Dependence of the Band Gap of CdSe Quantum Dots on the Surface

Jul 24, 2015 - Michael S. AzzaroAmro DodinDiana Y. ZhangAdam P. WillardSean T. .... Bryan Lau , Alexander B. Nepomnyashchii , and Emily A. Weiss...
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Dependence of the Band Gap of CdSe Quantum Dots on the Surface Coverage and Binding Mode of an Exciton-Delocalizing Ligand, Methylthiophenolate Victor A. Amin, Kenneth O. Aruda, Bryan Lau, Andrew M. Rasmussen, Kedy Edme, and Emily A. Weiss* Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208-3113, United States S Supporting Information *

ABSTRACT: Displacement of native octylphosphonate (OPA) ligands for methylthiophenolate (CH3-TP) on the surfaces of CdSe quantum dots (QDs) causes a moderate (up to 50 meV) decrease in the band gap (Eg) of the QD. Plots of the corresponding increase in apparent excitonic radius, ΔR, of the QDs versus the surface coverage of CH3-TP, measured by 1H NMR, for several sizes of QDs reveal that this ligand adsorbs in two distinct binding modes, (1) a tightly bound mode (Ka = 1.0 ± 0.3 × 104 M−1) capable of exciton delocalization, and (2) a more weakly bound mode (Ka = 8.3 ± 9.9 × 102 M−1) that has no discernible effect on exciton confinement. For tightly bound CH3-TP, the degree of delocalization induced in the QD is approximately linearly related to the fractional surface area occupied by the ligand for all sizes of QDs. Comparison of the dependence of ΔR on surface coverage of CH3-TP over a range of physical radii of the QDs, R = 1.1−2.4 nm, to analogous plots simulated using a 3D spherical potential well model yield a value for the confinement barrier presented to the excitonic hole by tightly bound CH3-TP of ∼1 eV.

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QDs, which we measure by monitoring the position of the first excitonic peak of the QDs with UV−vis absorption spectroscopy, Figure 1B. We report the decrease in Eg as an increase in the apparent radius of its quantum-confined exciton, ΔR (Figure 1B). Contraction of the band gap occurs through delocalization of the exciton into interfacial states of mixed QD−ligand character.3,4 We have previously discussed this ligand-induced delocalization of excitons extensively in the context of the more dramatic effects of phenyldithiocarbamate ligands on the band gaps of metal chalcogenide QDs (decreases in Eg of up to 1 eV).5−8 Those studies showed that the major mechanism for exciton delocalization is a decrease in the confinement potential for the excitonic hole (as opposed to the electron) upon replacement of the interfacial states presented by the native phosphonate or carboxylate ligands with the energetically accessible interfacial states presented by the sulfurcontaining dithiocarbamate ligands. Here, we choose to study exciton delocalization by thiophenolates, rather than dithiocarbamates, even though the values of ΔR upon ligand exchange to thiophenolates are, on average, ∼25% of that observed for dithiocarbamates, because, relative to dithiocarbamates, thiolates are more chemically stable in solution and therefore are easier to quantify by NMR. Alkylthiolates are also delocalizing ligands, but, unlike alkylthiolates, thiophenolates have a convenient NMR signal

INTRODUCTION This paper describes the dependence of the excitonic radius of CdSe quantum dots, QDs, on the surface coverage of an exciton-delocalizing ligand, methylthiophenolate, CH3-TP, and the use of this dependence to estimate both the number of binding geometries (with corresponding adsorption constants) for the ligand and the magnitude of the confinement potential that each binding mode presents for the exciton. Exciton delocalizing ligands, such as thiolates1−4 and dithiocarbamates,5−8 allow for increased electronic coupling of a quantum-confined exciton with the immediate surroundings of the QD, and therefore facilitate charge carrier or exciton extraction into proximate redox or energy acceptors, without changing the physical size or chemical composition of the QD core or broadening their optical spectra.5−9 Exciton delocalization is also associated with an increase in the oscillator strength of band-edge transitions3,4 and a resultant increase in the photoluminescence quantum yield of ensembles of QDs.10 In addition to the benefits of delocalizing ligands for use of QDs as photovoltaic active materials, photocatalysts, and luminescent tags, the response of the excitonic energy of the QD to its surface chemistry is a sensitive probe of the degree of quantum confinement of its carriers,6,8 and, as we show here, the chemical and electronic structure of the QD−ligand interface, which is often difficult to probe using traditional analytical techniques, especially in the solution phase. Displacement of native octylphosphonate ligands (OPA) by CH3-TP on the surfaces of the QDs, Figure 1A, causes a moderate (up to 50 meV) decrease in the band gap (Eg) of the © XXXX American Chemical Society

