Stacking of Colloidal CdSe Nanoplatelets into Twisted Ribbon

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C: Physical Processes in Nanomaterials and Nanostructures

Stacking of Colloidal CdSe Nanoplatelets into Twisted Ribbon Superstructures: Origin of Twisting and Its Implication in Optical Properties Whi Dong Kim, Da-Eun Yoon, Dahin Kim, Sungjun Koh, Wan Ki Bae, Weon-Sik Chae, and Doh C. Lee J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b09987 • Publication Date (Web): 07 Mar 2019 Downloaded from http://pubs.acs.org on March 12, 2019

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The Journal of Physical Chemistry

Stacking of Colloidal CdSe Nanoplatelets into Twisted Ribbon Superstructures: Origin of Twisting and Its Implication in Optical Properties Whi Dong Kim†, Da-Eun Yoon†, Dahin Kim†, Sungjun Koh†, Wan Ki Bae*,‡, Weon-Sik Chae*, ∥

†Department

and Doh C. Lee*,†

of Chemical and Biomolecular Engineering, KAIST Institute for the

Nanocentury, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea. ‡Sungkyunkwan

Advanced Institute of Nanotechnology, Sungkyunkwan University, Suwon, Gyeonggi-do 16419, Korea.

∥Daegu

Center, Korea Basic Science Institute, Daegu 41566, Korea.

ACS Paragon Plus Environment

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ABSTRACT

Relatively large faces of colloidal CdSe nanoplatelets (NPLs) drive the anisotropic nanomaterials into one-dimensional superstructures through stacking of NPLs when solvent evaporates. We observe that the assembly could result in the formation of twisted ribbon superstructures with varying pitch length depending on lateral dimensions of CdSe NPLs. Transmission electron microscopy images and simulated projection reveals that stacked NPLs are distorted. The estimation of contact area between distorted NPLs suggests that this distortion leads to lower energy of overall nanoribbon superstructures. Average pitch length of superstructures on the lateral dimension of NPLs turns out to hinge on the dimension of NPLs as it alters the distortion angle of NPL and thus rotation angle between NPLs. We investigate the energy transfer between NPLs in the context of the lateral dimension of NPL and geometric structure of their superstructures via transient photoluminescence decay measurements. Our analysis on energy transfer rate indicates that extinction coefficients, which are determined by lateral dimension of NPLs, are more responsible for the energy transfer change than rotation angle between CdSe NPLs within twisted ribbon superstructures. The dependence of the energy transfer rate on the lateral dimension of NPLs highlights the importance of geometry of individual NPLs in the context of optical properties of NPLs in ensemble.


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INTRODUCTION Versatility of colloidal synthesis via arrested precipitation has enabled the growth of inorganic nanocrystals with narrow size distribution.1 Now that semiconductor nanocrystals of size smaller than exciton Bohr radius show size-dependent energy gap, the ability to produce monodisperse semiconductor nanocrystals would translate into narrow emission bandwidth.2, 3 The sharp emission peak of semiconductor nanocrystals, typically referred to as quantum dots, makes them highly suited for high color-gamut display devices.4, 5 Recent development in the growth of two-dimensional nanocrystals, or nanoplatelets (NPLs), has resulted in more remarkable uniformity of energy band gap: for example, CdSe NPLs show unprecedentedly narrow photoluminescence (PL) peak, with full-width at half maximum (FWHM) as narrow as 10 nm.6,

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The ultranarrow emission bandwidth is attributed to the narrow distribution of

thickness of NPLs, as a result of self-regulated lateral growth.7-9 While thickness of CdSe NPLs dictates emission energy via quantum confinement effect, lateral dimensions of NPLs influence other optical properties, such as PL efficiency or polarization in absorption and emission.10-13 On a relevant note, Olutas et al. reported that lateral size of CdSe NPLs plays a major role in determining the PL quantum yield (QY) and PL lifetime.10 Recently, it turned out that a trivial change in ligand concentration can result in the growth of CdSe NPLs with controllably varying lateral aspect ratios.11, 14 In a previous study, we observed that the fluorescence polarization has correlation with lateral aspect ratio of CdSe NPLs: the higher the lateral aspect ratio, the more polarized the emission, as a result of anisotropic local field effect.11 The controllably varying lateral aspect ratio of CdSe NPLs could also influence the way NPLs assemble into a film. Relatively large faces of NPLs in thickness direction force NPLs to stack into ribbon superstructures during solvent evaporation due to large van der Waals interaction. The stacking results in proximity of neighboring NPLs, which would promote and


