Single Particle Electrochemical Oxidation of Polyvinylpyrrolidone-Capped Silver Nanospheres, Nanocubes, and Nanoplates in Potassium Nitrate and Potassium Hydroxide Solutions

Triangular ∼53 nm side length × ∼10 nm thick PVP-capped nanoplates (AgTNPls, lot number ALJ0009, 650 nm peak absorption), 30 (29 ± 3) nm PVP-capped AgNSs, and 30 (29 ± 3), 50 (51 ± 6), and 70 (73 ± 8) nm citrate-capped AgNSs (used in the KNO₃ studies) were purchased from nanoComposix (Prague, CZ). The 40 nm PVP-capped AgNSs (39 ± 4 nm) and 40 nm citrate-capped AgNSs (39 ± 5 nm) (used in the KOH studies) were purchased from nanoComposix (San Diego, CA). PVP for all AgNPs obtained from nanoComposix is reported to be M_w = 40,000 g mol⁻¹. PVP-capped (M_w = 55,000 g mol⁻¹) AgNCs (used in the KNO₃ and KOH studies) and PVP-capped (M_w = 8,000 g mol⁻¹) round nanoplates (AgRNPls) (used in the KOH studies) were synthesized in-house (see details below). Agar powder and potassium nitrate (99.99%) were purchased from Sigma Aldrich (Germany) and Sigma Aldrich (St. Louis, MO). MasterMet2 0.02 μm colloidal silica suspension for polishing and the MasterTex Polishing pad were acquired from Buehler (Lake Bluff, IL). Ultrapure water with resistivity measuring 18.2 MΩ cm was used for the sample preparation. For synthesis of AgNCs and AgRNPls, ethylene glycol (EG) was acquired from J. T. Baker; sodium hydrogen sulfide (NaHS), hydrochloric acid (HCl), silver trifluoroacetate (AgTFA), sodium borohydride (NaBH₄), silver nitrate (AgNO₃) and 30 wt% hydrogen peroxide (H₂O₂) were obtained from Alfa Aesar; and sodium citrate and PVP of M_w = 55,000 g mol⁻¹ and M_w = 8,000 g mol⁻¹ were purchased from Sigma Aldrich. The 10 μm platinum (Pt) disk working electrode was obtained from BASi (West Lafayette, IN).

AgNCs were synthesized by the polyol method in which silver precursor was reduced by EG using PVP as the capping agent. ⁵⁶ In short, 50 ml EG was added to a 250 ml round-bottom flask equipped with a stirring bar and placed in an oil bath at 150 °C. After the temperature equilibrated (30 - 45 min), EG solutions of 0.6 ml of 3 mM NaHS, 5 ml of 3 mM HCl, 12.5 ml of 0.25 g PVP and 4 ml of 282 mM AgTFA were sequentially added to the reaction flask. Once the peak due to light scattering plasmon resonance (LSPR) in the UV–vis spectrum (Agilent Cary 50) reached ∼430 nm (∼35 min after addition of AgTFA), the reaction was quenched in an ice bath. Upon cooling, the product was collected by adding acetone to the reaction solution at a ratio of 5:1 and centrifuging at 6,000 rcf for 10 min. The resulting pellet was purified twice with H₂O and collected by centrifugation at 20,000 rcf for 10 min and resuspended in 10 ml of H₂O for future use.

Figure 1A depicts a transmission electron microscopy (TEM, JEOL JEM-1011, with an accelerating voltage of 100 kV) image of the resulting nanoparticles, with mostly a cubic shape. The size distribution Fig. 1B was obtained by analyzing the TEM image and is indicative of relatively uniform size of 33.8 ± 2.9 nm. The hydrodynamic diameter of these nanoparticles measured by dynamic light scattering (DLS, Brookhaven ZetaPALS) in aqueous solution was on average of 89.0 nm with the polydispersity index (PDI) of 0.198. The DLS measurements reflect the size of these nanoparticles in aqueous solution and relatively small PDI value suggests that the sample was quite uniform which agrees with the TEM results. The concentration of AgNCs in the aqueous stock solution was measured by flame atomic absorption spectroscopy (AAS, GBC 932) to be 1.5 ppm.

