Disorder in Aqueous Solutions and Peak Broadening in X-Ray

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Disorder in Aqueous Solutions and Peak Broadening in X-Ray Photoelectron Spectroscopy Jian Liu, Hui Zhang, Yimin Li, and Zhi Liu J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b10325 • Publication Date (Web): 25 Oct 2018 Downloaded from http://pubs.acs.org on October 31, 2018

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The Journal of Physical Chemistry

Disorder in Aqueous Solutions and Peak Broadening in X-Ray Photoelectron Spectroscopy Jian Liu,

†,‡

‡

Hui Zhang, Yimin Li,

∗,†,‡

and Zhi Liu

∗,†,‡

†School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China  ‡State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China E-mail: [email protected]; [email protected]

Abstract The microscopic structure and photoelectron spectra of an aqueous solution are investigated with ab initio molecular dynamics simulations and ambient pressure X-ray photoelectron spectroscopy (AP-XPS). The simulation results show that the structural fluctuations in an aqueous solution can lead to a remarkable peak broadening ( ∼ 1 eV) of ionic species, which is in good agreement with the results from AP-XPS experiments. We find this broadening of the XPS peaks can be directly correlated with the local structural fluctuations in the aqueous solution, such as the evolution of solvation shell. This work demonstrates that the rich dynamics of solvation shells in aqueous solutions can be revealed by combining advanced simulations with in situ AP-XPS, and may stimulate new developments in in situ XPS characterization of complex electrochemical reactions.

Introduction The X-ray photoelectron spectroscopy (XPS) can provide physical and chemical information of a matter at the atomic and molecular level. To apply XPS to the liquid and gas phases, AP-XPS systems have been realized and used at various near ambient pressure conditions, particularly in the presence of water and water vapor. [1–3] Recently, we have developed a “dip & pull” method that can prepare a thin water film on a metal surface with a thickness of 10–30 nm. This is a new approach to probe the solid/liquid interface. [4–6] These methods enable surface sensitive techniques such as AP-XPS to monitor the real processes taking place at the liquidsolid interface under real conditions. The binding energy and intensity of an XPS peak are the two most used parameters of XPS analysis. The deconvolution of XPS peaks allows us to determine the chemical state and elemental identifications. The quantitative composition can then be determined from the intensity of the XPS peaks. In addition, XPS Spectrum are typically presented as a set of peaks with finite peak widths, which are due to the limited core hole lifetimes and disordering effects in a matter. For example, large broadenings of the XPS peaks for species in a liquid were observed from several experiments [1,2,4–18]. In 1986, H. Siegbahn et al. [7] pioneered the experiments of APXPS for a water solution and observed a large linewidth of the O 1𝑠 peak in a LiCl solution of

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1.8 eV compared with the gas phase value of 0.9 eV. He speculated that a reason for the broadening was the disordered structure of liquids, and proposed further study with both experiment and simulation techniques. In aqueous solutions, thermal fluctuations are ubiquitous and fundamentally important in almost all physical/chemical/biological processes, such as molecular diffusion [19,20], chemical reaction [21], ice formation [22,23], water evaporation [24], aggregation of solute molecules [25], motion of molecular machines [26] and transportation through nanochannels [27–31]. The key to the fluctuations in liquids is the motions and collisions at the molecular level, such as broking/forming of hydrogen bonds and the structural changing of the ions’ solvation shells [32,33]. Thermal fluctuations must provide an additional contribution to the broadening of the XPS peaks, however, there are few detailed studies in the response of photoelectron spectroscopy to thermal fluctuations have been carried out. Herein, we used density functional theory (DFT)-based ab initio molecular dynamics (AIMD) simulations associated with XPS calculations to estimate the magnitude of disorder broadening in the core level of liquids and compared these results with our AP-XPS measurements. Our simulation results show that there is indeed an additional broadening of the XPS peaks, ∼ 1 eV, for ions and water in solution, owing to structural disordering, in good agreement with experimental values. Our results show that fluctuation of the solvation shell plays a key role in XPS broadening by both the hydration number of ions and the distance of water molecules from the ions to be ionized, in agreement with the mechanism proposed by H. Siegbahn et al. [7]. This also indicates that the XPS peak broadening is sensitive to and can be used as a qualitative tool for the study of the local structure in the liquid phase. Thus, our findings are expected to provide a new insight of the ion local structure inside an aqueous solution.

