Additions and corrections
Molecular dynamics simulations of atomically flat and nanoporous electrodes
with a molten salt electrolyte
Jenel Vatamanu, Oleg Borodin and Grant D. Smith
Phys. Chem. Chem. Phys., 2010, 12, 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 CEDLeff was used. In this addendum we augment the original
analysis by exploring behavior of the integral capacitance Ci. It will be shown that
that CEDLeff and Ci behave quite differently as a function of voltage and usage of the
conventional definition of Ci is preferred.
The effective integral EDL capacitance is given by eqn (13) in ref. 1 and repeated in
eqn (1) here:
where Qelectrode is the electrode charge, A is the electrode area and ΔUEDL 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 CEDLeff 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 CEDLeff [see eqn (1)] shows a discontinuity near the
potential of zero charge (UPZC) and negative values as shown in Fig. 8 of the original
paperError! Bookmark not defined., Fig. A1a of this Addition (see below), and Fig. 5b of ref.
2. Discontinuity in CEDLeff is also apparent in Fig. 6 of ref. 3. Such behavior originates
from the particular definition of CEDLeff employed,Error! Bookmark not defined. 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. Error!
Bookmark not defined.), 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” Ci [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 CEDLeff 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
paperError! Bookmark not defined. with the integral electrode capacitance data calculated
using the conventional definition from Bard and Faulkener,5
The integral capacitance Ci [eqn (3)] reflects the charge stored in an electrode with the
unit area upon potential change from UPZC to a given EDL potential. The integral
capacitance Ci does not lead to discontinuities and large negative values near UPZC
provided that the value of UPZC is known precisely. It also allows one to make a more
transparent comparison than CEDLeff 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,Error! Bookmark not defined.Error! Bookmark not defined. 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 nonfluctuant flat electrode charge setup.Error! Bookmark not defined. The integral electrode
capacitance [eqn (3)] was evaluated by assuming a PZC potential of -0.124 V. As
expected, the integral capacitance Ci 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.Error! Bookmark not defined. Note that
close to UPZC 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.