Chapter 15 Charge Effects in Catalysis by Nanostructured Metals

Chapter 15

Charge Effects in Catalysis by Nanostructured Metals S.A. Gurevicha, V.M. Kozhevina, I.N. Yassievicha, D.A. Yavsina, T.N. Rostovshchikovab, and V.V. Smirnovb a

Ioffe Physico-Technical Institute of RAS, Polytekhnicheskaya 26, St. Petersburg 194021, Russia b Chemistry Department, Lomonosov Moscow State University, Leninskie Gory, Moscow 119992, Russia 1. 2.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Catalyst Fabrication and Structural Properties. . . . . . . . . . . . . . 2.1. Catalyst Fabrication by Laser Electrodispersion of Metals 2.2. Structural Properties of the Catalyst Coatings . . . . . . . . . 3. Charge State of Metallic Nanostructures . . . . . . . . . . . . . . . . . . 4. Effect of Nanoparticle Charging on the Catalytic Properties . . . . 4.1. Analytical Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Experimental Results and Discussion . . . . . . . . . . . . . . . 5. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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The catalyst structures, which are thin granulated films consisting of Cu, Ni, or Pd nanoparticles, were fabricated by means of laser electrodispersion technique. This technique allows producing nearly monodispersive and amorphous metal nanoparticles (the particle sizes are 5.0 nm for Cu, 2.5 nm for Ni, and 2.0 nm for Pd; the size dispersion is less than 10%). These particles were deposited on dielectric (thermally oxidized silicon) or semiconductor (naturally oxidized Si) supports and the resulting particle surface densities were closely controlled by the time of deposition. The most important common feature of the fabricated catalysts is their unusually high (up to 105 product mole per metal mole per hour) specific catalytic activity measured in several chlorohydrocarbon conversions (Cu, Ni) and hydrogenation (Ni, Pd) reactions. In all the reactions, strong dependencies of the specific catalytic activity on the particle surface density and solution polarity have been observed. The nature of the support affected the activity as well, for instance, different activities were measured when using p- or n-doped Si supports. These experimental facts are explained assuming that, along with

THIN FILMS AND NANOSTRUCTURES, vol. 34 ISSN 1079-4050 DOI: 10.1016/S1079-4050(06)34015-X

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the small size and amorphous state of the particles, particles charge fluctuations (resulting from inter-particle or particle–support tunnel electron transitions) determine the catalytic activity of these structures. A theoretical model is developed providing means for calculating the number of the charged particles in case when the structure is deposited on a dielectric or on a conducting support. The speculations on the mechanism of tunnel electron transfer from the charged nanoparticle to the chemisorbed reagent molecule show that, for the reactions proceeding with the electron transfer, nanoparticle charging may result in substantial reduction of the reaction activation energy. Combining these two models allows quantitative estimation of the effect of the particle charge on the catalytic activity. Estimations made on this basis are in good agreement with the experimental results. Utilization of the described phenomenon of particle interaction (related with their charging) opens up a new way for managing the catalytic properties of immobilized metallic nanoparticles.

1. Introduction Recently, a profound interest in studies of properties of granulated metals, structures constituted by metallic nanoparticles, has been aroused. Problems associated with the application of these structures in the development of new nanoelectronic devices [1], devices for ultrahigh-density magnetic recording [2], new functional coatings [3], and high-efficiency solid-state catalysts [4] are widely discussed in the literature. This chapter is concerned with catalytic properties of metallic nanostructures. Catalysis by metallic nanoparticles is a highly important area of the modern science of catalysis. In most of the presently used catalysts, the active substance is deposited onto a support in the form of nanoparticles, which, in the first place, makes large the surface area of a catalyst and thereby provides a significant increase in its capacity. For example, quite a number of largetonnage techniques for processing of hydrocarbon raw materials (hydrogenation and dehydrogenation, not to mention the fine organic synthesis) employ metal nanoparticles and metal compounds fixed on various, mostly oxide or carbon supports [5–7]. A successful strategy of development of this area is passing from determination of properties of nanosize catalysts to their prognostication and, further, to synthesis of catalysts with optimal properties. In the development of nanostructured metal catalysts, one should take into account their principal distinctive feature, the dependence of the catalytic activity and/or selectivity on the particle size. This dependence, or the size effect, is due to the simple relationship between the catalyst surface area and

