NANOPARTICLES AND POWDERS
2.4 CASE STUDY 2: GOLD NANOPARTICLES .1 Introduction
also provide places where holes can be trapped but in a delocalized form; therefore, they are EPR invisible.
The fact that local electronic structure is modified at surface features of MgO NPs also has consequences for their optical properties. Bulk MgO is transparent to photons with energies less than 7.7 eV (160 nm), although defects (known as color centers) do give some absorption in the visible part of the spectrum. However, in nanopowders additional bands are observed at 6.6 eV, 5.3 to 5.7 eV, and 4.6 eV, which have been attributed to terrace, edge, and corner excitations, respectively (29) and this is confirmed by theoretical calculations. Following excitation, electrons and holes can recombine, leading to photoluminescence. Photon emission is observed experimen-tally at 3.3 to 3.4 eV. This is interpreted as charge recombination at three-coordinated ions with a large Stokes shift (.1 eV) due to structural relaxation. A more extreme example of structural modification under excitation is the photodesorption of low coor-dinated ions which has been observed experimentally and explained theoretically (30).
2.3.3 Summary
As the structural and electronic properties of MgO have been well studied in the bulk, at surfaces, and for numerous defects and impurities therein, it represents a useful model system on which to explore the properties of metal oxide NPs. Experimental and theoretical studies have shown that low coordinated ions, which have increased concentrations in NPs, have different electronic and optical properties compared to the bulk and can act as charge traps. The trapping of electrons and holes in insulating oxide materials, which can be both very useful and harmful, is an important issue of wide interest. Commonly used experimental probes such as x-ray- and UV-photoelectron spectroscopy and transmission electron microscopy (TEM), for example, may cause charge to be trapped in the material (often powder) directly, or as a consequence of secondary processes. Although the Coulomb interaction favors the recombination of electrons and holes, they may become separated and trapped in configurations that are thermally stable over long time scales. Associated with trapped charge at the NP surfaces is an increase in chemical reactivity, and the possi-bility to tailor chemical properties by controlling the arrangement of surface ions on the NP has received interest for numerous applications in catalysis.
2.4 CASE STUDY 2: GOLD NANOPARTICLES
was an active heterogeneous catalyst for numerous reactions, such as the oxidation of CO, the partial oxidation of hydrocarbons, and the hydrogenation of carbon oxides (e.g. see Reference 31 and references within). This has since been the focus of a great deal of research. While the exact origin of activity is still debated it has become clear that it results from a complex interplay between both geometric and electronic factors. Au NPs also exhibit quite different optical properties from the bulk. The plasmon resonance that dominates their absorption spectrum is very sensitive to both size and shape (32) and is useful for applications such as plasmonic waveguides, surface enhanced spectroscopies, and biological markers.
As in the previous section, before considering Au NPs we briefly review the properties of the bulk material. Gold adopts the fcc crystal structure with lattice constant 4.08 A˚ and remains solid up to temperatures of about 10008C. Its electronic structure consists of a wide free electron-like sp band that is hybridized with a narrower d band. The Fermi level is positioned just above the filled d band explaining its high electronic mobility. Gold surfaces have been studied in detail both experimentally and theoretically. The (111) and (100) surfaces are the most thermodynamically favorable, which are both observed to be reconstructed. These reconstructions involve surface atoms adjusting into more closely packed arrangements and the corresponding unit cells can be quite large.
2.4.2 Properties of Au Nanoparticles
2.4.2.1 Morphology Au NPs can be fabricated using a wide range of techniques that can result in an equally wide range of morphologies. Ionized mass selected clus-ters can be produced by plasma sputtering in an inert gas and may subsequently be deposited onto various substrates (33). Alternatively, gold can be evaporated directly onto a substrate allowing NPs to nucleate and grow at defects or steps, for example.
Wet synthesis methods, which are the preferred industrial route due to their cost and scalability, can also be used to form NPs on oxide supports (31).
To experimentally determine the atomic structure of small gold clusters is very dif-ficult. Indirect information in the form of mass spectra indicates that certain cluster sizes are particular stable (e.g. see Reference 7). Such magic number clusters show up as peaks in the mass spectra and theoretical calculations have been very useful to interpret these experiments. For very small Au clusters (N, 20) the lowest energy structures have been determined at a quantum mechanical (DFT) level. A tendency towards planar atomic arrangements has been found which has been connected to relativistic effects in the electronic structure of Au. Small Au clusters have also been studied on various substrates where they tend to interact strongly with defects such as vacancies. For example, on oxide surfaces Au clusters can exchange electrons with surface color centers, making them partially charged and highly reactive.
