The connectedness of packed circles and spheres with application to conductive cellular materials

Li-Ion Permeability of Holey Graphene in Solid State Batteries: A Particle Dynamics Study

Lithium (Li)-ion permeability of holey graphene (hG) for use as an electrically conducting scaffold in solid-state battery electrodes is explored through the means of a particle dynamics simulation model. While carbon materials do not typically exhibit Li-ion conductivity, the unique structural motif of hG, which consists of two-dimensional nanosheets with arrays of through-thickness holes, may present an opportunity for Li-ion conductors (i.e., solid electrolyte (SE) particles) to make contacts through the holes. In our model, the SE is presented as a system of hard elastic spheres conductive to Li-ions. The SE spheres are in contact with each other through compression between two plane current collectors. One hG layer is inserted between the current collectors and parallel to them. Randomly distributed circular holes in the hG allow for contact between the SE particles on both sides of the hG layer. By solving the Li-ion conducting network formed between the electrodes through the contact points of all the particles, the overall conductivity of the system was calculated as a function of SE particle size and the size and number of the hG holes (i.e., hG porosity). A critical ratio of around 4 between the SE particle size and the pore size was found. Below this critical value, the hG layer becomes practically transparent for Li-ions. This study helps to guide the design of highly efficient solid-state electrode composition and architectures using hG as a unique electrically conducting scaffold.

Electrically conductive bulk composites through a contact-connected aggregate

This paper introduces a concept that allows the creation of low-resistance composites using a network of compliant conductive aggregate units, connected through contact, embedded within the composite. Due to the straight-forward fabrication method of the aggregate, conductive composites can be created in nearly arbitrary shapes and sizes, with a lower bound near the length scale of the conductive cell used in the aggregate. The described instantiation involves aggregate cells that are approximately spherical copper coils-of-coils within a polymeric matrix, but the concept can be implemented with a wide range of conductor elements, cell geometries, and matrix materials due to its lack of reliance on specific material chemistries. The aggregate cell network provides a conductive pathway that can have orders of magnitude lower resistance than that of the matrix material - from 10¹² ohm-cm (approx.) for pure silicone rubber to as low as 1 ohm-cm for the silicone/copper composite at room temperature for the presented example. After describing the basic concept and key factors involved in its success, three methods of implementing the aggregate into a matrix are then addressed – unjammed packing, jammed packing, and pre-stressed jammed packing – with an analysis of the tradeoffs between increased stiffness and improved resistivity.