Analytical modeling of orientation effects in random nanowire networks

Films made from random nanowire arrays are an attractive choice for electronics requiring flexible transparent conductive films. However, thus far there has been no unified theory for predicting their electrical conductivity. In particular, the effects of orientation distribution on network conductivity remain poorly understood. We present a simplified analytical model for random nanowire network electrical conductivity that accurately captures the effects of arbitrary nanowire orientation distributions on conductivity. Our model is an upper bound and converges to the true conductivity as nanowire density grows. The model replaces Monte Carlo sampling with an asymptotically faster computation and in practice can be computed much more quickly than standard computational models. The success of our approximation provides theoretical insight into how nanowire orientation affects electrical conductivity.