Polymer conformational statistics. I. Probability distribution

The probability distribution P(R) of the end-to-end distance is studied for the rotational-isomeric model of polymer chains. A Monte Carlo investigation provided reliable numerical data for P(R), which was then compared with results from two relatively analytic studies. The first of these, and by far the more complicated, was a steepest descent inversion of the characteristic function. This method was found to be more satisfactory, particularly for large R, than Hermite function expansions that have been used in the past. However for chains of N bonds the method fails, for N<40, to show the stiffness evident for small R. A second quite simple method was to maximize the entropy functional of P(R) subject to assigned 〈 R2〉 and 〈 R4〉. The results for P(R) were in good agreement with Monte Carlo results down to N=12, and for all R.