Quantifying the Thermodynamics of Ligand Binding to CsPbBr₃ Quantum Dots

Abstract

Cesium lead halide perovskites are an emerging class of quantum dots (QDs) that have shown promise in a variety of applications; however, their properties are highly dependent on their surface chemistry. To this point, the thermodynamics of ligand binding remain unstudied. ¹H NMR methods are used to quantify the thermodynamics of ligand exchange on CsPbBr₃ QDs. Both oleic acid and oleylamine native ligands dynamically interact with the CsPbBr₃ QD surface, having individual surface densities of 1.2–1.7 nm⁻². 10-Undecenoic acid undergoes an exergonic exchange equilibrium with bound oleate (K_eq = 1.97) at 25 °C while 10-undecenylphosphonic acid undergoes an irreversible ligand exchange. Undec-10-en-1-amine exergonically exchanges with oleylamine (K_eq = 2.52) at 25 °C. Exchange occurs with carboxylic acids, phosphonic acids, and amines on CsPbBr₃ QDs without etching the nanocrystal surface; increases in steady-state PL intensities are correlated with more strongly bound conjugate base ligands.

Graphical Abstract

The surface matters: The thermodynamics of the surface chemistry of CsPbBr₃ quantum dots is explored using ¹H NMR methods. Ligand exchange was performed with carboxylic acids, amines, and phosphonic acid ligands and it is revealed that upon the addition of amines or phosphonic acid that the photoluminescence of CsPbBr₃ quantum dots is improved.

Quantum dot (QD) properties are heavily influenced by the coordination environment of their surface.^[1] The ligands coordinated to their surfaces affect both the chemical and colloidal stability of the QD, in addition to its ensuing electronic structure. An up-and-coming class of QDs is the colloidal lead halide perovskites (APbX₃, where A = CH₃NH₃⁺, CH(NH₂)₂⁺, Cs⁺; X = Cl⁻, Br⁻, I⁻) because of their excellent optoelectronic properties, such as bright photoluminescence (PL) with narrow spectral line widths that cover a wide color gamut.^[2–4] These properties have made lead halide perovskite QDs intriguing for use in a multitude of optical devices, such as LEDs^[5–7] and solar cells.^[3,8] Unlike the more traditional II-VI QDs, lead halide perovskite QDs are much more ionic in their bonding, including bonding with ligands. Accordingly, polar solvents promote ligand desorption, resulting in loss of colloidal stability and PL quantum yield,^[9] and in some cases, QD dissolution may occur. Because of these challenges, and the relative newness of these QD materials, more in depth and quantitative studies on the surface chemistry of these lead halide perovskite QDs are needed.

De Roo et al.^[10] analyzed the surface ligands of as-prepared CsPbBr₃ QDs synthesized by the prototypical hot-injection method developed by Protesescu et al.,^[11] whereby equal volumes of oleylamine and oleic acid were added after QD purification to promote colloidal stability. They determined, using solution ¹H NMR spectroscopy, that ligand binding is highly dynamic, and that oleylamine selectively binds to the surface as oleylammonium bromide in an NC(X)₂ binding motif. Only in the presence of excess oleylamine added after purification does oleic acid bind to the surface, in the form of oleylammonium oleate. However, as a result of the nearly identical chemical environments of the diagnostic alkenyl protons for both oleylamine and oleic acid, quantitative analysis of the separate native ligands was rendered impossible. Herein, for the first time, we quantify the thermodynamics of ligand binding to CsPbBr₃ QDs using a method developed by Knauf et al. through the use of carboxylic acid, phosphonic acid, and amine-based ligands possessing a terminal vinyl group that is spectroscopically distinct from the internal alkenyl protons of the native oleylamine and oleic acid ligands.^[12] This allows the free and bound fractions of both ligands to be simultaneously tracked, thereby providing valuable thermodynamic data on ligand binding for this important class of QD materials.

The CsPbBr₃ QDs used here were synthesized using a modified hot-injection method as first reported by Protesescu et al.,^[11] with diphenyl ether being substituted for 1-octadecene as the primary reaction solvent as to avoid spectral overlap in the vinylic region of the ¹H NMR spectra (vide infra). To study carboxylate surface binding, CsPbBr₃ QDs were synthesized with oleic acid and dodecylamine, thereby eliminating spectral overlap in the internal alkenyl region of the ¹H NMR spectrum between the native ligands. In contrast to the previous work by De Roo et al.,^[10] no additional ligands were added during or after QD purification. Synthetic details are provided in the Supporting Information. The resulting CsPbBr₃ QDs were characterized by powder X-ray diffraction (XRD) and transmission electron microscopy (TEM) to confirm the orthorhombic phase^[13] and cuboidal morphology of the 12.4-nm QDs obtained through our modified synthesis (Figures S1 and S2a).