Received: May 5, 2015 Revised: July 23, 2015

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DOI: 10.1021/acs.jpcc.5b04306 J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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RESULTS AND DISCUSSION We use the 1H NMR spectra of the QD−ligand mixtures to distinguish freely diffusing CH3-TP from adsorbed CH3-TP in order to calculate the surface coverage of the ligand on CdSe QDs using a method also detailed in Aruda et al.11 Figure 2A

Figure 1. (A) Diagram of the ligand exchange from octylphosphonate (OPA) to methylthiophenolate (CH3-TP) on a truncated CdSe nanocrystal. Both ligands have a 1− charge and coordinate to Cd2+ on the surfaces of the QDs. (B) Displacement of OPA by CH3-TP on the surfaces of QDs causes a moderate decrease (up to 50 meV, depending on the physical radius of the QD) in Eg of the QDs, observed as a shift of the first excitonic peak to lower energy. Rphys is the physical radius of the QD core that corresponds to the band gap of the QDs coated with their native ligands. Robs is the excitonic radius that corresponds to the band gap of the QDs after ligand exchange with CH3-TP. ΔR is defined as the increase in excitonic radius that corresponds to the observed decrease in Eg.

Figure 2. (A) 1H NMR spectra in the aromatic region of 0.34 mM CH3-TP (black) and the same concentration of CH3-TP in the presence of 10 μM CdSe QDs (Rphys = 2.0 nm) (red); both samples are in CDCl3. The doublets at 7.08 and 7.20 ppm correspond to protons on the CH3-TP phenyl ring, as labeled. In the presence of the QDs, both CH3-TP doublets decrease in intensity by ∼90%. The small residual doublets at 7.08 and 7.20 ppm correspond to unbound CH3TP. The doublet at 7.12 ppm (and another doublet at 7.40 ppm, not shown) is from bis(p-CH3 phenyl) disulfide. (B) A plot of the integrated signal of the 7.08 ppm doublet for a series of samples of CH3-TP (black), and for a series of mixtures of CH3-TP with 10 μM CdSe QDs (Rphys = 2.0 nm) (red) vs the concentration of CH3-TP added to the sample. The concentration of bound CH3-TP per QD within the mixture for a given concentration of added CH3-TP is calculated from the difference between these two integrated signals. Error bars are calculated from the standard error of the slope of the calibration curve constructed with our QD-free samples of CH3-TP, which we use as an external NMR standard.

signal in the aromatic region that distinguishes them from the native oleate ligands. The primary motivation behind this work is to link the observable (the average exciton delocalization radius for the ensemble, ΔR) to the electronic structure of the interface. We do this by developing a model that, coupled with electronic structure calculations on idealized particle-in-a-sphere systems, relates the delocalization radius per bound ligand (Δr) to the height of the tunneling barrier presented by the ligand to the excitonic hole. The secondary motivation is to use the dependence of ΔR on surface coverage to determine a chemical property of the QD−thiophenolate interface, specifically, that there exist at least two binding modes for thiophenolate on these QDs with distinct binding constants that elicit distinct responses of the exciton. This type of information is not available from NMR-derived binding isotherms for the samples alone. We develop the model linking ΔR to the electronic and chemical structure of the QD/ligand interface for thiophenolates, but small variations of it will apply to complexes of QDs with alkylthiolate (or other delocalizing) ligands, whether or not those ligands have multiple binding modes.

