Brightness-equalized quantum dots

As molecular labels for cells and tissues, fluorescent probes have shaped our understanding of biological structures and processes. However, their capacity for quantitative analysis is limited because photon emission rates from multicolour fluorophores are dissimilar, unstable and often unpredictable, which obscures correlations between measured fluorescence and molecular concentration. Here we introduce a new class of light-emitting quantum dots with tunable and equalized fluorescence brightness across a broad range of colours. The key feature is independent tunability of emission wavelength, extinction coefficient and quantum yield through distinct structural domains in the nanocrystal. Precise tuning eliminates a 100-fold red-to-green brightness mismatch of size-tuned quantum dots at the ensemble and single-particle levels, which substantially improves quantitative imaging accuracy in biological tissue. We anticipate that these materials engineering principles will vastly expand the optical engineering landscape of fluorescent probes, facilitate quantitative multicolour imaging in living tissue and improve colour tuning in light-emitting devices.

) and cadmium myristate (Cd(MAc) 2 ) synthesis. Cd(BAc) 2 was prepared using literature methods. 2,3 CdCl 2 (5 mmol) was dissolved in methanol (200 mL), filtered to remove any undissolved debris, and transferred to a 500-mL dropping funnel. BAc (15 mmol) was dissolved in a mixed solvent of methanol (1.25 L) and chloroform (150 mL) with the addition of TMAH (25% wt. in methanol, ~8 mL). The mixture was stirred for >1 h until complete dissolution of the white BAc powder, and the solution was filtered to yield a clear, colorless solution. The CdCl 2 solution was added dropwise to the BAc solution with vigorous stirring in a 2-L beaker. The entire CdCl 2 solution was added in ~1 h and the mixture was left stirring for an additional 1 h. Cd(BAc) 2 was collected by vacuum filtration and washed three times with methanol (150-200 mL per wash) on a filter funnel. The product was dried on the funnel for several hours and then dried under vacuum at ~50°C overnight. Cd(MAc) 2 was synthesized using the same process except BAc was replaced with MAc and chloroform was not used to dissolve MAc.
Hg(OT) 2 synthesis: Hg(OT) 2 was synthesized by following literature protocols. 4 Briefly, Hg(Ac) 2 (2 mmol) was dissolved in methanol (100 mL) and filtered. OT (6 mmol) was mixed with methanol (1 L) and KOH (6 mmol). Hg(Ac) 2 solution was added dropwise to the OT solution while vigorously stirring to produce a white Hg(OT) 2 precipitate. Hg(OT) 2 was collected by vacuum filtration and washed multiple times with methanol, and once with ether. The product was dried overnight under vacuum.
40% octylamine-modified polyacrylic acid (amphiphol) synthesis: Amphipol was synthesized and purified using methods described in the literature. 5 Table S1. The QDs were purified by diluting the reaction mixture with toluene (3 mL) followed by precipitation with excess methanol (~40 mL). After two more cycles of dissolution in toluene and precipitation with methanol, purified QDs were dissolved in hexane and stored as a pure stock solution.

nm
CdSe -CdO (0.6 mmol), TDPA (1.33 mmol), and ODE (27.6 mL) were mixed in a 250-mL r.b.f. and heated to ~320°C under nitrogen until the mixture became a clear colorless solution. HDA (7.1 g) was added and the temperature was stabilized at 300°C. A Se precursor solution was prepared by mixing a Se/TOP stock (1 M, 3 mL), DPPSe (52.5 mg), and TOP (4.5 mL) under nitrogen. QDs were grown by swiftly injecting the Se solution into the Cd solution with vigorous stirring using a 10-mL syringe with a wide bore (16 G) needle. 30s after the Se injection, the heating mantle was quickly removed and the reaction solution was rapidly cooled under a stream of air. The reaction solution was divided into two 50-mL tubes and QDs were precipitated by adding a mixture of methanol (15 mL) and acetone (15 mL). QDs were then redispersed in hexane and purified by methanol extraction. Finally, purified QDs dispersed in hexane were stored as a concentrated stock solution. Purification was performed by precipitating the QDs through the addition of a mixture of methanol (15 mL) and acetone (15 mL). QDs were redispersed in hexane (~20 mL) and extracted twice with methanol (5-10 mL per cycle) followed by precipitation with excess methanol. Finally, QDs were washed with a few mL of acetone to ensure that there was no methanol remaining, and dispersed in hexane as a stock solution. , and ODE (4 mL) were mixed in a 50-mL r.b.f. and dried under vacuum at ~100°C for 2 hours. Then CdS QDs were grown by raising the temperature to 230°C at a rate of ~20°C/min under nitrogen. The temperature was maintained at 230°C for 15 min before cooled to ~110°C for purification. The purification procedure was the same as for the 3.0 nm CdSe synthesis.

