Designing Janus Ligand Shells on PbS Quantum Dots using Ligand

Mar 11, 2019 - XXXX American Chemical Society. A ... In situ NMR is unfortunately limited to ligand exchange ... ment) show much higher cooperativity,...
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Designing Janus Ligand Shells on PbS Quantum Dots using Ligand-Ligand Cooperativity Noah D Bronstein, Marissa Martinez, Daniel M. Kroupa, Márton Vörös, Haipeng Lu, Nicholas P. Brawand, Arthur J Nozik, Alan Sellinger, Giulia Galli, and Matthew C. Beard ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.9b00191 • Publication Date (Web): 11 Mar 2019 Downloaded from http://pubs.acs.org on March 12, 2019

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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, Nicholas P. Brawand,4 Arthur J. Nozik,1,2 Alan Sellinger,1,6 Giulia Galli,3,4,5 and Matthew C. Beard1* 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, University of Chicago, Chicago, Illinois 60637, United States 6. Department of Chemistry and Materials Science Program, Colorado School of Mines, Golden, Colorado 80401, United States. Corresponding Authors ([email protected]) #

These authors contributed equally.

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Abstract We present a combined experimental and theoretical study of ligand-ligand cooperativity during X-type carboxylate-to-carboxylate ligand exchange reactions on PbS quantum dot surfaces. We find that the ligand dipole moment (varied through changing the substituents on the benzene ring of cinnamic acid derivatives) impacts the ligand-exchange isotherms; in 1 ACS Paragon Plus Environment

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particular, ligands with large electron withdrawing character result in a sharper transition from an oleate-dominated ligand shell to a cinnamate-dominated ligand shell. We developed a 2dimensional lattice model to simulate the ligand-exchange isotherms that accounts for the difference in ligand binding energy as well as ligand-ligand cooperativity. Our model shows that ligands with larger ligand-ligand coupling energy exhibit sharper isotherms indicating an orderdisorder phase transition. Finally, we developed an anisotropic Janus-ligand shell by taking advantage of the ligand-ligand cooperative ligand exchanges. We monitored the Janus-ligand shell using 19F NMR showing that when the ligand-ligand coupling energy falls within the order region of the phase-diagram, Janus-ligand shells can be constructed. Keywords: PbS Quantum Dots, Ligand-QD interactions, ligand coupling, QD optical properties, QD surface science

Quantum dots1 and other colloidal nanocrystals have seen a tremendous amount of research over the last three decades.2 A large body of work has focused on synthesis with shape, size, and composition control of the inorganic core.3 Subsequent work 4has examined the surface chemistry, and shown that the surface chemistry is itself responsible for much of the very same synthetic control. Often, important features of the nanocrystal shape can be traced to an impurity in the solvent, precursor, or preparation,5 which can result in various molecules binding preferentially to particular surface facets during NC synthesis. Beyond the preparation of nanocrystals, control of the ligand shell is a prerequisite for any application: the surface of the quantum dot is key to QD-QD electronic coupling to make conductive films;6-8 and ligand-shell vacancies can be the source of electronic defects that degrade performance.9 Despite their importance, ligand binding and exchange isotherms on nanocrystal surfaces remain underexplored. Most recent work on the QD surface chemistry has focused on understanding the binding head-group chemistry through Green’s definition of X-, L-, and Z-type interaction,10,11 while, the interaction of ligands with neighboring ligands has seldom been reported. Widmer-Cooper and co-workers12 unveiled some of the richness of the interactions of long aliphatic chains, showing coverage- and size-dependent phase transitions, differences in the binding site vs ligand tail symmetry, and coverage- and size-dependent inter-particle interaction potentials. Other work by Jana and coworkers13 showed the importance of ligand coverage in creating chiral distortions of nanoplates, which can propagate through micron-long assemblies of those plates. The most thorough characterization of ligand exchange isotherms was done by Zeger Hens and co-workers using Nuclear Magnetic Resonance (NMR), showing that ligand-ligand interactions are indeed important for the shape of the isotherm, as a Fowler isotherm reproduced the data much better than a Langmuir isotherm.14 In-stiu NMR is unfortunately limited to ligand exchange reactions in 2 ACS Paragon Plus Environment

