Elementary Charge Characterization of Single Quantum Dots in Solution

Abstract

Measuring quantum dot properties at the single-particle level in their native liquid environment provides a powerful means of deepening our understanding of quantum dot systems and advancing their applications. In this work, we successfully measure the electrical charge of individual CdSe/CdS core/shell quantum dots, with diameters of 15 and 25 nm, in a nonpolar liquid, with precision at the elementary charge level. This is accomplished by combining laser scanning microscopy with high-field electrophoresis, where the observed electrophoretic mobilities show clear clustering around values corresponding to discrete charge states. A thermodynamic charging model captures the dominant features of the probability distribution and size dependence of the observed charges. This research opens the possibility to study charge-related optical and electronic phenomena at the single-quantum-dot level in solution.

Colloidal quantum dots (QDs) are used in a wide range of applications due to their exceptional properties such as size-tunable emission, high photoluminescence quantum yield, broad absorption spectra, and narrow emission line widths. , In recent years, characterization and manipulation of the surface charge of QDs has gained significant attention due to the key role played by electric charge in the QD performance. Surface charge is not only responsible for blinking and spectral shifts in the QD emission spectrum, it also impacts the QD’s overall electronic structure, optical stability and emission efficiency, all of which may affect device performance. − It also plays a critical role in determining colloidal stability by means of electrostatic repulsion, , in cellular uptake and other interactions with the surrounding environment, , and in applications relying on electrophoretic deposition of QDs such as LEDs, and solar cells. , Overall, these surface charge effects can significantly influence both the optical behavior and the suitability of QDs for specific applications in optoelectronics, bioimaging, or photovoltaics.

Most studies of QD properties are performed on the ensemble level, e.g., based on absorption or photoluminescence spectroscopy or dynamic light scattering (DLS) analysis, while studies carried out on single QDs typically rely on particles deposited on a substrate. − Ensemble-averaged results intrinsically hide important information about the heterogeneity in terms of size, shape, or charge, which may make it difficult to correlate optical properties to electric charge and size. The presence of a substrate may significantly alter measured QD properties. This highlights the need for characterization of the QD charge and other properties on a particle-to-particle basis in the native liquid environment.

Several techniques have been developed for analyzing single QDs in solution, such as particle tracking, − optical trapping, or electrical trapping. In recent years, considerable progress has been made in the high-precision charge measurements of single nanoparticles. Charge measurements with a precision better than one elementary charge have been carried out on microparticles in nonpolar liquid, as well as on 100 nm particles in water. Recently, elementary charge characterization (limited to absolute values) was also performed on 44 nm silver nanoparticles in nonpolar liquid. However, this approach has not yet been applied to QDs, despite their relevance for the abovementioned applications. The main challenges originate from their small size, which leads to faster Brownian motion, and from their lower photon flux, both of which make single-QD electrophoresis technically difficult.

In this work, we successfully measured the number of elementary charges on individual QDs in their native liquid environment, achieving the smallest particle sizes for which this method has yet been demonstrated. To overcome the challenges posed by the fast Brownian motion and low photon flux of single QDs, we combined fast, sensitive laser scanning microscopy with high-field electrophoresis, enabling direct observation of the electrophoretic motion of single QDs. Whereas Strubbe et al. used bright field microscopy, Beunis et al. and Ussembayev et al. used optical tweezing electrophoresis, and Pan et al. used scattering, our study is the first to employ fluorescence-based detection. By analyzing the phase of the electrophoretic motion, we can determine the sign of the electric charge. The resulting electrophoretic mobility histograms established for 15 and 25 nm CdSe/CdS QDs exhibit distinct peaks corresponding to discrete charge states. These charge histograms and their dependence on QD size are analyzed by using a thermodynamic charging model that captures the dominant charging behavior. Additionally, this method also enables determination of the ensemble-averaged hydrodynamic QD size. In future research, this method opens up the possibility to study the correlation between external charge and size on the emission spectrum and other optical properties at the single-QD level and in solution.

