Intermittent photocatalytic activity of single CdS nanoparticles

Significance

Semiconductor photocatalysis holds promising keys to address various energy and environmental challenges. While conventional wisdom suggests a continuous photocatalytic reaction under constant light illumination, in the present article we report the discovery of intermittent photocatalytic activity at single CdS nanoparticle level. The observed intermittent photocatalysis is a photochemical consequence of its intrinsic photoexcitation processes. The latter is also responsible for the well-known fluorescence photoblinking of single-semiconductor quantum dots, a photophysical phenomenon that was discovered in the 1990s. The intermittent photocatalysis (a photochemical process) reported here could be an exciting complement of the beautiful picture of semiconductor photophysics and photochemistry, with significant implications in many application fields from clean energy to pollution treatment.

Abstract

Semiconductor photocatalysis holds promising keys to address various energy and environmental challenges. Most studies to date are based on ensemble analysis, which may mask critical photocatalytic kinetics in single nanocatalysts. Here we report a study of imaging photocatalytic hydrogen production of single CdS nanoparticles with a plasmonic microscopy in an in operando manner. Surprisingly, we find that the photocatalytic reaction switches on and off stochastically despite the fact that the illumination is kept constant. The on and off states follow truncated and full-scale power-law distributions in broad time scales spanning 3–4 orders of magnitude, respectively, which can be described with a statistical model involving stochastic reactions rates at multiple active sites. This phenomenon is analogous to fluorescence photoblinking, but the underlying mechanism is different. As individual nanocatalyst represents the elementary photocatalytic platform, the discovery of the intermittent nature of the photocatalysis provides insights into the fundamental photochemistry and photophysics of semiconductor nanomaterials, which is anticipated to substantially benefit broad application fields such as clean energy, pollution treatment, and chemical synthesis.

Photocatalytic H₂ production based on semiconductor nanocatalysts is one of the most promising solutions for the energy crisis via solar-to-chemical energy conversion (1–3). In recent years, single-nanoparticle catalysis, which studies the catalytic activity at single-nanocatalyst level, has received great attention due to its unique strengths to understand the microscopic catalytic kinetics and mechanism (4–6). For semiconductor photocatalysts, single-nanoparticle photocatalysis is particularly interesting because of their comprehensive photophysical processes including photoinduced carrier generation, migration, and recombination. For example, the fluorescence photoblinking of individual semiconductor quantum dots has been a longstanding mystery since its discovery two decades ago (7), and its underlying mechanism remains an open question (8–10). When considering the fact that the photocatalytic activity of semiconductor nanomaterials is intrinsically associated with their photophysical processes, it naturally raises a question of whether the photocatalytic activity is also intermittent at single-nanoparticle level, or is it simply constant or monotonically decaying (due to photocorrosion and photopassivation), as one could intuitively predict.

This question has not been answered by the existing techniques for studying single-nanoparticle catalysis such as single-molecule fluorescence (4–6) and dark-field scattering (11–13). Although it is applicable to image individual dielectric nanoparticles with dark-field microscope (14), most studies so far have been focusing on plasmonic nanomaterials due to their relatively large scattering cross-section and the sensitive spectral dependence on the surrounding environment. Single-molecule fluorescence microscopy is one of the most adopted techniques in this field by monitoring the counts and locations of fluorescence bursts in a fluorogenic reaction, which indicate the formation of fluorescent product molecules (15). Although powerful, fluorescence microscopy requires a fluorogenic model reaction and might compromise the nature of many important reactions where products are nonfluorescent (for example, photocatalytic H₂ production reactions). Besides, because it often takes tens of minutes to accumulate enough counts for statistical analysis, it has been mostly used to study the spatial heterogeneity at a cost of temporal resolution (4–6, 16). A previous study reported the inhibition and reappearance of photocatalytic activity of single Sb-doped TiO₂ nanorods as a result of the absorption and desorption of surface adsorbates (17). Analysis of the burst correlation times have also suggested the activity fluctuations of individual gold (5) and platinum (18) nanoparticles due to the dynamic surface restructuring of metal atoms. However, intermittent photochemical activity (i.e., stochastic blinking between ON and OFF states) of single semiconductor nanoparticles that is regulated by its intrinsic photophysical processes has been largely unexplored.

