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A Quantitative Description of the Binding Equilibria of para-Substituted Aniline Ligands and CdSe Quantum Dots Martin D. Donakowski,† Jacqueline M. Godbe,† Rastko Sknepnek,‡ Kathryn E. Knowles,† Monica Olvera de la Cruz,‡ and Emily A. Weiss*,† Department of Chemistry, Northwestern UniVersity, 2145 Sheridan Road, EVanston, Illinois 60208-3113, United States, and Department of Materials Science and Engineering, Northwestern UniVersity, 2220 Campus DriVe, EVanston, Illinois 60208-3108, United States ReceiVed: September 30, 2010; ReVised Manuscript ReceiVed: NoVember 16, 2010
This paper describes the use of 1H NMR spectroscopy to measure the equilibrium constants for the solutionphase binding of two para-substituted aniline molecules (R-An), p-methoxyaniline (MeO-An) and pbromoaniline (Br-An), to colloidal 4.1 nm CdSe quantum dots (QDs). Changes in the chemical shifts of the aromatic protons located ortho to the amine group on R-An were used to construct a binding isotherm for each R-An/QD system. These isotherms fit to a Langmuir function to yield Ka, the equilibrium constant for binding of the R-An ligands to the QDs; Ka ≈ 150 M-1 and ∆Gads ≈ -19 kJ/mol for both R ) MeO and R ) Br. 31P NMR indicates that the native octylphosphonate ligands, which, by inductively coupled plasma atomic emission spectroscopy, cover 90% of the QD surface, are not displaced upon binding of R-An. The MeO-An ligand quenches the photoluminescence of the QDs at much lower concentrations than does Br-An; the observation, therefore, that Ka,MeO-An ≈ Ka,Br-An shows that this difference in quenching efficiencies is due solely to differences in the nature of the electronic interactions of the bound R-An with the excitonic state of the QD. Introduction This paper describes the use of 1H NMR spectroscopy to measure equilibrium constants for the solution-phase binding of two para-substituted aniline molecules (R-An), p-methoxyaniline (MeO-An) and p-bromoaniline (Br-An), to colloidal CdSe quantum dots (QDs). Organic ligands serve many functions with respect to QDs: they prevent aggregation of the QDs, control their dispersibility, and donate electron density to or accept electron density from incompletely coordinated metal ions on their surfaces.1-9 When unpassivated, these defect sites trap excitonic charge carriers and thereby provide nonradiative decay pathways for the excitonic state of the QD.5,10-12 The quantum yield of photoluminescence (PL) of an ensemble of QDs, therefore, depends on the degree of coverage of the surface by organic ligands and on the electronic properties of the ligands. By controlling the relative populations of certain ligands on the surfaces of QDssfor instance, PL-quenching aromatic amines,8 such as the anilines studied here, and PL-enhancing alkylaminesswe can determine the decay pathways available to the excitonic state and thereby engineer the optical and electronic properties of the QD. To control the population of ligands bound to the QDs, we need accurate methods to measure the equilibrium constants for binding of ligands to QD surfaces. Here, we present the first measurements of the equilibrium constants for binding of small, conjugated ligandssparasubstituted anilinessto CdSe QDs. We made solutions of R-An and CdSe QDs with diameters of 4.1 nmspassivated by phosphonate ligands (octylphosphonate (OPA) and P,P-(di-noctyl) pyrophosphonate (PPA))swith molar ratios of [R-An]: * To whom correspondence should be addressed. E-mail: e-weiss@ northwestern.edu. † Department of Chemistry. ‡ Department of Materials Science and Engineering.
[QD] between 25:1 and 1025:1. We monitored the changes in the chemical shifts of the aromatic protons located ortho to the amine group on R-An as a function of [R-An]:[QD] to construct a binding isotherm for each R-An/QD system. Previous studies of QD-ligand equilibria examined ligands with alkyl chains,13-22 but QD-ligand complexes containing short, conjugated molecules, such as R-An, are better candidates for energy applications than the well-characterized systems containing long-chain aliphatic molecules because shorter ligands minimize insulating tunneling barriers between QDs within films.23-26 The isotherms we constructed fit to a Langmuir function to yield Ka, the equilibrium constant for binding of the R-An ligands to the QDs, which is ∼150 M-1 for both R ) MeO and R ) Br despite the fact that MeO is an electron-donating substituent and Br is an electron-withdrawing substituent and, therefore, should affect the electron density on the amine binding group.8 We use these values of Ka to calculate free energies of adsorption, ∆Gads, of -19.3 kJ/mol for both MeO-An and Br-An. We also present coarse-grained molecular dynamics (MD) simulations, which suggest that the coordination of weakly binding R-An ligands to CdSe QDs passivated by strongly binding phosphonates is enabled by van der Waals interactions between the aliphatic tails of the phosphonate ligands; these interactions cause the phosphonates to form bundles on the surfaces of the QDs and, consequently, leave patches of empty surface sites, unobscured by the tails of the phosphonate ligands, to which the R-An ligands can bind. The values we obtain for the free energy of adsorption place the R-An ligands in the category of “weak-binding” ligands, as described by Rempel et al.;6 however, these ligands can dramatically affect the excitonic decay of the QDs and their PL. As we have seen previously8 and confirm here, MeO-An quenches the PL of CdSe QDs much more efficiently than does Br-An; the ratio of R-An:QD necessary to quench the PL of