nm CdS
-TBPS was synthesized by sonicating S powder in TBP under nitrogen with 1:1 Sto-TBP molar ratio. Cd(BAc) 2 (0.2 mmol), HDD (0.2 mmol), and ODE (3.2 mL) were mixed in a 50-mL r.b.f. and dried under vacuum at ~100°C for 2 hours. TBPS (1.25 M) in an ODE stock solution (0.8 mL) was injected under nitrogen and the temperature was increased to 230°C at a rate of ~20°C/min. CdS nucleated at ~110°C. The temperature was maintained at 230°C for 30 min before cooled down to ~110°C for purification. The purification procedure was the same as for the 3.0 nm CdSe synthesis.

nm
CdS -A solution of S in ODE was prepared by mixing S powder (1 mmol) with ODE (10 mL) under nitrogen and heating to ~200°C until the mixture became a clear colorless solution. Cd(BAc) 2 (0.2 mmol), S (0.2 mmol), 2,2'-dithiobisbenzothiazole (0.0625 mmol), HDD (0.2 mmol), and ODE (3.4 mL) were mixed in a 50-mL r.b.f. and dried under vacuum at ~100°C for 2 hours. Then CdS QDs were grown by heating the solution to 230°C at a rate of ~20°C/min under nitrogen. After keeping the temperature at 230°C for 15 min, the dropwise addition of 0.1 M S/ODE stock solution (1 mL) over ~40 min allowed additional particle growth.

HgCdSeS alloy core synthesis
HgCdSeS QDs were prepared through Hg cation exchange reactions on CdSe or CdSeS QDs using method developed by Smith & Nie 4,6 with several modifications.
Hg exchange using Hg(OT) 2 -A CdSe or CdSeS QD stock in hexane (~100 nmol in a few mL of hexane) was injected into OLA (5 mL) under nitrogen and hexane was evaporated completely under vacuum at 40-50°C. Hg exchange was initiated by adding Hg(OT) 2 (2x excess of total Cd atoms) either as powder or as a solution in OLA (0.1 M). The reaction rate was adjusted by gradually increasing the temperature (40-150°C). Changes in the bandgap energy and the absorption extinction were carefully monitored by removing precise aliquot volumes (typically 200 µL, then diluted 10-fold with chloroform) every 3-5 min to measure the UV-vis-NIR absorption spectrum. Detailed reaction parameters are provided in Table S2. When a desired amount of redshift was induced, reaction quenching and purification were performed by precipitating the QDs through the addition of a 1:1 mixture of methanol /acetone (~30 mL total). The QD precipitate was washed two times with methanol then finally dispersed in hexane to be used as a stock solution. The stock solution was left at room temperature for at least a day before use in core/shell QD synthesis because there was typically an additional 10-15 nm redshift in the absorption spectra over time due to internal diffusion of Hg ions.
Hg exchange using Hg(Ac) 2 -CdSe QDs (100-200 nmol) were dispersed in a 0.2 M solution of OLA in chloroform (4-5 mL). A 0.1 M Hg(Ac) 2 (OLA) 2 stock solution was prepared by dissolving Hg(Ac) 2 (0.5 mmol) in a 0.2 M OLA solution in chloroform (5 mL). Hg exchange was initiated by swiftly injecting the Hg(Ac) 2 (OLA) 2 solution (3x excess of total Cd atoms) into the CdSe QD solution under vigorous stirring. The extent of Hg exchange was carefully monitored by taking absorption spectra of aliquots (~100 µL, then diluted 10-fold with chloroform) every 3-5 min. After the desired amount of redshift, the reaction was quenched by adding OT (~100 µL) and precipitating the QDs with a 1:1 mixture of methanol/acetone (~20 mL total). QDs were further purified by three cycles of redispersion in hexane (~10 mL) with OLA (~200 µL) and OAc (~100 µL) and precipitation with methanol/acetone. Finally, the QDs were dispersed in hexane and stored as a stock solution for at least a day before use in core/shell QD synthesis.

