Simple cubic self-assembly of PbS quantum dots by finely controlled ligand removal through gel permeation chromatography

The geometry in self-assembled superlattices of colloidal quantum dots (QDs) strongly affects their optoelectronic properties and is thus of critical importance for applications in optoelectronic devices. Here, we achieve the selective control of the geometry of colloidal quasi-spherical PbS QDs in highly-ordered two and three dimensional superlattices: Disordered, simple cubic (sc), and face-centered cubic (fcc). Gel permeation chromatography (GPC), not based on size-exclusion effects, is developed to quantitatively and continuously control the ligand coverage of PbS QDs. The obtained QDs can retain their high stability and photoluminescence on account of the chemically soft removal of the ligands by GPC. With increasing ligand coverage, the geometry of the self-assembled superlattices by solution-casting of the GPC-processed PbS QDs changed from disordered, sc to fcc because of the finely controlled ligand coverage and anisotropy on QD surfaces. Importantly, the highly-ordered sc supercrystal usually displays unique superfluorescence and is expected to show high charge transporting properties, but it has not yet been achieved for colloidal quasi-spherical QDs. It is firstly accessible by fine-tuning the QD ligand density using the GPC method here. This selective formation of different geometric superlattices based on GPC promises applications of such colloidal quasi-spherical QDs in high-performance optoelectronic devices.

Tetrachloroethylene (>99.0%, TCE) was purchased from Kanto Chemical CO. INC., Tokyo, Japan. All these chemicals were used as received.

Synthesis of PbS QDs
PbS QDs (average diameter: 7.3 nm) were synthesized using the following, slightly modified literature procedure 1 : In a glove box, a four-neck flask (25 mL) was charged with elemental sulfur (0.040 g, 1.247 mmol) and OAm (7.5 mL). The mixture was heated at 120 °C for 5 min under nitrogen, before the temperature was decreased to 80 °C. Then, PbCl 2 (1.25 g, 3.5 mmol) and OAm (7.5 mL) were added into a separate four-neck flask (100 mL), and the mixture was heated at 140 °C for 30 min, which afforded a clear Pb-oleate solution.
Then, the temperature was decreased to 110 o C and the sulfur solution (2.25 mL, 0.374 mmol) was injected into the Pb-oleate solution. After 30 min at 110 o C, the reaction was stopped by cooling in a water bath for 2 min, followed by injection of OA (20 mL) and further stirring for 2 min. An aliquot (5.0 mL) of the resulting dispersion was mixed with hexane (10 mL) and centrifuged at 4000 rpm for 3 min. The supernatant was further centrifuged at 4000 rpm for 3 min in order to remove any unreacted chemicals. Then, a butanol/methanol mixture (20 mL, 2:1, v/v) was added to the solution. The precipitated PbS QDs were collected by centrifugation at 4000 rpm for 3 min. The obtained powder was redispersed in toluene (1 mL) for the GPC measurements, and this sample is referred to as 'before-GPC' (PR1). Further precipitation and redissolution (PR) cycles (each cycle: 2 mL toluene and 4 mL butanol/methanol mixture; 4000 rpm/3 min) furnished PR2 (two cycles), PR3 (three cycles), and PR4 (four cycles).
Small PbS QDs (average diameter: 4.3 nm) were synthesized by a similar procedure. In a glove box, elemental sulfur (0.040 g, 1.247 mmol) and OAm (7.5 mL) were added to a four-neck flask (25 mL) before the mixture was heated at 120 °C for 5 min under nitrogen. Then, the temperature was decreased to 50 °C, before PbCl 2 (2.5 g, 7.0 mmol) and OAm (15 mL) were added into a separate four-neck flask (100 mL). The mixture was then heated at 140 °C for 30 min to afford a clear Pb-oleate solution. These reaction vessels were kept at their respective temperatures for 15 min, before the reaction mixture changed to a clear Pb-oleate solution. Then, the temperature was decreased to 50 o C and a sulfur solution (4.5 mL, 0.748 mmol) was injected into the Pb-oleate solution. After 70 s, the reaction was stopped via the injection of OA (40 mL), followed by further stirring for 2 min. An aliquot (7.0 mL) of the resulting dispersion was mixed with toluene (10 mL) and centrifuged at 4000 rpm for 3 min. The supernatant was further centrifuged at 4000 rpm for 3 min (twice) in order to remove any unreacted chemicals. Then, a butanol/methanol mixture (20 mL, 2:1, v/v) was added to the obtained solution. The precipitated PbS QDs were collected by centrifugation at 4000 rpm for 3 min and the resulting powder was redispersed in toluene (2 mL) for GPC measurements.

Gel permeation chromatography (GPC)
GPC was conducted on polystyrene cross-linked with divinylbenzene as the stationary phase and toluene as the eluent. Polystyrene beads (10 g) were soaked in toluene (100 mL) overnight, before the beads in toluene were loaded into a glass column (Φ diameter 10*L length 1000 mm). The flow rate of the eluent was set to 0.8 mL/min by peristaltic pumps to make the beads tightly packed, and the length of beads was stabilized at about 72 cm.
Then, before-GPC (PR1) sample in toluene (2 mL) was carefully loaded onto the top of the column. When the sample liquid interface was level with the beads, toluene as an eluent was added to column and the peristaltic pumps was connected. The flow rate was set to 0.8 mL/min. When the QDs sample flowed through the GPC column and was just about to flow out from the bottom of the column, the GPC samples began to collect. To ensure the same volume of collected fractions, the time for collecting the samples was set to 1 min. When the QDs completely flowed out from the GPC column, the consecutive fractions of PbS QD solutions (0.8 mL) were collected and labeled in order of outflow as GPC-1 to GPC-5 for further experiments.

