Pockels Effect of Interfacial Water on a Mono-Electrode Induced by Current Parallel to the Electrode Surface

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Light modulators, sensors, and non-contact evaluation of thermoelectric performance as potential applications.

Abstract

When an electric field is applied between two electrodes facing each other immersed in a liquid, the interfacial Pockels effect, a refractive index change proportional to the electric field, occurs in the electric double layer at the liquid–electrode interface. Here, we report that the Pockels effect of interfacial water can be observed even when an electric field is applied parallel to the surface of a “single” electrode in an electrolyte solution. This is a non-trivial result since the electric field parallel to the interface should not cause a broken spatial inversion symmetry, which is required for the Pockels effect. The Pockels signal was detected as a change in the transmitted light intensity due to the field-induced spectral shift of the interference fringes of the transparent conductive oxide electrode layer on a glass substrate. The magnitude of the signal increased as it approached the ends of the electrode, and the sign reversed across the center of the electrode. The electric field distribution calculated from the interfacial potential difference due to the in-plane parallel current showed that an electric field perpendicular to the interface was induced, whose distribution was consistent with the position dependence of the Pockels signal. A similar phenomenon was also observed for a single copper electrode, confirming that this is a universal effect.

1. Introduction

The electric double layer (EDL) at the electrode–solution interface plays an important role as a stage for electrochemical reactions [1,2,3,4]. In addition, it finds a large variety of applications such as EDL capacitors [5], EDL transistors [6,7,8], light-emitting and power-generating devices [9,10], electric field-induced ferromagnetism [11,12], and electric field-induced superconductivity [13,14]. Furthermore, the electrode interface is an interesting research target from the viewpoint of nonlinear optics [15,16,17] because of its broken spatial inversion symmetry. In other words, second-order nonlinear optical effects such as sum frequency generation [18,19] and Pockels effect appear.

The interfacial Pockels effect was first observed at the interface of a transparent oxide electrode and an aqueous electrolyte solution [20,21], and has since been observed not only on various electrodes [22,23,24,25] and with polar solvents [26] but also at solid–solid interfaces [27]. Recently, it has been successfully demonstrated that the Pockels effect of interfacial water can be applied as an electro-optic modulator (=EDL light modulator) [28,29]. Although the response speed is currently limited, deep optical modulation is realized at an extremely low cost and with a simple configuration, and there is potential for applications such as optical sensors in liquids. In previous reports on the interfacial Pockels effect, two electrodes have always been used, one for observing the Pockels effect of water at the interface and the other for its counter electrode. In this paper, in contrast, we report the observation of the Pockels signal by applying a potential difference to both ends of a single electrode. The signal’s magnitude and sign change depending on the location of the electrode, and this behavior is found to be correlated with the electric field distribution perpendicular to the electrode interface, generated by the potential distribution due to the in-plane parallel current.

The results of this paper may stimulate fundamental research on the properties of the electric double layer in orientations parallel to the electrode surface, which have not been dealt with extensively, and may lead to useful general-purpose techniques for non-contact observation of current and voltage distributions on electrode surfaces, as described below. In anticipation of the arrival of the Internet of Things (IoT) society [30], there is a growing interest in harvesting and reusing energy that was discarded at present. In particular, attention is being paid to thermoelectric power generation [31], which can supply power to devices such as low-power sensors by using waste heat that is ubiquitous around us. For this purpose, the search for novel materials with highly efficient thermoelectric conversion functions is being conducted worldwide [32,33,34]. This exploratory research is experimentally conducted through contact measurements involving wiring, where a spatial temperature difference is applied to the sample, and the potential difference generated in the section is measured. This requires a process associated with wiring, making exhaustive experiments difficult. In contrast, if the presence of a potential difference could be detected only through non-contact optical measurements without wiring, it would contribute to the screening of potential thermoelectric materials. We would also like to mention the potential applications of the results of this paper in this field.