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accelerate energy or charge transfer between NPLs. The high extinction coefficient and dipole orientation in addition to short inter-NPL distance in the stacks give rise to very fast energy transfer (ET) (~4 ps) compared to the case of spherical nanocrystals (NCs) (~>100 ps).15, 16 Since lateral dimensions influence a range of optical properties, one would expect energy and charge transfers between NPLs in aggregates to depend on the shape of NPLs and structure of aggregates. Recent progress in assembly of NPLs into aggregates such as linearly stacked, twisted ribbon and needle-like superstructures alludes to the significance of morphology of individual NPLs, calling for in-depth mechanistic investigation.15, 17-19 In this study, we examine the effect of lateral dimensions of CdSe NPLs on assembly and the carrier dynamics in ensemble. CdSe NPLs aggregate into twisted ribbon superstructures with a pitch length depending on lateral dimension of NPLs. We estimate van der Waals interaction between NPLs so as to verify structural stability of the helical aggregate structure. In addition, the relationship between the assembly structure of NPLs and their optical properties is investigated using time-resolved photoluminescence (TRPL) spectroscopy and fluorescence lifetime imaging microscopy (FLIM) in the context of orientation between NPLs and lateral dimension of NPLs.

METHODS

Chemicals. The following chemicals were used as received: sodium hydroxide (Sigma Aldrich, ≥98%), myristic acid (TCI, ≥99%), cadmium nitrate tetrahydrate (Sigma Aldrich, ≥99%), cadmium acetate dihydrate (Sigma Aldrich, ≥98%), copper acetate (Sigma Aldrich, 99.99%), selenium (Se, Alfa Aesar, 99.999%) and oleic acid (Sigma Aldrich, ≥90%). Synthesis of Cd myristate (Cd(My)2). 0.24 g of sodium hydroxide and 1.37 g of myristic acid were dissolved in 240 mL of methanol. Separately, 0.617 g of cadmium nitrate tetrahydrate


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was introduced in 40 mL of methanol. Prepared cadmium nitrate solution is slowly injected to the sodium myristate solution under vigorous stirring. After filtration process, white precipitate was washed with methanol. Dry the precipitate under vacuum overnight. Synthesis of 4.5-monolayer (ML) CdSe nanoplatelets. 0.17 g of Cd(My)2, 0.012 g of Se and 15 mL of ODE were added into a 3-neck flask and heated to 100 oC. The solution was heated to 200 oC from 100 oC within 7 min to form a yellow solution and rapidly cooled down to 100 oC.

Then, varying amount of cadmium acetate was introduced into the flask under positive Ar

flow for CdSe NPLs. In order to synthesis a NPL with relatively large lateral area such as NPL-5, we additionally introduced copper acetate with cadmium acetate. The flask was rapidly heated to 240 oC and maintained for several minutes. Here, the amount of injected cadmium acetate relates to the lateral aspect ratio of CdSe NPLs and reaction time at 240 oC determines lateral area of CdSe NPLs (See Supporting Information for detailed experimental conditions). In order to separate CdSe NPLs from byproducts such as 3.5 and 5.5 ML CdSe NPLs and CdSe NCs, the resulting products were centrifuged with different rpm. After centrifugation at 2500 rpm for 10 min, the supernatant was discarded and precipitant dispersed in 5 mL of hexane. The dispersed product was centrifuged at 3500 rpm for 10 min and colloidal CdSe NPLs with 4.5 ML were obtained from supernatant. Assembly of CdSe NPLs. In order to prepare the ribbon superstructure made of assembled CdSe NPLs, 50 μL of oleic acid was injected to 5 mL of prepared colloidal CdSe NPL solution. Table S1 summarizes the concentration of colloidal CdSe NPL for assembly. 50 μL of CdSe NPL solution is dropped on TEM grid and naturally dried at room temperature for 1h. Characterization. The colloidal NPLs and formation of assembly were examined using transmission electron microscopy (TEM, Tecnai F20 (200 kV), FEI company). PL QYs were measured by absolute PL quantum yield spectrometer (Quantaurus-QY C11347, Hamamatsu).


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Time-resolved

photoluminescence

(TRPL)

and

fluorescence

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lifetime

imaging

microscopy (FLIM) measurement. We conducted TRPL and FLIM measurement of ribbon superstructure made of CdSe NPLs using an inverted-type scanning confocal microscope (Picoquant MicroTime-200) with a 100× oil-immersion objective. An excitation source is a 470-nm single-mode pulsed diode laser (LDH-P-C-470, Picoquant, Germany) with a pulse width of 30 ps and a 10 MHz repetition rate, and an average power of 10 uW. Emission from the assembled NPLs was collected by a dichroic mirror (AHF 490 DCXR), a long-pass filter (AHF HQ500lp), a 50 μm pinhole, and a single-photon avalanche diode (SPAD) after pass the neutral density filter, in which photon counting rate was maintained around 1 % of excitation rate. Data acquisition was based on a time-correlated single photon counting technique. Measured FLIM images were presented in fast FLIM imaging mode provided by the SymPhoTime-64 operating software (Ver. 2.2). The fast FLIM images typically present a longer average lifetime than the average (1/e) PL lifetime measured from TRPL spectroscopy. For each sample, we estimated average lifetime from FLIM images by measuring 5 or more superstructures.

