Theoretical and Experimental Insights into the Surface Chemistry of

Article pubs.acs.org/Langmuir

Theoretical and Experimental Insights into the Surface Chemistry of Semiconductor Quantum Dots Johannes T. Margraf,†,‡ Andrés Ruland,‡ Vito Sgobba,‡ Dirk M. Guldi,*,‡ and Timothy Clark*,† †

Computer Chemie Centrum, Department of Chemistry and Pharmacy, Friedrich-Alexander-Universität Erlangen-Nürnberg, Nägelsbachstraße 25, 91052 Erlangen, Germany ‡ Department of Chemistry and Pharmacy and Interdisciplinary Center for Molecular Materials, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany S Supporting Information *

ABSTRACT: We present a series of non-stoichiometric cadmium sulfide quantum-dot (QD) models. Using density functional theory (DFT) and semi-empirical molecular orbital (MO) calculations, we explore the ligand binding and exchange chemistry of these models. Their surface morphology allows for these processes to be rationalized on the atomic scale. This is corroborated by ultraviolet−visible (UV−vis), infrared (IR), and inductively coupled plasma−optical emission spectroscopy (ICP−OES).

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INTRODUCTION Semiconductor quantum dots (QDs) have been studied extensively in the last 3 decades, with respect to both their fundamental properties and their incorporation in devices, such as solar cells.1,2 However, the atomistic structure of the QD surface remains unknown, although it has become evident that QD/ligand and QD/QD interfaces play a decisive role in improving device performance.3−5 Investigating the surface structure and chemistry of QDs is therefore essential. Unlike molecules, a batch of QDs is never perfectly monodisperse, which prevents classical methods of structure determination (e.g., single-crystal X-ray diffraction). Furthermore, QDs behave dynamically, which may change their properties and reactivity. Examples for this dynamic behavior are temporary trap formation (attributed to diffusion and desorption of organic ligands at the surface) and the relatively easy substitution of ligands and even cations or anions (e.g., from cadmium telluride to copper(II) telluride).6−10 For this reason, several computational studies have been conducted to provide an atomistic description of QDs. Because of the abundance of experimental data and their technological and scientific relevance, cadmium selenide QDs have been particularly popular for such studies. Most prominently, many density functional theory (DFT) studies have focused on stoichiometric models, such as the wurtzite (CdSe)33 cluster.11 In this context, the binding strength of different ligands, the relaxation of surface atoms, electron-transfer properties, and band gaps have been calculated and shown largely to be in agreement with experimental observations.12−16 © 2013 American Chemical Society

Because stoichiometric models are intrinsically chargeneutral, they can be treated easily as long as the ligands are also neutral (e.g., amines or phosphine oxides). For anionic ligands, such as carboxylates or thiolates, the protonation of Se atoms on the surface allows for charge neutrality to be conserved. This type of model system has its experimental equivalent in “magic-sized” clusters.17 These are chemically quite different from the CdSe QDs commonly used in nanoelectronic devices. The latter are known to be nonstoichiometric (with Cd excess) and significantly larger (with diameters on the order of 3−5 nm) and may exhibit both zinc blende (ZB) and wurtzite (W) structures (depending upon the synthesis and ligand shell).18−20 Several theoretical studies have taken this into account. For example, very large stoichiometric clusters, such as (CdSe)891, have been simulated using classical force fields.21 Voznyy et al. have considered acetate (Ac)-capped, Cd-rich ZB clusters, such as Cd56Se50(Ac)12, and were able to obtain a detailed understanding of the dynamic behavior of ligands and their effect on the electronic structure of the QDs.22,23 Experimental studies on the surface chemistry of CdSe QDs with different ligands have resulted in a complex scenario concerning the structure and dynamics of the ligand shell and QD surface. Cao et al. showed that carboxylate-to-amine ligand exchange leaves the crystal phase of the QDs intact and attributed changes in optical properties to a change of the Received: September 20, 2013 Revised: November 14, 2013 Published: November 22, 2013 15450