Computational Methods Modeling System and Molecular Dynamics To simulate the KF solution measured in the AP-XPS experiments, a modeled solution system was constructed using 50 water molecules and 5 KF pairs in a cubic unit cell (Fig. 1). Periodic boundary conditions were applied in all directions of space to mimic an infinite bulk system. The cell dimension was 12.0 Å, estimated from a constant pressure simulation at 400 K/1 bar, which gave a concentration of 5 M that was close to our experimental settings of 6 M [4]. We also simulated a pure water system consisting of 50 water molecules with a cell dimension of 11.5 Å. The convergence against the unit cell sizes was tested (Fig. S4). The 400 K in our DFT simulations is responding to room temperature in experiment. [34,35] Additionally, the systems were also simulated at 300 K to investigate the effects on broadening by temperature.


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Figure 1. Snapshot of the 𝐾𝐹 solution. Ions are shown as spheres with 𝐹 ― in green and 𝐾 + in blue; Water molecules are shown as spheres with oxygen in red and hydrogen in white. The cubic box represents the periodic unit cell of the infinite bulk system. DFT-based ab initio Born-Oppenheimer molecular dynamics simulations have been performed with the CP2K/QUICKSTEP package [36,37]. The MD trajectory was conducted in a constant volume and constant temperature (NVT) ensemble for the structural and XPS analyses presented in this work, after constant pressure equilibration was achieved. The total time of each NVT simulation was 55 ps with an MD time-step of 1 fs. The initial 5 ps was used to ensure the thermal equilibrium of the system. Statistics were collected from the last 50-ps simulations with the initial 5 ps omitted since the water and ion needed time to reach their preferred positions. It was shown that the velocity autocorrelation function of water almost reached to 0 at 500 fs [38], which suggested a 500-fs-sampling could provide independent snapshots for the structure of water and ions. The lifetime of hydrogen bonds and solvation shells were 3 and ∼ 10 ps (see Supporting Information S2), which were much smaller than the total simulation time, and indicated that the 55-ps simulations were statistically accurate.

XPS Calculations and Deconvolution The final state (FS) approximation was used to determine the core-level BE changes by individually examining the statistical snapshots. In the FS approximation, the core-level BEs were calculated following the procedure of Eq. 1 described in Refs. 39–42: these were calculated by the difference of total energies between the ground state and excited state BE = 𝐸(𝑛𝑐 ―1) ― 𝐸(𝑛𝑐)

(1)

where 𝐸(𝑛𝑐) is the ground state total energy, and 𝐸(𝑛𝑐 ―1) is the total energy of the excited system with one electron removed from the specific core orbital to the vacuum (see the benchmark test in Supporting Information S3) using a constrained ground state calculation with an electron core hole, which were calculated separately. In the FS approximation, the electrons were allowed to relax after the core electron had been removed, so that the final state effects on



