Quantitative Interpretation of Simulated Polymer Mean-Square Displacements

The time-dependencies of polymer mean-square displacements g(t) provide significant tests of some modern theories of polymer dynamics. Familiar models propose that g(t) is described by a series of power-law regimes g(t)∼tα, the models predicting values of α and time regimes within which those values will be found. g(t) has been obtained quantitatively over a wide range of times by means of computer simulations, permitting comparison of simulation measurements with these models. Here, we demonstrate a path for quantitatively analyzing g(t). We show that we can readily distinguish between regimes in which g(t) actually follows a power law in time, does not follow a power law in time, or has an inflection point. The method accurately determines local values of the exponent, without imposing any a priori assumption as to the exponent's value.