12116
J. Phys. Chem. C 2008, 112, 12116–12121
Redox Behavior of Nanoparticules: Nonextensive Thermodynamics Approach Pierre Letellier, Alain Mayaffre, and Mireille Turmine* UniVersite´ Pierre et Marie Curie-PARIS6, UMR7575, and Ecole Nationale Supe´rieure de Chimie Paris-ENSCP, CNRS, UMR7575, Paris, F-75005 France, and Energe´tique et Re´actiVite´ aux Interfaces, UniVersite´ Pierre et Marie Curie, Case 39, 4 Place Jussieu, 75252 Paris Cedex 05, France ReceiVed: February 4, 2008; ReVised Manuscript ReceiVed: May 14, 2008
We show here that the concepts of nonextensiVe thermodynamics (NET), described previously (J. Phys. Chem. B, 2004, 108, 18980), can be used to express the variations of a redox couple according to the size of the reduced solid species by a power law. The Gibbs-Thompson relation then appears as a particular case of this formulation. The NET adopts the same conceptual basis as classical thermodynamics but uses an extensity, χ, in the expression of internal energy. This extensity is an Euler’s function of the particle mass with a homogeneity degree, m, which can be other than one; m is the thermodynamic dimension of the system. The consequences are that the functions of state are no longer extensive and that the magnitudes such as the chemical potential or the pressure are no longer intensive extents. This approach can be used to describe complex systems (for example, nanoparticles, porous substrates, and dispersed or interpenetrated phases). We checked the validity of the relations established by considering experimental data concerning the Ag/ Ag+ system. The silver clusters which grow on AgBr and AgBr in the presence of gelatin indeed have the properties of nonextensive phases of which we specify the characteristics. I. Introduction Recent advances in nanotechnology have led to the development and production of many new nanomaterials for industrial and biomedical uses. The many ways to obtain these materials and their most important physicochemical properties have been presented in various feature reviews.1–3 Their chemical reactivity4 has been the subject of numerous studies. This reactivity depends largely on the shape5–10 and the size11–15 of the clusters. Thus, at nanometric scale, noble metals, such as silver16 (E*Ag+/Ag,NHE ) 0.799 V) and gold (E*Au3+/Au,NHE ) 1.42 V) embedded as nanoparticles11 in a silica matrix, react with hydrochloric acid, leading to the metal chloride with hydrogen release. Silver clusters can readily reduce many inorganic and organic compounds.17–19 The high chemical reactivity of nanoparticles is undoubtedly a limitation, still poorly understood, that must be considered before their use for technological applications. Thus, in nanoelectronics,20 it was shown that the nanocontacts achieved in silver or in gold are corroded by oxygen in atmospheric air21,22 at room temperature. The possible use of the nanoparticles in the laboratory, in the industrial sector, or for applications in everyday life requires that the relations between the reactivity of a solid, its size, and its form are better understood. This is the aim of this study. These behaviors can be analyzed by applying a nonextensive approach of thermodynamics which we described and illustrated in previous works.23–26 Here, we consider the case of redox equilibria where the reduced species (referred to as red.) is a pure metal in shaped clusters. II. Relations between Reactivity, Size, and Shape The specific properties of the clusters of nanometric size and their redox reactivity have been studied experimentally by many * To whom correspondence should be addressed. E-mail: mireille.turmine@ upmc.fr.