Here we use a surface plasmon resonance microscopy (SPRM) to continuously monitor the H₂ production rate of individual CdS nanoparticles in an in operando manner, and report the discovery of intermittent photocatalytic activity of single CdS nanocatalyst. SPRM is an optical microscopy that we recently developed to image the local refractive index (RI) distribution with a temporal resolution up to microseconds and a spatial resolution around the diffraction limit (19–21). SPRM is capable of monitoring local H₂ concentration due to the large difference in the RI between H₂O and H₂. Instead of being constant or monotonically changing, it was surprisingly found that the photoinduced H₂ production rate of single CdS nanocatalyst switched between active (ON) and inactive (OFF) states frequently and alternatively. While OFF event follows a full-scale power-law distribution, ON event exhibits a truncated power-law distribution. The location of truncation depends on the maximum interfacial electron transfer rate (k_et) occurring at the single nanoparticle. The remarkable intermittency of photocatalysis and its statistical characteristics are well modeled by hypothesizing multiple reaction sites with stochastically distributed k_et on each site.

We first demonstrated the principle of SPRM for monitoring the photocatalytic hydrogen production at individual CdS nanoparticles (Fig. 1A). These CdS nanoparticles had a diameter of ∼100 nm, which were synthesized and characterized according to the procedures described in SI Appendix, Figs. S1–S3. Subsequently, they were deposited onto a gold-coated glass coverslip for SPRM imaging (SI Appendix, Figs. S2 and S3). The gold film was passivated by a self-assembled monolayer of HS–(CH₂)₁₇–CH₃ molecules before CdS deposition, to block the possible electron transfer between CdS nanoparticles and gold film (22, 23) (SI Appendix, Figs. S4 and S5). The root-mean-square roughness of gold film was determined to be ∼0.4 nm, which showed negligible interference to the surface plasmon polaritons (24). The coverage of the nanoparticles was tuned to be sufficiently low to minimize interference in the photocatalytic reactions between adjacent nanoparticles. Light with wavelength of 680 nm (2.5 mW·mm⁻²) was used to excite planar surface plasmons on the gold film with an objective-based total internal reflection configuration (19–21). Light reflected from the gold film was collected via the same objective and directed into a camera to form an SPRM image. A typical SPRM image of seven CdS nanoparticles is shown in Fig. 1A, which reveals each nanoparticle as a bright spot with a long parabolic tail. This parabolic tail is due to scattering of the surface plasmonic waves by the nanoparticle that has a diameter smaller than the diffraction limit (21, 25). The CdS nanoparticle-covered gold film was illuminated from the top with a blue light (λ < 500 nm, 14 mW·mm⁻²) to generate photocatalytic reactions at the CdS nanoparticles. Hydrogen produced by the reaction reduced the local RI surrounding each CdS nanoparticle, which was monitored continuously with SPRM. The change of the local RI over time was determined from the change in the average SPRM intensity of the tail region for each nanoparticle.

Fig. 1.

(A) Schematic illustration of SPRM setup for monitoring the H₂ production rate on single CdS NPs. Upon the illumination of blue light, photoexcited electrons and holes are separated and move to different sites to reduce protons to generate H₂ and to oxidize S²⁻ to produce S₂²⁻, respectively, accompanying with nonradiative recombination. SPRM images the time trace of local RI around each single CdS NP and background region simultaneously during the illumination of blue light, from which the photocatalytic activity of single CdS NP is revealed from the large reduction in the local RI of surrounding medium caused by the hydrogen production. (Scale bar: 10 μm.) (B, Top) RI trajectories of NP1, NP2, and a background region during a continuous illumination of 2 h are displayed as red, blue, and black curves, respectively. (Bottom) Zoom-in trajectory of NP2 during 3,460th and 3,750th reveals alternatively switching RI between a high value (photocatalysis OFF state) and a low value (photocatalysis ON state). (C) Statistical analysis reveals a truncated and full-range power-law distribution of ON and OFF state duration time, respectively. The ON and OFF probability densities of NP1 (red curves) are offset up by two scale factors for clarity.