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The AgRNPls were synthesized using a modified method previously reported. ⁵⁷ Briefly, 24.14 ml of ultrapure water, aqueous solutions of silver nitrate (0.05 M, 50 μl), sodium citrate (75 mM, 0.5 ml), PVP (M_w = 8,000 g mol⁻¹, 17.5 mM, 0.1 ml) and H₂O₂ (30 wt%, 30 μl) were subsequently added in a 50 ml round-bottom flask and vigorously stirred at room temperature in air. Sodium borohydride (NaBH₄, 100 mM, 50 μl) was then injected immediately into the reaction mixture. The solution turned to a deep-yellow color at 5 min due to the formation of small silver nanoparticles. The color of the solution changed from yellow to deep purple at 30 min indicating the formation of AgRNPls. The reaction was allowed to proceed for 2 h. The product was collected by centrifuging at 20,000 rcf for 10 min, purified with ultrapure water twice by centrifugation, and redispersed in ultrapure water for further use.

Figure 2 shows the TEM image and UV–vis spectrum of the as-synthesized AgRNPls. The average lateral size of AgRNPls was measured to be 24.1 ± 2.4 nm with the thickness of 3.6 ± 1.5 nm. The UV–vis spectrum of the sample exhibits an extinction peak at 555 nm which agrees well with the LSPR of AgRNPls.

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Single nanoparticle oxidation experiments were performed in either 50 mM KOH or 50 mM KNO₃ electrolyte, using a 10 μm diameter Pt disk working electrode (WE) and a Pt wire counter electrode (CE). (These solutions were not degassed.) A Pt WE was used mainly out of convenience and the ability to achieve reproducible electrochemical responses. However, as is evident in the raw data herein, a Pt microelectrode produces a relatively high background current presumably due to water oxidation. This would not be expected for another material like a carbon fiber or gold that has poorer catalytic properties. Nonetheless, the electrochemical responses from the AgNPs impacts on Pt—both the silver oxidation spikes and the current steps that trails them—are clearly distinguishable over this background and easily analyzed.

Homemade silver/silver chloride (Ag/AgCl) reference electrodes (RE) containing 3 M KCl for studies in KNO₃ solutions and saturated KCl for studies in KOH solutions were equipped with a conductive agar junction to prevent contamination of nanoparticle solutions with chloride. To prepare the agar junction, agar powder was added to 50 mM KNO₃ in an oil bath heated to ∼90 °C and stirred until the consistency began to thicken. The agar/KNO₃ was then drawn into a trimmed glass pasture pipette and left to set at room temperature. Only junctions that resulted in a firm, uniform gel were used.

Prior to all electrochemical experiments, the working electrode was polished using MasterMet2 polish for 2 min, then with only water on a MasterTex polishing pad for 2 min to remove residual polish from the electrode surface. The platinum CE wire was scrubbed with a damp Kimwipe. A total of 200 μl of suspension of approximately 30 pM AgNPs in the electrolyte was prepared in a shortened 1.5 ml Eppendorf microcentrifuge tube, which served as the electrochemical cell and was immediately used.

Prior to each set of nanoparticle experiments with a freshly cleaned microdisk electrode, ten chronoamperometry (CA) experiments in a blank solution of either 50 mM KNO₃ or 50 mM KOH (without nanoparticles) were performed to confirm that no anodic current spikes could be observed from possible contamination of AgNPs that may have carried over from previous experiments. If current spikes were observed, the cleaning procedure and evaluation in blank electrolyte were repeated. Studies with AgNPs were only performed when all CA responses in the blank showed no evidence of particle contamination. Only then could we be certain that anodic current spikes in solutions containing AgNPs were solely from the AgNPs being investigated. Agar junctions and the electrochemical cell were not reused for new experiments to avoid contamination of AgNPs from prior experiments.

CA in suspensions of AgNPs in electrolyte at a microelectrode was performed to obtain the anodic current responses of the individual particles. These experiments were performed using an npi VA-10X voltammetric amplifier (npi electronic GmbH, Germany) paired with an analog-to-digital converter, which used a low-pass 8-pole Bessel filter with a cutoff frequency of 5 kHz, as it has been previously shown to largely preserve the signal shape of a very brief current spike. ⁵⁸ The response of the potentiostat was tested via the procedure previously described by Kanokkanchana et al. ⁵⁸ Briefly, a function generator was connected to a 1 pF capacitor, which was connected to the potentiostat and the voltage was ramped for 0.5, 1, or 2 ms. The recorded signal width and height were measured and compared with the expected values. Sampling rate of 30,000 and 50,000 Hz for the single particle experiments were used in KNO₃ and KOH solutions, respectively.

