_g vs. x equation and the values of the initial glass transition temperature, T_g0, the fully reacted system glass transition temperature, T_g∞, and the ratio of the change in specific heat from the liquid or rubbery state to the glassy state (Δc_p) at T_g0 and T_g∞, Δc_p∞/Δc_p0. The values of T_g0, T_g∞, and Δc_p∞/Δc_p0 can be measured generally from two differential scanning calorimetric experiments. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 64: 3–14, 1997