Comment pubs.acs.org/ac
Comment on “Development of a Measurement Technique for Ion Distribution in an Extended Nanochannel by Super-Resolution-LaserInduced Fluorescence” Kenji Anzo and Tetsuo Okada* Department of Chemistry, Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan
Anal. Chem. 2011, 83 (21), 8152−8157. DOI: 10.1021/ac201654r
T
Considering that only a few experimental attempts have been made for the quantitative evaluation of the ionic distribution in the EDL, we believe that the detailed comparison of their results with established theory such as the GC model is significant because such assessments provide further insights into the EDL itself and are expected to stimulate novel experimental and theoretical studies, whether the theoretical calculations agree or disagree with the experimental results. Kazoe et al.16 determined pH or the concentration of hydrogen ions as a function of the distance from the fused silica channel wall by measuring spatially resolved fluorescence intensity. Assuming a solution confined in a narrow channel of the width of d, the one-dimensional PB theory predicts the ionic distribution by the following equation.1
he electrical double layer (EDL) is an important concept for understanding electrostatic force acting between changed entities and describing the ionic distribution in the vicinity of a charged surface.1,2 According to the theories and relevant experiments, the thickness of the EDL depends on the ionic strength of a solution in contact with a charged surface. When the solution contains an appreciably high concentration of an electrolyte, i.e., millimolar or higher, the thickness of the EDL becomes as thin as a few nanometers. Difficulty in direct measurements of such a thin layer has facilitated theoretical work rather than experimental approaches. The Gouy− Chapman (GC) model derived from the Poisson−Boltzmann (PB) theory, which is one of the simple and intuitively understandable theories, basically well interprets a number of experimental facts, including the behavior of an electroactive solute at an electrode interface, the zeta potential of colloidal particles and charged surfaces, and even the separation behavior of ions in ion-exchange chromatography.1,3−7 However, there are some criticisms against the PB theory because it deals with ions as point charges and, therefore, the characters of ions are ignored. Theoretical simulations have been extensively attempted to reveal the distribution of ions and electrostatic potential in the EDL.8−12 Some results have suggested more complex distributions than that predicted by the GC model, while a number of studies still support this classical model particularly in the region apart from the charged surface.8−10,12 On the other hand, experimental measurements of the ionic distributions in the EDL have attracted researchers despite practical difficulties. It is so far a challenge to reveal any phenomena occurring in the nanometer regime in direct fashions. However, such work becomes of increasing importance with recent developments of nanotechnology and nanoscience because the imbalance of the distributions of ions of different charges possibly becomes critical in such a small dimension.13,14 However, relevant challenges have been very few due to experimental difficulties.15 A recent paper by Kazoe et al.16 reports a quite interesting approach, which directly probes the distribution of hydrogen ions in an extended nanospace. They proposed the super high spatial resolution with a stimulated emission depletion (STED) fluorescence technique as a promising way to reveal the EDL. The fluorescence coming from a pH-sensitive dye was in their work detected with a spatial resolution of 74 nm, which allowed the direct evaluation of the dependence of the ionic distribution on the ionic strength in a channel of a width of 410 nm. The results were discussed on the basis of the Debye length as a parameter representing the thickness of the EDL in their paper. © 2012 American Chemical Society
⎛ ze(ψ (x) − ψ (0)) ⎞ n(x) = exp⎜ − ⎟ ⎝ ⎠ n(0) kT
(1)
where n(x) and n(0) are the concentration of an ion with a charge of z at a given distance of x from the center of the channel and that at x = 0, respectively, ψ(x) and ψ(0) are the electrostatic potential at x and x = 0, respectively, and e, k, and T are the electronic charge, the Boltzmann constant, and absolute temperature, respectively. Equation 1 suggests that (ψ(x) − ψ(0)) can be directly determined from the local concentrations of the hydrogen ion, n(x) and n(0). The width of the channel used in the work by Kazoe et al. is 410 nm, which is larger than the expected thickness of the EDL in aqueous 1 × 10−2 and 1 × 10−4 M KCl solutions;16 the Debye lengths, which are good measures of the EDL thickness, in these media are ∼3 and 30 nm, respectively. The ionic concentration near the center of the channel is not influenced by the surface potential in these cases and, therefore, should be equal to the corresponding bulk concentration. This readily leads to ψ(0) = 0 as well. From the data shown in Figure 5 in their paper, we calculated ψ(x) as shown in Figure 1. The n(0) values for the hydrogen ion in 1 × 10−2 and 1 × 10−4 M KCl solutions were taken from those measured in the middle of the channel. The bulk pH values were read from the data as 6.00 and 5.80 for 1 × 10−2 and 1 × 10−4 M KCl solutions, respectively, which are slightly different from the corresponding experimental values reported in the paper, 5.92 and 6.03. Since the pH value adjusted prior to measurements are subject to perturbations when it is put in a channel, the measured pHx=0 should be more reliable than the absolute values. Published: November 12, 2012 10852
dx.doi.org/10.1021/ac302013b | Anal. Chem. 2012, 84, 10852−10854
Analytical Chemistry
Comment
nave =
∫Δx n(x) dx Δx
=
ψ (x) ∫Δx n(0) exp(− zekT ) dx
⎛ kT nave ⎞ ψ (x) = −ln⎜ ⎟ ⎝ ze n(0) ⎠
Once the spatial distribution of the electrostatic potential is determined, we can fit it with an appropriate theory. The GC model, for example, predicts the electrostatic potential as a function of distance. 2kT ⎧ 1 + γ exp( −κ(x − d /2)) ⎫ ⎬ ln⎨ ze ⎩ 1 − γ exp( −κ(x − d /2)) ⎭
⎧ zeψ ( −d /2) ⎫ ⎬ γ = tanh⎨ ⎭ ⎩ 4kT
(4)
(5)
