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Exciton Migration and Amplified Quenching on Two-Dimensional Metal−Organic Layers Lingyun Cao,† Zekai Lin,‡ Wenjie Shi,† Zi Wang,† Cankun Zhang,† Xuefu Hu,† Cheng Wang,*,† and Wenbin Lin*,†,‡ †

Collaborative Innovation Center of Chemistry for Energy Materials, State Key Laboratory of Physical Chemistry of Solid Surfaces, Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, P. R. China ‡ Department of Chemistry, University of Chicago, 929 East 57th Street, Chicago, Illinois 60637, United States W Web-Enhanced Feature * S Supporting Information *

ABSTRACT: The dimensionality dependency of resonance energy transfer is of great interest due to its importance in understanding energy transfer on cell membranes and in low-dimension nanostructures. Light harvesting two-dimensional metal−organic layers (2D-MOLs) and three-dimensional metal−organic frameworks (3D-MOFs) provide comparative models to study such dimensionality dependence with molecular accuracy. Here we report the construction of 2D-MOLs and 3D-MOFs from a donor ligand 4,4′,4″-(benzene-1,3,5-triyl-tris(ethyne-2,1-diyl))tribenzoate (BTE) and a doped acceptor ligand 3,3′,3″-nitro-4,4′,4″-(benzene-1,3,5triyl-tris(ethyne-2,1-diyl))tribenzoate (BTE-NO2). These 2D-MOLs and 3D-MOFs are connected by similar hafnium clusters, with key differences in the topology and dimensionality of the metal− ligand connection. Energy transfer from donors to acceptors through the 2D-MOL or 3D-MOF skeletons is revealed by measuring and modeling the fluorescence quenching of the donors. We found that energy transfer in 3D-MOFs is more efficient than that in 2D-MOLs, but excitons on 2D-MOLs are more accessible to external quenchers as compared with those in 3DMOFs. These results not only provide support to theoretical analysis of energy transfer in low dimensions, but also present opportunities to use efficient exciton migration in 2D materials for light-harvesting and fluorescence sensing.

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INTRODUCTION In photosynthesis, chlorophylls and carotenoids form twodimensional networks on the thylakoid membranes to harvest sunlight energy.1 Similarly, in two-dimensional heterojunctions, excitons migrate in restricted dimensions before dissociating to electron−hole pairs.2 Exciton migration in low dimensions is thus of great interest to scientists, and has been studied on restricted surfaces, such as external surface of silica spheres,3 internal surface of porous glasses,4,5 Langmuir−Blodgett films,6−9 micelles,10 and liposomes.10,11,12 We envisioned that photoactive metal−organic frameworks (MOFs) and metal− organic layers (MOLs) with well-defined crystalline structures can help to uncover more details of dimension-restricted energy transfer.13−16 While MOFs have been extensively studied in the past two decades,17−42 their 2-D relatives, MOLs, have only recently been obtained by top-down 43−46 and bottom-up approaches.47−50 These ultrathin sheets with ordered repeating units in 2D are constrained in the third dimension to a single layer or a few layers. The structures of several MOLs have been confirmed by a number of different characterization techniques, including transmission electron microscopy (TEM), atomic force microscopy (AFM), and extended X-ray absorption fine structures (EXAFS).43,48,50 We can rationally design both 2DMOLs and 3D-MOFs from the same bridging ligand as the © 2017 American Chemical Society

light-harvesting chromophore and the same metal ion as the connecting node. These chemically similar but dimensionally different structures provide ideal platforms to compare energy transfer in 2D vs 3D. Previous studies suggest that energy transfer happens in three-dimensional space in isotropic 3D-MOFs, but can have features of lower dimensions in highly anisotropic 3D structures.13−16,51−53 For example, we and collaborators found the energy transfer of triplet excited states from Ru(bpy)32+ to Os(bpy)32+ in structurally anisotropic MOFs to be dominant in one or two directions.54 Morris and co-workers later studied Förster-type energy transfer of Ru(bpy)32+ in UiO67 and revealed a concentration dependent dimensionality change.55 Hupp, Farha, and co-workers modeled anisotropic Förster-type energy transfer in porphyrin-based MOFs as onedimensional exciton migration.56 They also demonstrated directional energy transfer in oriented MOF thin films on surface.15 Here we report the first study of exciton migration on true 2D molecular networks. We designed two ligands of the same shape and size but different fluorescence behaviors, 4,4′,4″-(benzene-1,3,5-triyltris(ethyne-2,1-diyl))tribenzoic acid (H3BTE) and 3,3′,3″Received: March 12, 2017 Published: May 3, 2017 7020

