  We present a study of connectivity percolation in suspensions of hard
spherocylinders by means of Monte Carlo simulation and connectedness
percolation theory. We focus attention on polydispersity in the length, the
diameter and the connectedness criterion, and invoke bimodal, Gaussian and
Weibull distributions for these. The main finding from our simulations is that
the percolation threshold shows quasi universal behaviour, i.e., to a good
approximation it depends only on certain cumulants of the full size and
connectivity distribution. Our connectedness percolation theory hinges on a
Lee-Parsons type of closure recently put forward that improves upon the
often-used second virial approximation [ArXiv e-prints, May 2015, 1505.07660].
The theory predicts exact universality. Theory and simulation agree
quantitatively for aspect ratios in excess of 20, if we include the
connectivity range in our definition of the aspect ratio of the particles. We
further discuss the mechanism of cluster growth that, remarkably, differs
between systems that are polydisperse in length and in width, and exhibits
non-universal aspects.
