Schulz—Zimm distribution parameters

To generate the necessary distribution functions, the ratio of is used to approximate the true molecular weight distribution by a Schulz-Zimm distribution. It is also assumed that the reactive functional groups are distributed randomly on the polymer chain. The Schulz-Zimm parameters used to calculate distribution functions and probability generating functions (see below) are defined as follows ... 

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). 

In eq 9.44 the distribution function is called generalized Schulz-Flory distribution (or Schulz-Zimm distribution) because of its introduction by Schulz in 1935, and by Flory in 1936. " To evaluate the polydispersity of polymers U = Mw/M - 1 is an important quantity. The quantity k of the Schulz-Flory distribution is given by k= IU. The two parameters f and k of the... 

These parameters are used calculate the site and mass distribution functions assuming a Schulz-Zimm molecular weight distribution. The Schulz-Zimm parameters are calculated in lines 930-950. The weight fraction of diluent (as a fraction of the amount of polymer) is then sought. If there is no diluent enter 0. If there is a diluent, the functionality and molecular weight of the diluent is requested (line 1040). The necessary expectation values are computed (lines 1060-1150). 

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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