DOI: 10.1021/jacs.7b02470 J. Am. Chem. Soc. 2017, 139, 7020−7029

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Journal of the American Chemical Society

synthesis adopted our previously reported strategy of using capping ligands and supersaturation to overcome high surface energy of thin layers.50 The H3BTE ligand and a doping amount of H3BTE-NO2 were mixed in the reaction to afford 2D-MOL-Mix (SI Section S4). Elemental analysis of the nitrogen content was used to determine the doping level of the acceptor, which is defined as the ratio of [BTE-NO2]/([BTE] + [BTE-NO2]). TEM images of the 2D-MOLs showed ultrathin, wrinkled nanosheets of ∼0.5 μm × 1 μm in size (Figure 2d and SI Figure S5), which agrees with dynamic light scattering (DLS) measurements of 2D-MOL showing a distribution of hydrodynamic diameter from 600 to 800 nm (Figure S5).

nitro-4,4′,4″-(benzene-1,3,5-triyl-tris(ethyne-2,1-diyl))tribenzoic acid (H3BTE-NO2). H3BTE serves as the donor and is highly fluorescent, while H3BTE-NO2 serves as the acceptor and is nonfluorescent. These donors and acceptors were incorporated into 2D-MOLs (HfBTE-MOL and 2D-MOLMix) or 3D-MOFs (HfBTE-MOF, 3D-MOF-Mix) with Hf-oxo clusters as the connecting nodes to study the dynamics of exciton migration. Importantly, we observed resonance energy transfer with 2D features in the MOLs and that with 3D features in the MOFs. Formulas for dimensionality-dependent energy-transfer dynamics in the literature included either exciton migration on a network or one-step energy transfer to a trap. We established unified formulations to consider both processes, which fully agreed with energy-transfer dynamics from time-resolved fluorescence measurements of the 3DMOFs and 2D-MOLs. We also tested fluorescent quenching with external quenchers. Although the energy transfer in 3D-MOFs is faster than that in 2D-MOLs, excitons in 2D materials are much more accessible to external quenchers or analytes than that in 3D materials, leading to a more pronounced amplified quenching in 2D. These results give valuable insights into the design of next-generation fluorescent chemical sensors and light-harvesting devices based on low-dimensional materials.

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RESULTS AND DISCUSSION Synthesis and Structures of 2D-MOLs. The ligands H3BTE and H3BTE-NO2 were synthesized following similar procedures in the literature.57 The details of ligand synthesis and characterization can be found in Section S2 and Figures S1−S4 in the Supporting Information (SI). The 2D-MOLs were prepared through solvothermal synthesis in DMF in the presence of formic acid (Figure 1a−c and SI Section S3). This

Figure 2. (a) Scanasyst-mode AFM topography of the 2D-MOL. (b) Height profile along the white line in (a). (c) PXRD pattern of 2DMOL compared with the simulated one from the double-decker model. (d) TEM imagine of 2D-MOL. (e) HRTEM and SAED images of 2D-MOL. (f) HAADF images of 2D-MOL overlaid with a structural model showing Hf12 SBUs in pink polyhedra.

We deduced the molecular structure of 2D-MOLs by combining several pieces of information about the arrangements and inner structures of the SBUs. First, AFM measurements gave a thickness of 2 ± 0.2 nm for more than 75% of the samples (Figures 2a,b), indicating the formation of monolayer or double-layer MOLs. The commonly observed Hf6 SBUs in MOFs and MOLs have a thickness of ∼1.1 nm while the Hf12 SBUs shown in Figures 1a-c have an expected thickness of 1.75 nm. Second, a hexagonal arrangement of the SBUs in 2D was observed under the scanning transmission electron microscope (STEM) in high-angle annular dark-field (HAADF) imaging mode (Figure 2f). This is consistent with a 3,6-connection

Figure 1. (a) Structure of the M12 SBU in 2D-MOL. (b) Top view and (c) side view of 2D-MOL. The elements are represented as C, black and orange ball; Hf, cyan and green polyhedra; O, red ball. (d) Structure of Hf6 SBU in MOFs. (e) Crystal structure of 3D-MOF and (f) a slice of the 3D-MOF as highlighted in green in (e). The elements are represented as C, black ball; Hf, purple polyhedra; O, red ball. 7021


