NANO LETTERS
Quantum Dot Chemiluminescence Sergey K. Poznyak,†,⊥ Dmitri V. Talapin,*‡,§,⊥ Elena V. Shevchenko,‡,| and Horst Weller‡
2004 Vol. 4, No. 4 693-698
Physico-Chemical Research Institute, Belarusian State UniVersity, 220050 Minsk, Belarus, and Institute of Physical Chemistry, UniVersity of Hamburg, Bundesstr. 45, 20146 Hamburg, Germany Received February 20, 2004
ABSTRACT We report the first observation of band gap chemiluminescence of semiconductor quantum dots in solution and in nanoparticulate layers. The spectral position of the band gap chemiluminescence of CdSe/CdS core shell and InP nanocrystals depends on their particle size, allowing thus an efficient tuning of the emission color with superior color purity inherent for monodisperse samples. The efficiency of nanocrystal chemiluminescence can be dramatically enhanced by applying a cathodic potential to the nanoparticulate layers made from CdSe or CdSe/ CdS core−shell nanocrystals. In this case electrochemical n-doping of the particles via electron injection provides a “quantum confined cathodic protection” against nanocrystal oxidative corrosion upon hole injection and allows the achievement of efficient and stable electrogenerated chemiluminescence.
The superior emitting properties of semiconductor nanocrystals (also referred to as quantum dots) attract the growing attention to applications of these materials in LED and display devices1,2 as well as in biological luminescent labels.3 In quantum dots, atomic-like electronic energy levels are formed due to the charge carrier confinement. The spacing of the highest occupied and lowest unoccupied quantum confined orbitals is a pronounced function of nanocrystal size, providing the advantage of continuous band gap tunability over a wide range simply by changing the size of the nanocrystal (the quantum size effect).4 Recent progress in the wet chemical synthesis of luminescent semiconductor nanocrystals allowed the preparation of a palette of materials emitting from UV to NIR with precisely adjustable position of the emission band. High quality nanocrystal samples exhibit bright luminescence that is superior to conventional organic fluorescence dyes with respect to color purity (narrow emission band) and photostability.1,3 The various types of luminescence differ from the source of energy to obtain an excited state that can relax into a ground state with the emission of light. In today’s applications of quantum dots, the required excitation energy is supplied either by absorption of a quantum of light given * Corresponding author. E-mail:
[email protected]; Fax: +49-40-42838-3452; Homepage: http://www.chemie.uni-hamburg.de/ pc/Weller/. † Belarusian State University. ‡ University of Hamburg. § Current address: IBM T. J. Watson Research Center, Yorktown Heights, NY. | Current address: Columbia University, Department of Applied Physics and Applied Mathematics, New York, NY. ⊥ S.K.P. and D.V.T. contributed equally to this work and should be regarded as a joint first author. 10.1021/nl049713w CCC: $27.50 Published on Web 03/19/2004
© 2004 American Chemical Society
rise to photoluminescence (PL), by electrical injection of an electron-hole pair (electroluminescence, EL), or by electron impact resulting in cathodoluminescence.5 However, the other types of luminescence, e.g., chemiluminescence (CL), which has developed to an important and powerful tool in biological and medical investigations, have not yet been observed for the novel class of quantum dot luminophores. To the best of our knowledge, all previous reports dealing with chemiluminescence in the presence of micro- or nanosized particles described either the emission of molecular species catalyzed by the particle surface or emission from localized states (e.g., surface traps) in a semiconductor solid,6-8 i.e., the emitting state had no relationship to the quantum-confined orbitals. In this communication we report on the first observation of the nanocrystal band gap chemiluminescence where semiconductor nanocrystals act as a chemiluminescent emitter. Also, we observed an efficient electrogenerated band gap chemiluminescence (ECL) on nanoparticulate layers in solutions. These new phenomena should lead to novel exciting applications of the quantum-sized particles. The first excited state of II-VI or III-V semiconductor nanocrystals corresponds to one electron and one hole which occupy the 1Se and 1Sh quantum confined orbitals, respectively.4 The possibility of an efficient injection of electrons into the 1Se shell of CdSe nanocrystals from chemical species (e.g., sodium diphenyl) has been recently demonstrated by Guyot-Sionnest et al.9 In contrast, the possibility of the hole injection in the 1Sh state of II-VI or III-V nanocrystals from some chemical species was still questionable. It was believed that such injection of a hole into compound semiconductor nanocrystal, such as CdSe, results in the irreversible oxidation of the nanocrystal.10-12
Figure 1. (a) Energy level diagram of CdSe nanocrystals in contact with an aqueous solution containing peroxodisulfate (S2O28 ) ions. The energies for 1Sh and 1Se quantum-confined orbitals of a 4 nm CdSe nanocrystal and standard redox potentials of S2O2ions 8 corresponding to the reactions 1 and 2 are taken from the literature [refs 1 and 14]. The redox potentials, measured with respect to the standard hydrogen electrode (SHE), were compared to the nanocrystal energy levels, measured with respect to vacuum, using the known value of the energy of SHE vs vacuum level (-4.5 eV). Dependence of the integral ECL intensity (b) and the cathodic current (c) on the potential applied to the CdSe nanocrystal film in 0.1 M K2S2O8 + 0.1 M KOH aqueous solution. The potential was swept from 0.2 V toward negative direction with a scan rate of 10 mV s-1.
