Spatially Resolved Probing of Electrochemical Reactions via Energy

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Spatially Resolved Probing of Electrochemical Reactions via Energy Discovery Platforms Jilai Ding,† Evgheni Strelcov,‡ Sergei V. Kalinin,‡ and Nazanin Bassiri-Gharb*,†,§ †

School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, United States Institute for Functional Imaging of Materials and Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States § G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, United States ‡

S Supporting Information *

ABSTRACT: The electrochemical reactivity of solid surfaces underpins functionality of a broad spectrum of materials and devices ranging from energy storage and conversion, to sensors and catalytic devices. The surface electrochemistry is, however, a complex process, controlled by the interplay of charge generation, field-controlled and diffusion-controlled transport. Here we explore the fundamental mechanisms of electrochemical reactivity on nanocrystalline ceria, using the synergy of nanofabricated devices and time-resolved Kelvin probe force microscopy (tr-KPFM), an approach we refer to as energy discovery platform. Through tr-KPFM, the surface potential mapping in both the space and time domains and current variation over time are obtained, enabling analysis of local ionic and electronic transport and their dynamic behavior on the 10 ms to 10 s scale. Based on their different responses in the time domain, conduction mechanisms can be separated and identified in a variety of environmental conditions, such as humidity and temperature. The theoretical modeling of ion transport through finite element method allows for creation of a minimal model consistent with observed phenomena, and establishing of the dynamic characteristics of the process, including mobility and diffusivity of charged species. The future potential of the energy discovery platforms is also discussed. KEYWORDS: tr-KPFM, nanostructured ceria, ionic dynamics, charge transport

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edge is inherently limited in that the obtained results are averaged over large volumes of material, and the observations cannot be directly correlated with the specific reaction sites. The second limitation of these approaches is related to the geometric scaling of system responses. The decrease of the lateral system size necessarily leads to the increase of corresponding resistances necessitating the high-impedance detection and decrease of associated capacitances. These considerations, in turn, limit the accessible frequency range and hence dynamic studies. Here, we introduce a universal approach for spatially resolved studies of kinetics and thermodynamics of coupled reactiontransport processes based on the synergy of lateral electrochemical device structures and noncontact scanning probe microscopy (SPM) measurements of time-dependent electrochemical potential distributions within the active device region. The device structures can be engineered by tuning materials’ composition and geometry to establish a broad variety of driving electrostatic fields. At the same time, surfaces and interfaces can be fabricated to introduce open or covered triplephase boundary regions or surface coatings, allowing for

onic transport underpins fundamental functionalities of many technological devices such as lithium ion batteries, fuel cells, and gas sensors.1−3 Electrochemical response in these systems often originates in multiple reactions and transport stages, involving generation of ionic species and charge injection on the surfaces, interfaces, and triple-phase boundaries, and surface and bulk transport of electrons and ionic species.4,5 To understand the fundamental mechanisms underpinning electrochemical functionality, it is vital to separate the spatial localization of reaction and transport processes. If achieved, this will allow exploring the role of temperature and partial pressure of volatile components, potentially recovering local kinetic laws and governing relations for elementary reaction stages. However, traditional electrochemical approaches have been limited to the averaged response of materials and device structures at much larger length scales. The currently available characterization techniques such as electrochemical impedance spectroscopy (EIS) and current voltammetry (I−V measurements) are mostly macroscopic in nature and extremely limited in resolving charge transport phenomena in the time domain, and dynamic modes (based on the length scales involved in the measurement). For example, while dielectric spectroscopic analysis of macro- and microscopic samples can result in identification of multiple conduction mechanisms, such knowl© XXXX American Chemical Society

Received: November 6, 2014

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Figure 1. Energy discovery platforms in their simplest form. Optical microscope (a) and scanning electron microscope (b) images of as prepared NC lateral device. (c) Schematics of the tr-KPFM technique.