Surprisingly, we found that the photocatalytic production of hydrogen at each of seven CdS nanoparticles switched on and off stochastically even though the light illumination was constant. Two representative time traces showing this intermittent nature of photocatalytic reactions are plotted in Fig. 1B (red and blue curves) and more examples are given in SI Appendix, Fig. S6. Zoom-in of the time trace for one CdS nanoparticle (NP2 from 3,460th to 3,750th s) reveals that the photocatalytic reaction was switched on and stayed ON for a certain time interval, and then switched off and stayed OFF for another time interval (see also Movie S1). As a control, the time trace of the local RI from a region where there was no CdS nanoparticle was also measured (black curve in Fig. 1B), which showed a flat line with no characteristic switching events. Note that the time traces for different CdS nanoparticles are uncorrelated, so ensemble average of a large number of nanoparticles would have washed out such intermittency. This observation underscores the need of single-nanoparticle studies to observe the intrinsic kinetics of the photocatalytic reactions. Similar intermittency was also observed on CdS nanoparticles with different crystal structures and shapes (nanorods), indicating that the intermittent nature of photocatalytic activity was a general phenomenon for various CdS nanomaterials regardless of their crystal structure and morphology (SI Appendix, Fig. S7). Please note that ∼80% of over 300 individual CdS nanoparticles exhibited similar intermittent behaviors in tens of independent experiments within a typical recording time of 3 h.

The time durations of ON and OFF states of the photocatalytic reactions are marked by red and black dots in Fig. 1B (Bottom), respectively, showing stochastic distributions over time scales spanning from 0.16 s (the temporal resolution in the present work) to hundreds of seconds. Statistical analysis (26) of the individual switching events for different nanoparticles shows that the OFF state follows a full-scale power-law distribution, and the ON state can be fitted with a truncated power-law distribution (solid curves in Fig. 1C and SI Appendix, Figs. S6 and S8). The two distributions can be expressed as

$$p\left(t_{\text{off}}\right)=C\cdot {t_{\text{off}}}^{-{\alpha }_{o\text{ff}}}$$

$$p\left(t_{\text{on}}\right)=\{\begin{array}{ll}C\cdot {\left(k_{\text{cutoff}}{t}_{\text{on}}\right)}^{-{\alpha }_{\text{on}}}& \text{for}\hspace{0.17em}{t}_{\text{on}}\ge 1\text{/}{k}_{\text{cutoff}}\\ C\cdot \exp \left(-{\alpha }_{\text{on}}\left(k_{\text{cutoff}}{t}_{\text{on}}-1\right)\right)& \text{for}\hspace{0.17em}{t}_{\text{on}}<1\text{/}{k}_{\text{cutoff}}\end{array},$$

respectively, where p(t_on) is the probability density of a certain on-event duration time (t_on), C is a constant, α_on is the power-law coefficient of ON events, and k_cutoff is the truncation factor. Note that the above functions are widely used to analyze fluorescence photoblinking (26) and many other stochastic processes in physical (27) and social sciences (28). A truncated power-law distribution indicates any process faster than k_cutoff is prohibited while processes slower than k_cutoff are stochastically distributed (27).

