The nucleation and growth of small particles play a critical role in a variety of electrochemical systems. Exerting control over nucleation and growth processes requires a firm understanding of their kinetics, which are inherently complex due to multistep reaction sequences that involve small clusters which are often thermodynamically unstable. 1 While a large body of prior work has demonstrated models capable of analysing nucleation and growth processes in bulk electrochemical systems, [2][3][4] the continued development of nanoelectrodes and high-resolution microscopy techniques has opened the exciting possibility of tracking discrete nucleation events [5][6][7][8][9][10][11] and mapping spatial variations in nucleation kinetics within surfaces. [12][13][14] Unfortunately, the kinetic models employed in many of these prior studies are not applicable to experiments involving the nucleation and growth of individual, discrete particles.
Here, we present single-particle studies of electrochemical nucleation and growth enabled by scanning electrochemical cell microscopy (SECCM). SECCM, which utilizes an electrolyte-filled pipet as a probe to locally interrogate the electrochemical properties of a surface, has been applied to great effect in studies of catalysis, [15][16][17][18][19][20][21] photoelectrochemistry, 22-24 corrosion, 25,26 and particle nucleation and growth. 12,27,28 Here, the high-throughput nature of SECCM enabled 100's of individual metal particles to be synthesized at a series of different applied potentials. By analysing the nucleation times in the context of an explicit time-dependent kinetic model, we demonstrate that it is possible to elucidate chemically meaningful quantities, such as surface energies and kinetic rate constants, through the analysis of single particle nucleation and growth data. The results from these experiments demonstrate a powerful new approach to the analysis of electrochemical nucleation and growth in heterogeneous systems.
Carbon film electrodes were fabricated through a process adapted from prior literature. 29 Fused quartz cover slips (25.4 mm diameter x 0.25 mm thick, SPI) were cleaning by annealing in air at 800 °C in a tube furnace and soaking in piranha solution (3:1 H 2 SO 4 :30% H 2 O 2 ) for 30 min. The substrates were then rinsed with DI H 2 O and dried under an N 2 stream. A 50% (v/v) solution of AZ 1518 photoresist in 1-methoxy-2propyl acetate was then spincoated onto the clean quartz substrates at 6000 rpm for 2 minutes. The resulting films were placed on a 90 °C hotplate for 12 minutes and transferred into a tube furnace (OTF-1200X, MTI). The furnace was purged three times with a 5% H 2 /95% N 2 mixture, after which a constant flow of the H 2 /N 2 mixture was maintained through the furnace. The samples were then heated at 5 °C/min to a temperature of 1000 °C and held at this temperature for 1 hr, after which the furnace was allowed to cool naturally to room temperature. Indium tin oxide (ITO, 18 mm x 18 mm, #1.5, 15-30 Ω/sq, SPI) electrodes were cleaned via sequential sonication in DI H 2 O, isopropanol, and DI H 2 O for 30 min each before use.
Atomic force microscopy (AFM) imaging was carried out using a Cypher ES AFM in tapping mode with standard probes (<8 nm Please do not adjust margins Please do not adjust margins tip radius, 325 kHz resonance frequency, 40N/m force constant, HQ:NSC15/Al BS, MikroMasch). SEM imaging was carried out using a ThermoFisher Helios 5 UX FIB-SEM operating at 5 keV.
SECCM probes were fabricated from quartz capillaries (1.2 mm outer diameter, 0.9 mm inner diameter, Sutter) using a Sutter P-2000 pipet puller. A two-line program was employed to yield pipets with ca. 500 nm terminal diameters (heat = 740, fil = 4, vel = 30, delay = 150, pull = 35/heat = 710, fil = 3, vel = 30, delay = 135, pull = 125). These probes were filled with an electrolyte consisting of 0.5 mM AgNO 3 (ACS reagent grade ≥ 99.8%, Sigma Aldrich) and 50 mM NaClO 4 (ACS reagent grade ≥ 98.0%, Sigma Aldrich) using a glass syringe (Microfil 34G) and a Ag wire (0.25 mm diameter, 99.997%, Goodfellow) was inserted in the open end of the pipet to complete the probe. All potentials cited herein are referenced vs. this QRCE. The geometry of the fabricated pipets evaluated using SEM imaging (FEI Quanta FEG 450 @ 5 keV).
A home-built setup was used to conduct all SECCM studies as detailed in previous reports from our lab. 20 A C or ITO substrate was attached to a ceramic holder and mounted onto an inverted optical microscope equipped with a 50x, 0.5 NA objective. An SECCM probe was mounted to a 3-axis piezo system (PI NanoCube). The SECCM probe was translated towards the sample while applying a cathodic bias to the ITO substrate, and probe-sample contact was detected as a sudden spike in current flow. A potential step waveform was then applied to the sample and the resulting current was recorded before retracting the probe and repeating this process at another location on the sample. Electrochemical measurements were made using a patch-clamp style amplifier (Dagan CHEM-CLAMP) and all instrumentation was controlled through custom LabView software.
