#### 3.1. Morphology Observation of CNTs/CFs

Using the aforementioned two-step method, a layer of coaxial CNTs was successfully grown on the CF surface. As shown in

Figure 3a–d, the entire surface of the CF is fully covered by slender CNTs, and the diameter of the CNTs/CF composite increases with increasing CNTs growth time. The inset in

Figure 3h shows a TEM image of a CNT, clearly indicating that the CNT has a hollow tubular structure like bamboo. The main constituent of a CNT is the carbon element, generated from the decomposition of acetylene on the surface of Ni nanoparticles. Sengupta and Jacob [

21] concluded that the dissolved carbon element would diffuse toward the bottom of the Ni particles and segregates as graphite on the CF surface. The Raman spectrum proved that the structure of the CNTs was multi-walled [

17]. As the CNTs growth time increases, carbon generated from the decomposition of acetylene increases, causing CNTs to grow in length (as shown in

Figure 3f–h), thus enlarging the thickness of the CNT layer, as revealed by Brukh and Mitra [

22]. Consequently, the diameter of a CNTs/CF is larger than that of the pristine CF, and increases with increasing CNTs growth time. As can be seen from

Figure 3e–h, the surface of the pristine CF is very smooth, but those of CNTs/CF samples are extremely rough and porous, indicating that a CNTs/CF has a larger SSA than a pristine CF. Since the SSA of a CNT (theoretical surface areas for multi-walled CNTs are diameter-dependent and estimated to be in the range of a few hundred m

^{2}·g

^{−1} [

23]) is much higher than a pristine CF (0.15 m

^{2}·g

^{−1} obtained from BET analyses), the thicker the CNTs layer, the larger the SSA of a CNTs/CF. Therefore, the SSAs of CNTs/CF-T5, CNTs/CF-T10, and CNTs/CF-T15 were increased remarkably from 0.15 m

^{2}·g

^{−1} to 35.95, 84.97, and 119.53 m

^{2}·g

^{−1}, respectively, demonstrating that the SSA of a CF will be significantly enlarged after its surface is covered with CNTs.

The as-fabricated CNTs/CFMEs are shown in

Figure 4a. Each CNTs/CFME has two exposed ends. One exposed end is a piece of copper wire, whose length (10 mm in this work) is selected based on the connection requirements to the outer circuits. The other exposed end is a piece of protruding CF monofilament (250–300 μm) modified with or without CNTs, which acts as the working electrode.

Figure 4b shows a magnified view of the protruding CF monofilament, which clearly shows that the CF was well encapsulated by epoxy resin. Following proper sample preparation and encapsulation protocols, the epoxy resin keeps the protruding CF clean and away from contaminants.

#### 3.2. Electrical Conductivity Analysis of CNTs/CFs

Our test results show that the electrical conductivities of CNTs/CF-T5, CNTs/CF-T10, and CNTs/CF-T15 were enhanced by 15%, 38%, and 57%, respectively, compared to that of the pristine CF (about 625 S·cm

^{−1}). This validates the beneficial role of CNTs: that longer, denser CNTs lead to better electrical conductivity in the CNTs/CF. Among the CF and CNTs/CFs, CNTs/CF-T15 has the largest electrical conductivity, of 965.94 S·cm

^{−1}, which can be attributed to the following two reasons. First, the highly conductive multi-walled CNTs (about 1000–2000 S·cm

^{−1} [

24]) significantly elevated the conductivity of a pristine CF. Second, and importantly, CNTs with a large length-to-diameter ratio would entangle with each other on the CF surface and form a three-dimensional (3D) coaxial conductive network, providing a larger contact area and additional electron conduction pathways, and thus enhancing the electrical conductivity [

25]. By extension, the microelectrodes fabricated from the CNTs/CFs monofilament would therefore have markedly improved electrical conductivity compared to the one made from the pristine CF.