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the relaxation/screening were considered. The precision of the FS approach has been estimated to be 0.02–0.05 eV in test calculations. [39] BEs were calculated by individually exciting each atom of interest in each snapshot. Photoelectron excitation is essentially instantaneous compared with the time scale of nuclear motions. We can thereby assume the structure of the system was frozen during the fast electronic excitation process (Franck-Condon principle), thus the configurations for XPS calculation were taken from the AIMD trajectories without further optimization. For the XPS calculations, the extracted snapshots for F and K calculations were collected every 0.5 ps (100 snapshots in total), and for water, O in both solution and pure water were collected every 5 ps (10 snapshots in total). Since the system contained 5 KF pairs and 50 water molecules, ensembles of 500 samples of each species were generated for XPS calculations. A BE change here was the difference in values of one atom at each extracted snapshot versus the sample- and time-average of the examined species. Consequently, the calculated BE changes were aligned to an average of 0 eV. The AP-XPS experimental settings and results for KF solutions on Pt surfaces have been reported in Ref. 4. To simulate the experimental XPS spectra, we should account for the experimental instrument broadening 𝐼inst due to the resolution of X-ray source and analyzer, and lifetime broadening 𝐼life. In solution systems, additional Gaussian contributions may also be related to structural disorder owing to thermal movements, denoted as disorder broadening 𝐼dis. The profile of the total broadening obtained from the analyzer 𝐼total is 𝐼total = 𝐼inst ⊗ 𝐼life ⊗ 𝐼dis

(2)

where ⊗ denotes convolution, and 𝐼inst, 𝐼life and 𝐼dis are the profile of instrument broadening, lifetime broadening and disorder broadening, respectively. The instrument broadening is Gaussian with the FWHM of ∼ 1 eV in the experiment conditions using an excitation energy of 4 keV [4,5]. Lifetime broadenings are Lorentzian, and the FWHM for O 1𝑠, F 1𝑠, K 2𝑝, Pt 4𝑓 are 0.12, 0.18, 0.156 and 0.19 eV, respectively. [43,44]. The disorder for Pt 4𝑓 is as only 0.07 eV (see Supporting Information S5) because of the homogeneity of chemical structures for pure bulk metal, and thus can be neglected. Therefore, the profile of Pt 4𝑓 is a Voigt profile convoluted from the Gaussian instrumental broadening and Lorentzian lifetime broadening. It is reasonable to assume the FWHM of Pt 4𝑓 with the lifetime broadening deducted to be the experimental instrumental broadening, which is equal for all the species in the same experimental conditions: 𝛤inst = 𝛤2total(Pt) ― 𝛤total(Pt)𝛤life(Pt)

(3)

where 𝛤inst is the FWHM of instrument broadening, 𝛤total(Pt) and 𝛤life(Pt) is the FWHM of Pt 7

4𝑓2 peak obtained from analyzer and lifetime broadening of Pt. The spectra profile of Pt 4𝑓 was strongly asymmetric, because in metallic systems, the ejected photoelectrons can interact with the conduction electrons and lose energy, which is described by the Doniach-Šunjić 7 function [45]. Thus, the FWHM of Pt 4𝑓2 peak were deterimented by fitting with Hybrid Doniach-Šunjić/Gaussian-Lorentzian line-shape in CasaXPS [46].


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The disorder broadening is also Gaussian for the liquid systems, as shown in Fig. 2. The experimental disorder broadening FWHM 𝛤dis were calculated from the following equation: 𝛤dis = 𝛤2total ― 𝛤total𝛤life ― 𝛤2inst

(4)

which can be used to compare with the calculated disorder broadening FWHM.

Results Broadening of XPS Peak The microscopic structure (Fig. 1) and core-level BEs (Fig. 2) of the KF solution and pure water were analyzed in the 55-ps AIMD trajectories. Considering 400 K is the ambient temperature of the PBE-D water models (see Supporting Information S1), the calculated data at 400 K were mainly discussed in this work. Fig. 2 shows the contribution of disorder broadening 𝛤dis by thermal fluctuation in a liquid. In the figure we can see the distributions of BE changes for species in liquid are Gaussian, suggesting the structural disorder leads to an extra Gaussian broadening of XPS peaks. A Gaussian distribution of BE is results from the validity of the thermal fluctuations due to the central limit theorem. FWHMs of 𝛤dis, summarized in Fig. 3, ― + were estimated to be 0.95, 1.01 and 1.13 eV for Faq 1𝑠, Kaq 2𝑝 and Osol 1𝑠 in KF solution, respectively, by fitting the histograms with Gaussian profiles.

