Modeling of the Free-Radical Copolymerization Kinetics with Cross Linking of Vinyl/Divinyl Monomers in Supercritical Carbon Dioxide

Abstract

A mathematical model for free-radical copolymerization kinetics with cross linking of vinyl/divinyl monomers in carbon dioxide at supercritical conditions was developed. The copolymerization of styrene and divinylbenzene is analyzed as a case study. The effects of the kinetic and physical parameters on monomer conversion, molecular-weight development, copolymer composition, appearance of the gelation point, gel fraction, and average cross-link density are studied. Model predictions show the expected trends, although the system is quite sensitive to pressure, which provides an interesting and promising way to tailor some of the polymer properties.

Modeling of RAFT Copolymerization with Crosslinking of Styrene/Divinylbenzene in Supercritical Carbon Dioxide

“…[39] Global crosslinker content, f 2 , and global accumulated copolymer composition, 2 F , were calculated using Equations (29) and (30), respectively. [36] It should be noted that global variables are represented without subscript ψ. Global values for amounts of low molar mass species and polymer molecules are given by the addition of their respective values in each phase (e.g., …”

“…Kiparissides et al [47] and Quintero-Ortega et al [35,36] used a simple model for the partition of monomer and initiator between continuous and dispersed phases in the modeling of dispersion polymerization of vinyl and vinyl/divinyl monomers in scCO 2 . Likewise, in our model it is assumed that the polymerization occurs in three stages.…”

“…[31][32][33][34] On the other hand, simplified models, such as the method of moments, and simple equilibrium calculations have been also used to describe the behavior of these simpler systems. [35][36][37] To the best of our knowledge, the modeling of copolymerization kinetics, molar mass development, and gel fraction evolution for vinyl/divinyl monomers in the presence of RDRP controllers, in scCO 2 , has not been addressed or has been addressed assuming a single phase situation. [38] In this contribution, we use a multifunctional polymer molecule approach developed in our group, [39] along with a simple partition of the main components in the scCO 2 -rich and polymer-rich phases, to model the RAFT copolymerization with crosslinking of vinyl/divinyl monomers in scCO 2 .…”

“…Number-and weight-average chain lengths for the postgelation period are calculated using Flory-Stockmayer expressions, Equations (36) and (37), assuming polymer molecules of uniform size. It is also assumed that gelation takes place only in the dispersed phase since the polymer produced in the continuous phase can only reach a finite critical size.…”

“…It is also assumed that gelation takes place only in the dispersed phase since the polymer produced in the continuous phase can only reach a finite critical size. [36] The variables needed to evaluate Equations (36) and (37) are calculated using Equations (38)- (40), and are defined as number-, weightaverage of primary chains, crosslink density of the sol fraction, sol fraction and gel fraction, respectively. (41)- (43), [45] where M r (g mol −1 ), d p (g cm −3 ), d s (g cm −3 ), ν and χ are molar mass of the repeating unit, polymer density, solvent density, fraction of swollen polymer, and polymer-solvent interaction parameter, respectively.…”