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2006, 110, 12211-12217 Published on Web 06/03/2006
On the Origin of a Permanent Dipole Moment in Nanocrystals with a Cubic Crystal Lattice: Effects of Truncation, Stabilizers, and Medium for CdS Tetrahedral Homologues Sachin Shanbhag†,‡ and Nicholas A. Kotov*,†,§,| Departments of Chemical Engineering, Biomedical Engineering, and Materials Science and Engineering, UniVersity of Michigan, Ann Arbor, Michigan
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ReceiVed: February 21, 2006; In Final Form: May 13, 2006
A large anomalous dipole moment has previously been reported for nanocrystals with a cubic crystal lattice. By considering truncations of a regular tetrahedral CdS nanocrystal, the hypothesis that shape asymmetry is responsible for the observed dipole moment was tested and verified. The location and degree of the truncations were systematically varied, and corresponding dipole moments were calculated by using a PM3 semiempirical quantum mechanical algorithm. The calculated dipole moment of 50-100 D is in good agreement with a variety of experimental data. This approach also affords simple evaluation of the potential effect of the media for aqueous dispersions of nanocrystals. The substitution of the truncated corner(s) by molecules of H2O typically results in a substantial increase of the dipole moment, and often, in the reversal of its direction. The molecular modeling approach presented here is suitable for detailed theoretical studies of the dipole moments of II-VI and other nanoparticles and interparticle interactions in fluids. The data obtained from these calculations can be the starting point for modeling of agglomeration and self-organization behavior of large nanoparticle ensembles.
Introduction Substantial progress has been made in describing transport and quantum mechanical phenomena in nanocrystals (NCs) over the past few years.1,2 As a result, one can now consider complex one-, two-, and three-dimensional systems of nanoparticles engineered to the specifications of a particular device. This inevitably brings up the need to understand the nature and magnitude of interparticle interactions and new effects due to nanoscale dimensions of the particles. Forces acting between the particles determine their assembly properties, interactions with other nanoscale entities, and methods of manufacturing and integration into nanoscale devices. Within this scientific realm, an important fundamental question is the origin of the dipole moment (DM) in semiconductor NCs with a cubic crystal lattice. The polar character of semiconductor NCs has been reported,3-5 but its nature remains elusive. The DM is the governing factor responsible for the assembly of NCs into structures such as nanowires and potentially more complex entities.6-10 It is also the primary property that regulates interactions with other nanoscale species such as proteins, as well as the thermodynamics of charge-transfer processes. A size-dependent permanent DM of about 40-100 D has been reported for wurtzite CdSe NCs with diameters of 2.7* Corresponding author. Present address: Chemical Engineering Department, University of Michigan, 3074 H.H. Dow, 2300 Hayward St., Ann Arbor, MI, 48109-2136. Phone: 734-763-8768. Fax: 734-764-7453. E-mail:
[email protected]. † Department of Chemical Engineering. ‡ Present address: 3074 H.H. Dow, 2300 Hayward St., Ann Arbor, MI, 48109-2136.Phone: 734-764-7487.Fax: 734-764-7453.E-mail:
[email protected]. § Department of Biomedical Engineering. | Department of Materials Science and Engineering.
