Quantitative Interpretation of Simulated Polymer Mean-Square Displacements

We propose a path for making quantitative analyses of mean-square displacement curves of polymer chains in the melt or in solution. The approach invokes a general functional form that accurately describes $g(t) \equiv \langle (\Delta x(t))^{2} \rangle$ for all times at which $g(t)$ was measured, and that gives values for the logarithmic derivative of $g(t)$ for the same times. By these means we can readily distinguish between regimes in which $g(t)$ follows a power law in time, does not follow a power law in time, or has an inflection point. In a power-law regime, the method accurately determines the exponent, without imposing any assumption as to the exponent's value.