― + Figure 2. Histograms of aligned binding energies for (a) 𝐹𝑎𝑞 1𝑠, (b) 𝐾𝑎𝑞 2𝑝, (c) 𝑂𝑠𝑜𝑙 1𝑠 in 𝐾𝐹 solution and (d) 𝑂𝑙𝑖𝑞 1𝑠 in pure water during the 50-ps AIMD simulation at 400 K.



In our recent experiments [4] performed using a synchrotron radiation based X-ray source with photon energy of 4 keV to the KF solution nanofilm formed on the Pt electrodes, we measured 7 the FWHM of the Pt 4𝑓2 to be 1.16 eV. The instrument broadening was determined to be 1.06 eV according to Eq. 3. The FWHM of the K 2𝑝, F 1𝑠 and O 1𝑠 in solution was measured to be 1.52, 1.63 and 2.06 eV, respectively. By assuming the instrument broadening of Pt was assumed to be the energy limit resolution for that the experimental system setting, then we can obtain the disorder broadening of K 2𝑝, F 1𝑠 and O 1𝑠 in solution as 0.97, 1.11 and 1.69 eV using Eq. 4 (see Computational Methods). The calculated disorder broadening was in good agreement with experimental values.

― + Figure 3. Calculated and experimentally observed disorder broadening 𝛤𝑑𝑖𝑠 of 𝐹𝑎𝑞 1𝑠, 𝐾𝑎𝑞 2𝑝, ― + + 𝑂𝑠𝑜𝑙 1𝑠 in 𝐾𝐹 solution, 𝑂𝑙𝑖𝑞 1𝑠 in pure water, and 𝐹𝐾𝐹 1𝑠, 𝐾𝐾𝐹 2𝑝 and 𝐾𝐾𝐼 2𝑝 in ionic crystals 𝐾𝐹 and 𝐾𝐼. Experiment data in solution are extracted from Ref. 4, in ionic crystals from Ref. 47 and in pure water from Ref. 11. Calculated data in ionic crystals can be found in Supporting Information S6. 𝛤𝑑𝑖𝑠 is the additional contribution to the XPS width arising from structure disorder according to Eq. 4.

We further investigated the correlation between disorder broadening and temperature to show that the FWHM of the XPS peaks could respond to external conditions. A comparison of disorder broadening between 300 and 400 K shows that the FWHM of all of the species at 400 K were generally ∼ 20% larger than at 300 K. Additional simulations on ionic crystals show that the FWHMs were proportional to the square root of the temperature (Fig. S13). This suggested that the FWHM of XPS peaks can also contain structural information and can also be used for the characterization of a liquid.


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Structure of Solvation Shell The BE of a photoelectron of a given atom is affected by its local bonding environment from its nearest-neighbor atoms. When the ions are dissolved in a water solution, water molecules will be around ions and come into being hydration structures, as shown in Fig. 1, evaluated from the AIMD simulations. In aqueous solutions, the major contribution of the BE changes was the local electrostatic potential energy (see the results in Supporting Information S4). By analyzing the solvation shell structures of ions, we can show that the fluctuation of the solvation shell plays a key role in XPS broadening of for liquids. To investigate the atomic structure, the X–O (X = F ― ,K + ,O) pair radial distribution functions (RDF) 𝑔 and the hydration number of ions in the KF solution were calculated and are shown in Fig. 4. It can be seen that the RDFs and hydration numbers show a noticeable distribution with X–O distances and hydration numbers, which indicated that the effects of thermal fluctuation on the disorder of the atomic structure would be significant. The shape of the first peak of the RDFs 𝑔 was analyzed and used as a measure for the structure disordering of the solution, which indicted the direct contact between ions and water molecules [Fig. 4(a)]. The positions of the first peak in the RDFs were at 2.7 and 2.8 Å for 𝑔FO and 𝑔KO. Especially, we noticed a wide dispersion of the first peak between 2.5 to 2.8 Å for 𝑔FO and 2.6 to 3.2 Å for 𝑔KO. The RDFs from simulations were in good agreement with the neutron diffraction data [48]. The wide dispersion of the first RDF peaks arose from the flexibility of the nonbonded interactions. The average hydration numbers of water molecules were calculated around the ions in a bulk water solution. The hydration numbers of ions were determined by the average number of water molecules within the distance of the first minimum in the RDF for the ion–O contact. In the KF solution, there was an average of 4.5 and 5.6 water molecules in the first solvation shell around the F ― and K + ions, respectively. There were three to six water molecules in the first solvation shell around the F ― ions, while there were three to eight water molecules in the first shell around the K + ions in bulk solution [Fig. 4(b)]. The obtained hydration numbers for K + and F ― ions in the bulk were in good agreement with the experimental data obtained from diffraction and EXAFS measurements. [49]



