Jenel Vatamanu, Oleg Borodin and Grant D. Smith

Phys. Chem. Chem. Phys., 2010, 12(1), 170–182 (DOI: 10.1039/b917592j). Amendment first published 26th March 2010

In our original publication of this work¹ the effective integral electric double layer (EDL) capacitance C_EDL^eff was used. In this addendum we augment the original analysis by exploring behavior of the integral capacitance C_i. It will be shown that that C_EDL^eff and C_i behave quite differently as a function of voltage and usage of the conventional definition of C_i is preferred.

The effective integral EDL capacitance is given by eqn (13) in ref. 1 and repeated in eqn (1) here:

where Q_electrode is the electrode charge, A is the electrode area and &DeltaU_EDL is the electric double layer potential, which is given by the potential difference between the electrode potential and bulk potential:

The effective integral EDL capacitance C_EDL^eff has been used by the simulation community (e.g., Feng et al.,² Reed et al., ³ and Kislenko et al.⁴). It is well known that the effective EDL capacitance C_EDL^eff [see eqn (1)] shows a discontinuity near the potential of zero charge (U_PZC) and negative values as shown in Fig. 8 of the original paper1, Fig. A1a of this Addition (see below), and Fig. 5b of ref. 2. Discontinuity in C_EDL^eff is also apparent in Fig. 6 of ref. 3. Such behavior originates from the particular definition of C_EDL^eff employed,² and from the fact that the potential drop within EDL could be zero for the charged electrode (Fig. 9 of our original work1). As the two individual electrodes can be considered two serial individual condensers (see the discussion from the page 084704 of ref. 3), infinite capacitance at one plate still leads to finite and positive capacitance for the entire capacitor which can be obtained by adding the electrode capacitances as given by eqn (1) in series.

Fig. A1 A comparison between (a) the "effective integral EDL capacitance" [eqn (1)] and (b) the "integral electrode capacitance" C_i [eqn (3)] from simulation data (symbols) and from the fitted behavior of the electrode charge versus charge EDL potential (solid lines). For comparison, the fitted differential EDL capacitance CD is shown in (b) as dotted lines.

While the definition of C_EDL^eff given by eqn (1) has been used in simulation studies,^2–4 we feel that it is highly beneficial to augment the results presented in the original paper¹ with the integral electrode capacitance data calculated using the conventional definition from Bard and Faulkener,⁵

The integral capacitance C_i [eqn (3)] reflects the charge stored in an electrode with the unit area upon potential change from U_PZC to a given EDL potential. The integral capacitance C_i does not lead to discontinuities and large negative values near U_PZC provided that the value of U_PZC is known precisely. It also allows one to make a more transparent comparison than C_EDL^eff given by eqn (1) with differential EDL capacitance:

The purpose of this comment is to emphasize that the effective integral EDL capacitance [eqn (1)] reported in a number of MD simulations,^1–4 yields (as expected) a different behavior near PZC from the integral electrode capacitance given by eqn (3). A comparative plot between the two capacitances is shown in Fig. A1a and b for molten LiCl at 900 K, under a non-fluctuant flat electrode charge setup.¹ The integral electrode capacitance [eqn (3)] was evaluated by assuming a PZC potential of −0.124 V. As expected, the integral capacitance C_i defined by eqn (3) does not have any discontinuity for the precisely known PZC. However, due to numerical errors, one particular point from simulations closest to PZC is out of trend with other simulation results (Fig. A1b).

The integral capacitance [eqn (3)] shows a U-shaped (Fig. A1b) behavior for LiCl molten salt next to the flat electrodes, which is similar to the behavior of the differential capacitance reported in the original paper.¹ Note that close to U_PZC the differential and integral capacitances are asymptotically equal as expected. In the original paper we focused on the analysis of the differential capacitance instead of focusing on the integral capacitance because the former is more useful in evaluation of the energy stored by the capacitor and allows a straightforward interpretation of the charge storing ability in the EDL as a function of applied voltage.

References used in this Addition:

1 J. Vatamanu, O. Borodin, G. D. Smith, Phys. Chem. Chem. Phys., 2010, 12, 170.

2 G. Feng, J. S. Zhang and R. Qiao, J. Phys. Chem. C, 2009, 113, 4549.

3 S. K. Reed, O. J. Lanning and P. A. Madden, J. Chem. Phys., 2007, 126, 084704.

4 S. A. Kislenko, I. S. Samoylov, R. H. Amirov, Phys. Chem. Chem. Phys., 2009, 11, 5584.

5 J. A., Bard, L. R., Faulkner, Electrochemical Methods: Fundamentals and Applications, Second Edition, John Wiley & Sons Inc, 2001, p. 541.

The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers.

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