Supplementary Note 3: CdS and ZnS shell growth
CdS and ZnS shell growth was performed using a layer-by-layer shell growth protocol developed by Bawendi and coworkers 10 with some modifications.
Cd precursor solution -A Cd precursor solution was prepared by mixing CdO (1 mmol), OAc (2.1 mmol), and ODE (3.9 mL) and heating to ~250°C under nitrogen until the brown mixture became a clear solution. After cooling to ~100°C, DA (2 mmol) was added. Then the solution was diluted 1:1 with TOP.
S precursor solution -A S precursor solution was prepared by dissolving (TMS) 2 S (0.5 mmol) in TOP (5 mL) under nitrogen.
Layer-by-layer shell growth -To prevent homogeneous nucleation of shell materials, CdS shell was grown as increments of 0.8 ML instead of 1 ML. 1 ML thickness was set to ~0.3 nm which is the thickness of a single CdS layer along the (100) ZB direction. The amount of precursors needed was calculated based on the volume increase by the shell growth in a single monolayer and the total number of cores in the solution. In a typical reaction, a purified core stock in hexane (50-100 nmol) was injected into a mixed solvent of ODE (2 mL) and OLA (1 mL) in a 50-mL r.b.f. and hexane was completely evaporated under vacuum at 40 -50°C. Next, the solution was heated under nitrogen to the temperature used for the first 0.8 ML shell growth (typically 120-130°C for 2-3 nm cores and HgCdSeS cores, and 150-170°C for >4 nm cores). An aliquot (200 µL) was withdrawn using a glass microsyringe and diluted 10-fold in chloroform to monitor the reaction. The S precursor for the first 0.8 ML shell was dropwise added within 3-5 min and allowed to react for 15-20 min. The same amount of Cd precursor was added in the same manner and allowed to react for another 15-20 min to complete the first cycle. Another aliquot (200 µL) was withdrawn and diluted 10-fold in chloroform to measure the absorption and emission spectra, fluorescence quantum yield, and extinction coefficient. The 0.8 ML shell growth cycle was repeated as desired. The reaction temperature was raised stepwise by ~10°C between each cycle until reaching a maximum of ~190°C. Aliquots were withdrawn after each cycle to monitor the optical property changes during shell growth.
After growing a desired amount of CdS shell, the metal precursor was switched to Zn to grow the ZnS shell, which was grown in either 0.5 ML (in Figure 4) or 0.8 ML (in Supplementary  Figures 7 and 9) steps. The reaction temperature for ZnS shell growth was 200-220°C. Aliquots were similarly withdrawn after each 1 ML (in 0.5 ML step growth) or 0.8 ML (in 0.8 ML step growth) of shell growth.
The reaction was quenched by reducing the temperature. For purification, the reaction solution was diluted 2-3 fold in chloroform in a centrifuge tube and the QDs were precipitated by adding acetone. QDs were redispersed in chloroform and centrifuged at 7,000 g for 10 min to remove any undissolved byproducts. Then this chloroform solution was used for optical analysis and phase transfer.