Figure 4. (a) 𝑋–𝑂 radial distribution function (RDF) of water-𝑂 atoms relative to the solvated 𝐹 ― /𝐾 + ions and other water-𝑂 atoms at 400 K. The position of the first minimum of RDF gives the region of the solvation shell, and the width of the first peak represents the thermal fluctuation. (b) Probability of the hydration number of 𝐹 ― and 𝐾 + ions. Two modeled ion–water clusters with one ion and a few water molecules (Fig. 5) show that the BEs of ions in solution are highly sensitive to the geometry and hydration number. BEs in the modeled clusters show that there were a wide-range ( ∼ 1 eV) of BEs for both F ― and K + with a change of ion-water distance or hydration number. These results suggested that the fluctuation of the solvation shell plays a key role in the XPS broadening by both the hydration number of ions and the distance of water molecules from the ions.


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Figure 5. BE changes of 𝐹 ― 1𝑠 and 𝐾 + 2𝑝 with (a) ion–water distance and (b) hydration number. Calculations were carried out in model systems with their optimized structures shown as inserts, 𝐹 ― and 𝐾 + are shown in green and blue, respectively, 𝑂 in red, and 𝐻 in white.

Discussion It is a powerful approach to combine the AIMD simulations and X-ray spectroscopic techniques to investigate the properties of liquid systems at the micro- and nano-levels, e.g., in the investigation of halides enhancement at the liquid/vapor interface [19,50]. AIMD simulations explicitly account for the detailed microscale picture of the dynamics and thermal fluctuation characteristics of a liquid by monitoring the evolutions of the structure. These methods have been widely accepted as a powerful and straight-forward tool for studying the structure, dynamics and spectroscopic properties of a system with high precisions, and have indeed been successfully used in the past decade to describe bulk water and solutions. [19,21,51,52] So that a direct comparison to experimental values of liquid dynamics can be made. Additional computational results on the binding energies of pure metal and ionic crystals (see the Supporting Information S5 and S6) were also consistent with the experimental results. A little extra broadening was observed in pure metal Pt 4𝑓. For ionic crystals, our simulations agreed with the trends observed in the experiments [47,53] and predicted by a phonon model [54], which included a the larger disorder broadening of K + 2𝑝 in KF than KI, the smaller disorder broadening of anions than cations in the same material, and the identical temperature dependence