To gain better insight into this point, we investigated the hole injection into CdSe nanocrystals13 from sulfate radicals which we electrochemically generated at the surface of CdSe nanocrystals via the following process: S2O82- + e- f SO42- + SO4-
(1)
This electrochemical reaction can occur at the surface of various n-doped bulk semiconductors with participation of electrons from the conduction band.14 The formed sulfate radicals, SO4-, can inject a hole (h+) into the valence band of semiconductor electrode: SO4- f SO42- + h+
(2)
In their turn, the injected holes can recombine with electrons from the conduction band with the emission of light.14 This process is known as electrogenerated chemiluminescence (ECL). Recently, Bard et al. have demonstrated ECL generation on colloidal Si nanocrystals in the presence of peroxodisulfate ions.10 However, in that work the generation of light occurred from carriers trapped on localized states present on the surface of Si nanocrystals. The redox potential of reaction 2 is favorable for the hole injection from sulfate radical in the 1Sh 3/2 state of CdSe nanocrystals (Figure 1a). To explore the possibility of efficient hole injection into the quantum confined states of CdSe nanocrystals from sulfate radicals, we carried out the electrochemical investigation of close-packed films of CdSe 694
nanocrystals in aqueous solutions containing peroxodisulfate ions (Figure S1, Supporting Information).15 Thin films (50150 nm thickness) of close-packed CdSe nanocrystals were prepared on platinum or F-doped SnO2 substrates.15 To improve the conductivity of the nanocrystal films, we crosslinked the CdSe nanocrystals by treatment of the film with 1,8-octanediamine.16 Figure 1c shows voltammograms for two ∼100 nm thick close-packed films of 5.1 and 3.6 nm CdSe nanocrystals in 0.1 M K2S2O8 aqueous solution (pH ∼ 13). The integral luminescence intensity was recorded simultaneously with the cathodic current as the potential was scanned in the negative direction (Figure 1b). Current-voltage and light intensityvoltage dependencies measured for the films of CdSe nanocrystals with different particle sizes show a relationship between the nanocrystal size and the ECL onset voltage. A general trend is that applying larger bias is necessary to generate luminescence of smaller nanocrystals. The crosslinking of CdSe nanocrystals by the treatment of a closepacked film with 1,8-octanediamine resulted in ∼25-fold increase of the current density and ∼100-fold increase of the ECL intensity. Close-packed films of CdSe nanocrystals exhibit the PL band slightly red-shifted with respect to the PL band observed for isolated nanocrystals, primarily due to the resonant energy transfer from smaller to larger nanocrystals.17 Cross-linking of CdSe nanocrystals by 1,8-octanediamine prevents swelling of the film in solution and decreases the average interparticle distance,12 facilitating the energy transfer between the nanocrystals. As a result, the PL band shifts further to the red after the cross-linking procedure. The ECL spectrum has the same shape and width as the PL band and is red-shifted by ca. 8 nm in comparison with the PL spectrum of the corresponding cross-linked film (Figure 2a). This can be understood if we take into account some local fluctuations of packing density inside the cross-linked nanocrystal film. In this case, the current responsible for generation of ECL will flow preferentially through the most densely packed regions in the film. In contrast, in the PL spectrum the signal from the least densely packed regions will be overweighted because the energy transfer in the nanocrystal film is accompanied by losses of the PL efficiency.17 For yellow and red emitting CdSe nanocrystal films, efficient ECL is clearly visible under daylight at electrode potentials of about -0.9 V (Figure 2b). The measured values of the integral ECL intensity were about 1 µW cm-2. This value can give us an estimate for the ECL external quantum efficiency