Cross-Linking and Tg
Quick Start
As you cure a crosslinked system, the glass transition temperature, Tg, increases. The basic Tg equation from Stutz1 has a few parameters that pose some problems, but the default values are a good start.
Cross-linking Tg
The app assumes you have a crosslinking system with a collection of reactive species with a degree of conversion, p from 0-1 and a crosslink density X, also 0-1. The two other crosslinking apps give a lot more background, plus some values for X: X-Links in reactive curing and X-Links in UV curing. For simplicity (and because the p effect is small, p is set equal to X in the calculations. For those who want an integrated view of this, there is a "Show Tg" option in the X-Links in UV app.
The equation assumes that you know the Tg at infinite MWt of "the" polymer without crosslinks. When in doubt assume that Tg∞ is something like 50°C. It uses two constants, K1 which you can assume to be ~50 and K2 which, for good theoretical reasons, can be assumed to be between 0.5 and 1, with 0.8 being the default value. The equation is:
`Tg=[(Tg_∞-K_1)(1-p)][1+(K_2X)/(1-X)]`
The Tg values in the equation are in terms of °K but the input and output from the app are in °C.
The effect of the term with p is to reduce Tg by having plenty of "loose ends". It is more-or-less an offset for the starting value of the system. The X/(1-X) term heads to infinity for a perfectly crosslinked system where X=1.
1H. Stutz, K.-H. Illers, and J. Mertes, A Generalized Theory for the Glass Transition Temperature of Crosslinked and Uncrosslinked Polymers, J. Polymer Science: Part B: Polymer Physics, 28, 1483-1498 (1990)