#### 3.3. Cyclic Voltammetry (CV) Analysis of CNTs/CFMEs

Figure 5 shows the CV curves of the as-prepared CFMEs in 5.0 mM K

_{4}Fe(CN)

_{6}, performed at a scan rate of 0.10 V·s

^{−1}. As shown, all of the CV curves exhibit highly symmetrical shapes for both the forward and reverse potential scans, indicating that highly reversible redox reactions are taking place at the CNTs/CFMEs. It demonstrates that the CNTs/CFMEs, as microelectrodes, exhibit an outstanding electrochemical property in the presence of K

_{4}Fe(CN)

_{6} and are able to reproduce the electrode reaction process of active substances [

26]. From

Figure 5a, it can be seen that the CV curve of the pure CFME has relatively gentle peaks, low peak currents, and a narrow area under the curve, similarly illustrated by Chen et al. [

27]. In comparison, the CNTs/CFMEs show better CV behaviors, e.g., more distinguishable peaks, as well as much higher response currents, as shown in

Figure 5b–d. In addition, the microelectrode decorated with longer and denser CNTs has more evident peaks and higher peak currents, demonstrating that the CNTs/CFME has a higher sensitivity than the unmodified CFME [

28].

Figure 6 shows the individual CV curves of pure CFME and CNTs/CFMEs at scan rates of 0.01 V·s

^{−1}, 0.05 V·s

^{−1}, 0.10 V·s

^{−1}, and 0.50 V·s

^{−1} in 5.0 mM K

_{4}Fe(CN)

_{6}. As shown, the peak potentials (including the oxidation peak,

E_{pa}, and reduction peak,

E_{pc}) of identical electrodes at different scan rates show a negligible difference, with

E_{pa} approaching 0.35 V and

E_{pc} displaying a value of 0.17 V for all four electrode samples.

According to the Nernst equation, the boundary condition of the reversible process can be expressed by [

29]:

where

$\Delta {E}_{p}$ is the peak-to-peak potential difference,

R is the universal gas constant (8.3143 J·K

^{−1}·mol

^{−1}),

T is the thermodynamic temperature (298.15 K for room temperature),

n is the number of electrons involved in the reaction, and

F is the Faraday constant (96,485.3383 C·mol

^{−1}). Consequently, Equation (1) can be simplified as:

Since the main electrode reaction in the K_{4}Fe(CN)_{6} solution is: [Fe(CN)_{6}]^{4−} − e^{−} = [Fe(CN)_{6}]^{3−}, the number of electrons involved n is one. Therefore, the boundary condition is theoretically equal to $\Delta {E}_{p}\le 59.0\text{}\mathrm{mV}$. Often, the experimentally observed $\Delta {E}_{p}$ values are greater than the theoretical value of 59.0 mV.

Figure 7a depicts the

$\Delta {E}_{p}$ values of CFMEs at different scan rates. All experimentally observed

$\Delta {E}_{p}$ values are larger than the theoretical value of 59.0 mV. However, as can be seen from

Figure 6, the peak currents

I_{p} for all electrodes increase remarkably with the increasing scan rates of potential, and the ratios of the oxidation peak currents

I_{pa} to the reduction peak currents

I_{pc} approach unity. Therefore, it can be concluded that the reactions occurring at the CNTs/CFMEs and its pristine CFME are reversible or quasi-reversible processes [

30].

Figure 7a shows that the

$\Delta {E}_{p}$ values of all CNTs/CFMEs are smaller than that of the pristine CFME at the same potential scan rate. Furthermore, for CNTs/CFMEs, as the CNTs growth time increases—hence producing greater CNT lengths and densities—

$\Delta {E}_{p}$ decreases proportionally toward the theoretical minimum. Such a decrease of

$\Delta {E}_{p}$ implies that the redox reactions taking place at the CNTs/CFMEs tended to be increasingly reversible processes as the dimensions and densities of CNTs increased [

31].