First monolayer of CdS shell growth on HgCdSe cores using TOP-free Cd & S precursor
solution -Because of the strong binding affinity of TOP toward mercury ions, TOP could degrade bare HgCdSeS QDs by extracting Hg ions out of the structure. Such extraction was accelerated at elevated temperatures. Thus, the first monolayer of CdS shell needed to b e grown in a TOP-free solution and at relatively low temperature. The first 0.8 ML portion of TOPfree S precursor was added dropwise starting at ~50°C while slowly raising the temperature up to 120-130°C in ~5 min. After allowing the S precursor to react for 15-20 min at 130°C, TOPfree Cd precursor for the first 0.8 ML shell was added dropwise at ~140°C and allowed to react for another 15-20 min. Once HgCdSeS QDs were passivated by a full monolayer of CdS shell, they were stable against TOP so that the regular TOP-containing precursors could be used for the further shell growth.
A TOP-free Cd precursor solution was prepared by mixing CdO (1 mmol), OAc (2.1 mmol) , and ODE (8.9 mL) and heating to ~250°C under nitrogen until the brown mixture became a clear solution. The solution was cooled to ~100°C and DA (2 mmol) was added. The solution was then cooled to room temperature.
A TOP-free S precursor solution was prepared by dissolving (TMS) 2 S (0.5 mmol) in ODE (5 mL) under nitrogen.

Supplementary Note 4: Quantum dot phase transfer
QD phase transfer with amphiphilic polymers. A purified core/shell QD dispersion in chloroform (~1 nmol/mL, 2-10 mL) was transferred to a vial with a stir bar. In a separate vial, amphipol (~200 mg) was dissolved in chloroform (10 mL) at room temperature. While vigorously stirring the QD dispersion, a 2,000-2,500x molar excess of amphipol was added dropwise. The vial was sealed with a septum screw cap and placed in a vacuum desiccator with a puncture on the cap using a disposable needle (20-22 G). Chloroform was slowly evaporated overnight under house vacuum while vigorously stirring the solution. After completely removing chloroform, 10 mM sodium hydroxide solution in distilled water was added (2-3 mL/nmol of QD) and stirred for several hours until amphipol-coated QDs were fully dispersed. Finally, the solution was centrifuged at 7,000 g for 10 min to remove any QD aggregates and used in optical characterization including brightness measurements in solution and at the single molecule level. For intravital imaging experiment, these amphipol-coated QDs were purified using a sizeexclusion column and dialysis. Typically, 30-40 nmol of amphipol-coated QDs in 1x phosphate buffered saline (PBS) was injected into a GE ÄKTAprime plus chromatography system using a Superose 6 column with PBS eluent at a flow rate of 0.5 mL/min. This separated amphipol-coated QDs with most of the free amphipol micelles. Then, these QDs were further purified by dialysis for 36 h in PBS using a 50 kDa dialysis tube.

PEG conjugation on polymer-coated QDs.
Amphipol-coated QDs show strong nonspecific binding in biological systems due to the negatively charged carboxylic acid groups covering the surface. Therefore, for the intravital multiphoton imaging experiments, amphipol-coated QDs were conjugated with amino-polyethylene glycol (amino-PEG). PEG coating was performed by following a protocol in the literature. 6 Typically, amphipol-coated QD solutions in 1x PBS (~1 nmol/mL, ~10 mL) were mixed with 40,000x molar excess of 750 Da amino -PEG in DMSO (~0.5 mL) at room temperature. Then, a 25,000x molar excess of freshly prepared solution of DMTMM in DMSO (0.5 M) was injected into the QD-amino-PEG solution and stirred at room temperature for 30 min. This DMTMM addition and reaction was repeated 4 more times to maximize the PEG conjugation on QD surface. The reaction was quenched by adding 1M Tris buffer (pH ~8.5), and QDs were purified by dialysis in PBS for 24 h. Finally, PEG-coated QDs in PBS were centrifuged at 7,000g for 10 min to remove any aggregates and filtered using a 200 m pore-size syringe filter.

QD phase transfer with multidentate polymers.
Purified core/shell QDs dispersed in hexane were phase transferred to NMF with the addition of TMAH (100 equivalent to the QD surface atoms). The resulted OH-capped QDs in NMF were then mixed with a multidentate polymer (5 equivalent of to the QD surface atoms). The mixture was stirred for 2 h at 50°C under N 2 . To remove excess free ligands and organic solvent, the QDs dispersion was first diluted with 50 mM sodium borate buffer (pH 8.5) and re-concentrated using an Amicon Ultra centrifugal filter (50 kDa MWCO). This dilution-concentration cycle was performed 4 more times.
QD phase transfer with hydrophilic thiols. Purified QDs in CHCl 3 were mixed with an aqueous solution of the thiol ligand. The biphasic mixture was stirred at 50°C for 2 h under N 2 . Phase transfer from organic phase to aqueous phase was indicated by disappearance of fluorescence in the CHCl 3 phase. To remove excess free ligands and organic solvent, the QDs dispersion was first diluted with 1x PBS (pH 7.4) and then re-concentrated using an Amicon Ultra centrifugal filter (50 kDa MWCO). This dilution-concentration cycle was performed 4 more times.