Figure 2. Surface potential as a function of time and distance from electrodes. (a) Line-averaged surface potential evolution as a function of time along the NC stripe from 0 to 20 s. The relation between the measurement points and distance from the grounded and biased electrode is shown in the corresponding AFM topographic image of ceria stripe with a schematic of a 3×31 tr-KPFM probing grid; (b) line averaged surface potential vs time at distance (d) = 10, 20, and 40 μm.

devices.17−19 Most of these applications are based on the ionic and electronic transport and ceria’s redox properties.20−23 As a result, the ionic and electronic conductivity of ceria and doped ceria has been widely studied.24−31 However, there is still no consensus with respect to the principal mechanism governing MIEC conductivity in NC. Zhang et al.24 gave an amount of anisotropic oxygen conductivity behavior, in which the cubic (100) ceria facets result in high oxygen storage capability, whereas Molinari et al.25 and Maier et al.32 have reported a proton-based conduction on the surface or open porosity area facilitated by either water adsorption or surface defects as catalytic sites. The conductivity behavior of ceria underpins its applications and calls for further investigation. NC was deposited on quartz substrate by physical vapor deposition (PVD) and patterned as needed via photolithographic techniques. The crystalline structure of NC was characterized by X-ray diffraction (XRD) (see Supporting Information, Figure S2). Cr/Pt stripes, serving dual function of catalytic sites and current collectors were created on top of

chemical and physical control of reaction space. The dynamics of electrochemical potentials induced by a given sequence of external voltage pulses is accessed using time-resolved Kelvin probe force microscopy (tr-KPFM). 6 This noncontact, scanning probe microscopy technique enables detection of surface potential with submicron spatial resolution, on the tens of milliseconds to tens of seconds time scale. Surface ionic motion has been previously explored in the context of gas sensor applications via monitoring surface potential profiles, indicating that potential evolution can be used to study charge transport.7 Additionally, tr-KPFM has been previously successfully used on memristive and ferroelectric samples.8 Here, these energy discovery platformsmicro/nanofabricated structures probed via local microscopy technicsare demonstrated with the model case of surface-mediated electrochemical phenomena in nanocrystalline ceria. Basic Concepts. Nanostructured ceria (NC) is a mixed ionic-electronic conductor (MIEC) with applications in solid oxide fuel cells (SOFCs),9−14 gas sensors,15,16 and catalytic B

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Figure 3. Comparison of the experimental time-dependent surface potential and finite element modeled behavior. Line-averaged surface potentials as a function of time and position from experimental results (a−c) and from modeled results with best degree of similarity (d−f) in a variety of environmental conditions: (a, d) 0% RH and room temperature; (b, e) 90% RH and room temperature; (c, f) 0% RH and 100 °C.

electric field. During the bias-off stage (green to red curves), the surface potential slowly levels down and reduces in amplitude due to charge dissipation and screening. Stronger polarization and relaxation responses are observed in a limited spatial region, in close proximity of the biased electrode, which will be referred to as “active area” henceforth. Clearly, numerical modeling of the observed phenomena can allow establishing estimates of the corresponding physical parameters and rate constants, as will be demonstrated below. A closer look at the surface potential evolution as a function of time at different locations along the NC suggests the presence of a strong variability in potential relaxation (See Supporting Information, Figure S3). To illustrate this, potential curves at three different locations are chosen. As shown in Figure 2b, at distance d = 10 μm, the potential first quickly increases and then gradually decreases during polarization. During the relaxation step, the surface potential first slightly decreases and then slowly increases in the same location. The change of potential over the 10 s of the bias-on period is approximately 0.4 to 0.5 V, which indicates a rather weak electrochemical behavior near the grounded electrode region. In comparison, at d = 40 μm (within the active area), the potential significantly increases during polarization and decreases during relaxation and the potential change from the beginning to the end of each process is as much as 5 V. Note that this is a typical surface potential behavior in the active area, indicating a strong charge transport process. The opposite direction and different potential amplitude change in these two cases imply that at least two charge generation and/or transport mechanisms are underway, each dominating a specific location on the NC strip. In the active area, a charge injection process may take place: positive charges can generate and accumulate on the NC in proximity of the biased electrode, leading to an increase in potential during the polarization stage. On the other hand, in the region close to the grounded electrode, negative charges may accumulate, resulting in a decreasing potential. These two mechanisms compete at d = 20 μm, where the potential change over time shows an averaged behavior of the previous two. At distances father away from the based electrode, the diffusion of the activated species from the

