Spatially Resolved In Situ Measurements of the Ion Distribution Near

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Spatially Resolved In Situ Measurements of the Ion Distribution Near the Surface of Electrode in a Steady-State Diffusion in an Electrolytic Tank with Confocal Micro X‑ray Fluorescence Song Peng,†,‡,§ Zhiguo Liu,†,‡,§ Tianxi Sun,*,†,‡,§ Yongzhong Ma,∥ and Xunliang Ding†,‡,§ †

The Key Laboratory of Beam Technology and Materials Modification of the Ministry of Education, Beijing Normal University, Beijing 100875, China ‡ College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China § Beijing Radiation Center, Beijing 100875, China ∥ Center for Disease Control and Prevention of Beijing, Beijing 100013, China ABSTRACT: Confocal micro-X-ray fluorescence (MXRF) technology based on a polycapillary focusing X-ray lens and a polycapillary parallel X-ray lens was used to carry out element-resolved and in situ analysis of ion distribution near the surface of the electrode in a steady-state diffusion in an electrolytic tank. The standard curve of the Cu Kα fluorescence intensity corresponding to the concentration of CuCl2 was measured to quantitatively determine the ion distribution near the surface of the electrode in a steady-state diffusion. The distribution of the electrolytic ions around the surface of the electrode in the electrolytic tank was measured in situ, and the effects of the concentration of the electrolyte and the bath voltage on the shape of the layer with a nonuniform distribution of the Cu2+ ions near the cathode surface in a steady state were analyzed with the confocal MXRF. The confocal MXRF has potential applications in spatially resolved analysis of the liquid mass transfer in electrolytic tanks in situ.

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electrode in the steady-state diffusion is studied by many methods: chronopotentiometry,1 Raman microspectroscopy,2 ultramicroelectrode,3 Mach−Zehnder interferometer,4 and visible absorption spectrometry.5 For the chronopotentiometric method, the transmembrane potential difference is measured to evaluate the concentration gradient.1 The Raman spectroscopy is very useful for visualizing in situ the transport of electroactive species in the vicinity of an active microscopic surface without affecting the diffusional concentration pattern by the local placement of a physical probe inside the diffusion layer. This Raman spectroscopy method also provides crucial spatially resolved molecular information on the species diffusing to or from an active surface on a micrometric scale.2 The concentrations of the electroactive substrate and of its electrogenerated product(s) inside the diffusion layer created by a larger working electrode can be monitored amperometrically by using an ultramicroelectrode. This allows a direct monitoring of the target species concentration profiles without any assumption, even when diffusion coefficients differ significantly.3 The path length change of the deflected light beam in the diffusion layer which can be measured by using a Mach−Zehnder interferometer is used to calculate the

iquid mass transfer in electrolytic tanks consecutively transports reaction ions to the vicinity of the electrode and moves reaction product away from the surface of the electrode. This property allows the electrochemical processes to be completed smoothly. In most cases, the mass transfer in the liquid phase determines the kinetic features of electrochemical processes. There are three primary modes of liquid mass transfer: electromigration, convection, and diffusion, which operate in concurrently and affect each other constantly. The electromigration causes the directional migration of charged particles primarily dependent on the electric field force in the solution. Natural convection normally exists in liquids and results in a temperature gradient or density gradient inside an electrolyte solution. Forced convection is often produced by a compressed air stirrer, rod or paddle agitator, rotating electrode, and an ultrasonic oscillator, which is often used to obtain a steady-state diffusion. With a diffusion in the solution, the components will migrate from the area of high concentration to that of low concentration, while a concentration difference is present. In unsteady-state diffusion, the distribution of the ion concentration changes with the time of the electrochemical reaction. However, in a steady-state diffusion, the ion distribution near the surface of the electrode is stable. Such steady-state diffusion can be obtained by using one kind of the forced convection and adding a supporting electrolyte. This steady ion distribution near the surface of the © 2013 American Chemical Society

Received: October 4, 2013 Accepted: December 13, 2013 Published: December 13, 2013 362