authors.27,28 Henglein17 reported that the standard potential of Ag/Ag+ decreases with the size of the metallic aggregate to a minimum of -1.8 V for single atoms. Throughout our analysis, we consider the case where the number of atoms per aggregate, or of nucleons in the medium, is sufficient for defining macroscopic behavior for which thermodynamic approaches apply. Malinowski et al.,29–32 indicate that the laws of thermodynamics probably apply to the nucleation phenomenon because, even if the nucleons are very small, they are very numerous in solution. The result is that the statistical requirements of thermodynamics are always fulfilled and the only flaw seems to be the use of the value of the interfacial tension defined for a bulk phase. Defay and Prigogine33 present a similar view. They used thermodynamic laws to describe the physicochemical properties of small spherical aggregates down to the nanometric scale; for the smaller particles (diameter smaller than or equal to 1 nm), the values of the interfacial tensions vary according to the particle size. The classical approaches which consider the relationships between the size of a component and its reactivity usually suppose spherical particles and use Laplace’s rule explicitly or implicitly to consider the particle-environment interface energy.33 Spherical nanoparticles exist, but current methods of preparation also yield nanosolids with very diverse shapes and sizes (including cubes, nanorods, tubes, and nanowires) either dispersed in a medium or embedded in nanoporous or mesoporous matrices. In such situations, the spatial structure of nanoparticles is difficult to specify from standard geometrical dimensions (length, area, and volume) and the concept of interfacial tension for material as a whole loses its meaning. For this main reason, it has been proposed in other fields to describe the behavior of nanosystems by fractal approaches (see capillary condensation in porous substrates,34–38 solubility,39 etc). This approach generally leads to the description of power laws. We previously developed a nonextensive approach to thermodynamics (NET)23 which also leads to power laws but which does not impose the use of the fractality concept. Its basis is
10.1021/jp801040u CCC: $40.75 2008 American Chemical Society Published on Web 07/23/2008
Redox Behavior of Nanoparticules
J. Phys. Chem. C, Vol. 112, No. 32, 2008 12117 the development of applications. The prolongation of this approach is considered in more detail in ref 23 To aid comprehension of the following developments, we will first consider various properties of χ and the main established thermodynamic relationships. The extensity χ is a function of the system content (n1, n2,..., ni):
χ ) χ(n1,n2,...,ni)
(2)
By convention, this extent has the property of an Euler’s function of order m. If the system content is multiplied by λ, then
χλ)χ(λn1,λn2,...,λni) ) λmχ
Figure 1. Scheme of fuzzy interface. NEP is the pressure of the cluster, and P is the pressure of the bulk medium.
the same as that of classical thermodynamics with the same functions of state but supposes that they can be nonextensive. This property is introduced by means of integer or fractional thermodynamic dimensions. This approach is particularly adapted to the physicochemical description of complex systems (such as porous substrates, interpenetrated phases, dispersed solutions, and nanoparticles). We showed that the wettability of smooth or rough substrates,24 such as the melting point of nanoparticles,25 can be suitably described by this approach. Here, we use this approach to tackle the issue of the redox properties of metallic nanoparticles. A. Conceptual Bases of Nonextensive Thermodynamics, The Concept of the Fuzzy Interface. We will briefly summarize the bases and the objectives of this new thermodynamic approach. The problem addressed is that of a system defined by its contents (n1, n2,..., ni moles), in contact with an external phase at pressure P and at temperature T. The “interface” between the studied system and the external medium is presumed to be vague and cannot be described by means of the usual geometrical variables such as length, area, and volume (Figure 1). This is the case of, for example, interpenetrated phases, various porous substrates, and dispersed media. By convention, we will name this type of interface a fuzzy interface.24,40,41 The variables of dimension relevant to characterizing the behavior of the studied system are not available in such cases. To solve this difficulty, we introduced into the expression of internal energy an extensity variable, χ, associated with an intensive tension extent, τ. The internal energy can then be written
