liquid interface using a Mach–Zehnder interferometer

Sensors and Actuators B 176 (2013) 509–513

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Sensors and Actuators B: Chemical journal homepage: www.elsevier.com/locate/snb

Sensing of the dynamic concentration field at the solid/liquid interface using a Mach–Zehnder interferometer Boyu Yuan a,b , Wei Li a,∗ , Chao Wang c,∗∗ , Liang Li c a b c

School of Mechanical and Electrical Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou, Jiangsu 221116, China School of Chemistry and Chemical Engineering, Jiangsu Normal University, Xuzhou, Jiangsu 221116, China

a r t i c l e

i n f o

Article history: Received 18 September 2011 Received in revised form 17 October 2012 Accepted 20 October 2012 Available online 2 November 2012 Keywords: Mach–Zehnder interferometer Concentration field Solid/liquid interface Diffusion

a b s t r a c t A Mach–Zehnder interferometer is employed to study the dynamic concentration field within diffusion layer in transparent liquid solutions at the solid/liquid interface. The method is applied to investigate the electrodeposition of nickel in 0.20 mol dm−3 NiSO4 solution. Interferograms of an object wave through an experimental cell containing diffusing solutions are recorded continually by a CMOS image sensor and displayed on a monitor in real time. The two-dimensional concentration change of the solution at the solid/liquid interface is determined according to the interference fringes. Software is developed to obtain the dynamic concentration field automatically. The calculated results match well with theory values. Its ease of fabrication offers the attractive applications in chemical and biological sensing. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Generally speaking, diffusion is the movement of a species under the influence of a concentration gradient in solution [1]. Diffusion and diffusion layer have important influence on wet-chemical reaction system. Study of concentration field with diffusion layer is a crucially important subject in the field of chemistry both from fundamental and technical standpoints. Knowledge of concentration field within diffusion layer is useful to understand reaction route, electro-dissolution, electro-deposition, diffusion and convection near electrode, and so on [2–5]. Moreover, the study of concentration field is also important in biology, materials, medicine, fluidics and other domains [6–13]. Many techniques have been explored to study the concentration profile within diffusion layer of solution, such as the refractometry [11], spectroscopy [14,15] and interferometry [4,16–18]. Optical methods provide a convenient and noninvasive tool for studying the concentration field and continue to shed light on dynamic processes. The interferometric technique is one of the most widely used techniques for concentration field study because it is a whole-field technique. Leger et al. used phase-shift Mach–Zehnder interferometer to first obtain quantitative proof of the diffusive character of the mass transport in thin gap electrodeposition

∗ Corresponding author. Tel.: +86 51683590798; fax: +86 51683590798. ∗∗ Corresponding author. Tel.: +86 51683403003; fax: +86 51683403003. E-mail addresses: [email protected] (W. Li), [email protected] (C. Wang). 0925-4005/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.snb.2012.10.097

experiments [4]. Anand et al. determined the diffusion coefficients automatically by use of digital holographic interferometry [17]. The convenient method can be suitable for continuous monitoring the diffusion process with high accuracy. Recently, You et al. employed a Michelson interferometer to measure the concentration profile within diffusion layer in a galvanic displacement reaction system [18]. It was proved to be a useful tool to further confirm the validity of theory model deduced by other electrochemists. During most electrochemical reactions, the diffusion layer changes with the wave of the concentration near the solid/liquid interface. For fast, quantitative and simultaneous measurements of the dynamic concentration field and the diffusion layer thickness, more suitable methods should be explored to give new insights into those processes. In this paper, a Mach–Zehnder interferometer is employed to investigate the two-dimensional concentration changes of transparent liquid solutions at the solid/liquid interface during electrochemical reactions. It can provide in situ measurement of full-field concentration changes at the interface during electrochemical processes without external effect on most electrochemical reactions. The resolution and measurement range of the interferometer can be adjusted in a wide range. With these advantages, it is well suited for a detailed study of mass transport processes in transparent media. Digital image/video processing methods have been used to analyze the interferogram video sequences obtained by the interferometer. The software for determination of the concentration distribution has been developed. The dynamic concentration changes in nickel electrodeposition

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-0.75

E/V

-0.80 -0.85 -0.90 -0.95 -1.00 0

5

10

15

20

t/s Fig. 1. The experimental set of the holographic recording system: M, mirror; BS, beam splitter; SF, spatial filter; L1 and L2, collimating lens; O, experimental cell; L3, object lens.

