Kohlrausch Parameter Determination for Simple Chain Models

The second Legendre polynomials of the end-to-end vector of freely jointed and freely rotating chains were extracted from molecular dynamics simulations and analyzed in terms of the Kohlrausch-Williams-Watts (KWW) function. Of particular interest is the variation of the stretching exponent, $\beta $, as a function of state point and, consequently, of the detailed compliance with time-temperature superposition. A new analysis methodology is introduced that permits the determination of $\beta $ at the needed level of precision. Detailed time-temperature superposition does not hold for freely-jointed or freely-rotating chain liquids. Indications of a breakdown in time-temperature superposition are also found in violations of Stokes-Einstein and Debye-Stokes-Einstein behavior.