Kinetics of Ion Transfer across the SWCNT Interfacial Films

The apparent rate constant (koapp) for the TMA+ and PF6– ion transfer in the presence of SWCNT films formed at different nanotube concentrations was

determined using the Nicholson method, in accordance with Equation 4.4.244

𝜓 = (𝐷𝑤/𝐷𝑜) 𝛼/2_𝑘

𝑎𝑝𝑝𝑜

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Where, for simplicity, the aqueous (Dw) and organic (Do) diffusion coefficients of the

transferring ions were assumed to be equal and the transfer coefficient (α) taken to be

0.5; 𝜓 is a dimensionless kinetic parameter and is related to ΔEp. The relationship between the former and the latter parameters was originally obtained by Nicolson for ΔEp values ranging from 61 to 212. Using numerical simulation, Mahe et al245

presented a working curve (nΔEp vs log 𝜓) that extended the limit to higher ΔEp

values. The remaining terms in Equation 4.4 have their usual meanings.

The ΔEp values measured at scan rates higher than 25 mV s-1 were used in

calculating the values of 𝜓. Figure 4.19 shows the koapp values determined for both

ions as a function of SWCNT concentration used in film formation. It is evident that

in the case of TMA+ ion transfer, increasing the SWCNT concentration resulted in a decrease in koapp as expected for an interfacial area becoming increasingly covered by

the SWCNTs. This behavior can be analysed using Amatore’s theory of

voltammetry246 at a partially blocked electrode if we assume that the SWCNTs have transformed the single continuous interfacial area into large number of smaller

randomly distributed micro/nano pores, the size and/or density of which decreases

with increased interfacial coverage. According to this theory,246 under conditions of total overlap of the diffusion layers, koapp is lowered by a factor of 1 – θ:

koapp = ko (1 – θ) (4.5)

Where, θ is defined as the fractional area covered by the blocking nanotube film. The

fact that the voltammetric profile of TMA+ transfer exhibited a peak shaped response rather than a sigmoidal one indicates that an overlapping linear diffusion field was

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software to be approximately 77.5%, 88.0% and 91.7% when the SWCNT

concentration used in film preparation was 6, 12 and 18 mg L-1 respectively. Therefore applying the (1 – θ) correction factor gave an average ko value of 100 ± 7

×10-4

cm s-1, which falls in the range of ko values reported for ion transfer.

Figure 4. 19. Plot of the apparent rate constant versus SWCNTs concentration used in film preparation. Black squares and red circles denote kinetic data for TMA+ and PF6

–

respectively.

Aside from the slower kinetics displayed by the PF6– ion compared to TMA+ transfer in the presence of interfacial SWCNT films at all concentrations (Figure

4.19), it is also clear from Figure 4.19 that the negatively charged probe ion also

show a less clear dependence of koapp on SWCNT concentration. The ion transfer and

the XPS data indicate that there is a potential-dependent change in surface

composition of the nanotubes, which in turn suggests that the nanotubes adsorb on

the interface from the organic phase, that is, they constitute part of organic double

layer. This effect is then associated with the high surface charge density exhibited by

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maximum blockage at the SWCNT concentration of 6 mg L-1, as against the TMA+ ion.

Facilitated K

Ion Transfer

In addition to simple ion transfer, the facilitated transfer of K+ ion by DB18C6 (ionophore) across the SWCNT-modified liquid/liquid interface was also

studied. Following the same procedure employed before, the transfer of this ion in

the absence of an interfacial SWCNT film was initially performed and the CV

obtained is shown in Figure 4.20a.

Figure 4. 20. (a) Cyclic voltammogram recorded for the K+ transfer facilitated by DB18C6 across unmodified water/DCE interface. Scan rate used: 0.005, 0.01, 0.025, 0.05, 0.075, and 0.1 V s-1 (b) Plot of forward peak current as a function of the square root of the scan rate.

The current is limited by the linear diffusion of the ionophore since its

concentration in the organic phase is far less (0.4 mM) than that of the K+ ion dissolved in the aqueous phase (10 mM). Similar to TMA+ the facilitated K+ ion transfer also shows a reversible behaviour; ΔEp measured at 50 mV s-1 was ca. 60

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mV and did not vary significantly with scan rate. A linear dependence of the Ip on the

square root of the scan rate (Figure 4. 20b) was also obtained. The diffusion

coefficient of the DB18C6 in the DCE phase was calculated from the negative

gradient of the plot shown in Figure 4.20b as 5.2 ×106 cm2 s-1,which agrees with a literature value of 4.8 ×106 cm2 s-1.139

When SWCNTs (6 mg L-1) were adsorbed at the interface, the CV response at increasing scan rates (Figure 4.21) exhibit clearly defined peak currents only when

slow scan rates were applied (10 and 25 mV s-1). The measured peak separation (254 mV) at the 25 mV s-1 scan rate is much higher than those obtained at the same scan rate in the case of TMA+ (76 mV) and PF6

–

(169 mV) ions. When higher scan rates

(> 25 mV s-1) were employed, the peak currents, especially the forward transfer ones (i.e. those corresponding to the K+ ion transfer from aqueous to organic phase), become very large and difficult to measure. This behaviour indicates that the kinetics

of the facilitated K+ transfer is more strongly inhibited by the SWCNT film than those of simple ion transfer of TMA+ and PF6

–

. Additionally, the nonlinear trend of

the plot of Ip against ν1/2 (Figure 4.21b) further support that the ion transfer kinetics is

more complicated when SWCNT film is present at the liquid/liquid interface. The

increased sluggishness of this ion transfer process may be attributed to the possible

interaction of DB18C6 and the SWCNT surface, since the ionophore (Figure 4.21) also possesses π-electrons and is also hydrophobic. This π-stacking interaction would slow transfer process further.

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Figure 4. 21. (a) Cyclic voltammogram for the K+ transfer facilitated by DB18C6 across SWCNT-modified water/DCE interface. CSWCNT used in film formation was 6 mg L-1. Scan rates: 10, 25, 50, 75 and 100 mV s-1 (b) Plot of the forward peak current as a function of the square root of the scan rate.