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Journal of the American Chemical Society between the ligand and the SBU with kgd topology. The interSBU distance of 2.5 ± 0.1 nm in the images match the expected value of 2.47 nm for the BTE ligand. This structure is also confirmed by high resolution TEM images (HRTEM) and selected area electron diffractions (SAED), which give interplane distances of 2.05 and 2.13 nm, respectively, for the (200) or (110) planes, close to the expected distance of 2.13 nm in the structure model (Figure 2e). Third, the ligand/metal ratio was determined to be 1:3 by thermogravimetric analysis (TGA) (SI Figure S6). The ratio between capping formate ligands on the SBU and the BTE ligands (or BTE+BTE-NO2 in doped samples) in the network was 1:1 as determined by 1H NMR spectra of digested samples (SI Figure S7). These ratios of the 2D-MOL are consistent with a chemical formula of [Hf6O4(OH)8(HCO2)2(BTE)2(H2O)x]n. Two molecular models can fit both the TEM/AFM images and the chemical compositions: (1) a bilayer of 2D-MOL with 6connected Hf 6 SBUs as reported previously for the Hf6O4(OH)4(HCOO)6(BTB)2 MOL (BTB = 4,4′,4″-(benzene-1,3,5-triyl)tribenzoate)50 or (2) a monolayer of 2D-MOL composed of 12-connected Hf12 SBU and double-decker BTE ligands as shown in Figure 1a−c. The latter is believed to be the molecular structure of our 2D-MOL because such SBUs and connection mode are observed in a single-crystal structure of MOF-L (L = layered). Single-crystal X-ray diffraction studies revealed MOF-L of kgd topology and a framework formula of Hf12(μ3-O)8(μ3OH)8(μ2-OH)6(μ1-OH)2(H2O)2(η2-HCO2)4(BTE)4. MOF-L is comprised of stacked layers of these BTE double-deckers with Hf12 SBUs (SI Table S1 for crystal refinement, Figure S8 for structural model). The observation of Hf12 SBU and doubledecker BTE ligands in MOF-L reinforces our structure assignment for the 2D-MOL. Fourth, we have used EXAFS analysis to support the assignment of the Hf12 SBU structural model (Figure 3). For both Hf6 and Hf12 SBUs, we have single crystals of related compounds as controls (SI Figures S9−S13), with eightcoordinated Hf4+ ions in both Hf6(μ3-O)4(μ3-OH)4(η2HCO2)6(η2-R-CO2)6 and Hf12(μ3-O)8(μ3-OH)8(μ2-OH)6(μ1OH)2(H2O)2(η2-HCO2)4(η2-R-CO2)12 (SI Section S3.6, Tables S4−S6, and Figure S13).50 The Hf12 SBU results from face-to-face linking of two Hf6(μ3-O)4(μ3-OH)4 clusters by six μ2-OH groups. The major difference between the first coordination spheres of Hf4+ in Hf12 and Hf6 SBUs is the positions of μ3-O and μ3-OH groups. In the Hf6 SBU, the μ3-O and μ3-OH groups reside in the middle of three Hf4+ ions with almost equal Hf−O distances of 2.14 Å for μ3-O groups and 2.18 Å for μ3-OH groups. In the Hf12 SBU, 12 of the 16 μ3-O/ μ3-OH groups reside off the centers of the Hf4+ triangles. They are closer to two of the Hf4+ ions with Hf−O distances of 2.05 Å for μ3-O groups and 2.14 Å for μ3-OH groups, but farther from the other Hf4+ ion with Hf−O distances of 2.74 Å for μ3O groups and 2.78 Å for μ3-OH groups. This long Hf−O distance in the first coordination sphere of Hf12 SBU can be identified in the EXAFS data of the Hf LIII-edge as χ(R) function after background removal and Fourier transform. The |χ(R)| at R = 2.39 Å in Figure 3c contains contributions from Hf−O single scattering paths with Reff around 2.74 Å that is also present in the |χ(R)| plot of the Hf12 single crystal but absent in that of the Hf6 single crystal. The agreement of experimental curves of the MOL to the Hf12 fittings but not to the Hf6 fittings for both real and imaginary parts of χ(R) around

Figure 3. Hf12 and Hf6 SBUs in the two structural models (a,b) and experimental EXAFS spectra and fittings (c,d) of 2D-MOL in R space showing the magnitudes (black hollow squares, black solid line) and real components (blue hollow squares, blue solid line). The fitting range was 1.3−4.6 Å in R space. C, metallic gray; Hf, cyan; O, red. The fitting with the Hf12 and Hf6 models gave R factors of 0.0068 and 0.010, respectively.

R = 2.39 Å supports the presence of Hf12 SBUs in the 2DMOLs. Fifth, the simulated PXRD patterns of this 2D double-decker model by a Matlab code match the experimental ones for the 2D-MOLs (Figure 2c and SI Figure S14). The experimental PXRD pattern of 2D-MOL clearly showed four reflection peaks, which could all be indexed to (hk0) reflections, including (200)/(110), (020), (400)/(220), and (420) reflections. The presence of only (hk0) reflections is indicative of a crystalline 2D material. Taken together, the 2D-MOLs adopt double-decker structure with Hf12 clusters as the SBUs and a framework formula of Hf12(μ3-O)8(μ3-OH)8(μ2-OH)6(μ1OH)2(H2O)2(η2-HCO2)4(BTE)4 (Figure 1a−c). If we simplify the Hf12 SBU as one connecting node and a pair of doubledecker BTE ligands as another connecting node which is doubly linked to an adjacent Hf12 SBU, we can obtain the topology of the 2D net as 3,6-connected kgd. Synthesis and Structure of 3D-MOF. The 3D-MOF was prepared by solvothermal synthesis using H3BTE and HfCl4 without the addition of water (SI Section S3.2). BTE-NO2 was also doped into the framework of Hf-BTE by mixing an appropriate ratio of H3BTE and H3BTE-NO2 during the synthesis to afford 3D-MOF-Mix with different doping levels (SI Section S4, Tables S7−10, and Figures S14 and S15 summarize doping for both 3D-MOFs and 2D-MOLs). The 3D-MOF possesses a framework formula of Hf6(μ3O)4(μ3-OH)4(H2O)4(BTE)4 with 12-connected Hf6 SBUs and 3-connected ligands to give 12,3-connected nets of llj topology as determined by single-crystal X-ray crystallography (SI Section S3, Tables S2 and S3, and Figures S9−S11) and PXRD (SI Figures S12 and S14). Two of the three carboxylates on the BTE ligand coordinate to two Hf4+ ions in an η2bridging mode and the remaining carboxylate coordinates in an 7022


