Cesium lead bromide perovskite nanocrystals synthesized via supersaturated recrystallization at room temperature: comparison of one-step and two-step processes

Over more than a decade, lead halide perovskites (LHPs) have been popular as a next-generation semiconductor for optoelectronics. Later, all-inorganic CsPbX3 (X = Cl, Br, and I) nanocrystals (NCs) were synthesized via supersaturated recrystallization (SR) at room temperature (RT). However, compared to the hot injection (HI) method, the formation mechanism of NCs via SR-RT has not been well studied. Hence, this study will contribute to elucidating SR-RT based on the LaMer model and Hansen solubility parameter. Herein, we also demonstrate the entropy-driven mixing between two dissimilar polar-nonpolar (DMF–toluene) solvents. Next, we find that, in a poor solvent (toluene ≫ DMF in volume), ∼60 nm sized CsPbBr3 NCs were synthesized in one step, whereas in a marginal solvent (toluene ≈ DMF), ∼3.5 nm sized NCs were synthesized in two steps, indicating the importance of solvent polarity, specifically the ‘solubility parameter’. In addition, in the presence of a CuBr2 additive, high-quality cubic NCs (with ∼3.8 nm and ∼21.4 nm edge sizes) were synthesized. Hence, through this study, we present a ‘solubility parameter-based nanocrystal-size control model’ for SR-RT processes.


Introduction
All-inorganic cesium lead halide perovskite (LHP) (CsPbX 3 , X = Cl, Br, and I) nanocrystals (NCs), also called quantum dots (QDs) in the case of zero dimension (0D), have received increasing attention as emerging semiconductors in nextgeneration optoelectronic devices, including light emitting diodes (LEDs), solar cells, photodetectors, 1,2 eld-effect transistors (FETs), 3 lasers, sensors, 4,5 and quantum communication elements. 6][9][10] In addition to their outstanding luminescence performance, CsPbX 3 NCs offer the advantage of tunable energy bands through chemical and morphology modulation. 11reen-emitting CsPbBr 3 NCs were tuned to a blue emitter by adjusting the stoichiometry of halide (bromide and chloride) anions. 12,13However, LHP NCs with mixed halides are known to have drawbacks such as low defect tolerance of chlorine anions and phase instability upon exposure to light and/or voltage when applied as a blue light source in lighting and display technology. 13The other strategy for blue-emitting LHP NCs relies on the quantum connement effect, a unique property of low-dimensional semiconductors.5][16][17] However, the fast nucleation and growth rate of CsPbBr 3 NCs, originating from their low particle formation energy and so ionic lattice structure, makes it difficult to control the size and morphology of NCs in the highly quantum conned region. 18o address the precise control of the size and shape of LHP NCs, several processing methods such as 'hot-injection (HI)', 'ligand-assisted reprecipitation (LARP)', and 'room-temperature (RT) supersaturated recrystallization (SR)' have been employed. 10,19,20For example, Kovalenko and coworkers

