A New, Practical Formulation of the Multicomponent Copolymerization Equation Enrique Saldı ´var-Guerra,* Iva ´n Zapata-Gonza ´lez This paper is dedicated to Dr. Leonardo Rı ´os for his contributions to polymer science. 1. Introduction Multicomponent copolymerizations involving 3–5 mono- mers are common in industry. The presence of even small amounts of an additional monomer can impart improved or differentiated properties to polymeric products; the sophistication of this approach can be significant and it may grow further in the future. For example, some monomers may improve the adhesion properties of an adhesive, increase the chemical resistance of a material or lead to some level of crosslinking in the polymer. Therefore, models that describe the evolution of composition or other features of the copolymerization reaction (rate, sequences, etc.) have always been of interest to the researchers and practitioners of polymer synthesis in academia and industry. Shortly after the publication in 1944 of the copolymer- ization equation, simultaneously proposed by Mayo and Lewis, [1] Wall, [2] and Alfrey and Goldfinger, [3] Walling and Briggs (W&B) [4] derived a generalized form of that equation for any number N of monomers. Unfortunately, the form of their solution requires the calculation of N determinants of matrices of dimension N  1, and apparently this fact has deterred the use and practical application of this solution to data analysis of multi- component copolymerizations. This formulation has remained as a mathematical curiosity or, at most, as a reference for comparison of other more appealing, although less general, formulations. That this is so, is inferred by looking at the relatively large number of papers published in the span of almost 65 years, dealing with simplified or alternate formulations of the copolymerization equations for limited number of monomers (mostly 3 and 4). [5–12] Alfrey and Goldfinger first developed a rigorous form of the equation for the terpolymerization case. [5] Valvassori and Sartori [6] used a simpler, but questionable form of the quasi steady-state assumption (QSSA), for the radical types and developed a simplified form of the equation for terpoly- merizations. Special solutions (when the kinetic constants satisfy some constraints) have also been studied. [7–9] The tetrapolymerization case was rigorously analyzed by Chen Full Paper E. Saldı ´var-Guerra, I. Zapata-Gonza ´lez Centro de Investigacio ´n en Quı ´mica Aplicada, Blvd. Enrique Reyna 140, 25253 Saltillo Coahuila, Me ´xico E-mail: esaldivar@ciqa.mx I. Zapata-Gonza ´lez Universidad Auto ´noma de Coahuila, Saltillo, Me ´xico A general and rigorous new formulation of the multicomponent extension to the Mayo Lewis copolymerization equation is presented based in matrix notation. In contrast to the original Walling and Briggs formulation, which was based on determinants and difficult to apply in practice, this new formulation is explicit, easy to implement, and introduces a natural scaling to the problem. The approach is illustrated with calculation of instantaneous composition and compositional drift with conversion for 4 and 6 monomers. 24 Macromol. Theory Simul. 2012, 21, 24–35 ß 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com DOI: 10.1002/mats.201100059