Fractional Brownian modeled linear polymer chains with one dimensional Metropolis Monte Carlo simulation

Abstract

The scaling expression for fractional Brownian modeled linear polymer chains was obtained both theoretically and numerically. Through the probability distribution of fractional Brownian paths, the scaling was found out to be 〈R2〉 ~ N2H, where R is the end-to-end distance of the polymer chain, N is the number of monomer units and H is the Hurst parameter. Numerical data was generated through the use of Monte Carlo simulation implementing the Metropolis algorithm. Results show good agreement between numerical and theoretical scaling constants after some parameter optimization. The probability distribution confirmed the Gaussian nature of fractional Brownian motion and the behavior is not affected by varying values of the Hurst parameter and of the number of monomer units.