Condensation polymerization nonlinear

Among the physical characteristics of these nonlinear condensation polymerizations, the occurrence of a sharp gel point is of foremost significance. At the gel point, which occurs at a well-defined stage in the course of the polymerization, the condensate transforms suddenly from a viscous liquid to an elastic gel. Prior to the gel point, all of the polymer is soluble in suitable solvents, and it is fusible also. Beyond the gel point, it is no longer fusible to a liquid nor is it entirely soluble in solvents. Linear polymers, on the other hand, remain soluble in suitable solvents and fusible to liquids as well (unless the melting point is above the temperature of thermal decomposition), regardless of the extent of condensation. 

They are discrete transforms and can therefore operate directly on the separate equations for each species, reducing them to one expression. Nonlinear terms arising from condensation polymerization can be handled and, with some difficulty, so can realistic terminations in free radical polymerization. They are a special case of the generating functions and can be used readily to calculate directly the moments of the distribution, and thus, average molecular weights and dispersion index, etc. Abraham (2) provided a short table of Z-transforms and showed their use with stepwise addition. 

Batch Polymerization. Batch polymerization with this mechanism was first treated by Flory (19) using a statistical development. The same results were obtained by Biesenberger (8) using a kinetic analysis with an analytical solution. This was also one of the cases treated by Kilkson (35) using Z-transforms. In the simple cases, his result reduces to the Flory, or random, MWD with the dispersion index of 2. In more complex cases, he solves directly for the moments of the distribution. The Z-transform is probably the most powerful tool for solving condensation MWD problems the convolution theorem allows the nonlinear product terms in the kinetic equation to be handled conveniently. 

The self-condensing copper-catalyzed polymerization of macromonomer of poly(tBA) with a reactive C—Br bond (H-6) affords hyperbranched or highly branched poly(tBA).447 Copolymerization of H-1 and TV-cyclohexylmaleimide induced alternating and self-condensing vinyl polymerization.448 The residual C—Cl bond was further employed for the copper-catalyzed radical homopolymerization of styrene to give star polymers with hyperbranched structures. Hyperbranched polymers of H-1 further serve as a complex multifunctionalized macroinitiator for the copper-catalyzed polymerization of a functional monomer with polar chromophores to yield possible second-order nonlinear optical materials.325... 

Furfural and HMF are readily prepared from various catalytic biomass conversion processes. Both furfural and HMF can be readily converted to a large variety of monomers for polymerizations by chain-growth and/or condensation mechanisms. As the transformation of furfural and HMF to fine chemicals or monomers for polymers has been well documented by several comprehensive reviews [107-113, 130, 131], this chapter has mainly focused on the bio-based furan polymers with self-healing ability through thermally reversible Diels-Alder reactions, which is a recently exploited prosperous research area. In addition, the furan-based DA reaction has also been used in the thermoreversible nonlinear polymerization and dendrimer chemistry. 

The polymers produced by condensation reactions can be either linear or nonlinear, depending on the number of functional groups per monomer. The polymerization process can be performed in bulk (liquid or solid state) or as an interfacial polymerization. 

The hydrodynamic description of complex condensed matter systems like superfluids, ferromagnets, polymeric solutions, etc. has been possible thanks to the deep understanding of the role played by the symmetries and thermodynamic properties of the system (Kadanoff and Martin P.C. 1963, Hohenberg and Matin P.C., Kalatnikov 1. M. 1965). The extension of this linear hydrodynamic to liquid crystals has been started in the seventies, (Parodi 0.1970, Forster D. 1975), and in recent years it has been generalized to the nonlinear case and to more complex liquid crystal phases (Brand H. R. Pleiner H. J. 1980). 

These monomers polymerize with W, Mo, and Rh catalysts, where the polymer yield usually decreases in the order of W>Mo>Rh. The cis content of the polymers inaeases in the order of Wpolymer solubility decreases in this order. Both 1- and 2-naphthylacetylenes polymerize in high yields with W catalysts. 9-Anthrylacetylene polymerizes with W catalysts into a polymer insoluble in any solvent. However, if a long n-hexoxycarbonyl group is introduced at the 10 position, the polymer formed becomes soluble. This polymer has dark purple color. 1- and 2-Anthrylacelylens are sterically less hindered and the polymers formed are solvent soluble. These polymers having condensed aromatic rings are generally deeply colored (dark brown to dark purple) and show third-order nonlinear optical properties. 

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