ceria by lift-off and sputtering (See Supporting Information, Figure S1). Details of the processing steps are described in the Materials and Methods section. A typical resultant structure is shown in Figure 1a and b. To probe the electrochemical reactions within the structure, we utilized the tr-KPFM approach, as shown in Figure 1c. The temporal evolution of the surface potential was recorded at all locations across a grid of points on the surface of the sample. For each grid point, a 30 V DC bias was applied between the (lateral) Pt electrodes during the first 10 s (bias-on, or polarization stage). During the next 10 s both Pt electrodes were grounded to allow the material to relax (bias-off, or relaxation stage). The surface potential data were averaged for all of the grid points equidistant from each of the electrodes (at least three data points were averaged to make the results reliable). The line-averaged potential change over time was then plotted as a function of distance (Figure 2). We note that the resultant maps allow for straightforward interpretation on the qualitative level. To illustrate the basic concepts of this method in further detail, the tr-KFPM surface potential profile for NC at 50 °C and 0% relative humidity (RH) is shown in Figure 2a, together with the corresponding atomic force microscopy (AFM) topographic image of the ceria stripe and the grid of points on which the tr-KPFM results were measured. The time-dependent colored curves represent the evolution of surface potential during polarization (initial 10 s) and relaxation (subsequent 10 s). Point defects such as oxygen vacancies and excess electrons present in the NC can interact with ambient gas under applied bias, generating different charge carriers, such as protons, hydroxyl groups, and oxygen vacancies. At a strong enough electric field, these charge carriers will migrate along the surface and cause variations in the surface potential profile. In the initial moment (dark blue curve), the potential profile corresponds to initial electrostatic potential distribution for frozen electrochemical degrees of freedom. During the polarization stage (dark blue to light blue curves), the surface potential in the NC region closer to the biased electrode gradually increases due to the change in concentration of charge carriers caused by diffusion, electrical migration or electrochemical reactions, in response to the C

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the RC constant of the NC lateral device and circuitry. The resistivity was estimated from the interelectrode current data as a function of time (see Supporting Information, Figure S5) and the capacitance was measured by impedance spectroscopy (see Supporting Information). Thus, the RC constant of the NC lateral device is estimated to be on the order of 100 s (resistance is ∼1014 Ω, and capacitance is ∼10−12 F), indicating that electrons respond rather slowly to electrical field, so electronic transport was not observed in this experiment. In temperature range from room temperature to 100 °C, oxygen vacancy migration is not likely to be activated due to the high energy barrier for oxygen diffusion through lattice. In fact, oxygen ion conductivity is significant only at temperatures as high as 500 °C for doped ceria.39 At room temperature and ambient humidity, a water layer is adsorbed on the NC surface, while at 100 °C in dry atmosphere, the presence of such water layer is expected to be minimal. However, it has been previously shown that a significant amount of water is adsorbed on the surface of ceria and intergranular area even under dry atmosphere at above 300 °C.40 As a result, protons and hydroxyl groups generated from water are thought to be the most probable charge carriers within the temperature range probed in this work. Therefore, five possible processes are presented here that may facilitate conduction and cause the change of potential profile: I. Water molecules from the layer adsorbed on the NC surface split into protons, electrons, and oxygen molecules under the electric field (eq 1). This process is expected to happen in the proximity of the triple-phase boundary area (TPB), which is at the interface of the NC, electrode and gas phase (atmosphere). The generated protons, however, are continuously injected into the NC and can migrate toward the grounded electrode.

