Supporting Information. for. Designing Janus Ligand Shells on PbS Quantum Dots using Ligand-Ligand Cooperativity

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1 Supporting Information for Designing Janus Ligand Shells on PbS Quantum Dots using Ligand-Ligand Cooperativity Noah D. Bronstein, 1 Marissa Martinez, 1,2 Daniel M. Kroupa, 1,2 Márton Vörös, 3,4 Haipeng Lu, 1 Nicholas P. Brawand, 4 Arthur J. Nozik, 1,2 Alan Sellinger, 1,5 Giulia Galli, 3,4 and Matthew C. Beard 1* 1. Chemistry & Nanoscience Center, National Renewable Energy Laboratory, Golden, Colorado 80401, United States. 2. Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309, United States. 3. Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States 4. Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States 5. Department of Chemistry and Materials Science Program, Colorado School of Mines, Golden, Colorado 80401, United States. Section S1: Constructing Absorption Isotherms To construct the absorption isotherms we follow the procedure detailed in Ref. 1. Breifly, optical absorbance spectra is collected using a UV-Vis-NIR spectrometer. A stock solution of 5-15 µm PbS QDs in DCM, standardized from absorbance measurements taken in TCE, is prepared under ambient conditions. Separately, a stock ligand solution is prepared by dissolving a known amount of the ligand in a compatible solvent (see Table 1). The stock ligand solution is combined with neat ligand solvent in separate vials to make diluted ligand samples of varying ligand concentration. In a 2 mm path length cuvette, 0.1 ml of a diluted ligand solution was added to a 0.6 ml of the stock QD solution (always maintaining a constant sample volume of 0.7 ml). The sample is thoroughly mixed, and an absorbance spectrum is immediately taken. This protocol was followed for diluted ligand samples with ligand content ranging from ligands per QD per addition. Solution measurement and mixing was performed with calibrated micropipettes. 1

We integrate the absorption spectrum from 1.0 to 2.5 ev, starting below the QD 1S-exciton and ending prior to any R-CA - /R-CAH ligand absorbance feature (see Fig. 1a, gray-trace).

1b, dashed-line); suggesting the ligand exchanges are governed by an equilibrium between surface bound and free ligands that is driven towards surface bound R-CA - by the addition of excess R- CAH.

2 We integrate the absorption spectrum from 1.0 to 2.5 ev, starting below the QD 1S-exciton and ending prior to any R-CA - /R-CAH ligand absorbance feature (see Fig. 1a, gray-trace). α/α 0 increases as cinnamate ligands bind to the surface (Fig. 1b), and at ligand equivalents larger than the number of OA - originally coordinating the QD surface (100 in these experiments, Fig. 1b, dashed-line); suggesting the ligand exchanges are governed by an equilibrium between surface bound and free ligands that is driven towards surface bound R-CA - by the addition of excess R- CAH. To construct the ligand absorption isotherms we need to relate α/α 0 to the addition of one bound ligand to the QD surface. Figure S1. Example of spectrophotometric tritrations. (a) Raw data for the 4(CN) 2 derivative. As the R-CA-/QD equivalents increases the absorption of the QD solutions increase. Integrating from 1eV to 2.5 ev to avoid contributions from the ligand absorption (gray-trace). (b) Plot of the absorption enhancement as a function of Ligand equivalents. After the addition of ~ 400 ligand equivalents the absorption enhancement saturates. Derivation of Square Root / cube-root dependence of oscillator strength. In our previous study, we also correlated the quantitative NMR spectroscopy data to the enhanced absorbance α/α 0. We determined that for the 2,6-F-CAH ligand exchange, α/α 0, is N b proportional to the where N is the number of bound or exchanged 2,6-F-CA - ligands. 2 b We now derive a relationship that provides a physical basis to allow for the generalization of this relationship within the PbS QD system. We want to find the relationship between the change in oscillator strength ( OS) and the addition of a new ligand ( N b ) that couples to the oscillator strength; OS Nb. Moreels et al. found that for PbS QDs, the 1 st exciton oscillator strength scales with the diameter of the QDs and not the volume of the QD, 3 thus, OS r = β where β is the coupling constant that depends upon the identity of the additional ligand and how it couples to the oscillator strength ( β depends on the ligand identity). We know that OS Nb = OS r r Nb, solving for OS we find that OS = α 3 N b, where α is a constant that encapsulates β and the effective size of the new ligand. Thus, we find that OS should vary with 2

the cube root of the additional ligands. However, in our experiments we integrate not just over the 1 st exciton transition but also higher energies.

3 Repeating the above calculation for a volume relationship we find that OS = γ N b, suggesting that the change in OS should be linear in the additional bound ligands.