dx.doi.org/10.1021/la403633e | Langmuir 2013, 29, 15450−15456

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surface structure.24 Li et al. showed that, in the presence of oxygen, amines can be used to etch the facets of QDs selectively.25 Additionally, nuclear magnetic resonance (NMR) studies on different ligand-exchange reactions have shown that Cd ions can be part of a dynamic surface layer and that ligandbinding sites may be non-equivalent.26−28 Despite these detailed studies, the affinity of different binding groups, such as amines, thiols, and phosphonates, is still commonly explained using hard and soft acid and base (HSAB) theory, although the application of this theory beyond its original scope has been criticized.29,30 We believe that theoretical models are an important tool that helps understand the chemistry of nanostructures on the atomic scale. In this paper, we therefore systematically construct a series of carboxylate-capped CdSe QD models with the aim of capturing their real chemical structure as closely as possible. The relative stability of small- to medium-sized clusters is investigated using DFT calculations. The models are then used to discuss ligand binding and exchange. Complementary experiments show that our models can rationalize the complex surface chemistry of QDs on the atomic scale.

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Figure 1. Selected acetate-capped ZB CdSe clusters: Cd9Se7Ac4, Cd51Se39Ac24, Cd236Se208Ac56, and Cd592Se538Ac108 (from top left to bottom right). Cd atoms are shown in beige; Se atoms are shown in orange; O atoms are shown in red; C atoms are shown in gray; and H atoms are shown in white.

RESULTS AND DISCUSSION Construction of QD Models. QD models were created using a systematic procedure based on the idea that, during QD growth, the number of dangling bonds and the charge of the cluster should be as low as possible. Acetate ions (Ac−) were used as ligands. Specifically, the procedure is as follows: (1) A sphere is cut out of a bulk W or ZB CdSe lattice.31 (2) All atoms with only a single binding partner are removed. (3) All Se atoms with only two binding partners are removed. If necessary, the procedure is repeated to obtain positively charged clusters with excess Cd at the surface. Surface Cd atoms are bound to two or three Se atoms, and surface Se atoms are bound to three Cd atoms. This selection process is justified by the known chemistry of small passivated II−IV semiconductor clusters, for which crystal structures are available.32 From this point on, two further considerations were made. First, ligands are likely to coordinate to unsaturated Cd atoms (i.e., those with only two binding partners), and second, the number of acetate ligands should compensate for the charge of the cluster. These considerations were combined into the condition that the number of unsaturated Cd atoms NCd(2) should be equivalent to the charge of the cluster QQD and the number of acetates NAc. NCd(2) = Q QD = 2(NCd − NSe) = NAc

It is remarkable that, even though our considerations are only based on the direct binding partners of each atom and not on long-range symmetry, they lead to faceted morphologies reminiscent of the Wulff construction approach (see Figure 2). In detail, the ZB nanocrystal surfaces consist of large Cd-

Figure 2. Geometry of Cd236Se208Ac56 with marked facets. Cd atoms are shown in beige; Se atoms are shown in orange; O atoms are shown in red; and C atoms are shown in gray. Hydrogen atoms are omitted for clarity.

(1)

Selected clusters from the ZB series formed in this manner are shown in Figure 1. Further details on the individual clusters and the W series are compiled in Table S1 and Figures S1−S11 of the Supporting Information. Interestingly, it is not possible to obtain very small clusters (smaller than approximately 50 atoms) that satisfy our conditions strictly. This is especially true for small W clusters, which always contain doubly coordinated Se surface atoms because of the hexagonal crystal structure. For ZB clusters, a higher coordination of Se can be achieved in small clusters, as in the example of Cd9Se7Ac4, which has no doubly coordinated Se. This indicates that the ZB structure may be favored during the nucleation stage. Indeed, carboxylate-based synthesis leads to ZB QDs.24

rich (111) and small Se-rich (−111) facets. These are separated by (001) facets, which are terminated with unsaturated Cd atoms and, therefore, most likely to bind ligands. This reflects recent experimental results, which indicate that the QD structure can be considered a (CdSe)n core with a Cd(Ac) ligand shell.27 Cluster Stability. To investigate the relative stabilities of the clusters, we performed DFT geometry optimizations using the Perdew−Burke−Ernzerhof (PBE) functional, a double-ζ quality numerical basis set with polarization functions on all 15451