The instrument was held at 110 mV between all CA experiments. In KNO₃ solution for each group of AgNPs, a CA experiment was stepped from 110 mV (where 1 s of data was collected) to 1500 mV or 1650 mV and held for 10 s. In KOH solution, CA were performed by stepping from 110 mV to 900 mV or 1000 mV and held for 10 s.

All experiments were completed within 15 min of introducing the electrolyte into the nanoparticle suspension to minimize the likelihood of particle agglomeration and aggregation. After data collection, the anodic current responses were analyzed using SignalCounter 8, a software kindly provided by Dario Omanovic, Ruder Boskovice Institute, Zagreb, Croatia.

Cyclic voltammetry of drop-cast particles was performed using a PalmSens4 potentiostat (PS4, Houten, The Netherlands), a 2 mm Pt disk working electrode (CH Instruments Inc., Austin, TX), Pt flag counter electrode, and Ag/AgCl (saturated KCl) reference electrode equipped with a conductive agar junction. A volume of 2 μl of stock particles was drop-cast onto the electrode and dried under a gentle nitrogen flow. Once the electrode was visibly dry, it was immersed into 50 mM of electrolyte (KOH or KCl) and cyclic voltammetry was performed at 25 mV·s⁻¹. To minimize the likelihood of any cathodic activity resulting from the silver particles, the starting potential was set to 0 mV when using the KOH solution and 100 mV when using the KCl solution. (These solutions were not degassed).

CA was performed at both 1500 mV and 1650 mV for suspensions of different AgNPs in 50 mM KNO₃, as oxidation peaks were most consistently obtained for the particles at potentials of 1500 mV and above. Representative single particle anodic current responses obtained for each particle type at 1650 mV are depicted in Fig. 3. There is a sharp current spike upon contact of the particle with the electrode, followed by a step in the baseline of the current that tails off relatively slowly with time. This spike-step response is different than responses observed at smaller overpotentials during oxidation of citrate- and PEG-capped AgNSs, where a step is not observed. ^16,19,20,22 Rather, only a single sharp peak or sometimes multiple sharp peaks for the same particle occur and one electron is transferred per silver atom (n = 1). Assuming a certain value of n for the faradaic process and that no substantial charging occurs, the area under the current spike, which is the charge transferred during the oxidative impact, can be used to directly calculate the number of silver atoms that were oxidized. Furthermore, by assuming a specific particle geometry (e.g. sphere, cube, triangular or round plate), this coulometric measurement can lead to an estimation of the size of that particle. ¹⁹ The presence of the step in the current response complicates this analysis. The spike-step behavior has been observed previously by the group of Zhang and attributed by the group of Willets to the oxidation of Ag to AgO_x nanoclusters, and subsequent water oxidation catalyzed by the newly formed AgO_x nanoclusters. ^43,52 However, a quantitative analysis of the different contributions from silver and water oxidation to the current response has not yet been investigated.

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Here, the immediate spike in current was analyzed separately from the increase in the baseline (or step height). The area under the current spike was attributed to the direct particle oxidation and integrated to determine the charge passed (Table I).

