The Theory of multiple copolymerization

Modern aspects of quantitative theory of free-radical copolymerization

“…In the opposite case when 0.5 < rs < 1 the composition distribution is unimodal. These conclusions derived at first [169][170] from the expressions (5.4) can also be obtained as a particular case from the general results [6,134] of the analysis of the trajectory behavior near SP for the copolymerization of any number m of monomers.…”

“…According to definition these values can be calculated in the case of the terminal model (2.8) from a system of non-linear algebraic equations: where the dependence of ~ on ~ is determined by the relationships (3.8) and (4.10). A great deal of literature is available dealing with the theoretical problems of azeotropy in the processes of copolymerization of three [121-124, 126-130, 135-142] or more monomers [46,125,[131][132][133][134].…”

“…[130] suggested an original procedure for the graphical representation of the copolymer composition dependencies on monomer feed composition, which, they believe, being the combination of O'Driscoll and Slocombe procedures, permits to eliminate their shortcomings. Considering multicomponent copolymerization theory, it is hard to overestimate the paper by Walling and Briggs [46] who managed to reduce the calculation of the azeotropic composition ~* j=l j=l Similar equations along with the various explicit forms of their solution were reported in a number of subsequent papers [99,[131][132][133][134], reviews [119,135,136], and in a monograph [6]. Note that having a physical meaning solutions ~* of both non-linear (4.13) and linear (4.14) sets of equations coincide as was conclusively proved in the general case at any m [46] and independently in the case of terpolymerization by virtue of another technique [137].…”

“…When the stable SP is azeotrope, necessary and sufficient conditions for its regularity are the following: the real parts Re ki of all roots ~i of the characteristic equation (5.11) are to exceed (-1) [6,134]. When inverse non-equalities Re kl < -1 hold for all i = t, ..., m -t, at the conversions close to the complete one in the composition distribution, we can observe a mode, the maximum of which corresponds to the azeotropic composition of the considered SP.…”

“…So, the unequality c~ 2 > c~2r can be considered as a sufficient condition for the copolymer to lose its transparency. 2 The value of c~r can be approximately considered as a universal parameter of the system which depends only on temperature [134,6]. To verify this assumption, the conversions p+, at which the system becomes turbid, were experimentally styrene with heptyl acrylate [310] determined in the course of bulk copolymerization of styrene and heptyl acrylate at various initial monomer feed compositions.…”