shows the 1H NMR spectra of two equimolar samples of CH3TP. One sample is 0.34 mM CH3-TP dissolved in CDCl3, and the other sample is 0.34 mM CH3-TP plus 10 μM CdSe QDs (with physical radius Rphys = 2.0 nm) dispersed in CDCl3. Most of the signal from CH3-TP protons disappears in the presence of QDs because adsorption onto a large particle induces dramatic broadening through several mechanisms;4,11,12 residual signals at 7.08 and 7.20 ppm, with line widths equal to those of the peaks for freely diffusing CH3-TP, correspond to unbound CH3-TP molecules within the sample. Broad signals corresponding to protons on the bound CH3-TP ligand do not appear at any concentration of ligand or QDs that we examined. Figure S2A shows that coating the QDs with CH3TP does not induce precipitation of the QDs. Figure S11 B

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The Journal of Physical Chemistry C further demonstrates that the ligand exchange is reversible and that the disappearance of the CH3-TP NMR signals upon mixing with QDs is not due to precipitation of CH3-TP-coated QDs (we use PbS QDs coated in oleate so that we can use the vinyl signal to more easily detect desorption of the native ligand). Upon oxidation of the CH3-TP to disulfide, some of it desorbs from the QD surface and is again detectable by NMR. The oleate then readsorbs, and its NMR signal broadens to its characteristic bound line width.12 The reversibility of the ligand exchange is also evidence that no dramatic surface reconstruction occurs upon treating the QDs with CH3-TP. For each QD/(CH3-TP) mixture, we calculate the number of CH3-TP bound per QD by subtracting the number of free CH3-TP per QD within the mixture from the number of CH3TP per QD that we add, determined from the signals at 7.08 and 7.20 ppm within a spectrum of a QD-free standard sample, Figure 2B. In some mixtures of CH3-TP with QDs, another pair of doublets appears at 7.12 ppm (Figure 2A) and at 7.40 ppm (not shown); these peaks correspond to bis(p-CH3 phenyl) disulfide. Because the conversion of CH3-TP to disulfide is not reversible under our experimental conditions, in cases where we observe the disulfide, we define the amount of CH3-TP added as the amount of CH3-TP added minus the amount of CH3-TP converted to disulfide (see Supporting Information). The Supporting Information contains 1H NMR spectra for all of the QD/(CH3-TP) mixtures used in the titration for QDs with Rphys = 2.0 nm (Figure S1), as well as a kinetic study confirming that the samples are equilibrated (Figure S2). Elemental analysis (specifically inductively coupled atomic emission spectroscopy) has been used previously to quantify the surface coverage of thiophenolate on PbS QDs.3,4 This approach is also useful, although, unlike our NMR-based approach, it requires the separation of the thiophenolate-coated QDs from the excess, unbound, thiophenolate. Figure 3A shows a plot of ΔR, the change in the apparent excitonic radius of the QD upon ligand exchange from OPA to CH3-TP, measured from the absorption spectrum of the sample and a preconstructed calibration curve of exciton energy versus size,13 versus the average number of CH3-TP bound per QD in the ensemble, measured by 1H NMR as described earlier. Above a threshold surface coverage of CH3-TP, the response of ΔR to adsorption of CH3-TP begins to saturate. There are two possible hypotheses to explain the decreasing sensitivity of ΔR to the binding of CH3-TP with increasing surface coverage of CH3-TP, as seen in Figure 3A. The first hypothesis is that the attenuated ΔR with increasing surface coverage reflects the quantum mechanically predicted functional form for the response of confinement energy to increasing surface coverage of an exciton-delocalizing ligand. The second hypothesis is that there is a difference in the binding geometry or chemistry between ligands that bind at low coverage and those that bind at high coverage and that these two (or more) distinct binding modes affect exciton confinement differently and thereby elicit different responses of ΔR to surface coverage. We eliminate the first hypothesis by calculating the confinement energy of a particle in a spherical potential well surrounded by a two-step potential barrier (Figure 4A) as a function of the relative coverages of a native insulating ligand, here octylphosphonate, and a delocalizing ligand, here CH3-TP. We then use these confinement energies to predict values of ΔR (see Figure S5) for different surface coverages of delocalizing ligand to simulate Figure 3A for an ideal system.

