Supplemental Material
Proton Transfer and the Diffusion of H+ and OH- Ions along
Water Wires
Song Hi Lee1,* and Jayendran C. Rasaiah2,+
1
Department of Chemistry, Kyungsung University, Pusan 608-736, South Korea
2
Department of Chemistry, University of Maine, Orono, ME O4469,
E-mail: *shlee@ks.ac.kr; +rasaiah@maine.edu
The initial configuration to study H+ ion transport along a water wire in a CNT using the
sOSS2 potential was made as follows. A water molecule near the middle of an equilibrated quasione dimensional hydrogen bonded chain filling the nanotube becomes a H3O+ ion by successive
transfer of chemically bonded hydrogen atoms to neighboring water molecules in one direction
along the tube axis, beginning with the water molecule above the upper end of the CNT (the red
arrows represent this transfer in Fig.S1 (a)) which becomes an OH- ion that is converted back to
water by adding an H+ ion (marked by a red circle). The one-dimensional chain is symmetrical
about the central H3O+ structure flanked on either side by chains of hydrogen bonded water
molecules with their dipoles oriented away from the excess charge as seen in Fig.S1 (b). The
central H3O+ structure is similar to an L-defect. The system was then equilibrated with the
central H3O+ ion fixed for 100 time steps (20 fs).
The OH- ion was introduced directly at the center of the CNT already filled with a
hydrogen bonded chain of water molecules. This was accomplished by successive transfer of
chemically bonded hydrogen atoms to neighboring water molecules in one direction along the
tube axis, beginning with the water molecule at the center of the CNT (the blue arrows represent
this transfer in Fig.S1 (a)). The last molecule in this chain below the CNT is a H3O+ ion from
which a chemically bonded H+ ion was removed (marked by a blue “x”). The hydroxide ion
introduced in this way at the center of the CNT has its hydrogen atom pointing towards wall of
the nanotube with its oxygen atom hydrogen bonded to water molecules on either side to
maintain an uninterrupted hydrogen bonded chain (see Fig.S1 (c)). The central OH- structure is
similar to an D-defect. The system was then equilibrated with only the central OH- ion fixed for
100 time steps (20 fs). When the tube was immersed in a water bath, a stationary Cl- or Na+
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counterion which interacts with O and H atoms by electrostatic and Lennard-Jones interactions,
was introduced at a corner of the cubic simulation box to maintain electro-neutrality.1
Fig.S1 (a) Configuration of 6 water molecules in the short CNT. (b) The initial configuration of
an H3O+ ion before equilibration. (c) The initial configuration of an OH- ion before equilibration.
The mechanism of proton transfer along the water chain is illustrated in Fig.S2 for (a)
H3O+ ion and (b) the OH- ion. Ion transport is in the same direction as PT for the H3O+ ion and in
opposite direction for the OH- ion.
2
Fig.S2 (a) Representative configurations showing the mechanism of proton transfer of an H3O+
ion originally at the center of a short carbon nanotube immersed in a water reservoir. The excess
protonic charge moves up the tube. (b) Representative configurations showing the mechanism of
proton transfer of an OH- ion originally at the center of a short carbon nanotube immersed in a
water reservoir. The OH- ion moves up the tube while a proton is transferred to an adjacent water
molecule in the opposite direction.
The MSDs of the excess charges as a function of time along the open water chains in
tubes with lengths from 29.6 to 174.8Å are shown in Fig.S3 from which the diffusion
coefficients are calculated and displayed in Table 1. The MSD in the tube of length 291.0Å is
shown in Fig.3(a). The MSD dips down beyond the time intervals shown below and in Table 1,
due to the interaction of the excess charge with effective charge from the dipole at the tube end
as described in the text. For the shorter tubes (Nw =12, 24 and 48) the short time intervals of the
linear regimes may introduce errors in calculating the diffusion coefficient of the free ions from
the MSD.
Fig.S3 Mean square displacements (MSD) of H+(solid line) and OH-(dotted line) in CNT with
Nw = 12, 24, 48, and 72.
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The free energy profiles for PT as a function of  at 298 K are shown in Fig.S4. The free
energy barrier for PT to the hydroxide ion from a water molecule is less than that for PT from a
hydronium ion to a water molecule in the tube, but this is compensated by greater proton rattling
between the initial and final states in PT to the hydroxide ion (see Fig.S4).
Fig.S4 (a) Free energy profiles for PT along water wires in CNTs as a function of  = RO*H RO^H at 298 K, where RO*H and RO^H are the respective distances of the shared proton from O*,
the oxygen atom to which the proton is chemically bonded, to O^ the oxygen atom to which it is
transferred. The long dashed line is free energy profile for PT from H2O and to OH- when the
donor-acceptor distance RO*O^ > 2.5 Å. (b) Representative trajectories of charge transfer for
H3O+ (solid line) and OH- (dashed line) ions, showing greater rattling associated with PT for the
OH- ion.
Reference
1. S. H. Lee and J. C. Rasaiah, J. Chem. Phys. 135, 124505 (2011).
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