RESULTS AND DISCUSSION

Twisted Ribbon Superstructures of CdSe NPLs. Figure 1a shows TEM image of dropcasted CdSe NPLs on TEM grid after solvent evaporation. We observed shortly stacked NPLs lying perpendicular to the TEM grid and flat-lying NPLs without any stacking. Colloidal CdSe NPLs are stacked into one-dimensional ribbon-shaped superstructures after the evaporation of solvent upon addition of oleic acid (See Figure 1b and c). The formation of these micro-ribbon superstructures was reported by Jana et al., who observed that the dimension of the ribbon superstructures depends on the concentration of oleic acid.19 Depletion interaction exerted by free oleic acid molecules is responsible for a strong attraction between large faces of NPLs,


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and thus induces the formation of one-dimensional superstructures. As shown in Figure 1S, we also observe a similar tendency that ribbon length increases with increasing oleic acid concentration. These nanoribbon superstructures appear twisted into a helical geometry with a constant pitch length (331 ± 26 nm) as shown in Figure 1c. The concentration of free oleic acid has little bearing on the pitch length of the twisted ribbon superstructures (See Figure 1S). Flat platelets would energetically favor stacking between the large faces of NPLs where the van der Waals or ligand-ligand interaction is maximized. In this sense, the most stable structure of stacked NPLs would look like ribbons without rotation between NPLs. Therefore, the twist in the ribbon superstructures observed in our study would contradict the thermodynamic intuition as the sequential rotation of NPLs would cause weaker van der Waals and ligandligand interaction between NPLs.20 The superstructures with helical geometry are supposed to be structurally unstable.


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Figure 1. (a) TEM image of drop-casted CdSe NPLs without addition of oleic acid. (b, c) TEM images of CdSe NPLs assembled into twisted ribbon superstructures upon addition of oleic acid. Inset in (c): high-resolution TEM image of CdSe NPLs. Scale bar in inset represents 10 nm. (d) Schematic illustration of simulated twisted ribbon superstructure, in which distorted CdSe NPLs are stacked with rotation. TEM images in (e) and (f) show ‘bow-tie’ and ‘lip’ shape pattern at the node of two helical superstructures, respectively. Scale bar represents 10 nm. Next to each TEM image, corresponding simulated twisted superstructure is shown. In order to clarify the formation of twisted ribbon superstructures, we investigated geometry of the superstructures. The TEM image in inset of Figure 1c suggests distortion of NPLs results from twisting, as the center and edges of CdSe NPLs exhibit discernible focal contrast. The observation is in agreement with a previous report that individual CdSe NPLs are distorted in the formation of twisted ribbon superstructures with well-defined pitch length.18 Jana et al. suggested that the distortion of NPLs results from ligand adsorption and ordering, which causes surface stress upon adding excess oleic acid.18 Based on the pitch length of superstructures, we estimated the rotation angle of each NPL to be 5.6 degrees from the image in Figure 1c. Our simulation using the 3D Max software shows that the two-dimensional projection appears very similar to structures observed in TEM analysis as shown in Figure 1d, hinting that the twisted ribbon structures result likely from rotation of individual NPLs in the aggregates. Unique patterns such as ‘bow tie’ or ‘lip’ shapes appear at the node of two twisted structures in Figure 1e and f. These patterns can be visualized only when distorted NPLs with constant twist angle are simulated to stack with rotation. When NPLs undergo no distortion, only a straight line appears at the node (See Figure S2). Juxtaposing the simulated 2-D projection with TEM images gives an obvious notion that the twisted ribbon geometry is formed by stacking of distorted NPLs with rotation.