10.1021/jp0611119 CCC: $33.50
5.6 nm.3,4 Measurements on CdSe nanorods have also reported a permanent DM that is proportional to the volume of the nanorod.5 These observations have been explained by calculations based on semiempirical pseudopotential methods,11 atomistic simulations,12 and deviations from ideal lattice structure.13 In essence, the origin of the DM has been ascribed to the intrinsic polar character of the wurtzite lattice based on the agreement between DM due to a NC and bulk polarization values.4 Transmission electron microscopy images have revealed CdSe NCs to be highly faceted with a C3V point group symmetry.14 While a DM may be expected for wurtzite NCs, it ought to be absent in cubic NCs, such as ZnS, CdS, ZnSe, PbSe, and CdTe, that have a Td point group symmetry and have been observed to form tetrahedral nanocrystals.15,16 However, on the basis of dielectric dispersion studies, Shim and Guyot-Sionnest found that ZnSe NCs exhibit a size-dependent DM as high as 40-60 D for NCs with a diameter of 3.3-4.8 nm.4 Similarly, dipolar interactions were conjectured to be responsible for the self-assembly of cubic PbSe NCs into nanowires.6 The difference in electronegativity between Pb and Se results in some of the facets of the growing PbSe NC being polar. On the basis of a random distribution of polar facets, Cho et al. showed that almost 90% of the supposedly centerosymmetric PbSe NCs are polar.6 Using a simple 2D lattice, Shim and Guyot-Sionnest argued that a minor deviation in the shape of a centerosymmetric NC could induce a DM but that not all asymmetric shapes would satisfy the observed linear variation of the DM with the size of the NC.4 Only NCs with neutral facets, or with polar facets whose area does not vary with the size of the NC, are consistent with the linear dependence.4 © 2006 American Chemical Society
12212 J. Phys. Chem. B, Vol. 110, No. 25, 2006 While these studies suggest that the DM could originate from shape asymmetry, they do not calculate its actual magnitude, or consider the influence of the stabilizing shell. In this study, we corroborate the ideas proposed in the previous papers by quantitatively demonstrating that relatively small deviations from the classical tetrahedral shape of a NC with a cubic crystal lattice can give rise to large values of DM. In essence, “incomplete versions” of tetrahedrons remove the symmetry constraints of cubic lattices. For instance, replacement of a corner of a tetrahedral NC with a flat crystal face lowers its symmetry from the Td to C3V point group, and imparts a significant polar character. In this study, the effect of shape asymmetry on cubic NCs is systematically investigated, using CdS as a model semiconductor. The obtained DM values correlate well with experimental data. The genesis of the DM phenomenon in small particles with presumably centrosymmetric atomic packing should be applicable to any binary cubic semiconductor. The approach described here is simple and convenient for the investigation of a variety of interparticle interactions that depend on the nonideal 3D structure of the nanoscrystals. Method To study the contribution of shape asymmetry to the DM, we considered a prototypical tetrahedral CdS nanocrystal with 84 cadmium atoms and 123 sulfur atoms as the base for calculations (Figure 1a). It is structurally analogous to the tetrahedral clusters of II-VI semiconductors, previously reported by Weller’s group,16,17 that were made in aqueous solutions with thiolic stabilizers necessary to satisfy unsaturated valences of metal ions on the surface. For simplicity, the atomic model assumes that the Cd ions are capped by S-H groups instead of S-R groups, where R is an organic group, resulting in a stoichiometric composition of H64Cd84S123-14. One can demonstrate that the reduction of the stabilizer molecules to a hydrogen atom has a relatively small effect on the DM, while considerably speeding up the calculation (a more detailed discussion of the effect of the stabilizer groups is given in the Results and Discussion section). The atomic pattern of the attachment of simplified capping groups is identical to that observed for organic thiols on the surface of tetrahedral crystals of CdS.18 While a variety of potential defects are possible, a probable deviation from the ideal geometric shape of a tetrahedron is the truncation of apex(es), which leads to lowering of the surface energy associated with the NC. Therefore, from an atomic perspective, clusters with truncated apexes could possess some thermodynamic advantage and, in fact, could be quite abundant in polar