Pore Confined Liquid–Vacuum Interface for Charge Transfer Study in

Subscriber access provided by UNIV OF NEW ENGLAND ARMIDALE

Letter

Pore Confined Liquid-Vacuum Interface for Charge Transfer Study in Electrochemical Process Jun-Gang Wang, Xin Hua, Hai-Lun Xia, and Yi-Tao Long Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.8b05051 • Publication Date (Web): 17 Jan 2019 Downloaded from http://pubs.acs.org on January 17, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Analytical Chemistry

Pore Confined Liquid-Vacuum Interface for Charge Transfer Study in Electrochemical Process Jun-Gang Wang, Xin Hua*, Hai-Lun Xia and Yi-Tao Long* Key Laboratory for Advanced Materials & Department of Chemistry, East China University of Science and Technology, 130 Meilong Road, Shanghai, 200237, P. R. China

ABSTRACT: A pore confined liquid-vacuum interface was created in liquid secondary ion mass spectrometry analysis in order to study the charge transfer in electrochemical reactions. The interfacial processes such as the critical diameter, influence of aperture properties on the morphology of the liquid-vacuum interface, pressure field, concentration filed and electric field were revealed by finite element simulation. Correlation between numerical study of the chemical changes at the electrodeelectrolyte interface and experimental results during dynamic potential scan was built successfully. Better understanding of these interfacial processes could promote further applications of liquid secondary ion mass spectrometry in energy storage and electrochemical catalysis.

Understanding of electrochemical reactions, ion solvation as well as mass transfer at the electrode-electrolyte interface during electrochemical processes is crucial in energy storage and biological sensing.1-2 In order to identify the chemical compositions and monitor the reactions near the electrode surface, numerous in situ spectroelectrochemical techniques such as in situ-infrared spectroscopy (IR)3, in situ-surface-enhanced Raman scattering (SERS)4, in situ-X ray absorption spectroscopy (XAS)5, in situ-Xray diffraction (XRD)6 and in situ-nuclear magnetic resonance (NMR)7 have been presented and great progress has been made in providing structural details of molecules adsorbed on the electrode surface.8-9 Compared with these approaches, direct electrochemistry in an electrochemical cell combined with mass spectrometry (MS) can provide direct molecular information at the electrode-electrolyte interface, which could benefit in better understanding of electrochemical processes. For example, electron ionization (EI)10-11, electrospray ionization (ESI)12,13 and desorption electrospray ionization (DESI)14 have been widely used to couple with electrochemistry to monitor redox reaction and provide molecular information unavailable solely from traditional ex-situ electrochemical or spectroscopic approaches.15-18 Owing to the high surface sensitivity, high depth resolution and fast response, in situ liquid secondary ion mass spectrometry (SIMS) combined with electrochemistry has been developed to investigate complex chemistries occurring at the electrode-electrolyte interfaces.19-20 It has been successfully applied to identify transient intermediates in redox reactions and formation mechanism of the solid electrolyte interphase in lithium-ion batteries.21-22 Moreover, it has the potential to acquire information about small ions solvation and transportation at the electrode-electrolyte interface. However, owing to the complicated physical chemical processes during in situ liquid SIMS analysis and lacking of appropriate analytical techniques23, the detailed information such as the critical diameter of the aperture, the influence of the interfacial property (i.e., hydrophobicity and hydrophilicity of the aperture) on morphology of the liquid-vacuum interface, mass transport in the aperture et al., are not clear so far. The goal of this work is to answer these