Control experiments were performed to show that the measured switching of the local RI was indeed due to the intermittent hydrogen production. First, the local RI did not change when the nanoparticles were not illuminated with light, or illuminated with red light (λ > 600 nm, SI Appendix, Fig. S9). Second, when replacing S²⁻/SO₃²⁻ with HPO₄²⁻ in the solution, no switching in the local RI was detected (SI Appendix, Fig. S9), which was expected because S²⁻/SO₃²⁻ was known to facilitate photocatalytic hydrogen production (3, 29). These results also demonstrated that the photothermal effect was not responsible for the intermittent photocatalytic activity because it would be independent of electrolytes. The illumination of blue light was found to increase the local temperature around single nanoparticles by 0.1 °C as determined by a photothermal conversion approach (30) (SI Appendix, Fig. S10), suggesting a small thermal disturbance to the local reaction. Third, the position of individual CdS nanoparticles did not move at all over the entire experiment (hundreds of switching events in 2 h), indicating Brownian motion of the nanoparticle was negligible. Fourth, CdS nanoparticles exhibited excellent photostability in the presence of S²⁻/SO₃²⁻ without the sign of photocorrosion (SI Appendix, Fig. S11). Besides, an irreversible photocorrosion process was anticipated to display a monotonic change in the SPR intensity (SI Appendix, Fig. S9) rather than switching between two states. Finally, the RI changes due to interfacial processes, such as the adsorption and desorption of ions and small molecules, were too small to be detected by SPRM.

We have discussed that photocatalytic production of hydrogen at a CdS nanoparticle leads to a decrease in the local RI. However, the produced hydrogen may either dissolve in the solution, or form nanosized hydrogen bubbles at the nanoparticle. If the former is true, we expect that the dissolved hydrogen molecules diffuse away to the surrounding environment with a rather large diffusion distance (200 μm) over 10 s (typical duration of the ON state) because of the large diffusion coefficient of hydrogen molecules in water (4.5 × 10⁻⁹ m²/s). We measured the spatial profile of RI drop and found that it was confined within a region defined by the diffraction limit, much smaller than the diffusion distance (Fig. 2A). This result indicated the formation of hydrogen nanobubbles with size below the diffraction limit. We further confirmed this conclusion with a three-dimensional modeling (with COMSOL; SI Appendix, Fig. S13). The model simulation demonstrated that the generation of a 66-nm nanobubble attaching to the CdS nanoparticle could produce an SPRM image consistent with the experimental observation (SI Appendix, Fig. S14). The present setup allows for the detection of a nanobubble as small as 30 nm. From the slope of the accumulative profile of SPRM intensity trajectories of all seven CdS nanoparticles, one can estimate the single-nanoparticle reaction rate to be 1.1∼7.0 × 10⁴ H₂ molecules per second per nanoparticle (Fig. 3A), corresponding to a single-nanoparticle apparent quantum yield of 0.01∼0.06% (SI Appendix, Fig. S14). This value is close to the reaction rate (7.4 × 10⁴ H₂ molecules per second per nanoparticle) we determined for ensemble catalysts with traditional techniques (SI Appendix, Fig. S16). Most importantly, it was found that an induction time of 800∼1,900 s was required to observe the decrease in SPR intensity after the blue-light illumination (Fig. 3B). During the induction time, the local reaction solution had to be saturated by photogenerated H₂ molecules to facilitate the formation of H₂ bubbles. Presaturation of the reaction solution with H₂, or increasing the surface density of CdS nanoparticles, was able to significantly shorten the induction time (Fig. 3C), strongly supporting that H₂ nanobubbles were responsible for the decrease in SPR intensity. The generation of H₂ molecules was further supported by analyzing the photochemical reaction products with gas chromatography (SI Appendix, Fig. S12).

Fig. 2.

(A) Experimental SPRM image during hydrogen production (Center) reveals that the local RI reduction is confined in a volume smaller than the optical diffraction limit. This observation supports the nanobubble hypothesis by comparing with the simulated SPRM image for nanobubble (Left) or homogeneous diffusion hypothesis (Right). (Scale bar: 1 μm.) (Lower) Horizontal profiles of three images crossing the center are displayed (red: nanobubble, blue: experimental, black: supersaturation). (B) RI trajectory of a single CdS NP during electrochemical reduced H₂ evolution at a potential of −400 mV vs. Ag/Ag₂S. Each cycle, consisting of a gradual RI decrease and a rapid RI recovery, represents the growth and eclipse of a nanosized H₂ bubble. (C) The bubble lifetime follows Gaussian distribution rather than a power-law distribution. (D) The bubble lifetime becomes shorter when electrode potential scans toward more negative, indicating a faster H₂ evolution rate at higher overpotential. The lifetime vs. potential is fitted with a single-rate exponential curve.