solvents. Therefore, a systematic progression of tetrahedral NCs with gradually varying degree and placement of truncation was evaluated in this work. The simplest case in this series is a NC in which one of the four corners of the regular tetrahedron is modified by deleting a Cd and S atom. The resulting NC, C1T1, is depicted in Figure 1b. Note that three sulfur atoms from the layer below the truncated apex are exposed. Parts c, d, and e of Figure 1 show NCs C2T1, C3T1, and C4T1 from the same progression that are similarly truncated at two, three, and four corners, respectively. Starting from C1T1 (Figure 1b), an increasing number of atomic layers were removed from a single corner to study the effect of the degree of truncation. The three exposed sulfur atoms at the truncated corner in C1T1 were deleted to obtain C1T2, which exposed three Cd atoms (Figure 1f). Deleting these three Cd atoms resulted in C1T3, which, in turn, exposed 7 S
Letters atoms (Figure 1g). The last model system in this family, C1T4, was obtained by removing these 7 S atoms (Figure 1h). As the reader may already understand, the labels assigned to the various asymmetric molecules have a general format CmTn, where m is the number of truncated corners and n is the number of layers removed from a corner. The software package Spartan (Wavefunction Inc., Irvine, CA) was used in all calculations. After building up the atomic model of a NC, its geometry was first optimized by using the Merck molecular force field (MMFF). The net formal charge on the molecule was calculated from the stoichiometry by associating H, Cd, S, and O with a charge of +1, +2, -2, and -2, respectively. For simplicity, we treated the two parameters, charge and DM on a NC, as independent entities. Since both of them are related to the structure of the truncated crystals, they may be interconnected, although no simple dependence can be observed at the moment. This issue is relegated to further studies. In this respect, we want to note that the mere presence of charge does not necessarily lead to a DM; rather, it requires that charge be distributed anisotropically. However, for anisotropic distributions, the magnitude of the DM depends on the excess charge, which may be modulated by the stabilizer. The optimization algorithm varied the bond lengths and angles to find the lowest energy structure. Using the equilibrium geometry, we used the single point energy mode to compute the DM using the semiempirical parameter model 3 (PM3) method, which typically gives good estimates of DM for inorganic structures with transition metals. Other methods capable of quantum mechanical calculations involving transition metal atoms/ions, such as density functional theory (DFT), can be potentially used as well. However, they are substantially more time consuming (orders of magnitude longer) and often have difficulties dealing with the large number of atoms required to adequately describe NCs. The PM3 method also has a limitation on the number of atoms involved (ca. 600 atoms) but is quite fast and gives, as we shall see, a very reasonable assessment of the DM in nanocrystals. Results and Discussion A. Effect of Capping Group. MMFF-optimized geometry yields the volume of the complete tetrahedral NC (C0T0) as 3.625 nm3. It corresponds to a regular tetrahedron with an edge length of 3.1 nm. The classical CdS tetrahedron exhibits a small DM of 8.82 D. From symmetry, we expect this molecule to be nonpolar. The apparent discrepancy can be resolved by taking into account the presence of the stabilizing shell. We hypothesized that this DM (which is relatively small compared to expected values in the range 50-100 D) originates from the orientation of the S-H bonds on the surface of the NC. To test the hypothesis, a core NC (see Figure 2) without terminal hydrogen atoms was constructed. The DM of this core NC (Cd84S123-78), when calculated using an identical calculation scheme, was 0.01 D. This supports the claim that the small DM obserVed in the base NC C0T0 is due to the orientation of the S-H capping groups. To check the dependence of the DM of a defect-free cubic NC on the length of the capping group R, we set the terminal group S-R to be S-H, S-CH2CH3, and S-CH2CH2CH3. Due to the limitations of the software (Spartan), we could not calculate the DMs of CdS clusters containing long stabilizer molecules and large cores at the same time. Therefore, we used a cubic NC with a smaller core (Cd8S17) for this exercise (Figure 3). The DMs of the NC with the terminal groups S-H, S-CH2CH3, and S-CH2CH2CH3 were 5.7, 8.6, and 8.1 D, respectively.