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which both the initially bound and incoming ligand have distinct NMR peaks, and where the dynamics of the ligand exchange equilibrium are slow on the NMR time scale. In this work, we examine in-situ ligand exchange isotherms via simple linear absorption spectroscopy. Giansante,15 and Kroupa16-18 recently reported that some classes of ligands significantly enhance the absorption intensity of the QD/ligand complex upon exchange. Similarly, Weiss and co-workers report a shift of the absorption onset upon ligand exchange.19-21 Kroupa introduced a library of functionalized cinnamic acids,18 which undergo simple 1:1 X-type ligand exchange with oleic acid16 and exhibit absorption enhancement that depends linearly on the cinnamate bandgap.17 Kroupa also demonstrated a simple analytical dependence of the extent of exchange with the absorption enhancement using in-situ NMR spectroscopy.16 This indicates that the absorption enhancement acts as a simple feedback on the extent of exchange, allowing for the measurement of ligand exchange isotherms for ligands without easily distinguishable NMR peaks. Here, we take advantage of this feedback to study the exchange of the oleate surface ligands with eight different functionalized cinnamic acids (R-CAHs, Scheme 1) that are classified by their functional group on the aromatic ring.18 We developed a custom 2-dimensional lattice model that reproduces the salient features of the adsorption isotherms. The energy of exchange, ∆𝐺𝑒𝑥𝑐, as well as a nearest-neighbor coupling energy between ligands, Δ𝐽, are outputs of the model. We find that the absolute magnitude of dipole moment of the cinnamic acid has a strong influence on the exchange energy, up to a few kBT for the largest dipoles used in this study. We also observe an interesting correlation between ligand dipole moment and the nearest neighbor coupling, Δ𝐽: ligands with large electron withdrawing character (negative dipole-moment) show much higher cooperativity , Δ𝐽 = -0.65 kBT, than those with large electron donating character (positive dipole-moment), Δ𝐽 = -0.15 kBT. We use these observations to design phase-segregated (e.g. patchy or Janus) ligand shells, which break the symmetry of an otherwise symmetrical nanocrystal. Patchy particles have received considerable attention in the literature, with the main focus on larger structures,22 or metallic nanoparticles,23,24 with one-report showing the impact on the optical properities of CdS QDs when the exchanging ligands group together.25 There are numerous potential applications where controlling the electrostatics, morphology and symmetry of the ligand shell is expected to have considerable influence over their emergent properties. Results We synthesized 3.2 nm diameter PbS QDs with 1st excition transition energy of 1.3 eV.26 They consist of a stoichiometric PbS core with Pb-oleate ligands. The number of OA- ligands initially bound to each QD is measured to be 100 ± 5 by quantitative 1H NMR, corresponding to 3.1 ligands/nm2, in agreement with literature values.4,18,19 This solution-phase ligand exchange procedure replaces the native oleate ligands with cinnamic acids to form cinnamate passivated 3 ACS Paragon Plus Environment

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PbS QDs through a 1:1 X-type ligand exchange.11 Incoming free cinnamic acid transfers a proton to a surface bound oleate to form free oleic acid and surface bound cinnamate. Adding excess cinnamic acid drives the exchange towards completion.16

Scheme 1: The functionalized cinnamic acids used in this study, along with their dipoles normal to the QD surface computed by DFT. The molecules are either electron donating (negative dipole) or electron withdrawing (positive dipole).