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Technical Note

refractive index gradient or the thickness of the diffusion layer.4 The absorption spectrometry techniques based on light absorption by an electrogenerated species rather than refractive index effects have the advantage of selectivity and much higher sensitivity.5 However, not all of the methods mentioned above can be utilized to carry out element-resolved analysis of liquid mass transfer in electrolytic tanks, and some of the methods are not able to measure the distribution of electrolyte concentrations directly. In this paper, the confocal X-ray technology based on capillary X-ray optics was used to perform the element-resolved and in situ analysis of the steady ion distribution near the surface of the electrode in the electrolytic tank. Polycapillary X-ray optics, also known as the Kumakhov lens, works on total external reflection.6 Polycapillary X-ray optics can be divided into two main types: polycapillary focusing Xray lenses (PCFXRL) and polycapillary parallel X-ray lenses (PCPXRL).7 In recent years, confocal X-ray technology based on capillary X-ray optics has become increasingly popular. Confocal technology was first proposed in the early 1990s by Gibson and Kumakhov,8 and it has been widely used in threedimensional micro-X-ray fluorescence (3D-MXRF) (3DMXRF), 9,10 3D X-ray absorption fine structure (3DXAFS),11−14 3D X-ray diffraction (3D-XRD),7 and confocal X-ray imaging technologies.15 The Confocal MXRF is based on a PCFXRL in the excitation channel and a PCPXRL in the detection channel. The PCPXRL is placed confocally with the PCFXRL. In such a confocal configuration, only the X-rays from the confocal volume defined by the overlap of the output focal spot (OFS) of the PCFXRL and the input focal spot (IFS) of the PCPXRL can be detected. By moving the sample located at the confocal position, the microvolume to be analyzed can be displaced laterally or in a direction perpendicular to its surface. Therefore, 3D information of the sample can be obtained nondestructively. Moreover, a better peak-to-background ratio can be obtained as a result of restricting the detector field of view.16 Tsuji et al. have proposed this confocal MXRF to analyze the solid−liquid interface, for example, analysis of the chemical deposition of Cu on an Fe plate and the dissolution of Fe in a CuSO4 solution.17 This confocal MXRF had potential application in analyzing the ion distribution near the surface of the electrode in the steadystate diffusion. This study investigated the performance of the application of the confocal MXRF on the element-resolved and in situ determination of the ion distribution near the surface of electrode in a steady-state diffusion in an electrolytic tank.

Figure 1. Scheme of confocal MXRF.

German). The maximum count rate of the detector system was 4 × 105 counts/s. The energy resolution of this detector system was 142 eV at 5.9 keV. An Nb filter placed between the source and the PCFXRL was used to obtain monochromatic incident X-rays (Mo Kα). A rectangular parallelepiped electrolytic tank, which was made of a 0.24 mm thick organic glass composed of carbon, hydrogen, and oxygen, was placed on a 5D stage. The materials of the anode and cathode were copper and zinc, respectively. The gain in power density of the PCFXRL and PCPXRL at 17.4 keV was 3100 and 6, respectively. Other parameters of the PCFXRL and PCPXRL are shown in Table 1. Table 1. Parameters of the PCFXRL and PCPXRL lens

PCFXRL

PCPXRL

length (mm) input focal distance (mm) output focal distance (mm) diameter of IFS at 17.4 keV/μm diameter of OFS at 17.4 keV/μm

72.2 98.9 11.2 198.7 23.5

18.3 11.5 not available 29.6 not available

At θ = 90°, the depth resolution dZ of this confocal system was 36.9 μm, and its lateral resolution dY and dX were 36.3 and 26.4 μm, respectively, which were measured with a metal filament. The photo flux in the focus of the PCFXRL was roughly estimated with the similar method used in ref 18. Corresponding to the gain G of the PCFXRL, an equivalent distance Leq can be calculated by L Leq = (1) G

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EXPERIMENTAL INSTRUMENT The confocal 3D MXRF is schematically shown in Figure 1, which is the vertical view. The PCFXRL and electrolytic tank are adjusted by using a five-dimensional (5D) stage, respectively. The PCPXRL combined with a detector is also adjusted with a use of a 5D stage. The divergent X-ray beam from the X-ray source placed at the input focal distance f1 away from the entrance of the PCFXRL was focused by the PCFXRL into an OFS at the output focal distance f 2 away from the exit of the PCFXRL. The PCPXRL was placed confocally at an input focal distance f 3 away from the OFS of the PCFXRL. The X-ray source was a Mo rotating anode X-ray generator (RIGAKU RU-200, 60 kV and 200 mA, Rigaku Corporation, Tokyo, Japan), whose spot size was 300 × 300 μm2. The detector system was an XFlash Detector 2001 RÖ NTEC with a RÖ NTEC MAX spectrometer (RÖ NTEC GmbH, Berlin,

where L is the distance from the X-ray source to the OFS of the PCFXRL.19 The Leq represents the distance where the density of radiation created by the X-ray source without the PCFXRL is analogous to the density of the radiation created by the PCFXRL with the same source in the focal spot.18,19 For the PCFXRL with a gain of 3100, the Leq is 3.3 mm. The theoretical count rate Nsource of Mo Kα from the Mo source was calculated by Nsource