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Figure 1. (a) Regular tetrahedral CdS NC with S-H terminal groups. The molecule is depicted using a space-filling representation: S (teal); Cd (green); H (gray). Starting from the (a) base NC, (b) one, (c) two, (d) three, and (e) four corners were truncated to obtain NCs denoted as C0T0, C1T1, C2T1, C3T1, and C4T1, respectively. Starting from C1T1, the truncated clusters (f) C1T2, (g) C1T3, and (h) C1T4 were obtained. The inset in each figure depicts the direction of the DM schematically, pointing from the positive end toward the negative end. Filled/unfilled circles represent untruncated/truncated corners of the tetrahedron.
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Figure 2. Core nanocrystal without S-H terminal groups. The molecule is depicted using a space-filling representation: S (teal); Cd (green).
It appears that, for ideal CdS NCs with S-R capping groups, the DM is not strongly influenced by the length of the capping group. Taking into account the fact that the stabilizers do have their own dipole moment, there are two important points to make regarding this observation. (1) Dipole moments of the stabilizer molecules largely cancel each other because they are pointing to opposite directions on different sides of the NC. Having said that, one also needs to remember that truncation destroys the symmetry and, therefore, completeness of the dipole moment cancellation, which can potentially lead to truncation-dependent stabilizer contribution to the total DM. (2) The stabilizer effect should be more noticeable in smaller nanoparticles, such as the one we calculated here, because the overall percentage of atoms in the organic shell is the highest in this case. Thus, we do not believe that ideal tetrahedrons of different structure would display variable DMs for the same stabilizers beyond a few debyes. Congruent nanocrystals from other semiconductors are likely to behave similarly. It needs to be emphasized though that the actual geometry of the seemingly similar compounds is to be carefully verified when extending these considerations to other nanocolloids. B. Location of Truncations. Truncation of one of the corners increases the DM dramatically (Figure 4a). However, NCs with two or three truncated corners did not reveal further change, and the dipole moment remained around 60 D. The DM arises due to the asymmetry in electron distribution caused by the atoms in existing (nontruncated) corners. When all corners are present, the polarity vectors are compensated. As soon as one corner is missing, the vectorial sum of three other contributions gives rise to a strong dipole moment. For a simple truncation model in Figure 1, one can see that the corners truncated by the plane with S atoms are analogous to electron acceptor groups
Letters in simple compounds because the missing corner corresponds to the negative end of the DM. As expected, the cases of one and three truncations, that is, C1T1 (Figure 1b) and C3T1 (Figure 1d), are symmetrically alike. The missing three corners can be treated as polarity vectors of opposite sign, as in the case of C1T1, and thus, their sum has an opposite direction and almost identical value (Figure 4a). The appearance of the dip in the DM for C1T2 (Figure 4a) is also quite clear from this phenomenological model. Two instead of three vectors as for C1T1 and C1T3 are added together, and partially compensate each other. The DM direction for C1T2 is parallel to the axis of symmetry, passing through the side connecting the truncated corners (Figure 1c). C. Size of the Nanocrystal. Previous experimental studies have reported that the magnitude of the DM increases with the size of the NC.3-5 Indeed, Shim and Guyot-Sionnest found that the DM varies linearly with the core radius of the NC for both CdSe, which has a wurtzite crystal lattice, and ZnSe, which is a cubic NC.4 To ascertain this linear correlation between the DM and the core radius (or equivalently, the cube root of the volume of the NC), we created a series of NCs similar to the prototypical NC C0T0 (H64Cd84S123) described in Table 1 and depicted in Figure 1a. As shown in Table 2, this series is denoted with the label c0t0, and the size of the NC increases from c0t0.A to c0t0.D. Note that the prototypical NC C0T0, described earlier, represents the next member in this series. As observed earlier in the case of C0T0, the DMs of these untruncated NCs are nonzero (Figure 5). However, they are still relatively small, with magnitudes of less than 10 D with no observable dependence on size. This definitely differentiates CdS and other cubic crystals from the analogous nanoparticles in the hexagonal phase and confirms that in order to observe size dependence of DM one should include a specific truncation. The simplest truncation of C0T0 was C1T1 (Table 1 and Figure 1b), in which a Cd-S-H group was eliminated from an apex. In an analogous manner, we modified each member of the c0t0 series to yield the corresponding truncated NC. This series of truncated NCs was labeled c1t1.A through c1t1.D (Table 2). Unlike the series of ideal tetrahedrons, the DM of the corresponding truncated sequence is proportional to the size of the NC (Figure 5), as described by the cube root of the volume of the NC. This is consistent with experimental data on cubic ZnSe NCs.4 D. Degree of Truncation. Using the same model, we also calculated the impact of removing larger fragments from one of the four corners of the tetrahedron (Figure 4b). The magnitude of the DM increases as the number of atoms exposed on the
Figure 3. Different capping groups S-R on a cubic NC Cd8S17: (a) RdH; (b) RdCH2CH3; (c) RdCH2CH2CH3. A tube representation is used to illustrate the length of the capping group. The color coding used is Cd (green), S (teal), C (black), and H (gray).
