Nanoscale electrochemistry in a copper/aqueous/oil three-phase system: surface structure–activity-corrosion potential relationships

Practically important metal electrodes are usually polycrystalline, comprising surface grains of many different crystallographic orientations, as well as grain boundaries. In this study, scanning electrochemical cell microscopy (SECCM) is applied in tandem with co-located electron backscattered diffraction (EBSD) to give a holistic view of the relationship between the surface structure and the electrochemical activity and corrosion susceptibility of polycrystalline Cu. An unusual aqueous nanodroplet/oil (dodecane)/metal three-phase configuration is employed, which opens up new prospects for fundamental studies of multiphase electrochemical systems, and mimics the environment of corrosion in certain industrial and automotive applications. In this configuration, the nanodroplet formed at the end of the SECCM probe (nanopipette) is surrounded by dodecane, which acts as a reservoir for oil-soluble species (e.g., O2) and can give rise to enhanced flux(es) across the immiscible liquid–liquid interface, as shown by finite element method (FEM) simulations. This unique three-phase configuration is used to fingerprint nanoscale corrosion in a nanodroplet cell, and to analyse the interrelationship between the Cu oxidation, Cu2+ deposition and oxygen reduction reaction (ORR) processes, together with nanoscale open circuit (corrosion) potential, in a grain-by-grain manner. Complex patterns of surface reactivity highlight the important role of grains of high-index orientation and microscopic surface defects (e.g., microscratches) in modulating the corrosion-properties of polycrystalline Cu. This work provides a roadmap for in-depth surface structure–function studies in (electro)materials science and highlights how small variations in surface structure (e.g., crystallographic orientation) can give rise to large differences in nanoscale reactivity.


S.2. Additional SEM images of SECCM scan areas
. SEM images of the droplet "footprint" residue remaining on the polycrystalline Cu surface after the chronopotentiometric anodic pulse (Movie S1).  aerated solution. 4 The pertinent initial concentrations were imposed as boundary conditions both at the top of the tip (labelled rp in Figure S5) and at the top of the dodecane layer (labelled rair in Figure S5).
In condition |2|, an equilibrium partition flux was imposed at the boundary between the aqueous solution and the dodecane layer (labelled Xint in Figure S5): where Kpart is the partition coefficient between the two phases. In this simulation Kpart = 7.8 (ref 5) while kout was set to be a high value (kout = 10 cm s −1 ), such that the system could be considered at equilibrium on the time scale of the calculation. This is reasonable as O2 transfer across immiscible liquid boundaries is diffusion-limited. 6 In condition |1|, this boundary was set to be a no-flux boundary, to demonstrated that O2 flux down the nanopipette barrel is negligible compared to the flux across the oil-water boundary. In addition, unless otherwise stated, the no-flux condition was imposed on all boundaries. The system was solved with stationary condition, adopting the PARDISO solver. 7 The current (i) at the electrode (labelled rdr in Figure S5) was calculated by integration of the O2 flux through the boundary, assuming a 2 electrons reduction reaction (n = 2): 8 dr 2 2 aq 00 with r, z and ϕ being the cylindrical coordinates represented in Figure S5.