Figure 1. (A) The schematic of the in situ liquid SIMS combined with electrochemistry. (B) ToF-SIMS depth profiles of representative positive ion species (Si2N+, Au+ and K+) in 2 mM KNO3 at open circle potential. The inset imaging shows the threedimension overlay of Si2N+ (royal), Au+ (orange) and K+ (pink). questions based on electrodynamics and physics via finite element simulation, which will give more insights into the understanding of the confined interfacial processes in liquid SIMS analysis. The fundamental process of in situ liquid SIMS combined with electrochemistry is shown in Figure 1. When the membrane was penetrated, significant increase of representative ion signal (K+) in the electrolyte was observed. Comparing the aperture diameter from both negative and positive total ions images with the theory value, excellent consistency was obtained indicating the well controllability for the penetration process (Figure S1). Owing to the small size of the aperture and hydrophobicity of SiNx membrane, the liquid can be confined in the aperture by surface tension without obvious deterioration of the vacuum system.24 When beyond the critical size of the aperture, the liquid-vacuum interface could not be withheld in the aperture due to the disturbance of the balance between the surface tension and the pressure difference.25 Although the increase of aperture size can improve the ion intensity and provide more spatial information in the aperture, the larger size of aperture will induce the overflow of the liquid and lead to the attenuation of the vacuum system. Considering the probability of the damage on the SIMS system induced by the leakage of liquid, the critical size of the aperture at which the abrupt change of liquidvacuum interface occurred was elucidated by finite element simulation. Given the circular hole structure of an aperture, a two-dimension axisymmetric geometry can be used to simplify its three-dimension geometry (Figure S2). The transport fluid through the aperture involves the two-phase flow dynamics which was governed by surface tension, wall adhesive forces and pressure difference.26 Detailed description of the equations for finite element calculation could be found in the Supporting Information. With enlarging of the aperture radius, an abrupt change of the interfacial height arises at 3305 nm which was considered as the critical size for the aperture (Figure 2A, Figure S3). When compared with the transient curve of interfacial height at 3304 nm, an obvious increase of the interface height was found at 3305 nm within 1.3 ms. Below the critical size,

ACS Paragon Plus Environment

Analytical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 2. (A) The height of liquid-vacuum interface as a function of the aperture radius. The inset shows the definition of the height of the liquid-vacuum interface which covers from the lower surface of the gold electrode to the highest point of the liquid-vacuum interface. (B) The comparison of interface height in the aperture with radius at 3304 and 3305 nm as a function of time. The inset shows the morphology of the liquid-vacuum interface at 6 ms in aperture with radius 3305 nm (left) and 3304 nm (right). (C) The pressure distribution on the liquid-vacuum interfaces in apertures with various radius. The distance covered from the liquid-vacuum interface to the center of the aperture. (D) The pressure at contact point between the liquid-vacuum interface and the aperture wall as a function of aperture radius. the interfacial height remains stable without obvious fluctuation (Figure 2B). Moreover, the obvious difference in the concentration field at the critical size and 3304 nm further proves that the critical size located at 3305 during in situ liquid SIMS analysis (Figure S4). After validating the critical size, a further investigation of the distribution of pressure on the liquid-vacuum interface below the critical size was performed (Figure 2C, D). The pressure between the liquid-vacuum interface and the rim of aperture reaches a maximum value at the aperture with 2 μm diameter, indicating a strengthened suction effect at the rim was achieved.27 Hence, in order to avoid the leakage of liquid, the aperture size at 2 μm was chosen in practical analysis and further finite element models (FEM) simulation. Appropriate design of the microfluidic device with desired interfacial properties will improve the confinement of the liquidvacuum interface in the aperture during in situ liquid SIMS analysis. Considering the significant influence of hydrophobic and hydrophilic properties of the aperture on the morphology of liquidvacuum interface, the FEM was further conducted under various interfacial conditions (Figure 3A). Here, the initial contact angles of hydrophilic and hydrophobic portion were fixed at 67 and 130°, respectively.28-29 Obviously, with the increase of the hydrophilic region, the liquid-vacuum interface height increases as well in various apertures with diameter between 1-3 μm (Figure 3B). In whole hydrophobic aperture, a concave meniscus can be seen, which was induced by the hydrophobic interaction between the inner wall and the liquid. On the other hand, the whole hydrophilic aperture causes the noticeable leakage of the liquid out of the aperture, further confirming the influence of the interfacial properties on the morphology of liquid-vacuum interface. For the aperture constituted by the hydrophilic SiNx (upper region) and hydrophilic Au (lower region), the liquid-vacuum interface was well confined in the aperture and the interface height reached 106

