The resistance between two arbitrary sites AA and BB is given by equation(8)RA,B=VA−VBI. Which can finally be expressed in terms of specific elements of the inverse of M as equation(9)RA,B=R0([M−1]A,A+[M−1]B,B−[M−1]A,B−[M−1]B,A).RA,B=R0([M−1]A,A+[M−1]B,B−[M−1]A,B−[M−1]B,A). Therefore, the resistance between two arbitrary points in any type of lattice can be calculated as long as we know the number of connections, and which sites are interconnected. It is not hard to generalise this PAI-039 result for the case where the resistance between nearest neighbours is not identical, or even for a distribution of different resistances. In order to do so, the 1R0 term in Eq. (3) would have to be replaced by the specific resistance connecting the corresponding sites, and could be absorbed into the definition of M.
3.1. Application
The method described above can be directly applied to model carbon nanotube films where the resistance between the two electrodes is calculated through Eq. (9). Generating a random configuration of rods and calculating the connectivities of the arrangement, the matrix M is written and the resistance between the electrodes is calculated. It is important to recall this approach is valid when the resistance along the nanotubes is very small, and the resistance of the film is dominated by the junctions.
3.1. Application
The method described above can be directly applied to model carbon nanotube films where the resistance between the two electrodes is calculated through Eq. (9). Generating a random configuration of rods and calculating the connectivities of the arrangement, the matrix M is written and the resistance between the electrodes is calculated. It is important to recall this approach is valid when the resistance along the nanotubes is very small, and the resistance of the film is dominated by the junctions.