3 the cube root of the additional ligands. However, in our experiments we integrate not just over the 1 st exciton transition but also higher energies. For higher order transitions (energies greater than the 1 st exciton transition energy) the linear OS relationship will gradually change to a volume relationship. 3 Repeating the above calculation for a volume relationship we find that OS = γ N b, suggesting that the change in OS should be linear in the additional bound ligands. The observed N b occurs because we are integrating over many different energies where the effective change in OS vs QD radius is in between linear and volume. We can verify that this relationship holds by plotting the quantitative NMR spectroscopy data from Ref. 2 vs. α/α 0 determined across the 1 st exciton rather than integrated over the entire absorption spectrum. The data integrated over the 1 st exciton transition clearly shows a cube root dependence (Fig. 7, blue triangles and trace) while the integration over a larger energy range shows the square root dependence (Fig. 7, red circles and red trace). Figure S2. The enhanced absorbance as a function of bound ligands (determined in Ref. 2 using quantitative 19 F NMR). The blue triangles are for integrating over the 1 st exciton transition while the red squares are for integrating over the larger energy range. The blue trace is a cube-root dependence while the red trace is the square dependence. To derive the cube root dependence discussed above first assume that the oscillator strength varies linear with the radius of the QDs, (OS = β r) then, OS r = β (S.1) where OS is the oscillator strength, r is radius, and β is the electronic coupling constant. The change in oscillator strength with the number of bound ligands is, 3

4 OS = OS N b r r V b V b N b (S.2) where N b is the number of bound ligands, and V b is the change in volume induced by bound ligands. The volume change is linearly related to the number of bound ligands, V b = α N b and V b N b = α. The total volume of the NCs after the ligand shell is added is given by, V tot = V 0 + V b = ( 4π 3 ) r3 (S.3) where V 0 is the volume of the QD core. Solving for r and substituting V b = α N b gives, thus, integrating gives, r = V b ( 4π) (V 0 + αn b ) 2 3 OS = α β N b ( 4π) (V0 + V B ) 2 3 OS = β ( 4π) V 3 0[( 1 + α N V b 0 ) ] (S.4) (S.5) (S.6) We could not reproduce our NMR results using a two-state model derived by Weiss and co workers. 4 They studied the exchange of octylphosphonate ligands on the surface of CdSe QDs with methylthiophenolate. In those experiments, they were able to correlate the shift of the 1 st - exiton transition energy with the addition of new ligands. They found that the shift of the 1 st - exciton energy is sub-linear with increasing additions of methylthiophenolate, similar to the square-root dependence that we observe in α/α 0. They attributed this dependence to a two-state model where the electronic interaction of ligands with the QDs depends upon the binding geometry. The first ligands bind to sites with greater electronic interaction causing a larger shift while the last ligands bind to sites with smaller electronic interaction causing a smaller electronic shift (per additional ligand). We tested whether this hypothesis could also explain our squareroot dependence, but it could not. Furthermore, for our system we do not have any evidence that there are two distinct binding geometries, and therefore, discount the two-state model for the PbS QDs studied here. 4

5 Section S2: Derivation of the 2-d lattice Ising model with conservation of ligand addition The free energy G A of a ligand of type A with NN A nearest neighbors of type A, nearest neighbor interactions J AA for A-A interaction and J AB for A-B interactions is defined as: G A = NN B J AB + NN A J AA (S.7) Similarly, the free energy G B of a ligand of type B with NN B nearest neighbors of type B is defined as : G B = ΔG exc + θδg MF + NN A J AB + NN B J BB (S.8) where ΔG exc is the difference in binding free energy between ligand B and A, θ is the fraction of all initial binding sites occupied by ligands of type B, and is a mean-field free energy ΔG MF difference between ligands of type B and type A when bound to the surface. The energy ΔG AB associated with replacing a ligand of type A with a ligand of type B is ΔG AB = ΔG exc + θδg MF + 2NN A ΔJ 2NN B ΔJ (S.9) where: NN A + NN B = 4 (S.10) Hence: The energy of S.9. ΔG BA ΔJ J AA = J BB = J AB G A = (2NN B 4)ΔJ (S.11) G B = ΔG exc + θδg MF + (4 2NN B )ΔJ ΔG AB = ΔG exc + θδg MF + 4ΔJ(2 NN B ) for replacing a ligand of type B with a ligand of type A is simply the negative We used the model free energy defined above to carry out Monte Carlo simulations. The simulation progresses by randomly selecting a grid point (each grid point is associated to a ligand site) and computing the probability P of changing the grid point occupancy from ligand A to ligand B. To compute P we use a Boltzmann factor Bf and we define the fraction of ligands in solution f(θ, N add ) with the identity of the new, incoming ligand ( f B when the incoming ligand has identity B, and f A when the incoming ligand has identity A). The number of species B added to the simulation is called N add, and the number of species A that were on the nanocrystal surface at the beginning of the simulations is called N sites ; the fraction of sites exchanged from A to B is called θ. Hence we have: B f = { exp ( ΔG tot) if ΔG tot > 0 1 if ΔG tot 0} (S.12) f A (θ, N add ) = θ N sites N add + N sites (S.13) 5

