research papers
Approach to electrochemical modulating differential extended Xray absorption fine structure
^{a}National Synchrotron Radiation Laboratory, CAS Center for Excellence in Nanoscience, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China, ^{b}Beijing Synchrotron Radiation Facility, Institute of High Energy Physics, Chinese Academy of Science, Beijing 100049, People's Republic of China, ^{c}University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China, ^{d}Department of Materials Sciences and Engineering, School of Chemistry and Materials Sciences, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China, and ^{e}State Key Laboratory of Particle Detection and Electronics, Institute of High Energy Physics, Chinese Academy of Science, Beijing 100049, People's Republic of China
^{*}Correspondence email: chusq@ihep.ac.cn, jzhang@ihep.ac.cn, song2012@ustc.edu.cn
The differential
technique holds promise for detecting surface changes, which benefits many chemical applications. Phasesensitive detection (PSD) analysis based on modulated excitation spectroscopy experiments is expected to obtain a highquality difference spectrum, while the mathematical relationship and experiment parameters remain to be discussed. In this article, an approach to obtaining the difference spectrum from the PSD demodulated spectrum is described and its applicability in different experiment settings is discussed. The results indicate that the demodulated spectrum is almost equal to the difference spectrum when the modulating period is 20 times larger than the constant. This approach was subsequently applied to an electrochemical modulation experiment and the demodulated spectrum was analyzed. A reversible lattice shrinking is observed via the fitting of demodulated spectra, which is proportional to the charge amount on the electrode. This approach could be used to quantitatively analyze the modulated excitation data and holds promise for a wide range of electrochemical studies.Keywords: differential XAS; modulation excitation spectrum; phasesensitive detection; electrocatalysis.
1. Introduction
Electrocatalysis has attracted tremendous attention due to its extensive application in the chemical industry as well as its promise for developing renewable energy sources. As a basic reaction in many electrolysis processes, the oxygen evolution reaction (OER) commonly occurs if no other sacrificial ions exist, but is usually sluggish as a fourelectron process, especially in an acid environment (An et al., 2021). Efficient catalysts are needed to reduce the energy barrier, while the rational design of the catalysts still meets obstacles regarding the insufficient fundamental understanding of the catalysts' atomic structure and the adsorption–desorption process (Jiang et al., 2018). Recent development of the in situ technique made it possible to discover the real state of the catalyst during the catalytic process and many instances of the structural response towards potential have been proved (Ding et al., 2021). It is vital to continuously develop characterization methods for electrocatalysis research.
For revealing the structural evolution of catalysts, in situ Xray absorption fine structure (XAFS) has been applied frequently (Cao, Liu et al., 2021). However, comes from an average of all the atoms of the detected elements, which makes the spectral change induced by surface processes not so obvious. To strengthen only the change of different states, making use of the difference spectrum (diffXAS, Δμ) is a powerful analysis technique. Generally speaking, diffXAS is the difference in the spectra obtained in different states,
Its mathematical form is well defined, thus allowing quantitative analysis of the change in the system. In a representative work, Pettifer et al. (2005) enhanced the accuracy of the interatomic distance into femtometres using diffXAS. In the Xray absorption nearedge structure (XANES) part, ΔμXANES is used to compare the and adsorption species (Ramaker & Koningsberger, 2010). However, it is difficult to obtain a highquality difference spectrum in the extended Xray absorption finestructure (EXAFS) range with static measurement, especially for in situ research where the solution environment contributes to a low signaltonoise (S/N) ratio. The modulated (MES) has been used to detect the tiny difference between different states given by periodic circumstances or fields which leads to a periodical response of the measured system (Ferri et al., 2011). For extraction of the periodical signal with known frequency, there is a mature solution in electronics called phasesensitive detection (PSD). PSD is a narrowband technique that can filter noise, thus enhancing the signaltonoise ratio. Our group has used a PSDbased electronic device to obtain difference via pressure modulation (Chu et al., 2012). One can also collect MES data via timeresolved methods and perform PSD analysis offline (König et al., 2012). However, the response of the system to external conditions may not be so rapid and show kinetic behavior. If the stimulation period is in the range of the of the system, amplitude decay and phase lag of the response will occur, which depend on the modulation frequency (Baurecht & Fringeli, 2001; Müller & Hermans, 2017). In this regard, it is incorrect to use the amplitude obtained from the PSD analysis as the difference spectrum. Instead, the phasesensitive properties of PSD can be used to analyze the dynamic properties of the system (Chiarello & Ferri, 2015). Still, PSD applied to MES data results in a special kind of difference spectrum between excited and nonexcited states (Gremlich & Yan, 2000), thus allowing qualitative analysis. In electrocatalysis research, MES experiments and PSD analysis have been used to catch the dynamic changes in adsorption species and surface structure (Czioska et al., 2021; Lawley et al., 2022; Ebner et al., 2022), which proved the great potential of this method. However, if the quantitative relationship between PSD demodulated and the diffXAS could be elucidated, PSD analysis can give more quantitative results. In fact, amplitude attenuation and phase lag are related to the modulation period and constant of the measured system as discussed in former modulation excitation infrared spectrum research (Baurecht & Fringeli, 2001; Urakawa et al., 2006), which could also be used in the MEXAS experiment.