For each of the functionalized cinnamic acids (Scheme 1), we performed quantitative spectrophotometric titrations (Fig. S1a,b ). We relate the absorption enhancement to square root of number of bound ligands (see Supporting Information for details).16 Thus, to construct the 2 adsorption isotherms (bound-ligands, R-CA-, vs added free-ligands) we plot (∆𝛼 𝛼0) vs. the number of free-ligand equivalents, where ∆𝛼 is (𝛼 ― 𝛼0), 𝛼0 is the integration of the assynthesized OA-/QD absorbance spectrum, and 𝛼 is the integration of the in-situ QD spectrum (Fig. 1, a-h, filled circles for each of the cinnamate ligands), details and raw data are provided in the supporting information.

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Figure 1. Adsorption isotherms (bound CA-ligands vs. free-ligands) of the ligand exchange reactions constructed from the quantitative spectrophotometric titrations. The number of bound ligands is 2 proportional to the (∆𝛼 𝛼) , see SI. Data are represented by filled circles and the solid lines are the bestfit lines obtained from a non-linear least squares fitting of a spin-lattice simulation. The best-fit parameters are displayed in Fig. 4. The dashed line is the number of binding sites available. The x-axis is the number of ligand equivalents added during the experiment.

Model of Ligand Exchanges In our previous study we found that a standard Langmuir isotherm for non-interacting ligands could not reproduce the adsorption isotherms,16, 18 similar to the findings of Hens and coworkers.14 In fact, the change in free energy upon ligand exchange, ∆𝐺𝜃𝑒𝑥𝑐, depends upon the extent of exchange, 𝜃. Such an observation is indicative of associative ligand/ligand interactions that can promote ligand exchange.27 There are many empirical modifications to the noninteracting Langmuir isotherm model, however none of them gives a good physical description of the surface dynamics. The coverage of surfaces by incoming gas molecules/atoms have been 5 ACS Paragon Plus Environment

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extensively studied, and various 2-dimensional (2D) statistical models have been developed to describe the dynamics of ligands, with the best-known being a lattice model isomorphic with the Ising spin lattice model.28 We adopted a simple 2D lattice model27 and use that to perform a Monte-Carlo simulation of the ligand exchange reactions at NC surfaces in solution. The simulations employ a square n x n binary lattice, where 𝑛 ∗ 𝑛 = 𝑁𝑠𝑖𝑡𝑒𝑠, with periodic boundary conditions to simulate the spherical NC surfaces. Our simulations differ from traditional 2D lattice simulations in one key way: we consider a finite number of added ligands (𝑁𝑎𝑑𝑑), originally bound ligands (𝜃 ∗ 𝑁𝑠𝑖𝑡𝑒𝑠), and binding sites (𝑁𝑠𝑖𝑡𝑒𝑠), where 𝜃 is the fraction of all binding sites occupied by the original ligands. For each binding site occupied by the orginal ligand (ligand A), we define a probability (𝑃𝐴𝐵) of exchanging ligand A for ligand B. While for each binding site that becomes occupied with the new ligand (ligand B) we define the probability (𝑃𝐵𝐴) for the reverse reaction (i.e., the freed-up oleic acid can replace the newly bound cinnamates). The probabilities are a product of a Boltzman factor, 𝐵𝑓, and a factor that accounts for the fraction of ligands in solution with the identity of a new or incoming ligand (𝑓𝐵 when the incoming ligand has identity 𝐵, and 𝑓𝐴 when the incoming ligand has identity 𝐴). Thus, 𝜃 ∗ 𝑁𝑠𝑖𝑡𝑒𝑠

(1)

𝑓𝐴(𝜃, 𝑁𝑎𝑑𝑑) = 𝑁𝑎𝑑𝑑 + 𝑁𝑠𝑖𝑡𝑒𝑠, 𝑓𝐵(𝜃, 𝑁𝑎𝑑𝑑) =

𝑁𝑎𝑑𝑑 ― 𝜃 ∗ 𝑁𝑠𝑖𝑡𝑒𝑠 𝑁𝑎𝑑𝑑 + 𝑁𝑠𝑖𝑡𝑒𝑠

(2)