Figure 3. (A) The schematic of the hydrophilic and hydrophobic regions of the apertures (a-e). (B) The evolution of the liquidvacuum interface height with changing interfacial properties of the apertures with diameter 1-3 μm. Vacuum region, SiNx/Au film and liquid region are indicated by orange, blue and green color, respectively. (C) The corresponding of the morphology of the liquid-vacuum interface in an aperture with diameter 2 μm with different interfacial properties (a-e). (D) The relative pressure on the liquid-vacuum interface in an aperture with diameter 2 μm with different interfacial properties (a-e). The distance covered from the liquid-vacuum interface to the center of the aperture. (E) The liquid-vacuum interface morphology in a 2 μm aperture corresponding to interfacial property (c). The concentration field is shown in inset. nm at steady state, which is lower than the depth of the aperture (170 nm) (Figure 3C). At this case (c), the pressure on the liquidvacuum interface becomes greater than other cases (a, b d and e) and is responsible for the enhanced confining effect (Figure 3D). Meanwhile, the rim of the liquid-vacuum interface contacted with the Au rather than the SiNx at 2 μm radius (Figure 3E), indicating that the liquid-vacuum interface has a good contact with the working electrode. Based on above modeling results, surface modifications to make the inner wall more hydrophilic and upper rim more hydrophobic will be favorable to confine the aqueous liquid in the aperture. Meanwhile, for non-aqueous systems, it is advisable to change the material of the aperture to make the lower part of the aperture hydrophobic and upper part hydrophilic. The above design will help to confine the liquid-vacuum interface of non-aqueous system in the aperture. These modifications will be helpful to the successful design of the vacuum compatible microfluidic electrochemical device. Under dynamic electric field, the ion mass transfer and charge transfer at the electrode-electrolyte interface is simulated by the Nernst-Planck-Poisson (NPP) equations.30 The potassium ions were attracted or repelled under cathodic or anodic polarized potential, respectively, which was in good accordance with electric double layer theory (Figure S5). To correlate the in situ liquid SIMS signal with the chemical information from the electrode-electrolyte interface, finite element models were built and compared with the experimental observation. In the first case, the liquid layers with various thickness (1~40 nm) from the liquid-vacuum interface were considered (Figure 4A). Figure 4C shows

ACS Paragon Plus Environment

Page 2 of 5

Page 3 of 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Analytical Chemistry