10.1021/jp109381r 2010 American Chemical Society Published on Web 12/03/2010
para-Substituted Aniline Ligands and CdSe QDs the QDs by 50% is approximately a factor of 1000 less for R ) MeO than for R ) Br. The observation that the substituent R does not affect ∆Gads shows that this difference in quenching efficiencies is due solely to differences in the nature of the electronic interactions of the bound R-An with the excitonic state of the QD. Previous Measurements of QD-Ligand Binding Equilibria. The equilibrium constants for ligands binding to QDs are difficult to establish by standard analytic chemistry techniques. Potentiometric measurements and isothermal calorimetry are designed for well-defined, aqueous solutions, but many applications of QD-ligand complexes require knowledge of binding equilibria in nonaqueous media.27,28 Within FTIR spectra, signals from bound ligands are often weak and/or buried under those from unbound ligands. Ground-state absorption spectroscopy is not an effective method for measuring the number of ligands bound to a QD because, although ligands may experience changes in energy or intensity of electronic absorption peaks upon binding, these peaks are obscured by the electronic absorptions of the QD, which increase in oscillator strength on going from the band edge to the UV. Several nanoparticle/ligand systems studied previously by NMRsincluding mixtures of nanoparticles with trioctylphosphine oxide, laurate anions, para-toluene-sulfonic acid, or acetylacetone13,14,19,29,30shad the advantages of (i) distinct peaks in the spectra from bound and free ligands and (ii) an exchange rate of ligands between bound and free states (in Hz) that was significantly slower than the difference (in Hz) between the signals from the bound and free species. These studies could, therefore, utilize 1H NMR diffusion ordered spectroscopy (DOSY) and pulse field gradient (PFG) spectroscopy to identify bound and unbound peaks of slowly exchanging ligands,19,29,30 and, in one case, to determine a binding constant for the QD/ ligand system.13 Ligands that undergo rapid exchange (relative to the difference between chemical shifts of the bound and free states) produce only one set of peaks in 1H NMR spectra of mixtures of the ligand and QDs. The observed peaks correspond to a weighted average of the signals from ligands in bound and free states.21 Fritzinger et al. used NOESY NMR to qualitatively show that the rapid-exchange ligand dodecylamine binds to the surfaces of CdTe QDs, but they could not calculate a binding constant because the binding produced a change in the observed chemical shifts of the ligand (δobs) of only 0.006 ppm.21 The R-An ligands used in this study also undergo rapid exchange between bound and free states, but the shifts in δobs for the peaks corresponding to protons ortho to the amine binding group were large enough (0.02-0.03 ppm) to allow us to determine Ka for these QD-ligand systems. Experimental Methods Synthesis and Purification of CdSe QDs. We synthesized CdSe QDs with a procedure modified from that in Qu et al. (see the Supporting Information).31 For each QD synthesis, after injecting the Se precursor, trioctylphosphine selenide (TOPSe, prepared and stored in a glovebox), we quenched the reaction mixture with 14 mL of room-temperature hexanes. Leaving the reaction mixture in the flask for 2 h allowed a white powder to precipitate; this powder was excess trioctylphosphine oxide (TOPO) and hexadecylamine (HDA). We decanted the solution, added methanol (1:1 v/v), and centrifuged the resulting mixture at 3500 rpm for 5 min to produce an orange pellet of precipitated QDs and excess TOPO and HDA. The supernate was discarded, and the pellet was dried under a flow of nitrogen gas, redispersed in 4.5 mL of hexanes, and allowed to sit in a sealed centrifuge
J. Phys. Chem. C, Vol. 114, No. 51, 2010 22527 tube in dark, ambient conditions for 12 h, after which centrifugation produced a white pellet of excess ligand and an orange supernate. The supernate was separated and combined with 4 mL of methanol; centrifugation of this suspension, separation, redispersal of the pellet in 4 mL of CH2Cl2, addition of 4 mL of methanol, and a final centrifugation yielded an orange pellet of QDs that we dried under nitrogen and redispersed in 40 mL of CH2Cl2. Addition of R-An to QDs. Five samples consisting of 3 × 10-8 moles of QDs in 7 mL of CH2Cl2sas measured by groundstate absorption spectroscopy32swere added to various volumes of a stock solution of R-An (0.03 M in CH2Cl2), such that the resulting mixtures had 25, 50, 75, 100, and 125 R-An ligands per QD. We evaporated the CH2Cl2 under a flow of dry nitrogen and redispersed the mixtures in 0.75 mL of deuterated CH2Cl2 before transferring the samples into NMR tubes. These samples were sealed with Teflon tape to prevent evaporation of solvent and allowed to equilibrate in dark, ambient conditions for 12 h before 1H NMR analysis. We prepared the R-An/QD solutions with [R-An]:[QD] ) 150:1-1025:1 by incrementally adding appropriate amounts of the R-An stock solution to these five samples. The volume of the NMR samples was maintained at 0.75 mL for all experiments. All three components of the binding reactionsthe free R-An ligands, the QDs with their native ligands, and the QDs substituted with R-An ligandsswere highly soluble or dispersible in CH2Cl2 and deuterated CH2Cl2. 