,

The free energy of ligand exchange, 𝛥𝐺𝑒𝑥𝑐 is the difference in binding free energy between ligand B and A; we define 𝑁𝑁𝐵 as the number of nearest ligand B neighbors and 𝛥𝐺𝑀𝐹 is a meanfield free energy difference between ligands of type B and type A when bound to the surface. The nearest neighbor ligand-ligand coupling energy is ∆𝐽 , and the total number of nearest neighbors is 4 (i.e., we use a square lattice) thus 𝑁𝑁𝐴 +𝑁𝑁𝐵 = 4. Then the exchange energy 𝛥 𝐺𝐴𝐵 associated with replacing a ligand of type A with a ligand of type B is (3) 𝛥𝐺𝐴𝐵 = 𝛥𝐺𝑒𝑥𝑐 + 𝜃𝛥𝐺𝑀𝐹 + 4Δ𝐽(2 ― 𝑁𝑁𝐵) Similarly, the energy 𝛥𝐺𝐵𝐴 of replacing a ligand of type B with a ligand of type A is simply the negative of expression (3). The Boltzman factor is thus: 𝐵𝐴𝐵 𝑓 =

{

}

exp ( ―𝛥𝐺𝐴𝐵 𝑘𝐵𝑇) 𝑖𝑓 𝛥𝐺𝐴𝐵 > 0 , 1 𝑖𝑓 𝛥𝐺𝐴𝐵 ≤ 0

(4)

and the probability of exchange is 𝑃𝐴𝐵 = 𝐵𝐴𝐵 𝑓 ∗ 𝑓𝐴(𝜃,𝑁𝑎𝑑𝑑), 𝑃𝐵𝐴 is defined similarly, for more details, see the supporting information section S2. We use 𝑃𝐴𝐵 and 𝑃𝐵𝐴 defined above to carry out Monte Carlo simulations. At the beginning of the simulation all binding sites are initially occupied by ligand A.The simulation progresses by randomly selecting a grid point (each grid 6 ACS Paragon Plus Environment

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point is associated to a ligand site) and computing the probability 𝑃𝐴𝐵 of changing the grid point occupancy from ligand A to ligand B or when the site is occupied by B and there is a probability of exchanging B for A, 𝑃𝐵𝐴. If 𝑃𝐴𝐵 or 𝑃𝐵𝐴 is larger than a random number between 0 and 1 the exchange occurs otherwise it doesn’t. This random sampling is repeated a large number of times (between 106 and 109) to collect sufficient statistics on the extent of exchanges between ligands. The simulation is run for a wide range of different 𝑁𝑎𝑑𝑑 values to create isotherms of coverage vs. ligand addition. To model our measured adsorption isotherms we use non-linear least squares fitting (solid-traces in Fig. 1 (a-h)) to find the computed isotherm with best-fit parameters 𝛥𝐺𝑒𝑥𝑒, 𝛥𝐺𝑀𝐹 and 𝛥𝐽. We find that our model reproduces the trends in the data fairly well, however, at the low and high exchanges the model deviates from the data. When setting the mean-field term 𝛥𝐺𝑀𝐹 to zero, the resulting best-fit values changed in a negligible way.

Figure 2. The isotherm for 4(CN)2-CAH exchanging with oleic acid. The red circles are the measured optical absorption values, scaled with the square-root dependence, and the solid red line is the simulated isotherm. The four square-lattice images show representative surface coverage patterns at equilibrium for four different ligand addition equivalents (Equiv.). The clustering of ligands with their own type clearly indicates strong nearest neighbor interactions.