Supplementary Note 5: Instrumentation
UV-Vis-NIR absorption spectroscopy. Absorption spectra of quantum dot solutions were obtained using a Agilent Cary 5000 UV-Vis-NIR spectrometer. If the solution was highly concentrated (e.g. QD solutions for elemental analysis), an aliquot was diluted 10 or 20 fold so that their absorbance was in the dynamic range of the spectrometer (absorbance < 4) in the entire spectral range (typically 200-800 nm).

Fluorescence and photoluminescence excitation (PLE) spectroscopy.
Fluorescence and PLE spectra of a QD dispersion were obtained using a Horiba NanoLog spectrofluorometer. Dispersions were diluted enough to eliminate self-quenching of fluorescence (typically, absorbance @ 490nm < 0.1). Signal acquisition conditions such as scan time, slit widths, and number of scans were adjusted so that the brightest sample was not saturating the detector (photomultiplier tube) and all spectra showed sufficiently high signal-to-noise ratios. Raw fluorescence signal measured by the detector was corrected by both the wavelength-dependent detector sensitivity factor provided by the manufacturer and the excitation power fluctuation monitored by a built-in photodiode before they were used in fluorescence quantum yield and brightness calculations. PLE spectra were usually obtained by fixing the detection wavelength at the fluorescence peak maximum scanning the excitation wavelength from ~300 nm up to 10-30 nm less than the detection wavelength.

Transmission electron microscopy (TEM). TEM images of QDs were obtained using a JEOL 2010 LaB 6 high-resolution microscope in the Frederick Seitz Materials Research Laboratory
Central Research Facilities at the University of Illinois. Samples were prepared by placing a drop of dilute QD solution in hexane or chloroform on an ultrathin carbon film TEM grid (Ted Pella, Product# 01824) and then wicking the solution off with a tissue.
Inductively coupled plasma-optical emission spectrometry (ICP-OES). Elemental analysis was performed with a PerkinElmer Optima 2000DV ICP-optical emission spectrometer in the Microanalysis Laboratory at the University of Illinois. Samples were prepared by digesting QDs with nitric acid under high pressure (60 bar) in a PerkinElmer/Anton Parr Multiwave 3000 microwave digester. Typically, a concentrated well-purified QD solution in hexane (band edge absorption near 30-40) was prepared and its absorption spectrum was carefully measured to calculate the extinction coefficient. Then, the solution (1 mL) was transferred to a Teflon tube and hexane was completely evaporated under nitrogen flow. Three identical samples were prepared simultaneously for a precise measurement. QDs were digested into ions in the microwave reactor and the entire product was diluted to exactly 20 mL in distilled water before injection into the ICP-OES spectrometer.
Fluorescence microscopy. All samples were imaged via wide-field illumination on a Zeiss Axio Observer.Z1 inverted microscope with a 100x 1.45 NA alpha Plan -Fluar oil immersion microscope objective with 100 W halogen lamp illumination. Excitation light was filtered using a 390/40 bandpass filter (Semrock Inc.), and emission light was filtered with a 496 longpass filter (Semrock Inc.). Images were acquired using a Photometrics eXcelon Evolve 512 EMCCD through Zeiss Zen software. All samples were uniformly excited and data was collected for 30 seconds at a rate of 19.4 frames/s. Excitation power was acquired using a PM121 optical power meter (Thor Labs).
Multiphoton fluorescence brightness measurement. All samples were measured using a Zeiss 710 confocal scanner Azio Observer.Z1 inverted microscope with a 10x 0.30 NA EC Plan-Neofluar microscope objective with tunable Mai-Tai Ti-Sapphire laser (Spectra Physics) excitation. Laser power was acquired using a PM121 optical power meter. Spectrally resolved emission spectra were acquired using a Zeiss 34-Channel QUASAR detection unit.