To investigate individual QDs in their native liquid environment, we developed a laser scanning microscope (Figure a). A 450 nm laser beam passes through a half wave plate (HWP) which controls the power influx into the setup and through two orthogonal acousto-optic deflectors (AODs) to scan a regular grid in a zigzag row-wise fashion (i.e., scanning each row in alternating directions) in the bulk of the liquid (Figure b). Whenever a QD appears within the field of view and is sufficiently in focus, it gets excited and emits photons with a longer wavelength. These photons are captured by the same objective and are transmitted via a dichroic mirror and emission filter to a single-photon counting module (SPCM) (90% of the photons) and a CMOS camera (10% of the photons). Here, CdSe/CdS QDs with diameters of 15 and 25 nm in the nonpolar liquid dodecane are investigated (detailed synthesis of both QD types is reported in ref ). To avoid background noise from neighboring QDs, the QD dispersion is diluted to 3.5 pM for 25 nm QDs and 15.7 pM for 15 nm QDs, such that typically only one QD is present in the field of view. To avoid destabilization of the colloidal QD suspension by loss of ligands under such large dilution, 0.005 wt % polyisobutylene succinic anhydride (PIBSA) is added. The QD solution is placed between two gold plated electrodes separated by 104 μm for 25 nm QDs and 131 μm for 15 nm QDs (Figure a). Due to the applied AC voltage with amplitude V = 50 V and frequency f = 30 Hz, the QDs undergo electrophoresis along the direction of applied field (i.e., the x-direction). From the number of photons collected by the SPCM at each position of the scanned grid (16 × 16), images are produced at a frame rate of 3300 frames per second (Figure c). By integrating the intensity profile of each acquired image along the x-direction and putting these in a time series, trajectories of single particles are obtained. These trajectories are the result of a combination of Brownian motion and a field-induced oscillation that depends on the particle charge. Figure shows a selection of five trajectories for the 25 nm CdSe/CdS QDs. Figure a gives the example of a QD carrying a zero net charge, demonstrating characteristic Brownian motion without an oscillatory component. Figure b,c illustrates the oscillatory motion of singly charged QDs carrying, respectively, +e and −e, where e is the elementary charge. We observe a +90° phase shift between the particle oscillation and the applied electric field (dashed black curve) for a positively charged particle and a −90° phase shift for a negatively charged particle. This is expected since the component of the particle velocity v(t) = μE ₀ sin­(ωt) induced by the field E(t) = E ₀ sin­(ωt) is in-phase with the field for a positively charged particle (and in counter-phase for a negatively charged particle), considering that the corresponding particle position $x(t)=\frac{\mu E_0}{\omega }\cos (\omega t)$ is shifted +90° with respect to this velocity.

1.

Schematic illustration of laser scanning microscopy combined with electrophoresis for single QD analysis. (a) Overview of excitation and emission pathways, highlighting the microfluidic device equipped with gold-plated electrodes used for electrophoresis. (b) Zigzag row-wise laser scanning in the plane of focus (in reality 16 × 16 pixels). (c) Raw image of a single 25 nm CdSe/CdS QD in solution.

2.

Measured trajectories of single 25 nm CdSe/CdS QDs in the presence of an oscillating electric field. (a) The trajectory of an uncharged QD, showing pure Brownian motion. (b, c) Trajectories of QDs carrying charges +e and −e, showing a clear oscillatory motion. (d, e) Trajectories of QDs carrying charges +2e and −2e. (f, g) Trajectories of QDs carrying charge +3e and −3e. The normalized electric field is represented by black dashed lines. The color bar ranges from zero to the maximum number of photons integrated along the x-direction.

