Probability segment length

Helfand and Tagami [75,76] introduced a model which considered the probability that a chain of polymer 1 has diffused a given distance into polymer 2 when the interactions are characterised by the Flory-Huggins interaction parameter x They predicted that at equilibrium the thickness , d c, of the interface would depend upon the interaction parameter and the mean statistical segment length, b, as follows ... 

Nj = the number of network chains per cm havingy statistical segments Py = the probability that a chain of j segments will have a vector distance, Rj, between its ends L === the statistical segment length. 

A widely held opinion is that the segment length distribution in the two-step process follows the most probable form no matter what the reaction conditions of the polyaddition are. However, this is only reasonable to be assumed if the reaction is carried out in solution, and there are indications in the literature that more or less pronounced deviations have... 

Next, we consider the situation of Figure 5.8b, where one end is anchored at a distance a, comparable to the segment length I, in front of the hole in the cavity. The probability Pi(N,R) of realizing all conformations corresponding to the situation of Figure 5.8b is (e.g., Muthukumar 2003)... 

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