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non-hydrogen atoms and DFT semi-core pseudo-potentials in Dmol3.33−36 Because this method is still prohibitively expensive for very large systems, we only treated clusters with up to 100 Se and Cd atoms. No counterpoise corrections for basis set superposition error were performed. The relative stability of the clusters was defined as the ratio of the calculated total energy of the optimized geometry and the sum of the total energies of the constituting units. stability =

E(CdlSemAcn) 2+

[lE(Cd ) + mE(Se 2 −) + nE(Ac−)]

(2)

Figure 3 shows a plot of the cluster stability versus the Cd/Se ratio. As expected, this stability criterion gives the highest value

Figure 3. Plot of QD stability versus Cd/Se ratio. Diamonds fitted by a solid line represent clusters strictly compliant to our conditions, and circles fitted by a dashed line represent charged clusters. Note that the two symbols at Cd/Se = 1.0 refer to W and ZB, with ZB being slightly more stable.

Figure 4. (Top) Geometry and (bottom) molecular electrostatic potential (MEP) of ZB Cd30Se22Ac20 from −0.1 (blue) to 0.1 (red) Ha e−.

for the bulk ZB and W phases (Cd/Se = 1.0), with the former being slightly more stable.37 As the clusters grow, the Cd/Se ratio decreases (see Table S1 of the Supporting Information) and the stability increases. This is equivalent to a decrease in the surface/volume ratio. On this scale, we find no difference in stability between W and ZB. QDs that deviate from charge neutrality and/or bear unpassivated Cd atoms are less stable than would be expected from their Cd/Se ratio. These observations provide an indirect validation of our strategy for constructing clusters because the criteria found for maximum stability correspond to the principles used to build the clusters. Ligand Coverage. The optimized binding geometries of the acetate ligands on the (001) facets vary depending upon the local surface morphology. As a consequence, in the ZB Cd30Se22Ac20 cluster, different binding motifs coexist on the surface (see the top panel of Figure 4). The ligand binding energy (BE) decreases from the chelate to the tilted to the bridging geometry. The BEs are summarized in Table 1, and the geometries are shown schematically in Figure 5 and in detail in Figure S12−S14 of the Supporting Information. All calculations (including geometry optimizations) were also performed in a solvent environment (acetonitrile, ACN implicitly considered via the COSMO model).38 The presence of the polar solvent causes a decrease in BE of almost 100 kcal mol−1. This is largely due to the solvation of Ac−, with an energy contribution of −69.8 kcal mol−1. As mentioned above, Cd-rich (111) and Se-rich (−111) facets remain ligand-free in our construction scheme, because

Table 1. BEs of Different Ligands and Configurations ligand type

BE in vacuo (kcal mol−1)

on Cd30Se20Ac20 Ac−, chelate −144.2 Ac−, tilted −141.6 Ac−, bridging −134.9 Ac−, addition on (111) −91.99 Ac−, second addition on (111) −55.70 NH2CH3, on (111) facet −29.46 NH2CH3, exchanging Ac− on −34.95 (001)

BE in ACN (kcal mol−1) −48.64 −44.04 −44.04 −37.95 −36.43 −25.64 −32.76

Figure 5. Schematic representation of acetate−Cd binding geometries.

they contain no unsaturated Cd atoms. Such free facets allow for the QD to interact with its environment, despite its ligand shell. Plotting the electrostatic potential on the electron 15452


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isodensity surface of the cluster (0.03 e− Å−3; see the bottom panel of Figure 4) reveals that the (111) facets can interact with electron-rich species. This is also corroborated by the nucleophilic Fukui function39 (see Figure S15 of the Supporting Information). To investigate the possibility of higher ligand coverage on these facets, we placed additional acetate ligands on them to form the clusters Cd30Se22Ac21− and Cd30Se22Ac222−. In both cases, the BE of the additional Ac− is exothermic yet significantly lower than in the neutral cluster. The (111) facets are therefore not necessarily ligand-free, but ligands may bind to them more weakly because of higher coordination of Cd and overall lower electrostatic attraction. Moving to larger systems, we replaced the acetate ligands with myristate (My) to obtain the Cd236Se208My56 QD shown in Figure 6. The geometry of this cluster was optimized using