Figure 3. (A) Plots of ΔR (measured by absorption spectroscopy) vs the number of bound CH3-TP per QD (measured by NMR) for four sizes of QDs. The solid lines correspond to global fits of the data to eq 3. (B) Plots of the number of bound CH3-TP per QD versus the total concentration of free CH3-TP in the sample for the same set of QDs presented in A. The solid lines correspond to global fits of the data to eq 1 with fitting parameters listed in Table 1. Error bars in A and B are calculated from the standard error of the slope of the calibration curve constructed with our QD-free samples of CH3-TP, which we use as an external NMR standard.

We do not consider the contribution from the Coulomb energy of the exciton in this calculation. Furthermore, in this model, we assume that ΔR is only related to a change in the confinement energy of the excitonic hole, not the electron, upon ligand exchange. This assumption is reasonable because (1) we know from studies of phenyldithiocarbamates that sulfur-containing ligands predominantly affect the confinement potential of the excitonic hole of CdSe QDs;6−8 (2) plots of ΔR versus the size of the core of the QD for adsorption of CH3-TP exhibit the same shape as those we used to prove holespecific delocalization in the case of phenyldithiocarbamate (see Figure S6);6 and (3) density functional theory (DFT) calculations show that the energy of the lowest unoccupied molecular orbital of CH3-TP differs by only 0.3 eV from that of the native ligand, OPA, whereas the energy of the highest occupied molecular orbital (HOMO) of CH3-TP is 2.2 eV higher than that of OPA (see the Supporting Information). The first step in the potential barrier depicted in Figure 4A represents the interface between the nanocrystalline core of the QD and the region where the ligand orbitals begin to contribute to the potential. We divide this first potential barrier into approximately equal radial volumes; each radial volume represents a ligand. We choose the density of these radial volumes to be 4 nm−2, on the basis of an estimate of the footprints of both insulating and delocalizing ligands (∼0.25 nm2), and we set the thickness of this first potential barrier to 0.6 nm on the basis of the dimensions of the HOMOs of OPA and CH3-TP (the orbitals into which the excitonic hole potentially delocalizes), as calculated by DFT, see the Supporting Information. If, as in the limiting case of a perfectly C

DOI: 10.1021/acs.jpcc.5b04306 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

For a mixed monolayer of insulating ligands and CH3-TP, the height of this first step varies across the surface of the inorganic core. The second step in the potential barrier represents the interface between the organic−inorganic interfacial region and the purely insulating part of the ligand (e.g., the alkyl chain within alkylphosphonates) or the solvent. We set the height of this second step to 6 eV relative to the bottom of the well; this height does not vary with ligand coverage and is homogeneous across the surface of the inorganic core, Figure 4A. Figure 4B shows the results of these spherical potential well calculations: plots of ΔR upon ligand exchange from the native insulating ligand to a delocalizing ligand, determined from calculated confinement energies, versus the fractional surface coverage of delocalizing ligands for delocalizing barrier heights of 2.8, 1.4, 0.7, and 0 eV. The x-axis of Figure 4B is related by a constant (namely, (total QD surface area)/(ligand footprint)) to the x-axis in the experimental plots in Figure 3A. For each barrier height in Figure 4B, we overlay simulated data for six different core sizes ranging from R = 1.1 to R = 3.2 nm. We only show data for fractional surface coverages up to 0.75 because the maximal packing of ligand footprints, which are approximately circular, cannot be 1 (i.e., there is some empty space between ligands even in the case of perfect packing) and because the surfaces of real nanocrystals are not uniformly and tightly packed with surface sites. Figure 4B yields two relevant conclusions: (1) In general, for this idealized model, ΔR is approximately linear with fractional surface coverage of the delocalizing ligand at low coverages, and, for low barrier heights, is hyperlinear at high surface coverages. The shapes of the experimentally measured plots of ΔR versus surface coverage of CH3-TP in Figure 3A are therefore not the quantum mechanically predicted functional form of ΔR versus surface coverage of a delocalizing ligand. The shape of these experimental plots instead must be attributable to a nonideality, such as an increase in the barrier height presented by the delocalizing ligand at some point in the ligand exchange. (2) The overlap of the plots in Figure 4B for several sizes of QDs (for each given barrier height) shows that, within this model, ΔR has the same dependence on the fractional surface coverage of the delocalizing ligand regardless of the absolute number of bound delocalizing ligands per QD. Our simple simulations have shown that the saturation of the experimentally measured plots of ΔR versus number of bound CH3-TP ligands per QD, Figure 3A, must be due to a difference in the delocalizing ability of ligands that bind at different surface coverages. Specifically, the data imply that the magnitude of the electronic interaction between valence band orbitals of the QD core and CH3-TP ligands that bind at low surface coverage is, on average, larger than that between the QD and the ligands that bind at high surface coverage. We therefore interpret the data in Figure 3A with a model that includes binding of CH3TP in two different modes or geometries, one at low surface coverage and one at high surface coverage. We do not know the structures of these two modes, see the Supporting Information for a description of the difficulties of interpreting Fourier transform infrared (FTIR) spectra of these systems, but, on the basis of the turnover in the plots of ΔR versus number of bound ligands in Figure 3A, we know that the two modes have different delocalizing effects and different binding constants. Consequently, although the binding isotherms for the system in Figure 3B fit satisfactorily to a single-site Langmuir model (see Supporting Information and Figure S3), the shapes of the plots

