  Control of transport processes in composite microstructures is critical to
the development of high performance functional materials for a variety of
energy storage applications. The fundamental process of conduction and its
control through the manipulation of granular composite attributes (e.g., grain
shape) are the subject of this work. We show that athermally jammed packings of
tetrahedra with ultra-short range order exhibit fundamentally different
pathways for conduction than those in dense sphere packings. Highly resistive
granular constrictions and few face-face contacts between grains result in
short-range distortions from the mean temperature field. As a consequence,
'granular' or differential effective medium theory predicts the conductivity of
this media within 10% at the jamming point; in contrast, strong enhancement of
transport near interparticle contacts in packed-sphere composites results in
conductivity divergence at the jamming onset. The results are expected to be
particularly relevant to the development of nanomaterials, where nanoparticle
building blocks can exhibit a variety of faceted shapes.