1.6 I ⎛ eV − eV0 ⎞ =C ⎜ ⎟ e ⎝ eV0 ⎠

(2)

where I is the source current, V is the source voltage, V0 is the ionization voltage for the anode material, 20 kV for Mo Kα, and C is typically about 5 × 10−4 photons/electron for an Mo source. For source settings of 50 kV and 50 mA, Nsource = 3 × 363

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Technical Note

1014 photons/s. For the PCFXRL with an equivalent distance of 3.3 mm, the photon flux (PF) in its focal spot was PF =

3 × 1014 = 2.2 × 1012 (photons s−1 mm−2) 4π × 3.32

= 2.2 × 106 (photons s−1 μm−2)

(3)

After an Nb filter with a thickness of 50 μm, the photon flux (PFt) in the focal spot of the PCFXRL was −4

PFt = PF e(−μm ρt ) = 2.2 × 106 × e(−17.1 × 8.6 × 50 × 10 = 1.1 × 106 (photons s−1 μm−2)

)

(4) Figure 3. Standard curve of the Cu2+ in solution.

where μm is mass attenuation coefficient of the Nb for the X-ray with energy of 17.4 keV, ρ is density of the Nb, and t is the thickness of the Nb filter. Compared with the MXRF using only a PCFXRL in the excitation channel, the confocal MXRF uses a PCPXRL, which has an IFS to restrict the detector field of view besides using a PCFXRL in the excitation channel. When the IFS of the PCPXRL is overlapped with the OFS of the PCFXRL, only the X-rays from this confocal volume can be detected. Therefore, 3D information of the sample can be obtained nondestructively by moving the sample located at the confocal position.

only the weak XRF of K+ ions with a concentration of 3 M in the standard electrolyte solutions to be detected (Figure 2). Distribution of the Electrolyte Concentration. The divergence of the focused beam before and after the focal spot of the PCFXRL is about 6.1° for the X-rays with energy of 17.4 keV (Mo Kα). If the angle between the central line of the beam focused by the PCFXRL and the normal of the electrode was set at 90°, when confocal micro volume is close to the surface of the electrode, the edge of the electrode would prevent some X-rays from the PCFXRL from entering its focal spot, which would result in errors of analysis. In order to move the confocal micro-volume extremely close to the surface of the electrode without the stop from the edge of the electrode, the angle between the central line of the beam focused by the PCFXRL and the normal of the electrode was set at 80°, namely α = 10°, as shown in Figure 4, which is a sectional view along the Y

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RESULTS AND DISCUSSION Standard Curve. To measure the concentration of the Cu2+ ions in solution in an electrolytic tank in situ, a series of standard electrolyte solutions of CuCl2 with 3 mol/L of KNO3 were prepared, and a series of corresponding fluorescence spectra, similar to that in Figure 2, were collected with the confocal MXRF. All measurements were carried out at 25 °C with a working voltage and a current of 50 kV and 50 mA, respectively.

Figure 4. Sectional view along the Y direction from Figure 1.

direction from Figure 1. As mentioned above, the minimum resolution along the X direction of the confocal micro-volume was dX = 26.4 μm. Therefore, the resolution at the scanning direction along the normal of the electrode was dX/cos 10°, 26.8 μm. The scanning direction paralleled with one plane of the electrolytic tank in order to ensure the incident X-rays, and the XRF signals from the confocal volume had the same length of path in air, wall of the electrolytic tank, and electrolyte solution, respectively, for different scanning points. This allowed the measurements at different scanning points to have the same matrix and absorption factor. The electrolyte solutions of 0.6, 0.8, and 1.0 mol/L of CuCl2 with 3 mol/L of KNO3 were prepared, respectively, for three electrolytic tanks. Cu2+ ions in the electrolyte were transferred in the process of liquid mass transfer as the electrolyte solutions of CuCl2 were electrolyzed, and the ions were deposited on the cathode forming a copper sponge. In the process of liquid mass transfer, the concentration of the Cu2+ ions was not uniform in the liquid layer with a depth of hundreds of micrometers near the cathode surface. Generally, such a layer with a nonuniform

Figure 2. XRF spectrum of CuCl2 in solution.