Fig. 2. The V–t curve of the galvanostatic electrodeposition of the nickel in 0.20 mol dm−3 NiSO4 solution.

2.3. Image processing

have been visually presented. The interferometer is proved to be useful and convenient to investigate the dynamic changes at the solid/liquid interface during electrochemical processes. The experimental setup and theoretical analysis of the method are introduced and discussed in detail.

2. Materials and methods 2.1. Optical setup Fig. 1 shows the experimental set of the holographic recording system. It consisted of an improved Mach–Zehnder interferometer. Light from a He–Ne laser source was split into two beams using a beam splitter. Each beam was expanded and collimated with a microscopic objective and a collimating lens. One beam passing through the experimental cell was the object beam. The other acted as reference beam. They interfered at a CMOS image sensor forming the interferograms. A personal computer was connected to the image sensor for recording the interferograms at 25 frames per second.

2.2. Electrochemical system The electrochemical cell is the same as that [19]. It contained a three-electrode system. An electrode of copper rod (2 mm diameter, 99.9%) was employed as the working electrode. The entire electrode was sealed with a thin layer of epoxy resin in a glass tube, with the end of the copper rod exposed to the solution. The counter electrode was a large sheet of nickel. A saturated calomel electrode (SCE) was employed as the reference electrode. A Luggin capillary was also employed between the working electrode and the reference electrode. Before each experiment, the Cu electrode was mechanically polished with emery paper and then cleaned by alcohol and triply distilled water in an ultrasonic bath. The electrolyte was 0.20 mol dm−3 NiSO4 solution, which was prepared from regents of analytical grade and triply distilled water. The galvanostatic electrodeposition of the nickel was performed by a CHI660B electrochemical workstation (CHI Instruments Inc.). The cathodic current density was kept at 1.91 mA cm−2 . All measurements were carried out at room temperature (20 ± 0.5 ◦ C). Fig. 2 shows the V–t curve of the galvanostatic electrodeposition of the nickel in 0.20 mol dm−3 NiSO4 solution.

2.3.1. Determination of the phase difference For obtaining the phase maps conveniently, carrier fringes were introduced by moving the object lens L3 in Fig. 1. The carrier wave was obtained by a slight displacement of L3 along with x or y axis (depend on the location of interface). In the present experiment, the solid/liquid interface was vertical (along with y axis), thus the displacement was horizontal (along with x axis). Fig. 3 shows two interferograms and the corresponding Fourier spectra with and without the carrier fringes. Because the light was shaded by the copper electrode, it presented a dark shadow at a half part of the interferograms. In experimental system of digital recording, the fringe pattern of the form can be found as, g(x, y, t) = a(x, y) + b(x, y) cos [2f0 x + (x, y, t)]

(1)

where the time-varying phase (x, y, t) contains the desired information; a(x, y) and b(x, y) represent irradiance variations arising from the non-uniform light transmission by the experimental cell; f0 is the spatial frequency of the fringe carriers given by the slight horizontal displacement of the object lens L3. In the experiment, the concentration at the solid/liquid interface changed as the electrochemical reactions carried out, which would cause the change of the refractive index of the solution. The interference fringes in the interferograms deformed accordingly. The changes in the phase ((x, y, t)) were brought about by the variations of the refractive index inside the electrochemical cell. If the recording is made with identical conditions of illumination, the intensity g(x, y, t) recorded on the interferograms at different times t1 and t2 are given by, g(x, y, t1 ) = a(x, y) + b(x, y) cos [2f0 x + (x, y, t1 )]