potential). This facet can therefore be expected to play an important role in the ligand-exchange process. Ligand Exchange. To test the quality of our models against experimental data, we performed oleate (OLA) to oleylamine (OAm) ligand exchange on ZB QDs at room temperature (RT) following a previously reported procedure.24 The reaction was performed in a 1:4 OAm/1-octadecene (ODE) mixture for 30 min and 24 h and in OAm/CHCl3 for 30 min (for further experimental details, see the Supporting Information). The samples were then studied with ultraviolet−visible (UV−vis), Fourier transform infrared (FTIR), and inductively coupled plasma−optical emission spectroscopy (ICP−OES) (see Figure 7 and Table S2 of the Supporting Information). Before ligand exchange, the asymmetric and symmetric stretching vibrations of the carboxylate groups (−COO−) appear at 1532 and 1438 cm−1, respectively.47 The gap between these two stretching vibrations is 94 cm−1, indicating that most carboxylate groups are bound to surface cadmium ions through chelating bidentate interactions.48,49 The C−H scissoring vibration at 1470 cm−1 remains unchanged in all spectra. After ligand exchange in ODE for 30 min and 24 h at room temperature, the IR spectrum clearly shows the coexistence of OLA and OAm on these QDs (i.e., partial ligand exchange), because the characteristic N−H bending vibration band at 1557 cm−1 emerges and the −COO− stretching vibrations shift to 1540 and 1436 cm−1, respectively.24 The gap between these two bands increases to 104 cm−1, suggesting that the chelating bidentate interaction between the carboxylate group and surface Cd2+ ion is weakened by the presence of OAm. After ligand exchange in CHCl3 for 30 min, the two strong carboxylate stretching bands disappear, whereas the N−H bending band remains. The shift of the N−H bending band to 1563 cm−1 suggests the change of bonding nature between the OAm ligands and the CdSe QD surface. Specifically, in the case of partial ligand exchange, there may be interactions between carboxylate and amine ligands (e.g., hydrogen bonds), which are absent for the completely exchanged case. Ligand−ligand interactions are also in line with the observed changes in carboxylate features when comparing unmodified to partially exchanged samples. The absorption and emission spectra (see the right panel of Figure 7) show a blue shift of 2−3 nm, which can be ascribed to a decrease in diameter. ICP−OES revealed a difference in the Cd/Se molar ratio of pristine and ligand-exchanged QD samples (1.3 and 1.2, respectively; see Table S2 of the Supporting Information for details). For the corresponding DFT calculations, we used methylamine as a ligand. Its solvation energy in ACN is −4.52 kcal mol−1. Accordingly, taking the solvent into account has a much weaker effect than that for Ac−. Methylamine is found to adsorb onto the (111) facet but less strongly than an additional acetate would (ΔBE = 12.31 kcal mol−1 in ACN; see Table 1). While the BE of amine on the (001) facets is higher, the substitution of a chelate acetate on a (001) facet with methylamine to form Cd30Se22Ac19NH2CH3+ is still endothermic by ΔH = 15.88 kcal mol−1 in ACN. This is reflected by the fact that, even after 24 h at RT, ligand exchange is not complete in ODE, whereas it is quantitative in CHCl3 after only 30 min. Clearly, the higher polarity of CHCl3 influences the thermodynamics of the exchange process in favor of the amines. Additionally, trace amounts of acid present in the CHCl3 may act as catalysts for the ligand exchange. Similarly,

Figure 6. Geometry and MEP of ZB Cd236Se208My56.

the universal force field (UFF).40 While this approach cannot describe the dynamic ligand−QD binding situation in detail, it does give a reasonable model of the surface morphology. Because of the interactions between the long myristate alkyl chains, the (111) and (−111) facets are still easily accessible from the environment. To assess the reactivity of this QD, we performed semiempirical MO calculations using the PM3 Hamiltonian41,42 as implemented in EMPIRE.43 A projection of the MEP on an isodensity surface (0.03 e− Å−3) (bottom panel of Figure 6) reveals that, in analogy to the findings from our DFT calculations, the (111) facets are likely to interact with nucleophilic species (red domains display positive electrostatic 15453


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Figure 7. (Left) FTIR spectra of QDs before and after 30 min and 24 h of ligand exchange in ODE and 30 min in CHCl3, as well as pure oleylamine. (Right) Absorption (solid line) and emission (dashed line) spectra of CdSe QDs before (black) and after (red) 30 min of ligand exchange in ODE.