For larger Au NPs many theoretical calculations have been made using empirical interatomic potentials. A number of different models have been developed to represent the many-body character of bonding in metals, for example, Finnis – Sinclair, Gupta, and glue models. Here, we discuss the embedded atom method (EAM), which has many similarities with the models mentioned above but can be considered as more
2.4 CASE STUDY 2: GOLD NANOPARTICLES 27
general (34). In the EAM the total energy takes the following form:
E¼X
i
Ei¼X
i
F(ri) þ1 2
X
j=i
f(rij),
where F is a function that gives the energy associated with embedding atom i in the electron density associated with all surrounding atoms ( ri), and f is a short range repulsive potential that depends on the separation between atoms, rij. This expression for the total energy is inspired by the ideas of density functional theory, namely that the total energy of a system is a unique functional of the electronic density. The next step is made by assuming that the electron density at atom i can be written as a linear sum of contributions from other atoms,
ri¼X
j=i
f (rij),
where f describes the electronic density around each atom. In general F, f, and f can be regarded as parameters that can be varied to fit various physical properties.
However, quantum mechanical models of electronic structure can give insights into appropriate functional forms.
Using these many body potential models atomic structures of unsupported Au clusters that have the lowest potential energy have been determined using various global optimization methods. These studies indicate that although three-dimensional morphologies are generally favored the bulk-like fcc structure is not always adopted.
For example, in the range 10 to 500 atoms a number of structures with fivefold sym-metry, for example, icosahedra (Fig. 2.4) and decahedra, have been found in addition
Figure 2.4 The atomic structure of Au NPs with different structural motifs: (a) icosahedron (Au147) and (b) truncated octahedron (Au116).
UNIQUE BONDING IN NANOPARTICLES AND POWDERS 28
to some with very low symmetry. For larger NPs it becomes computationally imposs-ible to employ global minimization algorithms. Instead one can compare the energies of different structures as a function of size (7). For Au, icosahedra are favored for fewer than 100 atoms, decahedra dominate until about 500 atoms, at which point fcc Wulff polyhedra take over. The ordering of these motifs is explained by a strain contribution to the total energy for non-fcc structures which grows linearly with particle size and is much larger for icosahedra than decahedra. At the NP surface, under-coordinated atoms relax inwards, decreasing their average bond lengths. This is predicted by empirical and first principles theoretical models and has recently been observed exper-imentally using coherent x-ray diffraction (35).
For Au NPs supported on the MgO(100) surface TEM has shown that even very small clusters are well faceted and fcc ordered (36). This is explained by the strong adhesion and small lattice mismatch (3%) between Au and MgO, which favors epi-taxial Wulf – Kaischew-like morphologies. For larger lattice mismatch (e.g. Pd/MgO) NPs may be significantly strained and contain dislocations. To model these effects theoretically requires careful treatment of the metal-substrate interaction (37). In contrast for weakly interacting supports, such as graphite, strained decahedral and icosahedral clusters have been observed by TEM (33).
2.4.2.2 Au NPs for Heterogeneous Catalysis While metallic NPs in general are of interest for numerous catalytic reactions, Au has received particular attention since it was found to be active for oxidation of CO to CO2. This activity, which is significant only for NPs smaller than about 8 nm, is exciting because it persists to very low temperature (down to 200 K). In contrast, traditional Pt- or Pd-based catalysts for CO oxidation that are used in car exhausts only work at elevated temperatures; there-fore, most CO pollution occurs during the initial few minutes after the engine is switched on. Au NPs have also been demonstrated to be active for a range of other reactions, including epoxidation of propylene, reduction of nitrogen oxides, and the selective oxidation of hydrocarbons, which is important in the manufacture of pharmaceutical compounds, for example.
Evidence suggests that more than one effect may contribute to the chemical activity of Au NPs. For example, it has been demonstrated experimentally that activity for CO oxidation increases with decreasing particle size (e.g. see Reference 38 for a summary of some data), suggesting a correlation with the number of exposed surface atoms. However, on a supported NP one can distinguish several different types of surface atom that are potential candidates for active sites. Near the interface between the NP and support there are Au atoms coordinated by both atoms of the support material and other Au atoms. The sites of this type accessible for molecular adsorption and reaction lie on the perimeter of the NP. One reason for believing these perimeter atoms may be important is the observation that the choice of support materials (often metal oxides such as TiO2are used) can strongly affect catalytic performance. To explain the origin of this activity a number of different ideas have been proposed.
For example, Au can become polarized and partially charged, either positive or nega-tive, by the oxide surface and by interaction with defects such as oxygen vacancies.
