Molecular weight distribution methods above

The present section analyzes the above concepts in detail. There are many different mathematical methods for analyzing molecular weight distributions. The method of moments is particularly easy when applied to a living pol5mer polymerization. Equation (13.30) shows the propagation reaction, each step of which consumes one monomer molecule. Assume equal reactivity. Then for a batch polymerization. 

The above analysis should not be construed as authors opinion that molecular weight distribution, MWD, of PE s should follow log-normal probability. The method of analysis is... 

As mentioned above, the new method Lewis acid promoted living polymerization of methacrylic esters, by using enolatealuminum porphyrin (2) as nucleophilic initiator in conjunction with organoaluminum compounds, such as methylaluminum bis(2,6-di-tert-butyl-4-methylphenolate) (3e), as Lewis acids has enabled us to synthesize poly(methacrylic ester) of narrow molecular-weight distribution [51]. On the other hand, some reactions of aluminum por-... 

When the relation between D and M is established, we can easily convert G(D) obtained by dynamic LLS into a differential molecular weight distribution, such as fw(M). We have successfully applied the above methods to various kinds of polymeric and colloidal systems, such as for Kevlar [15, 23], fluoropolymers (Tefzel Teflon) [12,30-35,52], epoxy [53-55],polyethylene [56,57], water-soluble polymers [18,50-51,58,59], copolymers [60-62], thermoplastics [63-65] and colloids [66-72]. Three of those applications are illustrated below. 

Here, it should be recalled that the average molecular weight indicates only an average value of a more or less broad molecular weight distribution, depending on the method of its determination. For pharmaceutical application great efforts should be made to reach a distribution as narrow as possible, since only in such cases the above statements are conclusive. 

The above results illustrate the utility of multiparticle Brownian dynamics for the analysis of diffusion controlled polymerizations. The results presented here are, however, qualitative because of the assumption of a two-dimensional system, neglect of polymer-polymer interactions and the infinitely fast kinetics in which every collision results in reaction. While the first two assumptions may be easily relaxed, incorporation of slower reaction kinetics by which only a small fraction of the collisions result in reaction may be computationally difficult. A more computationally efficient scheme may be to use Brownian dynamics to extract the rate constants as a function of polymer difflisivities, and to incorporate these in population balance models to predict the molecular weight distribution [48-50]. We discuss such a Brownian dynamics method in the next section. 

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