dU ) T dS - P dV +
∑
µi dni + τ dχ
(1)
S, V, and ni are respectively the entropy, the volume, and the numbers of moles of the system components. In thermodynamics, the extensity variables associated with the tension extents, conventionally, are extensive variables, i.e., Euler’s functions of the system mass of order m ) 1. We considered the possibility that these extensity variables are not extensive but nevertheless remain an Euler’s function of the system mass of degree of homogeneity, m, different from 1 (m * 1). This convention, without modifying the conceptual base of thermodynamics, allows new approaches for analysis and
(3)
The parameter m is the homogeneity degree of the Euler’s function. This is, by convention, the thermodynamic dimension of the system. Its value can be equal to 1 in which case classical thermodynamics apply. The introduction of the nonextensivity into the extensity magnitudes implies that the functions of state of thermodynamics (U, S,...) are no longer extensive. Consequently, the tension extents associated with the extensities may not be intensive. We chose, by convention, to conserve this property for the temperature T [in physics, there are several developments of nonextensive thermodynamics using conventions in which the temperature is considered as nonintensive variable: (a) Abe, S.; Martinez, S.; Pennini, F.; Plastino, A. Phys. Lett. A 1998, 261, 534; (b) Toral, R. Physica A 2003, 317, 209] and for τ. For consistency, the chemical potentials and the pressures become nonintensive extents; this means that they vary with the system mass. For the variable pressure, we showed that, for a nonextensive (NE) system constituted by n moles of compound, of volume V, of extensity χ, and of dimension m, there is a relationship between the pressure of the nonextensive system, NEP, and the pressure of the environment, P (Figure 1):
dχ τχ )m (NEP - P) ) τ dV V
(4)
This relation generalizes Laplace’s relationship for nonextensive systems. It does not involve a defined curvature or specific geometrical frontiers of the nonextensive system. This relation is defined from only its physicochemical parameters and, obviously, allows the known results for simple geometry to be obtained. In the case of a drop of liquid L1 in a liquid L2, of interfacial tension γL1L2, of radius r, and interfacial area AL1L2, the pressure difference between the inside of the drop (NEP ) Pd) and the external pressure of the gaseous atmosphere is obtained by replacing in eq 4 τ by γL1L2 and χ by AL1L2. When the drop volume is multiplied by λ, the area AL1L2 is multplied by λ2/3. The area is then an extensity of order m ) 2/3 toward the mass or the volume of the drop. The liquid drop is a nonextensiVe phase of thermodynamic dimension equal to 2/3. Then,
(Pd - P) ) m
τχ 2 γL1L2AL1L2 γL1L2 ) )2 V 3 V r
(5)
which corresponds to Laplace’s relationship. We will apply these NET relationships to a system constituted by a redox pair, in which the metallic reductant (referred to as red.) is the nonextensive phase and is in a solution (solvent S) comprising the oxidant (ox.) at temperature T. B. Reactivity of Metal Cluster. The metal species, red., is at pressure NEP, and its environment containing the oxidant is at pressure P (Figure 1). The chemical potential of the metal species in the nonextensive phase varies with the pressure P; thus,
12118 J. Phys. Chem. C, Vol. 112, No. 32, 2008
( ) ∂µred. ∂P
)V*red.
Letellier et al.
(6)
T,nred.
* Vred.
is the molar volume of the metal. As its value presumably varies little with the pressure, the previous equation can be integrated, and P P * NE µNE red. ) µred. + Vred.( P - P)
(7)
In view of eq 4, then NE
µred.P ) µPred. + V*red.mτ
χ V
(8)
V corresponds to the volume occupied by the reductant in the system. Thus, the chemical potential of species i in the nonextensive phase differs from that at pressure P such that there is a reactivity difference of the metallic species. In the case of a sphere, of radius r, the relation described by Defay and Prigogine33 is found NE
µred,P ) µPred. + V*red.