(2)

g(x, y, t2 ) = a(x, y) + b(x, y) cos [2f0 x + (x, y, t2 )]

(3)

Because spatial variations of a(x, y), b(x, y) and (x, y, t) are slow compared with f0 , the central lobe and the two side lobes in the frequency domain of the images g(x, y, t) are separated, as illustrated in Fig. 3d. It is feasible to employ two-dimensional Fourier transform method to analyze the fringes. A band-pass filter centered at f0 was applied to obtain one of the spectral side lobes of the images. For g(x, y, t1 ) and g(x, y, t2 ), the filtered images can be written in the following form, g(x, y, t1 ) = 

g(x, y, t2 ) =

1 b(x, y) exp i[2f0 x 2

+ (x, y, t1 )]

(4)

1 b(x, y) exp i[2f0 x 2

+ (x, y, t2 )]

(5)

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Fig. 3. Two interferograms and the corresponding Fourier spectra. (a) An interferogram without carrier fringes; (b) the Fourier spectrum of (a); (c) an interferogram with carrier fringes; (d) the Fourier spectrum of (c).

Then, the phase difference (x, y) between t1 and t2 can be calculated by,

 (x, y) = arctan

∗

Im[g(x, y, t1 ) g(x, y, t2 ) ] ∗

Re[g(x, y, t1 ) g(x, y, t2 ) ]

 (6)

Generally, the phase change between two frames (0.04 s interval) is less than 2. Phase differences greater than 2 give rise to an indeterminacy that can be resolved by use of standard phaseunwrapping methods. In Eq. (6), the distribution of phase difference can be obtained for any time instant after the recording of the first interferogram. 2.3.2. Measurement of the concentration field For a single-component solution, there is proportionality between the concentration and the refractive index. In the experiment, the concentration change C of NiSO4 solution at the interface led to a refractive index variation n. The relationship between the refractive index and concentrations of various solutions (0.04, 0.08, 0.12, 0.16 and 0.20 mol dm−3 ) is shown in Fig. 4. An Abbe refractometer was used to measure the refractive indices at room temperature (20 ± 0.5 ◦ C). The relationship can be considered as linear over experimental concentration range, as illustrated in Fig. 4. It can be formulated as, C(x, y) = k n(x, y)

(7)

When the refractive index variation appeared at the electrode/solution interface, the phase distribution of the object wave changed synchronously, compared with the former state. The phase difference  caused by the refractive index variation n is given by [20], n(x, y) =

0 (x, y) 2d

(8)

Fig. 4. Concentration-dependence of the refractive index of NiSO4 solution at 20 ± 0.5 ◦ C.

where 0 is the wavelength of the light used; d is the thickness of the liquid traversed by the light. So n and C are average variations inside the diffusion cell. Then the relationship between concentration change and phase difference is obtained as, C(x, y) =

k0 (x, y) 2d

(9)

Eq. (9) yields the concentration field during the dynamic reactions due to the change in the interference phase between t1 and t2 . The time evolution of the electrochemical processes can be studied from consecutive interferograms. Software was developed with MATLAB® (copyright by The Mathworks, Inc.) to acquire the video sequences, process the interferograms and display the distribution of concentration changes. The initial interferogram at the time when the reaction began was selected. Then, the concentration field

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Fig. 5. Four snapshots of computer-processed concentration maps at different times during the processes of the galvanostatic electrodeposition of nickel. The x axis is in horizontal direction from the electrode surface toward the bulk solution while the y axis in vertical direction is parallel to the surface of electrode. A full sequence is available in Video 1 (lower part). The V–t curve in Fig. 2 and dynamic concentration field during the process are synchronized carefully in Video 1.

with diffusion layer can be obtained quantitatively and displayed continually on the monitor.