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Figure 4. (a) Excitation (black) and emission (blue) spectra of H3BTE and absorption spectra of H3BTE-NO2 (red). (b) Atomic transition densities of BTE and BTE-NO2 shown as the encoded color of the atoms, and transition dipoles of donor and acceptor. (c,d) Steady-state fluorescence spectra of 3D-MOF-Mix (excited at 325 nm) and 2D-MOL-Mix (excited at 315 nm) with different doping levels of BTE-NO2.

Figure 5. (a) Intensity quenching in 2D-MOLs and 3D-MOFs; (b) Lifetime quenching in 2D-MOLs and 3D-MOFs; (c) kET values of 2D-MOLs and 3D-MOFs.

η1-mode to one Hf4+ ion (Figure 1d). Compared to commonly observed Hf6/Zr6 SBUs of related Hf/Zr-MOFs with all carboxylates in η2-mode, the eight-coordinated Hf4+ ion in this 3D-MOF has an additional water molecule coordinated to the site left by the η1-carboxylate. The arrangement of the BTE ligands in the 3D-MOF can be depicted as two sets of honey-comb sheets perpendicular to each other and interconnected by sharing the metal cluster nodes (Figure 1e). On each honey-comb sheet, BTE coordinates to three Hf6 clusters which connect with six BTE molecules roughly on the same plane to afford a 3,6-connected topology similar to the 2D-MOLs (Figure 1f). This structural similarity between part of the 3D-MOF and the 2D-MOL is a result of the correlated Hf12 SBU and Hf6 SBU in the two, which share similar angles between adjacent connections and lead to similar arrangement pattern of the BTE ligands. This structural similarity allows the comparison between the 3D-

MOF and 2D-MOL in energy-transfer studies to uncover the dimensionality dependency. The averaged distance between two adjacent ligands in the same plane in the 3D-MOF (1.52 nm) is similar to that in the 2D-MOL (1.41 nm). The distance between two adjacent BTE molecules on two perpendicular planes in the 3D-MOF is 1.29 nm. Each BTE molecule in the 3D-MOF has 8 other BTE molecules as the nearest neighbor as compared to 4 nearest neighbors in the 2D-MOL. There are also square channels of 2.1 nm × 2.1 nm in size along the c-axis in the crystal structure, which are interconnected by channels in perpendicular directions. Donor-to-Acceptor Energy Transfer Revealed by Fluorescence Measurements. The overlap between the absorption spectrum of H3BTE-NO2 and the emission spectrum of H3BTE (Figure 4a) indicates possible resonance energy transfer (RET) from the donor (BTE) to the acceptor 7023


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MOF-Mix and 2592 molecules in 18×18 unit-cells for 2DMOL-Mix (SI Section S8). In these simulations, the excitation population Pi(t) at each donor site was calculated by the interconnected master equations:

(BTE-NO2), which is confirmed by the quenching of donor emission in the doped samples (Figure 4c,d). Energy transfer is more efficient in the 3D-MOF-Mix than in the 2D-MOL-Mix as measured by quenching efficiency. For example, as the doping level of BTE-NO2 increases to 2.4% in the 3D-MOF-Mix, the BTE emission drops to 9.6% of the initial intensity (after correction for acceptor absorption, see SI Section S5). Similarly, the lifetime of the BTE excited state is reduced by more than 10 times. By contrast, the BTE emission in the MOL at a similar doping level of 2.3% drops to 30% of that of the undoped sample, and its emission lifetime is only halved (Figure 5a,b). We have prepared five samples for 2DMOL-Mix with the BTE-NO2 doping levels ranging from 0.77% to 18.0%, and five samples for 3D-MOF-Mix with the BTE-NO2 doping levels ranging from 0.39% to 20%. As shown in Figure 5a,b (data in SI Section S6, Figure S16, and Tables S11 and S12), both the emission intensities and fluorescence lifetimes decrease with increasing doping level of the BTE-NO2, and the quenching in the 3D-MOF is consistently more pronounced than that in the 2D-MOL. Experimental emission measurements and elemental analyses were obtained multiple times for each doping level and their averaged values were used in the analyses. The error bars representing the ranges of these data are shown as black crosses in Figure 5a,b, respectively. We also calculated an effective energy-transfer rate kET defined by eq 1 at different doping level α. Detailed analyses of different contributions to kET will be given in the following sections. kET =