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Figure 2. (a) Schematic illustration of distorted and flat NPLs without rotation viewed from side. ‘Lslip’ represents the shift of the short edge of NPL in reference to that of neighboring NPL. (b) Schematic depiction of distortion angle of NPLs and rotation angle between NPLs. Structural Stability of Twisted Ribbon Superstructure. Figure 2 shows schemes of superstructures based on flat and distorted NPLs without rotation and the depiction of distortion and rotation angles used in this paper. Both van der Waals and ligand-ligand interactions drive NPLs to have larger overlap area between neighboring NPLs. Therefore, flat NPLs would stack into one-dimensional superstructures without rotation. When short edges of NPLs are distorted, the stacking exhibits staggering with length ‘Lslip’ as shown in Figure 2a. Obviously, the contact area between distorted NPLs normalized with the lateral area of NPL depends on distortion angle (See Supporting Information for detailed calculation). The distortion angle is defined as angle between reference axis parallel to short lateral edge of NPL before twisting and the same axis after twisting, as depicted in Figure 2b. As shown in Figure 3a and b, the contact area between adjacent NPLs is highest in the stacked flat NPL (distortion angle = 0°)


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and gradually decreases with increasing distortion angle of NPL. This estimation indicates that the straight shape of ribbon superstructure is no longer structurally most stable for distorted NPLs. Figure 3c and d show that how the reduced contact area between distorted NPLs increases as the NPLs rotate. Here, we define the rotation angle as the angle between the long axes of the neighboring NPLs, as depicted in the Figure 2b. As the rotation angle increases, the normalized contact area between NPLs gradually increases and eventually begins to decrease beyond a threshold rotation angle as shown in Figure 3c. Figure 3d visualizes this trend of contact area change: rotation between neighboring distorted NPLs would result in maximum contact area between NPLs. This sequential rotation of NPLs ultimately results in twisted ribbon shape of assembled superstructures.


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Figure 3. (a) Calculated contact area between distorted NPLs normalized with the lateral area of NPL depending on distortion angle. (b) Schematic depiction of NPLs with varying ‘Lslip’ contingent on distortion angle of NPL without rotation. (c) Calculated contact area between two distorted NPLs with distortion angle 30o normalized with the lateral area of NPL depending on rotation angle between NPLs. (d) Schematic depiction of NPLs with fluctuation of length ‘Lslip’ and distortion angle 30o at various rotation angles between neighboring NPLs. Short edge and long edge of NPLs for calculation is 8.1 nm and 36 nm, respectively. In order to quantify the structural stability of NPL ensembles, we varied distortion angle of NPLs and observed the Lslip value in different distortion angle conditions. When the distortion angle increases, Lslip also increases, in which case, NPLs need to make more significant rotation


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to minimize Lslip (See Figure 3b). This series of correlation indicates that the distortion angle of NPLs dictates the rotation angle in NPL stacks and ultimately geometry of twisted ribbon superstructure, such as its pitch length. To experimentally control the distortion angle and examine the relationship between distortion angle of NPL and rotation angle between NPLs, we prepared CdSe NPLs with varying lateral dimension by controlling the amount of hydrate source of cadmium acetate and reaction time during synthesis of NPLs (See Figure S3).11, 14 With applied torque along the axis of the 2-dimensional materials, the distortion angles are determined by the dimension of materials such as lateral length and thickness. 𝐴𝐿

(1)

𝐷θ = 𝐽𝐺

where 𝐷θ is the distortion angle in radians, 𝐴 is the applied torque, 𝐿 is the length of long edge of a CdSe NPL, 𝐽 is the torsional constant and 𝐺 is the modulus of rigidity of the material. Here, torsional constant (𝐽) can be expressed as

(

𝐽 = 𝑎𝑏3

1 3

𝑏

(

𝑏4

))

― 0.21𝑎 1 ― 12𝑎4

(2)

where 𝑎 is the length of short edge of CdSe NPL and 𝑏 is the thickness of CdSe NPL.21, 22


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Figure 4. (a-e) TEM images from assembled nanoribbon superstructure made of NPLs with varying kinds of lateral dimension. Arrow markers indicate half pitch length in twisted ribbon structure. Scale bar represents 50 nm. The sample numbering follows the order of NPL lateral area (ANPL). a is the average length of short edge of CdSe NPLs, L is the average length of long edge of CdSe NPLs, PL is the pitch length of twisted structure and Rϴ is the rotation angle between NPLs. (f) Length of long edge of CdSe NPLs divided by distortion constant (L/J) plotted against distortion angle calculated by pitch length. Figure 4 shows nanoribbon superstructures made of colloidal CdSe NPLs with varying lateral dimension, and the average pitch length varies from 363 nm to 265 nm depending on the NPL dimension. NPLs nearly square shaped do not show clear pitches in their superstructures and therefore were not included in the pitch length analysis (See Figure S4). Assuming equal rotation between neighboring NPLs in a given superstructure, we can estimate the average rotation angle between neighboring NPLs by dividing 360 degrees with the average number of NPLs forming one pitch. As a result, average rotation angle of the twisted structure are 5.9o, 7.1o, 6.7o, 5.2o, and 5.6o in Figure 3a, b, c, d, and e, respectively. It becomes clear that rotation


