3
10
-3
10
-2
10
-1
10
0
10
-3
10
-2
10
-1
10
0
Fractional Coverage Θ  of Ni Occupied Vacancies
0.1 1 10 100
CO Concentration [ppm]
10
-4
10
-3
10
-2
10
-1
10
0
O 2
CO
COClean
O 2
O 2
Clean
(a) Monovacancy
(b) Divacancy I
(c) Divacancy II
10
2
10
3
0.1 1 10 100
CO Concentration [ppm]
-10
1
0
10
1
Monovacancy
Divacancy I
Divacancy II
Change in Resistance ∆R [Ω / Ni Occupied Vacancy]
(d)
FIG. 3: Fractional coverage Θ in thermal equilibrium of Ni in a (a)
monovacancy, (b) divacancy I, (c) divacancy II and (d) change in
resistance ∆R per dopant site as a function of CO concentration in
a background of air at room temperature and 1 bar of pressure. The
reference concentration of CO is taken to be C0 =0.1 ppm. Note the
change from linear to log scale on the y-axis at ∆R =10 Ω.
For a given background composition we may thus estimate
the fractional coverages for each available adsorbate for a
given type of doping. As an example, Fig. 3(a)-(c) shows the
fractional coverage of a Ni atom occupying a monovacancy,
divacancy I, and divacancy II, versus CO concentration in a
background of air at room temperature and 1 bar of pressure.
Due to the relatively small binding energy of N 2 and H2O as
compared to O 2 and CO, all Ni sites will be either empty or
occupied by O 2 or CO. In particular, Ni in a monovacancy
(top panel of Fig. 3) will be completely oxidized for all rel-
evant CO concentrations. For the Ni occupied divacancy II
structures we ﬁnd the coverage of CO changes signiﬁcantly
around toxic concentrations (∼10 ppm).
To estimate the effect of adsorbates on the electrical con-
ductance of doped CNTs, we ﬁrst consider the change in con-
ductance when a single molecule is adsorbed on a metal site of
an otherwise pristine CNT. In Fig. 2(b) we show the calculated
change in conductance relative to the metal site with no ad-
sorbate. In contrast to the binding energies, there are no clear
trends in the conductances. The sensitivity of the conductance
is perhaps most clearly demonstrated by the absence of cor-
relation between different types of vacancies, i.e. between the
three panels in Fig. 2(b). Close to the Fermi level, the conduc-
tance of a perfect armchair CNT equals 2 G0. The presence
of the metal dopant leads to several dips in the transmission
function known as Fano antiresonances [20]. The position
and shape of these dips depend on the d-levels of the transi-
tion metal atom, the character of its bonding to the CNT, and
is further affected by the presence of the adsorbate molecule.
The coupling of all these factors is very complex and makes
it difﬁcult to estimate or rationalize the value of the conduc-
tance. For the spin polarized cases, we use the spin-averaged
conductances, i.e. G = (G↑+ G↓)/2.
Next, we estimate the resistance of a CNT containing sev-
eral impurities (a speciﬁc metal dopant with different molecu-
lar adsorbates). Under the assumption that the electron phase-
coherence length, lφ, is smaller than the average distance be-
tween the dopants, d, we may neglect quantum interference
and obtain the total resistance by adding the scattering resis-
tances due to each impurity separately. The scattering resis-
tance due to a single impurity is given by
Rs(X) = 1/G(X) −1/(2G0), (6)
where G(X) is the Landauer conductance of the pristine CNT
with a single metal dopant occupied by molecule X and
1/(2G0) is the contact resistance of a (6,6) CNT.
We may now obtain the total resistance per dopant site rel-
ative to the reference background signal as a function of the
target molecule concentration
∆R
N ≈
∑
X
Rs(X)(Θ[X, C] −Θ[X, C0]), (7)
where N is the number of dopants, Θ[X, C] is the fractional
coverage of species X at concentration C of the target and C0
is the reference concentration. Notice that the contact resis-
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-