Fig. 3.

(A) Time traces of the accumulated amount of hydrogen production from each single CdS NP and the averaged hydrogen production from these seven NPs. (B) Representative SPR intensity curves for a single CdS NP in the reaction solution presaturated with N₂ (black curve) and H₂ (red curve), respectively. (C) The induction time was significantly reduced when presaturating the reaction solution with H₂ (Left Bar), or when increasing the surface density of CdS NPs (Right Bar). Over 30 NPs were analyzed under each condition.

We believe that the photocatalytic reaction led to the generation of hydrogen nanobubbles with sizes balanced by production of hydrogen at the nanoparticle and dissolution of hydrogen into the surrounding solution. Once the photocatalytic activity stopped, the nanobubble disappeared rapidly due to the high Laplace pressure (31, 32), i.e., the hydrogen molecules dissolved in the solution and diffused away from the nanoparticles, leading to the recovery of the local RI. The stop of photocatalytic activity could not be attributed to the surface blockade by nanobubble. If the blockade hypothesis is true, the nanobubbles would immediately regrow once they were collapsed. That is because the collapse of nanobubble restarts the photocatalytic activity and leads to the immediate regrowth of nanobubble if the hydrogen production rate is constant. This is opposite to the experimental results where long OFF events (no nanobubble) lasting up to hundreds to thousands of seconds were often observed.

Despite the nanobubble formation, we show below that the observed ON and OFF switching events reflected intrinsic intermittent nature of the photocatalytic activity, rather than the formation and dissolution kinetics of the nanobubbles, by comparing results between photocatalytic and electrochemical hydrogen reduction. The electrochemical measurement was performed under the same condition as the photocatalytic experiment except that an applied electrochemical potential, instead of blue light, was used to trigger hydrogen production (SI Appendix, Fig. S15). An electrochemical reduction potential of −400 mV vs. Ag/Ag₂S also leads to the formation of nanobubbles at the locations of individual CdS nanoparticles (Fig. 2B), but the distribution of bubble lifetimes follows a Gaussian distribution (Fig. 2C), which is in contrast to the power-law distribution for photocatalysis (Fig. 1B). For fair comparison, the potential was selected such that the bubble growth rate (nanobubble lifetime ranging from 5 to 40 s) in the electrochemical reaction was similar to and sometimes much slower than that in the photocatalytic reaction (lifetime ranging from 1 to 10 s). Another sharp difference between the electrochemical reduction and photocatalytic reactions is that the OFF state in the former does not have a finite duration (Fig. 2B), even with lower reaction rate (slower kinetics; SI Appendix, Fig. S15B). In other words, once a nanobubble disappears, a new nanobubble starts to form immediately, indicating the electrochemical production of hydrogen never stops. In contrast, in the case of photocatalytic production of hydrogen, it stochastically stays off for a time interval ranging from subsecond to thousands of seconds before it switches on again. Increasing the overpotential simply reduces the average bubble lifetime but does not change the Gaussian distribution and the lack of time duration for OFF states, as shown in Fig. 2D and Movie S2. The exponential dependence of the ON-state duration time with the overpotential (Fig. 2D, Inset) demonstrates that the bubble lifetime is regulated by hydrogen production rate.