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angle has much to do with distortion angle, which can be modulated with our experimental control in lateral dimensions of NPL. Two calculation steps are necessary to quantitatively comprehend the correlation between distortion and rotation angles; (i) calculation of ‘expected distortion angle’, converted from a rotation angle value and (ii) calculation of ‘actual distortion angle’ using Eq. (1). The expected distortion angle is estimated from rotation angle within twisted ribbon superstructures under the assumption that the NPLs rotate to make Lslip = 0. If the distortion angles estimated from assumption (expected distortion angle) and measured from experimental data (actual distortion angle) coincide, rotation of the NPLs becomes a reason for maximum van der Waals interaction energy and structural stability of twisted ribbon aggregates. To calculate ‘expected distortion angle’, we used the relation between rotation angle ( 𝑅θ) and expected distortion angle (𝐷expθ)

(

𝐷expθ = 𝑠𝑖𝑛 ―1

𝐿 2𝐿𝑁𝑃𝐿 ― 𝑁𝑃𝐿

∙ sin (𝑅θ)

)

(3)

where 𝐷expθ is the expected distortion angle, 𝐿 is long edge of NPL, 𝐿𝑁𝑃𝐿 ― 𝑁𝑃𝐿 is the distance between center to center of NPL and 𝑅θ is the rotation angle obtained by pitch length analysis. This relation is derived on the premise that the rotation occurs in a way to minimize Lslip value (See Supporting Information for detailed derivation processes). Based on the calculated rotation angle value of each helical superstructure from TEM analysis and Eq. (3), we calculated expected distortion angle. The actual distortion angle can be calculated using Eq. (1). Figure 4 summarizes the dimensional information of CdSe NPLs to calculate torsional angle using torsional constant (J) and the length of long edge of a NPL (𝐿). Quantifying the value of applied torque (𝐴) and


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modulus of rigidity of the material (𝐺) was impossible within this particular set of study. Instead, we let applied torque (A) and modulus of rigidity of the material (G) as fixed constants, since all helical superstructures have the identical ligand ordering energy per surface area by same surface ligand types (i.e., oleic acid) and crystal structure is zinc blend structure regardless of the dimensions of NPL. Based on the relation in Eq. (1), the computed L / J values are supposed to follow the linear proportionality to the actual distortion angle. Therefore, we can infer the relationship between the actual distortion angle and the expected distortion angle throughout comparing the L / J values with the expected distortion angles. Indeed, the L / J values and the expected distortion angles (𝐷expθ) show proportionality, corroborating our hypothesis that rotation of NPLs occurs to minimize Lslip value (See Figure 4f). Scheme 1 summarizes the process of determining the final pitch length of the superstructure depending on dimension of NPLs. Dimension of NPLs dictates distortion angle, so do the rotation angle between NPLs and resulting pitch length of superstructures to ensure the structural stability. By fitting the L / J values with a linear equation, we can obtain the slope value, which represents A / G value, as shown in Figure 3f. Even though modulus of rigidity value (G) depends on the size and shape of NCs,23 the consideration of G values gives a ballpark estimation of the applied torque (A). With the modulus of rigidity (G) being 17.25 GPa,18, 23 applied torque (A) of each NPL corresponds to 28 eV. Recently, the ordering energy of a long-alkyl chain ligand has been reported to be ~90 meV based on molecular dynamics calculation, suggesting that ordering of about 300 ligands per NPL is required to apply torque.24 Considering the typical ligand densities of semiconductor NCs (0.6 to 4.6 ligands/nm2) and total lateral areas of both NPL faces in the cases of NPL-1 to NPL-5 (i.e. 197.8 to 584.8 nm2, respectively),18 the actual number of surface ligands per NPL in all of the samples is in proximity with the required number of ligands to apply the calculated torque.


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How does the ordering of ligands turn into torque? The surface ligands at the top and bottom of faces of NPL are supposed to be equal in numbers because the opposite faces are exposed with same Cd-covered facet. With the symmetric ligands, torque would make little sense. For the cubic CdSe crystal, modulus of rigidity is minimum in the [110] direction and maximum in the [100] and [010] directions, when stress is applied in the [001] direction.25 In the case of rectangular NPLs with large aspect ratio, the short and long edges are along the [100] and [010] directions, respectively, while the thickness of NPL is along the [001] axis.26 Because of relatively small modulus of rigidity along the [110] direction, it is expected that the NPLs start to scroll along the [110] direction, even though the equal stress is applied along the [001] direction by ligand ordering. Indeed, it has been reported that scrolled CdSe NPLs roll along the [110] direction.27 Therefore, we speculate that this asymmetric rolling of NPL with respect to long axis of NPLs is responsible for origin of torque.