Supporting this idea, quantum mechanical calculations have shown that small anionic
2.4 CASE STUDY 2: GOLD NANOPARTICLES 29
Au clusters are able to oxidize CO with low barriers to reaction (39). Another sugges-tion is that perimeter atoms provide places where molecules can adsorb in favorable configurations. For example, one molecule can be adsorbed on the oxide and the other on a nearby Au atom. Quantum mechanical calculations for Au supported on the MgO(100) surface have demonstrated that such effects can also lead to low barriers to reaction (40).
Besides atoms in direct contact with the support Au NPs possess other atoms with low coordination at edges and vertices which have also been proposed as active sites (38). On the close packed Au(111) surface adsorption energies for CO and O2are low because the d band states that participate in bonding are too low in energy to interact significantly with the frontier orbitals of the molecules. However, as the Au atom coordination is reduced the local electronic structure is modified such that the d band is narrowed and moved to higher energy. Therefore, at low coordinated Au atoms adsorption energies are higher and barriers to reaction are lower.
While it is clear that Au NP structure strongly influences the adsorption and reac-tion of molecules, the reverse is also true: molecules can influence NP structure.
For example, it has recently been shown that supported Pd NPs cyclically exposed to CO and NO undergo reversible changes in morphology driven by molecular adsorption (41). For large NPs changes in morphology can be rationalized in terms of modified surface energies as discussed in Section 2.2.1, but for small clusters atomic-scale models are needed. A theoretical study of CO adsorption on an unsup-ported Au79cluster suggests that morphology transformations should also be expected for Au (42). As CO favors adsorption on low coordinated Au atoms the NP is predicted to adopt compact structures that expose higher numbers of low coordinated atoms, as illustrated in Figure 2.5. These effects may play an important role in catalysis;
however, in realistic reactor conditions the situation can be quite complicated as molecules and their by-products may block certain sites and kinetically hinder diffu-sion processes.
Figure 2.5 Transformation of the atomic structure of the Au79NP in the presence of CO mol-ecules. (a) The equilibrium truncated octahedral structure in vacuum and (b) the equilibrium structure for an average CO coverage of four molecules (42).
UNIQUE BONDING IN NANOPARTICLES AND POWDERS 30
2.4.2.3 Optical Properties The interaction of electromagnetic radiation with Au NPs can stimulate collective excitations of conduction electrons known as plasmons.
At certain frequencies a resonance condition can be fulfilled resulting in intense scat-tering in the visible part of the spectrum. The frequency and width of the resonance depend on both the size and shape of the NPs and the dielectric medium in which they are embedded (43). Although these effects are inherently quantum in nature they can be modeled using classical electromagnetism, for example, Mie theory, and are of interest for a wide range of applications. For example, ordered arrays or chains of NPs can be used as nanoscale photonic waveguides allowing one to beat the diffraction limit of light (e.g. see Reference 44 and references within). They can be employed as biomolecular sensors due to the sensitivity of the plasmon resonance peak position on the dielectric media. They also have potential application as biologi-cal markers. For example, wet chemistry methods can be used to produce Au NPs that are passivated by a layer of molecules, for example, thiols. By binding relevant functional groups to these NPs they can be attached to specific molecules or proteins which can then be easily identified using optical microscopes.
As Au NPs find more and more applications there has been increasing concern about their possibly harmful interaction with biological organisms (nanotoxicity).
Recent studies indicate that prolonged exposure of cells to high concentrations of NPs does cause cell damage. These effects appear to be related to the penetration of NPs into cells and the generation of active oxygen species (45).
2.4.3 Summary
The perception of gold as a highly inert material has been transformed by the dis-covery that nanosized gold particles are chemically active for numerous reactions.
They also possess unique electronic and optical properties which can be tuned for specific applications by controlling their size and atomic structure. Surface science studies and theoretical models that have helped to understand these complex structure-property relationships suggest that confinement of electronic states, under-coordination of atoms, charging, and NP-support interactions all play important roles. These effects are not only relevant to Au but to other metallic NP systems as well, such as transition metals. However, Au is a particularly interesting example because its bulk surfaces are inert whereas bulk transition metal surfaces are active cat-alysts. Many of the applications of Au NPs, for example, in biology, gas sensing, and catalysis, involve interactions with molecules that can influence NP structure. The dynamical interplay between molecules and NPs is, in general, both complex and nonequilibrium in nature. Understanding these processes is an important problem that underpins many applications in nanotechnology and which presents a challenge for both theory and experiment.