A representative solution ¹H NMR spectrum of a suspension of purified CsPbBr₃ QDs is given in Figure 1; as is typical in colloidal QD systems, the resonances corresponding to the coordinated ligands are shifted and broadened relative to that of their free ligand counterparts. We focus specifically on the diagnostic alkenyl region (δ = 5.4–5.9 ppm) of the ¹H NMR spectrum, which allows for ready analysis of oleic acid binding without interference from the saturated amine ligand. Line broadening and a downfield shift are observed in the alkenyl region of oleic acid (δ = 5.73 ppm vs 5.54 ppm for free oleic acid), which implies ligand interaction with the QD surface. Since excess dodecylamine is not present in this system, this result reveals that an excess of amine is not required for oleic acid binding to the CsPbBr₃ QD surface, as has been previously reported (albeit for a slightly different synthesis and purification method).^[10] Additionally, there is a third alkenyl peak (δ = 5.65 ppm) that we assign to physisorbed oleic acid, possessing both a chemical shift and line width intermediate between the chemisorbed and the free ligand peaks. This physisorbed species can be described as being entangled (or interdigitated) in the primary, more tightly bound ligand shell, as has been previously observed with oleic acid bound to CdSe QDs.^[14] To investigate the exchange amongst the three different alkenyl resonances of oleic acid, we utilized selective presaturation, and saturated each ¹H NMR peak (bound, physisorbed, and free) to understand the exchange dynamics between the three states (Figure S3). It was found that when the free peak was saturated, neither the bound nor free peak intensities are altered, implying that the exchange between free and physisorbed or bound oleic acid is slow (i.e., > 2 s). Additionally, it was demonstrated that when the bound proton peak was saturated, the physisorbed proton peak intensity decreased. Conversely, when the physisorbed proton peak was saturated, the bound proton peak intensity decreased. This suggests that exchange between the bound and physisorbed state is happening within a 2 s timescale (see Supporting Information for further discussion). Based on the concentration of CsPbBr₃ QDs determined by UV-vis spectroscopy, the bound oleate surface density was calculated to be 1.2–1.5 oleate nm⁻² by integrating the bound alkenyl resonance of oleic acid against an internal ferrocene standard. Because the ligands bind in a NC(X)₂ motif, we can assume that for every oleate, there is a dodecylammonium ion pair, therefore leading to an overall ligand density of 2.4–3.0 ligands nm⁻², which is similar to the previously calculated theoretical monolayer value of 2.9 ligands nm⁻².^[10]

Figure 1.

¹H NMR spectrum of 12.4-nm CsPbBr₃ QDs (1.6 mM) synthesized with oleic acid (OAc) and dodecylamine (DAm) and dispersed in toluene-d₈ (denoted by *) with a 0.3 μM ferrocene standard. Residual diphenyl ether (DPE) reaction solvent is present after purification. The individual ¹H NMR spectra of oleic acid and dodecylamine in toluene-d₈ are given for comparison.

Diffusion ordered NMR spectroscopy (DOSY) was performed on a suspension of the CsPbBr₃ QDs to gather binding information for oleic acid. The average diffusion coefficient for the peaks in the alkenyl region was 327 μm² s⁻¹ for oleic acid, which is considerably smaller than the value for free oleic acid in toluene-d₈ (610 μm² s⁻¹). The decrease in the diffusion coefficient confirms interaction with the QD surface; however, this diffusion coefficient, as determined by the Stokes-Einstein equation, is higher than what would be expected for a 12.4 nm cuboidal QD. This means that the ligands are fluxional on the CsPbBr₃ QD surface, manifesting as an average diffusion coefficient between various bound and free states. Quantifying the experimentally determined concentrations of the bound oleate ligands gives a bound fraction that typically ranges between 20–30% of the total oleic acid present in the system (for QD concentrations ranging from 1.6–6.1 mM), corroborating our interpretation of the DOSY data.

