Lansing-Kraemer distribution

Fractionation Data and Distribution Analysis of the HEC Before Hydrolysis. The results of the fractionation of HEC not subjected to cellulase attack are given in Table I. It appeared that the distribution of these fractionation data could be described by the Lansing-Kraemer distribution (39), also known as the logarithmic normal distribution, i.e. ... 

The unhydrolyzed HEC obeys the Lansing-Kraemer distribution a straight line was obtained, putting the z values against the logarithm of the molecular weights. The following experimental equation was obtained ... 

Fractionation Data and Distribution Analysis of HEC After One Hour of Cellulase Attack. The results of the gel chromatographic separation of HEC after one hour of enzymic hydrolysis are given in Table II. These fractionation data did not correspond to any of the distribution functions mentioned by Peebles (41) and by Tung (42). In the middle of the distribution it corresponded to the Lansing-Kraemer distribution functions, but deviations occurred at the low- and high-molecular-weight ends. 

Neither the Wesslau nor the Lansing-Kraemer distribution has as yet been related to a definite polymerization mechanism. 

The broadness of the distribution is given by the parameter j, obtained from the slope (tan 0) of the log-normal plot where tan d = 7A/2. The polydispersity ratio (Af /Afp = exp(7 /2) no and x are constants in the distribution function not determinable from the log-normal line. (Special cases of the general distribution function have also been employed, e.g., the Lansing and Kraemer relationship where x = 0 [304] and the Wesslau relationship [305], where x = —1). Fractionation data can also be adequately represented by other exponential distributions such as that of Tung [306] W(n) dn = abn exp(—an ) dn. (W(n) = 1 — exp(—an )). Fig. 14a(c). 

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