Tuning the Binding Energy of Surfactant to CdSe Nanocrystal: A

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Tuning the Binding Energy of Surfactant to CdSe Nanocrystal: A Theoretical Study Haitao Liu* Department of Chemistry, Columbia UniVersity, 3000 Broadway, New York, New York 10027 ReceiVed: September 16, 2008; ReVised Manuscript ReceiVed: January 03, 2009

The effect of substituent group on the binding energy of phosphonic and carboxylic acids to the Cd6Se6 cluster was studied within density functional theory. The binding energies of 12 para-substituted phenylphosphonic acids, 5 para-substituted benzoic acids, and 5 para-substituted benzoates to the Cd6Se6 cluster were calculated. For all the three types of surfactants, a linear correlation was observed between the calculated binding energy and the substituent constant of the functional group. Electron-donating groups increase the binding energy, while electron-withdrawing groups decrease it. The range of binding energy one can adjust by changing the functional group is about 3 kcal mol-1 for both phenylphosphonic acids and benzoic acids and about 12 kcal mol-1 for the benzoates. Such tunability of the surfactant binding energy offers a novel method to control the nucleation and growth kinetics of CdSe nanocrystals. Introduction The use of organic surfactants to control the growth of colloidal nanocrystals has had tremendous impact on the field of nanocrystal synthesis. This approach has been used to make a wide range of nanocrystals, including metallic,1-3 oxide,4,5 and semiconductor6-10 ones, with controlled size and shape. Most surfactants used in these syntheses consist of a polar functional end group (e.g., -COOH, -PO3H2, -NH2), which binds to the nanocrystal surface, and a long alkyl chain (usually C6-C18), which provides steric hindrance to prevent the aggregation of nanocrystals. The surfactant plays an important role in the nanocrystal synthesis by controlling the nucleation and growth kinetics.6 To make monodispersed nanocrystals, the reaction should produce a burst of nucleation events which is followed by slow growth. In addition, the surfactant also determines the shape evolution of the nanocrystal by binding to different crystal facets with different affinity.11-13 To achieve good control over the nanocrystal size and shape, the surfactant used in the synthesis should have the “right” binding energy to the nanocrystal. If the surfactant binds to the nanocrystal too strongly, nucleation and growth would be too slow; however, if the surfactant binds too weakly, it would be difficult to control the reaction. Unfortunately, there is no simple rule to predictably select a surfactant with the ‘right’ binding energy for a given synthesis. When designing a new nanocrystal synthesis, trial-and-error is often the only way to screen a large number of potential surfactants in order to find the balance between nucleation and growth. In addition, there is no known way to independently control the nucleation and growth kinetics, which makes it very difficult for experimentalists to rationally improve a known synthesis by adjusting the two kinetic processes. For example, changing the reaction temperature not only changes the nucleation and growth kinetics but also changes the diffusion constants of the reagents, the viscosity of the reaction mixtures, the rate of monomer production, and the relative stability of * To whom correspondence [email protected].

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different crystal phases. Complications like this make it almost impossible to design nanocrystal syntheses with predictable outcomes. A simple way to independently fine tune the nucleation and growth kinetics is by adjusting the binding energy of the surfactant to the nanocrystal surface. In theory, binding energy can be adjusted simply by changing the end functional group of the surfactant that binds to the nanocrystal. In reality, however, changing the end functional group of the surfactant is not desired for a number of reasons. First of all, there is only limited number of functional groups (e.g., -COOH, -PO3H2, -NH2, -SH, -PR2) that one can choose from. The binding energy of functional groups differs very much from one to the other.11-13 As a result, small changes of binding energy could not be realized by changing the functional group of the surfactant. Second, changing the functional group also significantly changes the relative affinity of the surfactant to different crystal facets, which could completely change the shape evolution of the nanocrystals.11-13 Such change makes the experimental outcome very unpredictable. Finally, the chemistry of the nanocrystal synthesis could also be changed when a different type of surfactant is used. Recent studies14-16 have demonstrated that, in many cases, the surfactant molecule is not only a protecting agent for nanocrystals but also a required reagent for the formation of the nanocrystals itself. Changing the end functional group of the surfactant could potentially change the whole underlying chemistry of the nanocrystal synthesis. I suggest that the binding energy of the surfactant can be predictably tuned by installing an inert (i.e., no affinity for the nanocrystal) substituent group onto the surfactant, while keeping the end functional group of the surfactant intact. To demonstrate this concept, I have carried out density functional theory (DFT) calculations to evaluate the effect of the substituent group on the binding energy of para-substituted phenylphosphonic acids, para-substituted benzoic acids, and para-substituted benzoates to a Cd6Se6 cluster. The results show that electron-donating groups on the benzene ring increase the binding energy of the surfactant, while electron-withdrawing groups decrease it. A linear correlation was observed between the calculated binding energy and the substituent constants of the functional groups