injection location to the position of interest requires more time, resulting not only in different time constants, but also in lower concentration of the charged species moving toward the grounded electrode. Thus, the correct mathematical description of the observed behavior should include transport equations for each of the multiple charged species that contribute to the conductivity behavior. Effects of Environmental Conditions. As the concentration and mobility of the charged species is likely to be affected by the presence of solvent, we proceed by studying the effects of ambient humidity on the polarization and relaxation behavior. As shown in Figure 3a, at 0% relative humidity (RH) and room temperature, the surface potential shows a rather weak polarization and relaxation, indicating that charge transport is limited at low temperature and humidity. However, with increase of RH to 90%, polarization and relaxation become stronger, and the active area widens, extending farther from the biased electrode (Figure 3b). Specifically, at the initial instant (0 s, dark blue line), the surface potential distribution over the entire ceria is almost identical to that observed in the absence of humidity (Figure 3a). During the following 10 s of polarization, the potential gradually increases at distance 30− 60 μm and decreases at 10−20 μm. The potential profile linearizes during the polarization stage (0−10 s). During relaxation stage, the potential profile goes down and finally forms an arc-shaped curve, with the highest point at ∼3 V, indicating the presence of residual charge carriers on the NC surface. The surface potential peak shifts to the center of NC during relaxation, i.e., leftwards toward the grounded electrode, as the positive charges accumulated at the biased electrode dissipate and diffuse toward the now-grounded electrodes. Such a strong dependence of the polarization and relaxation responses on the relative humidity indicates the central role of this parameter in the conduction mechanisms in NC. Upon an increase in RH, a water layer is formed on the NC surface and exposed intergranular area. The water layer may have a multistep interaction with ceria surface under electric field, generating charge carriers. When bias is applied, electrochemical splitting of water molecules may happen, especially in the proximity of the biased electrode.33−35 Nanostructured materials often include a high concentration of defects, both due to the far-from-equilibrium processing conditions and because of the large surface areas present. Oxygen vacancies and various cation interstitials are some of the most common defects reported in NC.32,36 Electrochemical water splitting can occur by catalytic interaction with oxygen vacancies resulting in free protons.37,38 Temperature is another environmental parameter that is expected to affect ion transport. As shown in Figure 3c, at 100 °C and in dry conditions, polarization and relaxation are much stronger than at room temperature (Figure 3a). Similar to the case of high relative humidity (Figure 3b), at high temperature, the potential increases and linearizes during the polarization stage. During relaxation, the potential goes down to almost 0 V, indicating a smaller remnant charge as compared to the room temperature measurements, due to a faster charge dissipation at higher temperatures. A detailed surface potential mapping as a function of humidity and temperature is available in Supporting Information, Figure S4. The observed surface potential change over time should be caused by migration and redistribution of charge carriers, including electrons, oxygen vacancies, protons, hydroxyl groups, etc. The electronic response time is determined by

2H 2O(l) ⇄ 4H+(aq) + O2 + 4e−

(1)

II. Water in the surface layer dissociates into proton and hydroxyl group (eq 2), with concentrations defined by the dissociation constant, Kw. The generated ions subsequently electromigrate in the liquid layer. Protons are expected to be the main charge carriers due to their higher mobility as compared to the hydroxyl group. H 2O(l) ⇄ H+(aq) + OH−(aq)

(2)

III. Protons in water layer are injected onto the surface of ceria and migrate on the solid surface under an applied electric field (eq 3).38,41 Oxo−H• in the equation stands for a proton chemisorbed onto the surface oxygen ion in the NC lattice through the hydrogen bond. Under electric field, protons migrate through debonding with one oxygen ion and bonding onto the neighboring one. H•(aq) + Oox (s) ⇄ Oox −H•(s)

(3)