Trajectories are shown for QDs carrying two elementary charges in Figure d,e and for three elementary charges in Figure f,g. The red curves in Figure represent the extracted position x of the QD trajectories (see Supporting Information). The particle position is obtained, first, by Gaussian fitting of the integrated intensity profile along the x-direction (i.e., the axis parallel to the applied field). The extracted position corresponds to the center of this fitted profile. Second, the extracted position is filtered with a low-pass Butterworth filter for noise reduction. And, finally, the absolute position x(i) is obtained for each image by using a pixel-to-μm conversion factor (i.e., 0.35 μm per pixel). By taking a discrete derivative, the particle velocity is calculated:

$$v_x(i)=\frac{x(i+1)-x(i)}{\Delta t}$$ 1

where Δt = 1/3300 s. These velocity data are then divided into segments corresponding to one period of the electric field. Since the contribution of Brownian motion to the particle velocity has zero mean, a sinusoidal function either in phase or antiphase with the electric field can be fitted to isolate the field-induced oscillatory component, effectively filtering out the Brownian contribution:

$$v(t)=\mu E_0\sin (2\pi ft+\varphi )$$ 2

where μ is the electrophoretic mobility, E ₀ is the amplitude of applied electric field and f is the frequency of the applied field. The value of ϕ is 0 for a positively charged particle, and π for a negatively charged particle. According to this protocol, electrophoretic mobilities μ _i are calculated for each period of the measured particle trajectory. To enhance the accuracy of the mobility for each particle, multiple mobility values μ _i are averaged per particle. Since there is a small probability that a particle’s charge state changes during measurement, potentially resulting in averaged mobilities that do not correspond to a discrete charge value, we restrict the maximum allowed variation in the measured mobility values for each particle (see Supporting Information for details). Figure shows histograms of the average electrophoretic mobilities for 209 QDs with a nominal diameter of 25 nm and for 251 QDs with a nominal diameter of 15 nm. This nominal diameter, corresponding to the average core QD diameter, is estimated from TEM images, as illustrated in the insets in Figure (details in Supporting Information). It can be observed that the electrophoretic mobility is clustered around discrete values, which are multiples of an elementary mobility μ_e(R), representing the mobility of a particle having a hydrodynamic radius R carrying a charge +e. Assuming spherical particles and Stokes’ law and considering a thick double layer approximation (Henry’s equation), the elementary mobility is given by the following equation:

$${\mu }_{\mathrm{e}}(R)=\frac{e}{6\pi \eta R}$$ 3

where η is the viscosity of the medium. A value for this elementary mobility is estimated for each ensemble of QDs with the same nominal size by examining the periodicity in the mobility histogram by means of a so-called R ² method (details in Supporting Information). Resulting values are μ_e = 3.0 × 10^–10 m² V^–1 s^–1 for 25 nm QDs and 4.3 × 10^–10 m² V^–1 s^–1 for 15 nm QDs. In Figure , the dashed black lines mark multiples of this elementary mobility. Consequently, peaks can be identified in the histograms that correspond to −2, −1, 0, 1, or 2 (or more) elementary charges. From these two elementary mobility values, hydrodynamic diameters d _H = 2R are calculated based on eq , as reported in Table .

3.

Electrophoretic mobility histograms of 25 nm (209 particles) and 15 nm (251 particles) CdSe/CdS QDs. Mobility histograms are shown for (a) 25 nm QDs and (b) 15 nm QDs. The dashed black lines indicate multiples of the elementary electrophoretic mobility μ _e and correspond to discrete numbers of elementary charges (see Supporting Information). The red curve represents the theoretical model.

1. Size Analysis of the QDs .

TEM diameter (nm)	Expected diameter (TEM + PIBSA monolayer) (nm)	Hydrodynamic diameter (nm)
15  ±  3	20 ± 3	30
25  ±  4	30 ± 4	43

^aTEM diameter is calculated from TEM images. The expected hydrodynamic diameter is based on the assumption of a 2.4 nm PIBSA monolayer around QDs in suspension. The hydrodynamic diameter (d _H = 2R) is calculated from the measured elementary electrophoretic mobility.