The results are depicted by solid curves in Figure 1A. The calculated values well explain the experimental electrostatic potential. The curve fitting gave the appropriate ψ(−d/2) values of 0.019 and 0.054 V for 1 × 10−2 and 1 × 10−4 M KCl solutions, respectively. Although the detailed discussion of the surface potential is not an aim of this Comment because of the severe limitation of the applicability of the GC model near the charged wall, the comparison of these values with the surface potential determined for silica should be significant. The surface charge density of a silica particle has, for example, been determined to be 1 μC cm−2 in a 1 × 10−2 M KCl solution at pH 6, leading to surface potential of 0.040 V according to the PC theory.17 Force measurements have also indicated that the surface potential of a silica surface is −0.08 V in 10−4 M NaNO3 solution at pH 6.18 Thus, the surface potential determined for 1 × 10−2 and 1 × 10−4 KCl solutions in Figure 1 should be reasonable. For 10−2 and 10−4 M KCl solutions, EDL overlapping does not have to be taken into account because the channel width is sufficiently larger than the EDL thickness. In contrast, EDL overlapping cannot be ignored for distilled water, in which the EDL thickness becomes almost equivalent to the channel width; the Debye length in distilled water at pH 6 is ∼300 nm. It was assumed here that EDL overlapping is represented by a simple sum of the electrostatic potential from one wall and that from the other wall comprising the channel geometry. This is not a rigorous way because an effect from the bottom and the distribution of ions in the exterior of the channel should be considered. However, such calculation requires the exact geometry of the channel and complex numerical analysis techniques. Interpretation even with such a simplified model should be useful for the evaluation of electrostatic potential experimentally determined. The result of fitting is shown in Figure 1B. The H+ concentration in bulk (in the absence of electrostatic potential effects, n∞) value was taken from pH stated in the Kazoe paper. The calculated electrostatic potential changes with the distance from the wall in a more gradual way than the experimental values as shown by open symbols in Figure 1B; an agreement is not very good compared to KCl solutions. A higher ionic strength (shorter Debye length) did not give better interpretations; such a situation possibly occurs when the surface silanol groups are dissociated. Although assuming higher pH for the bulk distilled water gives better fittings as shown by solid symbols in Figure 1B (pH 6.8 was assumed), such a deviation from the experimental setting is not realistic. The results shown in Figure 1 clearly suggest that the GC model well interprets the experimental data determined in KCl solutions, whereas there is an obvious disagreement between those for distilled water. It has been known that the PB theory is not valid for higher surface potential, which results from low ionic strength as well as from the high charge density of a wall. Thus, the comparison of experimental values reported by Kazoe et al. with the GC model indicates that (1) the electrostatic potential at a given distance from a charged wall can be
Figure 1. Electrostatic potential in an extended nanospaces of the width of 410 nm determined by Kazoe et al. (plots) and calculations based on the GC model. (A) KCl solutions: broken curves, calculated electrostatic potential simply derived from the GC model; solid curves, average values calculated by taking the spatial resolution into account. (B) The prediction of the GC model for distilled water (ionic strength of 10−6 M). Electrostatic potential overlapping from both walls was taken into consideration because of a large Debye length. Solid and open symbols were calculated assuming the bulk pH values (pH∞) of 6.8 and 6.22, respectively. Curves were also derived assuming these pH values.
ψ (x − d /2) =
Δx
(2)
(3) −1
where κ is the Debye shielding parameter (κ is equal to the Debye length) and ψ(−d/2) = ψ(d/2) is the surface potential. The results of fitting with eqs 2 and 3 with ψ(−d/2) as an unknown parameter are given in Figure 1A as broken curves for 1 × 10−2 and 1 × 10−4 M KCl solutions. The agreements between measured and calculated values are not very good particularly near the channel wall for 1 × 10−2 M KCl. The proton concentration reported in the paper by Kazoe et al. is the averaged one measured over the distance 74 nm (Δx). Therefore, the electrostatic potential calculated from the H+ concentration in their paper should also be compared with the corresponding averaged value derived from 10853
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Analytical Chemistry
Comment
evaluated by the proposed approach; (2) the distance dependence of the electrostatic potential can be explained by the GC model in diluted electrolyte solution; (3) the GC model cannot interpret the electrostatic potential distribution in distilled water, in which EDL overlapping restricts the applicability of the GC model and possibly the validity of the PB theory. In distilled water, hydrogen ions are accumulated in the extended nanochannel and their concentration in the interior of a channel should be higher than the external solution. In addition, the concentration of H+ should become lower near the edge of the extended nanospaces because the infinity of the charged wall is lost near the outlet of the channel. From this perspective, the lengthwise measurements are also interesting. The reliable measurements of such an imbalance of ionic charges are important not only from fundamental perspectives but also for designing nanochannel ionic devices.19,20 The attainment of higher spatial resolution should help discuss this aspect in more detail. Also, the assessment of the method in more concentrated ionic strength is highly required to reveal the applicability of the GC model.
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AUTHOR INFORMATION
Corresponding Author
*Phone and fax: +81-3-5734-2612. E-mail: tokada@chem. titech.ac.jp. Notes
The authors declare no competing financial interest.
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REFERENCES
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