Configurational statistics of short polymeric chains
The end-to-end distances (r) of configurations of model polymethylene chains of up to 30 bonds having independent and interdependent rotational states have been determined over the complete range of temperatures by direct numerical evaluation. From these, the second to tenth moments ([graphic omitted] to [graphic omitted]) of the radial frequency functions (W(r)) have been found. The moments have been determined exactly for the chains of up to 12 bonds and approximately for the longer chains. Using the values of [graphic omitted] to [graphic omitted] it has been possible to define equivalent freely-jointed chains for all the polymethylene chains investigated. The number of real bonds equivalent to one freely-jointed link is found to increase smoothly with chain length and to decrease with increase in temperature. [graphic omitted] to [graphic omitted] have also been used to determine W(r). The forms of W(r) are compared to those of the freely-jointed chain, and the variation of W(r) with both temperature and chain length is discussed.