The step height associated with each electrochemical response was attributed to the catalyzed water oxidation on the newly-formed AgO_x nanoclusters. The enhanced water oxidation made possible by these single particle events over the underlying oxidative background of the Pt microelectrode is intriguing. It was observed that larger AgNPs produced bigger average step heights. This trend is consistent with observations made by Zhang et al. ⁴³ who reported a similar trend of particle size with step height and duration of the tail, but using citrate-capped AgNSs on a gold microelectrode in a KNO₃/citrate buffer solution at different pHs. The distributions of step heights that we obtained for citrate- and PVP-capped AgNSs as well as for the PVP-capped AgNCs in 50 mM KNO₃ at the Pt microelectrode are shown in Fig. 4A. The most frequent step height for the citrate-capped 51 nm AgNS and the PVP-capped 34 nm AgNCs was ∼200 pA, which is similar to the average step height (243 pA) at 1100 mV for the 40 nm AgNSs of Zhang et al. Dividing the step height (in Amperes) by the total charge passed within the spike (in Coulombs) produces a ratio (in s⁻¹) that can quantify this water-catalysis/NP-size relationship. The resulting distributions are shown in Fig. 4B. The distribution of step-height for the 73 nm citrate-capped AgNSs narrowed substantially when normalized to the charge passed under the spike. In contrast, the initial narrow distributions of step-height for the 29 nm citrate and PVP-capped AgNSs broadened when normalized. This may be a consequence of the difficulty in reproducibly measuring the smaller step heights for the smaller particles. The PVP-capped AgNCs and AgNSs yielded normalized step-height distributions with a slightly higher step-height-to-spike-area ratio than the citrate-capped AgNPs. More studies would be desirable to substantiate this observation. The oxidation of the AgTNPls did not result in a measurable step above the baseline (likely becuase they contain far less silver than the other AgNPs), and thus, they were not included in this discussion.

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It is likely that the current spikes occurring at large overpotentials represent a combination of the formation of Ag (I), higher ordered silver oxide complexes (AgO_x), ^48,49,59,60 and oxygen (from water oxidation). ^43,52 To perform the quantitative analysis in a consistent way, a line was drawn from the start of the spike where it rose from the current baseline to the spike's other side where it intersected with step. Figure 5 illustrates this line that defines the base of a spike. The area under the spike and above this line is used in discussions here concerning the charge passed to oxidize the silver in the nanoparticle. We name the difference in time where the line intersects the sides of the spike the "peak width" and relate it to the rate at which the charge is transferred during the oxidation.

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The integration of the area under the current spike was used to investigate if the oxidation of silver is the primary reaction occurring during that event. Thus, the charge passed during the current spike is useful for estimating the size of the AgNPs. Equations 1 and 2 were used to estimate the radius (r_ns ) of the AgNSs and the edge length (l_nc ) of the AgNCs, respectively.

$$\begin{eqnarray}&&{r}_{ns}={\left(\displaystyle \frac{3Q{N}_{A}}{4\pi nF{\rho }_{2}}\right)}^{1/3}\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{l}_{nc}={\left(\displaystyle \frac{Q{N}_{A}}{nF{\rho }_{2}}\right)}^{1/3}\end{eqnarray} \tag{ 2 }$$

where Q is the charge passed under the current spike, F is the Faraday constant, n is the number of electrons transferred per Ag atom, N_A is Avogadro's number, and ρ₂ is the number density of silver, 5.86 × 10²⁸ m⁻³. Because several different oxidation states of silver may be generated in KNO₃ solution, the nanoparticle size was calculated with an n value of 1, 10/7, ⁴⁹ 10/6, ⁵⁹ and 2; the results of which are summarized in Table II, along with the sizing results from TEM measurements. Results for the AgTNPl sample, which has a very large distribution of nanoparticle sizes and shapes, are excluded from Table II).

Integration under the current spikes obtained at 1500 mV revealed that most oxidations were incomplete, where only a few particles completely oxidized during the current spike with n = 1. In contrast, the spikes at 1650 mV contained significantly more charge and suggest total oxidation, as well as additional chemistry occurring within the current spike. The populations of each particle type contained a slightly larger charge than anticipated for the formation of Ag(I), indicating the possibility of catalysis of water oxidation ^43,47,52,53 or higher ordered AgO_x ^61,62 contributing to the measured charge.

The TEM-measured length of PVP-AgNCs (34 ± 3 nm) can be compared to the electrochemically-determined lengths obtained for different values of n at 1650 mV: of 36 ± 6 nm, (n = 1) 32 ± 5 nm (n = 10/7), 31 ± 5 nm (n = 11/7), and 28 ± 5 nm (n = 2). An average oxidation state of silver cannot be conclusively determined from making this comparison. When n = 1, a size greater than that obtained by TEM is determined and when n = 2, the size is smaller. Thus, a mixed-valence state complex that includes both Ag(I) and Ag(II) or silver oxynitrate is possible.

