Copolymerization of styrene and methyl methacrylate. Part I: Experimental kinetics and mathematical modeling Kiyumars Jalili a, b , Farhang Abbasi a, b, * , Morteza Nasiri a, b a Institute of Polymeric Materials, Sahand University of Technology, 5331711111 Tabriz, Iran b Faculty of Polymer Engineering, Sahand University of Technology, 5331711111 Tabriz, Iran article info Article history: Received 6 December 2010 Received in revised form 26 June 2011 Accepted 16 July 2011 Available online 23 July 2011 Keywords: Styrene-methyl methacrylate Copolymerization Pentane Population balance abstract A population balance approach is described to follow the time evolution of molecular properties in free- radical copolymerization. The model formulation is based on the two dimensional orthogonal collocation on finite difference (2-OCFD) and method of generating functions (GF) which was properly adopted to calculate time-conversion behavior of styrene-methyl methacrylate copolymerization. A comprehensive model which uses the free volume theory to account for diffusion controlled termination and propa- gation reactions as well as the variation of the initiator efficiency with respect to the monomer conversion was developed. The model is capable of predicting the conversion, composition and molecular weight development up to limiting conversions. The plasticizing effect of a blowing agent on the rate of copolymerization has been investigated. The phenomenological aspect of rate data is analyzed for the copolymerization of styrene with methyl methacrylate over a full range of conversion and the gel effect index is used to systematize the observations. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Mathematical modeling plays an important role in the under- standing of polymerization processes. A comprehensive and accu- rate model is an invaluable tool, able to aid in several areas of science and engineering from selection of a suitable catalyst to process design and optimization. The modeling of free radical polymerization in bulk, solution or emulsion is an immense field of research with too many references to list. The synthesis of linear and branched copolymers by free-radical reactions is of significant economic importance to the polymer industry, for the copolymer- ization of two or more monomers can lead to the production of polymers with desired physical, chemical, and mechanical end-use properties. Free radical random copolymers are typically obtained as a mixture of macromolecules with different composition, chain length, degree of branching, and chain sequence characteristics. Except for a few special cases of initial monomer compositions, i.e., the azeotropic mixtures, products of a typical free-radical copoly- merization show a gradual drift in the copolymer composition over the course of copolymerization. This well-known copolymer composition drift phenomenon stems from the different reactiv- ities of the monomers to combine with the growing polymer radicals. Hence, the more reactive monomer is depleted at first, causing the product to become gradually enriched in the less reactive monomer as reaction progresses. The gradual buildup of the macromolecule causes an increase in the viscosity of the reacting mixture. Hence, termination as well as propagation steps can both be affected by diffusion limitations. Diffusion-controlled reaction may also lead to both composition and molecular weight drifts and become more critical for reactions carried to high conversions [1]. With increasing the viscosity of the reaction medium, the diffusion of the macro radicals and, thus, the termi- nation of the reactive chains are impeded whereas the diffusion of the smaller monomer molecules to the reactive centers at the chain ends continues undisturbed [2]. The reason of this apparent increase in reaction rate and degree of polymerization is, therefore, a strong drop of the termination rate with growing polymer frac- tion in the reaction medium. This phenomenon is called gel effect or Trommsdorff effect [3] and especially intense in the methyl methacrylate (MMA) homo and copolymerization, but occurs also for monomers like styrene, vinyl acetate and others. The conversion level in free radical polymerization of vinyl monomers can be divided into three stages [4]. An initial stage in which the rate of polymerization decreases; an intermediate stage in which the rate of polymerization increases (the gel effect); and a final stage in which, monomer being depleted or the reaction mixture approaching its glass transition point, the rate falls to zero. Also as a consequence of these changes in the rate of * Corresponding author. Faculty of Polymer Engineering, Sahand University of Technology, 5331711111 Tabriz, Iran. Tel.: þ98 412 3459090; fax: þ98 412 3444313. E-mail address: f.abbasi@sut.ac.ir (F. Abbasi). Contents lists available at ScienceDirect Polymer journal homepage: www.elsevier.com/locate/polymer 0032-3861/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymer.2011.07.023 Polymer 52 (2011) 4362e4376