Schulz-Zimm distribution model

The first approach assumes that the sample is composed of a discrete number or a specific distribution of components. Then the deviations from linearity for the proposed model can be included as higher order c-orrections in Equations 25 or 27. Current techniques are limited to the consideration of two discrete size populations of particles or to a size profile defined by two parameters such as the Schulz-Zimm distribution (7,26,27,28,29,30). If there is evidence that such a model describes the sample, it is certainly the best way to proceed. This approach has been applied recently to polydispersity analysis based on the assumption of a particular distribution model by Chen et al. (35, 36) and McDonnell et al. (26,37). 

Several theoretical models have been published which predict the change in MWD during degradation especially for a random mechanism. For detail, the reader is referred to specialized books (see, for example, Conley [2]). Kotliar, using Monte Carlo techniques, calculated the changes in distribution for pol)miers with Schulz-Zimm distributions of varying initial breadth. He considered random scission [3-6] and scission plus cross-linking. He concluded that an increase in amount of chain scission for a broad MWD, M jMn > 2, results in a decrease in the MWD, for the case of random... 

The theoretical treatments of Ajg discussed here were motivated by the question of the effects of molecular weight dispersion on measured second virial coefficients. Once Ajf Mjy Mj ) is available it is obvious in principle how to obtain A 2 or. 4 2 for any desired form of distribution. Detailed calculations using the hard-spherelike interaction model with the familiar Schulz-Zimm distribution indicate that the ratio of virial coefficients increase wi out limit with the... 

The importance of molecular weight distribution in studies of polymerization, polymer processing and the physical and mechanical properties of polymers creates a need for mathematical description of the distribution. Several models are commonly used (Flory [1], Schulz-Zimm... 

As with the Schulz-Zimm model, one needs to evaluate (3N-1) parameters to characterize a blend. A graph of the blend cumulative distribution on probability log paper will result in a curve composed of several straight segments. 

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