2. Materials and Methods

Figure 1 shows a block diagram of the experimental setup. We used a commercially available transparent conductive-oxide (TCO) electrode on glass substrates (Geomatec, Yokohama, Japan). The electrode consisted of a TCO substrate made of soda-lime glass (1.1 mm)/ITO (300 nm)/SnO₂ (100 nm) with 5 $\mathsf{\Omega }$/sq. ITO (Indium Tin Oxide) is an n-type semiconductor and is transparent in the visible spectrum. The thickness, resistivity, and carrier density of the ITO substrate were measured at 300 nm, 1.2 $\times {10}^{-4}\mathsf{\Omega }\mathrm{c}\mathrm{m}$, and 1.0 $\times {10}^{21}\mathrm{c}{\mathrm{m}}^{-3}$, respectively. Compared with ITO, TCO is highly resistive to acid and can withstand a higher applied voltage in an electrolyte aqueous solution.

Electric field modulation spectroscopy of water at the electrode interface was performed by applying an AC voltage between the terminals attached to both ends of a single TCO electrode immersed in aqueous electrolyte solution. The AC voltage of frequency $f$ was generated by a Function Generator and amplified by a High Speed Power Amplifier (4020, NF Corporation, Yokohama, Japan) because of the large current flow in this arrangement. White collimated light (with a beam diameter of about 10 mm) was extracted from a Laser Driven Light Source (LDLS EQ-99 X, wavelength range of 170 to 2100 nm, Energetiq Technology, Wilmington, MA, USA), which is an Xe lamp source, and the light ($T$) transmitted through the TCO in the aqueous solution was incident through a fiber into the entrance slit of a monochromator (SpectraPro 300i, Acton Research Co., Acton, MA, USA). The white light was monochromatized with a grating of 150 gr/mm and 500 nm blaze, and then received through a bundle fiber array on the monochromator output focal plane by 128 avalanche photodiodes (S5343, Hamamatsu Photonics, Hamamatsu, Japan) for each wavelength. The components modulated at frequency $f$ were dual-phase lock-in detected by a 128-channel lock-in amplifier (7210, Signal Recovery, Edinburgh, UK) as $\Delta T_x$ and $\Delta T_y$. This yields the electric field modulated transmittance change spectrum ($\Delta T_{x,y}/T$) of the electrode, using the $T$ spectrum measured beforehand by chopper modulation. All lenses were SQ lenses, and the experiments were performed at room temperature (293 K). The transmission spectrum of the TCO electrode in air was measured separately with a spectrophotometer (SolidSpec-3700DUV, Shimadzu, Kyoto, Japan).

In order to measure the electrode position dependence of the transmitted light, a TCO electrode, cut to a size of 60 mm (width) $\times$ 40 mm (height), was used and immersed about 3/4 into a glass cell filled with a 0.1 M NaCl aqueous solution. The two corners of the electrode above the water surface were clamped with alligator clips, with an indium wire inserted to improve the contact, and an AC voltage was applied. The position of the transmitted light was set to No. 1–No. 5 at 1 cm intervals, as shown in Figure 1, with No. 3 being the center of the electrode, No. 1 being grounded, and No. 5 being supplied with the voltage. The transmission position was changed by moving the cell by 1 cm to the left and right, and the dependence of the $f$ signal on the transmission position was measured.