Nanoscale Advances
PAPER controlled the size of CsPbX 3 NCs in the range of 4-15 nm edge lengths by varying the reaction temperature from 200 to 140 °C in 2015. 10Rogach et al. demonstrated the size-tuned bandgap of CH 3 NH 3 PbBr 3 NCs by varying the precipitation temperature from 0 to 60 °C via LARP routes. 19Later, in 2016, Zeng and coworkers invented an RT-SR (a special case of LARP) method for the synthesis of CsPbX 3 NCs within a few seconds at ambient conditions without any inert gas and local injection operation. 20urthermore, ligand composition and LHP precursor concentration were varied to control the size of the NCs. 21,22Son et al. accurately controlled the CsPbX 3 NC size with high ensemble uniformity utilizing thermodynamic equilibrium. 18Pradhan et al. reported the precise step-growth process of CsPbBr 3 NCs via unit cell size (∼0.6 nm) increment. 16Zhang et al. demonstrated the size and shape control of LHP NCs using suitable amounts of water, contrary to the common preconception that LHPs may rapidly decompose when exposed to polar solvents such as water. 23Interestingly, Yang et al. achieved the controlled synthesis of ∼3 nm sized CsPbBr 3 NCs using the cryogenic temperature synthetic strategy. 24][27][28] The nucleation and growth processes of LHP 29,30 and cadmium chalcogenide (CdX, X = S, Se, and Te) 31,32 NCs have been interpreted based on the classical LaMer model introduced in the 1950s. 33,34However, studies on the formation mechanism of colloidal NCs have been mostly focused on the popular HI 10,35 and heat-up 31,32 processes instead of the SR (LARP) 19,20,36 method operating at RT. Hence, this work is dedicated to elucidating the NC formation mechanism for the green-and blue-emitting CsPbBr 3 NCs synthesized via one-step and two-step SR processes at RT, respectively.For this purpose, we additionally employ, for the rst time, the Hildebrand and Hansen solubility parameters 37 determining the NC size (green or blue emitter) through the balance between the formation and dissolution of CsPbBr 3 NCs in solvent mediumgood (polar), marginal (partially polar) or poor (nonpolar).We nd that the partially-polar marginal solvent medium is suitable for blueemitting NCs whereas the nonpolar poor solvent quality is acceptable for green-emitting NCs.Furthermore, to understand the solvent-antisolvent (e.g., the binary DMF-toluene system) miscibility, we employ the Flory-Huggins theory 38,39 predicting the entropy-driven mixing between two dissimilar polarnonpolar solvents, enabling the SR routes using solvent-antisolvent engineering for the synthesis of CsPbBr 3 NCs at RT.

Synthesis of CsPbBr 3 NCs: one-step process
The precursor solution was prepared by dissolving PbBr 2 (0.2 mmol), CsBr (0.2 mmol), OA (0.5 mL), and OAm (0.25 mL) in DMF (5 mL) under stirring for 2 hours at room temperature.Then, 1 mL of the solution was added to 10 mL toluene (i.e., toluene [ DMF in volume) under vigorous stirring.Immediately, the formation of CsPbBr 3 NCs was veried with a bright green-light emission in the solution under a 365 nm UV lamp.

Synthesis of CsPbBr 3 NCs: two-step process
The precursor solution was prepared by dissolving PbBr 2 (0.2 mmol), CsBr (0.2 mmol), OA (0.5 mL), and OAm (0.25 mL) in DMF (5 mL) under stirring for 2 hours at room temperature.Then, 5 mL of toluene was added to the 5 mL solution (toluene z DMF in volume) under vigorous stirring to obtain the rst stage of crystallization.Then, aer aging for 2 min, 1 mL of the solution was added to 10 mL toluene (toluene [ DMF) to nalize the crystallizationthe second stage in the two-step process.Immediately, the formation of CsPbBr 3 NCs was veri-ed with a bright blue-light emission in the solution under a 365 nm UV lamp.Note that all the synthesis reactions were carried out without any inert gas in the air.

Purication
For comparison purposes, the solutions of both NCs synthesized by one-step and two-step processes were centrifuged at 9000 rpm for 5 min, and the precipitates were collected and characterized.In this report, for the two-step synthesis, the precipitant is referred to as the unpuried CsPbBr 3 NCs.To purify the NCs synthesized by two steps, the solution was rst centrifuged at 3500 rpm to separate larger NCs and/or aggregation as precipitate and smaller ones as supernatant.The supernatant was collected and further centrifuged at 8500 rpm for 10 min to separate NCs from the solution, and the NCs are referred to as the puried CsPbBr 3 NCs in this report.Finally, the supernatant was discarded, and the precipitate was dispersed in toluene for further characterization.In this study, CsPbBr 3 NCs synthesized via the one-step process were used without further purication.