Calculation of extinction coefficient () and absorption coefficient ()
Extinction coefficients,  (cm −1 M −1 ), of QDs were calculated using the Beer-Lambert law of absorbance described in eq. 1, where A is the absorbance of a QD solution (unitless), l is the path length (cm), and c QD is the concentration of QD (M). A of a QD solution was directly measured using UV-vis-NIR absorption spectrophotometry. l was determined by the dimension of the cuvette holding the solution in the beam path. c QD was derived from two independent measurements: average QD size (radius), r (nm), obtained by transmission electron microscopy (TEM) and elemental concentration of Cd in the solution, c Cd (M), acquired from elemental analysis. Then, r is used to calculate the average number of Cd atoms in a single QD, n Cd , relying on the assumption that all QDs are spherical and have density of the bulk material, d Bulk , as expressed in eq. 2, where, M is the molecular weight of the material (g·mol −1 ) and N A is the Avogadro constant (6.022 × 10 23 mol −1 ). Then c Cd can be converted to c QD by eq. 3, The absorption coefficient,  (cm −1 ), was then derived from the absorption extinction coefficient by the relationship given in eq. 4, 11  and  of CdSe, CdS and CdSeS cores were obtained by carrying out the above steps.
Whereas, those of HgCdSe(S) alloy cores and all core/shell QDs were acquired by carefully measuring the changes in absorption spectra during Hg cation exchange and shell growth reactions, respectively, based on the assumption that total QD concentration remains constant through the reaction.

Supplementary Note 7: Quantum yield measurements
Detailed mathematical formulations and experimental protocols for fluorescence quantum yield (QY) measurements are well described in the literature. [11][12][13] The QYs of our QD samples were obtained by following standard relative QY measurement protocols described in those literature reports. This section briefly covers the basic equations necessary for QY calculation and discusses in detail the protocols for excitation energy-dependent QY measurement of QD samples.

Relative QY calculation
QY of a fluorophore ( f ) is defined as the ratio of the number of emitted photons ( N Em ) to the number of absorbed photons (N Abs ) as eq. 5, 12 QY of a fluorescent sample is often determined by comparing its fluorescence with that of a reference with known QY (e.g. molecular dyes) both measured using the same instrumental setup. The ratio between the QY of a sample excited at  Ex,x ( f,x ( Ex,x )) and that of a reference excited at  Ex,Ref ( (6) where the subscript "x" and "Ref" denote the sample and reference, respectively, F( Ex ) is the integrated fluorescence photon flux with excitation at  Ex , q P ( Ex ) is the excitation photon flux at  Ex , f( Ex ) is the absorption factor at  Ex , and n is the refractive index of the solvent. Therefore eq. 6 indicates that N Em and N Abs are proportional to F( Ex ) (total amount of emitted photon flux) and q P ( Ex ) × f( Ex ) (total amount of excited photons), respectively, and the refractive index difference needs to be considered when comparing two different fluorophores.
F( Ex ) is the fluorescence photon flux generated by exciting the fluorophore at  Ex and measured at  Em (q P,Ex f ( Em )) integrated over the entire emission spectrum ( a   Em   b ) as in eq. 7,  (7) q P,Ex f ( Em ) is the emission intensity measured at  Em (I Ex ( Em )) corrected by the wavelengthdependent responsivity of the detector (s( Em )). Since the QY is the ratio between the number of photons, I( Em ) should be presented as a photonic quantity (e.g., photon counts per second (cps)). If I( Em ) is measured as a radiometric quantity (e.g. W/s), it should be converted to a photonic quantity by dividing with f( Ex ) is defined as the fraction of excitation photons absorbed by the sample at  Ex which can be formulated in terms of transmittance (T( Ex )) or absorbance (A( Ex )) using eq. 8, q P ( Ex ) is excitation source intensity at  Ex measured by photodetector are corrected by the wavelength-dependent sensitivity of the detector as in the emission photon flux calculation. Also it must be read as or converted to a proper photonic quantity that is linearly proportional to the number of excitation photons.
Excitation wavelength-dependent quantum yield calculation using the photoluminescence excitation spectrum Photoluminescence excitation (PLE) spectra provide the change in the fluorescence intensity at a specific emission wavelength ( Em Max ) depending on the excitation wavelength, or a plot of q P,Ex f ( Em * ) versus  Ex . If the shapes (e.g.  Em Max , FWHM) of the fluorescence spectra obtained at different excitation wavelengths are identical, the integrated fluorescence photon flux F( Ex ) can simply be derived from the PLE spectrum and one F( Ex ) measured at a reference excitation wavelength according to eq. 9,