⎧ ⎪ d 1 Pi(t ) = Pi(t )⎨− − ⎪ dt ⎩ τi

j≠i

I(t ) = ΓD∑ Pi(t )

Figure 5c shows kET as a function of α for 2D-MOL and 3DMOF with slopes of 20 ± 2 ns−1 and 79.6 ± 0.3 ns−1 respectively, verifying faster energy-transfer rate in 3D vs 2D. The slope dkET is equivalent to the Stern−Völmer constant in dα dynamic quenching that describes the effectiveness of the quenching process. Table 1 provides a summary of key parameters of amplified quenching and exciton migration in 2D-MOL and 3D-MOF.

I (t ) = A 0 +

0.30 0.41 20 ± 2 1.98 43.1 97.8 7.23 × 10−4 41.5 0.84 43 ± 6

0.096 0.091 79.6 ± 0.3 2.35 17.1 58.2 1.01 × 10−3 94.4 0.96 190 ± 30

(2)

(3)

∑ A i e −t / τ

i

i

τ̅ =

Table 1. Parametes of Amplified Quenching and Exciton Migration in 2D-MOLs and 3D-MOFs 3D

j≠i

where ΓD is the rate of radiative emission of the donor molecule. Weighted average fluorescence lifetimes of the MOLs and MOFs, τ,̅ can then be obtained by fitting this simulated I(t) curves to exponentials.

(1)

2D

⎭

where τi is the lifetime of the excited state on site i and ki,j/kj,i is the energy-transfer rate constant between sites i and j. These rates were calculated using a generalized Förster resonance energy transfer (FRET) formulation with atomic transition densities beyond the point-dipole approximation, as detailed in Section S7 in the SI. The rates of the reverse energy transfer from the quencher sites to the donor sites were set to zero. The quencher sites were introduced randomly into the framework based on the doping level in the simulation. Calculations were repeated five times with different random assignments of the quenchers and were then averaged. Initially at t = 0, all the Pi(t = 0)’s at the donor sites were set to one. All the Pi(t)’s of the acceptor sites at any time were set to zero. The whole matrix of excitation populations then evolved according to eq 2 and was calculated using matrix algebra in the Matlab software suite. The emission intensity of the donors in the MOL or MOF at a given time, I(t), was proportional to the summation of all excited-state populations at the given time. i

1 1 − τ τ0

I/I0 at a doping level ∼2.3% τ/τ0 at a doping level ∼2.3% dkET/dα, ns−1 R0(Förster distance), nm rDA (one step), ns−1 rtotal, ns−1 Deff, cm2·s−1 ϵ = Dτ0/R02 β dK/dα

⎫ ⎪

∑ ki ,j⎬⎪ + ∑ kj ,iPj(t )

∑i Ai τi2 ∑i Ai τi

,

(4)

i = 1 or 2 (5)

The total emission intensities of the donors, ID, can also be calculated as integration of I(t) in time: ID =

∫0

∞

I (t ) d t

(6)

As shown in Figure 5a,b, these simulated τ ̅ and ID for doped 3D-MOFs and 2D-MOLs all agree with experimental values when expressed in I/I0 and τ/τ0, where I0 and τ0 are intensities and lifetimes of undoped samples respectively. Central to these simulations, the atomic transition densities of the donor and acceptor ligands were obtained from singly excited configuration interaction calculations based on an INDO ground-state wave function using the Gaussian 09 software suite (SI Section S7).61 The oscillator strengths of the calculated results were normalized to experimental absorption spectra of the donor and acceptor to obtain consistent values of transition dipole moments. The calculated values of atomic transition densities were encoded into the red (positive) and blue (negative) colors of the atoms in Figure 4b. Modeling Exciton Diffusion in 2D and 3D. Two kinds of energy transfers are involved in the quenching events in MOLs and MOFs: the energy transfer from the donor to the acceptor

Modeling Donor-to-Acceptor Energy Transfer in 2DMOLs and 3D-MOFs. The experimental quenching curves roughly match the simulated ones from molecular models (Figure 5a,b). The simulations are based on Förster energytransfer theory with atomic transition density calculations (beyond the point-dipole approximation, see SI Section S7)58−60 of 2744 molecules in 7×7×7 unit-cells for 3D7024


