Improved path integration method for estimating the intrinsic viscosity of arbitrarily shaped particles

In previous work, we have established that the intrinsic viscosity [eta] of an object is nearly proportional to the average electrical polarizability tensor <alpha(e)>=tr(alpha(e))/3 of a conducting object having the same shape, or equivalently, to the intrinsic conductivity [sigma]=<alpha(e)>/V, which characterizes the conductivity of a dilute mixture of randomly oriented conducting objects (V being the volume of the object). This hydrodynamic-electrostatic analogy is useful because alpha(e) can be determined accurately and efficiently by numerical path integration for objects of arbitrary shape. Here, we show that the uncertainty in [eta] can be reduced to a relatively small value (< 1.5% relative uncertainty) by utilizing additional information from the full tensor alpha(e), rather than just its average. Specifically, we determine the exact constant of proportionality between [eta] and [sigma] for triaxial ellipsoids as a function of the ratios of the eigenvalues of alpha(e) and apply this relation to particles of general shape. In addition to an improved estimation of [eta], the ratios of the components of alpha(e) provide useful measures of particle anisotropy. We also present an improved method for applying the technique to flexible particles, which requires performing a conformational ensemble average. Conformational averages of alpha(e) generate systematic errors that can be avoided by performing the conformational average at an earlier stage in the computation.