3. Results and discussion At the beginning of the experiment, there was no evident change shown in the interferograms. As the reaction went on, the nickel ions transported continuously through diffusion layer from bulk solution to reaction surface. Through real time observation in the interferograms, it was found that the fringes near the interface slightly deformed according to the concentration changes. The dynamic processes of the electrochemical reactions can be quantitatively investigated for any time instant. According to the relationship between the phase difference and the concentration change in Eq. (9), the dynamic concentration field can be obtained after the recording of the first interferogram. Fig. 5 shows four snapshots of computer-processed concentration maps at different times during the galvanostatic electrodeposition of the nickel in 0.20 mol dm−3 NiSO4 solution. The concentration field refers to the concentration difference C(x,y) (mmol dm−3 ) between the given time points and the initial (0.20 mol dm−3 ). A full sequence is available in Video 1 (lower part). The color indicates the value of concentration change. The left part of them is set to be constant as it is electrode area. The color variation appears only at the solid/liquid interface, showing that the concentration of solution is rather stable in most of the region (bulk solution), but it decreases from the bulk to the electrode, which brings about the diffusion layer. The layer is small during the first few seconds of the experiment (Fig. 5a), and it grows up with the time (Fig. 5b–d). The maps show that the concentration near the electrode decreases gradually as the Ni2+ is reduced to Ni, which can be formulated as, Ni2 + 2e → Ni

(10)

Both the dynamic concentration changes and thickness of diffusion layer were obtained from the concentration maps. After 20 s of the reaction, the concentration within diffusion layer became relatively stable. The maximum concentration change was about 8.2 mmol dm−3 and the thickness of diffusion layer was about 150 ␮m, which were derived from Fig. 5d. The results matched well with the concentration field with diffusion layer of an electrode obtained by other techniques [1,15,18]. Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.snb.2012.10.097. 4. Conclusions In the present paper, we propose a Mach–Zehnder interferometer to sense the dynamic concentration field automatically. It can provide the quantitative information of the concentration change and the thickness of diffusion layer simultaneously. The actual spatial resolution is about 1.7 ␮m in the experiment. The maximum is confined by diffraction limited resolution, which is defined by the diameter of the lens and the wavelength of laser light. The actual time resolution is 0.04 s since the video camera is set to obtain 25 images per second. The minimum refractive index variation n effectively detected is about 5 × 10−6 , which is confined by image noise of interferograms. Because the phase difference is obtained by the substrate of two images, the noise of this system has been counteracted to some extent. This system provides useful information for dynamic processes in transient solutions. It could find many applications in chemistry and biology. Acknowledgments This research was supported by the Fundamental Research Funds for the Central Universities (No. 2012LWA06) and the Project

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Biographies Boyu Yuan received a B.S. degree (2004) in Optics and Electronics, as well as M.S. degree (2007) in Signals and Information Processing, both from Shandong University. He is presently a Lecturer in the School of Physics and Electronics Engineering at Jiangsu Normal University and a Ph.D. candidate in the School of Mechanical and Electrical Engineering at China University of Mining and Technology. His research interests include optical interferometry and signal processing. Wei Li received a Ph.D. degree (2004) in Mechanical Design and Theory from School of Mechanical and Electrical Engineering, China University of Mining and Technology. He is currently a Professor in the School of Mechanical and Electrical Engineering at China University of Mining and Technology. His research interests include the fabrication and test of MEMS devices, information processing and intelligent control of mechanical systems. Chao Wang received a Ph.D. degree (2000) in Electrochemistry from Department of Chemistry at Shandong University. Dr. Wang is currently a Professor in the School of Chemistry and Chemical Engineering at Jiangsu Normal University. His research interests include have centered on new techniques and experiment methods in electrochemistry and corrosion electrochemistry, with an emphasis on holographic microphotography study of electro-dissolution, electro-deposition and electrochemical oscillation of metals. Liang Li received a B.S. degree (1989) in Chemistry and M.S. degree (1995) in Surface Electrochemistry from Nanjing University, and the Ph.D. degree (2004) in Electrochemistry from Shandong University, respectively. Dr. Li is currently a Professor in the School of Chemistry and Chemical Engineering at Jiangsu Normal University. His research interests include electrochemical oscillations and effects of magnetic field on electrochemical reactions.