1 H NMR Measurements. We acquired the 1D 1H NMR spectra of the R-An/QD samples on a 500 MHz Bruker AvanceIII NMR instrument with a 5 mm 13C-detect DCU cryoprobe and Z-axis pulsed field gradients. The temperature of the samples was maintained at 25 °C with a BCU-05 chiller. The spectra were obtained with the ICON-NMR utility in Topspin 2.1.6. We averaged 128 scans for each sample and used tetramethylsilane (TMS) as an internal chemical shift reference. The scans had a spectral width of 20.00 ppm (10 000 Hz) with a 1 s relaxation delay time. We acquired the 2D NOESY spectra at ambient temperature on a 400 MHz Varian Inova NMR instrument with a 5 mm Varian AutoX broad-band-observe, 1H-decouple probe. Data were acquired with VNMRJ 2.2D software. Our samples were in CD2Cl2 and had an R-An:QD ratio of 350:1 or an equivalent absolute concentration (0.014 M) of R-An in the absence of QDs in order to acquire a reference spectrum of free R-An. We averaged 8 scans and sampled 1024 data points with 256 t1 increments and a 1 s delay time. The data were processed with a sine window function and then Fourier-transformed to a 512 × 256 data set. 31 P NMR Measurements. We acquired 31P NMR spectra of the R-An:QD samples at ambient temperature on a 400 MHz Varian Inova spectrometer with a 5 mm Varian AutoX broadband-observe, 1H-decoupled probe. Data were recorded using VNMRJ 2.2D software. The probe was positioned at 162 Hz, and we recorded the spectra with a spectral width of 150 ppm (24 300 Hz) and averaged 2048 scans for each sample. We scanned each sample using a relaxation delay time of 1 s. ICP-AES. We prepared samples and calibration standards as previously reported33 to measure the elemental ratios of Cd/ Se and P/Cd in the QD dispersions. We prepared samples by digesting a portion (3 × 10-9 moles) of each of the CdSe QD batches in 0.5 mL of aqua regia and diluting these to 10 mL in Millipore filtered water. Calibration standards were made by diluting standard solutions of TraceCERT Ultra Cd (997 ppm) and TraceCERT Ultra Se (1004 ppm) obtained from Fluka in 2% HNO3 solutions, and phosphonic acid (999 ppm) in 5%
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HNO3 solutions from Sigma. The spectra were acquired within 24 h of standard and sample preparation and analyzed with Varian’s ICP-expert II software. To determine concentration, we averaged the concentrations obtained from the intensities of the two most intense peaks for phosphorus (213.618 and 214.914 nm) and three most intense peaks for Se (196.026, 203.985, and 206.279 nm) and Cd (214.439, 226.502, and 228.802 nm). The reported uncertainty in the calculated elemental concentration for each element is the standard deviation of three separate measurements on the same CdSe QD sample. We used the measured concentrations of Cd, Se, and P to establish the number of Cd2+ ions on the surface of the QDs and the surface coverage of phosphonate ligands (see the Supporting Information).34 PL Measurements. We measured the PL magnitude of the solution-phase CdSe QDs as a function of added R-An as described previously.8 Immediately after purification, the CdSe QDs were dispersed in distilled CH2Cl2 to a concentration of 1.1 × 10-7 M and allowed to equilibrate in dark, ambient conditions under a nitrogen atmosphere for 72 h. The R-An ligands were then added to the QD solutions to obtain a range of [R-An]:[QD] molar ratios (0-50 000:1). The CdSe QD/RAn dispersions were stirred for 24 h to allow the solutions to equilibrate. The PL emission spectra of these solutions were measured by excitation at 480 nm and integration of the PL intensity over the emission region of 500-700 nm (see the Supporting Information). The integrated intensities were divided by the integrated intensity of a solution of CdSe QDs with no R-An added to obtain PL/PL0. Results and Discussion Binding of R-An to CdSe QDs in Solution. The 1H NMR spectra of R-An contain two multipletssthat each resemble doubletsscorresponding to protons positioned meta (Hm) and ortho (Ho) to the amine headgroup (Figure 1). Upon addition of R-An to CdSe QDs, R-An coordinates to Cd2+ sites on the surfaces of QDs via electron donation from the amine group. This donation decreases the electron density in the aromatic ring and deshields the Ho protons, which causes their NMR signal to shift downfield (higher ppm, Figure 1). We have observed this trend previously8 in preliminary experiments on R-An/CdSe QD systems (R ) N(CH3)2, MeO, H, Br, and OCF3) in deuterated CHCl3 but did not obtain quantitative information about the chemical shift because the signals from Ho and Hm overlap with the signal from residual CHCl3. Comparison of NOESY NMR spectra of R-An in the presence and absence of QDs (Figure 2) confirmed that the shifting of peaks that we observed in the 1H NMR spectra is due to binding of R-An ligands to the CdSe QDs.18,21 Spectra of reference samples of both free Br-An and free MeO-An in CD2Cl2 exhibit cross-peaks due to coupling among protons on a single aromatic ring; these cross-peaks have the antiphase line shape characteristic of fast-tumbling, small molecules (Figure 2B,D, insets).21 In the spectra of solutions with [R-An]:[QD] ) 350 (Figure 2A,C), the loss of the antiphase line shape in these same crosspeaks indicates that the molecules are tumbling more slowly than in the free state.21 The spectra of the QD/R-An mixtures also show strong cross-peaks, not present in spectra of R-An alone, that arise from coupling with the aliphatic protons of the native phosphonate ligands that are on the QD (which have signals between 1 and 2 ppm). Both of these sets of cross-peaks indicate that there are populations of R-An ligands bound to the surfaces of the QDs.