IV. Water molecules in the surface liquid layer interact with the surface oxygen ions and form protons and hydroxyls that can be transported along the surface (eq 4). Note that eq 4 is a sum of eqs 2 and 3. H 2O(l) + Oox (s) ⇄ OH−(aq) + Oox −H+(s)

(4)

V. Water molecules are chemisorbed onto NC, filling oxygen vacancies that are present on NC, each releasing two protons. The two protons can both bond to a single lattice oxygen ion (eq 5) or each bond to one oxygen ion (eq 6).38,41 Similar to D

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case III, chemisorbed protons migrate through bonding and debonding along lattice oxygen ions. However, in this case defects (oxygen vacancies) take part in the reaction and facilitate the water dissociation. H 2O(l) + V o··(s) ⇄ Oox −2H•(s)

(5)

H 2O(l) + V o··(s) + Oox (s) ⇄ 2Oox −H•(s)

(6)

where t is time, ni is concentration, Di is diffusivity, μi is charge mobility, zi is the charge number per each ion, Si is the charge injection rate and f i is the decay rate for the ith species (i = H+,OH−). Φ is the surface potential, F is Faraday’s constant, ε0 is permittivity of free space, and εr is the relative permittivity of NC. The first term on the right side of eq 7 represents internal contributions, while the second term represents external effects. We postulate that ni changing over t is determined by internal migration, or by Di from Fick’s law (chemical gradient) and μi from electron migration (electric potential gradient). In addition, charged species can also be generated externally or supplied from outside the system. Specifically, Si is a source term, which can describe proton generation during polarization stage due to the water splitting reaction at TPB. The threshold potential for anodic water splitting reaction is estimated to be at or below 5 V, and the influence of the ambient conditions can be ignored (see Supporting Information, Figures S6 and S7, and accompanying discussions). In this model, the surface potential in proximity of the biased electrode (>20 V) is well above the estimated threshold potential for anodic water splitting, thus it is reasonable to assume that the reaction is a transport limited process. Therefore, we assume that the proton generation SH+ is a step function of distance, with a nonzero constant value at a 1-μm-long area in the immediate vicinity of the TPB, and zero on the remaining 59 μm along the ceria stripe. To account for the observed behaviors, we further introduce the first order decay rate, f i. In this model, we assume that no ions will transport through the ceria/Pt interface, so the accumulated H+ will not dissipate through the Pt electrodes. This will lead to the surface potential being almost constant during relaxation stage, contradictory to the experimental results. By introducing a decay factor f i, we take into account the possibility of charge neutralization from ambient gas or capture of the charged species by bulk of the material with subsequent dielectric screening. The time-dependent concentration will determine surface potential Φ through Gauss’s Law (eq 8). The basic assumptions, boundary conditions, and initial conditions for the model are as follows: (a) we assume an ion blocking electrode, which means ions will not migrate outside or inside ceria through the electrodes. The mathematical description is −Di∇ni + ziμini∇Φ = 0 for all six facets of the ceria stripe. (b) Φ = 0 V at grounded electrode and outer boundary of air box, and 30 V at the biased electrode. (c) Φ is assumed to be null all over ceria, at t = 0 s. (d) Finally, the dissociation constant Kw = 10−14;44 hence at pH = 7, initial conditions are chosen as ni = 10−7 mol/L = 10−4 mol/m3 for both protons and hydroxyl groups. (d) The observed potential evolution is assumed to be resulting only from proton generation and migration. That said, the screening effect of the surface potential by mobile charges is ignored here. (For justification, see Supporting Information, Figure S8 and accompanying discussion). The unknown values for parameters optimization are simplified as follows. (i) Diffusivity and mobility of protons are assumed to be two times that of hydroxyl groups: DH+ = D = 2DOH−, μH+ = μ = 2 μOH−.45 (ii) Water splitting generates protons during polarization stage, but not for relaxation stage, and no hydroxyl groups are generated: Sp_H+ = S, Sp_OH− = Sr_H+ = Sr_OH− = 0. (iii) The decay rates of both species are assumed to be the same f H+ = f OH− = f.