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Binding Energy of Surfactant to Cd6Se6 Cluster

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Figure 1. Optimized structures of (A) the Cd6Se6 cluster, (B) para-substituted phenylphosphonic acid (X ) H), (C) para-substituted benzoic acid (X ) H), (D) Cd6Se6-phenylphosphonic acid complex, and (E) Cd6Se6-benzoic acid complex.

on the benzene ring. By choosing different substituent groups, the binding energy of the neutral surfactant could be tuned almost continuously within about 3 kcal mol-1. In the case of benzoates, the binding energies showed much stronger dependence on the substituent group and can be tuned within about 12 kcal mol-1. At 250 °C, a typical temperature for CdSe nanocrystal synthesis, an increase (decrease) of 3 kcal mol-1 in the binding energy corresponds to a 2 times increase (50% decrease) in the surfactant binding equilibrium constant. Theoretical Methods All calculations were carried out using the pcGAMESS program17 at the B3LYP18-21 level of theory. The following basis sets22 were used: LANL2DZ basis augmented with polarization functions and the associated effective core potential (ECP) for all post-first-row atoms;23-26 the 6-31G* basis for H and first row atoms.27 For the calculations involving anionic ligands, the 6-31G**++ basis set was used for H and the first row atoms,27-29 and the LANL2DZDP23 basis set and the associated ECP was used for the post-first-row atoms. The molecular geometries were relaxed in vacuum without constraint until the maximum energy gradient was smaller than 5 × 10-5 hartree/ bohr. Frequency calculation was performed at the same level of theory to confirm that the obtained geometry is a minimum. The binding energy was calculated as Ebinding ) Ecomplex - ECd6Se6 - Esurfactant, where Ebinding, Ecomplex, ECd6Se6, and Esurfactant are the binding energy of the surfactant, energy of the Cd6Se6-surfactant complex, energy of the Cd6Se6 cluster, and energy of the free surfactant, respectively. Basis set superposition error (BSSE) is not corrected in these calculations. This should not affect our conclusion since BSSE should be very similar for the same class of surfactant and our analysis is based on the relative difference, instead of the absolute value, of the binding energy. Results and Discussion The large size of a typical CdSe nanocrystal makes it computationally expensive to model its interaction with surfactant molecules at the DFT level. Previously, this problem was circumvented by substituting the CdSe nanocrystal with either a smaller CdSe cluster13 or a slab of bulk CdSe crystal.11,12 I choose to study the binding of surfactant to a Cd6Se6 cluster in lieu of a much larger CdSe nanocrystal on the basis of the following arguments. First, a previous study showed that the binding energy of surfactant to the CdSe cluster does not differ