Donakowski et al.
Figure 1. Aromatic regions of 1H NMR spectra of 4.0 × 10-5 M samples of CdSe QDs in CD2Cl2 with [R-An]:[QD] ratios of 25:1, 525:1, and 1025:1, and of 0.01 M samples of free R-An (no QDs) for R ) Br (top) and MeOAn (bottom). Ho and Hm indicate the protons located ortho and meta, respectively, to the amine group. The Hm peaks of Br-An are located further downfield, outside the parts per million range shown above. The spectra with QDs (black, red, and blue) are normalized to the height of the lower-ppm peak of the Hm doublet for both sets of spectra.
Equation 1 defines the equilibrium between the free QDs and R-An molecules and the bound R-An:QD state.
QD + R-An h QD:R-An
(1)
The 1H NMR spectra of mixtures of R-An and QDs (Figure 1) contain one set of Ho peaks that shift and broaden upon binding, rather than one set of peaks corresponding to Ho protons on bound ligands and one set corresponding to Ho protons on free ligands, because the rate of exchange between bound and free states is faster than the difference, in hertz, between the chemical shifts of bound and free ligands. This fast exchange has been observed previously in amine/QD systems.15,18,21 The chemical shift of the single set of Ho peaks, therefore, corresponds to the average of the chemical shifts of Ho for free and bound R-An, weighted by their relative populations (eq 2).18,35
δobs )
[R-An]b [R-An]f × δb + × δf [R-An]tot [R-An]tot
(2)
In eq 2, [R-An]tot is the total concentration of R-An added to the QD solutions, [R-An]b is the concentration of R-An bound to Cd2+ sites on the surfaces of CdSe QDs at equilibrium, [R-An]f is the equilibrium concentration of free R-An in solution, δb is the average of the chemical shifts of the Ho proton “doublet” peaks of R-An bound to a Cd2+ surface site, δf is the average of the chemical shifts of the Ho proton “doublet” peaks of R-An measured in the absence of CdSe QDs, and δobs is the observed average chemical shift of the Ho proton doublet peaks
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Figure 2. NOESY spectra of (A) Br-An and CdSe QDs in CD2Cl2 at [Br-An]:[QD] ) 350:1, (B) Br-An in CD2Cl2 (no QDs) with the same [Br-An] (0.014 M) as the spectrum of (A), (C) MeO-An and CdSe QDs in CD2Cl2 at [MeO-An]:[QD] ) 350:1, and (D) MeO-An in CD2Cl2 (no QDs) with the same [MeO-An] (0.014 M) as the spectrum of (C). The peaks between 6 and 8 ppm (boxed) are due to the protons on the aromatic rings of R-An (see insets for zoomed-in pictures of these regions). The peaks between 3 and 4 ppm are due to amine protons, except for the peak at 3.8 ppm in the spectra of MeO-An, which is due to the methoxy protons. The peaks located between 2.5 and 0.5 correspond to methylene and methyl protons of the native OPA and PPA ligands. The peaks at 5.3 ppm are due to residual CH2Cl2, and the streak at F1 ) 0.2 ppm in the Br-An/QD spectrum is due to grease. The colors indicate the relative phases and intensities of the signals.
for various [R-An]:[QD] ratios (Figure 1). To find the average chemical shift of a doublet peak, we fit the doublet to a sum of Lorentzian functions and averaged the peak positions of the two Lorentzians (see the Supporting Information). Derivation of an Equation to Fit the Chemical Shift Data and Find the Binding Constant, Ka, for each R-An/ QD System. Figure 3 shows plots of δobsversus [R-An]tot for four trials (two trials for the MeO-An/QD system and two trials for the Br-An/QD system), where a trial is a set of 43-51 NMR experiments for samples that contained 25-1025 R-An ligands per QD. We used one synthetic batch of QDs for each trial. For all four trials, the average diameter of the QDs was 4.1 ( 0.7 nm, as determined by ground-state absorption and PL spectra (see the Supporting Information).34,36 To use the measured values of δobs to calculate the binding constant, Ka, that defines the association reaction within the equilibrium in eq 1, we need to know the value of δb. This value is not apparent from our chemical shift data because even the values of δobs at [R-An]:[QD] ) 25:1 have some contribution from free R-An ligands. We fit our plots of δobsversus [R-An]tot to eq 3, which we derive in the Supporting Information, and extract δb for each trial.
