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Design of a hole trapping ligand Andrew D. La Croix, Andrew O'Hara, Kemar R. Reid, Noah J. Orfield, Sokrates T. Pantelides, Sandra J. Rosenthal, and Janet E. Macdonald Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b04213 • Publication Date (Web): 16 Jan 2017 Downloaded from http://pubs.acs.org on January 16, 2017
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Design of a hole trapping ligand Andrew D. La Croix†, ϟ, Andrew O’Hara‡, Kemar R. Reid †,ϟ, Γ, Noah J. Orfield†,ϟ, Sokrates T. Pantelides‡,ξ, Sandra J. Rosenthal†,‡,§,ϟ ∆,Γ, and Janet E. Macdonald*,† ,ϟ, Γ †
Department of Chemistry, ‡ Department of Physics and Astronomy, ξ Department of Electrical Engineering and Computer Science, § Department of Pharmacology, ∆ Department of Chemical and Biomolecular Engineering, Γ Interdisciplinary Materials Science, ϟ The Vanderbilt Institute of Nanoscale Science and Engineering, Vanderbilt University, Nashville, Tennessee 37235, USA KEYWORD: hole transfer, dithiocarbamate, CdSe/CdS nanorod, density functional theory, mid-gap states
ABSTRACT: A new ligand that covalently attaches to the surface of colloidal CdSe/CdS nanorods and can simultaneously chelate a molecular metal center is described. The dithiocarbamate-bipyridine ligand system facilitates hole transfer through energetic overlap at the inorganic-organic interface and conjugation through the organic ligand to a chelated metal center. Density functional theory calculations show that the coordination of the free ligand to a CdS surface causes the formation of two hybridized molecular states that lie in the band gap of CdS. The further chelation of Fe(II) to the bipyridine moiety causes the presence of seven mid-gap states. Hole transfer from the CdS valence band to the mid-gap states is dipole allowed, and occurs at a faster rate than what is experimentally known for the CdSe/CdS bandedge radiative recombination. In the case of the ligand bound with iron, a two-step process emerges which places the hole on the iron, again at rates much faster than band gap recombination. The system was experimentally assembled and characterized via UV-vis absorbance spectroscopy, fluorescence spectroscopy, time-resolved photoluminescence spectroscopy, and energy dispersive x-ray spectroscopy. Theoretically predicted red-shifts in absorbance were observed experimentally, as well as the expected quench in photoluminescence and lifetimes in time-resolved photoluminescence.
With the growth in global energy demands comes the need for an alternative, clean energy source.1, 2 Hydrogen gas has for the past few decades been heralded as a potential alternative-energy candidate owing to its high energy storage capacity and lack of hazardous byproducts upon combustion.3 The possibility of cleanly splitting water into hydrogen and oxygen gas has driven a broad field of research to investigate water splitting.4-7 Utilizing nanoparticle (NP) systems to perform water splitting has been under intense investigation, as NPs have increased surface areas, tunable valence bands (VB) and conduction bands (CB), and synthetic control over size and shape; these NP features provide the opportunity to ACS Paragon Plus Environment
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study electronic level alignment of excitons in the nanoparticle core vs organic ligands,8 and spatial attachment of multicomponent photocatalysts in a far more systematic manner. For example, CdS and CdSe/CdS nanorods (NRs) with attached metallic and metal oxide domains have been well studied for their ability to photoreduce water to H2.9-11 These systems and studies continue to suffer from limited stability of the particles and the requirement of sacrificial reductants, as the excited electron used for water reduction must be replenished from a molecule in solution.9, 12-14 Recent reports have highlighted that the interaction of sacrificial reductants for hole removal from the rods is the primary factor affecting quantum efficiency of hydrogen production,15 and that near perfect photohydrogen conversion is possible.16 Improved methods for hole transfer are, therefore, needed which will ultimately lead to complete water splitting. The time for hole transfer to ligands on the surface of a CdS or CdSe/CdS NR with coordinated metal centers has been reported to occur as quickly as 0.1-1 ns; Alivisatos et al. showed hole transfer to chemically inert thiol-tethered ferrocene derivatives, Figure 1.
