The nano-collision method is highly regarded for its convenient operation and excellent sensitivity [1,2]. It can rapidly capture the electrochemical behavior of individual entities in solution, thus finding wide applications in the study of single nanoparticles (NPs) [3-5], nano-bubbles [6-8], and even single molecules [9,10]. As an emerging advanced measurement technique, it offers high temporal and spatial resolution characteristics, enabling direct measurement of the physical structure and chemical activity of single NPs [11-14]. The Compton group pioneered the use of carbon fiber ultramicroelectrodes (UME) to detect the oxidation transient events of single Ag NPs and accurately calculate the particle size through corresponding coulombic integral charges [15,16]. However, due to the weak adsorption interaction between Ag NPs and the detecting UME, multiple consecutive collision events can easily occur when a Ag NP lands on the electrode interface, potentially leading to deviations in the results of particle size analysis [17].

To explore and address this issue, the Long [18], Zhang [19], White [20], and Unwin [21] groups studied the dynamic collision behavior of Ag NPs with different electrode interfaces under weak adsorption conditions. They found that a single transient signal does not necessarily represent the complete oxidation of a single Ag NP (e.g., size-determined degree of oxidation). Among them, the Zhang and White groups discovered that increasing the concentration of sodium citrate could significantly enhance the stability of Ag NPs as well as the electrostatic adsorption between NPs and the electrode interface, thereby increasing the probability of adhesive collisions [19]. Subsequently, the Long group significantly enhanced the adhesion of Ag NPs to Au-UME by in situ generating AgO_x, achieving the complete oxidation of single Ag NPs and distinguishing measurements of mixed-size samples for the first time [22]. The Zhang group improved the adhesion ability of colliding Ag NPs on the electrode interface by modifying Au-UME with ultra-thin polysulfide layers [23]. The Crooks group utilized a positively charged polyelectrolyte to modify Au-UME, effectively strengthening the adsorption between NPs and the electrode interface through electrostatic attraction with the negatively charged metal NPs [24]. These studies demonstrate that regulating the interaction between NPs and electrode interfaces is an effective means to achieve precise analysis of single NPs [25,26].

Traditional carbon fiber UMEs are known for their excellent inertness (sufficient electrochemical window) but poor adhesion to metal NPs [27,28]. The Schuhmann group utilized etched carbon nanocone electrodes (CNCEs) to investigate the nano-collision of single Ag NPs, finding advantages such as low background currents and high diffusion flux of detected moieties [29,30]. Subsequently, we developed heteroatom N-doped CNCEs aiming to enhance the adsorption between metal NPs and electrode interfaces, enabling their non-dynamic electrochemical measurements [31]. However, this electrode preparation method is complex and challenging for quality control. Here, we successfully constructed PC‑CNCEs by surface modification with positively charged poly(diallyldimethylammonium chloride) (PC) on CNCEs. In an alkaline environment, negatively charged Ag NPs collide and adsorb onto positively charged PC‑CNCE surfaces; upon reaching a sufficiently positive potential, the adhered Ag NPs are fully oxidized into AgO NPs (retaining the initial surface negativity) [22,32,33] and anchored to the electrode interface via electrostatic attraction (Fig. 1a). This optimized PC‑CNCE can accurately measure the size distributions of single/mixed-sized Ag NPs (Fig. 1b) and detect ultra-low concentrations of fmol/L Ag NP solutions (Fig. 1c), providing strong technical support for the analysis of metal nanoparticle colloids.