In this article, we obtained the mathematical relationship between the difference spectrum and PSD demodulated MEXAS data in a slowrelaxation system using an electrochemical system as an example. Our results show that if the modulation period is 20 times more than the system
constant, after a certain correction, the quantitative difference between the PSD demodulated spectrum and the difference spectrum can be less than 2% while the S/N ratio could be enhanced using PSD analysis. Thus, it is possible to obtain the difference spectrum from the PSD method. This method was further applied to the electrochemical system and a reversible shrinking of bond length along with increasing potential was found. This study provides a feasible approach for quantitative analysis of MEXAS data, which may inspire many other modulated excitation experiments.2. Theory
2.1. Fourier series
According to the well known Fourier decomposition, any periodic function can be written as a superposition of a series of sinusoidal functions in a finite interval. Let its period be T; in the interval [0, T], it can be written as the following Fourier series expansion,
The coefficients a_{k} and b_{k} can be seen as the projection of a vector on the xaxis and the yaxis, respectively. Therefore, the Fourier series can be further written in the following form,
Thus, a periodical signal can be written as a superposition of a series of sine functions with different amplitudes (modulus) and phase angles, which forms the basis of frequency domain analysis.
2.2. Modulation and phasesensitive detection
If a periodically changing external circumstance or field (sine wave, square wave, etc.) is applied to a system during a spectrum test, the resulting spectrum signal will also oscillate at the same frequency. In an MEXAS experiment, the absorbance signal μ(E, t) can be expressed in the form of a Fourier series,
where k is the order of the Fourier transform, ω is the frequency of the external excitation, and μ_{k} and φ_{k} are the corresponding amplitude and phase angle. To extract the amplitude and phase information, the basic formula for obtaining the Fourier transform coefficients can be used,
where is the PSD demodulating phase angle. This is the basic function of PSD. If = , then = , thus the result of this formula is the coefficient of the Fourier series. There are also the following relationships for other values,
The result of the PSD is therefore phase sensitive. To obtain the phase difference between an input signal (reference signal) with a known phase and an output signal with an unknown phase, one can carry out trigonometric function processing on the results when the demodulation angle equals 0° and 90° via equation (2), or directly find to make achieve the maximum value.
2.3. Phase lag and kinetics
For an ideal system where the output signal has the same phase as the input signal, the system's response is immediate. However, in a real system, the response has a kinetic behavior which leads to phase lag and amplitude decay. Taking a squarewave input as an example for a more intuitive understanding, the ideal output is as follows,
where T = 2π/ω is the period and A/2 is the amplitude. The result of its Fourier transform is easily obtained,
For an ideal square wave, firstorder (k = 1) sinusoidal demodulation will give the best demodulation angle of 0 and an amplitude of 2A/π, which has a clear 2/π multiple relationship with the difference A. However, the actual response often exhibits relaxation properties. Consider a common relationship which can be described by the following equation,
This is called a firstorder system. Its step response in the time domain is as follows,
where τ is usually called the time constant and describes how fast the system changes. Inputting a square wave with different periods will result in the output shown in Fig. 1. It can be seen that when the modulation period is much larger than the time constant, the relaxation of the system is sufficient. At this time, the fundamental frequency component contained in the signal has a smaller phase delay and amplitude attenuation than a perfect square wave. However, when the modulation period becomes shorter, the oscillation needs several cycles to stabilize first. The amplitude of the waveform is significantly attenuated, and the phase of the fundamental frequency is also significantly delayed. Thus, the phase lag and amplitude attenuation depend on the modulation period and constant. Using this, we can obtain the phase lag through PSD analysis and analyze the kinetics of the system.