6 f B (θ, N add ) = N add θ N sites N add + N sites P = B f(θ, N add ) (S.14) (S.15) During the simulations, the probability P is compared with a random number between zero and one. If P exceeds the random number, the site undergoes a ligand exchange; otherwise, there is no change of the site occupancy. This random sampling is repeated a large number of times (between 10 6 and 10 9 ) to collect sufficient statistics on the extent of exchanges between ligands. The simulation is run for a wide range of different values to create isotherms of coverage N add vs. ligand addition. Derivation of the 2-d lattice Ising model isomorphism Based on physical reasons, the nearest neighbor coupling energies between oleates with oleates, cinnamates with oleates, and cinnamates with cinnamates are expected to have different values. When constructing an Ising model, these different values can be incorporated by considering two different coupling energies (two ΔJ values) instead of just one. The construction of a model with two ΔJ values and then its mathematical simplification to a single ΔJ model is presented below. The free energy G A of a ligand of type A with NN A nearest neighbors of type A, nearest neighbor interactions J AA for A-A interaction and J AB for A-B interactions is given by equation S.7 and.the free energy G B of a ligand of type B with NN B nearest neighbors of type B is: G B = ΔG 0 + θδg MF + N A J AB + N B J BB S.16 Where here ΔG 0 is the difference in binding free energy to the substrate between ligand B and A, θ is the fraction of binding sites occupied by ligands of type B, and ΔG MF is a mean-field free energy difference between ligands of type B and type A when bound to the surface. Then the energy ΔGAB associated with replacing a ligand of type A with a ligand of type B is Using the definitions where k is a constant,we have: ΔG AB = G B G A S.17 ΔG AB = N A J AB + N B J BB N B J AB N A J AA + θδg MF + ΔG 0 S.18 N A + N B = 4 J BB J AB = ΔJ k J AA J AB = ΔJ + k ΔG AB = N B (J BB J AB ) + N A (J AB J AA ) + θδg MF + ΔG 0 ΔG AB = N B (ΔJ k) N A (ΔJ + k) + θδg MF + ΔG 0 ΔG AB = N B (ΔJ k) (4 N B )(ΔJ + k) + θδg MF + ΔG 0 ΔG AB = (2N B 4)ΔJ + 4k + θδg MF + ΔG 0 S.20 S.21 S.22 S.23 S.19 6

25 Coupling energy and order-disorder phase transition. In the standard Ising model a phase transition occurs at a critical temperature of T c = 2.

7 Since both k and ΔG exc are both constants, we can define: ΔGexc = ΔG0 + 4k S.24 We can also define that J BB = J AA = J = J AB and then we obtain the expression used in the main text: ΔG AB = ΔG exc + θδg MF + 4J(2 N B ) S.25 Coupling energy and order-disorder phase transition. In the standard Ising model a phase transition occurs at a critical temperature of T c = J kb, which corresponds to a coupling energy of J = 0.441k B T. To verify that our model also exhibits the same phase transition we display below the results of a simulation where J is varied from -1 k B T to -1.0 k B T. The simulation is stopped when the ligand occupation is 50% and a correlation function is calculated.. Figure S3. Configurations at 50% ligand exchange(top) and corresponding correlation functions (bottom) for coupling energies varying from -1 to 1 k B T. When the coupling energy is less than k B T a phase transition occurs (top row) corresponding to phase segregation of the ligands. When the coupling energy is greater than 0.44 k B T the anti-correlated phase transition occurs (bottom row). 7