Schematic representation of the
17
and Dukovic et al. demonstrated 0.1-1 ns hole trans-
A 2,2’-bipyridine group
fer to an adsorbed Ru complex, followed by 10-100
covalently linked via a dithiocarbamate func-
ns recombination with the electron on the Ru metal
tional group for the use of hole transfer to an
center.18
attached metal center for catalytically oxida-
mations such as disulfide formation from thiolate
tive reactions.
ligands occur on the order of 104 ns.19 It is also
proposed system.
Meanwhile, oxidative chemical transfor-
worthwhile to note that some of the fastest water oxidation on organometallic catalysts occur in 106 ns.20 In comparison, the time of electron transfer to a Pt tip on a CdSe/CdS rod has been reported as 0.001-0.01 ns. The electron transfer and water reduction occurs on a much faster time scale than the oxidative processes.21-23
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The focus of this research was to develop a system which could extract holes from a NR system on the same time-scale that electrons can be shuttled to a Pt tip, while also trapping the charges long enough for catalytic reaction to occur. Four points were considered in the design of a ligand for fast movement of holes: firstly, spatial overlap and continuous conjugation will promote ease of movement through the π orbitals of the ligand; secondly, a functional group known to be stable to oxidative processes while still being prone to hole trapping is necessary; thirdly, the ligand should contain a metal chelating moiety for potential catalytic reactions; and lastly, electronic transitions between the ligand and the CB should be disfavored in order to slow charge recombination. All of these properties are possible in a dithiocarbamate (DTC) functional group directly conjugated to 2,2’Figure 2. Level alignment and orbital charge bipyridine (Bipy). Previous reports have indicated that density of (a) DTCBipy and (b) DTCBithe DTC functional group is capable of sub-picosecond pyFe(acac)2 on the CdS surface. For DTCBicharge transfer when DTC is attached to known molecupyFe(acac)2, only the three levels (1, 2, and 4)
lar hole acceptors.24 DTC functional groups have shown
with the fastest calculated hole transfer rates to chelate CdS and CdSe while also showing spatial and from the CdS VB as well as the highest midenergetic overlap with the VB,
25-28
while Bipy is a
gap state (7) are shown (see Supplementary known chelator of water oxidation catalysts.20 A repreInformation for all). The arrows indicate the sentation of this system is seen in Figure 1. different optically allowed transitions between Herein we report a theoretical and experimental study levels. ACS Paragon Plus Environment
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of a new ligand for CdS, 2,2’-bipyridine-4-ylcarbamodithioate (DTCBipy), and its further chelation of Fe(II). Fe(II) was chosen as it readily undergoes one-electron oxidation, has analogous chemistry to highly active Ru based water oxidation catalysts, is identified as a water oxidation catalyst in its own right, and the nanorod-ligand-metal hybrid system was experimentally accessible.29, 30 DFT calculations were performed using the Vienna ab initio simulation package (VASP)31 for a free ligand and for a slab of CdS with the ligand covalently bound on the surface in order to determine the existence of midgap hole acceptor states. Hybridized energy levels and hole transfer dynamics from the CdS surface state were computed and indicated that successive hole transfer from the CdS to the ligand, then to the iron center, was faster than the radiative recombination from the CB to the VB of the CdS. Experimental assembly of the DTCBipy ligand system with chelated Fe(II) on fluorescent CdSe/CdS nanorods validated the theoretical predictions of the resulting absorbance spectra. The expected fluorescence quenches and Time Resolved Photoluminescence (TRPL) lifetimes were shortened due to the opening of new efficient non-radiative pathways. A simple comparison of the ligand and CdS energy levels gave encouraging results (see SI), and motivated more detailed calculations of a slab of CdS with the ligand covalently bound on the surface. The
(
)
calculations of the pristine slab with a 10 1 0 CdS facet do not have any midgap states. The optimized structure, as obtained by DFT energy minimization, for DTCBipy on CdS has two filled mid-gap molecular states just above the surface confined VB. The charge densities for the four relevant states are plotted in Figure 2A. The relevant electronic states exhibit differing levels of contribution from the ligand and CdS wave functions. The wave functions for the mid-gap molecular states are predominantly comprised of the molecular wave functions, with a small contribution from the CdS. Likewise, the VB contains partial contribution from the ligand but retains predominantly CdS surface character. In contrast, the CB is almost purely of CdS origin with even spatial distributions throughout. As result, only a small narrowing of the CdS band gap is expected.