Except for eq 4, the other five equations are independent. Among these, eq 1 describes proton generation reaction that leads to potential increase during polarization. The remaining eqs 2, 3, 5, and 6 describe four possible pathways for proton and hydroxyl groups to be transported along NC, between electrodes. Among these, ions transport in water layer (eq 2) + and Ox− o H (formed on oxygen vacancy) transport (eq 6) are most likely to happen: double-proton on oxygen lattice (eq 5) has more steric effect;38 and oxygen vacancy is believed to be an active spot for reactions and can significantly reduce energy barrier of the formation of chemisorbed protons.42,43 The important effect of oxygen vacancy involvement will be discussed in a subsequent paper. The generated protons and hydroxyls determine the conduction behavior of the material, albeit only on the surface and intergranular area where water is present. Driven by the applied electric field, protons are generated at the TPB and accumulate in the proximity of the biased electrode, which causes a potential increase in this area. Simultaneously, at the grounded electrode, protons are annihilated, and hydroxyl groups are accumulated, so the surface potential slightly decreases in this region. This results in linearization of the surface potential, which agrees well with the experimental data. During relaxation, without an external driving force provided by electric field, the accumulated charges slowly dissipate and later discharge on the two electrodes, which are infinite reservoirs of electrons. The charge carriers may also be transported from the surface to an inner porosity region, where the screening effect is significant. This is evidenced by the gradual reduction of the surface potential and shifting of the maximum potential location. The final residual positive charge is consistent with the presence of both a space charge layer and long “dissipation” time for the remaining charges on NC surface. At higher RH, a thicker layer of water is expected to form on the NC surface, increasing both the mobility of the surface ionic species (i.e., conductivity) and rate of proton generation at the TPB. An increase in temperature leads to a competition between the decrease of the water concentration on the surface and simultaneous thermal activation of water splitting. As a result, a significant enhancement of the polarization and relaxation behavior is observed. Finite Element Modeling. According to the previous analysis, we consider that the observed surface potential behavior is caused by the charge carrier (namely protons and hydroxyls) transport under electric potential gradient and chemical (concentration) gradient. This process is modeled through finite element methods. The following equations show the coupled changes in ionic concentrations and electric potential. ∂ni = ∇·( −Di∇ni + ziμi ni∇Φ) + (Si − fi ni) ∂t

(7)

∇2 Φ = −∑ niziF/ε0εr

(8) E

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RT 0% 90% 0%

S (mol/m3 s) −4

3 × 10 30 × 10−4 100 × 10−4

f (s−1)

D (m2/s) −11

1 × 10 2 × 10−11 10 × 10−11

0.2 0.4 1

μ (cm2/V·s)