of about 0.01%. However, this value is, probably, strongly underestimated because of a very large leakage of electrochemical current originating from the catalytic reduction of peroxodisulfate ions on the Pt substrate. The addition of peroxodisulfate resulted in ca. 200-fold increase of the cathodic current in the potential range corresponding to the efficient ECL generation. Also note that the internal quantum efficiencies of nanocrystal layers are usually substantially higher than the external quantum efficiencies due to the internal reflection.2,18 We observed a substantial increase of the ECL intensity and quantum efficiency upon increasing the thickness of the nanocrystal film. This might be an Nano Lett., Vol. 4, No. 4, 2004
Figure 2. (a) Absorbance of 5.1 nm CdSe nanocrystals dispersed in chloroform (black line) and PL spectra measured on the same nanocrystals dispersed in chloroform (red line) and cross-linked by 1,8-octanediamine into a close-packed film (blue line). The ECL spectrum of the cross-linked film is shown by red dashed line. (b) True color photographs of the electrode with a film of 4.3 nm CdSe nanocrystals (left), and ECL observed on CdSe nanocrystals with a diameter of 4.3 nm (middle photo) and 5.1 nm (right photo). (c) ECL spectra of the cross-linked films of 2.8, 4.2, and 5.1 nm CdSe nanocrystals.
evidence that the ECL generation occurs in the bulk of the nanocrystal film rather than at the interface. Unfortunately, thick (>300 nm) films of CdSe nanocrystals have a tendency to crack after cross-linking of nanocrystals with 1,8octanediamine. It makes difficult an estimation of the optimal thickness of CdSe nanocrystal film. We believe that further optimization can result in the ECL efficiencies comparable to the EL efficiencies of solid-state nanocrystal LEDs. Films of ∼3 nm CdSe nanocrystals emitting in the green region exhibited much weaker ECL with spectra consisting of a sharp band of 1Se-1Sh transition and a broad band of trapped emission (Figure 2c). The ECL of CdSe nanocrystals was surprisingly stable (Figure S2, Supporting Information),15 the performance of the electrode retained after ∼102 on/off cycles. Note that our experiments were performed under air and in aqueous solutions in the presence of very reactive species, i.e., under conditions which were previously considered as very aggressive with respect to the nanocrystals.10,12 The films of cross-linked CdSe/CdS core-shell nanocrystals show ECL intensities similar to that which we observed for the CdSe nanocrystals, whereas CdSe/ZnS core-shell nanocrystals13 exhibit ECL ∼2 orders of magnitude weaker compared to that of CdSe nanocrystals. A reason for the weak ECL of CdSe/ZnS nanocrystal films might be their poor conductivity, due to which did not allow us to reach reasonable current densities through the film. The superior ECL properties of CdSe nanocrystal films together with their high stability against oxidation with SO4radicals can be understood if we consider the mechanism of Nano Lett., Vol. 4, No. 4, 2004
the charge transport in close-packed nanocrystals recently reported by Guyot-Sionnest et al.16 It is known that a film of close-packed CdSe nanocrystals is a very poor conductor.16 However, the conductivity of the CdSe nanocrystal film can be increased by many orders of magnitude by an electron doping of nanocrystals into the lowest unoccupied quantumconfined orbital, 1Se. After half-filling of the 1Se shell, the nanocrystal film becomes n-type conductive due to the shellto-shell transport.16 The doping of CdSe nanocrystals into the 1Se shell manifests itself by bleaching of the first excitonic transition in the absorption spectrum of the film.11 In our experiments, the ECL onset potentials coincided well with the bleaching onset potential, indicating that the efficient ECL is possible only from n-doped CdSe nanocrystal films. The electron transport in the film occurs only through the n-doped CdSe nanocrystals, which can also behave as active