Single-particle electrodeposition studies were carried out using SECCM in a manner similar to prior work from our lab. 27 In SECCM, an electrolyte-filled pipet with µm-or nm-scale dimensions is employed as an electrochemical probe. When the pipet is brought into contact with a sample, a miniaturized solidelectrolyte interface is created which enables local electrochemical measurements to be carried out by applying a bias between the sample and a quasireference-counter electrode (QRCE) immersed in the electrolyte at the opposite end of the probe.
An illustration of the SECCM measurements carried out in this work is provided in Figure 1. In these studies, the samples were planar C or ITO electrodes. The SECCM probes were quartz pipets filled with an aqueous electrolyte containing Ag + ions and containing a Ag wire which served as a QRCE. Example SEM images of a typical probe are provided in Figure 1c. In each measurement, an anodic bias was applied between the sample and QRCE while moving the probe towards the sample surface. An anodic current spike was observed upon probe-sample contact, at which point probe movement was stopped and the bias switched to a cathodic potential. This potential was held while monitoring the pA-scale currents flowing in the miniaturized SECCM cell. Due to the application of the cathodic potential, Ag + ions are reduced, resulting in the formation of Ag nanoparticles (NPs) which is observed experimentally as a cathodic current transient which begins at some time after application of the cathodic bias, hereafter referred to as the nucleation time, 𝑡 𝑛. After a certain amount of charge has passed in the system, the probe is retracted and moved to a new lateral location on the sample surface. This process, illustrated in Figure 1b, is repeated to map nucleation across a series of points in a rectangular array following a "hopping-mode" protocol. This process produces a rectangular array of Ag particles on the substrate which persists after termination of the experiment.
The nucleation and growth of Ag NPs can be assumed to follow a series of one-electron transfer reactions:
Here, 𝐴𝑔 𝑛 represents a NP consisting of 𝑛 atoms and 𝑘 𝑛/ 𝑘 -𝑛 represent rate constants describing the additional/removal of an atom to/from the NP. 𝐴𝑔 0 would represent a vacant surface site where nucleation is initiated. At small values of 𝑛, the free energy of formation for a particle of size 𝑛 can be expressed as: Please do not adjust margins
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Here, Δ𝐺 0 represents the free energy of the electrodeposition of Ag + onto bulk Ag (negative at cathodic potentials) and the second term represents the free energy due to the surface energy of the Ag NP. 𝜒 is a positive unitless quantity proportional to the surface energy of the interface(s) involved in the electrodeposition process:
Where 𝑉 𝑎 is the atomic volume of the material and 𝐵 is a geometric factor describing the particle shape (see SI for details). As this surface energy term decreases with 𝑛, it has the effect of making Δ𝐺 𝑛 positive at low values of 𝑛, creating an energetic barrier which must be overcome for NP growth to proceed spontaneously. The "critical" particle size where Δ𝐺 𝑓,𝑛 reaches a maximum (𝑛𝑐) can be found as:
A majority of studies of electrochemical nucleation reported to date employ kinetic models which assume a quasi-equilibrium exists among particles of different size on the substrate. Such a model predicts a static nucleation rate of the familiar form: 1,30
Where 𝐴 is a pre-exponential factor and Δ𝐺 ‡ is the maximum particle free energy during the nucleation process. In single particle nucleation and growth experiments, where statistical distributions in nucleation times are analysed, a static nucleation rate would yield an exponential probability density for the nucleation time, 𝑡 𝑛: 𝑃 𝑛 (𝑡) = 𝑘 𝑛𝑢𝑐 𝑒 -𝑘 𝑛𝑢𝑐 𝑡
Conceptually, the application of a static nucleation and growth model to single particle experiments would be inappropriate due to the relatively low density of nucleation sites being interrogated. I.e., if one is tracking discrete nucleation events, quasi-equilibrium conditions obviously do not apply. Alternative models are thus required to properly analyse data from single particle experiments.
To properly treat experiments wherein quasi-equilibrium conditions cannot be established, a fully time-dependent approach is required. Following the reaction scheme above, the differential equations describing the change in the number of NPs of size 𝑛 on a surface can be written as:
where Γ 𝑛 is the density (cm -2 ) of NPs of size 𝑛 on the surface. The rate constants in such a scheme will depend upon the difference in free energy of formation between particles of adjacent size:
While explicit solutions to the resulting set of coupled differential equations would be overly cumbersome, they can be straightforwardly solved numerically to yield timedependent solutions for Γ 𝑛.The resulting probability densities for nucleation times can be calculated from these solutions in a straightforward manner. Alternatively, Monte Carlo-type simulations can be carried out to yield similar results. Both approaches are described in detail in the SI.
