Step polymerization statistical theory

Floiy Statistics of the Molecular Weight Distribudon. The solution to the complete set (j= 1toj = 100,000) of coupled-nonlinear ordinary differential equations needed to calculate the distribution is an enormous undertaking evai with the fastest computers. However, we can use probability theory to estimate the distribution. This theory was developed by Nobel laureate Paul Flory. We have shown that for step polymerization and for free radical polymerization in which termination is by isproportionation the mole fraction of polymer with chain lengthy is... 

Macosko and Miller (1976) and Scranton and Peppas (1990) also developed a recursive statistical theory of network formation whereby polymer structures evolve through the probability of bond formation between monomer units this theory includes substitution effects of adjacent monomer groups. These statistical models have been used successfully in step-growth polymerizations of amine-cured epoxies (Dusek, 1986a) and urethanes (Dusek et al, 1990). This method enables calculation of the molar mass and mechanical properties, but appears to predict heterogeneous and chain-growth polymerization poorly. 

The formation of polymer networks by step-growth polymerization has been modeled using statistical theories, such as the Flory-Stockmayer classical theory [61-64], the Macosko-Miller conditional probability model [65-70], and Gordon s cascade theory [71-74]. However, statistical methods have not been successful for modeling of polymer network formation in chain-growth polymerization systems. 

While step polymerization methods lead to more or less statistical networks and good agreement with theory, addition polymerization and vulcanization nonuniformities lead to networks that may swell as much as 20% less than theoretically predicted (115,116). 

The theory of Carothers is restricted to the prediction of number-average quantities. In contrast, simple statistical analyses based upon the random nature of step polymerization allow prediction of size distributions. Such analyses were first described by Flory. 

Consequently, while I jump into continuous reactors in Chapter 3, I have tried to cover essentially aU of conventional chemical kinetics in this book. I have tried to include aU the kinetics material in any of the chemical kinetics texts designed for undergraduates, but these are placed within and at the end of chapters throughout the book. The descriptions of reactions and kinetics in Chapter 2 do not assume any previous exposure to chemical kinetics. The simplification of complex reactions (pseudosteady-state and equilibrium step approximations) are covered in Chapter 4, as are theories of unimolecular and bimolecular reactions. I mention the need for statistical mechanics and quantum mechanics in interpreting reaction rates but do not go into state-to-state dynamics of reactions. The kinetics with catalysts (Chapter 7), solids (Chapter 9), combustion (Chapter 10), polymerization (Chapter 11), and reactions between phases (Chapter 12) are all given sufficient treatment that their rate expressions can be justified and used in the appropriate reactor mass balances. 

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