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Figure 4. Variation of the DM of a CdS nanocrystal as (a) the number of truncated corners increases (C0T0, C1T1, C2T1, C3T1, C4T1 progression) and (b) the number of layers removed from a single corner of a regular tetrahedron (C0T0, C1T1, C1T2, C1T3, C1T4 progression).
TABLE 1: Summary of the Stoichiometry, Charge, and Dipole Moment of the Prototypical Nanocrystal (H64Cd84S123) and Its Truncated Versionsa molecule
stoichiometry
excess charge
dipole moment (D)
C0T0 C1T1 C2T1 C3T1 C4T1 C1T2 C1T3 C1T4
H64Cd84S123 H63Cd83S122 H62Cd82S121 H61Cd81S120 H60Cd80S119 H60Cd83S119 H61Cd80S119 H54Cd80S112
-14 -15 -16 -17 -18 -12 -17 -10
8.82 60.17 54.6 60.68 8.82 55.36 87.88 75.47
a Note that the calculated excess charge significantly overestimates the experimentally measured total charge of dispersed nanocrystals.19
TABLE 2: Summary of the Stoichiometry, Charge, and Dipole Moment of Nanocrystals Smaller than the Prototypical Nanocrystal (H64Cd84S123)a molecule
stoichiometry
excess charge
dipole moment (D)
c0t0.A c0t0.B c0t0.C c0t0.D c1t1.A c1t1.B c1t1.C c1t1.D
H16Cd8S17 H28Cd17S32 H40Cd32S54 H52Cd54S84 H15Cd7S16 H27Cd16S31 H39Cd31S53 H51Cd53S83
-2 -2 -4 -8 -3 -3 -5 -9
5.70 9.76 4.13 7.82 12.96 7.66 26.26 40.80
a
These smaller nanocrystals prefixed with c0t0 and c1t1 resemble configurations C0T0 and C1T1 of the prototypical nanocrystal depicted in parts a and b of Figure 1, respectively. Note that the calculated excess charge significantly overestimates the experimentally measured total charge of dispersed nanocrystals.19
TABLE 3: Summary of the Stoichiometry, Net Charge, and Dipole Moment of NCs in Aqueous Solutions molecule
stoichiometry
excess charge
dipole moment (D)
C1T1Wa C1T1Wb C1T1Wc C1T1Wd C1T3Wa C3T1Wa C3T1Wb
H66Cd83S119O3 H69Cd83S116O6 H68Cd83S117O5 H68Cd83S117O5 H68Cd80S112O7 H70Cd81S111O9 H71Cd81S110O10
-12 -9 -10 -10 -10 -8 -7
84.02 17.47 70.01 29.18 109.36 92.58 28.17
truncated facet increases, for example, C1T1 and C1T3 or C1T2 and C1T4, and decreases as the distance of this facet from the plane defined by the three nontruncated corners decreases. The direction of the DM depends on the apparent charge of the surface atoms at the truncated facet. Thus, when the terminal surface is made of electron acceptor groups such as S, the DM points to the truncated corner, along the axis of rotation.