Scheme 1. Schematic illustrates structural difference of superstructures caused by dimension of NPLs. According to dimension of NPLs, distortion angle of NPL is determined. (a) For distorted NPLs with high distortion angle, high rotation angle is required for stable structure during the NPL stacking, and leads to short pitch length of superstructure. (b) For distorted NPLs with low distortion angle, structural stability is ensured by relatively low rotation angle during the NPL stacking, which leads to long pitch length of superstructure. Exciton Dynamics in Twisted Ribbon Superstructure. Structural controllability of twisted ribbon superstructures allows in-depth study of exciton interaction between stacked NPLs in


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terms of dimensional effect of NPL and structural difference of superstructures. We measured the PL decay times at different regions of NPL ensemble using FLIM. Figure 5 shows FLIM images of twisted ribbon superstructures with a color index of PL lifetime in each pixel area. FLIM analysis with NPL-1, 2, 3 and 4 reveals the PL lifetime of twisted superstructures as shown in Figure 4a, b, c and d, respectively. In all of the microscopy images, we observed the entangled lines indicating PL signal are in good agreement of entangled form of superstructures found from TEM images (e.g., Figure 1b).

A homogeneous color reveals that the

superstructures are regularly assembled in entire area. It is noteworthy that the average PL lifetime exhibits a surprising, yet coherent, difference depending on morphology of superstructures, as evidenced by the distinct color change in a FLIM images.

Figure 5. FLIM images of (a) NPL-1, (b) NPL-2, (c) NPL-3 and (d) NPL-4 with photoluminescence-lifetime represented by gradient color bar. The results of lifetime imaging of NPL-1, NPL-2, NPL-3 and NPL-4 are from twisted ribbon superstructures in Figure 4a, b, c and d, respectively.


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Figure 6. Ensemble PL decays of colloidal CdSe NPLs with varying lateral dimension in (a) solution and (b) film. (c) Average PL lifetimes of ensemble of superstructures estimated by experimentally obtained PL decay curves (black solid circle) and modeled PL decay rate (orange solid circle). To clarify the difference of exciton dynamics depending on assembly structure and NPL dimension as shown in FLIM results, we performed TRPL analysis on (i) NPL solutions in hexane and (ii) twisted ribbon superstructures. In Figure 6a and b, PL decay curves of ensembles of samples before and after assembly are plotted, respectively. We estimated average lifetime, in which PL intensity becomes 1/e of the initial intensity as summarized in Table 1. For the solution samples, the average lifetime was decreased with increasing of the lateral area of NPL in solution.28 Such PL lifetime change was reported in a previous study, which demonstrated that extension of lateral area leads to decrease of PL QY and average PL lifetime by increasing number of defect sites.10 Therefore, the difference in average lifetime


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of solution samples is attributed to number of defect sites. After assembly process, it is noteworthy that average lifetime drops dramatically from several nanoseconds to a few hundreds of picoseconds for all samples. To account for decline of PL lifetime, we consider the resonance energy transfer (ET) in the assembled superstructure. ET between semiconductor NCs is known to reduce the average lifetime by “opening” a new nonradiative recombination pathway in assembled structure.29, 30 In general, ET rate is given by

𝐾𝐸𝑇 =

𝑄𝐷𝜅2 9000(ln 10) 𝜏𝐷𝑟6

(

128𝜋5𝑁𝑛4

)∫ 𝐹 (𝜆)𝜀 (𝜆)𝜆 𝑑𝜆 𝐷 0 𝐷

𝐴

4

(4)

where 𝑄𝐷 is the quantum yield of the donor in the absence of an acceptor, 𝑛 is the refractive index of the medium, 𝑁 is Avogadro’s number, 𝑟 is the distance between a donor and an acceptor, 𝜏𝐷 is the lifetime of the donor in the absence of an acceptor, 𝜀𝐴(𝜆) is the extinction coefficient of the acceptor at λ, and the term of 𝜅2 is a factor describing the relative orientation of the transition dipoles of the donor and acceptor. From the small angle X-ray scattering (SAXS) results, we observed that scattering peaks centered at qy = 1.21 nm-1 in all cases regardless of the assembly structure (See Figure S6). This scattering vector was converted to real space of center-to-center distance of stacked NPLs as a 5.1 nm (2π/qz). Except for the thickness of CdSe NPLs (~1.2 nm), the average distance between NPLs (𝑟) was 3.9 nm, which corresponds to the thickness of an oleic acid bilayer.31 Extinction coefficient (𝜀𝐴(𝜆)) was estimated based on average lateral area.32, 33 Direction of transition dipole of NPLs dictates orientation factor (𝜅2). It has been reported that transition dipole of stacked NPLs is isotropically oriented within the plane of NPL without preference for the long- or short-axis of NPLs.34 Gao et al. estimated orientation factor of stacked NPLs as 1/2, based on isotropic dipole distribution within the plane of NPL.34 Because the dipole orientations are randomly


