'Manuscript\_Anisotropy.bib'
title: Anisotropy in electrical conductivity and transparency of films of aligned conducting rods
---

Introduction {#sec:intro}
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Thin films filled with highly conductive rodlike particles (such as carbon nanotubes, metal nanowires, etc.) are of increasing interest, particularly, for the production of flexible transparent conductors (for review, see, e.g., [@Hecht2011] and the references therein). Transparent conducting electrode devices find diverse applications in solar cells, touch-screens and transparent heaters [@De2010; @Mutiso2013; @Ackermann2016; @Kumar2016; @Kumar2017]. These promising applications are inspiring both theoretical and experimental studies in this field [@Taherian2016].

Geometrical percolation is defined as the formation of a connected cluster of particles that spans the whole system [@Stauffer1992]. In the different models, it may be assumed that the particles can either penetrate each other (soft overlapping particles), or may contain both internal “hard cores” (an impenetrable part of the particle) and external “soft shells” responsible for charge transfer [@Balberg1987]. It is useful to introduce a number density term, $n$, defined as the number of particles per unit volume for three-dimensional (3D) systems or per unit area for two-dimensional (2D) systems. For randomly distributed, overlapping particles, the total fraction of the space covered by the particles (the filling fraction) can be evaluated as 