much with respect to the cluster size, at least for the case of phosphonic acid.13 In addition, the current study focuses on the binding energy change upon changing the substituent group of the surfactant, which should be even less sensitive to the size of the cluster. Finally, small clusters play an important role in the nucleation of CdSe nanocrystals.30,31 Understanding and controlling the binding of surfactant to a small CdSe cluster will provide valuable insight to the nanocrystal nucleation process. The binding energies of 12 para-substituted phenylphosphonic acids and 5 para-substituted benzoic acids to the Cd6Se6 cluster were calculated at the B3LYP level of theory. Figure 1 shows the optimized structures of the Cd6Se6 cluster, phenylphosphonic acid, benzoic acid, and the two surfactant-Cd6Se6 complexes. For both surfactant systems, the surfactant binds to one of the Cd atoms of the Cd6Se6 cluster using its oxygen atom while the acid proton points to one of the adjacent Se atoms. Consistent with previous results, the current study found that the binding energies of phosphonic acids are higher than their benzoic acid counterparts.11-13 The binding energy of the surfactant can be systematically changed by installing functional groups onto the benzene ring at the para position. Relative to the hydrogen atom, electronwithdrawing groups decrease the binding energy, while electrondonating groups increase it. This trend can be understood by analyzing the interaction between the surfactant and the Cd6Se6 cluster. The dominating interaction between the Cd6Se6 cluster and the surfactant is the partial electron donation from the double-bond oxygen atom to the surface Cd atom. Functional groups on the benzene ring modulate the electron density of the oxygen atom through inductive and resonance effects mediated by the aromatic ring. As a result, electron-donating groups increase the binding interaction while electron-withdrawing groups decrease it. The correlation between the reaction equilibrium and the change in the molecular structure has been systematically studied in the field of physical organic chemistry. It has been well established that the electron-donating or electron-withdrawing ability of most functional groups can be quantitatively described by their substituent constants.32,33 Relative to the hydrogen atom, electron-withdrawing groups have positive substituent constants while electron-donating groups have negative substituent constants. In this case, plotting the calculated binding energy as a function of the substituent constant (Hammet plot) clearly shows a linear correlation (R2 > 0.97) between the two (Figure 2).

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Figure 2. Effect of functional group on the binding energies of para-substituted (A) phenylphosphonic acids and (B) benzoic acids to the Cd6Se6 cluster. The lines are linear fit of the data. The slops of the fits are 1.96 ( 0.07 and 2.21 ( 0.18 for A and B, respectively.

Figure 3. (Left) Effect of functional group on the binding energies of 5 para-substituted benzoates. The line is the linear fit of the data (R2 > 0.98). The slope of the fit is 8.24 ( 0.41. (Right) Optimized structures of benzoate, the Cd6Se6 cluster, and the Cd6Se6-benzoate complex.

The highly linear correlation suggests that it is possible to predictably and almost continuously adjust the binding energy of the surfactant to the CdSe nanocrystal by changing the functional group on the benzene ring. The known substituent constants range from -0.66 for -NH2 to 0.90 for -SO2OR and -+SMe2.32 This range of substituent constants translates into a range of binding energy from about -28 to -25 kcal mol-1 for para-substituted phenylphosphonic acids and from about -22.5 to -19.5 kcal mol-1 for para-substituted benzoic acids. In contrast, by changing the end functional group from phosphonic acid to carboxylic acid, one can only obtain two discrete binding energies: -26.97 kcal mol-1 for phenylphosphonic acid and -21.19 kcal mol-1 for benzoic acid. A very recent study suggested that both deprotonated and neutral surfactants bind to CdSe nanocrystal during its growth.34 In light of this suggestion, I have also modeled the binding of para-substituted benzoates to the Cd6Se6 cluster. Unlike the case of benzoic acid, the binding of benzoate severely distorts the structure of the Cd6Se6 cluster (Figure 3). The benzoate binds to a surface Cd atom with both oxygen atoms. One of the neighboring Se atoms moves away from the bound Cd atom. Figure 3 shows the binding energies of 5 para-substituted benzoates to the Cd6Se6 cluster. Depending on the substituent, the binding energies of the para-substituted benzoates are about 30-40 kcal mol-1 larger than their neutral counterparts. For example, the binding energy of benzoate is -59.02 kcal mol-1, while that of benzoic acid is only -21.19 kcal mol-1. The effect of the substituent group on the binding energy was found to be the same as in the case of neutral ligands, i.e., the electronwithdrawing groups decrease the binding energy, while the electron-donating groups increase it. The range of the binding energies one can adjust by changing the substituent group is much wider for the benzoates (∼12 kcal mol-1) than for the

