J. Phys. Chem. B 2006, 110, 12581-12587
12581
Direct Measurement of Ion Accumulation at the Electrode Electrolyte Interface under an Oscillatory Electric Field Gaurav Singh and Ravi F. Saraf* Department of Chemical Engineering, UniVersity of Nebraska-Lincoln, Lincoln, Nebraska 68588 ReceiVed: January 30, 2006; In Final Form: April 12, 2006
The ionic charge accumulation at the metal-electrolyte interface is directly measured by using differential interferometry as a function of magnitude and frequency (2-50 kHz) of external electric field. The technique developed probes the ion dynamics confined to the electrical double layer. The amplitude of modulation of the ions is linearly proportional to the amplitude of applied potential. The linearity is observed up to high electrode potentials and salt concentrations. The frequency response of the ion dynamics at the interface is interpreted in terms of the classical RC model.
1. Introduction Manipulation of electrolyte and polyelectrolyte (such as DNA, proteins) solutions, and suspension of biological systems (such as cells) in water, by an oscillatory (i.e., AC) electric field has become of great interest in the recent years spurred by the need to design microfluidic and nanofluidic systems for various biomedical devices to reduce precious sample volumes and analysis time. AC fields in such electrofluidic microsystems are shown to manipulate,1 separate,2 and trap DNA3,4 and protein molecules, self-assemble and manipulate colloid particles,5 separate and manipulate cells and vesicles,6,7 analyze DNA hybridization for gene sequencing,8 and pump and manipulate electrolyte solutions in microfluidic and nanofluidic channels.9,10 Due to the high surface-to-volume ratio of these devices, understanding the dynamics of ion motion at the electrode/ electrolyte interface is central to the performance of these electrokinetic-fluidic systems.9 An Electrical Double Layer (EDL) is formed at the solution/electrode interface because of the electrostatic interaction between the ions in the solution and the electrode surface.11 The result is an ion-concentration gradient that typically extends from angstroms to 10’s of nanometers into the bulk depending on the ionic strength of the aqueous solution.12 Because most of the interfacial charge is screened within the double layer, the thickness of the EDL is also the length scale of interaction between charged moieties in electrolyte solution. For a simple salt solution, the thickness of EDL is given by the Debye length, ζ ) [0kT/ (∑NAc∞,ie2zi2)]0.5, where 0 is permittivity in a vacuum, is the dielectric constant of the liquid (i.e., water), NA is Avogadro’s number, kT is thermal energy, c∞,i is the (bulk) molar concentration of the ith ion and zi is its valency, and e is charge of the electron. Typically, for NaCl in water, ζ ) 0.303/[NaCl]0.5 nm, where [NaCl] is the molar concentration. The theory for the static structure of EDL (i.e., ion distribution at the interface) under constant (or zero) bias between electrodes is a two-layer structure13,14 comprised of a relatively immobile, densely packed Stern layer and a diffuse ionic layer with high mobility. For the dynamics of EDL there is a considerable lag between theory15-17 and experiment. To our knowledge no direct measurement on ionic motion due to AC field has been * Address correspondence to this author. E-mail:
[email protected].
performed. Although equivalent RC-circuit models for the metal-electrolyte interface have been established for over a century, their applicability has been questioned at a fundamental level over the years.18 The proposed equivalent circuits vary significantly to explain the data at different frequency and concentration regimes. Furthermore, the relevant time scale is a geometric mean of the characteristic relaxation time of the ion-dynamics in the bulk and the EDL that are difficult to decouple.15 Thus, the need for a direct experimental approach that exclusively measures the ion accumulation at the electrodeelectrolyte interface under AC-field polarization is acutely felt. In this report, we describe, to our knowledge, a first attempt to directly measure the ionic accumulation at the electrodeelectrolyte interface due to AC field using high sensitivity differential interferometry. Our results indicate that most of the charge accumulation occurs in the EDL formed at the metalelectrolyte interface with the dynamics being surprisingly linear up to much higher electrode potential (i.e., ∼2 V) and salt concentrations (i.e., ∼0.5 M). Although the RC model explains the trends qualitatively, and at low concentration (1 kHz. The optical method has two distinct advantages over the conventional electrical measurement: (i) From Figures 5a and 7a, the change in I is only 30% compared to a 10-fold change in ∆ as a function of ω. This indicates that the capacitive effect of EDL is eclipsed by the bulk effect in the electrical
Figure 8. A phase diagram with respect to the VL fixed along the real axis, VR, at an angle φ and ∆ at a phase angle of θ with respect to VL. All the modulations are at the same fixed frequency, ω.
measurement while optical measurement observes the charging directly. (ii) In the optical measurement the local ion dynamics is measured as opposed to integrated current over the whole electrode in the electrical method. The local measurement allows for simpler electrochemical cell design where the electrode edge effects and fringe fields can be avoided by simply choosing a “sweet” spot on the electrode. Furthermore, the local probing with the optical technique can be extended to combinatorial measurements and microelectrode geometries. Acknowledgment. We acknowledge the Office of Naval Research (grant N00014-01-1-0977) for financial support. Appendix: Derivation of Equation 2 The real part of the potential difference between the working and reference electrode, VL - VR cos φ, produces an in-phase and an out-of-phase path length modulation of ∆X and ∆Y, respectively. Similarly, the imaginary part of the potential difference, VR sin φ, produces in-phase and out-of-phase modulations of ∆Y* and ∆X*, respectively. (Note that for the imaginary part of the potential difference, the in-phase modulation is along the imaginary axis as opposed to the real axis.) Since the in-phase and out-of-phase modulation is linear with respect to the potential difference as discussed in Figure 2
∆X ∆Y* ) VL - VR cos φ VR sin φ ∆X* ∆Y ) VL - VR cos φ VR sin φ
(in-phase modulation) (4a)
(out-phase modulation) (4b)
Ion Accumulation at the Electrode Electrolyte Interface The total path length modulations, ∆, measured along the real and imaginary axes, respectively, are
∆ cos θ ) ∆X + ∆X*
(modulation along real axis) (5a)
∆ sin θ ) ∆Y + ∆Y* (modulation along the imaginary axis) (5b) Thus substituting for ∆X* and ∆Y* from eq 4 in eq 5, the modulation ∆X and ∆Y corresponding to potential difference of VT ) VL - VR cos φ is given by
∆0 ) ∆X ) ∆90 ) ∆Y )
∆(a sin θ - cosθ) a2 - 1 ∆(a cosθ - sin θ) a2 - 1
The above equations are the same as eq 2. References and Notes (1) Washizu, M.; Kurosawa, O. IEEE Trans. Ind. Appl. 1990, 26, 1165-72. (2) Chebotarev, V. Y.; Rekesh, A. N. Mol. Biol. 1990, 24, 488-500.
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