2γSL r
(9)
γSL is the interfacial tension between the solid reductant and the surrounding solution. In this situation, as the radius of the sphere decreases, the chemical potential of the reductant in the nonextensive phase increases and the species becomes more reactive. The behavior of the nanoparticles can be generalized from this example: they are systematically more reactive than the bulk material. However, eq 8 allows other behaviors to be * considered. Indeed, the term Vred. mτχ/V can be positive or negative according to the sign of τ. If it is positive, the reactivity of the reduced species will indeed increase. But one cannot exclude the possibility of experimental situations where τ is negative, in which case the reduced species would be more stable in nonextensive phase than in the bulk. Such behaviors have been observed in other fields, particularly for liquid-vapor equilibria described by Kelvin’s relations. In the capillary condensation phenomenon, the liquid is stabilized by the porous substrate in which it is included. The effect of size and form results in a decrease of the reactivity of the liquid which condenses with a value of vapor pressure lower than that characteristic of equilibrium between unlimited phases.33 For the same system, the opposite effect is observed when the liquid is in the shape of a drop surrounded by its vapor. The consequence of this is that simply dispersing a compound does not necessarily increase its reactivity. Experiments are required to determine the characteristics of the situation. Using these relations the influence of the size of the reduced particle on the position of the redox equilibrium can be determined. III. Variations of the Standard Potential of a Redox Couple with the Shape and the Size of the Reduced Particle A. Conditions of Redox Equilibrium. The behavior of redox pairs is conventionally referred to the pair H2/H+. The behavior of a redox pair involving ν electrons is described by the conventional reaction of Nernst
ν ox. + HR2 )red. + νH+,R 2
(10)
For reasons of clarity, we did not include the charges number (ν+) carried by the oxidized species. At the considered temperature, hydrogen (H2R) is taken in its standard state (perfect gas with the pressure of 1 bar, µH2R ) µH* 2). The protons (H+,R)
are considered in their hypothetical standard state at infinite dilution in the medium, (activity and concentration values are simultaneously equal to 1, µH+,R ) µH∞+). The reduced species constitutes a nonextensive phase at pressure NEP. The free Gibbs energy of this reaction is written according to the chemical potentials of the various species involved NE ν ∆redoxG ) νµH∞+ + µred.P - µPox. - µH* 2 2
(11)
From eq 8, the standard free energy of the conventional reaction of electronic exchange at ambient pressure P is written as
χ ν ∆redoxG ) νµH∞+ + µ*red. + V*red.mτ - µ∞ox. - µH* 2 V 2 ) -νFEapp redox (12) µ∞ox. is the standard chemical potential of the oxidized form with the reference state being the infinitely dilute solution (values of the activity and the concentration simultaneously equal to 1). By definition, Eapp redox is the apparent standard Nernst potential of the considered redox pair at given conditions. If the redox reaction is considered in unlimited phases, at standard conditions, then
ν ∆redoxG * ) νµH∞+ + µ*red. - µ∞ox. - µH* 2 ) -νFE*redox 2 (13) Thus, this indicates that the apparent standard potential of the redox pair is different from the standard potential referred to the pair H+/H2 and varies with the parameters of the nonextensive phase according to * * E*,app redox)Eredox-Vred.
mτ χ νF V
(14)
We will examine the consequences of this relation by considering various experimental models. B. Interface and Extensity. Interface is a surface and the extensity is an area. First, we will consider the case where the geometry of the nonextensive phase is sufficiently well defined that the extensity χ can be identified with an area. B.1. Spherical Particle. A metal spherical particle of radius r is considered: the dimension m ) 2/3. The extensity is identified with the solid-liquid area, ASL, the tension τ with the surface tension, γSL, and the volume of the nonextensive phase to that of the particle. The Gibbs-Thompson relation usually applied to formalize the variation of the standard potential42 with the particle radius is then found: *
* E*,app redox)Eredox -
*
Vred. 2γSL 2 Vred. SL 4πr2 ) E*redox γ (15) 3 νF 4 3 νF r πr 3
In this situation, the reduced species is more easily oxidizable as the particle radius decreases. B.2. Not Spherical Particle. Nanoparticle engineering allows the preparation of items of defined shape and size, such as cubes or nanorods.10 The standard potential variations for redox systems involving such aggregates can be described by means of the relations reported above. Thus, for a cube of a reduced solid species of edge a and of volume a3, the redox potential is written as
Redox Behavior of Nanoparticules * E*,app redox)Eredox -
V*red. 4γSL νF a
J. Phys. Chem. C, Vol. 112, No. 32, 2008 12119
The apparent standard potential of the redox couple decreases as the cube edge length decreases. For nanorods43 which grow without any change in base area but with increasing height, h, we can consider the surface area of the base to be negligible relative to surface area of the cylinder sides (where h . d/2), giving the following relation * E*,app redox)Eredox -
V*red. 4γSL νF d
(17)