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Figure 6. (a,b) Exciton occupation probabilities at t = 100 ps after injecting one exciton at the center at t = 0 ps in 3D-MOFs (a) and 2D-MOLs (b). See also Movie 1 and Movie 2. (c,d) The M(R,t) vs r2/t plots in the 3D-MOFs (c) and the 2D-MOLs (d) with fittings from approximated Fickian diffusion model (truncated at second order).

and the energy transfer between two donors. The inter-donor energy transfer does not directly eliminate excited states of the donor, but enables their migration to visit sites closer to the traps in the framework, amplifying the quenching efficiency. Similar effects are used in conductive polymers for fluorescence sensing with enhanced sensitivities.62,63 We aim to quantify the relative contributions from these two kinds of energy transfer to the dimensionality-dependent quenching. The energy-transfer rate between adjacent donor and acceptor in 3D-MOF-Mix is 17.1 ns−1 on average and that in 2D-MOL-Mix is 43.1 ns−1 on average based on the simulations. The rates are thus much higher in the 2D-MOL-Mix than in the 3D-MOF-Mix, because of favored parallel alignment of donor/ acceptor transition dipoles that are constrained in the 2D plane in the MOL. The summation of energy-transfer rates from the nearest 2591 donors to one acceptor in the model 2D network is 97.8 ns−1 and that from 2743 donors in the 3D network is 58.2 ns−1. The higher connection numbers in 3D help increase the overall energy-transfer rate which is still lower than that in 2D-MOL-Mix. As a result, this direct energy transfer from the donor to the acceptor cannot account for the higher quenching efficiency in the 3D-MOF-Mix than that in the 2D-MOL-Mix. We can also isolate out the diffusion dynamics of the excitons due to donor-to-donor energy transfer. Strictly speaking, the diffusion of Förster exciton is non-Fickian because of the nonlocality of long-range energy transfer (SI Section S9 and Figure S18). However, it can still be approximated as Fickian diffusion with a small higher order correction in most cases. The diffusion constant D under these conditions contains both local and long-range contributions (SI Section S9). We can write the diffusion equation of the excited-state populations:

∂P(r , t ) = Done‐step∇2 P(r , t ) + higher orders ∂t ≈ (D local + D long‐range)∇2 P(r , t ) = Deff ∇2 P(r , t )

(7)

where ∇ is the Laplace operator and P(r,t) is the excited-state population at a given position and a given time. For simplicity, we also ignored the anisotropy of the diffusivities in 3D-MOFs and 2D-MOLs, as the simulated diffusion distances of excitons in the fastest and slowest directions at a given time only differ by factors of 1.17 and 1.16 in the 3D-MOFs and 2D-MOLs, respectively. The diffusivities reported here can be understood as averaged effective diffusivities. We injected one exciton at the center of the model networks at t = 0, and then simulated the evolution of the excitation populations P(r,t) as in the previous section (see Figure 6a,b and the corresponding Movie 1 and Movie 2 showing the exciton diffusion). To derive the effective diffusivity from the simulations, we first extract the amount of excited states within radius R from the center at a given time t from the model as M(R,t). Generally M(R,t) can be expressed as a function of R2/ 4Dt in the Fickian diffusion limit. For 2D: 2

M(R , t ) = 2π

∫0

R

P(r , t )r dr = γ(1, R2/4Dt )

(8)

For 3D: M(R , t ) = 4π

∫0

R

P(r , t )r 2 dr =

2 γ(3/2, R2/4Dt ) π (9)

where γ is the lower incomplete gamma function. Fitting the M(R,t) from simulations to eqs 8 and 9 gives satisfactory agreement (Figure 6c,d). The goodness of the 7025


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Figure 7. (a) The β parameter as a function of ϵ in 2D and 3D. (b) Plot of K vs different BTE-NO2 doping levels. (c,d) Fitting to the time-resolved fluorescent emission of 3D-MOF-Mix (c) and 2D-MOL-Mix (d) with different doping levels of BTE-NO2.

fitting can be further improved by considering higher order terms in the diffusion equation (SI Figure S19). The effective diffusivities are 7.23 × 10−4 cm2/s for 2D-MOLs and 1.01 × 10−3 cm2/s for 3D-MOFs, suggesting a difference of about 1.5 times. Moreover, even with the same effective diffusivity, diffusion in 3D is faster than that in 2D. For example, we can define the diffusion distance at a given time as the median of exciton displacements, which is the solution of eq 10: M(R , t ) = 1/2

on SI eq S12. The R0’s are determined to be 1.98 nm in the 2DMOL-Mix and 2.35 nm in the 3D-MOF-Mix. The core equation for energy migration and transfer is eq 12 (SI Section S10), considering energy transfer to one quencher at the center of a sphere: ∂P(r , t ) 1 ⎛R ⎞ 1 = D∇2 P(r , t ) − ⎜ 0 ⎟ P(r , t ) − P(r , t ) ⎝ ⎠ ∂t τ0 r τ0 6

(12)

where P(r,t) is the excited-state population at a given time and position. The first term on the right-hand side of eq 12 represents the diffusion of the excitons on the networks, while the second and the third terms refer to energy transfer to the quencher at the center and natural decay of excited states, respectively. The emission intensity of the donor at a given time is proportional to the summation of all the excited-state population at the time over the whole networks.