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the particle size: the smaller the particles, the larger the effective surface area of the catalyst. There are, however, two other, and even more important, reasons. First, the energy parameters of metal nanoparticles are known to be dependent on their size. The second is that the surface structure of a particle changes with its size. In particular, the surface curvature, the appearance of different crystal planes on the surface, and the presence of surface defects may all strongly depend on the particle size [8–11]. Combined, these factors most frequently lead to an increase in the catalytic activity upon a decrease in the particle size (direct size effect). In some cases, however, the activity of a catalyst may decrease as particles become smaller (inverse size effect) or reach its maximum value at a certain particle size. The reasons why the size-related properties are manifested in catalysis have been analyzed in detail in the literature [12]. Most frequently, dramatic changes in physical and catalytic properties occur at particle sizes of several nanometers to several tens of nanometers. The properties of such nanoparticles containing hundreds and thousands of atoms are fundamentally different from those of bulk metals, on one hand, and from the properties of isolated atoms and small clusters, on the other. It is particles of this kind that are used in real catalytic processes, and these particles are the subject of present chapter. It is important to emphasize that an adequate understanding of the mechanisms of catalytic processes that involve nanoparticles requires not only the properties of individual particles, but also those of the whole macroscopic system comprising a large number of particles (ensemble) and the support. This concept was first formulated in the late 1990s in Refs. [13–15] and was further developed by other authors [16–18]. An analysis of the properties of a catalytic system constituted by particles and a support requires that interaction between its separate components should be taken into account. In doing so, it is necessary to consider both the interaction of particles with one another within the ensemble and the interaction of the particles with the support. The nature of such an interaction may vary, being associated with local electric or magnetic fields, charge or mass transfer, etc. For example, it will be seen from what follows that charge transfer between particles in the ensemble or between the particles and the support may occur under certain conditions, which leads, in the end, to charging of the system of particles and markedly changes their energy state. Depending on the fabrication technology, and on properties of particles and the support, particle ensembles of various densities and varied type of particle arrangement on the support surface can be obtained. All these factors affect the catalytic activity and it is necessary to take them into account when designing a catalytic system [4,19,20]. This chapter is focused on charge-related effects in catalysis on metallic nanoparticles. The role of these effects was first discussed in the already mentioned studies [13–15] and was reviewed in Ref. [21], but it has not been

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conclusively elucidated until now. At the same time, it can be stated that analysis of charge effects in the catalysis by metal nanoparticles is one of the main research areas, which may prove to have key importance in the development of new highly effective catalytic techniques. When considering the charge effects, it is necessary to keep in mind their relationship with structure properties of a catalyst. There exist various methods for producing metallic nanoparticles and structures on their base, which can be conditionally divided into two large groups. In the first of these, nanoparticles are formed via aggregation of atoms (or small clusters), and in the second, as a result of dispersion of bulk metals. Methods based on aggregation of atoms into nanoparticles include thermal evaporation and condensation [22], reduction from solutions and that in microemulsions [23], and cryochemical synthesis [24] (see also Chapter 10 of this handbook). To the second group should be referred, e.g., the technology described in [25], in which nanoparticles were obtained by thermal evaporation of an overheated metal. Most of the methods described above can produce metallic particles 3–100 nm in size, which have, in certain cases, rather narrow size scatter. However, a common disadvantage of most of the mentioned techniques (except cryochemical synthesis) is that they cannot give structures with high particle density on the support surface. At the same time, structures of just this type exhibit most clearly charge effects, which lead in many cases to a significant rise in catalytic activity. One of the main difficulties is due to the fact that nanoparticles, which have a large specific surface area, tend to coagulate into larger aggregates and this tendency is particularly noticeable in high-density structures. The appearance of coarse aggregates leads to loss of the unique properties of separate nanoparticles. For this reason, a search for methods that can improve the coagulation stability of the metallic nanostructures is the task whose accomplishment governs the development of new promising areas in catalysis. In Section 2 of this chapter, a method for synthesis of high-density nanostructured catalyst is discussed. This method is based on the technique of laser electrodispersion of metals, developed at the Ioffe Physico-Technical Institute, Russian Academy of Sciences [26]. The same section discusses structural properties of the catalysts fabricated. It is demonstrated that these catalysts are composed of metallic nanoparticles of a strictly specified size, which, in addition, have amorphous structure. A consequence of the amorphous state of the particles is that they do not coagulate on coming in contact and retain their unique physico-chemical properties even in densely packed multilayer coatings. Section 3 is devoted to processes of tunnel charge transfer in a system of densely packed metallic nanoparticles and to effects of particle interaction with the support, which give rise to specific charge states of a catalyst. Owing to this effect, and also to structural

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features of nanoparticles, high-density coatings produced by laser electrodispersion exhibit an extremely high catalytic activity in quite a number of different catalytic processes.