2.5 CONCLUDING REMARKS AND FUTURE OUTLOOK
One of the reasons NPs are attractive for a wide range of applications is the potential to engineer their electronic, chemical, and optical properties through their structure.
Varying the composition of the NP provides an additional degree of freedom and
2.5 CONCLUDING REMARKS AND FUTURE OUTLOOK 31
is receiving increasing interest for a wide range of systems. The structure and compo-sition of NPs are closely interrelated as one can influence the other. For example, atoms of one type may prefer to segregate to particular locations on the NP surface modifying its structure. Multicomponent NP systems often exhibit properties that are characteristic of neither component in isolation and can be tailored for various applications. For example, doped semiconductor and metal oxide NPs have interesting optical properties and bimetallic NPs (e.g. AuPt, AuPd) are highly active catalysts.
The work on NPs to date has shown us that theoretical modeling and experiment must work closely together to unravel the precise nature of structure-property relation-ships. Recent advances in techniques such as TEM (33), STM, and atomic force microscopy mean that atomic-scale resolution of NP structure is now becoming possible. This is complemented by increasingly powerful computers that allow for quantum mechanical calculations on larger and more complex NP systems (e.g.
including the substrate or interfaces between NPs). One of the key remaining chal-lenges (for experiment and theory) concerns the atomic-scale dynamics of NPs.
This is important for understanding NP growth, an important step towards controlling structure, and for understanding the role of temperature in real applications. A related issue concerns the interaction of NPs with their environment, for example, molecules in a surrounding liquid or gas, which can influence their structure and properties. To address this problem in situ experimental studies are becoming increasingly common and can be complemented by similar developments in theoretical modeling.
SUGGESTED FURTHER READING
K. J. Klabunde. editor. Nanoscale Materials in Chemistry. New York: Wiley-Interscience, 2001.
D. G. Pettifor. Bonding and Structure of Molecules and Solids. Oxford: Oxford University Press, 1995.
J. Venables. Introduction to Surface and Thin Film Processes. Cambridge: Cambridge University Press, 2000.
G. A. Ozin, A. C. Arsenault. Nanochemistry: A Chemical Approach to Nanomaterials. Royal Society of Chemistry, 2005.
R. L. Johnston. Dalton Trans. 2003, 4193.
C. Noguera. Physics and Chemistry at Oxide Surfaces. Cambridge: Cambridge University Press, 1996.
K. P. McKenna, P. V. Sushko, A. L. Shluger. J. Am. Chem. Soc. 2007, 129: 8600.
F. Beletto, R. Ferrando. Rev. Mod. Phys. 2005, 77: 371.
D. Astruc, editor. Nanoparticles and Catalysis. New York: Wiley-VCH, 2007.
L. M. Molina, B. Hammer. Phys. Rev. B 2004, 69: 155424.
S. Utamapanya, K. J. Klabunde, J. R. Schulp. Chem. Materials 1991, 3: 175.
S. I. Stoeva, B. L. V. Prasad, U. Sitharaman, P. Stoimenov, V. Zaikovski, C. M. Sorensen, K. J. Klabunde. J. Phys. Chem. B. (invited paper for A. Henglein Special Issue) 2003, 107: 441.
UNIQUE BONDING IN NANOPARTICLES AND POWDERS 32
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PROBLEMS
1. Due to the finite number of valence electrons in a metallic NP its electronic states are discrete and separated in energy (e.g. see Reference 46) and as a consequence they become electrically insulating below a critical temperature. Estimate the metal-insulator transition temperature for a 2 nm and a 10 nm lithium NP (hint: compare the gap near the Fermi energy to the available thermal energy).
Some properties of Li you may find helpful are EF¼ 4.74 eV, r ¼ 535 kg m23, and M¼ 6.941 g mol21.
2. Derive an expression for the average binding energy per atom of a metallic NP and the dependence on its diameter (e.g. see Reference 47).
3. Using the equation derived above estimate the melting temperatures of a 1 nm and 10 nm diameter Au NP. Note the cohesive energy of Au is 3.9 eV.
4. The specific surface area of an NP is defined as the total surface area per unit mass, usually measured in m2g21. Calculate the specific surface area for a cubic MgO NP with 3 nm diameter. Note the density of MgO is 3.58 g cm23.
5. Calculate the relative proportion of 3C (corner), 4C (edge), 5C (terrace), and 6C (bulk) ions in MgO NPs assuming perfect cubes of length L and lattice constant a.