8 Hammet coefficient vs. computed dipole moments. Figure S4. Relationship between calculated R-CAH ligand dipole and corresponding tabulated Hammett Constant. The solid points represent ligands with functional groups that have tabulated Hammett Constants, and the dashed line is a fit to this data. The open points represent ligands with extrapolated Hammett Constants based off of calculated dipole moments. Section S3: Derivation of the relationship between dipole moment and the total free energy of exchange. The interaction energy between two dipoles at the surface of a semiconductor is given in Ref. 5 5 Eq. 28 for dipoles aligned parallel to one another as, W vert e (γ) = 2(μsin (γ))2 ε m ε o ε ml d 3 (ε ml + ε m ) (S.26) where γ is the angle the dipole makes with the substrate, ε m is the dielectric constant of the substrate (PbS in this case), ε ml is the dielectric constant of the dipolar monolayer, d is the distance between dipoles. Eq. S.26 is repulsive as the two dipoles are aligned with one another. As the dipoles tilt with respect to the substrate the effect dipole is smaller (when γ = 0, W vert e = 0). In this case the dipole interaction energy for dipoles aligned parallel to the substrate is given by Eq. 35 of Ref. 5 5 μ 2 (S.27) e (γ) = d 3 [cos(α γ) + 3cos(α + γ)] ε 0 (ε ml + ε m ) W planar here α is the angle between the two dipoles. e can be either attractive if the dipoles are aligned head-to-tail ( α = 0) or repulsive if the dipoles are aligned head-to-head ( α = 180 ). We use α = 0 for these calculations which implies that the dipoles tilt and stack together (see Fig. in W planar 8

9 main text). Figure S4 shows how both S.26 and S.27 vary as a function of angle. For angle less than about 45 the total interaction energy is attractive when the ligands align head-to-tail (that is, they tilt in the same direction). Figure. S5. Plot of Eq. S.26 and S.27 as a function of angle from the subtrate. In order to use eq S.26 and S.27 we also need to calculate the dielectric constant of the dipole monolayer. The dielectric constant of the dipolar monolayer is calculated following Ref ε ml = 1 + C d 3α ( 2ε m ε m + 1) (S.28) α is the polarizability of the ligands, and C is a constant describing the geometry of the lattice. We use the assumption that the polarizability is proportional to the dipole square: α = Yμ 2 (S.29) where Y is a constant that can be extracted by fitting the dipole moment vs the polarizabilities obtained from DFT calculations: 9

10 Figure S6: The quadratic behavior of the polarizability as a function of the dipole moment for the series of cinnamic acids used in this study. The red filled squares are the isotropic polarizability (1/3 of the trace of the polarizability tensor) and the hollow black squares are the polarizability tensor projected onto the ligand s long axis. The results from this fit are Y = 1.35 for the isotropic polarizability and Y = 2.98 for the projected polarizability, where a dipole offset has been used to account for a systematic error in the projected dipole calculation. Calculation of the angle formed by the ligand and the direction normal to the QD surface Furthermore, we need to know the angle at which the dipoles sit relative to the surface of the NCs (see Figure 3 of the main text). The change in potential across a two-dimensional layer of aligned dipolar molecules can be calculated as, 7 μ cos(γ) ρ φ = ε (S.30) where ρ is the ligand density and ε is the dielectric constant of the monolayer. Following ref. 5, the dielectric constant of a monolayer is estimated using Eq. S28. We show in Table S1 the results of estimating the tilt angle based upon the shift in the ionization energy measured in Ref. 8 Table S1. Results of Eq. S28 and Eq. 30 for the dipolar ligands used in this study. Ligand μ ε φ θ 4-CN Not measured 69 4-CN CF ,5-F H

11 2,6-F OCH N(CH 3 ) For the best agreement between the measured free-energy of exchange and the dipole-dipole interaction energy the angle of the dipole to the substrate needs to be slightly modified. The values used in the calculation are shown in Fig. S5 and S6. Figure S7. Dashed-line is the dielectric constant of the dipolar monolayer used in the calculation of the dipole-dipole interaction energy. The red-points are the values calculated from the dipole moment. 11

12 Figure S8. Angle of dipolar molecule from the NC surface. Blue squares are the angle calculated from the measured shift in ionization potential. Dashed-line is the angle used in the calculation of the interaction energy in Fig. 3a. Section S4: NMR of Janus-ligand shell QDs. 12

Figure S9. (a) 1 H NMR spectra of 20, 26, 44, 52, 79, and 100% PbS/CF 3 -CA - in the oleate vinyl (δ = 5.3-5.4 ppm) region, which shows some unbound oleate by the sharp up-field resonance.

4 ppm) at the same percentages as (a) fitted with multiple Gaussian peaks. The 100% CF 3 -CA- sample (pink trace) shows a significant amount of unbound cinnamate with a resonance at 64.