Interestingly, the step current is larger for the citrate-capped AgNSs compared to the PVP-capped AgNSs. Because PVP preferentially binds to the (100) facet of silver, ²⁹ it is reasonable to assume that cubes contain a more uniform coating of PVP than the spheres, resulting in an even greater slowing of water oxidation for the cubes. This suggests that the presence of PVP on the particle surface decreases the contribution of water oxidation to the transferred charge, allowing the current spike to be more representative of the nanoparticle size for PVP capped AgNPs than citrate-capped AgNPs and for PVP-capped AgNCs than for PVP-capped AgNSs. Note that oxidation of agglomerated or aggregated nanoparticles could also explain the larger spike charge, yet sizing of the nanoparticles by DLS in the used electrolyte did not indicate that this had occurred under the experimental condition within the duration of the measurement sets. To further rule out aggregation that might take place in electrolyte, which diminishes electrostatic repulsions between particles, Fig. S1 (available online at stacks.iop.org/JES/169/056508/mmedia) of the Supporting Information contains TEM images and normalized UV-Vis spectra of suspensions of PVP-capped AgNCs in water and 50 mM KCl (both before and after electrochemical analysis). The AgNCs are well separated on the TEM images, indicating that their corresponding suspensions ought to be well-dispersed and the peak positions at 417 nm and full widths at half maximum are essentially unchanged.

Electrochemical characterization of PVP-capped AgNSs drop-cast onto an electrode was performed to obtain a preliminary evaluation of electrochemical oxidation of these particles in solutions of KCl and KOH. Figure 6 compares the anodic stripping voltammetry for equal amounts of drop-cast silver nanoparticles in these two electrolytes. In the presence of KCl, there is no evidence of particle oxidation. The cathodic peak near −0.1 V is likely due to the reduction of oxygen. In contrast, there are two anodic stripping peaks for the drop-cast particles in the presence of KOH. Firstly, these conditions appear to provide an environment that allows electrochemical access through the PVP-capping ligand to the underlying AgNPs. Secondly, the CV results suggest multiple forms of oxidized silver for the nanoparticles may form under these conditions depending on the applied potential. Droog and Hjuisman observe two distinctive anodic peaks in a CV response at a polished silver electrode in 1 M NaOH due to the formation of Ag₂O and AgO, respectively. ⁴⁶ They also describe that oxidation of the electrode at 900 mV (vs Ag/AgCl (3 M KCl)) to Ag (II) via chronoamperometry occurs in a multi-step process. We attribute the peaks in Fig. 6 at 380 mV and 700 mV for the drop-cast PVP-capped AgNSs in 50 mM KOH to the formation of Ag₂O and AgO, respectively. In a 50 mM KOH suspension of the PVP-capped AgNPs, however, we observed single particle oxidations at 900 mV. Lower potentials yielded few peaks. Potentials higher than 1000 mV exhibited an oxidative step, similar to the peaks observed in the KNO₃ solution at 1650 mV.

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Figure 7 shows typical anodic current responses for oxidation of individual PVP-capped AgNSs, AgRNPls, and AgNCs in 50 mM KOH at 900 mV. Unlike in 50 mM KNO₃ solution, oxidative spikes for these kinds of particles are readily observable at this potential. Also, there is very little evidence of a step from water oxidation. Consistent with this is the much lower background current at the Pt microelectrode (≤2 nA) than was observed at the large overpotentials in the KNO₃ solution in Fig. 3 (≤20+ nA). Therefore, data analysis of spikes involving PVP-capped AgNPs at 900 mV in 50 mM KOH should be more reproducible in comparison to that from the KNO₃ studies. (Note that a limited number of studies were performed at 1000 mV in 50 mM KOH, but because of the underlying current step, the main focus was on 900 mV).

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The average integrated charge for current spikes in the 50 mM KOH solution at 900 mV was 0.17 ± 0.08 pC for 39 nm PVP-capped AgNSs and 0.24 ± 0.15 pC for 39 nm citrate-capped AgNSs. These values are expected when full oxidation of the Ag atoms in the nanoparticle form Ag(I). Table III summarizes the particle sizes that were calculated using Eqs. 1 and 2 for the radii of AgNSs and side lengths of AgNCs, respectively, and Eq. 3 for the radii of AgRNPls, r_rnpl , where the height, h, was determined from TEM. For all of these calculations, n = 1 was used.

$$\begin{eqnarray}&&{r}_{rnpl}={\left(\displaystyle \frac{Q{N}_{A}}{2\pi hnF{\rho }_{2}}\right)}^{1/2}\end{eqnarray} \tag{ 3 }$$