3. Results

Figure 2 shows the dependency of the normalized transmittance change spectrum $\Delta T/T$ on the position of the transmitted light. The reproducibility of the experimental results was confirmed in multiple experiments, since a $\Delta T/T$ spectrum with sufficient S/N (S/N > 100 for the largest signal around 300 nm in Figure 2, $X$, No. 1) could be measured in only 90 s (Time Constant 30 s), thanks to simultaneous measurement over the entire wavelength range using the multi-lock-in amplifier. The magnitude and phase of the signal changed depending on the position of the transmitted light. The signal was larger in magnitude at both outer sides (No. 1, 5) than at the inner sides (No. 2, 4), and almost no signal was observed at the center (No. 3). The signal phase was reversed on the left and right sides across the center. The signal at No. 5 is consistent with the transmittance change spectra observed on the electrode to which a positive voltage was applied in the experiment with two electrodes (voltage-applied electrode and grounded electrode) [20,21,26]. This indicates that the refractive index change is negative, and the response of the refractive index change has a phase delay with respect to the input AC voltage (as evidenced by the fact that for shorter wavelengths, the $X$ signal is positive and the $Y$ signal is negative) [21,24]. In fact, the transmittance change spectrum can be fitted by the first derivative of the transmission spectrum with respect to wavelength, as shown in Figure 3. This represents the shift of the interference fringes of the TCO thin film due to the refractive index change in the interfacial layers [20].

In Appendix A, we report that a similar interfacial Pockels effect was also observed in electroreflectance measurements of a single copper electrode, suggesting that this phenomenon occurs universally on a variety of electrode surfaces.

Let us explain the physical meaning of the $X$ and $Y$ components of the lock-in signal. The multichannel lock-in amplifier functions as a dual-phase lock-in amplifier to yield $X$ (cos or in-phase) and $Y$ (sin or quadrature phase) components as output signals. When an AC electric field of frequency $f$ ($\omega =2\pi f$): $F\left(t\right)=F\cos \omega t=F\mathrm{R}\mathrm{e}\left(e^{i\omega t}\right)$ is applied to a sample with an impulse response function $\chi \left(t\right)=\theta \left(t\right)e^{-t/\tau }$, where $\theta \left(t\right)$ is the step function, the first-order electro-optic (Pockels) signal of the sample is calculated as:

$$S\left(t\right)=\mathrm{R}\mathrm{e}{\int }_{-\infty }^{\mathrm{\infty }}d{t}^{\prime }\chi \left(t^{\prime }\right)F\left(t-t^{\prime }\right)=\mathrm{R}\mathrm{e}\frac{\frac{1}{\tau }-i\omega }{{\omega }^2+\frac{1}{{\tau }^2}}{e}^{i\omega t}=\mathrm{R}\mathrm{e}\frac{X+iY}{\sqrt{{\omega }^2+\frac{1}{{\tau }^2}}}{e}^{i\omega t}=\frac{\cos \left(\omega t-\theta \right)}{\sqrt{{\omega }^2+\frac{1}{{\tau }^2}}}=\frac{1}{{\omega }^2+\frac{1}{{\tau }^2}}\left(\frac{1}{\tau }\cos \omega t+\omega \sin \omega t\right)$$

(1)

with $\cos \theta =\frac{\frac{1}{\tau }}{\sqrt{{\omega }^2+\frac{1}{{\tau }^2}}}\left(=X\right),\mathrm{a}\mathrm{n}\mathrm{d}\sin \left(-\theta \right)=-\frac{\omega }{\sqrt{{\omega }^2+\frac{1}{{\tau }^2}}}(=Y).$ The $\cos \theta$ and $\sin \theta$ signals are measured as $X$and$Y$ components in the lock-in outputs. Since $\sin \omega t$ is delayed from $\cos \omega t$ by a quadrature phase ($\cos (\omega t-\pi /2)=\sin \omega t),$ or as evident from Figure 4, $Y<0$ when $X>0(Y>0\mathrm{w}\mathrm{h}\mathrm{e}\mathrm{n}X<0)$. Thus, from the largest $\Delta T/T$ signal at 305 nm for position No. 1 in Figure 2, the phase delay is evaluated as $\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}(Y/X)=\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}(-1.10\times {10}^{-3}/4.54\times {10}^{-3})=-0.239\mathrm{r}\mathrm{a}\mathrm{d}=-13.7°$. The response time $\tau$ is evaluated from $-Y/X=\omega \tau =2\pi f\tau =40\pi \tau =0.242$ to be$\tau =1.9\mathrm{m}\mathrm{s}$. This phase delay can be explained by the equivalent circuit of the measurement system (transparent electrode and aqueous solution) and is thought to mainly reflect the time taken for the electrolyte ions to migrate and form an EDL at the electrode interface. Measurements of the electric field modulation frequency dependence of the Pockels effect of water at the transparent electrode interface and evaluation of the equivalent circuit by AC impedance measurement have been performed [20,21,26], and the EDL formation time can be explained by the RC time constant of the equivalent circuit.

