Modeling Gel Effect in Branched Polymer Systems: Free-Radical Solution Homopolymerization of Vinyl Acetate George D. Verros, 1 Dimitris S. Achilias 2 1 Department of Electrical Engineering, Technological and Educational Institute (TEI) of Lamia, Lamia GR-35100, Greece 2 Department of Chemistry, Laboratory of Organic Chemical Technology, Aristotle University of Thessaloniki, Thessaloniki GR-54124, Greece Received 19 February 2008; accepted 9 June 2008 DOI 10.1002/app.29252 Published online 11 November 2008 in Wiley InterScience (www.interscience.wiley.com). ABSTRACT: In this work a comprehensive mathematical framework is developed for modeling gel effect in branched polymer systems with application in the solution polymer- ization of vinyl acetate. This model is based on sound prin- ciples such as the free-volume theory for polymer chains diffusion. The model predictions for monomer conversion and number- and weight-average molecular weights were found to be in good agreement with published data in the literature. Moreover, the joint molecular-weight distribu- tion–long chain branching distribution is calculated by direct numerical integration of a large system of nonlinear ordinary integral-differential equations describing the mass conservation of macromolecular species in a batch reactor. This allows studying the effect of process conditions such as initiator and solvent concentration on the product qual- ity. It is believed that this work might contribute to a more rational design of polymerization reactors. V C 2008 Wiley Peri- odicals, Inc. J Appl Polym Sci 111: 2171–2185, 2009 Key words: theory; radical polymerization; diffusion; molecular-weight distribution; modeling; simulation; vinyl acetate INTRODUCTION The free-radical polymerization of vinyl acetate (VAC) is an industrial process with significant finan- cial interest because branched polymers with diverse end-use properties are produced. The importance of the VAC free-radical polymerization has led to numerous experimental 1–6 and theoretical 7–20 stud- ies. The main characteristic of this process is the existence of autoacceleration phenomena (gel effect) at high conversion. These autoacceleration phenom- ena are caused by a decrease in the termination rate constants at high conversion because of the small mobility of polymer chains. Autoacceleration phenomena, such as the gel effect in polymerization reactors, have been the sub- ject of numerous studies. 21–60 These studies could be classified as deterministic models or stochastic mod- els based on comprehensive modeling techniques and recently reviewed in Ref. 61. The deterministic models are based either on the free-volume theory 62–64 or on the reptation theory 65–68 for polymer diffusion, both combined with the Smoluchowski 69 model to describe the variation of the diffusion controlled ki- netic rate constants with process conditions. The main difficulty in building a deterministic model for the specific process is the coexistence of both branched and linear polydispersed polymers in the reaction mixture. A model for the gel effect in free- radical polymerization necessitates a comprehensive theory for diffusion describing the variation of diffu- sion coefficients with process conditions. The challenge in our case is to describe the variation of diffusion coefficients as a function of the process conditions in the reaction mixture containing both polydispersed linear and branched chains. The aim of this work is to overcome these difficul- ties and propose a unique model based on the free- volume theory to describe the solution free-radical homopolymerization of VAC. This work is organ- ized as follows: In the following section the kinetic mechanism along with the polymerization rate func- tions are briefly reviewed, the mathematical model A preliminary version of this work was presented at the International Conference of Computational Methods in Sciences and Engineering 2003 (ICCMSE 2003), Kastoria, Greece, September 12–16, 2003. Correspondence to: G. D. Verros (gdverros@otenet.gr or verros@eng.auth.gr) Journal of Applied Polymer Science, Vol. 111, 2171–2185 (2009) V C 2008 Wiley Periodicals, Inc.