Self-assembly of 2D and 3D superlattices
2D self-assemblies of the GPC-processed QDs were prepared by slow solvent evaporation of the QD toluene solution (0.5 mg/mL) on a TEM grid under a toluene-saturated atmosphere. 3D self-assembly supercrystals were prepared by slow solvent evaporation of the QD toluene solution (5 mg/mL) on a TEM grid under a toluene-saturated atmosphere and by immersing silicon wafer into the QD toluene solution (5 mg/mL) follow slow solvent evaporation under a toluene-saturated atmosphere.

Measurements
TGA measurements were carried out on a TA-60 with a TGA-50 workstation (Shimadzu Co., Tokyo, Japan) at a heating rate of 10 °C/min under nitrogen. XRD measurements were carried out on a SmartLab (RIGAKU Co., Tokyo, Japan). PbS QDs samples in toluene (2.0 mg/mL) were drop-cast onto a reflection-free Si wafer, and dried in vacuo at room temperature. UV-Vis-NIR spectra were recorded on a UV-3600 Plus (Shimadzu Co., Tokyo, Japan) spectrophotometer. NIR-PL spectra were measured on a PMA-12 C10028-02 NIR detector (Hamamastu Co., Tokyo, Japan). Solution samples were prepared by dissolving QDs (0.5 mg) in TCE (3 mL). The film samples were obtained by drop-casting PbS QD toluene solutions (2 mg/mL) on quartz substrates, followed by drying in vacuo at room temperature. Microscopy and selected-area electron diffraction (SAED) images were measured using transmission electron microscopes operating at 200 kV (JEM-2100F/SP, JEOL Co., Tokyo, Japan) or 80 kV (JEM-1230, JEOL Co., Tokyo, Japan). Carbon-reinforced polyvinyl formal membranes on Cu grids (Okenshoji Co., Tokyo, Japan, PVF-C10 STEM Cu100P grid) were used for the TEM measurements. Scanning electron microscopy (SEM) and STEM images were recorded on a Quattro S SEM (Talos, Thermo Fisher Scientific Co., Massachusetts, USA) operating at 5-30 kV. Samples for SEM measurements were prepared on TEM grids and hydrophilic Si wafers by self-assembly. NMR measurements were conducted on a JNM-ECZS 400M (JEOL Co., Tokyo, Japan) spectrometer. Experimental details are described for the determination of the oleate surface coverage (vide infra). For that purpose, Rutherford backscattering spectrometry (RBS) measurements were conducted on a Pelletron 5SDH2 (National Electrostatics Corp., Middleton, USA) with a He 2+ -ion-beam source (2.274 MeV). The detector was placed at a backscattering angle of 160°. RBS samples were prepared by spin coating PbS toluene solutions (10 mg/mL) on Si wafers (2×2 cm) with a rate of 1500 rpm for 30 s, followed by storing under vacuum until the measurements were carried out. Scattering signals were collected until the charge integration had reached 10 μC.

Determination of the Pb/S and Cl/Pb ratios
RBS was used to measure the atomic Pb/S ratio (R) of GPC-2 and before-GPC (PR1) QDs. The measurements were carried out using a 2.274 MeV He 2+ -ion beam. Based on the backscattered yield, R is determined by: where A Pb and A S are the peak area of the Pb and S atoms, respectively, while Z Pb and Z S are the atomic number of Pb and S, respectively 2 .

Determination of the ligand density from TGA
TGA was used to determine the ligand density of GPC-processed QDs. The weight ratio of the ligand OA and QD can be determined using the TGA curves. The number of atoms (N) in a single QD can be estimated from: where d is the QD diameter and a is the lattice constant of the PbS rocksalt structure 2 . The weight of a single QD can be calculated by N and the atomic Pb/S ratio (1.27) obtained from RBS. Based on the weight of the QD and the ligand OA, the ligand density (the number of the ligands per square nm) can be calculated.

Determination of the ligand density by NMR spectroscopy
The ligand density (nm -2 ) was also determined by 1 H NMR spectroscopy and optical absorbance following a modified version of a reported procedure 3 . GPC samples with the known weight were dispersed in anhydrous toluene-d 8 (0.6 mL) with ferrocene (0.05 mg/mL). The molar concentration of the oleate ligands was determined via the internal reference according to: (3) [ ] = [ ] × 10 × 2 where [OA] and [FC] are the molar concentration of the oleate ligands and ferrocene, respectively. I FC and I OA are the integral peak area of ferrocene and oleate ligands in the 1 H NMR spectra, respectively 3 . Due to the presence of free OA in the samples, the integral area of the ligand was calibrated by a Gaussian fit to subtract the peak of free OA ( Figure S3).
The molar concentration of the QDs was determined by optical absorption of the QDs used in the NMR measurements according to the size-dependence of the molar extinction coefficient of QDs 2 . For that purpose, the NMR solutions were diluted with TCE, and the absorbance of these solutions was measured at 3.1 eV (400 nm). The molar concentration of the QDs (C) was estimated according to: where A 3.1 eV is the absorbance at 3.1 eV, l is the path length (cm), and d is the QD diameter (nm). According to the molar concentration of the ligand OA and QD, the ligand density (the number of the ligands per square nm) can be calculated 3 .

Preparation of liquid/air assembly films
Liquid/air assembly films were prepared according to a literature procedure 4 . A before-GPC toluene solution was carefully dropped onto the liquid plane of DMSO in a small container. TEM grids and quartz glass were used as substrates, and the self-assembled films were transferred on these. The self-assembled films on the substrates were immersed into methanol in order to remove excess DMSO and then dried in vacuo at room temperature.