4. Discussion

In order for the Pockels effect to become active, the spatial inversion symmetry of the system must be broken before the application of the electric field [23]. The water at the electrode interface satisfies this condition, but when the applied electric field is parallel to the electrode interface, the two states with reversed directions of the electric field are superimposed by mirroring about the plane perpendicular to the electric field. Consequently, even though the refractive index change is induced by the electric field, the sign reversal due to the reversal of the direction of the electric field cannot occur [35]. Therefore, the observed result seems to contradict physical intuition at first glance, but the position dependence of the magnitude and sign of the observed signal suggests that the application of an in-plane parallel electric field to the electrode causes the distribution of the electric field around the electrode immersed in water and the generation of a component of the electric field perpendicular to the electrode interface (Figure 5), as discussed in Ref. [35]. The behavior of the signal shown in Figure 2 may reflect the spatial distribution and orientation of the electric field perpendicular to the interface.

In order to verify the above model, the electric field distribution in the cell was calculated numerically. When a voltage is applied to both ends of the TCO electrode, an in-plane current flows, and a potential difference is generated depending on the location. Using the interfacial potential difference as a boundary condition, the two-dimensional Laplace equation:

$$\mathsf{\nabla }·\left(\epsilon \mathsf{\nabla }\varphi \right)=0$$

(2)

was solved using the Finite Difference Method in the horizontal plane, which is perpendicular to the electrode interface and parallel to the direction of the in-plane current to obtain the potential $\varphi$ and the electrostatic field distribution $\mathit{E}=-\mathsf{\nabla }\varphi$ in the aqueous solution. We also considered the difference in the dielectric constants ε of the transparent electrode TCO and water. The experimental condition of the dissolved electrolyte was not taken into account. Since the resistance of the electrode and that of the aqueous solution are comparable in size, the electric field distribution on the electrode surface is affected by that in the aqueous solution (the current flowing through the solution cannot be ignored in comparison to the current flowing through the electrode). However, for the purpose of grasping the qualitative characteristics, the following simplified procedure was adopted: first, we calculated the two-dimensional potential distribution when a potential difference was applied between two points on the electrode surface. Then, assuming that the electrode was vertically immersed in water while maintaining that potential distribution, we calculated the potential distribution on the surface at the height where transmitted light measurements were made in water, using the (one-dimensional) potential distribution on the electrode surface at that height as the boundary condition. The dielectric constant of TCO was set to 3.1 [26] and that of water to 80. The potential distribution was smoothed until convergence using a self-made program in the C language, and the image was visualized using Gnuplot.

The geometric configuration and conditions assumed in the calculation are detailed in Figure 6a. First, the distribution of the potential $U\left(x,z\right)$ in the electrode plane ($xz$ plane $0\le x\le 60,0\le z\le 40$) standing vertically ($z$-axis) was solved with the potential $U\left(5,35\right)=0$,$U\left(55,35\right)=100$, and the boundary condition $\partial U/\partial n=0$ ($x=0,60,z=0,40$, where $n$ is perpendicular to the boundary). Next, the direction perpendicular to the electrode plane was defined as the $y$-axis (with the electrode at $y=24$), and the distribution of the potential $\varphi \left(x,y\right)$ in the $xy$-plane perpendicular to the electrode ($0\le x\le 60,0\le y\le 24,z=25$) at height $z=25$ was solved with the boundary condition $\varphi \left(x,y=24\right)=U\left(x,z=25\right),\partial \varphi /\partial n=0(x=0,60,y=0)$. It was assumed that the boundary between the electrode and the water is at $y=23$ and that $\epsilon =3.1$ for $y>23$ and $\epsilon =80$ for $y<23$.