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The optical absorption profile was obtained from the transition matrix elements between occupied and unoccupied states using VASP (SI). It was determined that the optical transitions between the mid-gap states and the CB minimum are dipole forbidden (with dipole oscillator strengths of less than 0.01), and consequently, the plotted calculated optical absorption (Figure S1) has no peaks in the relevant wavelength region. The DTCBipy LUMO derived state sits significantly above the CB minimum of CdS and so the intramolecular excitations of the ligand are of sufficient energy to be occluded by the transitions of the semiconductor. Relevant for through-bond charge transfer, there is spatial overlap of the wave function of the surface confined VB and the mid-gap states, and the two have differing wave function symmetry. Therefore, we can expect allowed electronic transitions between the VB and mid-gap states to be dipole allowed if either contains a hole. Using the calculated oscillator strengths for transitions between each mid-gap molecular state and the VB, we calculate a hole transfer time of 370 ns from CdS to the DTCBipy. It is important to point out that this calculation assumes a density of 0.34 ligands per nm2 whereas the experimental data (Table S1) show the actual surface coverage on CdS NRs is almost an order of magnitude higher. As the hole acceptor states are localized molecular states, interactions between ligands should be a second order effect. This means rates can be scaled linearly with ligand coverage.17 Therefore, linearly scaling for the experimentally relevant coverage of 2200 ligands per CdSe/CdS NRs, a theoretical hole transfer time of 167 ps is calculated. Since hole localization to the CdS surface occurs in times only slightly longer than localization to the CdSe core32-36 and the calculated rates for transfer to the ligands are much faster than exciton recombination for CdSe/CdS NRs,17, 37 this implies that hole transfer to the ligand states via the CdS surface state is a competitive process to core localization. In the case of surface-attached DTCBipyFe(acac)2, a similar small red shift of the CdS bandgap is expected due to hybridization of the VB with ligand states. Seven filled mid-gap molecular states are expected (Figure 2B). States 2 and 4 are similar to the two mid-gap states in the Fe-free case. States 1, 2, and 3 demonstrate the conjugation of the dithiocarbamate group through to the Fe center. The upper
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three states are primarily due to molecular orbitals of the Fe d-states with surrounding atoms (essentially the three eg-type states of a d6 metal with octahedral coordination). These states are depicted in Figures 1a and S2. As in the case of DTCBipy, all transitions between mid-gap molecular states of DTCBipyFe and the CB are dipole forbidden, and the oscillator strength is less than 0.01. The additional features seen in the absorption spectra (Figure S1) are due to intramolecular excitations from the mid-gap states to unoccupied ligand molecular states above the CB. The transitions between the VB and DTCBipyFe(acac)2 midgap molecular states are dipole allowed. The oscillator strength of these transitions was used to calculate a hole transfer time to a single ligand of 303 ns. As above, if the rate is adjusted for the experimental ligand density, a hole transfer rate is 137 ps is calculated. This represents an increase of 22% in rate versus the non-metal center chelated form. In addition to the transitions from surface states to the ligands, tunneling from the quantum dot to the metal chelating ligands is in theory possible and the rate can be comparable,17 further enhancing the quenching of the quantum yield. Again, these rates are two orders of magnitude faster than band edge recombination of CdSe/CdS. The four lower DTC-dominated molecular states predominantly account for the hole transfer rate from CdS to DTCBipyFe, rather than the upper three Fe d-orbital dominated molecular states. Therefore, we calculated the transition rate between the upper three and lower four molecular states and found
Figure 3. Synthesis of ammonium-[2,2’-bipyridin]-4-ylcarbamodithioate, ligand exchange onto CdSe/CdS NRs and coordination of Fe(acac)3. ACS Paragon Plus Environment
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that the transfer rates are either similar or an order of magnitude faster compared to the initial transfer from the VB to the lower four states. This indicates that a hole can be transferred from the CdS VB to the upper Fe-based mid-gap states through a two-step process in which the initial transfer from the semiconductor to the ligand is rate determining. The ability to transfer the hole to the Fe is important for future applications to catalytic oxidation at the metal site. Given the promising theoretical predictions, experiments were designed to synthesize and study the proposed ligand system.