For nanorods, the standard potential of the pair varies with the inverse of the cylinder diameter but is independent of its length. There are many examples which can be used to illustrate the value of applying eq 14 to objects of various sizes and forms. C. General Case: Fuzzy Border System. We will consider the case of clusters whose spatial structure cannot be simply described from the classical dimensions (volumes, areas, and lengths). C.1. Nanoparticles of Dimension m and of Mass Mp. A metal in the form of identical nanoparticles is considered, having the same property of nonextensive phase of dimension m. The mass of each particle is Mp; its volume, Vp; and its extensity, χp. We will assume that any addition of solid to the system will only increase the number, N, of nanoparticles. This situation is described by the following relations,
V ) NVp χ ) Nχp
(18)
The volume being a homogeneous function of order 1 of the mass and the extensity χ of order m, the ratio between χ and V is therefore a homogeneous function of order m - 1 of the mass of the solid. This property corresponds to
χ χp ) )kMpm-1 V Vp
(19)
The redox potential depends on the mass of the reduced nanoparticles according to * E*,app redox)Eredox -
V*red. mτkMpm-1 νF
(20)
Thus, the Variation of standard potential depends on the mass of the aggregate in the system and does so according to a power law. C.2. BehaWior of Real Systems. The validity of the previous relations is difficult to judge because the data in the literature are mostly based on presumed particle radii, even when the particles are not spherical. We thus modified the form of the previous equations so as to make them more generally applicable and take into account all the shapes of nanosolids without having to specify them. Our reasoning is as follows. Suppose that the nanosolid size is characterized experimentally by a dimension (radius, diameter, or thickness) which we will denote as ω. We will suppose that the extensity, χ, and the volume are Euler’s functions of order p and q, respectively, of ω so
V ) V(ω) ) Rωq χ ) χ(ω) ) βωp
P-P)τ
NE
(16)
(21)
R and β are coefficients of proportionality. The pressure difference between the nonextensive solid phase and the solution is then written as
dχ βp ) τ ωp-q dV Rq
(22)
Similar reasoning leads to the redox potential variation with the measured size, ω, of the particles according to a power law * E*,app redox)Eredox -
V*red. τβp p-q * ω )Eredox-Yωωη νF Rq
(23)
* By convention, we will note p - q ) η and Yω ) (Vred. /νF)(τβ/ -η R)(p/q) (unit, u ) volts m ). The form of the Gibbs-Thompson relation can be verified by taking the radius of a sphere as dimension ω ) r, p ) 2, * and q ) 3, in this case, Yω ) 2γSLVred. /νF (u ) volts m). We will now test the validity of eq 23 under its logarithmic form for published data.
* log(E*redox - E*,app redox))log(∆Eredox) ) log(Yω) + η log(ω)
(24) Although there are a great number of descriptions of the behavior of redox systems involving metal clusters as the reductant, there are few experimental values suitable for illustrating the diversity of the situations which can be expected from eq 24. IV. Analysis of the Behavior of the Ag/Ag+ System Most of the experimental values in the literature relate to the Ag/Ag+ system and generally come from the study of the phenomena associated with photography.44 Malinowski et al.29–32 in four successive publications present values of the Ag/Ag+ redox potential according to the size of the silver aggregates whose radii are generally greater than 2 nm. Thermodynamics is applicable for such sizes because a silver spherical aggregate of 2 nm comprises approximately 2000 atoms. In all their experiments, they used a developer containing a ferrous-ferric redox buffer. The equilibrium potential of small silver aggregates can in all cases be determined by the Gibbs-Thompson equation whatever the nature of the substrate (carbon or silver bromide) on which the silver particles are deposited. The samples were coated or not coated with a very thin layer of gelatin by dipping in 0.1% solution at 35 °C. However, the Ag/Ag+ equilibrium potential values reported in the three earlier papers differ slightly according to the developing method. Thus, the authors noted that chemical developer31 leads to equilibrium potentials different from those with the physical developer.30 Nevertheless, for both methods, the relationship between ∆E*redox and 1/r was always linear; however, the straight lines obtained with the chemical developer do not start from the origin (shift of 13 mV). The authors assigned this shift in the silver potential to an increase of the ionic strength of the medium due to the introduction into the solution of Fe2+/ Fe3+ pair used as developer. In his paper published in 1979,32 Malinowski analyzed his previous work and clearly preferred to emphasize the data of ref 30, which are well-described by the Gibbs-Thompson equation. In this case, our approach is of a lesser interest as η ) -1. For this reason, we examined here the experimental data of ref 31 (Table 1) in light of our approach using eq 24. Using the log values on both axes leads to excellent lines of correlation for the two substrates (Figure 2). For silver aggregates on AgBr, a straight line is obtained with a slope η ) -1.397 and a y-axis intercept Yω ) 0.2743 u; for silver particles developed on AgBr coated with gelatin the correlation line has a slope η ) -2.2399 and a y-axis intercept Yω ) 0.1951 u. From these parameters, we simulated the
12120 J. Phys. Chem. C, Vol. 112, No. 32, 2008
Letellier et al.