Absorption factor (f) vs absorbance (A) in quantum yield calculation
For very dilute samples (A < 0.1), the absorption factor f( Ex ) is often replaced by absorbance A( Ex ) by using a power series expansion as shown in eq. 9 and eq. 10. . Moreover, such deviation quickly becomes enormous when the absorbance of a sample further increases relative to the absorbance of the reference. In fact, this is generally the case for calculating an excitation wavelength-dependent QY of a QD sample from its PLE spectrum. Although for a dilute QD solution with an absorbance < 0.1 near the bandedge, the solution can still show very high absorbance as the wavelengths gets shorter due to the band-type electronic structure of a QD as shown in panel b. Hence, it is unavoidable that the sample is excited at regions where the sample absorbance is much higher than the reference absorbance when collecting a PLE spectrum, and there can be a significant error when absorbance is used instead of absorption factor in the QY calculation.

Measurement of excitation wavelength-dependent quantum yield of quantum dots
Sample preparation: A fluorescein solution in 1 mM NaOH water ( f,Ref = 0.92; n = 1.333) was used as the QY reference. [13][14] The fluorescein absorbance at the lowest energy absorption peak (490 nm) was adjusted to 0.03-0.05. QD sample solutions were prepared in either chloroform (organic soluble QDs; n = 1.445) or 10 mM NaOH water (amphipol-coated water-soluble QDs; n = 1.333). QD solutions were centrifuged to remove any QD aggregates or undissolved debris that may induce scattering. Then the solutions were diluted to make the absorbance at 490 nm 0.03-0.05.

Relative quantum yield measurement:
The absorption spectrum of a sample or the reference was first obtained by absorption spectrophotometry. The spectrum was then converted to an absorption factor spectrum for the QY calculation. The emission spectrum was obtained by exciting the sample either at 490 nm ( Ex of fluorescein) or 400 nm. Data acquisition conditions such as excitation & emission slit width, emission acquisition time, and number of scans were adjusted to obtain the signals with the highest signal-to-noise ratio within the dynamic range of the detectors. Then the condition was kept the same for all samples and the reference. The emission intensity was recorded in cps unit (photonic scale). The spectrum was corrected by the blank spectrum of solvent then multiplied by the wavelength-dependent sensitivity correction factor for the detector acquired from the manufacturer to represent the emission photon flux. Then, this corrected emission spectrum was integrated over the entire emission wavelength range to calculate the total fluorescence photon flux ( N Em ). The photon flux of the excitation source was monitored simultaneously by a silicon photodiode built in the sample compartment of the fluorometer. The diode read the relative photon flux in microAmp unit (a photonic scale) and it was also corrected by its wavelength-dependent sensitivity given by the manufacturer. Then, excitation photon flux was multiplied by the absorption factor at the same wavelength (  N Abs ), and used to normalize the total fluorescence photon flux ( N Em /N Em ). Finally, QY was determined by calculating the ratio between this normalized quantity of a sample against that of the fluorescein reference. A PLE spectrum was obtained by monitoring the emission signal at the peak maximum and sweeping the excitation wavelength (typically from ~350 nm up to 20 -40 nm shorter than the peak maximum. Both emission and excitation photon fluxes were corrected by the detector sensitivities and the PLE curve was obtained by plotting the emission photon flux divided by the excitation photon flux against the excitation wavelength. Excitation wavelength-dependent QY was then calculated by dividing the PLE spectra with the absorption factor spectra.