Random flight polymerization

It follows from this that Bernoulli and Markov mechanisms differ in whether the transition probabilities of the crossover, or hetero, steps are the same as or different from the homo steps (see Table 15-6). In addition, both types of mechanism can be subclassified as to whether the transition probabilities for the homo linkages are symmetric or asymmetric. In copolymerization, a symmetric Bernoulli mechanism with constitutionally different monomers is called azeotropic copolymerization with configurationally different monomers, it is called random flight polymerization and in stereocontrolled polymerization with nonchiral monomers, it is also called ideal atactic polymerization. ... 

The theory of cyciization in condensation polymerization was first investigated by Kuhn in the 1930s with the introduction of the concept of effective concentration (Ceff), which is the local concentration of two chain ends of the same molecule for a Gaussian chain. This measurement provides a relationship between the end-to-end length of a polymer chain and that same chain s propensity to cyclize. Therefore, C s provides a method of quantification for the propensity of intramolecular interactions and cyciization, and Kuhn predicted that the cyciization probability decreases as where N is the number of bonds in the chain. Several other treatments have addressed the calculation of C s as a function of chain length using either random-flight statistics or a particle-in-a-sphere approximation. ... 

The classic use of the rotational isomeric state model is for the rationalization of the mean square unperturbed dimensions of a long-chain molecule, as measured either in dilute solution in the absence of excluded volume (ie, in a solvent) or in the bulk amorphous state (7). A much simpler model for such a chain uses random flight statistics to write a temperature-independent (r )o as the product of a term N that is directly proportional to the degree of polymerization and another term (L ) that specifies the mean square step length of a segment. 

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