Figure 4. (A) 3D and 1D representations of the two-step spherical potential well used to model ΔR vs surface coverage of CH3-TP. Red regions represent the volumes occupied by delocalizing ligands (CH3TP), and blue regions represent volumes occupied by native ligands (OPA). Everything outside the ligand shell is solvent. (B) Values of ΔR calculated using this model vs fractional surface coverage of delocalizing ligands that present barrier heights of 0.0, 0.7, 1.4, and 2.8 eV, for cores with R = 1.1−3.2 nm. (C) Black solid circles: Plot of ΔR per bound CH3-TP (Δr1) extracted from fits of the data in Figure 3A to eq 3 vs the band gap of the QD used in the experiment. Red and green open circles: Calculated values of ΔR per bound ligand, equal to the slopes of the lines in Figure 4B for delocalizing ligands that present 0.7 and 1.4 eV confinement potentials, vs the band gap of a QD with the simulated core size.

insulating native ligand, there is no mixing between the ligand orbitals and the delocalized orbitals of the semiconductor core, then the height of this first step is simply the difference in energy between the edge of the semiconductor valence band and the energy of the HOMO of the ligand: 5.0 eV for OPA (see Figure 4A and the Supporting Information). If mixing between semiconductor and ligand orbitals occurs, as is the case for a delocalizing ligand like CH3-TP, then the interfacial region represented by this first potential barrier acquires the character of both materials, and, in the simplest representation of the system, the height of the step is lowered relative to that imposed by the (unmixed) insulating native ligands. We do not know, a priori, the degree of mixing between CdSe valence band (VB) orbitals and CH3-TP orbitals, so, for regions coated in CH3-TP, we calculate values of ΔR for step-heights ranging from 2.8 eV (the barrier presented by free CH3-TP, representing the limit of no QD−ligand electronic coupling) to 0 eV (representing perfect QD−ligand electronic coupling). D

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The Journal of Physical Chemistry C Table 1. Results of Global Fits of Figure 3A to eq 1 and Figure 3B to eq 3a QD physical radius (nm) 1.13 1.50 1.73 1.86 2.05 2.22 2.37

Ka,1 (M−1) (shared across all data sets) 1.0 1.0 1.0 1.0 1.0 1.0 1.0

± ± ± ± ± ± ±

0.3 0.3 0.3 0.3 0.3 0.3 0.3

× × × × × × ×

Ka,2 (M−1) (shared across all data sets)