δobs ) δf +
{
(δb - δf) × 2Ka[R-An]tot Ka([R-An]tot + [QD]tot) + 1 (
[Ka2([R-An]tot - [QD]tot)2 + 2Ka([R-An]tot + [QD]tot) + 1]1/2
}
(3)
We note that, in deriving eq 3, we assume that our chemical shift data fit to a Langmuir isotherm. The Supporting Information contains plots of our data in the more commonly used form of the Langmuir isotherm, θ versus [R-An]f, that validates this assumption. Equation 3 contains two possible expressions for δobs because of the ( sign in front of the square root quantity. Only one of the expressions, that with the “-” sign, fits the data (see the Supporting Information for the fit with the other solution). There are two parameters in eq 3, [QD]tot and δf, that we determined using independent experiments and input as fixed parameters when in our fits of eq 3 to plots of δobs versus [R-An]tot. We determined the concentration of available sites, [QD]tot, for each batch of QDs by measuring the surface coverage of alkylphosphonate ligands using ICP-AES and assuming that only the remaining sites were available for binding by R-An ligands (Table 1). We made this assumption because 31 P NMR spectra of the R-An/QD solutions show that R-An ligands do not displace the OPA and PPA ligands upon binding, even at the highest concentrations of added R-An (see the Supporting Information).4,33,37 In addition to the known disparity in adsorption energies between alkylphosphonates on CdSe and amines on CdSe,6,38-40 we believe that the R-An ligands do not displace OPA and PPA because displacement of these ligands requires protonation of an anionic oxygen atom that is bound to the Cd2+ site22 and R-An ligands cannot provide these protons. Positive or negative deviation from the ICP-AES-predicted value of [QD]tot in eq 3 yields either an unacceptable fit of the data or unreasonably large values of δb (see the Supporting Informa-
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Figure 3. Plots of δobs vs [R-An]tot for R ) MeO and R ) Br and fits of these plots to eq 3. Table 1 contains the values of the binding constants, Ka, and the chemical shift of a bound R-An, δb, that we extracted from the fits.
TABLE 1: Parameters for the QD and R-An/QD Systems Obtained from ICP-AES and 1H NMR Experiments from ICP θmax Br-An trial 1 Br-An trial 2 Br-An avg MeO-An trial 1 MeO-An trial 2 MeO-An avg
b
0.13 0.04 0.09 0.07 0.12 0.10
from fit of δobs vs [R-An]tot to eq 3a δb (Hz)c 3314 ( 2 3380 ( 11 3347 ( 6 3431 ( 5 3349 ( 3 3390 ( 3
Ka (M-1)c ∆Gads (kJ/mol)d 180 ( 28 126 ( 23 153 ( 18 113 ( 8 202 ( 32 158 ( 16
-19.7 ( 0.4 -18.8 ( 0.5 -19.3 ( 0.3 -18.5 ( 0.2 -19.9 ( 0.4 -19.3 ( 0.3
a Uses the value of θmax from ICP measurements to calculate [QD]tot in eq 3. b θmax ) 1-fractional surface coverage of phosphonate ligands (as determined by ICP-AES; see the Supporting Information). c The uncertainty in these values is derived from the standard error of the least-squares nonlinear curve fit, not from performing multiple experiments. d Calculated from Ka ) exp(-∆Gads/kBT), where Ka ) Ka (M-1) × 15.6 M, and 15.6 M is the molarity of our solvent, CD2Cl2. The error is propagated from the uncertainty in Ka.
tion). We denote the fraction of total surface sites available for binding by R-An as θmax (the maximum surface coverage by R-An ligands) in Table 1. The Supporting Information contains the calculations of θmax from the ICP-AES data. In this calculation, we define a “surface site” as any atom within 0.4 nm of the surface; we know from ICP-AES measurements of the elemental ratio Cd/Se that, as observed previously,34 these QDs are cadmium-enriched and that ∼100% of surface sites are Cd2+ ions and, therefore, capable of binding to R-An. We measured the chemical shift of the Ho protons of free R-An, δf, as a function of the concentration of free R-An in solution, [R-An]. The value of δf depended approximately linearly on [R-An] due to hydrogen bonding between R-An molecules; this effect has also been observed in phenols.41 Hydrogen bonding had a more dramatic effect on the observed δf of Ho protons in MeO-An than in Br-An (see the Supporting Information). We attribute this result to the fact that amine
protons of one MeO-An can form hydrogen bonds with either the amine nitrogen or the methoxy oxygen on another MeOAn, whereas amine protons of one Br-An can only hydrogen bond with the amine nitrogen of another Br-An. This hypothesis is supported by the NMR data: we observe that all of the aromatic protons (those ortho to the amine and those meta to the amine group) and the methoxy protons shifted as a function of [MeO-An], whereas only the protons ortho to the amine group shifted as a function of [Br-An]. The Supporting Information contains the fit functions for the calibration curves of δf versus [R-An]. We inserted these fit functions as “δf” in eq 3 for the MeO-An and Br-An trials, respectively. We emphasize that the dependence