SCHEME 1: Proposed Synthesis of 3-Alkyl-4-X-benzoic acid: (i) NBS, (ii) Pd-PEPPSI-IPr,35 R-9-BBN, R ) alkyl, X ) NO2, CN, CF3, COOCH3, F, Cl, H, CH3, OCH3, NR2, etc.

benzoic acids (∼3 kcal mol-1). This indicates that, compared with the benzoic acids, the electron density of the oxygen atoms of the benzoates is more susceptible to the perturbation of the substituent group on the benzene ring. Though computationally convenient, the model compounds used in the calculation are not suitable for the nanocrystal synthesis. These model compounds do not have the long alkyl chain that protects the nanocrystal from aggregation. This issue can be easily addressed by installing a long alkyl chain onto the benzene ring in the meta position while adjusting the binding energy by changing the substituent in the para position. Scheme 1 shows just one of the many possible synthetic pathways to prepare a library of such surfactants. Bromination of the commercially available para-substituted benzoic acid 1 gives bromide 2, which can be alkylated with alkyl-9-BBN35 to give the desired poly substituted benzoic acid 3. With single substituent at the para position, the range of binding energy one can adjust is about 3 kcal mol-1 for both benzoic acids and phenylphosphonic acids and about 12 kcal mol-1 for benzoates. At 250 °C, a typical temperature for nanocrystal synthesis, an increase (decrease) of 3 kcal mol-1 in the binding energy corresponds to a 2 times increase (50%

Binding Energy of Surfactant to Cd6Se6 Cluster decrease) in the surfactant binding equilibrium constant. A similar degree of tunability in the nucleation and growth kinetics is expected by employing these surfactants in the CdSe nanocrystal synthesis. The above estimate assumes that the change of entropy for the surfactant binding event is the same for the same type of surfactant. The binding energy can be extended to an even wider range by installing multiple functional groups onto the benzene ring. I now discuss the limitations of the present study. First of all, all the calculated binding energies are between a single surfactant molecule and a rather small CdSe cluster in vacuum. This simple model does not take into account the collective electronic effects of a closely packed surfactant monolayer, which is expected to form on a real nanocrystal surface. In a similar vein, steric interaction between the close packed surfactant molecules is not modeled in the current study. These two effects can be taken into account by modeling the nanocrystal as a slab of bulk CdSe crystal. It remains to be seen, however, whether the linear correlation between the binding energy and the substituent constant will hold in the slabbased calculation. Second, solvation effect was not modeled in the current study. Solvation energy will be especially large in the case of anionic ligands. The lack of solvation energy in the calculation may artificially increase the calculated binding energies for the benzoates. One unique advantage of the molecular model, compared with the slab-based model, is the possibility to calculate solvation energy in various solvents.36 Conclusion I have shown that the binding energies of phenylphosphonic acids, benzoic acids, and benzoates to the Cd6Se6 cluster can be fine-tuned by introducing functional groups onto the benzene ring. There exists a linear correlation between the binding energy and the substituent constant of the functional group. By changing the binding energy of the surfactant, one can presumably adjust the nucleation and growth kinetics of CdSe nanocrystal in a controlled, predictable manner. Precise control of these two kinetic processes will be useful in designing new nanocrystal synthesis as well as improving existing ones. Acknowledgment. The author thanks Professor Martin P. Head-Gordon for helpful discussion and Dr. Jeffery C. Grossman for providing computational resources. References and Notes (1) Burda, C.; Chen, X. B.; Narayanan, R.; El-Sayed, M. A. Chem. ReV. 2005, 105, 1025–1102. (2) Jana, N. R.; Peng, X. G. J. Am. Chem. Soc. 2003, 125, 14280– 14281. (3) Murphy, C. J.; San, T. K.; Gole, A. M.; Orendorff, C. J.; Gao, J. X.; Gou, L.; Hunyadi, S. E.; Li, T. J. Phys. Chem. B 2005, 109, 13857– 13870. (4) Jana, N. R.; Chen, Y. F.; Peng, X. G. Chem. Mater. 2004, 16, 3931– 3935.

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