Figure 5. Variation of the DM of the truncated (circles) and untruncated (diamonds) CdS nanocrystals described in Table 2 as a function of size of the nanocrystal. The data on C0T0 and C1T1 are appended to the truncated and untruncated series, respectively. The DM of the untruncated series (c0t0.A, c0t0.B, c0t0.C, c0t0.D, C0T0) is small, and is less than 10 D in all cases. The DM of the truncated series (c1t1.A, c1t1.B, c1t1.C, c1t1.D, C1T1) is proportional to the cube root of the volume of the nanocrystal, in accordance with experimental data.4
Similarly, when the positive Cd atoms are exposed, the DM direction is opposite and points away from the truncated surface. There is no apparent correlation observed between the total excess charge and the magnitude of DM (Table 1). Also, it is important to remember that the actual charge associated with the nanoparticle in solution is substantially smaller than the calculated excess charge, that is, 2-6 electron charges, as was recently determined experimentally.19 It can also vary depending on the ionization status of the stabilizer and physical adsorption of other ions. E. Surface Hydration. Since cubic CdS nanocrystals are often obtained and used in aqueous solutions, the possibility of surface hydration reactions in the asymmetric NCs must also be considered. Some stabilizer molecules associated with Cd ions could potentially be replaced with H2O connected to Cd by a Cd-O coordinating bond. Thus, we substituted -SH groups with H2O groups at different locations to obtain a variety of new NCs depicted in Figure 6. We believe that substitution under normal conditions does occur, but not extensively because of the destabilization of dispersions associated with it. Thus, we limited the number of water molecules attached to a NC to be between 3 and 10. The placement of the substituting water molecules tends to be in the (truncated) apexes, since thiol stabilizers are more accessible there. An additional reason for
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Figure 6. Starting from C1T1 shown in Figure 3b, some of the terminal S (teal spheres) atoms are substituted with O (red spheres) atoms to yield molecules (a) C1T1Wa, (b) C1T1Wb, (c) C1T1Wc, and (d) C1T1Wd. Parts e, f, and g show molecules C1T3Wa, C3T1Wa, and C3T1Wb, respectively. The inset in each figure depicts the direction of the DM schematically, pointing from the positive end toward the negative end. Filled and empty circles represent untruncated and truncated corners of the tetrahedron, respectively. The large empty circles denote the more heavily substituted corner.
Letters considering apical substitution was that its effect on the DM would be the most significant due to the distance from the center of mass of the NC. Considering the electronic effect of hydration, the following points should be made. (1) The magnitude of the DM increases because O is a more electronegative atom than S. Thus, the dipole moment of NCs in aqueous solutions can potentially reach very significant magnitudes exceeding the 40-50 D mark necessary for the energy of dipole-dipole attraction to become greater than the energy of thermal motion. This explains why the formation of the chains of nanoparticles often requires partial removal of the stabilizer.20 (2) When comparing the direction of dipole moments in NCs with analogous truncation (for instance, Figures 1g and 6e), one will see that H2O substitution often reverses the direction of the DM, which is attributed to the effect of hydrogen atoms in sp3 hybridized oxygen, effectively acting now as the