figure reference

5 × 10−8 5 × 10−8 10 × 10−8

Figure 3d Figure 3e Figure 3f

literature (7.6 × 10−9 m2/s at room temperature and 1.5 × 10−8 m2/s at 100 °C),45,46 this is probably due to the fact that the nanolayer of water on NC is discontinuous and the effect of hydrogen bond with surface lattice oxygen ions is significant. In summary, the experimentally observed behavior is simulated and well-explained using four parameters. As demonstrated above, the time dynamics of the surface potential behavior on NC are successfully obtained from the energy discovery platform. Finite element modeling provides a practical way to model the charge transport and electrochemical reactions on the sample. By combining the qualitative analysis of the experimental behavior and the quantitative calculation of parameters that affect the transport mechanisms, the different charge dynamics at the nanoscale can be unmixed and studied separately. These platforms are expected to be universally suitable for electrochemical studies on a wide range of materials, including fast ionic conductors, ferroelectric materials, etc. Conclusions and Outlook. Energy discovery platforms, exploiting a synergy of nanofabricated devices and timeresolved Kelvin probe force microscopy (tr-KPFM), are explored in this study. The tr-KPFM technique measures the surface potential variation over time, which is directly related to the variation of local charge concentration and distribution, rather than charge migration itself, which can be substantially more challenging. Based on its outstanding spatial resolution, this technique overcomes also the limitations of traditional macroscopic characterization methods. With respect to temporal resolution, the slow dynamics of ionic processes are comparable with the time scale of SPM techniques, and therefore the use of such SPM techniques should prove a great tool for the electrochemical kinetics studies. Nanostructured ceria is presented here as a case study, and we find that the detected surface potential change over time is mainly a result of transport of protons and hydroxyl groups. Finite element modeling is performed to break the total response into separate potential behavior and then connect individual electrochemical mechanisms to changes in the charged species’ concentration. The presence of water within ceria is, in most cases, inevitable during the operation of electrochemical devices. Based on our results, water interaction with the ceria surface and interfacesas well as the protons and hydroxyl groups’ transport along the ceriais expected to play a large role in the functionality of SOFCs, catalytic devices, etc. especially at lower working temperatures. The energy discovery platforms are also envisioned to provide a way for in operando study of poisoning mechanisms and charge injection mechanisms for the operation of such devices. Provided the fact that the low temperature proton generation and transport is significant even in absence of humidity, the proton conductivity is therefore believed to be highly sensitive to the microstructure, i.e., surface porosity, grain boundaries, and/or defect concentration. Thus, the preparation method and dopant level is expected to greatly affect its conduction mechanisms, which means the proportion of surface proton conduction in the total conduction can be

Based on the above assumptions and simplifications, four unknown parameters remain in this model: (1) proton diffusivity, DH+; (2) proton mobility μH+; (3) proton charge injection rate at TPB during polarization S; (4) charge decay rate f. These four unknown parameters determine the basic properties of charge carriers and electrochemical reaction processes on the NC, and thus the variations of shape of the modeled potential curves. The finite element modeling was interfaced with a Matlab code to find optimized parameters, which result in calculated potential profiles that best match the experimental results. The tested parameters space was: D: 10−12 ∼ 10−10 m2/s, μ: 10−8 ∼ 10−7 cm2/(V s), f: 0.1−2 s−1, and S: 10−4 ∼ 10−2 mol/m3 s. For each set of parameters, a resultant matrix was solved from the finite element modeling, which was the surface potential value as a function of time and distance. The calculated matrix is optimized with respect to the experimentally obtained matrix in Matlab using the correlation coefficient method (see Supporting Information, Note S1). The surface potential profiles that are in best agreement with the corresponding experimental results obtained at various environmental conditions are shown in Figure 3d, e, and f. The corresponding fitting parameters are listed in Table 1. A close consideration of these parameters and curves provides a quantitative measure of how each parameter can affect the shape of the surface potential profile. An increase of S will lead to a stronger polarization, which is reasonable because higher S means that more protons are injected into the system. An increase of f will result in a faster decay rate of surface charge and thus a faster change rate of surface potential. This leads to a smaller time constant, or, in a visualized way, more separation between subsequent (in the temporal scale) potential curves, as can be seen from the comparison between Figure 3e and f. D and μ determine the charge transport dynamics on NC. Higher mobility (μ) means a quicker response to the electric field and a faster migration speed. Therefore, it will facilitate the motion of the protons generated at biased electrode leftward, resulting in more positive charges accumulated in proximity to the grounded electrode. Finally the increase of diffusivity (D) will result in a more uniform distribution of charge carriers, and thus in an overall “flatter” surface potential profile. The effects of environmental conditions on these parameters are also studied. As shown in Table 1, at room temperature and 0% RH, the best fitted parameters are S = 3 × 10−4 mol/m3 s, f = 0.2 s−1, D = 1 × 10−11 m2/s, and μ = 5 × 10−8 cm2/(V s). At elevated humidity, S significantly increases to a higher value due to a thicker water layer, which provides more reactant for water splitting reaction. And f also increases due to faster charge neutralization from ambient water. At increasing temperature, S significantly increases as compared to room temperature, which is consistent with the decreasing energy barrier for water splitting reaction. f increases mainly due to the charge screening process through diffusion into the bulk porosity area. Diffusivity and mobility also increases, which agrees with the actual physical trend of these parameters at high T. While value obtained for diffusivity here is about 2 orders of magnitude lower than the value for proton diffusion in water reported in F