The standard curve of the Cu Kα fluorescence integral intensity corresponding to the concentration of CuCl2 is shown in Figure 3. The accuracy of the application of this standard curve in determining the concentration of the Cu2+ ions in solution was better than 4%, and the corresponding precision was better than 5%. When the confocal MXRF was used to measure the ion distribution near the surface of the electrode in an electrolytic tank, both the energy and the intensity from the XRF of the ion should be high and intense, respectively, enough to pass through the electrolyte solution, the wall, and the air and arrive at the detector. For example, because the energy of the XRF of K+ ions was low, the heavy absorption from the matrix caused 364

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Technical Note

concentration distribution of the Cu2+ ions was not a steady state. The reason for this was that there were three forms of liquid mass transfer, electromigration, convection, and diffusion, which were affected by various factors, such as the temperature, the density of the solution, and pressure. Therefore, KNO3 working as the supporting electrolyte, which was used to decrease the electromigration of Cu2+ ions in order to reduce the impact from the electromigration on the diffusion and continuous stirring with a mechanical agitator were used to obtain a steady-state nonuniform concentration distribution of Cu2+ ions in a layer near the cathode surface. To evaluate the precision of the measurement of the distribution of Cu2+ ions around the electrode, the CuCl2 specimen of 0.8 mol/L was scanned three times with a step of 10 μm (Figure 5). As shown in Figure 5, the profiles of the

where Ci is the concentration of element i in the sample, Ii,B and Ii,N are the measured background and characteristic X-ray intensity of element i in counts per second, respectively, and t is the acquisition time in live seconds. The MDL of copper in the electrolyte solution was approximately 0.1 mol/L with a working voltage and a current of 50 kV and 50 mA, respectively. Therefore, as shown in Figure 6, the confocal setup in this paper was not able to detect Cu2+ ions with a concentration less than 0.1 mol/L in the region closed to the surface of the electrode. To analyze the effects of the concentration of the electrolyte on the shape of the layer with a steady-state nonuniform concentration distribution of the Cu2+ ions near the cathode surface, the layer of the electrolyte solutions of CuCl2 with a concentration of 0.6, 0.8, and 1.0 mol/L were measured (Figure 6A). As shown in Figure 6A, the thickness of the layer with a steady-state nonuniform concentration distribution of Cu2+ ions near the cathode surface decreased with the increasing concentration of the electrolyte. To analyze the effects of the bath voltage on the shape of the steady state layer, the concentration distributions of CuCl2 with a bath voltage of 6, 8, and 10 V were measured (Figure 6B). As shown in Figure 6B, the thickness of the layer with a steady-state nonuniform concentration distribution of Cu2+ ions near the cathode surface also decreased with the increasing bath voltage. The confocal configuration ensured that the confocal MXRF could be used to carry out the spatially resolved in situ measurements of the liquid mass transfer in the electrolytic tank. However, even though the PCFXRL and PCPXRL have a high gain in power density, the X-ray fluorescence of the electrolytic ion was absorbed by the electrolyte solution and the wall of the electrolytic tank when the X-ray fluorescence passed through them. Such absorption would increase the MDL of the confocal MXRF, and therefore, the electrolytic ion with a low concentration near the cathode surface would not be detected by the confocal MXRF based on the conventional X-ray source. To measure such electrolytic ions with a low concentration near the cathode surface, a high power X-ray source, such as synchrotron radiation, might be used for confocal MXRF.

Figure 5. Distribution of electrolyte concentration for three successive scans, respectively.

three scans were similar, indicating that not only the concentration distribution of the Cu2+ ions in the layer near the cathode surface was in an approximately steady state but also that the precision of the measurement of the distribution of Cu2+ ions around the electrode was acceptable. Furthermore, the minimum detection limit (MDL) of the confocal MXRF spectrometer depended on the gain in power density of the PCFXRL and PCPXRL and the working voltage and current of the rotating anode X-ray source. The MDL was calculated by the following formula:20 MDL = 3Ci

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CONCLUSIONS The performance of the confocal MXRF on the spatially resolved in situ determination of the ion distribution near the surface of the electrode in a steady-state diffusion in an electrolytic tank was presented. The standard curve of the Cu

Ii ,B Ii ,N t

(5)

Figure 6. (A) Distribution curve of the Cu2+ ions as a function of the electrolyte concentration. (B) Distribution curve of the Cu2+ ions as a function of the bath voltage. 365

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Analytical Chemistry

Technical Note

Kα fluorescence intensity corresponding to the concentration of CuCl2 was measured to determine quantitatively the liquid mass transfer in electrolytic tanks in situ with confocal MXRF. The effects of the concentration of the electrolyte and the bath voltage on the shape of the layer with a nonuniform distribution of the Cu2+ ions near the cathode surface in a steady state could be analyzed with confocal MXRF. Confocal MXRF has potential applications in analyzing the liquid mass transfer in electrolytic tanks in situ.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (Grants 11075017 and 11375027) and the Fundamental Research Funds for the Central Universities (Grant 2012LZD07).

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REFERENCES

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