The numerical solution for the electric field ($E_y$) distribution perpendicular to the electrode plane is drawn in Figure 6b,c. The perpendicular electric field at the interface ($y=23.5$) was zero at the center ($x=30$) and increased toward the outside ($x=10,50$), and the sign was reversed across the center. The dielectric constant difference between TCO and water induces a polarization charge at the TCO–water interface, weakening the electric field in the water compared to the electric field on the TCO surface. The calculated results qualitatively reproduce the electric flux density, which is high in the EDL at the electrode interface. It is important to note, however, that as a mechanism for the formation of the electric field distribution, the actual polarization caused by the movement of electrolyte ions to the interface is hypothetically replaced by the polarization associated with the dielectric constant difference.

This calculation result qualitatively explains the position dependence of the Pockels signal observed in the experiment. When a voltage was applied to both ends of a mono-electrode, the current flowing in the electrode caused a voltage drop, which generated an interfacial perpendicular electric field according to the potential at each position. Depending on its magnitude and direction, the refractive index change in the EDL of water and in the space–charge layer of TCO at the water–electrode interface changed continuously from positive to negative, leading to the observed position dependence.

Let us also discuss the quantitative validity of the experimental results. From Figure 6, when a voltage of 6.28 V is applied between the clips, the plane-perpendicular electric field $E_y$ at the TCO electrode interface at position No. 1 ($x=10$) is evaluated to be 0.288 V/mm. Therefore, it is reasonable that a signal with a magnitude nearly equal to the experimental results obtained with two electrodes (an electric field of about 0.5 V/mm applied between electrodes, on average) [21,26] is observed in Figure 2. However, the calculation of the electric field distribution in the present paper assumes that both the TCO electrode and the water are pure dielectrics and does not consider their conductivity, nor the EDL (its dielectric constant and conductivity) generated between the electrode and the bulk water. If the TCO is assumed to be a conductor with conductivity $\sigma$, the in-plane potential distribution on the TCO is yielded by $\mathsf{\nabla }·(\sigma \mathsf{\nabla }\varphi )=0$, so the shape of the in-plane distribution agrees with the result of Equation (2). Therefore, it is considered that the present calculation qualitatively explains the location dependence of the Pockels signal in Figure 2, but a more detailed analysis of the electric field distribution is needed to explain the signal magnitude quantitatively.

5. Conclusions

It was found that the Pockels effect of interfacial water on an electrode can be observed using a single electrode without the need for a separate counter electrode. The magnitude and polarity of the Pockels signal change following the distribution of the electric field perpendicular to the electrode surface, which is generated depending on the potential distribution in the electrode plane. Although the interfacial Pockels effect of water is largest on the surface of transparent conductive oxide electrodes to date, it has been found to occur not only with the combination of transparent oxide electrodes and water but also with a variety of electrodes and polar organic solvents, although the magnitude of the signal varies depending on the combination [22,23,24,26]. Recently, there have been reports of light modulators using the interfacial Pockels effect [28,29], so the single-electrode Pockels effect will enable light modulators using a variety of materials in an even simpler arrangement. The fact that the signal depends on the surface potential distribution generated may be useful for sensor applications in solution, such as measuring electric field distribution. In addition, since the generation of a Pockels signal indicates the occurrence of a potential difference on the interface, it may be applied to the non-contact search and screening of thermoelectric materials [32,33,34] without the need for wiring. This can be achieved by creating a temperature gradient upon pump light irradiation and detecting the generation of the potential difference from probe light reflection change on the material surface immersed in water or alcohol solution [26]. However, since quantitative evaluation of thermoelectric constants such as Seebeck coefficient is difficult with this method as long as the interfacial Pockels coefficient of the sample is unknown, a theory that can predict the Pockels coefficient at the interface between arbitrary materials is demanded.