Table 1.

Constraints on the hopping distance between charge carriers and on the reorganization energy (λ) as calculated via the master equation for the 2D cylindrical mechanism, assuming ~1000 sites couple to each electrode. The parameters were fit to eqn (2.7) to give a current magnitude on the order of 10¹⁰e s⁻¹. The length of the pilus was taken as 600 nm, k_BT = 1/40 eV and β = 10 nm⁻¹. N_col is the number of columns in the 2D mechanism (the maximum value of a bridge site subscript in Fig. 2), with 1000 rows. k° is the heterogeneous electron transfer rate constant at zero potential bias (see Appendix A.1). λ values listed are values for charge transfers within the bridge. The electrochemical λ was taken as 1/2 the value for the bridge hops. Note that the measured current magnitude could not be achieved for n = 10 or 100 without exceeding a charge transfer kinetic limit³ of 10¹³ s⁻¹

rnn (nm)	Ncol	λ (eV)	k° (s−1)	ΔG (eV)
0.35	1700	≤0.3	≥1010	0.0006
0.5	1200	≤0.21	≥1010	0.0008
0.7	860	≤0.1	≥1010	0.0012
1	600	≤0.01	≥1010	0.0017