We further studied the correlation between k_cutoff and the bulk hydrogen production rate by varying the concentration of S²⁻ ([S²⁻]) and the power density of blue-light illumination; both are confirmed to be relevant to the hydrogen production rate (SI Appendix, Fig. S16) (3). When [S²⁻] was reduced from 500 to 200 mM, intermittent photocatalysis remained but the ON-state duration increased significantly (SI Appendix, Fig. S17). Statistical analysis of the ON-state duration reveals a sixfold decrease in k_cutoff associated with the reduction of [S²⁻] and a significant shift of the truncation toward a longer time scale (Fig. 4A). A similar analysis shows that k_cutoff decreases with illumination power density (Fig. 4B). Plotting k_cutoff vs. hydrogen production rate shows a linear relationship (Fig. 4C), suggesting that k_cutoff reflects the photochemical reaction rate of single CdS nanoparticles. We also examined the effect of [S²⁻] and illumination power density on the OFF-state duration distribution, and full-scale power-law distributions remained in all cases (SI Appendix, Fig. S18).

Fig. 4.

(A) Probability density of ON events in the presence of 500 (magenta) and 500 (black) mM Na₂S. (B) Probability density of ON events under the blue-light power density of 14 (blue), 9 (magenta), and 6 (black) mW·mm⁻². (C) Correlation between k_cutoff (extracted from the probability density curves in A and B) and bulk H₂ production rate (measured from conventional photocatalysis experiment using ensemble materials). (D) Calculated truncated power-law distributions by adjusting the maximum rate k_cutoff in a multiple-rate stochastic process.

In addition to the ON/OFF event time, the growth rate of nanobubble is also able to quantify the H₂ generation rate associated with single nanoparticles (SI Appendix, Fig. S17B). If we compare the growth rates of nanobubble in different ON events under the same conditions, they are also stochastic and vary by up to 10× (SI Appendix, Fig. S17C). When increasing the apparent photochemical reaction rate, growth rates of nanobubble also increase. We chose ON/OFF event time instead of growth rate in power-law analysis, because the reliable curve fitting for growth rate required significantly more data points and it tended to induce uncertainties when the signal/noise ratio was not good enough.

A similar power-law distribution has been observed in fluorescence photoblinking of single quantum dot, which has been attributed to photoionization and multiple rates during carrier recombination (8, 10). These processes may also contribute to the intermittent photocatalytic activity of single CdS nanoparticles observed here because of the intrinsic connection between the photochemical reactions and the photophysical processes. For example, previous studies have suggested that the interfacial electron transfer activity of semiconductor nanoparticles was modulated by the fluorescence photoblinking dynamics (33). The absence of power-law distribution in electrochemical reduction of hydrogen further supports this point, as photophysical processes are solely involved in the photocatalysis but not in the electrochemical reduction. When looking at the photochemical reactions at single CdS nanoparticles, multiple reaction sites could exist simultaneously on the nanoparticle surface, resulting in a stochastic distribution of the reaction energy barriers at each active site due to the heterogeneous coordination states and dangling bonds (34, 35). Therefore, the photophysical processes as well as multiple interfacial electron transfer rates are believed to be the key for the observed power-law distribution. While general power-law distributions of ON/OFF events are attributed to the intermittent photophysical processes, the truncation (k_cutoff) is a consequence of the interfacial photochemical reactions, because such truncation is a unique distribution that has been rarely observed in fluorescence photoblinking. Therefore, it reflects the reaction rate at the single-nanoparticle level (Fig. 4C). The existence of multiple reaction sites was also supported by two experimental observations. First, multiple nanobubble generation sites were often found for CdS nanorods (SI Appendix, Fig. S7 E–H). Second, multiple states rather than two states existed on the projection of SPR trajectory curves on the intensity axes (SI Appendix, Fig. S20 and Fig. 5). We attributed this feature to the different locations (vertical distances to the substrate) and different sizes of the nanobubbles as a result of the multiple reactive sites. SPRM signal of a bubble sensitively relies on the vertical distance and the size. Note that the varied SPRM intensity does not affect the power-law analysis which relies on the duration time of ON/OFF events, rather than its intensity.

Fig. 5.

Zoom-in of the projection histograms of the corresponding SPR intensity of NP1 (A) and NP2 (B) reveal the existence of multiple states (multiple ON and single OFF) rather than two states (single ON and single OFF).