Synthesis of the ligand ammonium-[2,2’-bipyridin]-4-ylcarbamodithioate
(Figure 3, 3) was completed via the nitration of commercially available 2,2’-bipyridine N-oxide to 4-nitro-[2,2’-bipyridine] 1-oxide (1).38 Reduction to 4-amino-2,2’bipyridine (2) was performed over Zn dust.39 The reaction of this amine with carbon disulfide
in
the
presence
of
ammonium
hydroxide40 yielded the desired dithiocarbamate as an ammonium salt (3). CdSe/CdS NRs were grown via a seeded growth approach as reported elsewhere (Supplementary Information). 41 Ligand exchange of DTCBipy onto CdSe/CdS NRs was performed by adding a solution of 3 in
Figure 4. A)UV/Visible spectrum of CdSe/CdS
toluene to NRs in toluene and stirring in the dark
NRs with native ligands (black), after ligand ex-
under Ar for 16 h. A concentration of 4.5 lig-
change with DTCBipy (red), and subsequent
ands/nm2 was determined to be optimal for sur-
treatment with Fe(acac)3 (gold) B) Fluorescence
face saturation. In order to complete the conjuga-
spectroscopy of NRs C) TRPL of NRs (see sup-
tion of a metal center to the CdSe/CdS rods, a so-
plementary information for parameters). D) PL
lution of Fe(acac)3 was added to the DTCBipy
and TRPL data.
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coordinated CdSe/CdS rods (Figure 4A, detailed experimental procedures available in SI). An additional absorbance feature appeared, peaking at 541 nm. This absorbance matches that of a free solution of DTCBipy and the iron precursor without the presence of the NRs. This absorbance also matches the computational absorbance profile of DTCBipyFe(acac)2 (Figure S4B,C) and the presence of crisp 1H NMR peaks further indicates paramagnetic low spin Fe(II) (Figure S5). Scanning transmission electron microscopy energy dispersive x-ray spectroscopy (STEM)-EDS mapping visualizes the distribution of Fe on the NRs (Figure 5). An additional wide field image (STEM)EDS map of DTCBipyFe ligand exchanged rods is available in the SI (Figure S7). Control experiments where Fe(acac)3 was mixed with NRs ligated with native ligands did not show any association between Fe and the NRs (Figure S8). Quantitative EDS (Table S1) of 10 different areas of sample revealed an average Fe signal of 2.41± 0.32 Fe atoms per nm2 of nanoparticle surface area were present. Since the amount of Fe added was 4.5 ligands/nm2 and this is greater than 2.41 ligands/nm2, this number shows persistence of the Fe only when bound to DTCBipy. Experimental validation of the predicted hole transfer from the NR to the ligands was performed by analyzing the samples via steady-state and time-resolved (TR) photoluminescence (PL) spectroscopy. Given the band alignment of CdSe/CdS, only fluorescence from the CdSe core can be observed. Ligand exchange of native ligand NRs with DTCBipy (Figure 3) resulted in a large quench in QY from 85% to 8.0% (Figure 4B), which was observed previously for DTC containing ligands.25 This is consistent with our predicFigure 5. STEM-EDS map of a CdSe/CdS tion that hole transfer from the CdS to DTCBipy is facrod ligand exchanged with DTCBipy then ile and prevents radiative recombination of excitons. treated with Fe(acac)3. Scale bar is 10 nm.
Formation of the DTCBipy-Fe complex caused a fur-
The overall picture omits S for clarity. ther quench in the QY to 0.16%, as expected since hole
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transfer was calculated to be even faster once Fe was coordinated. This QY quench was over a factor of ten larger than that seen by only adding Fe(acac)3 to a solution containing native ligand capped NRs (Figure S3). The latter is likely due to charge trapping at a small amount of Fe adsorbed to the surface, as was similarly observed by Shevchenko et. al. in the case of CdSe/CdS mixed with Au.42 Similar QY quenches were observed when exciting primarily the CdSe core, which denotes that the charge transfer process is primarily surface mediated. (Figure S11). Fits of the TRPL data for the CdSe/CdS NRs capped with native ligands showed a τavg of 23.5 ns for the fluorescence of the CdSe core, which is in good agreement with those reported elsewhere in literature.37 The bi-exponential decay (Figure S10a-b) was assigned to band edge recombination and a small amount of trapping of charges to surface states. Upon ligand exchange with DTCBipy, τavg decreased slightly to 20.9 ns (Figure 4D). The combined large QY quench and consistent lifetime dynamics indicates that the holes are mostly extracted from the photoexcited CdS rod to the ligands before they can be localized to the CdSe core. The VB offset of CdSe is 0.55 eV from the CdS VB,43 and sits above the mid-gap states so they are not accessible for hole transfer from the CdSe core. Upon chelation of Fe to the surface coordinated DTCBipy ligand, τavg quenches to 455 ps (Figure 4D) and is best fit by a tri-exponential decay with time constants of 133 ps, 1.24 ns, and 15.03 ns. While directly assigning these pathways to specific processes is difficult, a lifetime of 1.24 ns is similar to those reported for intrinsic CdSe core recombination,44 and the 133 ps component is similar to our calculated value for transition from the CdS to the ligand molecular states. The 15.03 ns component is of very low contribution to the weighted average (for more details see Figure S11c). We note that the 133 ps process is significantly longer than the sub-picosecond hole transfer times experimentally measured by the Weiss group for a conjugated DTCBipy ligand.24 This can be expected as the driving force reported for the sub-picosecond hole transfer ligand is -1.2 eV, while in the DTCBipy system the driving force for transfer from the CdS to the molecular ligand state is much smaller, as it was calculated to only be between 0.02 to - 0.38 eV.