Figure 4. The schematic of the locations adopted to calculated the concentration of K+ during dynamic potential scan. (A) The volumes with different thickness of liquid layer; (B) The interface region includes liquid-vacuum interface (LVI) and different length of electrodeelectrolyte interface (EEI). FEM simulated distributions of K+ concentration in (C) various volumes with different thickness of liquid layer (a-g: 1, 3, 6, 12, 18, 24 and 30 nm; h: the whole liquid volume in the aperture) and (D) interfacial regions (a: electrode interface; b: liquidvacuum interface; c-j: liquid-vacuum interface and various length of electrode (1, 3, 6, 12, 18, 24, 30 nm and the whole electrode) during dynamic potential scan from - 0.20 to + 0.18 V at a scan rate of 10 mV s-1. (E) The schematic of K+ accumulation at the electrode-electrolyte interface under cathodic polarization is shown in the inset I. Comparison between the differential curves of the experimental K+ mass intensity (dash line) and simulated K+ concentration trends (solid line) at various interfacial regions (a-j, a is shown in the inset II) as a function of polarized potential. that the potassium concentration decreased under anodic polarization and increased under cathodic polarization. With the increase of the thickness of liquid layer, the concentration of potassium is closer to the bulk value (2 mM), indicating that the applied dynamic potential scan cannot induce the drastic fluctuation of potassium concentration in the aperture. In the second case (Figure 4B), owing to the important role of electrodeelectrolyte interface in electric double layer theory, where the accumulation and repulsion of potassium ion mainly occurred, the potassium concentration at the liquid-vacuum interface and the electrode surface with different length (1~40 nm) was calculated. Figure 4D shows that the concentration of potassium change with the dynamic potential scan and a U-shape can be found. The more electrode-electrolyte interface was included, the fluctuation of the concentration of potassium was more noticeable, confirming that the accumulation of potassium ion mainly occurred at the electrode-electrolyte interface. Comparing these modelling results with experimental observations, the trends of potassium concentration change during dynamic potential scan at the electrode-electrolyte interface agreed well with the in situ liquid SIMS results, which further validated the correlation between the in situ liquid SIMS signal and the chemical information from the electrode-electrolyte interface (Figure 4E and S6). In conclusion, the critical size of the apertures during in situ liquid SIMS analysis is achieved according to the simulation results. Based on the influence of surface properties of aperture on the morphology of liquid-vacuum interface, it is advised to make the lower part of the aperture hydrophilic and upper part hydrophobic for aqueous system. Moreover, the correlation between MS signal and the chemical information from the electrode-electrolyte interface was built successfully. This work represents an improvement in understanding of the liquid interface processes where the depletion layer is constrained and the mass transport is

confined in the aperture. It will provide more insights into the design of the vacuum compatible electrochemical micro-device and understanding of the physical and chemical processes at the electrode-electrolyte interface.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: Detailed information about SEM images of punched apertures, numerical simulation and in situ liquid SIMS experiment.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. *E-mail: [email protected].

Notes The authors declare no competing financial interests.

ACKNOWLEDGMENT This research was supported by National Natural Science Foundation of China (21705046, 21421004), Innovation Program of Shanghai Municipal Education Commission (2017-01-07-0002-E00023), the Fundamental Research Funds for the Central University (222201718001, 222201717003), Shanghai Sailing Program (17YF1403000) and Shanghai Natural Science Foundation (17ZR1407700).