Figure 2. Plot of log(∆E) against log(r) for silver nanoparticles developed on (a) AgBr substrate and (b) AgBr substrate coated with gelatin.
Figure 3. Experimental data (black squares) and calculated values (solid line) from parameters determined using eq 24 for (a) AgBr substrate and (b) AgBr substrate coated with gelatin.
behavior of these two systems and we plotted the variations of experimental and calculated ∆E*redox against 1/r: the experimental data are perfectly positioned on the curve starting from the origin (Figure 3). In such a case, the nonzero intercept could be explained without using the notion of ionic strength as suggested by the authors. The interpretation of the parameters η ()p - q) and Yω is delicate because without knowing the shape of the metal particles, the value of p cannot be specified without making assumptions about the value of q. However, q is classically equal to 3, and the consequences of this assumption can be considered: for pure AgBr, the thermodynamic dimension of the silver aggregate is p ) 1.60. This value means that the extensity implied in the growth phenomenon varies with the size (the radius) of the system less quickly than with the surface (p ) 2) but more quickly than with the length (p ) 1). In such cases, the silver particles involved in the growth phenomenon are unlikely to be perfectly spherical. This is in good agreement with the classical observations made for direct or chemical development leading to silver grains with filamentary structure.45 With regard to the silver aggregates on AgBr coated with gelatin, their mode of growth is completely different. The thermodynamic dimension (p ) 0.7701) is thus smaller than 1. Therefore, for silver particles on gelatin, the extensity varies less quickly than the measured size of the particles. This dimension implies that not all the mass of the silver particles contributes to the extensity involved in redox equilibrium. In the papers of Malinowski et al.,29–31 the difference in the behavior of silver particles during their growth on AgBr coated or not coated with gelatin is only dependent on the changes of the nature of the interface between the silver and the solution. Caution is required for such interpretations. Indeed, the ratio between the two values of Yω is 1.4, leading to τAgBrβAgBr/ τAgBr/gelβAgBr/gel ) 0.67, which may represent both the modification of the nature of the interface (value of τ) and also the modification of the morphology of the aggregates (value of β). To our knowledge, there has been no other series of experimental data published concerning aggregates of adequate sizes which allows the validity of our approach to be assessed.
TABLE 1: Variation of Silver Equilibrium Potential (∆E ) Esilver - EFe3+/Fe2+) with the Silver Aggregate Radius (r) Measured by Electron Micrography (See Ref 31)a uncoated AgBr substrate
AgBr coated with gelatin
r /nm
∆E /V
2.3 2.7 3.3 3.3 3.9 4.9 5.4 6.6 2.8 3.0 4.1 4.8 5.1 5.4
0.0830 0.0692 0.0548 0.0530 0.0411 0.0308 0.0263 0.0193 0.0193 0.0170 0.0085 0.0067 0.0051 0.0042
a The small silver aggregates were developed on silver bromide layers covered or not covered with gelatin.