2.4. Transfer function
If the response of the system is linear, the abovementioned frequency attenuation and phase lag can be analyzed using the transfer function. In the Laplace domain, the transfer function G(s) relates the input function U(s) of the system to the output function Y(s),
When the input function is a sinusoidal signal with frequency ω, the output signal can be expressed as
where G(iω) is the modulus of G(iω) in the complex plane, and φ(ω) is the phase angle, so the amplitude attenuation and phase delay between the sinusoidal input and output of different frequencies can be easily obtained from the transfer function. For the aforementioned exponentially decaying response, the transfer function has the following form,
The amplitude–frequency characteristics and phase–frequency characteristics can be obtained,
A plot of these two relationships is called a Bode plot. It can be seen that the amplitude attenuation and frequency change are only related to ωτ, as shown in Fig. 2.
When the frequency is fixed, increasing the time constant also leads to an increase in the phase delay, so the kinetics of the system can be analyzed by obtaining the phase lag. For different systems, if the transfer function can be obtained according to its physical model, the phase lag can be used to obtain the kinetic parameters. When performing dynamic analysis, it is best to select the region where the phase delay changes rapidly with frequency, generally set to 0.1 < ωτ < 10, which corresponds to the region in the gray background of the τ = 10 curve in Fig. 2.
2.5. Relationship between PSD and difference spectrum
According to the above analysis, the relationship between PSD amplitude and absolute amplitude can be obtained when the transfer function is known. In the actual MES experiment, the frequency of the modulating external field is known, and the phase difference of the response signal can be given by the PSD so that the dynamic parameter τ can be obtained, and the ratio of the amplitude attenuation at a specific frequency can be obtained from τ, thereby obtaining the absolute amplitude. The absolute amplitude has a definite relationship with the difference value since the input waveform is known. This is the mathematical relationship between the PSD result and the difference spectrum.
When a sine wave is input, the output of a linear system is also a sine wave. For a squarewave input, it can be decomposed as a superposition of infinite sine waves after the Fourier transform. Due to the additivity of the linear system, it can be considered that the sine waves of each frequency component contained in the square wave will output the corresponding sine wave of the same frequency but with different amplitude and phase according to the relationship in the Bode diagram. The superposition of these signals becomes the output waveform. According to the aforementioned amplitude correction method, the following formula can be obtained to describe how to use the PSD analysis of the fundamental frequency to obtain the difference spectrum,
where π/2 is the coefficient between the amplitude of the squarewave signal and the fundamental frequency sine signal. φ(ω) can be obtained by finding the demodulation angle used to maximize the integral in PSD analysis. Then, the amplitude attenuation A(ω) is obtained from the kinetic parameters through equation (13). There is also a benefit to using squarewave modulation that the kinetic parameters can be obtained from analyzing the relaxation curve. Although the absolute amplitude can be obtained theoretically, the model is usually simplified and the acquisition of the kinetic parameters may be inaccurate, so there is also an error in the acquisition of the absolute amplitude, which will also lead to inaccurate corrections. Therefore, to obtain the differential spectrum from the PSD, amplitude attenuation should be as small as possible. We recommend controlling the experimental conditions so that the correction value is less than 5%, which needs ωτ < 0.33, or approx,imately, T/τ > 20, as seen in Fig. 2. For higher accuracy, the value of ωτ should be smaller, as in experiments with fast response such as high pressure (Chu et al., 2012), magnetostriction (Ruffoni et al., 2008), etc.