sites for the electrochemical reduction of peroxodisulfate ions (reaction 1). In this case, the formed SO4- radical injects a hole into a negatively charged CdSe nanocrystal19 and fast 1Se-1Sh recombination dominates over oxidation processes. So, the n-doping caused by the applied potential provides a “quantum confined cathodic protection” of CdSe nanocrystals, making them stable against destruction after the hole injection and allowing efficient ECL. If the holes were electrochemically injected into nondoped CdSe or CdSe/ZnSe nanocrystals, the intensity of electrogenerated chemiluminescence was extremely low,20,21 many orders of magnitude lower than in our case. We have introduced the term “quantum-confined cathodic protection” because in the case of nanocrystal films the protection effect is “quantized”. Injection of one electron in the 1Se shell immediately provides some level of protection to one nanocrystal and has no effect to the other nanocrystals. Injection of the second electron in the 1Se shell abruptly changes the nanocrystal resistance against oxidation, etc. This is different to bulk solids where the protection is achieved by changing the electrochemical potential of whole biased electrode. The concept of prior n-doping of nanocrystals before the hole injection might be interesting for different nanocrystal-based devices, e.g., solid-state LEDs, providing the general way of improving the device lifetime and other characteristics. We have demonstrated that a hole can be efficiently injected from dissolved molecular species in the 1Sh quantum confined orbital of the CdSe nanocrystal. If the hole is injected into the negatively charged (n-doped) nanocrystals, radiative recombination will dominate over the oxidation processes upon the hole injection. So, it is reasonable to expect the generation of a band edge CL if one electron and one hole are simultaneously injected into a nanocrystal from the same solution. Indeed, we found that an addition of H2O2 induces CL of CdSe/CdS core-shell nanocrystals. In a typical experiment, the film of close-packed CdSe/CdS nanocrystals22 (∼100 nm thickness) on a Pt substrate was placed into a quartz cell with 3 mL of 0.1 M aqueous solution of KOH. Injection of 0.3 mL of 1 M aqueous solution of H2O2 under stirring resulted in a fast increase of the integral luminescence as shown in Figure 3a. Similar results were observed for the films prepared on Pt, F-doped SnO2 and quartz substrates. 695
the surface of Pt or SnO2 substrate, respectively. The redox potential of reaction 3 is E0 ≈ (0.6-0.06 pH) V vs SHE. The charging of CdSe/CdS nanocrystals via reaction 3 is impossible because of their high ionization potential (Figure 3a, inset). However, we also consider the chemical oxidation of sulfur atoms at the nanocrystal surface, S2surface + H2O2 • f S-• + OH + OH , which should occur at considersurface ably more negative potentials than the oxidation of the nanocrystal lattice. The redox potential of surface atoms is strongly dependent on the type of surface-capping groups and needs to be determined for each particular material and capping agent. The formed OH• radical should be able to inject a hole (reaction 4) in the 1Sh quantum-confined orbital of the CdSe core. The standard redox potential of the reaction OH• + e f OH- is E0 ≈ (2.84-0.06 pH) V vs SHE, which is sufficient for the hole injection at the pH values used (Figure 3a, inset): Figure 3. (a) Temporal evolution of the integral chemiluminescence intensity of a film of CdSe/CdS nanocrystals induced by the addition of H2O2 in 0.1 M KOH (solid line) and in 0.1 M Na2SO4 (dashed line) solutions. Inset shows proposed energy level diagram of CdSe/CdS nanocrystals in contact with an aqueous H2O2 solution. The redox potentials shown on the diagram correspond to the reactions 4 and 7. (b) CL spectra measured from the films of CdSe/ CdS nanocrystals with different size of CdSe core (red lines) and PL spectra of the corresponding films (black lines).
