Polymer crystallization bell curve

The proof that these expressions are equivalent to Eq. (1.35) under suitable conditions is found in statistics textbooks. We shall have occasion to use the Poisson approximation to the binomial in discussing crystallization of polymers in Chap. 4, and the distribution of molecular weights of certain polymers in Chap. 6. The normal distribution is the familiar bell-shaped distribution that is known in academic circles as the curve. We shall use it in discussing diffusion in Chap. 9. 

Table 3.4 refers to a number of crystaUizable miscible polymer blends for which the sphemhte growth rate as a function of the crystallization temperature has been investigated. For most blends, only a part of the bell-shaped curve could be measured. In Fig. 3.8, the complete bell-shaped spherulitic growth rate curve of iPS in iPS/PS blends containing 0,15, and 30 wt% PS is shown. Due to the addition of impurity (e.g., the amorphous PS), a suppression of the growth rate is observed, which is greater than the concentration of the impurity added. Important parameters of the impurity added to the crystaUizable component are the type, concentration, and molecular weight (Keith and Padden 1964). 

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