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controlled as needed. In addition, controlling such preparation technologies may allow fabrication of functional materials with MIEC behavior at even lower temperatures, which broadens the applications of ceria. Lastly, the energy discovery platforms are expected to be broadly applicable to a wide range of functional materials. Such is the case for example for ferroelectric and flexoelectric materials, where the effects of defects and surface chemical states on the functional properties have been the subject of many controversial and inconclusive studies. The same approach is also expandable to other material systems, with applications to solid oxide fuel cells, lithium batteries and super capacitors, where temporal characterization of functional properties at multiple length-scales are fundamental to further understanding of the underlying phenomena and, ultimately, design of new and improved energy systems. Materials and Methods. Nanostructured Ceria Preparation. Nanostructured ceria was prepared by physical vapor deposition (PVD). A Kurt J. Lesker PVD 75 sputterer with a 99.9% CeO2 target were used. Ceria was deposited at 80 W for 40 min in argon atmosphere (5 × 10−3 Torr), generating an approximately 60 nm thin film. Lateral Electrode Device Fabrication. Ceria stripes (60 μm long and 10 μm wide) were patterned by photolithography and etching in HCl-FeSO4 solution for 30 s on quartz substrates (500 μm thick). Lateral Cr/Pt electrodes (20 nm/80 nm thick) were subsequently created by sputtering and patterned by a liftoff method. The electrodes were 10 μm wide with interelectrode distance of 50 μm. Characterization. Ceria film microstructure was detected by optical microscopy and scanning electron microscopy (SEM). The surface topography of ceria was detected by contact atomic force microscopy (AFM). The thickness of silicon nitride and ceria was measured by optical reflectometery and contact profilometer, respectively. X-ray diffraction (XRD) was employed to probe the crystalline structure of the ceria film. The tr-KPFM and open-loop band-excitation Kelvin probe force microscopy (OL BE-KPFM) measurements were performed on a commercial AFM (Bruker Multimode with Nanonis controller). Cantilevers with conductive Cr/Pt coated tips (Budget Sensors, Co.; resonance frequency ∼75 kHz) were used. During measurements, 15 V of DC bias and 1 V of AC bias (ω = 44 kHz) were applied to the cantilever. The information on the surface potential distribution over time, topology, and current were collected for further analysis. An external lock-in amplifier (SR844, Stanford Research) was used for signal processing, and a function generator (DS345, Stanford Research) applied AC waveform to the tip. Data processing was done using custom-written Matlab codes. Some of the outlier points in the maps and averaged data that corresponded to abrupt changes in topography (SPM tip encountering surface particle or electrode edge) were removed manually. Measurements were performed in a temperature range from room temperature (23 ± 2 °C) to 100 °C, and relative humidity ranging from 0% to 90% at room temperature using a gas cell. Finite Element Modeling. The finite element modeling was performed using COMSOL Multiphysics 4.4. The export of model solution and parameter fitting was done on COMSOL LiveLink for MATLAB 4.4.

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ASSOCIATED CONTENT

S Supporting Information *

Additional details, Figures S1−S8, and Note S1. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.5b01613.

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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 N.B.G. and J.D. gratefully acknowledge funding from the US National Science Foundation through grant no. DMR-1255379. The tr-KPFM portion of this research was conducted at the Center for Nanophase Materials Sciences, which is sponsored at Oak Ridge National Laboratory by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy under user proposal CNMS2013-123.

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DOI: 10.1021/acs.nanolett.5b01613 Nano Lett. XXXX, XXX, XXX−XXX