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Computer Simulation of Polymer Conformation. II. Distribution Function for Polymers with Excluded Volume

Stellman, Steven D.; Gans, Paul J.

Numerical distributions of end-to-end distances were generated by a Monte Carlo method for hard-sphere off-lattice polymers of length N = 20, 40, 60, 80, 98, and 298 atoms. Comparison by xz tests against five recently proposed theoretical distribution functions showed that for N = 80 and N = 98, the data could be described, with 95% confidence, by the equation f(r) = exp[ -(ar2 + br + c)], where a and b are fitted parameters and c is a normalization constant. For N = 298, limitations of sample size lead to lower confidence limits (about 80%), but good fit. The above equation, and not its gaussian counterpart exp( -cr^2), is probably the limiting distribution function. The function accurately predicts the 1st through 12th observed moments at all chain lengths.


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April 4, 2014