tance drops out as we evaluate a change in resistance.
In Fig. 3(d) we show the change in resistance calculated
from Eq. (7) as a function of CO concentration for Ni occu-
pying the three types of vacancies. The background reference
concentration of CO is taken to be C0 = 0 .1 ppm. For the
monovacancy there is very little change in resistivity. This is
because most active sites are blocked by O 2 at relevant CO
concentrations, as shown in the upper panel of Fig. 3. For Ni
in the divacancies there is, however, a change in resistance on
the order of 1Ω per site. For concentrations above ∼1 ppm,
the CO coverage of Ni in the divacancy II increases dramati-
cally and this leads to a signiﬁcant increase in resistance.
We now return to the discussion of the validity of Eq. (7).
As mentioned, the series coupling of individual scatterers
should be valid when lφ < d. However, even for lφ > d
and assuming that the Anderson localization length, lloc in
the system exceeds lφ, Eq. (7) remains valid if one replaces
the actual resistance R by the sample averaged resistance ⟨R⟩
[29]. At room temperature under ambient conditions, interac-
tions with external degrees of freedom such as internal CNT
phonons and vibrational modes of the adsorbed molecules
would rapidly randomize the phase of the electrons. There-
fore Eq. (7) should certainly be valid in the limit of low dop-
ing concentrations. On the other hand, the total number of
dopants, N, should be large enough for the statistical treat-
ment of the coverage to hold. Finally, we stress that Eq. (7)
represents a conservative estimate of the change in resistance.
In fact, in the regime where lφ > lloc, i.e. in the Anderson
localization regime, the resistance would be highly sensitive
to changes in the fractional coverage of active sites. Calcula-
tion of the actual resistance of the CNT in this regime would,
however, involve a full transport calculation in the presence of