Multiple Histogram Method and Static Monte Carlo Sampling

Abstract

Summary: We describe an approach to use multiple‐histogram methods in combination with static, biased Monte Carlo simulations. To illustrate this, we computed the force‐extension curve of an athermal polymer from multiple histograms constructed in a series of static Rosenbluth Monte Carlo simulations. From the complete histogram of the distribution function of the end‐to‐end vectors of the polymer chain, we can efficiently compute the polymer force‐extension curve.Comparison of the stress‐strain curves for the stress ensemble (symbols) and the strain ensemble (lines). Results obtained for N = 100, 200, 400, and 600. For small x, f(x) = −F′(x) was computed by aproximating F(x) by a second degree polynomial and then taking the derivative. For large x, f(x) = −F′(x) was computed numerically.imageComparison of the stress‐strain curves for the stress ensemble (symbols) and the strain ensemble (lines). Results obtained for N = 100, 200, 400, and 600. For small x, f(x) = −F′(x) was computed by aproximating F(x) by a second degree polynomial and then taking the derivative. For large x, f(x) = −F′(x) was computed numerically.

Effect of Chain Stiffness on Polyelectrolyte Condensation

“…The force−extension curve calculated in this manner is equivalent to the strain ensemble, in which one measures the internal retractive force of a chain at fixed elongation. It is possible to convert the results into the stress ensemble, in which one measures the elongation of a chain subjected to a stretching force, but only by recording the connecting information during a simulation …”