Characterization
The ultraviolet-visible (UV-Vis) absorption spectra of asprepared NCs in toluene solution were obtained using the P9 UV-Vis spectrophotometer, China.The luminescence of NCs was recorded by the Cary Eclipse Fluorescence spectrophotometer, Malaysia.The crystal structure of the NCs was examined by X-ray diffraction (XRD) with Cu Ka radiation, l = 1.5406Å at 30 kV and 25 mA (Drawell XRD 7000, China).The morphology and microstructure as prepared NCs were analyzed by high-resolution transmission electron microscopy (HR-TEM)

Computational details
In order to understand the electronic structures of CsPbBr 3 perovskite, the density functional theory (DFT)-based rstprinciple calculations as in the Quantum ESPRESSO package were carried out. 40The generalized gradient approximation (GGA) functional of Perdew-Burke-Ernzerhof for solids (PBEsol) is used to describe the exchange-correlation potential. 41,42he interactions between the atomic core and the valence electrons were described by the ultraso pseudopotentials.The valence electronic congurations for Cs, Pb, and Br atoms are 5s 2 5p 6 6s 1 , 5d 10 6s 2 6p 2 and 4s 2 4p 5 , respectively.A plane wave cut off 38 Ry and 7 × 7 × 7 k-point mesh was used in the calculation process.Accordingly, the electronic band structure and the projected density of state (PDOS) of CsPbBr 3 are summarized and displayed in Fig. S1 in ESI.†