of δf on [R-An]tot was a minor perturbation to the plots of δobs versus [R-An]tot: the Ho protons shifted a maximum of 2 Hz due to hydrogen bonding and a maximum of 20 Hz due to binding to the QDs, over the concentration range we studied. For each trial, a fit of eq 3 to a plot of δobs versus [R-An]tot yielded values for the fitting parameters, Ka and δb, for that trial (Figure 3 and columns 2 and 3 in Table 1). The derived values of Ka varied between trials for a given R-An, but the average Ka from the two trials was very similar for the two R-An molecules: Ka,avg(MeO-An) ) 153 M-1 and Ka,avg(Br-An) ) 158 M-1. The uncertainty in Ka for a given R-An is not surprising considering the sensitivity of this parameter to the shape of the plot of δobs versus [R-An]tot. We attempted to minimize the noise in these plots by using QDs from the same batch for every measurement in a given trial. This strategy, however, requires that the QDs in some samples age longer than QDs in other samples, and although we minimized exposure of the QDs to air and light, oxidation of their surfaces over the 2 weeks it took to complete a trial is certainly a potential source of error in the observed binding constant. When we convert our values of Ka (M-1) to a unitless Ka by multiplying Ka (M-1) by the activity (which equals the molarity
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TABLE 2: Comparison of Measured and Calculated Adsorption Energies for Various QD-Ligand Systems ligand MeO-An Br-An octadecylamine short-chain alkylamines octadecanethiol trioctylphosphine oxide phosphonic acids
QD
∆Gads (kJ/mol) method reference
CdSe CdSe CdSe CdSe
-19.3 -19.3 -10 -25
NMR NMR NMR PL
CdSe InP
-56 -31
PL 5 DOSY 13 NMR DFT 6, 38, 40
CdSe clusters -62 to -117
this work this work 15 43
in this case) of our solvent, CH2Cl2 (15.3 M),42 and calculate ∆Gads, we obtain values of ∆Gads for the two trials that are within 5% of each other for Br-An and within 8% of each other for MeO-An (Table 1). The calculated average values of ∆Gads for Br-An and MeO-An are identical: -19.3 kJ/mol. In general, these data suggest that the para substituent, R, on the aniline does not affect its ability to bind to CdSe QDs. For reference (see also Table 2), previously measured values of ∆Gads to CdSe QDs are -10 kJ/mol for octadecylamine using NMR (where the octadecylamine was in a competitive equilibrium with pyridine),15 -25 kJ/mol for shorter-chain alkylamines using PL,43 and -56 kJ/mol for octadecanethiol using PL.5 A value for ∆Gads of -31 kJ/mol was found for binding of trioctylphosphine oxide (TOPO) to InP QDs using DOSY NMR.13 Highlevel DFT calculations estimate values of ∆Gads of -62 to -117 kJ/mol for binding of phosphonic acids to CdSe clusters.6,38,40 Binding of R-An Facilitated by Attractive Forces among Phosphonate Ligands. Considering the high surface coverage (∼90%) of tight-binding phosphonate ligands on the QDs and the observation that these ligands are not displaced upon addition of R-An, it is surprising that the steric hindrance provided by the long alkyl chains of OPA and PPA does not prevent R-An from approaching the surface of the QD. To clarify the mechanism of R-An binding, we performed molecular dynamics simulations of the evolution of the QD/R-An system. In these simulations, for simplicity, we assumed that all bound phosphonate ligands are OPA (no PPA). A quantitative comparison with experiments would require a full set of atomistic simulations, which, at present, is computationally unfeasible. This simulation, therefore, uses a simplified coarse-grained model rich enough to qualitatively capture relevant processes. A QD is modeled as a collection of identical beads fixed on the surface of a sphere. An OPA molecule is modeled as a chain of five beads, strongly attracted at one of its ends to the QD surface. Note that the bead diameter corresponds roughly to 0.35 nm, but there is no direct mapping between the number of atoms and the size of the coarse-grained beads. The R-An ligands are represented as pairs of beads connected with a harmonic spring. The interaction energy between R-An ligands and the QD is set to 3kBT, where kB is the Boltzmann constant and T is the temperature. The strength of the attraction between the OPA head groups and the QD surface sites is set to be five times stronger than that between R-An and the QD, that is, 15kBT (we observe no significant migration of the OPA molecules over the surface of the QD during the simulation). The interaction between OPA chains is tuned between 0 and 2kBT per bead within the chain. Solvent effects are treated implicitly by adjusting parameters of the interaction potentials between different types of beads. All simulations were performed with the HOOMD-Blue molecular dynamics package44 on NVIDIA GTX 480 graphics cards. Further details of the model are in the Supporting Information.