terminal atoms. (3) As expected, the DM is substantially smaller in C1T1Wb and C1T1Wd than in other NCs, due to the greater structural symmetry of the molecules, whereas it is marginally lowered in C1T1Wc. A similar DM reduction is also observed in C3T1Wb. This confirms the general trend observed both for original (Figure 1) and substituted (Figure 6) NCs. Conclusions In summary, we found that minor deviations from a tetrahedral shape of CdS nanocrystals could result in DMs of the order of 30-100 D. The underlying presence of this large ground state DM even in symmetric cubic lattices due to nonideality of the crystal lattice implies that the existence of a DM is an inherent attribute of many NCs. The good match of the quantum mechanical modeling data presented here with the experimental observations also validates the use of the PM3 algorithm and simple approach to DM calculations described here to further studies of the dipolar properties of the NCs. The polarity of the media may play a substantial role in determining the dominant shape of the particle, with polar media favoring more polar NCs. The assortment of current works on interesting but poorly understood self-organization phenomena in NCs illustrates the importance of understanding the interactions
J. Phys. Chem. B, Vol. 110, No. 25, 2006 12217 between NPs, among which dipole-dipole attraction can apparently play a crucial role. Last but not least, it is also important to note that the described relationship between structural defects and DM is a fundamental feature of inorganic nanoscale colloids differentiating them from both macroscale particles and molecular compounds. Acknowledgment. The authors would like to acknowledge financial support from National Science Foundation and Air Force Office of Scientific Research for the support of this work. References and Notes (1) Bawendi, M.; Steigerwald, M.; Brus, L. Annu. ReV. Phys. Chem. 1990, 41, 477. (2) Alivisatos, A. Science 1996, 271, 933. (3) Blanton, S.; Leheny, R.; Hines, M.; Guyot-Sionnest, P. Phys. ReV. Lett. 1997, 79, 865. (4) Shim, M.; Guyot-Sionnest, P. J. Chem. Phys. 1999, 111, 6955. (5) Li, L.; Alivisatos, A. Phys. ReV. Lett. 2003, 90, 0974021. (6) Cho, K.-S.; Talapin, D. V.; Gaschler, W.; Murray, C. B. J. Am. Chem. Soc. 2005, 127 (19), 7140. (7) Duan, X.; Huang, Y.; Cui, Y.; Wang, J.; Lieber, C. Nature 2001, 409, 66. (8) Holmes, J. D.; Johnston, K. P.; Doty, R. C.; Korgel, B. A. Science 2000, 287 (5457), 1471. (9) Tang, Z.; Wang, Y.; Kotov, N. Langmuir 2002, 18, 7035-7040. (10) Polleux, J.; Pinna, N.; Antonietti, M.; Niederberger, M. AdV. Mater. 2004, 16 (5), 436. (11) Rabani, E.; Hetenyi, B.; Berne, B.; Brus, L. J. Chem. Phys. 1999, 110, 5355. (12) Rabani, E. J. Chem. Phys. 2001, 115, 1493. (13) Nann, T.; Schneider. Chem. Phys. Lett. 2004, 384, 150. (14) Shiang, J.; Kadavanich, A.; Grubbs, R.; Alivisatos, A. J. Phys. Chem. 1995, 99, 17417. (15) Mews, A.; Kadavanich, A. V.; Banin, U.; Alivisatos, A. P. Phys. ReV. B 1996, 53 (20), R13242. (16) Vossmeyer, T.; Katsikas, L.; Giersig, M.; Popovic, I.; Diesner, K.; Chemseddine, A.; Eychmuller, A.; Weller, H. J. Phys. Chem. 1994, 98, 7665. (17) Dollefeld, H.; Hoppe, K.; Kolny, J.; Schilling, K.; Weller, H.; Eychmuller, A. Phys. Chem. Chem. Phys. 2002, 4, 4747. (18) Vossmeyer, T.; Reck, G.; Katsikas, L.; Haupt, E. T. K.; Schulz, B.; Weller, H. Science 1995, 267, 1476. (19) Yaroslavov, A.; Sinani, V.; Efimova, A.; Yaroslavova, E.; Rakhnyanskaya, A.; Ermakov, Y.; Kotov, N. J. Am. Chem. Soc. 2005, 127 (20), 7322. (20) Tang, Z.; Kotov, N. A.; Giersig, M. Science 2002, 297 (5579), 237.