Results and discussion
Fig. 1 shows a schematic representation of the quantum connement effect, e.g., size-dependent light emission, of CsPbBr 3 NCs.This phenomenon is observable when the electron and hole wave functions are reduced to be smaller than the excitonic Bohr radius, e.g., ∼7 nm for CsPbBr 3 . 10,43-45Specically, when the size of CsPbBr 3 NCs is less than ∼4 nm, the pure blue emission could be expected. 46Hence, this study focuses on the processing-nanostructure-optical property relationship of these CsPbBr 3 NCs with emphasis on the formation mechanism of green-and blue-emitting CsPbBr 3 NCs via the SR method at RT. Briey, in the LaMer model (Fig. 2a), 33,34 the total free energy (DG) for the formation of a spherical particle with radius r could be expressed as where g is the solid/liquid interfacial energy per unit area and DG V is the volume free energy.Here, DG V can be expressed as where k B , T, and V are Boltzmann constant, temperature, and the volume of monomer (e.g., Cs[PbBr 3 ] aggregate or precursor ions/complexes in this study), respectively.Thus, the degree of supersaturation (S) is the driving force for the reduction of DG V .Under unstable equilibrium, vDG/vr = 0, the critical radius is r c = −2g/DG V = 2gV m /RT ln S and concomitantly, the total free energy DG . Then, the nucleation rate (dN/dt) could be dened as follows, 31,32 which describes that the burst nucleation is largely governed by the degree of supersaturation (S) and interfacial energy (g) in the case of SR at RT (constant temperature).Here, A is a prefactor.Importantly, the factor S can be controlled by the amount of nonpolar antisolvent (typically, toluene) at SR-RT.
According to eqn (2), when a large amount of antisolvent is added to the perovskite precursor solution, S will increase, resulting in a high rate of nucleation.Fig. 2b and c show the LaMer diagrams for the one-and twostep syntheses, respectively, which are composed of three regions, 'Cs[PbBr 3 ] aggregate' accumulation (I), burst nucleation (II) and rapid growth (III), followed by the Ostwald ripening process.In this study, the 'one-step process' indicates that the perovskite precursor in polar DMF (1 mL) was injected into 10 mL of the nonpolar antisolvent toluene at RT, resulting in the green-emitting NC synthesis via a high degree of supersaturation.
On the other hand, the 'two-step process' denotes the sequential mixing of the perovskite precursor solution with the antisolvent.The rst stage is the mixing of 5 mL DMF (perovskite precursor) and 5 mL toluene, resulting in the blue-emitting NC synthesis via a low degree of supersaturation.However, for collecting these blue emitters, the second stage is usually required.For example, 1 mL of the rst stage sample is mixed with 10 mL of antisolvent (Fig. 2c), resulting in a bimodal distribution of NCs, i.e., the blue and green emitters.Note that in Fig. 2c, the solubility of the eventual solvent systems (marginal vs. poor) is Here, C max is the maximum supersaturation concentration, C min is the minimum supersaturation concentration (i.e., the critical monomer concentration), and C sol is the solubility limit for a given solvent system (hence, the solubility parameter is essential for the SR-RT process).The superscripts 1 and 2 in the concentration (C) symbol denote the rst and second stages, respectively.Furthermore, S can be expressed by C/C sol as long as C is larger than C sol .
To understand the miscibility between the polar solvent DFM and the nonpolar antisolvent toluene (Fig. 3a) in the SR-RT process, we employ the Flory-Huggins theory (reduced to the regular solution theory when two solvents are equal in molar volume) as follows, 38,47,48 where DG mix is Gibbs free energy of mixing, DH mix is the enthalpy of mixing, DS mix is the entropy of mixing and c 12 is the Flory-Huggins interaction parameter.f 1 and f 2 are the volume fractions of DMF and toluene, whereas r 1 (=1) and r 2 are the relative molar volumes of DMF and toluene, respectively.Note that when r 2 is 1, eqn (1) is reduced to the regular solution theory.However, in this work, the molar volumes of DMF and toluene are 77.4 cm 3 mol −1 and 106.3 cm 3 mol −1 , respectively.Hence, we used eqn (3) with r 2 = 1.37 = 106.3/77.4(=toluene/ DMF, molar volume ratio).Here, the interaction parameter (c 12 ) between DMF and toluene is dened as where V 1 is the molar volume of DMF, whereas d 1 and d 2 are the solubility parameters of DMF and toluene, respectively.For example, c 12 is 1.34 when V 1 is 77.4 cm 3 mol −1 , R = 1.987 cal K −1 mol −1 , T = 298 K, d 1 = 12.1 cal 1/2 cm −3/2 and d 2 = 8.9 cal 1/2 cm −3/2 .Accordingly, the enthalpy, entropy and Gibbs free energy of mixing were predicted for the binary DMF-toluene system (Fig. 3).First of all, the poor affinity between DMF and toluene opposes mixing by showing the positive enthalpy of mixing (Fig. 3b).However, because of the entropic gain (Fig. 3c), the Gibbs free energy of mixing decreases when DMF and toluene are mixed together as shown in Fig. 3d.Hence, when the toluene molecules were added to the perovskite precursor solution, they could replace DMF contacting the perovskite precursor molecules, resulting in the burst nucleation and growth of NCs via enhanced supersaturation.Note that through the water contact angle (q c ) data for the CsPbBr 3 (bulk) and CsPbBr 3 NC lms, we can estimate their solubility parameters (see the ESI † section for details). 49,50For example, when q c = 10.57°for the CsPbBr 3 lm, 51 the surface energy was calculated to be 71.594mJ m −2 , resulting in the solubility parameter d CsPbBr 3 = 15.5 cal 1/2 cm −3/2 and d 0 CsPbBr3 ðSI unitÞ ¼ 31:8 MPa 1=2 .This estimation is based on the relation, df ffiffiffi g p . 47,48,52In the case of CsPbBr 3 NCs complexed with the surface ligands (OA and OAm), q c = 37.57°. 53Accordingly, the surface energy (g) was estimated to be 61.603mJ m −2 , resulting in CsPbBr3-NC ¼ 29:5 MPa 1=2 for the CsPbBr 3 NCs.Hence, the polarity of CsPbBr 3 is partially reduced when complexed with OA and OAm.Note that OA and OAm have the solubility parameters of 7.9 cal 1/2 cm −3/2 and 8.0 cal 1/2 cm −3/2 , respectively, exhibiting they are nonpolar, like antisolvent. 54However, the CsPbBr 3 -surface ligand complex is still polar, allowing the polar DMF to act as a good solvent.In addition, it is notable that DMF is a retrograde solvent, 55 indicating that the degree of supersaturation will be enhanced with increasing temperature because the solubility of perovskite precursor in DMF will decrease with increasing temperature.Table 1 shows the summary of the solubility parameters related to this study. 56,57ig. 4 shows the TEM images of CsPbBr 3 NCs synthesized by one-step (Fig. 4a and b) and two-step (Fig. 4d and e) processes.In the one-step process, the average size of CsPbBr 3 NCs is ∼60 nm, which is far from the excitonic connement regime because its Bohr diameter is ∼7 nm.On the other hand, in the two-step process, the CsPbBr 3 NCs exhibit a bimodal distribution (i.e., two separate groups) with average NC sizes of ∼13.5 ± 2.5 nm (green emitter) and ∼3.5 ± 0.4 nm (blue emitter),   Here, it is worth noting that in the one-step process, there is a high degree of supersaturation (unstable colloidal dispersion) allowing the perovskite precursor components (Cs + , Pb 2+ , Br − , and its complexes in the presence of OA and OAm) to form Cs [PbBr 3 ] monomer aggregates resulting in the burst nucleation and fast growth of ∼60 nm sized NCs (Fig. 2b).Here, the entropy of mixing between DMF (∼1 mL) and toluene (10 mL) is the driving force (Fig. 3c) initiating the aggregate formation of Cs [PbBr 3 ] monomers because of the repulsive interactions between the polar perovskite precursors and the nonpolar toluene.Interestingly, the phase inversion membrane in polymer science uses the same principle, i.e., the exchange of antisolvent and solvent molecules for the membrane formation.58 On the other hand, in the case of the two-step process, the perovskite precursor molecules can contact the good solvent DMF molecules in the rst stage (Fig. 2c) because it is approximately equal mixing between DMF (∼5 mL) and toluene (5 mL), resulting in a low degree of supersaturation, i.e., relatively a limited formation of Cs[PbBr 3 ] monomer aggregates allowing the formation of blue-emitting CsPbBr 3 NCs.It is probably in a metastable state (or weak unstable state) because the larger green-emitting NCs were not allowed to be formed except for the smaller blue-emitting ones.
At this moment, if we employ the Hildebrand and Hansen solubility parameter, 37,56,57 the supersaturation phenomena could be quantitatively analyzed during the one-step and twostep processes for the CsPbBr 3 NC synthesis via the RT-SR processes.For DMF, d = 12.1 cal 1/2 cm −3/2 , whereas for toluene, d = 8.9 cal 1/2 cm −3/2 . 56,57The polar perovskite precursors (d ∼ 14.4-15.5 cal 1/2 cm −3/2 ) can aggregate easily in the nonpolar medium (toluene in the one-step process), whereas they can barely aggregate in the DMF-toluene (5 mL : 5 mL mixture) mixture with the average d= (12.1 + 8.9)/2 z 10.5 cal 1/2 cm −3/2 , i.e., a (partially polar) marginal solvent.Hence, in the rst stage of the 'two-step process', the nucleation and dissolution of CsPbBr 3 could reach an unstable equilibrium (Fig. 2a), resulting in the blue-emitting CsPbBr 3 NC formation with an average size of ∼3.5 nm.However, to collect these small blueemitting NCs, some processing solvents, such as nonpolar ethyl acetate and/or toluene, should be used.Resultantly, the colloidal dispersion with the blue-emitting CsPbBr 3 NCs may undergo additional burst nucleation and rapid growth of greenemitting CsPbBr 3 NCs in spite of some depletion of monomers in the rst stage, stipulating the purication step for separating the blue-emitters from the green ones.
XRD was employed to characterize the crystal structures of CsPbBr 3 NCs.It has been reported that the tilt of corner-sharing {PbBr 6 } 4− octahedral building blocks causes CsPbBr 3 to exist as Nanoscale Advances Paper polymorphs.The crystal phase symmetry of bulk CsPbBr 3 increases with temperature, undergoing the phase transformation from orthorhombic to tetragonal (P4mm) at 88 °C and from tetragonal to cubic (Pm3m) at 130 °C. 47However, Fig. 5 clearly demonstrates that, due to the well-known high surface energy at the nanoscale, CsPbBr 3 NCs have a cubic phase at RT by displaying the XRD peaks at 2q = 16°, 22°, 28°, and 31°, which correspond to the (100), ( 110), (111), and (200) crystallographic planes, respectively. 59Importantly, in comparison to the one-step process, the two-step process exhibits slightly shied XRD peaks to a higher degree, revealing a lattice contraction in the nanoscale particles with an edge size of ∼3.5-13.5 nm. 24g. 6 shows the UV-Vis absorption and PL emission spectra for (a) one-step and (b) two-step processes before purication, respectively.Fig. 6a shows the absorption peak at 515 nm and the green-light emission peak at 519 nm with a full width at half maximum (FWHM) of ∼30 nm.Fig. 6b displays the two absorption peaks at 455 nm and ∼511 nm and the two PL emission peaks at 455 nm and ∼511 nm (the blue PL from ∼3.5 nm NCs and the green PL from ∼14 nm NCs), respectively (see Fig. S2 † for NC's size distribution TEM data).The broad band spectrum of the unpuried two-step process samples is due to the wide range distribution of NCs from 2.5 nm to 25 nm, covering both the non-quantum conned (larger than 7 nm) and the quantum-conned (less than 7 nm) regions (see Fig. S2 †).
Then, for collecting the blue-emitting CsPbBr 3 NCs, we puried the two-step processed samples (Fig. 4d and e).Fig. 7a shows the UV-Vis absorption and PL emission spectra of the puried blue-emitting NC samples, displaying the absorption peak at 452 nm and the PL emission peak at 457 nm with FWHM of ∼23 nm.Here, this narrow FWHM data implies the relatively uniform distribution of CsPbBr 3 NCs with a low trap density. 24,46Importantly, through the Tauc plot equation, (ahn) n = B(hn − E g ), we can quantify the optical bandgap (E g ) of the NC samples (Fig. 7b).Here, hn is the photon energy, a is the absorption coefficient, B is a constant relative to the material, and n is either 2 for a direct transition or 0.5 for an indirect transition. 60As shown in Fig. 7b, the one-step and two-step   We expanded the aforementioned two-step process by incorporating CuBr 2 as an additive into the perovskite precursor solutions with CuBr 2 : PbBr 2 = 1 : 4 (molar ratio) for the rst time via SR at RT. Here, by adding Cu 2+ cations as well as Br − anions with high Gutmann's donor number (D N = 33.7,Lewis basicity), 61 we may modify the interactions between perovskite precursor-solvent (DMF with D N = 26.6;2][63] Fig. 8a and  b show the HR-TEM images of CsPbBr 3 NCs processed with the CuBr 2 additive, displaying the clear cubic NCs, indicating that the additive may stabilize the nanoscale cube with a sharp vertex in spite of its increased surface energy (compared to the spherical structure).Here, we observed again a bimodal distribution, composed of average ∼3.8 ± 0.7 nm and ∼21.4 ± 9.5 nm sized NCs (Fig. S3 †).Note that this NC size is slightly larger than that of NCs without the additive in Fig. 4  Compared to the unpuried sample in Fig. 6b (without CuBr 2 ), the unpuried sample in Fig. 9a (with CuBr 2 ) shows a slight red-shi (UV-Vis absorption peaks from '455 nm and 511 nm' to '566 nm and 521 nm' whereas PL emission peaks from '464 nm and 501 nm' to '466 nm and 501 nm') (compare Fig. 6b and 9a).The same trend was also observed in the puried samples by displaying the minor red shi (UV-Vis absorption from 452 nm to 458 nm whereas PL emission from 457 nm to 460 nm).This red shi could be rationally understood by observing the partial increase of the CsPbBr 3 NC size in the presence of the CuBr 2 additive, as shown in Fig. S1 and S6.† Furthermore, it is interesting to observe the reduced PL FWHM of ∼18.5 nm (Fig. 9b), which is signicantly smaller than ∼23 nm in Fig. 7 (without CuBr 2 ), indicating that the size-focusing effect is available when processed with the CuBr 2 additive.However, because of the