Results and Discussion.
As addressed in previous studies, 1, 9, 10 the configuration of SECCM mimics a gas diffusion electrode, to some extent, with an enhanced flux of gaseous reactants/products across the meniscus-cell (i.e., at the three-phase boundary). Thus, before considering the grain-dependence of the ORR on polycrystalline Cu examined in the main text, finite element method (FEM) simulations were carried out to understand the transport of O2 across the oil-water interface in SECCM (see Figure 1 of the main text for experimental schematic). As outlined above (see Figure S5), the simulations consider two different conditions: |1| O2 transport limited to only the aqueous phase (i.e., no gas exchange with the surrounding oil phase) and; |2| O2 transport in both the aqueous and surrounding oil phase (i.e., gas exchange occurs between oil and aqueous phases). Note that condition |1| was explored to determine the relative contributions of mass-transport down the nanopipette barrel vs. across the liquid-liquid (oil-water) phase boundary, to overall O2 flux. Simulated O2 concentration profiles, obtained from a diffusion-controlled four-electron process (e.g., the ORR at high overpotentials) are shown in Figure S6.
Under condition |1| (i.e., no gas exchange with the surrounding oil phase), a diffusionlimited current of 7.9 pA (1.6 mA cm −2 ) was calculated, which is 5 % of that expected at the same sized inlaid disc microelectrode, in agreement with previous reports of mass transport in SECCM. [11][12][13] In this case ( Figure S6a), as the O2 is depleted exclusively from the reserve in aqueous solution, the diffusion layer extends tens of μm into the probe, with the concentration reaching 90% of the bulk value (CO 2 = 0.26 mM) at ca. 80 μm from the working electrode surface.
Under condition |2| (i.e., gas exchange occurs between oil and aqueous phases), because the solubility and the diffusion coefficient for O2 are greater in the oil phase (2.02 mM and 4.11•10 −5 cm 2 s −1 , respectively) than the aqueous phase, O2 transport across the oil-water boundary leads to a greatly enhanced flux ( Figure S6b), and diffusion-limited current of 423 pA (84 mA cm −2 ). As such, the diffusion layer is compressed compared to condition |1|, with the concentration reaching 90% of the bulk value at only ca. 20 μm into the pipette probe from the working electrode surface. As highlighted by the constant concentration contours within the oil phase ( Figure S6b), the O2 assumes a radial-spherical diffusion profile, with the oil supplying > 98% of the reactant flux to the electrode surface, at diffusion-control. Condition |2|, where O2 transport occurs in both the aqueous and surrounding oil phase (i.e., gas exchange occurs between oil and aqueous phases). In both cases, the green, black and white contours represent increments of 0.05, 0.02 and 0.002 mM, respectively. Note that in (b), the concentrations of O2 in the aqueous phase and the oil phase are represented with different colour scales and data ranges.
As alluded to above, as Iapp (0.88 mA cm −2 ) is small compared the steady-state limiting current (ca. 1.6 and 84 mA cm −2 under condition |1| and |2|, respectively), so no transition from the ORR to the HER plateau is observed experimentally. Indeed, given the ease with which O2 can be supplied through a nanodroplet environment, the simulations carried out above demonstrate the importance of O2 availability and ORR kinetics for modulating the corrosionaction of acidic nanodroplets.

S.4. Movie captions
Movie S1. Electrochemical surface potential (Esurf) movie recorded in the SECCM configuration (127 by 81 pixels, hopping distance 1 μm), obtained by applying an anodic chronopotentiometric pulse to a polycrystalline Full grain orientation correlation analysis of EOCP from (a) versus the average grain orientation, extracted from Figure3b, main text. Details on the calculation of the projection coordinates adopted in (b) are discussed in Section S.6, while details of the data extracted for each single grain can be found in Section S.7 ( Figure S8 and Table S1).
The inset in (b) shows the statistical distribution of EOCP extracted from grains α and β, marked in Figure3b, main text.