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In summary, we have modeled and synthesized a CdSe/CdS NR system with an organic ligand capable of electronically coupling with the energetics of the NR while chelating a molecular metal center. DFT studies revealed the presence of two hybridized mid-gap molecular states on CdS in the presence of DTCBipy; these states show promising calculated hole transfer rates between CdS and DTCBipy with minimal recombination via the CB. The experimental quench in quantum yield supports this prediction, though these experiments alone cannot entirely rule out the existence of trapping or separation caused by other pathways.45-47 The chelation of Fe(II) by this complex resulted in seven mid-gap states. The calculations indicate that the rate of hole trapping should further increase and proceed most efficiently by a two-step process from the CdS to the DTC group orbitals, followed by a faster transition to the Fe center. The measured hole transfer time is slower than those seen for other DTC based ligands,24 but comparing the energetic driving forces of the processes the transfer time follows the expected trend. One of the potential advantages of this conjugated ligand design is that transitions from the ligand midgap states to the CdS CB are dipole forbidden, which in the future should facilitate slow oxidative catalytic processes to occur on the metal center, rather than facile recombination with the electron. The assembly of this system indicates great potential in the use of light as a driving force for oxidative and reductive processes in a single colloidal nanoparticle system.
ASSOCIATED CONTENT
Supporting Information. Computational procedures, nanoparticle and ligand syntheses, ligand exchange and Fe(acac)3 coordination procedure, TRPL details, procedures for collecting quantitative EDS results, calculated absorption for slab calculations, orbital charge density plots, absorbance and NMR spectra of DTCBipy-Fe free in solution, control STEM-EDS maps, and TRPL fits. This material is available free of charge via the Internet at http://pubs.acs.org.
AUTHOR INFORMATION
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Corresponding Author
* Email:
[email protected] ACKNOWLEDGMENT
The theoretical work was supported by Department of Energy grant DE-FG02-09ER46554 and by the McMinn Endowment at Vanderbilt. Computations were done using using the Extreme Science and Engineering Discovery Environment (XSEDE)48 supported by National Science Foundation grant number ACI-1053575 as well as the National Energy Research Scientific Computing Center (NERSC), a DOE office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.