Nanoscale Advances Paper
partial increase of NC size, the optical bandgap is accordingly reduced from 2.7 eV (Fig. 7b) to ∼2.6 eV (see the inset in Fig. 9b), displaying the quantum size effect.The two-step process produces a bimodal distribution, as demonstrated through the TEM data in Fig. 4d, S2, 8a, and S3.† Hence, it would be valuable to examine the stability and crystallization of the original solution samples aer the rst stage 'separately' in the two-step process.For this purpose, aer the initial mixing of 'the precursor solution in 5 mL DMF' and '5 mL toluene', the solution was stored for aging effect at RTthis is a low degree of supersaturation state.Fig. 10 shows the UV-Vis absorption and PL emission spectra as a function of aging time at RT. Fig. 10a displays clearly that the absorption increases with time.However, based on the peak's location, we determined that there is only the blue-emitting CsPbBr 3 NCs without the Oswald ripening effect related to the green emitter growth (the quenching mechanism is simply all monomer consumption at RT).Furthermore, when the UV-Vis absorption data was plotted at the wavelength (l) of 410 nm with aging time, a saturation behavior was observed aer ∼50-100 hours (Fig. 10b).Subsequently, we examined the PL emission behavior as a function of aging time.As shown in Fig. 10b, the PL increases initially but decreases aer 24 hours, indicating NCs might be deactivated, i.e., quenching the PL emission.Furthermore, the PL red-shi was observed, indicating a partial growth of blue-emitting CsPbBr 3 NCs, but still, it is a blue emitter, indicating that there might be a balance between formation and dissolution of the blue-emitting NCs in this low degree of supersaturated state.However, recall that for collecting these NCs, additional nonpolar antisolvent should be