6. Comment on how the answers to Problems 4 and 5 may be modified for NPs in a powder.
UNIQUE BONDING IN NANOPARTICLES AND POWDERS 34
7. In Reference 21 the optical absorption spectrum of an MgO powder is measured and a band observed at 4.6 eV is attributed to three-coordinated anions.
Considering the electronic structure and morphology of the NPs what is the origin of the higher frequency band at 5.4 eV?
8. (a) Determine the nearest neighbor coordination number for atoms in the (100) and (111) surfaces of an fcc crystal (assuming no reconstruction).
(b) Calculate the surface area per atom for each of these surfaces (with nearest neighbor separation, d ).
9. If we assume the binding energy per atom in the problem above is linearly pro-portional to its coordination number, what is the ratio of (111) and (100) surface energies?
10. Low coordinated atoms on metallic NPs have been proposed to be catalytically active sites. How many atoms with a coordination of six or lower are there on icosahedral, octahedral, and truncated octahedral Au NPs.
ANSWERS
1. First we need to estimate the number of atoms in the NP. This can be done by assuming it is approximately spherical in shape and has a similar density to bulk Li. This gives N¼ (Na/M )(4/3p r3r), where Na is Avogadro’s number. From Reference 46 the average spacing between energy levels at the Fermi energy is: D¼ 4EF/3N. Note that Li is a simple metal with one valence electron per atom. Finally we need to equate the thermal energy, kBT to the spacing between energy levels to obtain: Tmet-ins¼ D/kB¼ (EFM )/(Nar3prkB).
Putting in the values we find that Tmet-ins(2 nm)¼ 47 K and Tmet-ins(10 nm)¼ 0.4 K.
2. There are various ways to do this but here is one example. Assume a spherical par-ticle of diameter, D, with nearest neighbor distance between atoms, d. The total number of atoms in the particle is approximately: N¼ (D/d)3, although this number is actually smaller due to the finite packing fraction. The number of atoms on the surface of the NP can be estimated as: Ns¼ 4(D/d)2. The total bind-ing energy of the NP is E¼ NEc2NsD, where Ecis the bulk cohesive energy and D is the average energy cost associated with each surface atom. To obtain a sim-pler expression it is useful to assume that D can be expressed as a fraction of the bulk cohesive energy, that is, D¼ fEc (e.g. where f, 1 and is related to the number of broken bonds). Rearranging we find E/N ¼ Ec[12 C(d/D)], where C is a constant related to the geometry of the NP and is approximately equal to unity for three-dimensional NPs.
3. We need to equate thermal energy to the binding energy per atom. The empiri-cal relationship that allows one to estimate melting temperatures is Tm¼ (0.032/kB) Eb (e.g. see Reference 47). For Au, using d¼ 2.88 A˚ we find that Tm(1 nm)¼ 1031 K and Tm(10 nm)¼ 1407 K.
ANSWERS 35
4. The surface area of a cube with diameter D is A¼ 6D2. The mass associated with this cube is m¼ D3r. Therefore, the specific surface area, A/m ¼ 6/(Dr). Using r(MgO)¼ 3.58 g cm23and D¼ 3 nm then A/m ¼ 559 m2g21.
5. There are eight 3C ions per cube, [(L/a)21] 24 4C ions per cube, [2(L/
a21)]2 6 5C per cube, 2(L/a21)36C per cube. The total number of ions per cube is (L/a)3and their relative proportions can be easily evaluated. For example, an MgO cube with 1 nm diameter has about 7% 3C atoms, while a 5 nm cube has less than 0.1%.
6. Interfaces between nanocubes in a powder will reduce the overall specific surface area and the number of low coordinated ions.
7. The band at 5.4 eV has higher intensity than that at 4.6 eV. If the band at 5.4 eV is due to excitation of four-coordinated ions (edges) then the difference in inten-sity can be understood in terms of the relative populations of three- and four-coordinated ions (see Problem 5).
8. (a) Z¼ 8 for atoms in (100) surfaces and Z ¼ 9 for atoms in (111) surfaces.
(b) The area per atom in a (100) surface is A100¼ d2. The area associated with each atom in a (111) surface is A111¼ [ ffiffiffiffiffiffiffiffi
3=2 p ] d2.
9. The surface energy for the (100) surface is g100¼ C(12 2 8)/A100and for the (111) surface is g111¼ C(12 2 9)/A111, where C is a constant. Therefore, g111/g100¼ (3/4) [2/ ffiffiffi
p3
]¼ 0.87.
10. Icosahedral NPs have 12 6C atoms, octahedral NPs have six 4C atoms, and truncated octahedral NPs have 24 6C atoms.
UNIQUE BONDING IN NANOPARTICLES AND POWDERS 36