(10)

This diffusion distance in 3D is calculated to be 2.366 Dt , and that in 2D is 1.665 Dt . Taken together, excitons in the 3DMOF move 1.68 times farther in a given time than that in the 2D-MOL. This ratio roughly matches the difference from the simulated diffusion dynamics as shown in Figure 6a,b. Modeling Time-Resolved Luminescence Quenching in 2D and 3D. The dimensionality-dependence of timeresolved emission intensity of mobile excitons in amplified quenching is mathematically complicated, and is not well treated in previous works. As in the above sections, we used an effective diffusivity D to represent exciton migration rate or the donor-to-donor energytransfer rate. To simplify the modeling, the energy-transfer rate k between the donor and the acceptor is described by a Förster distance R0 as shown in eq 11: 6 1 ⎛R ⎞ k = ⎜ 0⎟ τ0 ⎝ r ⎠

∫

I(t ) = ΓD P(r , t ) dr

(13)

The numerical solution for excited-state dynamics can be written in the following forms: ⎡ ⎛ t ⎞β⎤ t I(t ) = I(0) exp⎢ − − K ⎜ ⎟ ⎥ ⎢⎣ τ0 ⎝ τ0 ⎠ ⎥⎦

(14)

where β is a parameter depending on both the dimensionality of the system and the mobility of the excitons but not on the doping level of the quenchers, while K is a parameter depending on the doping level. Equation 14 is a numerical solution of a model to describe exciton dynamics in amplified quenching with mobile excitons (SI Section 10) under the assumptions of Fickian diffusion of the excitons and quenching by Förster energy transfer to the quencher via dipole−dipole interactions. Specifically, the exciton mobility or the relative rate of donor-to-donor energy

(11)

Such an expression captures the 1/r6 dependency for Förstertype energy transfer in the dipole−dipole limit, although it will break down at short inter-donor distances. R0 is the distance to achieve 50% energy-transfer efficiency, which can be calculated from the overlap integral of the emission spectra of the donor and the absorption spectra of the acceptor (Figure 4a), based 7026


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3D-MOF, so the quenching can only take place at the surface. In contrast, coumarin-343 should be small enough to enter the channels of 3D-MOF. We observed rapid and striking quenching of exciton emission on 2D-MOL by both quenchers, while the quenching effects in 3D-MOF were very limited (Figure 8 and SI Figure

transfer vs donor-to-acceptor energy transfer, can be represented by a unitless quantity ϵ = Dτ0/R02. A more mobile exciton and slower energy transfer to the quencher corresponds to a larger ϵ. We have plotted the theoretically predicted β as a function of ϵ in both the 2D and 3D cases. The ϵ values for the 2D-MOLMix and 3D-MOF-Mix were calculated to be 41.5 and 94.4, respectively, with the corresponding β values of 0.84 and 0.96 as shown in Figure 7a. The time-resolved emission traces of the donors were obtained experimentally, and fitted to the general formula of eq 14 after deconvolution of the excitation pulses (Figure 7c,d). We have plotted the K values in eq 14 vs the acceptor doping levels α for both 2D-MOLs and 3D-MOFs. These K values are proportional to the doping levels and are unitless descriptors of effective energy-transfer rate, similar to the kET in eq 1 (Figure 7b). The slope dK/dα is also a unitless analogue to the Stern− Völmer constant, which is 43 ± 6 for 2D-MOL and 190 ± 30 for 3D-MOF. From eq 14, we can see that with very small ϵ the systems enter the region of immobilized exciton with the limiting β = 1/ 2 for 3D and β = 1/3 for 2D. The numerical solution for excited-state dynamics of eq 14 reduces to that of Inokuti− Hirayama function, which describes the dimensionality-dependent quenching of fixed excitons.64−66 ⎡ ⎛ t ⎞d /6 ⎤ t ⎢ I(t ) = I(0) exp − − K ⎜ ⎟ ⎥ ⎢⎣ τ0 ⎝ τ0 ⎠ ⎥⎦

Figure 8. I0/I and IDye/ILigand plots of the fluorescence quenching of the 3D-MOF and 2D-MOL, by the H3BTE-NO2 (a) and coumarin343 (b).

S17). The energy transfer between BTE and coumarin-343 gave rise to coumarin-343 emissions. The intensity ratio between coumarin-343 emission and BTE emission can serve as an internal figure of merit for the energy-transfer efficiency. This value is 5 times larger in 2D-MOL than that in 3D-MOF with the same coumarin-343 concentration in solution (Figure 8b). In 3D materials, the quenchers preferentially adsorb on the outer shell of the particles even for porous materials. Such an uneven distribution of the quencher significantly reduced the quenching efficiency. In contrast, the adsorbates distribute evenly on 2D materials since every molecule on the 2D sheets are on the external surface, suitable for energy transfer to outside quenchers. The accessibility of the excitons in 2D materials thus compensates for the slower exciton migration in 2D, leading to superior performance in exciton extraction by the quenchers.