The previous work has detailed the preparation method of carbon nanoelectrodes (CNEs) [34]. Starting from CNEs, geometrically consistent CNCEs can be repeatedly prepared by controlling the HF etching time [29]. Fig. 2a shows that when a negative potential is applied, positively charged PC is electrochemically densely adsorbed on the surface of CNCEs (referred to as PC‑CNCEs). It is found that a mere 2-min electrochemical assisted self-assembly process achieves a monolayer high-density loading of PC on the CNCE surface (evidenced by O₂ detection on its surface as discussed later). The scanning electron microscopy (SEM) image and energy-dispersive X-ray spectroscopy (EDX) imaging in Fig. 2b reveal the surface morphology and element distribution of PC‑CNCE. The depth of the nanocone is ca. 50 µm, the radius of the tip disk is ca. 150 nm, and the half-cone angle is ca. 6°. It is noteworthy that due to the limited surface concentration of PC in the self-assembled monolayer, reliable detection of nitrogen (N) elements was not achieved in the EDX analysis of PC‑CNCE (Fig. S1 in Supporting information). Limited by the spatial resolution of X-ray photoelectron spectroscopy (XPS) technique, characterization of the micro-nanoscale PC‑CNCE surface is challenging. However, XPS characterization of PC-modified carbon film electrodes (large area) reveals the presence of pyrrolic N (399.8 eV) and quaternary N (401.8 eV), with a nitrogen content of 7.51% (Figs. S2-S4 in Supporting information) [35]. These results indirectly indicate the presence of a high-density PC loading on PC‑CNCE. Fig. 2c provides the surface roughness measurement of PC‑CNCE (roughness of ca. 2 nm within a 100 nm square), slightly higher than that of CNCE [31]. This highly smooth electrode surface is believed to be beneficial for adhesive landing during single NP collisions. Fig. 2d illustrates the differences in electrochemical response of different molecular probes on a CNCE and a PC‑CNCE: The FcMeOH molecules (outer-sphere fast electron-transfer) respond similarly on both electrodes, while O₂ molecules (inner-sphere slow electron-transfer) exhibit significant differences. This indicates geometric consistency between the two electrodes and the high-density assembly of PC on the modified electrode (i.e., extensive coverage of active sites for electrocatalytic oxygen reduction reaction). Furthermore, Fig. 2e shows that in typical neutral and alkaline electrolytes, PC‑CNCE exhibits a sufficiently wide electrochemical window similar to CNCE (i.e., adequate chemical inertness).

To validate the proposed single Ag NP collision detection principle, Ag NPs with a concentration of 2 pmol/L and a size of 40 nm (Figs. S6 and S7 in Supporting information) were uniformly dispersed in various electrolytes, and their nano-collision behavior was systematically observed in different electrolytic environments. The diameters of Ag NPs (d_NP) were calculated using Eq. 1:

where Q is the integrated charge from the current transient, M is the atomic molecular mass of Ag (107.9 g/mol), n is the number of electrons transferred per Ag atom (in this work, n = 1 for neutral and n = 2 for alkaline conditions), F is the Faraday constant, ρ is the density of Ag (10.5 × 10⁶ g/m³).

Previous studies have indicated that despite inadequate adsorption between Ag NPs and UMEs, small-sized Ag NPs may undergo nearly complete oxidation, yet the actual collision frequency is considerably lower than anticipated. In neutral electrolyte environments (Fig. 3a; KNO₃, phosphate buffer solution (pH 7.2), KCl), the transient current signals generated by collision events of Ag NPs exhibit similar peak amplitudes, durations, and integrated coulombic charges (Figs. S8 and S9 in Supporting information). However, statistical analysis indicates that Ag NP sizes corresponding to the integrated coulombic charge are smaller than the actual values. This suggests that under neutral conditions, Ag NPs may experience a higher degree of oxidation, with the unoxidized portion escaping from the detection electrode interface. In contrast, in alkaline electrolytes (Fig. 3b; KOH), all relevant characteristic parameters of the transient current signals show significant increases, particularly in collision frequency. The Ag NP sizes calculated from the statistical coulombic charge closely matches the actual values (Fig. S10 in Supporting information). This phenomenon aligns with the mechanism of adhesive collisions between negatively charged Ag NPs and positively charged PC‑CNCE under alkaline conditions.

Moreover, it was observed that under sufficiently positive potentials, Ag NPs were entirely oxidized to AgO NPs (retaining the initial surface negative charge) and firmly adhered to the interface through electrostatic attraction. To further validate this mechanism, the technique of double-potential steps reported by Long et al. were used to detect the oxidation and reduction of single Ag NPs after landing [36]. Fig. 3c illustrates the pulse current-time curves of individual Ag NPs recorded while switching between anodic potential (+600 mV) and cathodic potential (−200 mV), where clear transient events of oxidation and reduction are visible, with the integrated charge of oxidation and reduction transients being equal, and the calculated sizes matching the actual values. This indicates that PC‑CNCE exhibits strong adhesion to both Ag and AgO NPs simultaneously. Furthermore, it was observed that in the same alkaline electrolyte PC‑CNCE was more adept at detecting sufficient nano-collision signals compared to CNCE, suggesting that PC modification is necessary for enhancing the performance of CNCE (Fig. S11 in Supporting information).