ACS Paragon Plus Environment

Analytical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

REFERENCES (1) Gauthier, M.; Carney, T. J.; Grimaud, A.; Giordano, L.; Pour, N.; Chang, H.-H.; Fenning, D. P.; Lux, S. F.; Paschos, O.; Bauer, C.; Maglia, F.; Lupart, S.; Lamp, P.; Shao-Horn, Y., Electrode-Electrolyte Interface in Li-Ion Batteries: Current Understanding and New Insights. J. Phys. Chem. Lett. 2015, 6, 4653-4672. (2) Kimmel, D. W.; LeBlanc, G.; Meschievitz, M. E.; Cliffel, D. E., Electrochemical Sensors and Biosensors. Anal. Chem. 2011, 84, 685-707. (3) Li, J.-T.; Zhou, Z.-Y.; Broadwell, I.; Sun, S.-G., In-situ Infrared Spectroscopic Studies of Electrochemical Energy Conversion and Storage. Acc. Chem. Res. 2012, 45, 485-494. (4) Wang, Y.-H.; Liang, M.-M.; Zhang, Y.-J.; Chen, S.; Radjenovic, P.; Zhang, H.; Yang, Z.-L.; Zhou, X.-S.; Tian, Z.-Q.; Li, J.-F., Probing Interfacial Electronic and Catalytic Properties on Well-Defined Surfaces by Using In Situ Raman Spectroscopy. Angew. Chem. Int. Ed. 2018, 57, 11257 -11261. (5) Gorlin, Y.; Lassalle-Kaiser, B.; Benck, J. D.; Gul, S.; Webb, S. M.; Yachandra, V. K.; Yano, J.; Jaramillo, T. F., In Situ X-ray Absorption Spectroscopy Investigation of a Bifunctional Manganese Oxide Catalyst with High Activity for Electrochemical Water Oxidation and Oxygen Reduction. J. Am. Chem. Soc. 2013, 135, 8525-8534. (6) Favaro, M.; Jeong, B.; Ross, P. N.; Yano, J.; Hussain, Z.; Liu, Z.; Crumlin, E. J., Unravelling the Electrochemical Double Layer by Direct Probing of the Solid/Liquid Interface. Nat. Commun. 2016, 7, 12695. (7) Cao, S.-H.; Ni, Z.-R.; Huang, L.; Sun, H.-J.; Tang, B.; Lin, L.-J.; Huang, Y.-Q.; Zhou, Z.-Y.; Sun, S.-G.; Chen, Z., In Situ Monitoring PotentialDependent Electrochemical Process by Liquid NMR Spectroelectrochemical Determination: A Proof-of-Concept Study. Anal. Chem. 2017, 89, 3810-3813. (8) Tripathi, A. M.; Su, W.-N.; Hwang, B. J., In Situ Analytical Techniques for Battery Interface Analysis. Chem. Soc. Rev. 2018, 47, 736-851. (9) León, L.; Mozo, J. D., Designing Spectroelectrochemical Cells: A Review. TrAC, Trends Anal. Chem. 2018, 102, 147-169. (10) Bruckenstein, S.; Gadde, R. R., Use of a Porous Electrode for in Situ Mass Spectrometric Determination of Volatile Electrode Reaction Products. J. Am. Chem. Soc. 1971, 93, 793-794. (11) Peng, Z.; Freunberger, S. A.; Chen, Y.; Bruce, P. G., A Reversible and Higher-Rate Li-O2 Battery. Science 2012, 337, 563. (12) Odijk, M.; Olthuis, W.; van den Berg, A.; Qiao, L.; Girault, H., Improved Conversion Rates in Drug Screening Applications Using Miniaturized Electrochemical Cells with Frit Channels. Anal. Chem. 2012, 84, 9176-9183. (13) Abd-El-Latif, A.; Bondue, C.; Ernst, S.; Hegemann, M.; Kaul, J.; Khodayari, M.; Mostafa, E.; Stefanova, A.; Baltruschat, H., Insights into Electrochemical Reactions by Differential Electrochemical Mass Spectrometry. TrAC, Trends Anal. Chem. 2015, 70, 4-13. (14) Brown, T. A.; Chen, H.; Zare, R. N., Identification of Fleeting Electrochemical Reaction Intermediates Using Desorption Electrospray Ionization Mass Spectrometry. J. Am. Chem. Soc. 2015, 137, 7274-7277. (15) Wang, J.-G.; Fossey, J. S.; Li, M.; Li, D.-W.; Ma, W.; Ying, Y.-L.; Qian, R.-C.; Cao, C.; Long, Y.-T., Real-time Plasmonic Monitoring of Electrocatalysis on Single Nanorods. J. Electroanal. Chem. 2016, 781, 257264.

