Four homologous mesogens of the hexakis(n-alkoxy)triphenylene series (HATn, n= 4,6,9,11), have been doped with the one electron oxidant NOBF4, and the electrical conductivity measured as a function of frequency in the hexagonal columnar Dh phase. The limiting low-frequency conductivities both parallel, σ‖, and perpendicular, σ⊥, to the column axes decrease exponentially with increasing side-chain length. The value of σ‖ decreases by three orders of magnitude in going from n= 4 to n= 11. This can be understood in terms of an increasing degree of disorder in the packing of molecules in the columns. The decrease of σ⊥ by some two orders of magnitude can be attributed to the increase in the distance between the columns.