the partial exchange in ODE is not due to kinetic reasons but because only weakly bound OLA ligands are removed. It is important to note that ligand exchange affects the net charge of the system. Hypothetically, exchanging all acetates to neutral amines for Cd30Se22Ac20 would lead to 20-fold positively charged particles, although this process never occurs. Any resulting charge must be compensated in some way. Indeed, as mentioned above, we observed a decrease in diameter and Cd/Se ratio upon ligand exchange. The charge is therefore likely compensated by the removal of excess surface Cd2+ ions. To simulate this, we studied the reaction

CONCLUSION

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ASSOCIATED CONTENT

In this paper, we have presented a series of model CdSe QDs based on a systematic construction scheme. DFT calculations have allowed us to assess their relative thermodynamic stability. These findings shed some light on the driving forces relevant to QD growth and the role of surface ligands. The observed facetation and related distribution of ligands serve as a likely rationale for ligand-controlled anisotropic growth of nanorods and other shapes.44−46 Analysis of the geometries of very small crystals reveals that coordination of Se is always low for W. This may be the reason for the preferred ZB structure of acidpassivated QDs. The dynamic binding behavior of Ac− ligands, the faceted geometry of the QDs, and the intrinsic positive charge of the CdSe core impose interesting conditions on the ligand exchange process. Specifically, carboxylate ligands display varying binding energies depending upon the local surface morphology and the polarity of the solvent. Furthermore, ligand exchange is predicted to be accompanied by the loss of surface Cd2+ ions to compensate for charges. Together with experimental FTIR, UV−vis, and ICP−OES studies, we have determined a likely mechanism for this process, namely the removal of Cd2+ dicarboxylate complexes. This corresponds to the back reaction of QD formation. The use of non-stoichiometric model clusters allows for the theoretical investigation of species relevant for nanotechnology. The systematically constructed models presented in this work show close agreement with experimental observations and are therefore ideal candidates for such studies. Effects of ligand exchange on optical properties or device performance should be discussed in terms of a possible change to the QD surface and not merely based on the ligand binding group.

Cd32Se22Ac 20 + NH 2CH3 → Cd31Se22Ac18NH 2CH3 + CdAc 2

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(3)

This reaction is essentially thermoneutral with ΔH = 0.5 kcal mol−1 in ACN. In Figure 8, Cd2+ and its ligands that were

Figure 8. Cd32Se22Ac20 with exchanging Cd2+ and Ac− ligands marked blue and the amine-coordinating Cd marked yellow.

S Supporting Information *

removed are marked blue and Cd to which the amine coordinates is marked yellow. One Ac− ligand is completely coordinated to the blue Cd, while the other is bridging between the blue and yellow Cd atoms. The formation of CdAc2 can therefore be expected to occur easily once the NH2CH3 ligand coordinates to the other Cd.

Full experimental details, images and details to all structures, Fukui function plot, ICP−OES data, UV−vis spectra of QDs before and after ligand exchange in CHCl3, and .xyz coordinates of Cd32Se22Ac20 and Cd236Se208Ac56. This material is available free of charge via the Internet at http://pubs.acs.org. 15454