Further funding for experimental work was provided
through TN-SCORE (NSF EPS-1004083) and NSF-CHE 1506587. ADL thanks the Stanley and Ann T. Tarbell Endowment Fund. REFERENCES
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23. Liu, C. M.; Qiu, F.; Peterson, J. J.; Krauss, T. D., J. Phys. Chem. B 2015, 119 (24), 7349-7357. 24. Lian, S. C.; Weinberg, D. J.; Harris, R. D.; Kodaimati, M. S.; Weiss, E. A., ACS Nano 2016, 10 (6), 6372-6382. 25. Frederick, M. T.; Weiss, E. A., ACS Nano 2010, 4 (6), 3195-3200. 26. Frederick, M. T.; Amin, V. A.; Cass, L. C.; Weiss, E. A., Nano Lett. 2011, 11 (12), 5455-5460. 27. Frederick, M. T.; Amin, V. A.; Swenson, N. K.; Ho, A. Y.; Weiss, E. A., Nano Lett. 2013, 13 (1), 287-292. 28. Frederick, M. T.; Amin, V. A.; Weiss, E. A., J. Phys. Chem. Lett. 2013, 4 (4), 634-640. 29. Fillol, J. L.; Codola, Z.; Garcia-Bosch, I.; Gomez, L.; Pla, J. J.; Costas, M., Nat. Chem. 2011, 3 (10), 807-813. 30. Wickramasinghe, L. D.; Zhou, R. W.; Zong, R. F.; Vo, P.; Gagnon, K. J.; Thummel, R. P., JACS 2015, 137 (41), 13260-13263. 31. Kresse, G.; Furthmuller, J., Phys. Rev. B 1996, 54 (16), 11169-11186. 32. Lupo, M. G.; Della Sala, F.; Carbone, L.; Zavelani-Rossi, M.; Fiore, A.; Luer, L.; Polli, D.; Cingolani, R.; Manna, L.; Lanzani, G., Nano Lett. 2008, 8 (12), 4582-4587. 33. Zavelani-Rossi, M.; Lupo, M. G.; Krahne, R.; Manna, L.; Lanzani, G., Nanoscale 2010, 2 (6), 931-935. 34. Xing, G. C.; Liao, Y. L.; Wu, X. Y.; Chakrabortty, S.; Liu, X. F.; Yeow, E. K. L.; Chan, Y.; Sum, T. C., ACS Nano 2012, 6 (12), 10835-10844. 35. Yan, Y. R.; Chen, G.; Van Patten, P. G., J. Phys. Chem. C 2011, 115 (46), 22717-22728.
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36. Keene, J. D.; McBride, J. R.; Orfield, N. J.; Rosenthal, S. J., ACS Nano 2014, 8 (10), 1066510673. 37. She, C. X.; Demortiere, A.; Shevchenko, E. V.; Pelton, M., J. Phys. Chem. Lett. 2011, 2 (12), 1469-1475. 38. Bair, J. S.; Harrison, R. G., J. Org. Chem. 2007, 72 (18), 6653-6661. 39. Aoyagi, Y.; Abe, T.; Ohta, A., Synthesis-Stuttgart 1997, (8), 891-894. 40. Humeres, E.; Debacher, N. A.; Franco, J. D.; Lee, B. S.; Martendal, A., J. Org. Chem. 2002, 67 (11), 3662-3667. 41. Hill, L. J.; Bull, M. M.; Sung, Y.; Simmonds, A. G.; Dirlam, P. T.; Richey, N. E.; DeRosa, S. E.; Shim, I.-B.; Guin, D.; Costanzo, P. J.; Pinna, N.; Willinger, M.-G.; Vogel, W.; Char, K.; Pyun, J., ACS Nano 2012, 6 (10), 8632-8645. 42. Demortiere, A.; Schaller, R. D.; Li, T.; Chattopadhyay, S.; Krylova, G.; Shibata, T.; Claro, P. C. D.; Rowland, C. E.; Miller, J. T.; Cook, R.; Lee, B.; Shevchenko, E. V., JACS 2014, 136 (6), 23422350. 43. Talapin, D. V.; Koeppe, R.; Gotzinger, S.; Kornowski, A.; Lupton, J. M.; Rogach, A. L.; Benson, O.; Feldmann, J.; Weller, H., Nano Lett. 2003, 3 (12), 1677-1681. 44. Knowles, K. E.; McArthur, E. A.; Weiss, E. A., ACS Nano 2011, 5 (3), 2026-2035. 45. Owen, J. S.; Park, J.; Trudeau, P. E.; Alivisatos, A. P., JACS 2008, 130 (37), 12279-12281. 46. Liu, I. S.; Lo, H. H.; Chien, C. T.; Lin, Y. Y.; Chen, C. W.; Chen, Y. F.; Su, W. F.; Liou, S. C., J. Mat. Chem. 2008, 18 (6), 675-682.
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47. Leatherdale, C. A.; Kagan, C. R.; Morgan, N. Y.; Empedocles, S. A.; Kastner, M. A.; Bawendi, M. G., Phys. Rev. B 2000, 62 (4), 2669-2680. 48. Towns, J.; Cockerill, T.; Dahan, M.; Foster, I.; Gaither, K.; Grimshaw, A.; Hazlewood, V.; Lathrop, S.; Lifka, D.; Peterson, G. D.; Roskies, R.; Scott, J. R.; Wilkins-Diehr, N., XSEDE: Accelerating Scientific Discovery. Science & Engineering, 2014; Vol. 16, pp 62-74.
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