To examine stability of nanocrystals during the CL generation, we removed the nanocrystal film from the H2O2containing solution after 120 min of CL generation, rinsed the film with 0.1 M solution of KOH, and left it in 0.1 M KOH solution for 2 h in darkness. Then, we added a fresh portion of H2O2 and observed even more efficient CL emission than the first time (Figure S3, Supporting Information). The spectrum of CL possesses one sharp peak which coincides very well with the PL spectrum of the nanocrystal film. Moreover, changing the size of CdSe core of the CdSe/ CdS nanocrystals results in the size-dependent shift of the CL band (Figure 3b). This provides an unambiguous evidence that the addition of H2O2 generates an excited state (1Se-1Sh exciton) in CdSe/CdS nanocrystals which relaxes with the emission of light.23 Weaker, but detectable CL was observed for CdSe/ZnS nanocrystals with a relatively thin (∼1.5 monolayers) ZnS shell, whereas no CL was detected for bare CdSe nanocrystals. This observation demonstrates the importance of the proper passivation of the nanocrystal surface dangling bonds. We can propose the following mechanism for generation of the 1Se-1Sh exciton in CdSe/CdS nanocrystals, leading to generation of CL in the presence of H2O2. First, H2O2 molecules can be catalytically decomposed at the Pt or F-doped SnO2 substrate. The mechanism of the catalytic decomposition proposed by Weiss24 starts from the following reaction: M + H2O2 f M + + OH- + OH• +
(3)
Here M and M represent uncharged and charged parts of 696
OH• + CdSe/CdS f OH- + CdSe(h+1S h)/CdS
(4)
Alternatively, the OH• radical can react with an H2O2 molecule yielding a superoxide ion:24 OH• + H2O2 f H2O + HO2•
(5)
HO2• + OH- f O2- + H2O
(6)
The efficient formation of O2- has been previously shown to accompany decomposition of H2O2 in an aqueous medium in the presence of charcoal, metals, and metal oxides.25,26 The superoxide ions are quite stable in aqueous solution, especially at high pH, and their lifetime approximate 1 min.25 They can easily donate one electron in the reaction O2- f O2 + e with E0 ≈ - 0.33 V vs SHE.27 This value of the redox potential allows the injection of an electron (reaction 7) from superoxide ion in the 1Se quantum-confined orbital of CdSe core (Figure 3a, inset): )/CdS + O2 O2- + CdSe/CdS f CdSe(e1Se
(7)
The shell of organic ligands strongly affects the rate of the reactions 4 and 7 as well as the nanocrystal oxidation rate. The highest stability of CL was observed in an aqueous medium, which can be explained by a slow penetration of H2O2 molecules through a highly hydrophobic shell containing hexadecylamine, trioctylphosphine oxide and trioctylphosphine molecules.22 As an alternative mechanism for the CL generation, we should consider electron injection from nanocrystal dissolution intermediates.28,29 Indeed, the first step of the dissolution reaction involves the hole capture by a surface bond with the formation of an electron-deficient surface bond. The electron can be thermally excited from this state to the conduction band29 followed by recombination with the hole injected by OH• radical. However, in our case this mechanism seems to be doubtful. Even if the CL intensity was very stable Nano Lett., Vol. 4, No. 4, 2004
Figure 4. Temporal evolution of the integral CL intensity of CdSe/ CdS nanocrystals in an aqueous solution containing 0.1 M sodium peroxodisulfate (pH 12.8). Inset shows the PL spectrum of the film recorded before adding Na2S2O8 (red line) and CL spectrum recorded 10 h after the addition of Na2S2O8 (black line).
in time, no nanocrystal dissolution was observed. For example, in basic aqueous solutions of sodium peroxodisulfate, the CL intensity remains nearly constant during many hours (Figure 4). Any decrease of the nanocrystal size should result in the blue shift of the emission band. However, no shift of the CL spectrum was observed after 10 h of CL generation (Figure 4). We also carried out experiments to generate CL in colloidal solutions of quantum dots. Indeed, adding H2O2 to a dispersion of CdSe/CdS nanocrystals in THF resulted in a flash of CL decaying within ∼1-2 s. Unfortunately, the addition of H2O2 also resulted in an immediate precipitation of the nanocrystal colloid. This problem was overcome for luminescent InP nanocrystals30 in n-butanol. Upon adding H2O2, clearly visible CL was observed under maintenance of colloidal stability.15 The InP nanocrystals exhibit a pure band edge CL (Figure 5). The treatment of InP nanocrystals with H2O2 usually results in a small (5-10 nm) blue shift of the PL band, manifesting some decrease of the nanocrystal size upon the CL generation (Figure S4, Supporting Information).15 It means that both mechanisms of the electron injection discussed above may take place in the case of InP nanocrystal colloids. Our experiments show that chemiluminescence can be generated on different nanocrystals, both in close-packed films and colloidal solutions. At the present stage, the efficiency of nanocrystal CL is much lower than that of luminol- or bis(2,4,6-trichlorophenyl)oxalate-based systems. However, we believe that the efficiency of the nanocrystal CL can be substantially improved by optimizing the nanocrystal composition, capping ligands, and the chemical “fuel” which provides energy for the generation of the excited state. In addition to the academic interest in this phenomenon that is novel for quantum dots, the nanocrystal chemiluminesNano Lett., Vol. 4, No. 4, 2004
Figure 5. (a) Chemiluminescence generated in a colloidal solution of 4.2 nm InP nanocrystals in butanol. The CL was generated by adding a butanolic solution of H2O2. We recorded the temporal evolution of CL signal at different emission wavelengths. (b) PL spectrum of a colloidal solution of InP nanocrystals (solid line) is compared with the integrated CL intensity measured at different wavelengths (red diamonds).
