Logarithmic distribution, Wesslau

Important differential mass-distribution functions (probability density function of mass-distribution) are the most probable distribution (Schulz-Flory), the Schulz-Zimm distribution, the Poisson distribution, Tung distribution, and logarithmic normal distribution (Wesslau distribution) [08IUP2]. Methods for the determination of distribution functions of molar mass are listed in Table 4.1.4. 

Wesslau MWD. The model based on the Wesslau MWD has been described previously (JS). The weight fraction distribution of x-mer, where X is the degree of polymerization (DP), measured as a function of the logarithm of the degree of polymerization, is given by... 

Figure 1. Wesslau and Flory-Schulz differential weight-fraction MWDs on a logarithmic scale, where W is the weight fraction and M is the molecular weight. Both distributions are for M = 10,000 gjmol and M /M = 2.0.

Figure 8-4. Integral mass distribution for a Wesslau distribution plotted on logarithmic-cumulative frequency graph paper. The mass fraction w, and viscosity average, ( (instead of, more correctly, < degree of polymerization of the fractions (O) were measured. The number...

For widely distributed polymers such as radically polymerized polyethene the Schulz-Flory distribution function is unable to describe the high degree of asymmetry in the distribution. In this case, the Wesslau distribution (logarithmic normal distribution) is used and given by ... 

Plot the Schulz distribution in cumulative form on logarithmic probability paper for xjx = 2. What parameter for the Wesslau model gives the best fit ... 

Compare the cumulative distribution of Problem 6.14 with the Wesslau model on logarithmic probability paper using the product ax as the measure of molecular weight. 

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