Example theoretical curves for modelling the statistical distribution of nucleation times via each method are presented in Figure 2. The quasi-equilibrium approach commonly employed in bulk studies predicts an exponential distribution of nucleation times. An explicit time-dependent approach yields a log-normal shaped distribution which reflects the nonnegligible time required to progress through the reaction sequence to reach stable nuclei sizes. The stochastic nature of this process at small particle sizes is illustrated in Figure 2c, which depicts results from Monte Carlo simulations of particle nucleation.
Beyond the basic differences in the shape of these distributions, it is also notable that these models differ greatly in terms of timescale, with the time-dependent model predicting nucleation times roughly 2 orders of magnitude smaller, further highlighting the need to carefully consider the model being employed if one is interested in extracting physically meaningful parameters (e.g., surface energies) from experimental data.
Results from SECCM studies of Ag NP nucleation on C film electrodes fabricated via the pyrolysis of photoresist films are presented in Figure 3. Example current transients recorded Please do not adjust margins Please do not adjust margins during SECCM experiments are provided in 3a. Upon probesample contact, small anodic currents are observed until application of the cathodic potential at t = 0. A cathodic charging transient is then observed which quickly decays (< 10 ms). The measured current then adopts a baseline value until it suddenly increases at a later time, signalling the nucleation and growth of an individual NP within the pipet-substrate interface. This process is highly stochastic, varying over seconds-long timescales between individual points in an SECCM experiment.
Figure 3b provides images of the measured NP nucleation times (𝑡𝑛) as a function of spatial position during SECCM experiments at different applied potentials. It is clear from these images that more negative applied potentials yield shorter nucleation times on average, as would be expected. There is also no discernible clustering of short or long nucleation times in these images, suggesting there are not any macroscopic structural features present on the electrode surface influencing nucleation kinetics.
Statistical distributions of the measured nucleation times at different applied potentials are provided in Figure 3c. The distributions become narrower and shift to shorter nucleation times at larger overpotentials, consistent with the conclusions from the images discussed above. The distributions are decidedly non-exponential in shape, particularly at smaller overpotentials, providing direct experimental evidence that a quasi-equilibrium is not appropriate in the analysis of these experiments. The distributions were analysed by fitting the experimental data to the predictions of the time-dependent kinetic model, varying 𝜒 and 𝑘 0 as model parameters. The resulting fits are shown in Figure 3c. Excellent agreement between the experimental data and theory are observed for parameter values of 𝜒 = 8.9 and 𝑘 0 = 1.9 s -1 . Assuming a hemispherical NP geometry, this value of corresponds to an effective surface tension of 𝛾 = 150 mJ m -2 for the NPs deposited via SECCM.
SECCM data acquired for the deposition of Ag NPs on ITO substrates are displayed in Figure 4. Here, similar current transients were observed during deposition at random times after the application of the cathodic potential (4a). The measured nucleation times exhibited the expected trend of shorter nucleation times at larger overpotentials, and no discernible spatial trends were visible in the SECCM images (4b), similar to the case for C. Significant difference were observed, however, in the experimental distributions of nucleation times provided in Figure 4c. Larger overpotentials are required on ITO in order to drive nucleation over reasonable timescales as compared to the C film electrodes. Also, the nucleation times appear to adopt distributions that are more exponential in shape at all but the lowest applied overpotentials (see Figure S1 in the SI). This difference in behaviour is likely attributable to the known heterogeneous nature of ITO, 31 making it likely that different populations of nucleation sites are contributing to the observed data. Fitting the distributions to a similar timedependent kinetic model yields values of 𝜒 = 14.4 and 𝑘 0 = 2.8 s -1 . This larger value of 𝜒 corresponds to an effective surface energy of 𝛾 = 240 mJ m -2 , reflecting significant differences in the stability of Ag-C and Ag-ITO interfaces. This is supported by significant morphological differences observed via SEM for Ag particles fabricated on C and ITO, with particles on C growing in a more conformal manner (see Figure S2 in the SI).
It is worth noting that these surface energies would correspond to critical particle sizes of 𝑛 𝑐 ≤ 2 for C and 𝑛 𝑐 ≤ 3 for ITO under the conditions employed. While these numbers should only be taken as rough estimates, it suggests that single particle nucleation experiments carried out over practical timescales will provide information which is biased towards the properties of particles or clusters only a few atoms in size. Please do not adjust margins Please do not adjust margins
The SECCM studies detailed above provide new insights into the analysis of particle nucleation and growth in electrochemical systems. A statistical analysis of particle nucleation times enabled by the high-throughput nature of SECCM demonstrated traditional quasi-equilibrium kinetic models are not appropriate for the analysis of single particle data. Explicit time-dependent kinetic models have been presented which can appropriately model single particle studies to extract chemically meaningful parameters such as surface energies and kinetic rate constants. Moving forward, the approach presented here could find great utility in differentiating nucleation kinetics within structurally heterogeneous systems with electrochemical microscopy techniques such as SECCM.
Open Access Article. Published on 06 July 2024. Downloaded on 9/13/2024 5:44:14 PM.
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View Article Online DOI: 10.1039/D4FD00131A