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sibly SWCNT density, both of which are expected to modify the transport characteristics. To capture the ef- fect of these network features in detail, we turn to sys- tematic model computations of nanotube assembly on experiment-scale channels. SWCNTs coarse-grained as rigid rods are employed to gain sufficient statistics on the interplay between topology and the nature of electri- cal percolation within the network; the effect of channel width W$_{c}$ is explored using 2D computations while multi- layer, quasi-2D computations are used to study the ef- fect of channel thickness. SWCNTs are randomly placed onto channels with prescribed dimensions until the de- sired network density ρ$_{NT}$ is obtained. The stochastic nature of this procedure allows us to capture the varia- tions in network topologies formed due to combination of hydrodynamic forces due to the receding contact line as well as the evaporation flux that drives the fluidic as- sembly. The average length of the SWCNTs is matched to that in the experimental samples, ¯ l ∼ 2 . 5 µ m and the distribution of SWCNT lengths is based on earlier exper- imental studies which indicate Weibull statistics [19]. 

The random stick model that has been employed in earlier studies [16] is clearly inadequate in capturing key phenomena such as CNT bundling during self-assembly (see Fig. 2). In order to generate realistic topologies, we further relax the network by allowing the coarse-grained SWCNTs to interact. The inter-CNT interactions, lo- calized at the junctions, are obtained by integrating the well-known Lennard-Jones (LJ) based description of the van Der Waals between graphene surface elements. As an example, for fully aligned CNTs, the axially averaged inter-CNT interaction energy per length U ( R, r ) is again a 6-12 LJ-type potential with constants that are scaled by surface integrals which depend entirely on the ratio of the inter-tube distance to the CNT radius R/r [20, 21]. 

Note that this inter-tube interaction is short-ranged and negligible for R ≥ √ 3 r , i.e. it is limited to first near- est neighbors. For partially aligned CNTs, the van Der Waals potential can again be integrated over the surfaces of the (pair) of CNTs. The resultant effective inter-CNT interactions are angular as they now depend on the de- gree of misalignment at the CNT-CNT junction φ , i.e. U ≡ U ( R, r, φ ) [Wang and Upmanyu, in preparation]. In the case of fully aligned bundles, this inter-tube po- tential accurately describes equilibrium inter-tube spac- ing, cohesive energy per atom and bulk modulus. The interactions serve as inputs for classical dynamical sim- ulations aimed at locally relaxing the random network with respect to both translational and angular degrees of freedom of the individual SWCNTs. Sliding between the CNTs at the junctions is ignored. A time step of 1 µ s is employed and the simulations are performed until the interaction energy associated with the network stabilizes. 

Figure 3(a) shows specific instances of the electrically heterogeneous network topologies obtained in three sim- ulations with varying widths, W$_{c}$ = 1 µ m, 500 nm and 100 nm. In each case, the SWCNT network is con- fined, ¯ l/W$_{c}$ < 1 which forces the topology to become increasingly aligned with decreasing width. While the as-generated random topologies are geometrically aligned along the channel, we find that the SWCNT interactions always work towards increasing the degree of alignment. This is not surprising as the orientation dependence of the interaction potential favors a nematic-like phase con- sisting of fully aligned nanotubes [22]. For each relaxed CNN with a prescribed network density, the electrical transport characteristics are extracted by fixing the over- all ratio of semiconducting to metallic SWCNTs to the theoretical heterogeneous density (3:1). To this end, each SWCNT is randomly assigned a metallic or semiconduct- ing character and the overall percolation across the CNN is measured. The overall percolation can result in i) open circuit (OC), ii) semiconducting, or iii) metallic conduc- tance across the network. Multiple simulations ( ∼ 100) are performed for each channel geometry and density to determine the form of percolation. 

Figure 3(b)-(d) shows the percolation probability through monolayered CNNs as a function of the net- work density for the three widths shown in Fig. 3(a). All CNNs exhibits two transitions as the network density is increased: OC-to-semiconducting at low densities, and a semiconducting-to-metallic at high densities. Qualita- tively similar transitions are also observed for unrelaxed networks that are used as input in random-stick models (shown as dotted lines) and comparisons with percola- tion in relaxed structures indicates that the enhanced alignment driven by the SWCNT interactions shifts the transitions to higher network densities. The effect of de- creasing width is similar as it also enhances the alignment along the channel - for a given network density, the net- 