104 104 104 104 104 104 104

8.3 8.3 8.3 8.3 8.3 8.3 8.3

± ± ± ± ± ± ±

9.9 9.9 9.9 9.9 9.9 9.9 9.9

× × × × × × ×

102 102 102 102 102 102 102

Nsites,1 (QD−1) 31 61 15 51 40 90 91

± ± ± ± ± ± ±

10 21 6 19 16 32 33

Nsites,2 (QD−1) = (2.5 ± 1.0) × Nsites,1 78 153 38 127 99 225 228

± ± ± ± ± ± ±

59 116 30 100 82 174 178

total ligand density (nm−2) 6.8 7.6 1.4 4.1 2.6 5.1 4.5

± ± ± ± ± ± ±

4.3 4.8 1.0 2.7 1.8 3.3 3.0

Δr1 (nm/CH3-TP ligand) 1.7 9.3 7.4 6.0 4.6 3.8 2.9

± ± ± ± ± ± ±

0.5 2.9 2.9 2.0 1.8 1.2 1.0

× × × × × × ×

10−3 10−4 10−4 10−4 10−4 10−4 10−4

Δr2 is fixed to zero for these fits. bError bars are standard errors obtained from least-squares fitting with a custom Python algorithm (see the Supporting Information). a

in Figure 3A demand the use of a two-mode binding picture, and so we use a two-site Langmuir model, eq 1, to fit the data in Figure

ΔR = ΔR1 + ΔR 2 Nsites,1K a,1Cfree Nsites,2K a,2Cfree = Δr1 + Δr2 1 + K a,1Cfree 1 + K a,2Cfree

Nbound = Nbound,1 + Nbound,2 =

Nsites,1K a,1Cfree 1 + K a,1Cfree

+

We then use this two-site Langmuir model to derive an expression for ΔR as a sum of contributions, ΔR1 and ΔR2, from each type of binding event, eq 2. We represent ΔR1 and ΔR2 as the product of the number of ligands bound in each geometry and a factor Δri (i = 1, 2), where Δri = ΔRi per bound ligand. The linear dependence of ΔR on surface coverage of delocalizing ligand incorporated into this expression is justified by the approximate linearity of the response of ΔR to surface coverage of a delocalizing ligand for a single binding mode with a nonzero confinement barrier at less than 50% surface coverage, as shown in Figure 4B. Solving eq 1 for Cfree, and substituting that expression into eq 2, yields eq 3.

Nsites,2K a,2Cfree 1 + K a,2Cfree

(2)

(1)

3B. In eq 1, Nbound is the total number of bound CH3-TP ligands per QD (i.e., the sum of the number of ligands bound in each binding mode, Nbound,1 + Nbound,2), and Cfree (M−1) is the total concentration of free (unbound) ligands in the sample. We measure Nbound and Cfree by NMR to construct Figure 3A and B. Nsites,1 and Nsites,2 are the number of available binding sites per QD for the strong and weak binding modes, respectively. Ka,1 and Ka,2 (M−1) are the adsorption constants for the strong and weak binding modes to Nsites,1 and Nsites,2, respectively.

⎛ ⎛ ⎜ ⎜ ⎜ ⎜ 1 ΔR = ⎜(Δr1 + Δr2)(K a,1 − K a,2)Nbound − (Δr1 + Δr2)⎜ − Nsites,1K a,1 − Nsites,2K a,2 2(K a,1 + K a,2) ⎜ ⎜⎜ ⎜ ⎝ ⎝ ⎞⎞ ⎟⎟ ⎟⎟ + Nsites,1K a,1) ⎟⎟ ⎟⎟⎟ ⎟ ⎠⎠

( −NboundK a,1 + NboundK a,2 + Nsites,1K a,1)2 +

+ 2Nsites,2K a,2(NboundK a,1 − NboundK a,2 + (Nsites,2K a,2)2

Equation 3 defines ΔR in terms of the number of ligands bound through both binding modes, Nbound, the quantity we measure experimentally by NMR. We fit the data in Figure 3B to eq 1 and the data in Figure 3A to eq 3 simultaneously by sharing the values of Ka,1 and Ka,2 across both data sets and all seven sizes of QDs. We show the data for only four sizes in Figure 3 for clarity of presentation; see Figure S4 for the data and fits for the remaining sizes. We allow the variables Nsites,1 (the average number of available sites per QD for binding mode 1) and Δr1 and Δr2 (ΔR per CH3-TP bound through binding mode 1 and 2, respectively) to float to different values for each size of QD. The saturation of ΔR with surface coverage of CH3-TP occurs at approximately the same fraction of total binding sites for all of the sizes of QDs (∼30%, see Figure S7), so Nsites,2 is defined as a multiple of Nsites,1, and the ratio Nsites,2/Nsites,1 is shared across all data sets to constrain the fit.