To obtain more quantitative information about ligand binding to the CsPbBr₃ QD surface, exchange reactions were performed with long-chain carboxylic acid and phosphonic acid ligands that possess a terminal vinyl group. In these studies, the free and bound fractions of both the native and incoming ligands can be quantified, allowing the surface equilibrium and associated thermodynamic parameters to be measured. Upon titration of 10-undecenoic acid into a suspension of CsPbBr₃ QDs at room temperature, the bound and free states of oleic acid (δ = 5.73 ppm bound, 5.54 ppm free) and 10-undecenoic acid (δ = 5.32 and 6.12 ppm bound, 5.13 and 5.90 ppm free) are well resolved in the solution ¹H NMR spectrum. As increasing amounts of 10-undecenoic acid are titrated into the QD suspension, the amount of bound oleate decreases as the amount of bound 10-undecenoate increases (Figure 2a). In addition, the alkenyl peak that is attributed to physisorbed oleic acid sharpens and shifts upfield toward the free oleic acid peak with increasing concentrations of 10-undecenoic acid, as expected (Figure S4a). Quantification of the bound and free fractions of oleic acid and the incoming ligand over the titration series gives an average equilibrium constant K_eq of 1.97 ± 0.10, which is in close agreement with the average K_eq of 1.93 ± 0.08 obtained by plotting [oleic acid_F][10-undecenoate_B] vs [oleate_B][10-undecenoic acid_F] (Figure S5). Addition of free oleic acid to the QD suspension after the titration series with 10-undecenoic acid leads to an increase in bound oleate and a concomitant decrease in bound 10-undecenoate (K_eq ca. 0.75, see Figure S6a and Supporting Information for further discussion), establishing that the exchange is reversible, but not as favorable in the reverse direction. We also observe that the ratio of [oleic acid_F] to [10-undecenoate_B] is 0.94:1.00, which suggests a small amount of 10-undecenoic acid binds to free sites prior to the displacement of oleic acid. The equilibrium constant for exchange with 10-undecenoic acid equates to a ΔG of −1.7 ± 0.1 kJ mol⁻¹, signifying the reaction is exergonic at room temperature. Variable temperature ¹H NMR spectra were acquired between 283 and 325 K on a concentrated suspension (6.1 mM QDs) and a less concentrated suspension (3.2 mM QDs) of CsPbBr₃ QDs with ca. 5 µM of added 10-undecenoic acid. A van’t Hoff plot of these data revealed an endothermic reaction (ΔH = 11.0 kJ mol⁻¹) with a positive ΔS (Figure 2b), indicating that ligand exchange with 10-undecenoic acid is spontaneous at elevated temperatures, including room temperature.

Figure 2.

a) Room-temperature ¹H NMR spectra of 1.6 mM CsPbBr₃ QD suspension possessing oleic acid (OAc) and dodecylamine native ligands, titrated with increasing amounts (0–2.9 µM) of 10-undecenoic acid (UAc) in toluene-d₈, showing both free (F) and bound (B) fractions. (b) Van’t Hoff plot of 6.1 mM and 3.2 mM CsPbBr₃ QD suspension with 5.1 μM and 4.7 μM 10-undecenoic acid, respectively, in toluene-d₈ at temperatures ranging from 283 K to 325 K.

The average ratio of Cs to Pb for the CsPbBr₃ QDs (as determined by energy dispersive X-ray spectroscopy) before and after titration with 10-undecenoic acid (1.00:0.95 and 1.00:0.94, respectively) remains unchanged. In the same way, the energy of band-edge PL emission at 2.42 eV does not change, suggesting there is no etching occurring during exchange (Table S1 and Figure 6a). The relative steady-state PL intensity also does not change after exchange with 10-undecenoic acid (Figure S7a), as expected given that the amount of free oleate to bound 10-undecenoate is ca. 1:1.