Paper
Nanoscale Advances required as a processing solvent, resulting in another nucleation and growth of green emitters from the new monomer aggregates generated by the enhanced degree of supersaturation (Fig. 2c).Moreover, in the two-step process (1st step), the UV-Vis and PL spectra display that the CsPbBr 3 NCs grow with a wide range of size distribution (Fig. 10).However, still, the majority of the NCs are in a quantum-conned regime.However, when the antisolvent toluene is additionally added for the second time, it may cause some of the NCs to aggregate and grow, resulting in non-quantum conned NCs.Hence, two competing peaks were observed in Fig. 6b.Fig. 11 is the summary of this work suggesting 'the solubility parameter-based nanocrystal size control model' for explaining the SR process at RT.When the perovskite precursors are in a good solvent like DMF, there is no nucleation and growth of NCs because they can stay as a well-dispersed colloidal system.However, by adding an antisolvent (toluene) into the perovskite precursor solution in DMF with a ∼50 : 50 volume ratio, the liquid medium becomes a marginal solvent with partial polarity, resulting in the burst nucleation and rapid growth of blue-emitting CsPbBr 3 NCs.Here, the DMF-toluene 50 : 50 mixture provides a signicant solubility for colloidal perovskite precursors (Fig. 2c), and no sufficient monomer aggregates remain for further growing to green emitters at this low supersaturation level.Finally, if the liquid medium is dominantly nonpolar (toluene [ DMF), the green-emitting NCs can be easily grown in the presence of blue-emitting NCs.Hence, the solubility parameters (or solubility) of the solvent and solvent-antisolvent mixture can serve as a key factor for the nanoscale size regulation in the SR process at RT, affecting

