Polydisperse Homopolymers

Equation (C.23) can be simplified further. We recall that Nj (n) is the number of units in the n-th generation of tree j of a special x-mer consequently 

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The new knowledge and understanding of radical processes has resulted in new polymer structures and in new routes to established materials many with commercial significance. For example, radical polymerization is now used in the production of block copolymers, narrow polydispersity homopolymers, and other materials of controlled architecture that were previously available only by more demanding routes. These commercial developments have added to the resurgence of studies on radical polymerization. 

We now illustrate how the moment method is applied and demonstrate its usefulness for several examples. The first two (Flory-Huggins theory for length-polydisperse homopolymers and dense chemically polydisperse copolymers, respectively) contain only a single moment density in the excess free energy and are therefore particularly simple to analyze and visualize. In the third example (chemically polydisperse copolymers in a polymeric solvent), the excess free energy depends on two moment densities, and this will give us the opportunity to discuss the appearance of more complex phenomena such as tricritical points. 

In the presence of size polydispersity, there is an additional incoherent contribution to C(, t) decaying through the self-diffusion coefficient Ds((/)) [42,43,91]. The latter can also be measured for monodisperse hard sphere suspensions at finite concentrations at qR corresponding to the first minimum of S( ), i.e., when the interactions can be ignored [91]. These three different diffusion coefficients exhibit distinctly different dependence on q and 0. From these three transport quantities, Z>cou( ) is absent in monodisperse homopolymers, whereas Ds can hardly be measured in polydisperse homopolymers due to the vanishingly small contrast. 

The polymers were formed by condensation of 4,4dihydroxy-benzene and 2,2 -dimethyl-4,4 dihydroxyazoxybenzene with various diacid chlorides acting as flexible spacer groups Polydisperse homopolymers and copolymers, sharp fractions of homopolymers and mixtures of polydisperse polymers with a low mass mesogen were investigated. Supercooling at the mesophase-isotropic and solid-mesophase transitions, sharpness of the nematic-isotropic transition (range of N+I biphase), polymer crystallization from the mesophase melt, and enhancement of crystallinity upon addition of a low mass nematic, were studied. 

However, traditional chemical thermodynamics is based on mole fractions of discrete components. Thus, when it is applied to polydisperse systems it has been usual to spht the continuous distribution function into an arbitrary number of pseudo-components. In many cases dealing, for example, with a solution of a polydisperse homopolymer in a solvent (the pseudobinary mixture), only two pseudo-components were chosen (reproducing number and mass averages of molar mass of the polymer) which, indeed, are able to describe some main features of the liquid-liquid equilibrium in the polydisperse mixture [1-3]. In systems with random copolymers the mass average of the chemical distribution is usually chosen as an additional parameter for the description of the pseudo-components. However, the pseudo-component method is a crude and arbitrary procedure for polydisperse systems. 

This review reports the state-of-art in the development and applications of continuous thermodynamics to copolymer systems characterized by multivariate distribution functions. Continuous thermodynamics permits the thermodynamic treatment of systems containing polydisperse homopolymers, polydisperse copolymers and other continuous mixtures by direct use of the continuous distribution functions as can be obtained experimentally. Thus, the total framework of chemical thermodynamics is converted to a new basis, the continuous one, and the crude method of pseudo-component splitting is avoided. 

Murdzek, J. S. Schrock, R. R. Low polydispersity homopolymers and block copolymers by ring-opening of 5,6-dicarbomethoxynorbornene. Macromolecules 1987, 20, 2640-2642. 

Polydisperse homopolymer blends, i.e., mixtures of polymers of identical chemistry but unequal molecular weights. For the binary case G = = 2 5 s 82 = 1. 

A comparison of Eq. (6.35) with (6.36) indicates that in the terminal region, the log Gb versus log Gb" plot for polydisperse homopolymers has a slope of 2, with the values of Gb shifted upward above the values of G in the log G versus log G" plot for monodisperse homopolymers, the extent of the shift being greater with an increase in polydispersity. In the linear region, where 0 x co < 1 holds and therefore the denominators in Eqs. (6.31) and (6.32) are no longer negligible, we have (Han and Kim 1989b)... 

The dependence of the crystallization rate on molecular weights was discussed in Chapter 9. The profound influence of molecular weight fractions on the rate raises the interesting question as to the role of polydispersity in governing the crystallization kinetics. Studies of the crystallization kinetics of polydisperse homopolymers... 

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