(16) Wang, J.-G.; Fossey, J. S.; Li, M.; Xie, T.; Long, Y.-T., Real-Time Plasmonic Monitoring of Single Gold Amalgam Nanoalloy Electrochemical Formation and Stripping. ACS Appl. Mater. Interfaces 2016, 8, 8305-8314. (17) Wang, J.-G.; Jing, C.; Long, Y.-T., Single-Nanoparticle Plasmonic Spectroelectrochemistry. In Frontiers of Plasmon Enhanced Spectroscopy Volume 2, American Chemical Society: 2016; Vol. 1246, pp 57-96. (18) Wang, J.; Cao, X.; Wang, X.; Yang, S.; Wang, R., Electrochemical Oxidation and Determination of Glucose in Alkaline Media Based on Au (111)-Like Nanoparticle Array on Indium Tin Oxide Electrode. Electrochim. Acta 2014, 138, 174-186. (19) Lu, J.; Hua, X.; Long, Y.-T., Recent Advances in Real-Time and in situ Analysis of an Electrode-Electrolyte Interface by Mass Spectrometry. Analyst 2017, 142, 691-699. (20) Liu, B.; Yu X.-Y.; Zhu Z.; Hua X.; Yang L.; and Wang Z. In Situ Chemical Probing of the Electrode-Electrolyte Interface by ToF-SIMS. Lab Chip, 2014, 14, 855-859. (21) Zhu, Z.; Zhou, Y.; Yan, P.; Vemuri, R. S.; Xu, W.; Zhao, R.; Wang, X.; Thevuthasan, S.; Baer, D. R.; Wang, C.-M., In Situ Mass Spectrometric Determination of Molecular Structural Evolution at the Solid Electrolyte Interphase in Lithium-Ion Batteries. Nano Lett. 2015, 15, 6170-6176. (22) Wang, Z.; Zhang, Y.; Liu, B.; Wu, K.; Thevuthasan, S.; Baer, D. R.; Zhu, Z.; Yu, X.-Y.; Wang, F., In situ Mass Spectrometric Monitoring of the Dynamic Electrochemical Process at the Electrode-Electrolyte Interface: a SIMS Approach. Anal. Chem. 2017, 89, 960-965. (23) Dwyer, J. R.; Harb, M., Through a Window, Brightly: A Review of Selected Nanofabricated Thin-Film Platforms for Spectroscopy, Imaging, and Detection. Appl. Spectrosc. 2017, 71, 2051-2075. (24) Yang, L.; Yu, X.-Y.; Zhu, Z.; Thevuthasan, T.; Cowin, J. P., Making a Hybrid Microfluidic Platform Compatible for in situ Imaging by Vacuumbased Techniques. J. Vac. Sci. Technol. A 2011, 29, 061101. (25) Zhou, Y.; Yao, J.; Ding, Y.; Yu, J.; Hua, X.; Evans, J. E.; Yu, X.; Lao, D. B.; Heldebrant, D. J.; Nune, S. K.; Cao, B.; Bowden, M. E.; Yu, X.-Y.; Wang, X.-L.; Zhu, Z., Improving the Molecular Ion Signal Intensity for In Situ Liquid SIMS Analysis. J. Am. Soc. Mass Spectrom. 2016, 27, 20062013. (26) Tian, H.; Shao, J.; Ding, Y.; Li, X.; Liu, H., Numerical Characterization of Electrohydrodynamic Micro- or Nanopatterning Processes Based on a Phase-Field Formulation of Liquid Dielectrophoresis. Langmuir 2013, 29, 4703-4714. (27) Zang, D.; Li, L.; Di, W.; Zhang, Z.; Ding, C.; Chen, Z.; Shen, W.; Binks, B. P.; Geng, X., Inducing Drop to Bubble Transformation via Resonance in Ultrasound. Nat. Commun. 2018, 9, 3546. (28) Smith, T., The Hydrophilic Nature of a Clean Gold Surface. J. Colloid Interface Sci. 1980, 75, 51-55. (29) Desai, S.; Kaware, R. D., Molecular Dynamics Modelling of Water Nanodroplet Impingement on Silicon Dioxide and Silicon Nitride Substrates. Int. J. Nanomanuf. 2014, 10, 432-452. (30) Wang, H.; Thiele, A.; Pilon, L., Simulations of Cyclic Voltammetry for Electric Double Layers in Asymmetric Electrolytes: A Generalized Modified Poisson–Nernst–Planck Model. J. Phys. Chem. C 2013, 117, 18286-18297.

ACS Paragon Plus Environment

Page 4 of 5

Page 5 of 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Analytical Chemistry TOC

ACS Paragon Plus Environment