To further support the above analysis, we simulated the probability density of ON-state durations with a stochastic model (27, 28) involving multiple active sites, each with a reaction rate (SI Appendix, Fig. S19). If assuming 100 active sites with rates uniformly distributed from 1 × 10⁻⁴ to 30 s⁻¹, the calculated probability density displays a full-scale power-law distribution ranging from 1,000 to 0.5 second (Fig. 4D, blue dots). In this case, k_cutoff is 30 s⁻¹. However, if reducing k_cutoff to 0.3 and 0.03 s⁻¹, truncated power-law distributions are predicted by the model (red and black dots), which reproduces key features of the experiments (Fig. 4 A and B). The truncation point shifts toward longer time scale for the smaller k_cutoff, accompanying with lower probability densities in the plateau region and constant slopes in the linear region. The agreement between the multiple reaction rates model and the experimental data supports the hypothesis that multiple photochemical reaction rates stochastically distributed in a certain range with a maximal rate are responsible for the truncated power-law distribution of ON-state durations observed on single CdS nanoparticles. The active sites at atomic scale are attributed to the unsaturated Cd atoms with dangling bonds, as well as some big curvatures in the irregular CdS nanoparticles (contacts, edges, and caves). Further efforts are certainly required to comprehensively understand the structural basis of these active sites. Combining the SPRM technique proposed here and high-resolution electron microscopy is a promising way to achieve this goal in the future.

In summary, we report the intermittent photocatalytic activity of single CdS nanoparticles, and propose a multiple reaction sites model for the full-scale and truncated power-law distribution of ON and OFF events, respectively. As photoblinking is a general phenomenon for various types of semiconductor nanomaterials, the discovery of the intermittent photocatalysis opens a field of semiconductor-based photocatalysis and paves the way toward the rational design and discovery of photocatalysts with excellent efficiency by studying the photocatalysis at single-nanocatalyst level. From the photophysical point of view, the present work also connects the single-nanoparticle photophysics and photochemistry, offering another opportunity to clarify the mechanistic origin of the mysterious photoblinking of single-semiconductor nanomaterials.

Materials and Methods

Experimental Setups, Synthesis, and Characterizations of the CdS Nanoparticles.

The plasmonic microscopy setup was built on an inverted total internal reflection fluorescence microscope using gold-film-coated glass coverslip as the sensor chip. CdS nanoparticles (NPs) were synthesized according to the previous work (29). The resulting CdS NPs were uncapped (or capped with S²⁻) to facilitate the photochemical reactions. CdS NPs with the cubic-phase were synthesized following a similar protocol as mentioned above, by switching the volume of Na₂S and Cd(OAc)₂. The CdS nanorods were synthesized with a solvent thermal method. Dynamic light scattering, diffuse reflection UV-vis spectrum, X-ray powder diffraction, X-ray photoelectron spectroscopy, etc. were used to characterize CdS NPs. Please see SI Appendix for more details. All of the photochemical and electrochemical reactions were performed in aqueous solutions.

Power-Law Analysis.

The power-law analysis of the SPRM trajectory curve was achieved with a self-developed MATLAB code using a threshold-based algorithm, which has been routinely adopted to analyze the blinking fluorescence trajectory. The ON/OFF event was differentiated by the amount of intensity fluctuation. A rapid decrease in the SPRM intensity (higher than a user-defined threshold) represents the beginning of an ON state, and a sharp increase represents the end of an ON state (and therefore the beginning of an OFF state). A detailed description on the MATLAB program is provided in SI Appendix, section 1.4. After collecting the duration times for a series of ON/OFF events, the probability density of each duration time was calculated with the following equation:

$$P\left({\tau }_i\right)=\frac{2\times \frac{N_{\tau ,i}}{N_{\text{total}}}}{\left({\tau }_{i+1}-{\tau }_i\right)+\left({\tau }_i-{\tau }_{i-1}\right)},$$

where P(τ_i) is the probability density of ON (OFF) event with duration time of τ_i, N_τ,i is the number of ON (OFF) event with duration time of τ_i, N_total is the total number of ON (OFF) events. The unit of P(τ_i) is s⁻¹.