In figure 2 we show snapshots of a representative Monte Carlo simulation of the ligand exchange titrations when the ligand-ligand coupling energy is less than -0.44 kBT (vida infra). At low additional equivalents (left-box) the ligand shell is primarily oleate (ligand A, blue-boxes). When the ligand concentration reaches 1 equivalent, the ligand exchange reaction starts and the cinnamates (ligand B, yellow-boxes) tend to group together (they form patches) because of the

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ligand-ligand cooperativity. Around 2 additional equivalents the ligand shell is roughly 50/50 and the ligands are completely segregated. ∆𝑮𝒆𝒙𝒄 and 𝜟𝑱 vs. Ligand Dipole The resulting model outputs (fitted parameters), ∆𝐺𝑒𝑥𝑐 and 𝛥𝐽, are plotted against the liganddipole computed using DFT calculations in Fig 3a-b. The computed dipole moments are linearly related to the tabulated Hammet parameters29 (see Fig. S4). It is important to note that ∆𝐺𝑒𝑥𝑐 and 𝛥𝐽 do not represent the binding free energy and nearest neighbor interactions separately. Instead, 𝛥𝐽 contains only the change in nearest neighbor interaction that does not contribute to the total free energy of exchange. Any component of the nearest neighbor coupling that does contribute to total binding free energy is included in 𝛥𝐺𝑒𝑥𝑐. This can be understood as follows: the total energy for exchanging all of ligand A with all ligand B on a nanocrystal surface is a sum of all individual ligand exchanges, i.e., ∆𝐺𝑡𝑜𝑡 = ∑∆𝐺𝐴𝐵. Since the lattice model used here is isomorphic with the Ising Model,28 and the site-to-site coupling energy in the Ising model is symmetric, thus the coupling term is equal for A-A and B-B interactions. In the sum ∑∆𝐺𝐴𝐵 the coupling terms cancel since the coupling energy is the same for A-A and B-B interactions (see SI). However, for intermediate exchanges this is not case since it takes a coupling energy ∆𝐽 to break or form A-A interactions. Thus, this term represents the differences in nearest neighbor coupling free energy between the oleate ligands and the cinnamate ligands that drive the cooperative ligand exchange. Larger negative values cause the ligand exchange isotherm to exhibit a sharper transition from all-oleate coverage at low ligand addition to all-cinnamate coverage at high ligand addition. This can be clearly seen for the 4CN2 and 4CN species (Fig 1a-b) compared to the 4OCH3 and N(CH3)2 (Fig 1g-h), and in the clustering evident in the surface coverage graphs for the 4(CN)2 exchange depicted in Fig 2. With this in mind, we can now interpret the behavior of 𝛥𝐺𝑒𝑥𝑐 as a function of the ligand-dipole (Fig 3a). For values of the dipole moment close to zero, the 𝛥𝐺𝑒𝑥𝑐 is maximum at ~ +2-3 kBT. However, as the cinnamic acid dipole increases, the polarization of the QD surface and ligand shell acts to stabilize the molecular dipole, working against the aciditydriven binding enthalpy difference. As the absolute magnitude of the dipole moment increases, 𝛥 𝐺𝑒𝑥𝑐 is reduced to ~ 0.7-0.8 kBT. To account for this reduction, we consider three contributions: a dipole-dipole interaction energy for dipoles oriented perpendicular to the NC surface, 𝑊𝑣𝑒𝑟𝑡 𝑒 , a dipole-diple interaction energy for 𝑝𝑙𝑎𝑛𝑎𝑟 dipoles oriented parallel to the NC surface, 𝑊𝑒 , and a term Δ𝐺0 that represents the difference in binding free energy based on the different binding groups (cinnamate vs. oleate); thus, ∆𝐺𝑒𝑥𝑐 = 𝑊𝑣𝑒𝑟𝑡 + 𝑊𝑝𝑙𝑎𝑛𝑎𝑟 + Δ𝐺0.The variations in pKa within the cinnamic acid derivatives 𝑒 𝑒 (pKa ~ 4)30 is much less than the difference in pKa between cinnamic acid and oleic acid (pKa ~10)31, i.e., oleic acid is a much weaker acid than are the cinnamic acids. Thus, oleic acid binds lead cations much more strongly than cinnamic acid does, overwhelming any energetic difference 8 ACS Paragon Plus Environment