13 Figure S9. (a) 1 H NMR spectra of 20, 26, 44, 52, 79, and 100% PbS/CF 3 -CA - in the oleate vinyl (δ = ppm) region, which shows some unbound oleate by the sharp up-field resonance. The broad peak was integrated to get the number of bound oleates. The 19 F{ 1 H} spectra (b) for the PbS/CF 3 -CA - (δ = ppm) at the same percentages as (a) fitted with multiple Gaussian peaks. The 100% CF 3 -CA- sample (pink trace) shows a significant amount of unbound cinnamate with a resonance at 64.4 ppm, as denoted by the vertical line, and samples 20-44% show small amounts of what is likely to be the unbound ligand, whereas 52 and 79% traces do not. Spectra of 100% CF 3 -CA - (c) from a purified sample (no residual CF 3 - CAH), and a sample with the sharp peak from the presence of residual unbound ligand. Since the two peaks have the same chemical shift, we can conclude that the presence of unbound cinnamate does not signifantly influence the chemical shift of the bound peak. To further show this, the shifts of the broad peaks in (b) are plotted versus the CF 3 -CA - coverage (d) and we find similar dependence as that shown in Fig. 4a. 13

Figure S10. The 19 F{ 1 H} spectra of the at 21, 41, 46, 62, and 65% PbS/2,6-F-CA - (δ =-109.85- -109.7 ppm).

Raw data for Fig. 4b. No evidence of free-ligand is detected. Figure S10.

14 Figure S10. The 19 F{ 1 H} spectra of the at 21, 41, 46, 62, and 65% PbS/2,6-F-CA - (δ = ppm). The peaks were fit and integrated to determine the number of bound 2,6-F-CA -. The peaks fit well to a single Lorentzian peak, indicating the samples were fully purified. Raw data for Fig. 4b. No evidence of free-ligand is detected. Figure S10. NOESY spectrum of the PbS/(69%) CF 3 -CA - with resonances from the oleate methyl and ethyl groups (δ = ppm), oleate vinyl (δ = 5.4 ppm), cinnamate aryl group (δ = ppm), and standard peaks (ferrocence δ = 4.15 ppm) and solvent (chloroform-d δ = 7.2 ppm). The coupling energy of the CF 3 -CA - is -0.46k B T. 14

15 References 1 Kroupa, D. M.; Voros, M.; Brawand, N. P.; Bronstein, N.; Mcnichols, B. W.; Castenada, C.; Nozik, A. J.; Sellinger, A.; Galli, G.; Beard, M. C., Optical Absorbance Enhancement in PbS Qd/Cinnamate Ligand Complexes. J. Phys. Chem. Lett. 2018, 9, Kroupa, D. M.; Anderson, N. C.; Castaneda, C. V.; Nozik, A. J.; Beard, M. C., In Situ Spectroscopic Characterization of a Solution-Phase X-Type Ligand Exchange at Colloidal Lead Sulphide Quantum Dot Surfaces. Chem. Commun. 2016, 52, Moreels, I.; Lambert, K.; Smeets, D.; De Muynck, D.; Nollet, T.; Martins, J.C.; Vanhaecke, F.; Vantomme, A.; Delerue, C.; Allan, G.; Hens, Z. Size-Dependent Optical Properties of Colloidal PbS Quantum Dots. ACS Nano 2009, 3, Amin, V. A.; Aruda, K.O.; Lau, B.; Rasmussen, A.M.; Edme, K., Weiss, E.A. Dependence of the Band Gap of CdSe Quantum Dots on the Surface Coverage and Binding Mode of an Exciton-Delocalizing Ligand, Methylthiophenolate. J. Phys. Chem. C 119, Gabovich, A. M.; Voitenko, A. I., Electrostatic Charge-Charge and Dipole-Dipole Interactions Near the Surface of a Medium with Screening Non-Locality (Review Article). Low Temp. Phys. 2016, 42, Iwamoto, M., Mizutani, Y. & Sugimura, A. Calculation of the Dielectric Constant of Monolayer Films on a Material Surface. Phys. Rev. B 1996, 54, Cahen, D., Naaman, R. & Vager, Z. The Cooperative Molecular Field Effect. Adv. Funct. Mater. 2005, 15, Kroupa, D. M.; Vörös, M.; Brawand, N. P.; McNichols, B. W.; Miller, E. M.; Gu, J.; Nozik, A. J.; Sellinger, A.; Galli, G.; Beard, M. C., Tuning Colloidal Quantum Dot Band Edge Positions through Solution-Phase Surface Chemistry Modification. Nat. Commun. 2017, 8,

Revisited Wurtzite CdSe Synthesis : a Gateway for the Versatile Flash Synthesis of Multi-Shell Quantum Dots and Rods

Supporting Information for Revisited Wurtzite CdSe Synthesis : a Gateway for the Versatile Flash Synthesis of Multi-Shell Quantum Dots and Rods Emile Drijvers, 1,3 Jonathan De Roo, 2 Pieter Geiregat, 1,3