Finally, it should be emphasized that in a nonlinear system the input sinusoidal signal will output higher harmonics. So there is no oneonone correspondence in the frequency domain, and there is no transfer function, making kinetics analysis very difficult. Still, if the response of the system is close enough to a square wave by setting the experimental conditions, the differential spectrum can be obtained within an acceptable error range.
3. Experimental
3.1. IrO_{x} electrode preparation and electrochemical measurement
The IrO_{x} electrode used for modulating differential experiment is synthesized by of Ir(III) acetate (Shanghai Macklin Biochemical Co. Ltd, Ir 50–54%). The Ir(III) acetate was dissolved in DI water to form a 60 g L^{−1} homogeneous solution. Then the solution was dropped onto carbon paper (Toray, TGPH060) at 200 µL cm^{−2} and dried at room temperature. Finally, the carbon paper was annealed in air for 2 h at 250°C. A similar process was used to prepare the electrode for electrochemical cyclic voltammetry (CV) test by 100fold loading.
All electrochemical measurements as well as the in situ test were performed using a CHI760e (CH Instruments, China) electrochemical workstation in a standard threeelectrode setup with graphite rods as a counter electrode and an Hg/Hg_{2}SO_{4} electrode as a The electrolyte was 0.5 M H_{2}SO_{4} with Ar saturation, and all potentials were calibrated to the reversible hydrogen electrode (E_{RHE} = E_{Hg/Hg2SO4} + 0.652 + 0.059 × pH) accordingly. The scanning rate of the electrochemical CV was 50 mV s^{−1}. The period used in the chronoamperometry (CA) test and the following modulation was 400 s.
3.2. measurement and data process
The experiment setting is shown in Fig. 3. All the experiments were performed at the 1W1B beamline at Beijing Synchrotron Radiation Facility (BSRF) (operating at 2.5 GeV with a maximum current of 250 mA). The main optics of this beamline consist of a front slit, vertical collimation mirror, Si(111) fixedexit doublecrystal monochromator, and toroidal mirror. The at the sample is of the order of magnitude of 10^{11} photons s^{−1} and the spot size is 0.9 mm (H) × 0.3 mm (V). A homemade electrochemical in situ cell is used in transmission mode. The windows on both sides are sealed by Kapton tap with a gap of about 1.5 mm, which is also the thickness of the solution. One end of the carbon paper electrode is connected to the platinum electrode clip (above the liquid surface), and the other end is immersed in the solution. The solution is stagnant as there is almost no gas generation involved in our experiment. The Ir L_{3}edge spectra were collected in QXAFS mode where a full spectrum was acquired in about 5 s. The spectra were continuously recorded with the potential changing for more than four complete periods (about half an hour). By using the ATHENA and ARTEMIS module of the IFEFFIT software package (Ravel & Newville, 2005), the obtained data were processed and fitted. We fitted the IrO_{2} standard sample first to obtain the amplitude attenuation factor S_{0}^{ 2}, whose value is 0.77 here. The parameter setting is discussed later.
4. Results and discussion
4.1. Electrochemical result
Electrochemical CV was performed to illustrate the basic properties of the IrO_{x} electrode. As shown in Fig. 4(a), the main oxidation/reduction peaks appear at 0.78 V/0.45 V, which are assigned to the Ir(III)/Ir(IV) redox couple as reported in earlier studies (Nong et al., 2018; Saveleva et al., 2018). The CV result determines the potential used for modulation where the low potential should be below 0.45 V and the high potential should be over 0.78 V to make the surface redox reaction occur. Then, we performed CA to reveal the charge–discharge property, where we alternately apply two potentials on the catalyst and record the current as a function of time. Based on the CV result, we choose the low potential at 0.4 V to reduce the high valence surface Ir to the initial state, and the high potential at 1.0 V, 1.2 V and 1.4 V to examine the surface charge property. The result of 0.4 V/1.4 V is shown in Fig. 4(b), where a typical exponential growth and decay of current can be found. The current curve shows a good periodicity, implying the stability of the system. The CA curve of bare carbon paper is also tested (Fig. S1 of the supporting information) and the current is much smaller than for the IrO_{x} loaded sample, proving that almost all the capacitance is from IrO_{x}. Different conditions of 0.4 V/1.2 V and 0.4 V/1.0 V show similar results and are given in Fig. S2 of the supporting information. The charge values accumulated on the catalyst surface are acquired from the integral of the cathodic current curve to avoid the influence of OER current in the anodic process as shown in Fig. S3 of the supporting information. As a result, the total charge is 13.4 mC, 18.1 mC and 23.8 mC at the high potential of 1.0 V, 1.2 V and 1.4 V, respectively, which are almost proportional to the voltage.