(15)

where d is the dimension (1, 2, or 3), and τ0 is the fluorescence lifetime of the donor in the absence of quenchers. On the other hand, when the ϵ is large, the excitons move freely and quickly search all the donor sites before any donorto-acceptor energy transfer happens. The eq 14 reduces to Stern−Völmer equation with β = 1 for both 2D and 3D cases. ⎡ t t ⎤ I(t ) = I(0) exp⎢ − − K ⎥ τ0 ⎦ ⎣ τ0

(16)

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Although no molecules are really moving during the quenching process, the migration of excitons on the framework is mathematically equivalent to a wondering molecule, leading to dynamic quenching behavior represented by the Stern− Völmer equation. Collecting Excitons in Two-Dimensional Materials for Chemical Sensing and Photocatalysis. In fluorescence chemical sensing, the analyte of interest comes in contact with the sensing materials and change their fluorescence behaviors. Here the efficacy of amplified quenching is related to the accessibility of the excitons to the analytes. Similarly, in photocatalytic reactions, reactants need to have access to the excitons to initiate redox reactions and charge-separation. The analytes and reactants are meaningful external quenchers and their accessibility to excitons determines the system performance in sensing and photocatalysis. We used H3BTE-NO2 or coumarin-343 molecules as external quenchers to extract the excitons from the materials of different dimensionalities. Note that here the H3BTE-NO2 was not doped into the networks, but added in the outside solution surrounding 2D-MOL and 3D-MOF. Both the H3BTE-NO2 and coumarin-343 possess carboxylic acid functional groups to interact with the Hf SBUs in the 2D-MOL and 3D-MOF. The molecular size of H3BTE-NO2 is larger than the channel size of

CONCLUSION We designed and synthesized 2D-MOLs and 3D-MOFs from similar hafnium SBUs and the same ligands to compare energy transfer in 2D vs 3D. We have not only quantified resonance energy transfer in 2D-MOLs and 3D-MOFs by quenching studies, but also decomposed the energy-transfer efficiencies to contributions from donor-to-trap energy transfer and exciton migration through a combination of experimental measurements and simulations. Although the donor-to-trap energy transfer rate is faster in 2D-MOLs than in 3D-MOFs due to favorable transition dipole alignment in restricted dimensions, the lower inter-chromophore connectivity and slower exciton migrations in 2D materials lead to lower efficiency of overall energy transfer in the 2D-MOLs than in the 3D-MOFs. By contrast, with an external quencher in solution, the MOL exhibits much more efficient energy transfer than the MOF, highlighting better accessibility of the excitons on a 2D material than in a 3D material. This exciton accessibility can be an important factor for efficient exciton extraction in chemical sensing and photocatalysis. These findings highlight the opportunities in using efficient exciton migration in lowdimensional materials for fluorescence sensing and light energy harvesting. 7027


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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.7b02470. Ligand syntheses, powder X-ray diffractions, thermogravimetric analyses, fluorescence and UV−vis spectra, model networks, and exciton dynamics simulations, including Sections S1−S10, eqs S1−S69, Figures S1− S19, and Tables S1−S12 (PDF) X-ray crystallographic data for 3D-MOF-I (CIF) X-ray crystallographic data for 3D-MOF-D (CIF) X-ray crystallographic data for MOF-L (CIF) W Web-Enhanced Feature *

Movies 1 and 2 in AVI format, showing the exciton diffusion in 3D-MOF and 2D-MOL, respectively, from t = 0 to 100 ps are available in the online version of the paper

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AUTHOR INFORMATION

Corresponding Authors

*[email protected] *[email protected] ORCID

Cheng Wang: 0000-0002-7906-8061 Wenbin Lin: 0000-0001-7035-7759 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Zhenghao Zhai and Prof. Weitai Wu for experimental help. The present research was financially supported by the National Natural Science Foundation and Ministry of Science and Technology of P. R. China (NNSFC21671162, 2016YFA0200700, NNSFC21471126), the National Thousand Talents Program of P. R. China, the 985 Program of Chemistry and Chemical Engineering disciplines of Xiamen University, and the U.S. National Science Foundation (DMR-1308229). Singlecrystal diffraction studies were performed at ChemMatCARS, APS, Argonne National Laboratory (ANL), which is principally supported by the National Science Foundation (NSF/CHE1346572). XAS analysis was performed at Beamline 9-BM, APS, ANL. Use of the APS, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science by Argonne National Laboratory, was supported by the U.S. DOE under Contract No. DE-AC02-06CH11357.

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