Exploring dynamic interactions of single nanoparticles at interfaces for surface-confined electrochemical behavior and size measurement

With the development of new instruments and methodologies, the highly dynamic behaviors of nanoparticle at the liquid-solid interface have been studied. However, the dynamic nature of the electrochemical behavior of individual nanoparticles on the electrode interface is still poorly understood. Here, we generalize scaling relations to predict nanoparticle-electrode interactions by examining the adsorption energy of nanoparticles at an ultramicroelectrode interface. Based on the theoretical predictions, we investigate the interaction-modulated dynamic electrochemical behaviors for the oxidation of individual Ag nanoparticles. Typically, significantly distinct current traces are observed owing to the adsorption-mediated motion of Ag nanoparticles. Inspired by restraining the stochastic paths of particles in the vicinity of the electrode interface to produce surface-confined current traces, we successfully realize high-resolution size measurements of Ag nanoparticles in mixed-sample systems. This work offers a better understanding of dynamic interactions of nanoparticles at the electrochemical interface and displays highly valuable applications of single-entity electrochemistry.

To estimate the relation between the average coordination number (nc) and particle radius (r), we approximated the AgNPs used in this work as 20 orderly arranged triangular-type (111) facets. 1 The icosahedral structure of AgNPs is shown in Supplementary Figure 1. The lowest-energy structures and the electronic properties of the icosahedrons were investigated based on a generalized gradient approximation.
In single NP collision electrochemical measurements at a C UME, a spike with closely spaced clustering was clearly observed (Fig. 2e). As for the experimentally measured current trace, two situations may occur during the electrochemical process. First, the consecutive multistep collisions attributed to one AgNP electrooxidation event. Second, there is the simultaneous collisions of two or more particles with the electrode and being detected at the same time. To clearly understand the stochastic collision process of individual NPs, we employed Poisson distribution treatment to statistically study the datasets of collision signals. In this theoretical model, we defined an interval time window of two collision events (t) during which only one or zero single NP can collide at the C UME surface with 99 % confidence. That is, there is a 99 % collision probability of up to one AgNP that occur within the time interval. This indicates that the experimentally observed multi-spikes within this time interval widow are clustered as the multi-collisions of the same AgNP with the CUME. Under the assumption of independent collision events, the time interval window can be quantified by the probability theory of a Poisson distribution as follows by equation (1) where P is the probability and is the number of collision events in a certain time interval t. is the average occurrence rate of such events, which can be calculated using a steady-state diffusion flux of the AgNPs to the C UME, (s −1 ) , by equation (2): where CNP is the concentration of AgNPs (37.8 pM), NA is Avogadro's constant (6.02 × 10 23 mol -1 ), and relec is the radius of the C UME (3.5 μm). The diffusion coefficient of an AgNP (DNP) can be determined from the Stokes-Einstein equation, equation (3): where B is the Boltzmann constant (1.38 × 10 -23 J K −1 ), is the absolute temperature (298 K), is the solution viscosity (8.94× 10 -4 P s) and NP is the radius of AgNP (17 nm). The diffusion coefficient of the AgNPs according to equation (3) The second anodic current peak (A2) could be attributed to the formation of a monolayer of Ag2O at the electrode surface on account of the precipitation of [Ag(OH)2]from its supersaturated solution as confirmed by optical studies. 4,7 The rate of anodic dissolution and the formation of [Ag(OH)2]were reduced by the formation of a monolayer of Ag2O 6 , which well correspond to the experimental results. The third peak A3 could be attributed to forming a multilayer of Ag2O by thickening of the basal monolayer 4,5 through the following reaction: The anodic peak A4 is ascribed to the electrooxidation of Ag2O and the formation of AgO through the following reaction: 3 Furthermore, the formation of Ag to AgO directly occurs within the potential range of peak A4: [8][9][10][11] Ag + 2OH − ⟶ AgO + H 2 O + 2e − where 0 is the diffusion coefficient of hydroxyl ions (6.8 × 10 −9 m 2 ‧s -1 ), C0 is the bulk hydroxyl ion concentration, and r0 is the radius of AgNP (17 nm). matom and ρ are the atomic mass and the density of silver, respectively. It can be expected from equation (9) that the maximum current (imax) of single AgNP linearly with the concentration of hydroxyl ion, when t = 0. As shown in Supplementary Table 3, the diffusion-limited maximum current of single AgNPs was obviously beneath the experimentally measured results, when pH 10, demonstrating the decreased current because of the deficiency of hydroxyl ions.
When the pH value further increased, the maximum current of AgNPs with the same size basically unchanged in the sufficient concentration of OH -, evidencing the electrochemical reaction rate-limited processes of AgNPs. While the oxidation time and integrated charge dramatically increased due to the enhanced attractive interaction between the silver oxide and the Au UME. Notably, the integrated charge of individual AgNPs at pH = 11.4 and 12.6 was almost twice that of neutral solution (pH = 7.4), resulting from the 2ecomplete oxidation of Ag to form AgO. 19 Supplementary Note 6. Thickness of AgO film.
By analyzing the integrate charge (q) of the initial spike with different particle sizes (diameter: 10 nm, 18 nm, 34 nm, 55 nm and 65 nm), we obtained the ratio of the average faradaic charge from the initial spike to the total charge (Q) (Supplementary Figure 13). The results illustrate that the correlation between the ratio and the size is approximately exponential relationship and could be well fitted by equation (10): where d is the diameter of AgNPs. In this work, we assume that all NPs are spherical, and the silver oxide layers form from the outside surface to the inside of AgNPs. Therefore, the AgO shell thickness (L) can be calculated through equation (11): where r is the radius of the AgNPs, q(t) is the integrate charge at any time, n is the number of electrons transferred per Ag atom, Ar is the atomic molecular mass of Ag (107.9 g mol -1 ), F is Faraday's constant, and ρ is the density of Ag (10.5×10 6 g m -3 ). According to equation (11) Figure 14). Considering 2eoxidation in alkaline media (pH = 11.4) at the potential of +600 mV vs Ag/AgCl wire, the Faradic current contributing to particle oxidation at any time i(t) during the collision event of an AgNP is given by: where ri is the radius of an AgNP at any time. By integrating the Faraday current, we can obtain the total charge associated with AgNP oxidation: where is the entire oxidation time of an AgNP, r0 is the initial size of AgNPs. According to equation (13), we can calculate r0 and extract the radius of an AgNP at any time: The thickness of AgO can be calculated by L = r0 -ri. As shown in Supplementary Figure 13a  the coverage or probability of these species on the surface would expect to be very low. Therefore, the adsorption of the possible species in the solution on the NP surface and the electrode interface could be ignored in our DFT calculation.