The histograms in Figure can be interpreted by considering several contributing effects. First, the width of the peaks includes two main contributions: Brownian motion and size polydispersity. The area under the peaks is related to the number of QDs having a discrete charge level. To confirm this, a theoretical model was developed (red curves in Figure ). In this model (see details in Supporting Information), we assume a Gaussian distribution of the QD hydrodynamic radius with averages R = 21.5 and 15.0 nm, obtained from the experimentally observed elementary electrophoretic mobility values determined by the R ² method. Since the variation of the hydrodynamic radius is not known, we incorporate the standard deviations on the core sizes, 2.0 nm for 25 nm QDs and 1.5 nm for 15 nm QDs based on TEM images, into the model (see Supporting Information). This means that we assume a fixed surfactant layer thickness, implying that the variations in hydrodynamic size arise solely from variation in core size.

Next, due to the effect of Brownian motion on the measured electrophoretic mobility, every value R of the size distribution contributes to the measured electrophoretic mobility with a series of normal distributions, corresponding to all charge states Z = −2, −1, 0, +1, +2, etc., centered around $\mu =\frac{Ze}{6\pi \eta R}$ and with standard deviation ${\sigma }_{\mu }=\frac{2}{E_0}\sqrt{\frac{2D}{\Delta t}}$ . Here, $D=\frac{kT}{6\pi \eta R}$ is the diffusion coefficient, k is the Boltzmann constant, T = 300 K and Δt represents the total measurement time per mobility measurement, which is on average Δt = 0.1 s, corresponding to three periods of the electric field on average. Additionally, weights are assigned to the mobility contributions of each charge state such that the total area of each charge state matches with the number of mobility measurements per charge state in the experimental histograms. As can be seen in Figure , the theoretical model agrees well with the experimental data in terms of peak width, indicating that intrinsic Brownian motion and size variation are the primary contributions to the width of the peaks.

If we assume a single monolayer of PIBSA surfactant with theoretically calculated size of 2.4 nm (detailed calculation is in ref ) around our QDs, their hydrodynamic diameter increases by 4.8 nm in diameter. However, the hydrodynamic diameter obtained from the elementary mobility μ_e is larger, by about 13 nm for 25 nm QDs and 10 nm for 15 nm QDs, than the values obtained by combining the TEM (core/shell) particle diameter with an additional thickness due to PIBSA ligands (see Table ). In principle, several factors could contribute to this large hydrodynamic size. To rule out the possibility of QD aggregation at higher dilution, we measured the intensity level of single QDs stuck on the glass interface from dispersions with various concentrations (see Supplementary Figure S6). The observation of similar intensity levels of observed objects across all dilution levels suggests that the QDs measured at higher dilutions in solution are indeed single QDs. Aggregation of QDs would result in significant size variations that should manifest in the electrophoretic mobility histogramscontrary to what is observed. Alternately, the amplitude of the applied electric field experienced by the particles could be overestimated. However, the accurate measurement of the applied voltage and the spacing between the electrodes (see Supplementary Figure S2) produces an accurate applied electric field amplitude. Therefore, our main hypothesis is that, as we strongly dilute the QD suspensions in our experiments while maintaining a fixed PIBSA concentration, the number of PIBSA molecules available per QD increases. Consequently, QDs may get loaded with a large amount of surfactant molecules, forming multiple layers rather than just a single monolayer. To support this hypothesis, we performed DLS measurements on different dilutions of the 25 nm QDs. These measurements indicate that with every dilution step by a factor of 10, the hydrodynamic size increased by a factor of 1.5 (see Supplementary Figure S5).