4.2. Extraction and correction of the PSD demodulated spectrum
As described above, we continuously recorded μ(E, t) containing all the spectra changing with time. As seen in Fig. 5(a), the shows good periodicity in two selected energy positions. We also find a point with no obvious vibration in the same scale plot, which proved that the vibration of the spectrum results from structural changes rather than other interference factors like the gathering of ions or the changing in liquid layer thickness, which will change similarly everywhere in the spectrum. We can also obtain two original spectra representing two different potentials via an average of the corresponding part of μ(E, t); the detailed method is shown in Fig. S4 of the supporting information and the results are shown in Fig. 5(b). It can be found that opposite phases at different energies in Fig. 5(a) represent opposite signs of the difference spectrum. Before performing equation (14), the kinetic parameter of the system should be obtained first, which was done with both fitting the relaxation curve and the PSD analysis. Fig. 5(c) shows the fitting results of the relaxation curve of the which fits the exponential function well. Details of the exponential fitting parameters are shown in Fig. S5 of the supporting information. The difference of the resulting time constants τ is not so significant for different energy and different redox process. Thus, it is reasonable to describe the system using equation (8). Although there are more elaborate models on the kinetic process of electrochemical systems, using the above model to correct the amplitude is already sufficient and further improvements should focus on experimental parameters. We also performed PSD analysis to obtain the kinetic parameter. As seen in Fig. 5(d), the amplitude of the demodulated spectrum varies in the form of a cos function, which fits equation (5). The amplitude takes its maximum value at = 16.0°, which is the value of the phase lag. The corresponding time constant τ = 18.2 s is also obtained via equation (13). Since the fit to the relaxation curve strongly depends on the values of the first few points, the PSD results should be more reliable and used for further correction. Then, we calculated the amplitude attenuation via equation (13), which gave a result of 0.961, thus a 3.9% correction is needed. Figs. 5(e) and 5(f) show the corrected and noncorrected spectra compared with the difference spectrum obtained from the direct difference of the reconstructed original spectra. As a result, the difference between the corrected PSD demodulated spectrum and the difference spectrum is less than 2% in Espace and 1% in Rspace. Considering the error in the measurement of the difference spectrum, the difference is acceptable, thus we can consider the corrected demodulated spectrum as the difference spectrum. In the following discussion, the amplitudecorrected PSD demodulated spectra are used for further analysis and we use the term `demodulated spectrum' to refer to it.
during the electrochemical CA test which periodically changes the potential. Thus, we will obtain a full matrix of absorption coefficients4.3. Quantitative analysis of demodulated spectra
The demodulated spectrum of IrO_{x} at two different potentials, 0.4 V and 1.4 V, and the corresponding reconstructed original spectra are obtained using the aforementioned approach. As shown in Fig. 6(a), the two spectra at different potentials are quite similar, indicating that the main phase of IrO_{x} has remained. The original spectrum at 1.4 V has a higher and blueshifted whiteline peak compared with 0.4 V, which is the typical feature of a higher As shown in Figs. 6(a) and 6(b), the demodulated spectrum has a smooth feature in both Espace and kspace even in the highk range, implying a good S/N ratio. The most important characteristic of the demodulated spectrum is a ∼90° phase difference compared with the original spectrum. As simulated in former research (König et al., 2012), the differential spectrum has no phase difference when and disorder changes, while 90° phase difference is typically observed if the bond length changes (Chu et al., 2012). Thus, the change in bond length may be the most important factor.