19


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distributed, the orientation factor of our sample is equal to 1/2 in all superstructures, regardless of the NPL rotation angle. Table 1 summarizes calculated values of these parameters in ET rate equation. Using the Eq. (1), the NPL-to-NPL ET time was theoretically calculated to be 18.7, 10.3, 7.8, and 7.5 ps in the NPL-1, NPL-2, NPL-3 and NPL-4, respectively. Based on calculated ET rate, we derive the theoretical PL decay kinetics reported by Demir and co-worker,15 and compare with experimental PL decay results to verify that ET is actually responsible for the change in PL decay of film. In the stack of 100 NPLs, m of defected NPLs are randomly distributed. The percentage of the defected NPL population is estimated by solution PL decay results using previously reported method.15, 35 Let 𝑛𝑖 denote the number of the excited NPLs located in the ith position in superstructures. Considering that the exciton is recombined or transferred to neighboring NPLs, the rate equations of 𝑛𝑖 can be expressed as: 𝑑𝑛1

1 = ― (𝑘1 + 𝑘𝐸𝑇)𝑛1 + 𝑘𝐸𝑇𝑛 𝑑𝑡 2 2

𝑑𝑛2

1 = ― (𝑘2 + 𝑘𝐸𝑇)𝑛2 + 𝑘 (2𝑛 + 𝑛3) 𝑑𝑡 2 𝐸𝑇 1 𝑑𝑛3

1 = ― (𝑘3 + 𝑘𝐸𝑇)𝑛3 + 𝑘 (𝑛 + 𝑛4) 𝑑𝑡 2 𝐸𝑇 2 ︙

𝑑𝑛𝑝 ― 2 𝑑𝑡

1 = ― (𝑘𝑝 ― 2 + 𝑘𝐸𝑇)𝑛𝑝 ― 2 + 𝑘 (𝑛 + 𝑛𝑝 ― 1) 2 𝐸𝑇 𝑝 ― 3

𝑑𝑛𝑝 ― 1 𝑑𝑡

1 = ― (𝑘𝑝 ― 1 + 𝑘𝐸𝑇)𝑛𝑝 ― 1 + 𝑘 (𝑛 + 2𝑛𝑝) 2 𝐸𝑇 𝑝 ― 2


20

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𝑑𝑛𝑝

1 = ― (𝑘𝑝 + 𝑘𝐸𝑇)𝑛𝑝 + 𝑘 𝑛 𝑑𝑡 2 𝐸𝑇 𝑝 ― 1

where, 𝑛𝑖denote the number of exciton in NPLs located in the ith positions of stacked NPLs in ensemble. p is the number of stacked NPL in superstructure. 𝑘𝑖 is the recombination rate of NPL located in the ith position and is defined as

𝑘𝑖 =

= 𝑑 , 𝑑 ,…,𝑜𝑟 𝑑 {𝑘 + 𝑘 𝑘, , 𝑖𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 ℎ𝑜𝑙𝑒

1

2

𝑚

where k is the recombination rate of the defect free NPLs and 𝑘ℎ𝑜𝑙𝑒 is the hole trapping rate in a defected NPLs.35 We solved the set of differential equations numerically to find 𝑛1(𝑡), 𝑛2 (𝑡)…, 𝑛𝑝(𝑡). Here, k value is average lifetime of solution NPLs and 𝑘𝐸𝑇 is calculated ET rate using Eq. (1). We takes the hole trap rate (𝑘ℎ𝑜𝑙𝑒) of CdSe NPLs as (35 ps)-1 based on the 𝑝

previously reported value.15, 36 The sum of the solved ni is the total PL decay as ∑𝑖 = 1𝑛𝑖(𝑡) . The average result of total PL decay was evaluated by randomly changing the location of defected NPLs 1000 times. Figure 6c and Table 1 show the PL lifetimes of stacked NPLs as 0.220, 0.164, 0.136 and 0.116 ns in the NPL-1, NPL-2, NPL-3 and NPL-4, respectively, based on modeled PL decay. These PL lifetimes are in good agreement with experimentally obtained PL lifetimes as shown in Figure 5c. The agreement of these results indicates that ET is mostly responsibility for decline of PL lifetimes as a result of stacking of NPLs, and different PL decay kinetics between samples is originated by difference ET rate. To better understand the changes in ET rate, and ultimately in exciton dynamics depending on structure of superstructures, we investigate what factors contributed significantly to the ET rate. There are two distinct differences between prepared superstructures, which are lateral dimension of NPL and rotation angle between NPLs. As shown in Table 1, while the ET rate