Conclusions
The nucleation and growth of CsPbBr 3 NCs were studied in view of the classical LaMer model when the supersaturated recrystallization was carried out at room temperature.For this purpose, we compared one-step and two-step processes to elucidate the formation mechanism of NCs.Resultantly, when the nonpolar toluene (antisolvent) was much larger in volume than the polar DMF (solvent), the ∼60 nm sized green-emitting NCs were synthesized via the one-step process under a high degree of supersaturation.On the other hand, when the antisolvent volume is comparable to that of the solvent, the ∼3.5 nm-sized blue-emitting NCs were synthesized via a two-step process using a low degree of supersaturation.In this study, by employing the Hildebrand and Hansen solubility parameter concept, we quantitatively explained the solvent quality (good, marginal, and poor).Hence, we named this approach 'the solubility parameter-based nanocrystal size control model' because supersaturation is a function of 'solubility and polarity' (expressed as solubility parameter) and 'antisolventsolvent volume ratio' (considered as average solubility parameter).Furthermore, based on the Flory-Huggins model, we predicted that the antisolvent-solvent mixing is driven by the entropy of mixing, allowing the crystallization of the perovskite precursor to aggregate via SR operating at RT. Finally, in the presence of the CuBr 2 additive in the two-step process, we observed a partial red-shi in both absorption and emission spectra from the quantum size effect (a slight increase of nanocube).In addition, the PL emission spectra showed a reduced PL FWHM of ∼18.5 nm (reduced size scattering and enhanced size focusing) from the ∼3.8 nm NCs.Finally, we believe that our nding, i.e., the importance of the solubility parameter as an NC size control factor for the SR method at RT, will contribute to further advancing the perovskite nanocrystal technology and beyond.Future work may include the formation mechanism of NCs via SR-RT as a function of the average solubility parameter from the versatile antisolvent-solvent mixtures.