(3)

Initial fits using these parameters and constraints yield values for Δr2 (ΔR per CH3-TP bound through binding mode 2) that are, on average, a factor of 107 smaller than Δr1. These values for Δr2 result in values of ΔR2 (=Δr2 × Nsites,2) below the experimental uncertainty of ΔR; therefore, for our final fits, those we show in Figure 3A and B, we set Δr2 to zero in order to further constrain the fit (see the Supporting Information for fits where Δr2 was not fixed at zero). These fits yield Ka,1 = 1.0 ± 0.3 × 104 M−1 for tightly binding CH3-TP and Ka,2 = 8.3 ± 9.9 × 102 M−1 for loosely binding CH3-TP. The tightly binding adsorption constant is consistent with many previous measurements of thiolates chemisorbed to Cd2+ in similar systems,14−17 and the FTIR and Raman spectra of a selected sample confirm the presence of metal-bound CH3-TP (see Figures S9 and S10). The loosely binding CH3 -TP could potentially correspond to CH3-TP binding as a thiol, rather than a thiolate E

DOI: 10.1021/acs.jpcc.5b04306 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C (a factor of ∼40 smaller binding enthalpy),2,18,19 or a bond through the π system of CH3-TP (e.g., a cation−π,20,21 CH−π,22,23 or π−π24 interaction). Both of these binding modalities would be expected to induce very small or no change in excitonic energy and are therefore consistent with Δr2 = 0. Our FTIR and Raman spectra contain no direct evidence to support or reject a π−x interaction as the binding mechanism for the loosely binding CH3-TP, but the change in the intensity of the bound OPA signal during titration of the QDs with CH3TP suggests that CH3-TP displaces OPA on the surface of the QD when binding in mode 1 but not when binding in mode 2 (see Figure S12). It is also possible that the two binding modes correspond to binding on a facet versus edge or vertex site, as it is known that thiolates have different affinities for such sites, and even different affinities for different crystal faces of metalchalcogenide particles.25 There have not been previous reports of two separate binding constants for thiophenolates on CdSe QDs, but we only detected the second binding mode by using the combination of a binding isotherm (Figure 3B) and the response of ΔR to surface coverage of CH3-TP (Figure 3A) that has not been used previously. Table 1 summarizes the results of the global fits to the data in Figure 3A and B for each QD size. In most cases, the fits yield ligand densities higher than the maximum geometric estimate (4 nm−2, assuming 0.25 nm2 footprint and ignoring packing inefficiencies); we attribute these higher ligand densities to the fact that real QD surfaces are not perfectly smooth, and so the surface area of a sphere with a certain radius is only a lower bound for the real surface area available for binding of ligands to the QD. The fact that Nsites,1 does not trend cleanly with the radius of the QD (and thus the shape of the binding isotherms in Figure 3B do not appear to correlate with radius) is not surprising: excess Cd2+ ions are the binding sites for CH3-TP, and we have found that, when we produce a series of sizes of CdSe QDs by taking sequential aliquots from a single reaction mixture, both the degree of cadmium enrichment of the QDs as-synthesized and the fraction of Cd2+ ions stripped by the purification procedure for the QDs do not trend with size as expected from geometric arguments.26−29 From the fits of the data in Figure 3A and B to eqs 3 and 1, respectively, we obtain Δr1 for each size of QD from R = 1.1 to 2.4 nm (Table 1). We find that, as expected (see Supporting Information), Δr1 decreases linearly with decreasing band gap of the QD and ranges from 1.7 ± 0.5 picometers/(CH3TP)bound for R = 1.1 nm to 0.29 ± 0.10 picometers/(CH3TP)bound for QDs with R = 2.4 nm, Figure 4C solid black circles. We estimate the height of the potential barrier presented by tightly bound CH3-TP ligands (the height of potential step 1 in Figure 4A) by comparing the experimental values for Δr1 with calculated values of Δr from the spherical potential well model for various barrier heights (the Supporting Information and Figure S5B and S5C detail the calculation of Δr from the spherical potential well model). The set of experimental values for Δr1 fall between the sets of theoretically predicted values for confining potentials of 0.7 and 1.4 eV (open circles in Figure 4C), and so we estimate that tightly bound CH3-TP ligands impose a confinement potential of approximately 1 eV for the excitonic hole of a CdSe QD.