as the broadening increased with the increase in temperature for both cations and anions. These consistencies demonstrate the robustness and reliability of the protocol of core level calculations associated within a unified AIMD simulation. The calculated disorder broadening for F ― 1𝑠 and O 1𝑠 were underestimated comparing to experimental values. Possible causes for these results may be the nuclear quantum effects (NQEs) arising from the light mass of H atoms. NQEs play important roles in the structure, dynamics, and macroscopic properties of water. [55–58] Fluctuations due to NQEs influence the short-range ordering of the hydrogen bond network, which broaden the spectra, e.g., the XAS preedge peak in water [59]. In aqueous solution, F ― contacts with the H atoms in its solvation shell, and its underestimate is possible results from the NQEs that fluctuates the distance of O–H ⋯F ― between F ― and its solvation shell, which will lead to an extra XPS broadening. The underestimate of water O is results from the distance fluctuations of intra-molecular O–H bonds and inter-molecular hydrogen bonds. K + does not contact with the H atoms in its solvation shell, and thus the calculated FWHM of K + consistents experiment well. The thickness of both soild-liquid and liquid-vapor interface is quite small (1 nm) compared to the thickness of film (10–30 nm) in our AP-XPS experiment. [4] The density of water on the surface exhibits a non-monotonic surface distribution for two layers and converges to the bulk density at 1 nm. The thickness of diffusion layer in the 6 M KF solution is only 1.2 Å, in the Gouy-Chapman electrical double layer model, [60] and the potential drop also exists in this region. Beyond the regions of non-monotonic water distribution and diffusion layer, the solvation shell structure and electrostatic potential would be same as in bulk. At the 4 keV phonon energy, the inelastic mean free path of phononelectrons would be about 10 nm, [61] suggesting the bulk solution contributes the majority of overall photoelectron signal. Therefore, the theoretical calculation with only the bulk solution is adequacy to compare with the APXPE experiment results. We should note that establishing an accurate and predictive simulation of liquids remains a great challenge. The simulations are sensitive to the description of the molecular interactions when employing different DFT functionals. In addition, the NQEs that are critical to account for the quantum nature of hydrogen atoms are usually neglected even in the AIMD framework. Furthermore, a 10–30 nm water film comprised of both liquid/solid and liquid/gas interfaces as well as electric double layers remains beyond the capacity of AIMD, hence the broadening arising from the liquid surface was not considered.

Conclusion In this paper, the microscopic structure and photoelectron spectra of an aqueous solution are investigated using AIMD simulations with core level binding energy calculations. Our simulation results indicate that the local structural fluctuations in an aqueous solution can lead to a remarkable broadening of XPS peaks of ionic species. At room temperature, a peak broadening can reach ∼ 1 eV, which is well resolvable by in situ AP-XPS experiments. We find that the broadening of the XPS peaks is correlated with the local structural fluctuations in the aqueous solution, such as the detailed structures of solvation shell. Our findings demonstrate that, by combining the advanced simulations with in situ AP-XPS, it is possible to capture the evolution of solvation shells in ionic solutions, a crucial elementary process in electrochemical reactions.


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Acknowledgement The authors thank Drs. Zhenhua Zeng, Baohua Mao, Yong Han, Zhaoru Sun, Rongzheng Wan, Guosheng Shi, and Zhi Zhu for their fruitful helps. This work was partially supported by the National Natural Science Foundation of China (11227902), Science and Technology Commission of Shanghai Municipality (STCSM) (14520722100), the China Postdoctoral Science Foundation (2016M600340), the Shanghai Yangfan Youth Talent Program from STCSM (17YF1428900) and the Shanghai Supercomputer Center of China. Y. M. L. would like to acknowledge the support from the “Hundred Talents Program” of the Chinese Academy of Science. The Advanced Light Source was supported by the Director, Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC0205CH11231.

Supporting Information Available The following files are available free of charge. •

Detailed simulation and calculation methodologies;

•

Reliability tests of the modeling system;

•

Benchmark tests of XPS calculations;

•

Core-level BE change in aqueous solution;

•

Computational details and results on the disorder broadening of XPS in metal Pt;

•

Computational details, results, discussion, and a simplified model on the disorder broadening of XPS in ionic crystals KF and KI.

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Graphical TOC Entry



407x412mm (72 x 72 DPI)


Page 18 of 22

Page 19 of 22

Counts

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Page 20 of 22

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Page 22 of 22

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