Impact of tunneling anisotropy on the conductivity of nanorod dispersions

Abstract

While the tunneling conductance between two spherical-like conducting particles depends on the relative inter-particle distance, the wave function overlap between states of two rod-like particles, and so the tunneling conductance, depends also on the relative orientation of the rod axes. Modeling slender rod-like particles as cylindrical quantum wells of diameter D and length L ≫ D, we calculate the matrix element of the tunneling between two rods for arbitrary relative orientations of the rod axes. We show that tunneling between two parallel rods is about L/ √ Dξ times larger than the tunneling matrix element for perpendicular rods, where ξ is the tunneling decay length. By considering the full dependence of the tunneling conductance on the angle between rod axes, we calculate within an effective medium theory the conductivity of dispersions of rods with different degrees of alignment. We find that for isotropically oriented rods, the effect of orientation in the tunneling processes is marginal for all rod concentrations. On the contrary, for systems of strongly aligned rods, the enhanced tunneling between nearly parallel rods increases significantly the system conductivity in a relatively large concentration range. Next, we consider systems in which shortrange attraction between rods is added, as in dispersions of rods with depletion interaction. We find that the strongly anisotropic attraction promotes enhanced tunneling between neighboring parallel rods, increasing the effective medium conductivity by several orders of magnitude compared to the case in which the angular dependence of tunneling is ignored, even for relatively weak attractions.

Tunneling conductivity in anisotropic nanofiber composites: a percolation-based model

“…This finding is similar to that reported in a recent EMA-based investigation [17]. However, the present work suggests that the conductivity may display a strong dependence upon the variance in the order parameter, in addition to the degree of particle clustering.…”

“…[17]), equations (22) and (27) of Ref. [17] yield the following result for the rod-to-rod tunneling conductance:…”

“…For a configuration such that the centers of each member of the pair of rods are both located on the line of shortest distance between the rod axes (figure 1 of Ref. [17]), equations (22) and (27) of Ref. [17] yield the following result for the rod-to-rod tunneling conductance:…”

“…A recent analysis [17] that employed the Effective Medium Approximation ("EMA") provided an estimate for the anisotropy in the effective tunneling conductance between a pair of rod-like particles, that is, for the dependence of the conductance upon the relative angle between the longitudinal axes of the particle pair.…”

Depletion-interaction effects on the tunneling conductivity of nanorod suspensions

“…This enhancement becomes significant only when the centers of the two rods are close and the angle between the two rods is small. A detailed analysis of the pairwise conductivity of rods will be the subject of a separate presentation [26]. …”