We chose not to consider the published values concerning aggregates of very weak nuclearity as proposed by Henglein46 and Khatouri et al.,27 because these situations do not correspond to traditional thermodynamic approaches. Many authors suppose that, for these systems, there is a new state of matter, intermediate between the atom and the crystal.28,47 In 1962, Kubo48 thus suggested that an isolated atom, or a few atoms linked together in a cluster as in a molecule, possesses discrete electron levels, introducing a quantum-size effect. It has been shown indeed that the thermodynamic properties of a metallic cluster vary with the number of atoms n which it contains, both in solutions17,49 and in the vapor phase.50,51 The paper by Halperin52 presents a comprehensive analysis of these various manners of tackling these problems of nucleation. V. Conclusion NET uses the concepts of classical thermodynamics as a basis, and constitutes a consistent whole of relations which can be
Redox Behavior of Nanoparticules used to obtain a satisfactory description of the physicochemical behaviors and the reactivity of complex systems (particularly nanoparticles and porous systems). It also allows consideration of situations not yet described, such as for example the increase in the redox potential with the size of the aggregates of reduced form. This situation could be found in systems of metal nanoparticles included in porous substrates. Our approach thus allows analysis of all the potential diversity of the variations of reactivity of the particles with their size and their form, and this is of fundamental importance for their use. Indeed, beyond the problems involved in obtaining these particles which can be of various natures (including metals, oxides, semiconductors,53 and polymers), sizes, and forms, both determined and undetermined, there is also the issue of the conditions of their use in industrial processes or of their introduction into finished products. The reactivity of nanoparticles contributes to their toxicity. The literature contains an abundance of publications54–57 describing this problem and reporting the potential risks to human population and ecosystem associated with nanoparticles of even common compounds. There is a general consensus that the impact of progress in nanotechnology on worker safety, consumer protection, public health, and the environment has to be considered carefully, especially as the toxicity of nanomaterials is not predictable a priori from that of bulk material. Responsible and beneficial development of the chemistry of nanoparticles will only be possible on the basis of a thorough knowledge of relationships between the reactivity of a material and its size and form. References and Notes (1) El-Sayed, M. A. Acc. Chem. Res. 2004, 37, 326. (2) Burda, C.; Chen, X. B.; Narayanan, R.; El-Sayed, M. A. Chem. ReV. 2005, 105, 1025. (3) Daniel, M. C.; Astruc, D. Chem. ReV. 2004, 104, 293. (4) Sun, C. Q. Prog. Solid State Chem. 2007, 35, 1. (5) Schmid, G.; Baumle, M.; Geerkens, M.; Helm, I.; Osemann, C.; Sawitowski, T. Chem. Soc. ReV. 1999, 28, 179. (6) Shipway, A. N.; Katz, E.; Willner, I. ChemPhysChem 2000, 1, 18. (7) Rao, C. N. R.; Kulkarni, G. U.; Thomas, P. J.; Edwards, P. P. Chem. Soc. ReV. 2000, 29, 27. (8) Schmid, G.; Chi, L. F. AdV. Mater. 1998, 10, 515. (9) Henglein, A. Chem. ReV. 1989, 89, 1861. (10) Pileni, M. P. J. Phys. Chem. B 2001, 105, 3358. (11) Shi, H. Z.; Bi, H. J.; Yao, B. D.; Zhang, L. D. Appl. Surf. Sci. 2000, 161, 276. (12) Ershov, B. G.; Janata, E.; Henglein, A.; Fojtik, A. J. Phys. Chem. 1993, 97, 4589. (13) Henglein, A.; Ershov, B. G.; Malow, M. J. Phys. Chem. 1995, 99, 14129. (14) Bi, H. J.; Cai, W. P.; Kan, C. X.; Zhang, L. D.; Martin, D.; Trager, F. J. Appl. Phys. 2002, 92, 7491. (15) Chaki, N. K.; Sharma, J.; Mandle, A. B.; Mulla, I. S.; Pasricha, R.; Vijayamohanan, K. Phys. Chem. Chem. Phys. 2004, 6, 1304.
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