21


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is more than doubled from NPL-1 to NPL-4, lateral area of NPLs is mainly responsible for the increase in ET rate, as the extinction coefficient increases by 1.8 folds. Figure 5c shows lateral area dependent exciton dynamics of superstructures. On the other hand, the change in the rotation angle between NPLs is not responsible for alteration of ET rate likely because of isotropic dipole orientation within the plane of NPL. To confirm that the difference in rotation angle did not effectively come into play in ET rate, we prepared straight ribbon superstructure made of square shaped NPLs with varying lateral area. Figure S4 shows that NPLs are stacked into one-dimensional shaped superstructures without rotation between NPLs.

Then, we

performed same measurements and analysis that we had done to analyze the exciton dynamics of twisted ribbon superstructures. As a result, theoretical PL lifetimes still exhibit a good agreement with experimental PL lifetimes shown in Figure S7, similar to the cases of twisted ribbon superstructures. It is pointed out that the model for PL decay rate works well and rotation of NPL does not have a significant effect on ET rate. Exciton dynamics analysis holds important implications. The ET rate of stacked NPLs can be easily modulated by changing the lateral dimension. Considering that extinction coefficient is an intrinsic property in spherical NCs with the same bandgap and diameter,37 this controllable extinction coefficient might be a key parameter of NPL design for device application to manipulate exciton dynamics. Table 1. Photoluminescence and energy transfer rate of colloidal and assembled CdSe NPLs

Sample

PL QY (%)

Percentage τ0 in τ0 in of the solution[a] film[a] defected (ns) (ns) NPL

τmodel in film[b] (ns)

τ ET[c]

J(λ)[d]

(ps)

(ⅹ10-11M1cm3)

κ2[e]

NPL-1

73

24

5.8

0.188

0.220

18.6

3.53

0.5

NPL-2

65

31

4.42

0.160

0.164

10.3

5.45

0.5


22

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NPL-3

61

36

3.71

0.120

0.136

7.8

6.46

0.5

NPL-4

59

39

3.58

0.096

0.116

7.5

6.63

0.5

[a] Average (1/e) PL lifetime in solution and film, [b] Modeled PL lifetime in film, [c] Calculated ET rate from ET rate equation, [d] integration term and [e] orientation factor in term of energy transfer rate equation.

SUMMARY

In summary, NPLs stack to form twisted ribbon superstructures because of structural distortion of individual NPLs. We have solved the reason why superstructures prefer twisted form rather than straight form, even though twisted shape is usually accepted as unstable superstructure. From the calculation of van der Waals interaction energy between distorted NPLs, it turns out that distortion of NPLs leads to structural instability of superstructure with straight form because of weakening van der Waals interaction. In order to ensure the structural stability of superstructures, NPL is stacked with subsequent rotation, appearing as a twisted ribbon superstructure. As delicate control of the distortion angle of NPL is allowed by manipulation of lateral dimension, pitch length of twisted ribbon superstructure is systemically controlled, supporting our hypothesis that distortion plays a key role of rotation between NPLs. We capitalized on previously reported reports that depletion interaction turns NPLs into twisted ribbon superstructures, by unveiling the mechanism and thereby controlling the pitch length of the superstructures. This understanding of pitch length control might be used for various applications utilizing helical structures. By comparison of theoretical and experimental PL decay kinetics, we found that ET is mostly attributed to alteration of exciton dynamics. In particular, ET rate varies depending on assembly structure and lateral size of NPLs in superstructures. Based on theoretically calculated ET rates, we conclude that this change in ET rate is mainly caused by alteration of extinction coefficient, which is determined by the lateral size of NPL. Considering that ET inevitably occurs in emitting layers and directly deteriorates


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the performance of light emitting devices,30 our finding suggests designing strategies of morphology of NPL and assembly structure of NPLs to improve the performance of optoelectronic devices. ASSOCIATED CONTENTS Supporting Information. Discussions about energy transfer rate and additional figures showing TEM images and TRPL spectroscopy of CdSe NPLs. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] *E-mail: [email protected] *E-mail: [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes The authors declare no competing financial interests. ACKNOWLEDGMENT This work was supported by the National Research Foundation (NRF) grants funded by the Korean government (Grant NRF-2016M3A7B4910618 and NRF-2017R1A2B2011066). The SAXS experiments at PLS-II were supported in part by MSICT and POSTECH.


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Stacking of Colloidal CdSe Nanoplatelets into Twisted Ribbon

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