Figure 4. (A) Snapshots from molecular dynamics simulations of the chain conformations of OPA ligands on the surface of a 4.2 nm QD for no attraction (left) and a 1kBT per bead attraction (right) between OPA chains. With no attraction, OPA chains form a nearly uniform brushlike coating on the QD that acts as a natural barrier through which R-An molecules must diffuse in order to bind to the surface. As the OPA-OPA attraction is switched on, chains cluster into bundles, opening the space in between. For clarity, R-An ligands (purple and blue) and the OPA chain beads (gold) are shown at 40% of their actual size. The QD contains 612 Cd surface sites (red), 85% of which are bound to OPA. (B) Fractional surface coverage of R-An ligands at equilibrium, as a function of the OPA-OPA interaction strength. Black circles represent simulation data; the red line is a guide for the eye. Molecular dynamics simulations were performed for [R-An]tot:[QD]tot ) 2000:1, for QDs with the same structural parameters as those in (A). The attraction energy between the R-An and the QD was set to 3kBT, and the attraction energy between the OPA and the QD was set to 15kBT.
Our simulation showed that the ability of the R-An ligands to bind to the QD surface is strongly affected by the van der Waals attraction among OPA chains. This OPA-OPA attraction, which results from the slightly higher affinity of OPA molecules for each other than for the CH2Cl2, leads to formation of bundles of bound OPA molecules. As a result, Cd2+ surface sites located between two bundles are exposed to solvent and accessible to the ligand. Figure 4A shows snapshots of the QD-OPA system without any chain-chain interaction (left), and with a moderately strong (1kBT = 2.5 kJ/mol per bead ) 10 kJ/mol per chain) interchain attraction (right). We note that intermolecular van der Waals forces between alkyl chains in a close-packed crystal stabilize a system by 7 kJ/mol per methylene group,45,46 for a total stabilization of ∼50 kJ/mol per chain of OPA. We explored interaction energies significantly lower than 50 kJ/mol per chain because the system is immersed in a solvent that, although more polar than the chains themselves, certainly decreases the stabilization achieved by bundling of the chains. We see from Figure 4 that, without any attraction, OPA chains tend to maximize their entropy and form a uniform, approximately 1.5 nm thick brushlike layer. To reach the QD surface, ligands have to diffuse through the OPA coating, so their ability to bind is suppressed. As the hydrophobicity of the OPA ligands is increased, OPA chains cluster into bundles. This process involves a loss of entropy that is compensated by the enthalpic stabilization gained through a reduction of contact with
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Figure 5. Plots of PL/PL0 vs equilibrium surface coverage of R-An, θ ) [An]b/[QD]tot, where [QD]tot is the total concentration of sites on the surfaces of the QDs, for R ) MeO and Br. We calculated θ using eq S4 (in the Supporting Information) and the measured average values of Ka and δb from Table 1. Inset: the same data (PL/PL0 vs θ) plotted on a linear x axis.
the solvent. Regions between separate bundles open up, revealing surface sites that are now accessible to the R-An molecules. Figure 4B shows the dependence of the equilibrium surface coverage of R-An on the strength of the OPA-OPA attraction. Even for moderate attraction (1kBT per bead), the number of bound R-An ligands increases by 50% over the case in which there is no attraction between the OPA ligands. We note that, in our simulations, it was necessary to study higher ratios of added R-An to QDs than we used in the experiments; for the data in Figure 4, [R-An]:[QD] ) 2000, whereas we measured NMR spectra for mixtures with [R-An]:[QD] ) 25-1025. The ligand-QD interaction is short-range, so in order for a ligand to bind to the surface, it has to diffuse through the solvent into the immediate vicinity of the QD. For a very dilute system, this process is very slow and a molecular dynamics simulation can take a prohibitively long time to reach thermodynamic equilibrium. Separation of the PL Response of CdSe QDs to Added R-An into Contributions from the Binding Isotherm and Electronic Effects. Figure 5 shows a plot of PL/PL0 (where PL0 is the integrated intensity of the PL of a sample with no added R-An) versus θ, the fractional surface coverage of the total QD sites (including those occupied by phosphonates) by R-An ligands. The MeO-An ligands begin to quench the PL of the QDs at θ = 0.002, quench the PL by 50% at θ = 0.003, and (extrapolating to PL/PL0 ) 0) quench the PL completely by θ = 0.1. Because, for these samples, the number of available surface sites, that is, surface sites that are not occupied by phosphonates, is ∼10% of the total number of surface sites, we can conclude that the MeO-An ligands begin to quench the PL of the sample when they occupy ∼2% of available surface sites, quench the PL by 50% when they occupy ∼3% of available surface sites, and completely quench the sample by the time their coverage reaches saturation. The Br-An ligands do not even begin to quench the PL until θ = 0.05 (when they occupy 50% of available surface sites) and, at even saturated coverage, only quench the PL by ∼50%. Clearly, as we suggested in a previous publication8 (but could not prove definitively because we had not yet measured the binding isotherms for the R-An/QD systems), the nonradiative process introduced by binding of MeO-An is much faster than that introduced by Br-An. Now that we have proven that the discrepancy in quenching efficiencies for Br-An and MeO-An is not due to a difference in binding affinity, we can attribute