Equation 4 depicts the chemical reaction that is most likely to occur during the current spike based on the observed results.

$$\begin{eqnarray}&&2{\rm{Ag}}+2{{\rm{OH}}}^{-}\rightleftarrows {{\rm{Ag}}}_{2}{\rm{O}}+{{\rm{H}}}_{2}{\rm{O}}+2{{\rm{e}}}^{-}\end{eqnarray} \tag{ 4 }$$

These results contrast with previous results reported by Hafez et al. ⁵⁴ in which integration of single oxidative impacts of 40 nm AgNSs in alkaline solution resulted in an average 0.34 ± 0.03 pC charge, indicating a 2 e⁻ transfer per Ag atom. Furthermore, CV of AgNSs dropcasted on a gold electrode suggests a transition to Ag(II) at approximately 0.35 V vs a Ag/AgCl wire reference electrode, almost immediately following the initial oxidation to Ag(I) at approximately 0.2 V. The system used by Hafez et al. involved a phosphate buffer, which might explain the differences between their observations and ours. ⁶³ Because the CV response in Fig. 6 for dropcast PVP-AgNPs in KOH exhibits two distinct oxidation peaks, a one-electron transfer during single silver nanoparticle oxidation in 50 mM KOH is plausible.

Compared to the average TEM diameter reported by the manufacturer of 39 ± 4 nm, the electrochemical sizing of the PVP-AgNSs in 50 mM KOH at 900 mV revealed a smaller size of 32 ± 5 nm. Considering that sizing via TEM assumes a perfect sphere, these results are unsurprising. Previous groups have reported that silver nanospheres are generally more icosahedral in shape, and only approximately 60% of the expected charge, assuming a perfect sphere, is actually present in the imperfectly spherical particles. ⁶⁴ Analysis of PVP-AgNCs further indicated that complete oxidation was occurring in 50 mM KOH at 900 mV, as the electrochemically-determined size of 33 ± 11 nm is comparable to the TEM-determined size of 34 ± 3 nm. Because nanocubes possess a more well-defined volume, TEM may provide a better estimation of their metal content than for spheres. Electrochemical analysis of PVP-AgRNPls was also performed in 50 mM KOH. The thickness of the plates based on the TEM images (3.6 ± 1.5 nm) was used in the calculation of their diameters from the electrochemical data. The resulting average diameter obtained from the electrochemical method is within a standard deviation of that from TEM.

The influence of the shape of AgNPs on the individual oxidative response at an electrode will most likely be present in a measurement that reflects its kinetic behavior, where the influence of surface area to volume ratio could play a role. A large difference in this ratio exists for plates when compared to spheres, for example. Several groups have shown that observing the total duration (peak width), t_max , or maximum peak height of single spikes is a powerful tool for analyzing the kinetics of single particle oxidation as long as the peak shape is properly preserved. ^40,42,65 Additionally, the peak duration can also be affected by multi-step oxidation, wherein the particle partially or completely loses and restores contact with the electrode at a very rapid pace, often more rapidly than the sampling interval. ^20,66,67 The instrumentation used to apply the voltage step and acquire the current response was carefully evaluated here (see Experimental section) to avoid missing these events.

Peak widths inherently depend on kinetics and particle size. Kätelhön et al. ⁴⁰ developed a model for the dependence of peak duration for the electrodissolution of nanospheres under kinetically (electron transfer)-limiting and solubility-limiting conditions. Under the "kinetically-limiting" model, the rate is directly proportional to the surface area of the particle, and the rate constant, k, is a function of the applied electrode potential. An expression for t_max was derived to be

$$\begin{eqnarray}&&{t}_{max}=\displaystyle \frac{{r}_{ns}{\rho }_{2}}{k}\end{eqnarray} \tag{ 5 }$$

For the other case, such as at large overpotentials where the release of species from the nanosphere is limited by their solubility and mass-transport away from the particle, the following expression was obtained,

$$\begin{eqnarray}&&{t}_{max}=\displaystyle \frac{{r}_{ns}^{2}{\rho }_{2}}{2\,\mathrm{ln}\left(2\right){N}_{A}D{C}_{max}}\end{eqnarray} \tag{ 6 }$$

where D is the diffusion coefficient, and C_max is the maximum solubility-allowed concentration.

