Multifunctional polycondensation: distribution functions obtained via the stirling approximation
The Stirling approximation was introduced into the Flory f-functional distribution function for polycondensation, and the accuracy of the resulting expressions was determined. An expression, which can be readily numerically integrated, was found to yield cumulative distributions which agree very well with exact summations of the classic f-functional polycondensation expression for low p and all mer sizes, i, as well as for p up to p = 1/(f − 1) and high i for functionalities, f, in the range 2 < f ⪙ 4. The agreement is quite good for low i and p up to p = 1/(f − 1) and f in the same range, with a clear trend to better agreement for lower f.
The expression obtained using the Stirling approximation yields unnormalised i-mer weight fractions. An equation is given which relates the normalisation factor with acceptable accuracy to p and f in the range 2 < f ⪙ 3.
KeywordsCumulative Distribution Weight Fraction Normalisation Factor Alkyd Resin Cumulative Weight
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