The oxidation peak current (

I_{pa}) values of all of the electrodes versus the square root of the scan rates (

v^{1/2}) are shown in

Figure 7b. The linear relationship between

I_{pa} and

v^{1/2} is demonstrated with linear fitting, and the coefficients of determination are all over 0.99. Compared to the unmodified CFME, all of the CNTs/CFMEs have increasingly larger linear slopes between

I_{pa} and

v^{1/2} as the thicknesses of the CNT layers increase, indicating that the peak currents of CNTs/CFMEs have a progressively higher sensitivity towards potential scan rates. As shown in

Figure 6, even at a slow scan rate of 0.01 V·s

^{−1}, the oxidation peaks and reduction peaks of each CNTs/CFME are clearly visible, especially for the CNTs/CFME-T15 electrode. On the contrary, no such peaks were observed for the pristine CFME. This phenomena proves that the CNTs are beneficial to enhancing the sensitivity of CFMEs, and a greater electrode sensitivity to scan rate can be achieved with thicker and denser CNTs [

32].

#### 3.4. Electrocatalytic Activity of the Microelectrode

An electrochemical effective area is a critical parameter for characterizing the electrocatalytic activity of an electrode, since it provides the reaction active sites and contact interface area between the electrode and analytes [

33]. In light of this, CNTs can appreciably improve the electrochemical performance of a CFME through enlarging its surface area and providing more reaction active sites. The chronoamperogram in

Figure 8a shows that the response currents of the CNTs/CFMEs are higher than that of the CFME, which is consistent with the results obtained by the CV method mentioned above. Moreover, the response current decays very slowly in the long time zone, so it can be recognized as a quasi-steady state [

34], and its current is defined as the quasi-steady state current

i_{qss}.

Szabo et al. [

35] reported an approximate formula describing the relationship between the current and time for cylindrical microelectrodes:

where

i is the current in amps,

A is the effective electrode area in cm

^{2},

D is the diffusion coefficient in cm

^{2}·s

^{−1},

c is the concentration of the electroactive species in mol·cm

^{−3},

r is the radius of the cylindrical microelectrode in cm, and

τ is a coefficient related to time and is equal to

$\tau =4Dt/{r}^{2}$. For a quasi-steady state, since

τ is very large in the long time zone, Equation (3) can be simplified as [

34]:

Figure 8b–e shows the scatter plots of the chronoamperometry response current vs. l/ln

τ for different CF electrodes. The response current decays very slowly with the increase of time (after about 0.2 s), confirming the occurrence of the quasi-steady state (the front part of the scatter plots). Therefore, a linear fitting was adopted to fit the plots of this part.

Table 2 lists the obtained equations of linear regression, whose coefficients of determination are all larger than 0.99, further validating the good linear relationship between the

i_{qss} and l/ln

τ. Assuming a diffusion coefficient for 5.0 mM ferrocyanide of 6.67 × 10

^{−6} cm

^{2}·s

^{−1} in 1.0 M KCl, as presented by Konopka and Mcduffie [

36], the effective electrode area

A can be calculated according to Equation (4). The results were listed in

Table 3. It indicates increased ratios in the effective electrode area of 79%, 443%, and 749% for CNTs/CFME-T5, CNTs/CFME-T10, and CNTs/CFME-T15, respectively, as compared to a pristine CFME. This result is consistent with the SSA variation of CNTs/CFs after the introduction of CNTs, as mentioned above. Thus, the electrocatalytic activities of CNTs/CFMEs are enhanced significantly, owing to the massive active sites provided by the CNTs.

The chronoamperometry response currents of the electrodes at the tenth second were selected as the quasi-steady state currents and the corresponding current densities were calculated (listed in

Table 3). The current densities of the CNTs/CFMEs are much higher than that of an unmodified CFME, with a maximum two times increase (CNTs/CFME-T5). It indicates that the CNTs/CFMEs have a higher mass transfer rate and reaction rate. In addition, the current densities of CNTs/CFME-T10 and CNTs/CFME-T15 are very close, and they are both less than that of CNTs/CFME-T5. It is possible that the diameter of the CF microelectrodes enlarges with the increased content of CNTs, resulting in the reduction of its mass transfer rate.