Because the radius of the particle can be calculated from the integrated area under the current spike ¹⁹ (i.e. the charge, Q, passed during oxidation of the nanoparticle), as in Eq. 1, t_max must also depend on Q. Replacing r_ns in Eqs. 5 and 6 with the expression for r_ns in Eq. 1, yields mathematical relationships where t_max is proportional to Q^1/3 and Q^2/3 , respectively. Below, we show that there is a strong correlation between t_max and Q^2/3 , and thus the latter model, not the "kinetically-limiting" one, is supported by our data. The full equation resulting from this substitution in Eq. 6 is

$$\begin{eqnarray}&&{t}_{\max }=\displaystyle \frac{{\left(\tfrac{3}{4\pi }\right)}^{2/3}}{2\,\mathrm{ln}\left(2\right)}\displaystyle \frac{{Q}^{2/3}{\rho }_{2}^{1/3}}{{n}^{2/3}{F}^{2/3}{N}_{A}^{1/3}D{C}_{\max }}\end{eqnarray} \tag{ 7 }$$

Generalizing the relationship for other geometries, where a represents a generic shape-dependent factor, yields Eq. 8,

$$\begin{eqnarray}&&{t}_{\max }=a\times \displaystyle \frac{{Q}^{2/3}{\rho }_{2}^{1/3}}{\,{n}^{2/3}{F}^{2/3}{N}_{A}^{1/3}D\,{C}_{\max }}\end{eqnarray} \tag{ 8 }$$

These equations do not account for shapes that are different than nanospheres, however. How non-spherical particles contact the electrode may further affect the anatomy of the electrochemical response. Their orientation will be determined by random rotation as well as alignment within the strong electric fields in the double layer at the electrode surface. If we consider only random rotation, the cubes and triangular plates most likely approach the electrode with a corner at the forefront. For a perfect cube, there are three basic surface types: a face, an edge, and a corner. The cube has only six orientations in space for the face to be perfectly parallel to a flat electroactive region of the electrode and be the contacting surface. Any rotation will place an edge or a corner into contact with the electrode. For an edge to be in contact, there are only 12 possible orientations and any minute rotation will put the face or corner into electrode contact. However, if the cube is diffusing toward the electrode and a corner is exactly perpendicular to the electrode surface, the corner will remain the primary contacting surface until the cube rotates 35.3° and 54.7° for an edge or a face to contact the electrode, respectively. Similar logic can be applied to the triangular nanoplates. The primary contact for the round nanoplates is expected to begin at the "rim" of the plate. The roughness of the electrode's surface will also play a role in encounters with nanoparticles having different shapes. If the roughness of the electrode surface is on a similar length scale as the nanoparticle, reverse arguments can be made. A cube's face is then more likely than the cube's corner to encounter protruding features at the electrode surface. As discussed further below, we did not observe a measurable effect for our experimental conditions of nanoparticle shape on spike widths for oxidative impacts.

The widths of the anodic spikes obtained at 1650 mV in 50 mM KNO₃ were measured as an indicator of duration of the silver oxidation event for citrate-capped 29 nm, 51 nm, and 73 nm AgNSs, and PVP-capped 29 nm AgNSs, 34 nm AgNCs, and ∼53 nm × ∼10 nm AgTNPls. Table I summarizes the averages of duration for the different particle populations. Plots of average peak width vs the average Q^2/3 and vs the average Q for each particle data set are shown in Fig. 8. The linear correlation (R² ) for the plot for all nanoparticles vs Q^2/3 is 0.9636, a slight improvement compared to the plot vs Q at 0.9188. This supports the hypothesis that the total time required for oxidation is more likely related to Q^2/3 , with no obvious correlation to the particle shape. Figure 8A provides this representation for all PVP-capped AgNPs (red dashed line) in comparison to all citrate-capped AgNSs (gray dashed line).