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based on proton transfer and causing oleate to bind ~2.5 kBT more favorably than the cinnamic acid with near-zero dipole (35F-CAH). Furthermore, if the variations in acidity across our ligand library were to dominate the binding energy, we would expect Δ𝐺𝑒𝑥𝑒 to vary linearly with dipole moment (or Hammet parameter) rather than showing the observed dependence For these reasons we expect Δ𝐺0 not to vary across the family of cinnamic ligands. Both electrostatic terms, and 𝑊𝑝𝑙𝑎𝑛𝑎𝑟 , are proportional to the magnitude of the dipole moment squared (𝜇2). 𝑊𝑣𝑒𝑟𝑡 𝑒 𝑒 sin(𝛾) 𝑑3 where d is the distance between However, 𝑊𝑣𝑒𝑟𝑡 𝑒 is purley repulsive and scales as ligands, and 𝛾 is the angle formed by the ligand with the substrate (when 𝛾=0 the ligands are laying flat on the surface). 𝑊𝑝𝑙𝑎𝑛𝑎𝑟 can either be repulsive or attractive depending on whether 𝑒 the ligands tilt together forming a head-to-tail alignment or tilt into each other forming a headto-head alignment. We assume here that the ligands tilt together (Fig. 3c) and thus the | > |𝑊𝑣𝑒𝑟𝑡 interaction parallel to surface is attractive (Fig. S5). When 𝛾 is less than 45°,| 𝑊𝑝𝑙𝑎𝑛𝑎𝑟 𝑒 𝑒 |, and the total interaction energy is attractive. We can estimate the angle the dipolar ligands form with the surface normal by recalling from our previous work that the dipolar ligands cause the bandedges of the QD films to shift by up to 2 eV.18 The shift of the bandeges (∆𝜙) is related to the magnitude of the ligand-dipole,  and the ligand tilt angle : ∆𝜙 = 𝜇 cos(90 ― 𝛾) (𝜀 𝑑2).32 The dielectric constant of the ligand monolayer, 𝜀, is calculated accounting for cooperative effects (see SI).33 We find that the ligands should be tilted by ~70-40 degrees from the direction normal to the surface (see SI for estimation) so 𝛾 varies between 20-50 degrees. Using these angles as starting values we can estimate both the attractive and repulsive terms,34 (see SI for details) and we find a general agreement between the calculation (Fig. 3a, dashed-line) and our data (Fig 3a, triangles) with slightly adjusted tilt angles (Fig. S6). We also find a correlation between the nearest neighbor coupling (𝛥𝐽) and the ligand dipole moment (Fig. 4b). There is a consistent trend in 𝛥𝐽 vs the ligand dipole, with the most electron withdrawing species having the largest negative 𝛥𝐽. As the ligand dipole changes from negative to positive, the 𝛥𝐽 reduces in magnitude, approaching zero. We have not determined a clear physical reason responsible for the observed trend of 𝛥𝐽 with the dipole moment. While recent literature35 argues that pi-stacking interactions are really dominated by dipole interactions, there is no obvious reason why the direction of the dipole should change the magnitude of the coupling between ligands. As the ligand is titled (Fig.3, bottom) next nearest neighbor interactions between the substituent group and the benzene ring may produce the observed trend.

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Figure 3. Parameters of the 2D lattice simulation for ligand exchange. (a) The change in free energy for the ligand/QD binding versus the cinnamate dipole moment (triangles) and dashed-line is a calculation of the electrostatic dipole-dipole interaction energy (described in text), (b) the ligand/ligand non-binding interaction energy versus the dipole moment. (bottom) A cartoon depiction of the dipoles and tilt angle (measured from the NC surface) considered in the interaction energy between dipoles at the surface of the NCs (see text).

Constructing a Janus Ligand Shell The negative coupling term, 𝛥𝐽, is indicative of how likely patches form during the ligand exchanges. In the Ising model an order-disorder phase transition occurs when the coupling energy is less than -0.44 kBT.28 For our modified model the phase transition occurs at the same coupling energy (Fig. S3). The implications are that for ligands whose coupling energy