Computer Chemistry Consultancy - XML4Pharma, Katzelbachweg 18, A-8052 Thal, Austria,

Polymer Network calculations using the Miller-Macosko applet

Thermosets are usully formed by a condensation reaction between A-functional monomers and B-functional monomers. If (at least) one of the A-functional monomers has a functionality of at least 3 (i.e. it has 3 reactive A-groups) and (at least) one of the B-functional monomers has a functionality of at least 2, then a polymeric network is formed.

Monomers for an A3 + B2 reaction

When the network becomes infinite, gelation occurs, and the mechanical properties sharply improve. This point is named the "gel point". At the gel point, the weight-average MW becomes infinity, but the number-averaged MW doesn't.

A polymeric network after gelation
After the gel point (if any), 3 fractions of material can be distinguished. The first fraction is the fraction of material between the crosslinks in the infinite network (effective chains). The second fraction is the so-called "pendant fraction" which consist of the dangling chains in the infinite network (gel). The third fraction is not in the gel yet and is called the "sol fraction".

In the seventies, Miller and Macosko developed a theory to calculate network properties of gelating thermosets. As the theory is rather complicated, not many computer programs have been developed that implement this theory.
From the original publications, we developed a Java applet that implements the theory. We did this for worlds largest Coatings company. Before the implementation, this company had only limited access to tools for predicting whether a thermoset composition will gel or not, and what properties it will have as function of reaction progress. After the implementation and deployment on their intranet, suddenly a large amount of researchers and developers had access to this technology, enabling them to perform their development work in a much more efficient way.

An analogous tool was developed for the case where a (mixture of) long chain polymer(s) is reacted with a low-molecular weight crosslinker (after the Bauer theory - not shown here).

The Miller-Macosko applet

The applet has a very user-friendly input screen. Using slider and textfields, the functionality, amount, and molecular weight of each of the A- and B-monomers (the picture only shows the part for the A-functional monomers). One click on the "Gel Point" button calculates the gel point within a fraction of a second.
A click on the "Pregel" button calculates the properties before gelation, i.e. number- and weight-averaged molecular weight as function of reaction progress. The pregel-results are shown in a graphical way, with a summary and interactive plots (you can zoom in and out in the plots).
When the "Postgel" button is clicked, the properties beyond the gel point are calculated and shown. These include the weight fractions of effecttive chains, pendant and sol as function of reaction progress, as well as the crosslink density and the average molecular weight between the crosslinks. Also a summary of the most important data is given. Also here the plots are fully interactive.

Computer Chemistry Consultancy, June 2001