Exchange of the native oleic acid with 10-undecenylphosphonic acid was performed under similar conditions. The bound and free states of 10-undecenylphosphonic acid (δ = 5.21 and 5.98 ppm bound, 5.10 and 5.89 ppm free) are well resolved in the solution ¹H NMR spectrum (Figure 3). As increasing amounts of 10-undecenylphosphonic acid are titrated into the QD suspension, the amount of bound oleate decreases as the amount of bound 10-undecenylphosphonoate increases. Unlike exchange with carboxylic acid, however, this exchange is not in equilibrium because the phosphonate displays only a bound peak until a critical concentration of 1 μM phosphonic acid is reached. The relative amount of oleic acid that becomes liberated from the QD surface upon phosphonate binding is 1.35:1, indicating that, on average, more than one proton per incoming 10-undecenylphosphonic acid is being deprotonated as oleic acid is displaced to maintain charge neutrality. The average Cs to Pb composition for the CsPbBr₃ QDs before and after titration with 10-undecenylphosphonic acid was 1.00:0.95 and 1.00:0.93, respectively, which implies no change in the composition of the surface (Table S1). The energy of band-edge PL emission at 2.42 eV does not change, again suggesting that no etching occurs during exchange (Figure S7b). Interestingly, the relative steady-state PL intensity increases with 10-undecenylphosphonic acid addition. The increase of PL may result from irreversible and tighter ligand binding by the 10-undecenylphosphonic acid as compared to the dynamic carboxylic acid binding.

Figure 3.

¹H NMR spectra of 1.8 mM CsPbBr₃ QD suspension possessing oleic acid (OAc) and dodecylamine native ligands, titrated with increasing amounts (0–1.9 µM) of 10-undecenylphosphonic acid (UPAc) in toluene-d₈, showing both free (F) and bound (B) fractions.

We now turn our attention to amine binding to the CsPbBr₃ QD surface. To investigate the amine binding, oleylamine and lauric acid (a saturated carboxylic acid that is absent of any alkenyl protons) were used to synthesize the QDs. This synthetic preparation yielded orthorhombic CsPbBr₃, as before; however, the morphology of the resulting QDs varies slightly from the oleic acid and dodecylamine preparation, forming nanoplatelets rather than cuboids (Figure S2c). This morphology has been previously reported for CsPbBr₃ QDs when using a long chain amine with a shorter carboxylic acid.^[15] Focusing on the alkenyl region (δ = 5.4–5.9 ppm) of ¹H NMR spectrum, there are two distinct peaks for oleylamine (Figure 4 and Figure S4b). The upfield peak corresponds to free oleylamine (δ = 5.55 ppm), while there is a broad downfield peak (δ = 5.68 ppm) corresponding to oleylamine interacting with the QD surface. Based on the concentration of CsPbBr₃ QDs determined by UV-vis spectroscopy, the surface density of oleylamine was then calculated to be 1.4–1.7 oleylammonium nm⁻² by integrating the bound alkenyl resonance of oleylamine against an internal ferrocene standard, suggesting an overall oleylammonium laurate surface density of 2.8–3.4 nm⁻². Oleylamine binds differently than oleic acid as evidenced by there only being two peaks in the alkenyl region, whereas oleic acid had three (i.e., chemisorbed, physisorbed, and free). To further investigate this, DOSY NMR was collected, and the average diffusion coefficient was determined to be 309 μm² s⁻¹, which is significantly smaller than the value for free oleylamine (894 μm² s⁻¹), implying dynamic interaction with the surface.

Figure 4.

¹H NMR spectrum of 12.9-nm CsPbBr₃ QDs (2.5 mM) synthesized with oleylamine (OAm) and lauric acid (LAc) and dispersed in toluene-d₈ (denoted by *) with a 0.3 μm ferrocene standard. Residual diphenyl ether (DPE) reaction solvent is present after purification. The individual ¹H NMR spectra of oleylamine and lauric acid in toluene-d₈ are given for comparison.

To gain insight into exchange processes occurring with oleylamine, an analogous experiment to the aforementioned ligand exchange procedure was performed with undec-10-en-1-amine. Upon titration of undec-10-en-1-amine into the QD suspension, the bound and free states of oleylamine (δ = 5.69 ppm bound, 5.55 ppm free) and undec-10-en-1-amine (δ = 5.17 and 5.79 ppm bound, 5.07 and 5.85 ppm free) are all resolved in the ¹H NMR spectrum. With increasing amounts of undec-10-en-1-amine, the broad alkenyl peak for oleylamine sharpens and gradually shifts upfield into the free oleylamine peak (Figure 5a). This behavior mimics that of the physisorbed oleic acid, leading to the conclusion that the broad peak represents a relatively weakly bound oleylammonium without an accompanying strongly bound fraction. To investigate this further, additional lauric acid was titrated into the QD suspension to see if the excess carboxylic acid would shift the acid/base equilibrium and cause oleylamine to associate more strongly with the surface in an ion pair NC(X)₂ motif. These experiments indeed showed a downfield shift and broadening of the bound oleylamine peak, meaning that the ratio of physisorbed-to-free oleylamine increases with added carboxylic acid (Figure S8b).