Fig. 2
Fig. 2 (a) Free energy change vs. particle size.LaMer diagram: (b) one-step process and (c) two-step process.The regions I, II and III correspond to (monomer) accumulation, burst nucleation and rapid growth, respectively.

Fig. 3
Fig. 3 (a) Chemical structures of DMF and toluene.Prediction of Flory-Huggins theory for (b) enthalpy of mixing, (c) entropy of mixing, and (d) Gibbs free energy of mixing as a function of volume fraction of toluene, f 2 at 298 K.
. S2 †).The selected area electron diffraction (SAED) patterns (Fig.4c and f) provide additional conrmation of the phases of the NCs.The one-step process displays the SAED pattern of a single crystal-like pattern, whereas the twostep process exhibits a polycrystal pattern because of two different NCs with versatile orientations.

Fig. 4
Fig. 4 TEM images of CsPbBr 3 NCs synthesized through (a and b) one-step synthesis and (d and e) two-step synthesis.SAED images: (c) one-step synthesis and (f) two-step synthesis.

Fig. 5
Fig. 5 XRD patterns of CsPbBr 3 NCs synthesized via the one-step and two-step SR method without purification.

Fig. 6
Fig. 6 UV-vis and PL spectra of CsPbBr 3 NCs: (a) one-step process and (b) two-step process without purification.
and S2.† Furthermore, Fig. 8c shows the corresponding SAED image, indicating that the cubic CsPbBr 3 NCs are oriented to the [110] direction on top of the TEM copper grid.On the other hand, the XRD pattern of the cubic CsPbBr 3 NCs (Fig. 8d) displays two strong peaks at 26.8°and 29.9°, corresponding to (111) and (200) crystallographic planes, indicating that the cubic NCs are oriented more to the [200] direction on top of the glass slide.Hence, compared to the XRD in Fig. 5, the XRD pattern in Fig. 8d is much more simplied, indicating the enhanced orientational order when processed with the CuBr 2 additive.Fig. 9 shows the UV-Vis absorption and PL emission spectra for (a) the unpuried and (b) puried CsPbBr 3 NCs with CuBr 2 .

Fig. 10
Fig. 10 Aging effect on the optical properties of CsPbBr 3 NCs (after the first step in the 'two-step process') at room temperature.(a) UV-vis absorption spectra as a function of aging time at room temperature.(b) The absorption at l = 410 nm.(c) PL emission spectra as a function of aging time at room temperature.(d) Normalized PL intensity as a function of aging time at room temperature.
(1) the nucleation and growth of NCs and (2) the balance between formation and dissolution of Cs[PbBr 3 ] monomers and NCs in line with the LaMer diagram in Fig. 2 and 11.

Table 1
Solubility parameter, molecular weight, density, and molar volume of the solvent, non-solvent, CsPbBr 3 (bulk) and CsPbBr 3 NC complexed with oleic acid and oleylamine.d 0 (SI unit) = d × 2.0455 a Surface ligands are not considered.