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(15) Chaban, V. V.; Prezhdo, V. V.; Prezhdo, O. V. Covalent linking greatly enhances photoinduced electron transfer in fullerene-quantum dot nanocomposites: Time-domain ab initio study. J. Phys. Chem. Lett. 2013, 4, 1−6. (16) Fischer, S. A.; Crotty, A. M.; Kilina, S. V.; Ivanov, S. A.; Tretiak, S. Passivating ligand and solvent contributions to the electronic properties of semiconductor nanocrystals. Nanoscale 2012, 4, 904− 914. (17) Cossairt, B. M.; Owen, J. S. CdSe clusters: At the interface of small molecules and quantum dots. Chem. Mater. 2011, 23, 3114− 3119. (18) Chen, O.; Chen, X.; Yang, Y.; Lynch, J.; Wu, H.; Zhuang, J.; Cao, Y. C. Synthesis of metal-selenide nanocrystals using SeO2 as the selenium precursor. Angew. Chem., Int. Ed. 2008, 47, 8638−8641. (19) Talapin, D. V.; Lee, J. S.; Kovalenko, M. V.; Shevchenko, E. V. Prospects of colloidal nanocrystals for electronic and optoelectronic applications. Chem. Rev. 2010, 110, 389−458. (20) Subila, K.; Kumar, G.; Shivaprasad, S.; Thomas, K. Luminescence properties of CdSe quantum dots: Role of crystal structure and surface composition. J. Phys. Chem. Lett. 2013, 4, 2774− 2779. (21) Schapotschnikow, P.; Hommersom, B.; Vlugt, T. J. H. Adsorption and binding of ligands to CdSe nanocrystals. J. Phys. Chem. C 2009, 113, 12690−12698. (22) Voznyy, O. Mobile surface traps in CdSe nanocrystals with carboxylic acid ligands. J. Phys. Chem. C 2011, 115, 15927−15932. (23) Voznyy, O.; Thon, S. M.; Ip, A. H.; Sargent, E. H. Dynamic trap formation and elimination in colloidal quantum dots. J. Phys. Chem. Lett. 2013, 4, 987−992. (24) Chen, O.; Yang, Y.; Wang, T.; Wu, H.; Niu, C.; Yang, J.; Cao, Y. C. Surface-functionalization-dependent optical properties of II−VI semiconductor nanocrystals. J. Am. Chem. Soc. 2011, 133, 17504− 17512. (25) Li, R.; Lee, J.; Yang, B.; Horspool, D. N.; Aindow, M.; Papadimitrakopoulos, F. Amine-assisted facetted etching of CdSe nanocrystals. J. Am. Chem. Soc. 2005, 127, 2524−2532. (26) Owen, J. S.; Park, J.; Trudeau, P. E.; Alivisatos, A. P. Reaction chemistry and ligand exchange at cadmium-selenide nanocrystal surfaces. J. Am. Chem. Soc. 2008, 130, 12279−12281. (27) Anderson, N. C.; Owen, J. S. Soluble, chloride-terminated CdSe nanocrystals: Ligand exchange monitored by 1H and 31P NMR spectroscopy. Chem. Mater. 2013, 25, 69−76. (28) Fritzinger, B.; Capek, R. K.; Lambert, K.; Martins, J. C.; Hens, Z. Utilizing self-exchange to address the binding of carboxylic acid ligands to CdSe quantum dots. J. Am. Chem. Soc. 2010, 132, 10195−10201. (29) Pearson, R. G. Hard and soft acids and bases. J. Am. Chem. Soc. 1963, 85, 3533−3539. (30) Mayr, H.; Breugst, M.; Ofial, A. R. Farewell to the HSAB treatment of ambident reactivity. Angew. Chem., Int. Ed. 2011, 50, 6470−6505. (31) Adachi, S. Optical Properties of Crystalline and Amorphous Semiconductors; Kluwer Academic Publishers: Norwell, MA, 1999. (32) Eichhöfer, A. Thermal properties of [M10Se4(SePh)12(PR3)4] (M = Zn, Cd, Hg) cluster moleculesSynthesis and structure of [Cd32Se14(SePh)36(L)4]; L = OPPh3, OC4H8. Eur. J. Inorg. Chem. 2005, 1245−1253. (33) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (34) Delley, B. An all-electron numerical method for solving the local density functional for polyatomic molecules. J. Chem. Phys. 1990, 92, 508−517. (35) Delley, B. From molecules to solids with the DMol3 approach. J. Chem. Phys. 2000, 113, 7756−7764. (36) Delley, B. Hardness conserving semilocal pseudopotentials. Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 66, 155125/1− 155125/9. (37) Datta, S.; Saha-Dasgupta, T.; Sarma, D. D. Wannier function study of the relative stability of zinc-blende and wurtzite structures in

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Deutsche Forschungsgemeinschaft as part of the Excellence Cluster “Engineering of Advanced Materials” and the Bayerische Staatsregierung as part of the “Solar Technologies go Hybrid” initiative. Johannes T. Margraf is supported by a Beilstein Foundation Scholarship. We thank Dr. Jochen Schmidt and Prof. Wolfgang Peukert for providing us access to the ICP−OES measurements.

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