Quantitative results are obtained via a combined fitting of the two original spectra and the demodulated spectrum. For the original spectra, one Ir–O path with four variables, N, E_{0}, ΔR and σ^{2}, were used. For fitting the demodulated spectrum, we used two Ir–O paths with the same variables as the corresponding original spectra, except one was set negative (Fig. S6 and Table S1 of the supporting information). Thus, the results equal the difference of the two spectra. A similar approach was used by König et al. (2012), who obtained the result of the static sample first and then use it to fit the difference. Considering the error of every single fitting, we choose to fit all of the spectrum in one fitting. As shown in Fig. 7(a), all the fitted curves have good consistency with the experimental data. The quantitative results are shown in Table 1. The difference in bond length is −0.047 Å, implying shrinking of the lattice at high potential. For a better comparison of the contribution of different parameters to the whole demodulated spectrum, we have simulated the differential spectrum where we let only one parameter change. As shown in Fig. 7(b), the most prominent factor is the bond length, while other fitting parameters exhibit a much smaller contribution, as in the aforementioned qualitative analysis.

Three different oxidation potentials, 0.4 V/1.0 V, 1.4 V/1.2 V and 0.4 V/1.4 V, have been applied to confirm the findings. The demodulated spectra obtained using the PSD method have been corrected and compared with the traditional difference spectrum as seen in Fig. S7 of the supporting information. The good agreement between them again proves the correctness of this correction method. The results are shown in Figs. 8(a) and 8(b). The spectra remain smooth although the amplitude of the demodulated spectrum became smaller for low oxidation potential. These spectra are similar in both Espace and kspace, meaning that similar structural changes occur in the system. The amplitude of the demodulated spectrum increases almost linearly with the potential. For contrast, we tested normal in situ spectra with static potential and made their differential spectra by direct subtraction. As shown in Fig. S8 of the supporting information, it is obvious that without modulation and filter the spectra have poor quality, especially in the highk range. Also, their change is not so regular compared with the spectra obtained from modulation. The above results demonstrate the advantages of the modulation approach. The main advantage is a better S/N ratio resulting from filtering. On the other hand, it is common that some irreversible change happens during the in situ test in OER (Cao, Shou et al., 2021), while surface adsorption is a reversible process. Therefore, the modulated spectra show better regularity to potential since the result only comes from the reversible change of the In this regard, the modulation approach is more convincing in studies of the electrochemical adsorption process.
Quantitative analysis is also performed for these spectra: the results are shown in Table 1 and the fitted curves are shown in Figs. S9–S11 of the supporting information. The difference in bond length improves with potential, while other parameters do not change significantly or within the error range. As shown in Fig. 9, a good proportional relationship is found between the charge amount and bond length. It is different from the potential induced which is a complete transformation only if the voltage exceeds the threshold. Considering the increase of we suppose that the shortening of the bond length at high potential is due to the detachment of protons (Kasian et al., 2018).
5. Summary
In this article, we discussed the quantitative relationship between the PSD demodulated spectrum and difference spectrum. The amplitude attenuation is related to the modulation period and system T/τ > 20 should be satisfied. Then, we chose IrO_{x} as a model catalysis system and studied its reversible surface redox reaction. As a result, a highquality demodulated spectrum has been obtained even in the highk region and thus the differential could be analyzed. We found that the change of bond length is almost proportional to the surface charge accumulation, which could offer a deeper understanding of the surface redox and adsorption–desorption process. Furthermore, modulating differential could be extended to wider applications in various electrochemical studies.
constant, which could be used to correct the amplitude. We propose a method for correcting the magnitude and give suggested experimental parameters. For good consistency, the condition6. Resources
Information about the code for PSD analysis used here can be found at https://staff.ustc.edu.cn/~song2012/mes/mescode.htm.
Supporting information
Table S1; Figures S1 to S11. DOI: https://doi.org/10.1107/S1600577522005616/ok5072sup1.pdf
Funding information
The following funding is acknowledged: National Key Research and Development Program of China (award No. 2020YFA0405800; award No. 2017YFA0403400); National Natural Science Foundation of China (award No. U1932201; award No. U2032113; award No. 22075264); CAS Collaborative Innovation Program of Hefei Science Center (award No. 2020HSCCIP002); USTC Research Funds of the Double First Class Initiative (award No. YD23100002004).
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