Finally, in Figure , we qualitatively analyze the distribution of observed charge states from the histograms in Figure . A charge distribution is observed that is quasi-symmetrical, for example, demonstrating slightly more QDs with charge +e than with charge −e. For the 25 nm QDs, the majority of QDs are uncharged, with a minority carrying one or two elementary charges, and with virtually no particles having three or more charges. The 15 nm QDs exhibit a higher fraction of particles with charge +e than neutral ones and much less doubly charged particles. This low number of charges can be expected from the low dielectric constant of the solvent, dodecane (ε_r = 2), which results in a large electrostatic charging energy. Although the exact origin of the net QD charge remains uncertain, potentially involving ionic impurities or traces of water, the observed charge distribution is likely dominated by thermodynamic charging (see ref for QDs and ref for inverse micelle systems). In this regime, the equilibrium charge distribution is primarily governed by the QD size, rather than by the concentration of ions, charged species, or nonionic surfactant PIBSA. Small asymmetries in the observed charge distribution may originate from additional chemical or physical interactions.

4.

Histogram of charge states extracted from the electrophoretic mobility data in Figure . The theoretical probability density distribution obtained from the thermodynamic charging model is shown for QDs with hydrodynamic radius (a) R = 21.5 nm and (b) R = 15 nm (red dashed line and dots).

If we focus on thermodynamic charging and approximate our QDs as spherical particles with hydrodynamic radius R, then the energy required to charge the particle surface with a single charge is given in first approximation by $E_{\mathrm{c}}=\frac{e^2}{8\pi {\epsilon }_0{\epsilon }_{\mathrm{r}}R}$ , where ε₀ is the vacuum permittivity. Here, we ignore effects related to the dielectric constant of the QD and the discrete nature of the charges. Using the hydrodynamic sizes from Table , we find charging energies E _c = 3.8 × 10^–21 J for R = 15 nm and E _c = 2.7 × 10^–21 J for R = 21.5 nm. This charging energy increases quickly for higher charge states, i.e., Z²E_c, but decreases for larger particle sizes. Given that the Bjerrum length l _B = e ²/8πε₀ε_r, 28 nm in dodecane, is roughly of the same order as the diameter of the QDs, one indeed expects only very low charge numbers to occur. Furthermore, one expects that for larger QD sizes, the distribution also extends to larger charge numbers. The fraction of charge states at equilibrium then follows Boltzmann statistics p(Z) ∼ e ^{–Z 2 E _c/kT} , which matches in first order with the experimental data, as can be seen in Figure . The small asymmetries in the charge histograms are not captured by this simple charging model.

In this study, we have developed a fast and sensitive laser scanning microscopy technique capable of measuring the electrophoretic mobilities of individual CdSe/CdS QDs of 15 and 25 nm in solution under a strong electric field. The resulting mobility histograms reveal distinct peaks corresponding to discrete numbers of elementary charges. Besides highly accurate charge estimates per QD, this method also provides information about the ensemble-average hydrodynamic size. Our findings suggest that the accumulation of surfactant PIBSA during dilution results in an increase in the apparent hydrodynamic size of the QDs compared to the bare TEM size. Furthermore, the observed charge histograms can be understood in the first approximation from the perspective of electrostatic charging in a nonpolar liquid. The presented technique not only provides detailed insights into the charge and size of QDs in solution but also holds promise for further applications. It can be extended to study real-time external charging dynamics and QD blinking, as well as the effects of external charge on the optical properties and emission spectrarelevant for technologies such as QD-LEDs. Additionally, it offers potential for characterizing the size, mobility, and binding behavior of single molecules on nanoparticle surfaces in water, opening new avenues for research in nanoscience and bioanalytical chemistry. ,

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.5c02731.

• Estimation of QD core/shell diameter from TEM images, microscopic image of fabricated microfluidic device, R ²-method to confirm the periodicity in charge histograms and extract elementary electrophoretic mobility values, theoretical model for charge histograms, DLS measurements on different concentrations of 25 nm QDs, intensity measurements at various dilutions of 25 nm QDs, power measurements in the back focal plane of microscope objective (PDF)

The authors declare no competing financial interest.