Statistics of flexible chain configurations

When Monte Carlo methods are employed to study the statistical dimensions of flexible polymer chains, it is necessary that the sampling be statistically unbiased. One Monte Carlo procedure is the so-called “slithering snake” technique, which has proved to be very useful. A question arises, however, as to how long it takes for a “slithering snake” to be completely regenerated to avoid biasing the samples around a particular configuration. It is demonstrated theoretically and verified by Monte Carlo studies that the number of iterations required to completely regenerate a sample polymer is a quadratic function of the chain length. This verification applies to chains in dilute solution but may not hold for bulk polymers.