S.6. Development and details of the 2-dimensional (2D) projections of crystallographic orientation relative to the low-index orientations
In order to represent the average orientation of each measured grain on a bi-dimensional plane, a new kind of 2D projection was developed herein, allowing the coordinates of each plane to be easily calculated and visualised from the Euler angles. The orientation of a generic plane, α, in space can be defined by three Euler angles, φ1, Φ and φ2. From these angles, it is possible to obtain the Miller indices (h,k,l) of the plane parallel to the normal direction (ND): As it can be seen from Eqs (S6) to (S8), the Miller indices depend only on the latter two Euler angles, with φ1 corresponding to the rotation of the plane relative to ND.
Due to the symmetry of the cubic system to which Cu belongs (crystal group 225), it was assumed that all the families of the plane {h,k,l} had equivalent structures, thus the Miller indexes of planes α (h,k,l) were simply ordered from smallest to largest, so that h' ≤ k' ≤ l', with h', k' and l' being the rearranged indexes. This was done in order to obtain comparable orientations for the following steps (vide infra). For instance, using this convention, planes (100), (010) and (001) are all taken to be equivalent to (001), sorting (h,k,l) from smallest to largest. Once the Miller indices for each plane α were calculated using Eqs (S6) − (S8), the angle between α and each of the three low-index planes employed for cubic system representation, (001), (011), (111), was calculated, respectively as γ1, γ2 and γ3: with (h'1,k'1,l'1) being the Miller index of α and (h'2,k'2,l'2) being the Miller indexes of the considered low index plane. Therefore, each plane α could be described respectively by three coordinates; for example, calculated values for each the low-index planes are shown in Table   S1. Note that as alluded to above, low-index grains (001), (011) and (111) were chosen to fulfil the requirement of sorting (h,k,l) from smallest to largest (vide supra).
Therefore, a useful and simple 2D representation of the grains is introduced by calculating the projection of each point in the (γ1, γ2, γ3) space on the plane passing through P1, P2 and P3. Such a plane will be represented by the following equation: a, b and c correspond to the angles defined above. In order to represent the points over this plane, two Cartesian coordinates were arbitrary defined as follows: x axis as the line passing through P1 and P3, y axis as the line passing through P1 and orthonormal, to x. The direction of the axis was defined in order of P2 having both positive coordinates in this projection. Such coordinates were called C1 (x-axis) and C2 (y-axis). Therefore, C1 and C2 can be calculated from γ1, γ2, γ3 for each considered plane. If the following constants are defined: Then for each generic plane, P: A Matlab script for calculating the two coordinates as per Eqs. S23 and S24, starting from the average Euler angles extracted from a generic EBSD map, is attached to the ESI.
The position of some representative planes in coordinates C1 and C2 are shown in Figure   S8. On this plot, in this coordinate system, P1 (0,0), P2 (66.5517˚,0), P3 (59.6074˚,50.336˚). All generic planes α (i.e., all grains) lay in a section delimited by the following three lines, as shown in Figure

S.7. Crystallographic details of the grains scanned by SECCM and additional
Structure-activity maps Figure S9. Definition of the grain ID for each grain analysed from Movie S1 (i.e., reproduction of the EBSD data shown in the main text, Figure 3b). The EBSD map was rotated anticlockwise by 90˚ for a clearer visualisation. Table S2. List of all grains analysed by SECCM (Supporting Information, Movie S1 and main text, Figure 3), with the average Euler angles, Miller indices and Projection Coordinates and Esurf listed for each one. The grain IDs correspond to those defined in Figure S9.    Figure S10). Table S3. List of all grains analysed by SECCM (Supporting Information, Movie S2, Movie S3 and Figure S10, and main text, Figure 4

and 5), with the average Euler angles, Miller indices and Projection Coordinates, τ and
Esurf listed for each one. The grain IDs correspond to those defined in Figure S11. S.8. Structure-electrochemistry analysis of surface defects: cathodic and anodic processes Figure S12. (a) Raw EBSD map (i.e., without grain boundaries drawn) of the area scanned in the ESI, Movie S2.
Five main surface defects (scratches), labelled fi, are identified. Note that scratches can be generally identified as a black zones in EBSD images, due to the fact that the "shadow effect" of the scratches walls generally do not allow the underlying crystallographic orientation to be determined. (b) EBSD misorientation colouring map of the same area. The colours in this map indicate inter-pixel misorientation, such that a visible colour difference between any two adjacent points within a given grain represents the misorientation angle between such points. (c) Comparison of the average Esurf−t curves recorded on the sections of scratches g, h and i (identified in Figure   S12a), embedded in grain γ (identified in the main text, Figure 4b), alongside the average curve of grain γ. Each graph plots the average curves (Esurf, continuous lines) and, for every scratch, the difference between the features and the grain average potential (ΔEsurf, dashed lines).