Figure 5.

(a) Room-temperature ¹H NMR spectra of 2.5 mM CsPbBr₃ QD suspension possessing oleylamine (OAm) and lauric acid native ligands, titrated with increasing amounts (0–8.0 µM) of undec-10-en-1-amine (UAm) in toluene-d₈, showing both free (F) and bound (B) fractions. (b) Van’t Hoff plot of 4.1 mM and 2.0 mM CsPbBr₃ QD suspension with 7.7 μM and 8.0 μM undec-10-en-1-amine, respectively, in toluene-d₈ at temperatures ranging from 283 K to 325 K.

An average equilibrium constant K_eq of 2.52 ± 0.06 was calculated for amine exchange, which is in close agreement with the average K_eq obtained by plotting [oleylamine_F][undec-10-en-1-ammonium_B] vs [oleylammonium_B][undec-10-en-1-amine_F] (Figure S9). Addition of free oleylamine to the QD suspension after the titration series with undec-10-en-1-amine leads to an increase in bound oleylammonium and a concomitant decrease in bound undec-10-en-1-ammonium (K_eq ca. 0.5, Figure S6b), suggesting that the exchange is reversible, but not as favorable in the reverse direction. The equilibrium constant for amine exchange gives a ΔG of −2.1 ± 0.1 kJ mol⁻¹ at room temperature, signifying the reaction is favorable, as with the carboxylic acid exchange reaction. Variable temperature ¹H NMR spectra were acquired between 283 and 325 K on a concentrated (4.1 mM QDs) and less concentrated (2.0 mM QDs) suspension of CsPbBr₃ QDs with ~8 µM added undec-10-en-1-amine. A van’t Hoff plot of these data yielded an average ΔH = −15.9 kJ mol⁻¹ and a negative ΔS, which implies that this reaction will become less spontaneous with increasing temperature. While the enthalpy and entropy terms are opposite in sign to the exchange reaction with carboxylic acid, both ligand exchange processes are overall favorable at room temperature.

The average ratio of Cs to Pb for the CsPbBr₃ QDs synthesized with oleylamine before and after titration with undec-10-en-1-amine remained 1.2:1.0 (Table S1), and the energy of the band-edge steady-state PL emission at 2.41 eV does not change, suggesting that no etching occurs during ligand exchange. However, there is an increase in the PL intensity after titration with undec-10-en-1-amine (Figure S7c), which may be a result of tighter carboxylate binding at higher amine concentrations due to a shift in the acid-base equilibrium, which has been previously observed.^[10] To further investigate, CsPbBr₃ synthesized with oleic acid was titrated with dodecylamine to see if the excess amine would have any effect on the alkenyl region of oleic acid, and indeed, there is an increase in the bound fraction of oleate ligands correlating with an increase in PL intensity upon dodecylamine addition (Figure S8a and Figure S10).

In summary, we studied the surface chemistry of CsPbBr₃ QDs capped with oleic acid and oleylamine native ligands. Ligand exchange reactions for carboxylic acids, amines and phosphonic acids were performed on CsPbBr₃ QDs. Using ¹H NMR spectroscopy, we determined thermodynamic parameters for carboxylic acid and amine exchange with the native ligands, and it was determined that both reactions are in dynamic equilibrium. In contrast, phosphonic acid irreversibly exchanges the native oleate ligands, resulting in tightly bound phosphonate. The quantitative investigation of ligand exchange parameters via NMR methods gives needed insight into the surface chemistry of CsPbBr₃ QDs, allowing for better understanding of the effects of carboxylic acids, amines, and phosphonic acids on the optoelectronic properties of these QDs. Indeed, consistent with prior empirical observations,^[16,17] we have demonstrated that more strongly bound conjugate base ligands correlate with increases in steady-state PL intensity. This may be a result of the more strongly bound ligands in this ionic system (with a higher on:off ratio) better passivating surface defects and reducing surface-trap-assisted quenching.^[18] It is expected that this method can be utilized to study ligand binding for other lead halide perovskite QDs, with varying A-site cations and X-site anions, in future studies.