Sequence Selection Problem in the Crystallization of Polymers

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Abstract
The crystallization of linear polymer chains is considered as a process involving the selection of crystallizable sequences from the melt. If, owing to the requirements of thermodynamic stability, such sequences must exceed in length some critical value less than the chain length, and if the selection process is random, then the melt will be increasingly subdivided into uncrystallized sequences of varying length. Some of these may be expected to be less than the critical length, so that the segments comprising them are ``wasted'' insofar as participation in further crystallization is concerned. An approximate sequence length distribution function for the uncrystallized sequences in the system is derived and utilized in connection with the problem of retardation in crystallization kinetics.