between the magnitude of exciton delocalization (ΔR) and the surface coverage of exciton-delocalizing CH3-TP ligands on CdSe QDs (Figure 3). By applying a simple two-step potential model for particle confinement (Figure 4A), we determined that relaxation of exciton confinement is proportional to the fractional surface area occupied by the delocalizing ligand (and not the absolute number of bound delocalizing ligands, Figure 4B) and that the observed decreasing sensitivity of ΔR to bound CH3-TP at high surface coverage is consistent with at least two distinct binding modes: (1) a tightly bound delocalizing mode (Ka = 1.0 ± 0.3 × 104 M−1) and (2) a weakly bound mode that has no discernible effect on exciton confinement (Ka = 8.3 ± 9.9 × 102 M−1). By applying the twosite binding model, we were able to experimentally estimate, for the first time, the confinement barrier generated by a bound delocalizing ligand. For CH3-TP bound to CdSe QDs, the confinement barrier presented to the excitonic hole is between 0.7 and 1.4 eV (Figure 4C). For the purpose of optimizing QDs and other nanocrystals to perform photovoltaic and photocatalytic functions, it is desirable to engineer the confinement potential at the nanocrystal−organic interface to control access to photoexcited charge carriers. Researchers have long applied simple 1D particle-in-a-box models, representing homogeneous shells of ligands around a spherical inorganic core, to understand the confinement energies of carriers and electronic spectra of QDs; these models are both simple and often predictive. Despite the additional complexity of the mixed monolayer system that we present here, we show that, in the limit where delocalizing ligands are at low surface coverage or present moderate confinement barriers, the 1D particle-in-a-box maintains its utility. Our 3D modeling reveals that the effective potential experienced by a QD with mixed ligand coverage can be represented in 1D as simply the average of the potentials presented by each ligand, weighted by their fractional coverage of the total surface area. This simple picture provides two key insights to guide efforts to integrate QDs into devices: (1) Locally, each ligand presents its own confining potential; surfaces can be fine-tuned to gate access to carriers by colocalizing low tunneling barriers with charge acceptors/ donors (e.g., by using linkers with delocalizing binding modalities) while maintaining good isolation (high confinement) elsewhere on the surface. (2) Globally, the confinement energies of the carriers, and therefore their energy level alignments and optical spectra, are sensitive to the average conditions at the QD surface (weighted by surface area); both spatial heterogeneity (e.g., different ligands, or a single ligand with multiple binding modes) and temporal heterogeneity (e.g., transiently bound solvent or ligands) average out and behave identically to an equivalent QD with a single effective potential.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b04306. Experimental and computational details, NMR, Raman, and FTIR spectra, ligand exchange kinetics, DFT calculations, and additional fits, including Figures S1− S13 and Tables S1−S3. (PDF)

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CONCLUSIONS We combined ground-state absorption spectroscopy (Figure 1B) with NMR (Figure 2) to investigate the relationship F

DOI: 10.1021/acs.jpcc.5b04306 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, through the Early Career Research Award (award #DE-SC0003998) to E.A.W. and by the National Science Foundation through a Graduate Research Fellowship (for V.A.) (award #DGE-1324585). This research was also supported as part of the Center for BioInspired Energy Science, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award # DESC0000989 (pseudopotential calculations). The authors acknowledge Shengye Jin for providing QD samples for preliminary experiments, David J. Weinberg for discussions on ligand counting by NMR, Christopher Thompson for the Raman measurements, and Matthew T. Frederick for discussions of ligand-mediated exciton delocalization.

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REFERENCES

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DOI: 10.1021/acs.jpcc.5b04306 J. Phys. Chem. C XXXX, XXX, XXX−XXX