Donakowski et al. this discrepancy to a difference in the electronic interaction between the R-An ligand and the QD once the ligand is bound at its equilibrium surface coverage. We are currently using timeresolved PL and transient absorption measurements to determine the mechanisms by which these two ligands quench the PL of CdSe QDs. An important conclusion from the data in Figure 5 is that, once the effect of binding is removed from the PL response of the QDs to added aniline, that is, once PL/PL0 is plotted versus θ rather than versus [R-An]tot, the relationship between PL/PL0 and θ is not linear. One, therefore, cannot, in general, use a ligand’s effect on PL (whether it be quenching or enhancement) to construct a binding isotherm for that ligand, unless the function PL/PL0 ) f(θ) is already known. There are reports in the literature of cases where PL/PL0 is linearly related to θ15 and reports where the relationship is decidedly nonlinear.11 One example that highlights the importance of this result is a report by Murphy, et al.,39 who used PL quenching to estimate equilibrium constants for binding of a series of para-substituted anilines to a bulk surface of single-crystal CdSe. They found values of Ka that ranged between 70 and 210 M-1 (very similar to our value of 150 M-1) for most of the R-An ligands they studied. The exception was MeO-An, for which Ka was ∼1000 M-1, based on its higher efficiency of PL quenching. Murphy, et al. suggested, and we have shown here, that the higher quenching efficiency of MeO-An is not due to a higher binding affinity, but rather a more efficient mechanism for PL quenching once bound. We believe, but have not yet proven, that this mechanism is the capture of the excitonic hole (i.e., charge transfer), whereas Br-An quenches by electron trapping. Conclusions We have used 1H NMR spectroscopy to calculate equilibrium constants, Ka, for binding of two para-substituted aniline molecules, MeO-An and Br-An, to 4.1 nm CdSe QDs that are initially passivated with tight-binding alkylphosphonate ligands. The R-An ligands are in fast exchange between free and bound states, and plots of the chemical shift of protons ortho to the amine headgroup of the anilines (Ho, Figure 1) as a function of the [R-An]tot fit to the Langmuir equation (Figure 3). We extract from these fit values for δb, the chemical shift for Ho when the R-An ligand is bound to the surface of a QD, and Ka (Table 1). The identity of the para substituent, R, does not appear to affect the affinity of R-An for the QD surface: Ka ≈ 150 M-1 and ∆Gads ) -19.3 kJ/mol for both MeO-An and Br-An. This result is not surprising in light of (i) Murphy et al.’s report39 (mentioned above) of similar binding constants for a series of p-substituted anilines on bulk CdSe surfaces (except for MeOAn, where the electronic interaction between the ligand and the surface was different), (ii) theoretical predictions that para substitution does not significantly affect the adsorption energies of phenylphosphonic acids or benzoic acids to CdSe clusters,40 and (iii) reports that p-phenylenediamine47 and o-phenylenediamine48 have the same binding constants for binding to CdSe QDs. Molecular dynamics simulations of the R-An/QD systems show that the binding of the R-An ligands is facilitated by bundling of the alkyl chains of the native phosphonate ligands, which, as shown by 31P NMR, are not displaced by R-An ligands, on the surface of the QD; this bundling reveals uncoordinated Cd2+ sites that would otherwise be obscured by the alkyl chains (Figure 4). In addition to mediating ligandexchange processes, ligands have been shown to act cooperatively to increase their binding affinity to a QD surface,49 and to stabilize QD assemblies.50
para-Substituted Aniline Ligands and CdSe QDs Plots of the PL of the QD sample as a function of surface coverage of R-An ligands, which quench the PL of the QDs at sufficient concentration, reveal that (i) the magnitude of PL quenching is not linearly related to the surface coverage of the R-An ligands and (ii) MeO-An introduces a faster nonradiative decay process to compete with radiative recombination than does Br-An (Figure 5). Critical to our analysis of the chemical shift data was the determination of δb, the chemical shift we would observe if every R-An ligand were bound to a QD. There is no way to ensure that a chemical shift observed experimentally corresponds to a fully bound state of the system; our method of including δb as a fitting parameter avoids this uncertainty and minimizes the error in Ka associated with assuming an incorrect value of δb. The differences (δb - δf) that we calculated by fitting our chemical shift data to eq 3 were, on average, 80 Hz for MeOAn and 62 Hz for Br-An, whereas these differences would have been 10 Hz for MeO-An and 16 Hz for Br-An if we had used our highest observed value of δobs as δb. Our method for determining δb and Ka did not directly determine the maximum surface coverage of R-An ligands, but our independent ICPAES measurement of available surface sites yielded a value for [QD]tot that allowed eq 3 to fit our chemical shift data (Figure 3), whereas changing the value of this parameter yielded an unacceptable fit of the data, or unreasonable values for δb. Combining ICP-AES measurements with the NMR measurements was, therefore, critical for determining Ka. The NMR method presented here for measuring binding constants of ligands to small colloids is convenient because it allows optical measurements and measurements of the binding constant to be performed on the same solution-phase samples, whereas other elemental analysis techniques, such as ICP and XPS, require treatment of the sample that disrupts the equilibrium. The NMR technique relies on our ability to spectrally distinguish the signals due to the added ligand from signals due to the native ligands on the QD; aromatic ligands, such as R-An, on QDs passivated by aliphatic ligands, meet this condition. As the variety and sophistication of spectroscopic techniques applied to QD/ligand systems increases, the importance of quantitative estimates of surface chemistry and structure is amplified because, as shown indirectly by the response of the PL of the QDs to
