In spite of the early advances made by Flory in deciphering the mechanistic progression of nonlinear polymerization, obtaining a proper understanding of the dynamic changes in polymer property distribution that accompany gelation could not be obtained because of modeling limitations. Most modeling approaches used break down at the gel point because of the divergence of the higher moments of the distribution. Various approximations were proposed but failed to provide realistic results beyond the gel point. I, along with Campbell, developed and introduced the Numerical Fractionation (NF) approach to enable the continuous modeling of the molecular weight distribution and polymer properties through the gel point. We were the first to offer a method that integrates smoothly through gelation and to predict the properties of both the sol and the gel properly. The method is based on the hypothesis that “geometrical growth” is necessary to transition towards the formation of “infinitely large” gel molecules. Selected publications illustrating the application of NF to various systems are given below:

• Teymour, F. and J. D. Campbell. "Analysis of the Dynamics of Gelation in Polymerization Reactors using the 'Numerical Fractionation' Technique." Macromolecules 27(9), pp.2460-2469, 1994.

• Kizilel, Seda, Georgia Papavasiliou, John Gossage, and Fouad Teymour, “Mathematical Model For Vinyl-Divinyl Polymerization.” Macromol. React. Eng. 1(6), pp.587-603, 2007.

• Papavasiliou, Georgia and Fouad Teymour. "Bifurcation Analysis of Nonisothermal Nonlinear Polymerization." Industrial and Engineering Chemistry Research 44(8), pp.2754-2766, 2005.

• Cozewith, C. and F. Teymour. "Polymer Cross-Linking in Post-Gel Region for Continuous and Batch Reactors." AICHE Journal 44(3), pp.722-732, 1998.