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A linear model fits peak width vs Q^2/3 for the three different shapes of PVP-capped particles alone and exhibits an even higher degree of correlation (0.9975). This more firmly demonstrates that at 1650 mV, the spike duration is dependent on the total charge passed during oxidation, independent of the particle shape. This means that shape and surface area are less important in the mechanism of AgNP oxidation than the total number of atoms. The linearity also further supports the hypothesis that water oxidation is less likely to occur within the spike of a PVP-capped particle than a citrate-capped particle, resulting in a more reproducible reaction at the electrode surface for those particles. It is proposed that the rapid formation of AgO_x particles and subsequent water oxidation occurring during the ∼1 ms current spike contributes to the deviation from linearity exhibited by the citrate capped AgNPs, as other investigators have suggested, i.e. the pattern of new AgO_x nanocluster formation is poorly controlled ⁵² which means the current produced from water oxidation within the spike would not be consistent from one oxidative impact to another. Because each sample of a given type of particle consists of a distribution of sizes, it is informative to plot the distribution of the peak width for each particle as a function of its own Q. This is done in Fig. 9 for citrate-capped and PVP-capped AgNSs of similar sizes. The capping ligand does not appear to have a significant effect on the overall rate of oxidation, i.e. a charge of x requires a y amount of time to transform all the atoms in the nanoparticle.

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At 1650 mV, the peak duration was 0.9 ± 0.5 ms and 1.3 ± 0.8 ms for the 29 nm PVP-capped AgNSs and 34 nm PVP-capped AgNCs, respectively. At 1500 mV (not listed in the tables), the peak durations were slightly longer, at 1.2 ± 0.7 and 2.4 ± 1.7 ms, respectively. This parallels our previous observations in KCl solutions. ⁴² This work indicated an increase in peak duration with an increase in potential between 500 mV and 660 mV in the presence of KNO₃, attributed to the release of Ag⁺ in the absence of chloride causing repulsion of the particle from the electrode surface resulting in a rapid multi-step oxidation. ⁴² The return to a pattern of decreasing peak duration with increasing potential further supports the hypothesis that silver oxide species are formed rapidly in the 1500–1650 mV potential range, diminishing repulsion of free Ag⁺ from the positively polarized electrode surface, and thereby decreasing the occurrences of multi-step oxidations.

Figure 10 shows a plot of peak width as a function of Q^2/3 for the PVP-capped particles of three different shapes that were analyzed in KOH at 900 mV. A linear model fits the data quite well, with R² = 0.9973. This linear relationship parallels that which was found in the KNO₃ solution at the large overpotentials for populations of different shapes of PVP-capped AgNPs. However, the slope of the line in Fig. 10 for the KOH solution (2.96 (±0.15) × 10⁸ (ms/C^2/3) ), is 1.8x that for the KNO₃ solution (1.61(±0.08) × 10⁸ (ms/C^2/3)), which is due to the increased time for oxidation that occurs in the more alkaline solution. The lower solubility of Ag₂O(s) at the higher pH ⁶⁸ may be one reason for the longer peak duration that is consistent with the model expressed by Eq. 8, but other mechanisms are also possible. The corresponding y-intercept of Fig. 10 (0.47(±0.06) (ms)) in KOH is also higher than that of Fig. 8A (0.35(±0.03) (ms)) in KNO₃ for PVP-capped particles. The meaning of a non-zero intercept and the information contained therein is unknown at this time. In addition, a geometric dependence, which is predicted by Eq. 8, is not supported by our data–peak widths from AgNPs having different shapes fall on the same line. A more quantitative analysis of these plots and development of a more suitable model will require further investigation. Nonetheless, the experimental results suggest that while the rate of AgNP oxidation depends on the chemistry of the solution environment, the rate of different AgNPs in that environment depends only on the amount of silver present in the particle, regardless of the shape or surface area. (The surface area to volume ratios are 0.18, 0.15 and 0.72 for the 34 nm PVP-AgNCs, 39 nm PVP-Ag NSs and 24 nm PVP-AgRNPls, respectively.)

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The effect of the capping ligand on the oxidation rate in the KOH solution was further addressed by considering the distribution of results for two populations of similarly sized nanoparticles, one of PVP- and the other of citrate-capped AgNSs, shown in Fig. 11. Two groupings can be clearly observed, where citrate-capped AgNSs exhibit peak widths that are ~1.7 times those of the PVP-capped AgNSs for a given charge. One possible explanation may involve an expanded structure of PVP in the KOH solution that facilitates the particle oxidation rate. The exact cause of the faster silver oxidation rate of the PVP-capped AgNSs requires further study.

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