Fig. 4a illustrates nano-collision records of Ag NP solutions with particle sizes of 20, 40, and 60 nm, revealing the transient event characteristics of peak shape, peak current, and peak width for Ag NPs of various sizes. Coulombic quantitation analysis yields Ag NP particle sizes concentrated at 21, 43, and 58 nm (Fig. 4b and Fig. S12 in Supporting information), consistent with measurements from transmission electron microscopy (TEM; Fig. 4c) and dynamic light scattering (DLS; Fig. 4d). Compared to previous studies, PC‑CNCE demonstrates excellent accuracy in detecting monodisperse Ag NPs, attributed to significantly enhanced electrostatic attraction facilitating adhesion between reactant Ag and product AgO NPs and the electrode interface. Based on this feature, further exploration for discriminating mixed-size Ag NPs was pursued to meet the analysis demands for polydisperse Ag NPs. Fig. 4e presents nano-collision measurements of Ag NP solution containing mixed sizes of 20, 40, and 60 nm (each at 2 pmol/L). Colored bands depict peak currents clustered at different amplitude levels corresponding to different sizes of Ag NPs. Typical transient events exhibit signal characteristics akin to those observed during single-size measurements. The average particle sizes of Ag NPs derived from these transient event sets are 20, 40, and 59 nm, respectively (Fig. 4f), consistent with results from single-size nano-collision measurements. Furthermore, statistical analysis of peak currents (Fig. 4g) and peak widths (Fig. 4h) from transient event sets reveal characteristic distributions of different-sized Ag NPs. Thus, PC‑CNCE, as an advanced analytical tool, is capable of in situ and accurate discrimination of size distributions of Ag NPs in solution mixtures. Compared to traditional size analysis methods such as SEM, TEM and DLS, this method offers the advantages of low cost, simplicity, and high throughput, promising new breakthroughs in the field of size analysis.

The Stokes-Einstein equation gives the diffusion coefficient of a single NP (D_NP) as Eq. 2 [37]:

where k_B is the Boltzmann constant (1.38 × 10⁻²³ J/K), T is the temperature (293 K), η is the solvent viscosity (8.94 × 10⁻⁴ Pa s), r_NP is the NP radius. Thus, for 40 nm diameter Ag NP, D_NP is 1.19 × 10⁻¹¹ m²/s.

According to previous reports, the theoretical frequency of nanoparticle collisions on a UME, denoted as f_UME, can be expressed as follows (Eq. 3) [11]:

where a is the UME radius, C_NP is the NP concentration, and N_A is Avogadro constant. Hence, for a 12.5 µm radius UME in a solution containing 5 pmol/L Ag NPs, the theoretical collision frequency is 1.7 Hz.

Based on the ratio of the diffusion-limited current on the PC‑CNCE to that on the aforementioned UME, which is 3.37 (not shown in the voltammetric measurements, see Eq. S1 in Supporting information), the theoretical collision frequency on the PC‑CNCE is determined to be 5.7 Hz. Assuming the lowest reasonable nano-collision frequency is 0.05 Hz (i.e., detecting 5 nano-collision signals within 100 s), the minimum detectable concentration of Ag NPs is estimated to be 50 fmol/L. As the concentration decreases from 5 pmol/L to 50 fmol/L, the observed collision frequency of Ag NPs gradually decreases (Fig. 5a). Below a concentration of 50 fmol/L, the credibility of the observed frequency becomes severely compromised due to excessively low observation frequencies. A linear relationship (with a fitting coefficient of 0.96) is obtained between the observed nano-collision frequency and the Ag NP concentration, which is very close to theoretical predictions (Fig. 5b). It is worth emphasizing that the PC‑CNCE demonstrates an extremely low detection limit of approximately 50 fmol/L for measuring Ag NP concentration, which is significantly better than other UMEs. This finding provides strong support for the precise measurement and calibration of ultra-low concentration NP solutions [38-40].

In this study, we overcame the limitations of traditional UMEs in terms of the electrochemical window and electrode interface adhesion. By applying PC for electrochemical high-density self-assembly on surfaces of CNCEs, we effectively prepared functionalized PC‑CNCEs. These modified electrodes exhibited an exceptional electrochemical window, especially suitable for single NP analysis requiring more positive or negative potentials, and significantly enhanced adhesion with colliding Ag NPs. Additionally, leveraging the advantage of high diffusion flux of detected moieties, PC‑CNCEs have been proven to accurately measure single or mixed-size Ag NPs and successfully detect Ag NP solutions at the fmol/L level. This achievement provides an effective technical approach for single NP analysis in complex environments [41].

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Xueqi Zhang: Writing – original draft, Visualization, Methodology, Investigation, Data curation. Han Gao: Writing – review & editing, Methodology, Investigation, Data curation. Jianan Xu: Writing – review & editing, Methodology, Funding acquisition, Data curation. Min Zhou: Writing – original draft, Resources, Methodology, Funding acquisition, Conceptualization.

M. Zhou acknowledges support from the Instrument Developing Project of the Chinese Academy of Sciences (No. YJKYYQ20210003) and Natural Science Foundation of Jilin Province (No. 20210101402JC). J.N. Xu acknowledges support from the National Natural Science Foundation of China (No. 22204159).

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.cclet.2024.110148.