2) Charge effect
Considering the inclusion of electrons on the electrode during the electrochemical processes, we introduced two kind of methods for correcting the charge effects in this DFT calculations.
Firstly, we employed a simple electrode potential-corrected energy method, which is widely used in the electrochemical reaction proposed by Nørskov,20 to investigate the charge influence to adsorption energy.
In addition to the normal adsorption energy obtained by standard DFT calculations, the adsorption energy change introduced by the change in the electrode potential can be realized through shifting the energy level by -neU, where n is the electron transfer number for a given reaction. Considering the same applied potential at +600 mV vs Ag/AgCl used in our electrochemical measurement, the electrode potential effect was normally ignored due to the same correction value.
On this basis, we further estimated the electrode potential dependent effect to the adsorption energy using another charge correction method. 21 In this correction, the electrode surface are assumed to be a planeparallel capacitor, and then corrected the value by the energy of 1/2CU 2 . By adding the different charges on the electrode surface, we calculated the potential changes of the systems by the DFT calculations (Supplementary Table 5). By the slop of q-U relations, we estimated the capacitances of the electrode surfaces (C = ∆q/∆U, Supplementary Figure 19). Clearly, we can see that the capacitances (C) are very similar. To make an equivalent comparison, the electrical potential at the same distance of NP on the electrode surface was used to describe the correction value. Although the electric potential U drops sharply with the increasing distance X according to Poisson Boltzmann equation, the electric potential U is still identical at a certain distance X on the electrode|solution interface. 22 As a result, the correction values of the electric potential (1/2CU 2 ) were usually approached to be similar for the Ag/C, Ag/Au and AgOx/Au systems. For example, at the electric potential of +600 mV vs Ag/AgCl (corresponding to the state that the NP adsorbed on the electrode surface at the distance X = 0), the correction values 1/2CU 2 are 0.918, 0.932 and 0.945 eV for the Ag/C, Ag/Au and AgOx/Au systems, respectively. Therefore, the potential dependent effect was negligible in our simulations due to the similar correction value. Two kinds of methods have both demonstrated that the correction values of the applied potential were usually approached to be similar, and thus charge effects were also ignored in our simulations.

3) Capping effect
In this work, citrate-capped AgNPs were used for the entire electrochemical experiment. We further investigated the capping agent effect of citrate ion to DFT results. According to the obtained results by the first principle DFT calculations, the adsorption energies of the citrate ion on the AgNP and AgO NP surface