Chain Molecules the Most Probable Distribution

Consider a linear condensation polymer of type i formed from a 

The probability that the carboxyl group of the first unit is esterified is equal to p. The probability that the carboxyl of the second unit is esterified, this probability being independent of whether or not linkage 1 has been formed, is likewise equal to p. The probability that this sequence continues for x — l linkages is the product of these separate probabilities, or This is the probability that the molecule con- 

If none but linear open chain polymer molecules are present, which for the present we assume to be the case, then obviously the probability, Nx, that any molecule selected at random is composed of x units must equal the mole fraction of x-mers. 

If the added weight of the end groups (equal to H+OH for each molecule) is neglected, the molecular weight of each species is directly proportional to X. Hence the weight fraction can be written 

The error introduced by this approximation will be significant only at very low molecular weights. Substituting from Eq. (2) 

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