cence might find use in analytical and biomedical applications. Thus, CL analysis, e.g., CL labeling and detection of immunoassays, is the most sensitive of any nonradioactive method, allowing attomolar amounts of target to be detected.31 CL analysis has many advantages over PL-based techniques primarily due to the absence of a background arising from unselective photoexcitation and is widely used in clinical diagnostics.32 The use of nanocrystals as chemiluminescent emitters can have potential benefits such as easy multicolor labeling for visible and NIR spectral regions. Acknowledgment. We thank V. Zhuravkov for making the photographs, A. Heinglein, S. V. Gaponenko, and P. Guyot-Sionnest for helpful discussions. This work was supported by the BMBF, Philips, NATO through the research grant PST.CGL.979631, and by the Deutsche Forschungsgemeinschaft through SFB 508. Supporting Information Available: Materials and Methods; Figures S1, S2, S3, and S4. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Coe, S.; Woo, W.-K.; Bawendi, M.; Bulovic, V. Nature 2002, 420, 800. (2) Tessler, N.; Medvedev, V.; Kazes, M.; Kan, S.-H.; Banin, U. Science 2002, 295, 1506. (3) Bruchez, M. P.; Moronne, M.; Gin, P.; Weiss, S.; Alivisatos, A. P. Science 1998, 281, 2013. (4) Gaponenko, S. V. Optical Properties of Semiconductor Nanocrystals; Cambridge University Press: Cambridge, 1998. (5) Rodriguez-Viejo, J.; Jensen, K. F.; Mattoussi, H.; Michel, J.; Dabbousi, B. O.; Bawendi, M. G. Appl. Phys. Lett. 1997, 70, 2132. (6) Corralles, T.; Peinado, C.; Allen, N. S.; Edge, M.; Sandoval, G.; Catalina, F. J. Photochem. Photobiol. A 2003, 156, 151. (7) Zhang, Z.; Zhang, C.; Zhang, X. Analyst 2002, 127, 792. 697
(8) McCord, P.; Yau, S.-L.; Bard, A. J. Science 1992, 257, 68. (9) Shim, M.; Guyot-Sionnest, P. Nature 2000, 407, 981. (10) Ding, Z.; Quinn, B. M.; Haram, S. K.; Pell, L. E.; Korgel, B. A.; Bard, A. J. Science 2002, 296, 1293. (11) Wang, C.; Shim, M.; Guyot-Sionnest, P. Science 2001, 291, 2390. (12) Guyot-Sionnest, P.; Wang, C. J. Phys. Chem. B 2003, 107, 7355. (13) CdSe and CdSe/ZnS nanocrystals capped with hexadecylamine, trin-octylphosphine oxide and tri-n-octylphosphine were synthesized as described in Talapin, D. V.; Rogach, A. L.; Kornowski, A.; Haase, M.; Weller, H. Nano Lett. 2001, 1, 207. (14) Pettinger, B.; Scho¨ppel, H.-R.; Gerischer, H. Ber. Bunsen-Ges. Phys. Chem. 1976, 80, 849. (15) Materials and methods are available as supporting online materials. (16) Yu, D.; Wang, C.; Guyot-Sionnest, P. Science 2003, 300, 1277. (17) Kagan, C. R.; Murray, C. B.; Bawendi, M. G. Phys. ReV. B 1996, 54, 8633. (18) Schlamp, M. C.; Peng, X.; Alivisatos, A. P. J. Appl. Phys. 1997, 82, 5837. (19) If the CdSe nanocrystal is discharged after reaction 1, the electron hopping time between cross-linked nanocrystals (