2. Catalyst Fabrication and Structural Properties This section describes the method of laser electrodispersion of metals, which was used to synthesize all the catalysts whose properties are discussed in this chapter. This method proved to be exceedingly promising both for synthesis and study of model catalytic systems and for fabrication of catalysts that exhibit a record-breaking high catalytic activity.

2.1. CATALYST FABRICATION

BY

LASER ELECTRODISPERSION

OF

METALS

The method of laser electrodispersion is based on laser ablation, which occurs when a target is irradiated by a high-power pulsed laser. Previously, the laser ablation has been widely used for deposition of metallic coatings. However, under the usual process conditions the target material was primarily converted into the vapor phase. Accordingly, the coatings obtained on a substrate were either homogeneous metallic films, or thin island-type films. Characteristic for laser ablation is also the formation at the target surface (and further deposition on a substrate) of fine micrometer- or submicrometersize metallic drops. This was regarded as an adverse effect and attempts were made to minimize it. The distinctive feature of our approach consists in that this adverse effect is made useful and the formation of microdrops becomes a predominant process. In the process developed, the initially generated liquid metallic microdrops are then divided into a large number of nanometer-size drops, which very rapidly cool down to solidification. The resulting nanoparticles are deposited on a substrate surface. This process is accomplished on turning the laser ablation to more severe target irradiation conditions characterized by a high temperature of laser torch plasma. Liquid metal drops coming from the target surface proceed into the laser torch plasma produced by optical breakdown of the evaporated target material. Entering plasma area, these drops become negatively charged (as any isolated body placed in plasma would do). At a plasma temperature of 20–30 eV, the charge of microdrops reaches the critical value, at which they become unstable and start to split into smaller drops. This process of drop fission, which results from the development of a capillary instability of charged liquid drops, has been analyzed in a number of studies [27]. The

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simple reason for the appearance of this instability is that the Coulomb repulsion force exceeds the surface tension. An estimate of the instability threshold, which makes it possible to determine the corresponding amount of charge, was first obtained by Rayleigh [28]: Q
8pð
0 aR3 Þ1=2 .

(1)

In this expression, Q and R are the drop charge and radius, a the surface tension of a molten material, and e0 the permittivity of free space. It is well known that the drop charge Q is proportional to the electron temperature of the plasma (Te) [29]. With this fact taken into account, it is readily clear that Te is to be raised to bring microdrops in the fission mode. The development of the capillary instability of drops commonly involves two stages. First, on exceeding the instability threshold, the drop loses its spherical shape and its fission starts, with a large number of finer (daughter) drops ejected from the prominence on the surface of the maternal drop. Analysis shows that daughter drops are also unstable. Accordingly, the drop fission process has a cascade nature (see Figure 15.1), with the drop size decreasing by approximately a factor of 10 at each stage of the cascade. A new feature, on which the laser electrodispersion method is based, consists in that the process of cascade fission terminates after the daughter drops reach a nanometer size. As charged drops immersed in plasma become smaller, the electric field on their surface increases, which results in a dramatic increase in the field emission of electrons. After the size of the daughter drops decreases to several nanometers, the flow of electrons emerging from the drop surface starts to exceed that coming in from the plasma. In this case, the drops discharge and become stable, so that the fission terminates. Thus, fission of micrometer and submicrometer drops in the laser torch plasma yields a tremendous number of nanometer drops with narrow size dispersion and a small amount of residues of maternal drops that had not enough time for total fission. The scheme by which nanostructures are formed by laser electrodispersion is shown in Figure 15.2. In accordance with this scheme, a laser pulse causes Maternal drop Daughter drops

Fig. 15.1. Scheme of the cascade fission of a charged liquid drop.

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Metallic target Molten layer Microdrops Plasma

Nanoparticles

Laser beam

Substrate E

Fig. 15.2. Schematic of the nanostructure formation process.

melting of the target surface and creates the laser torch plasma near the surface. Microdrops of molten metal, which escape from the target and arrive into the plasma, are charged and their fission occurs to give nanosize drops. Estimates show that nanosize drops formed in the plasma fly apart at a velocity of 104 cm/sec, whereas the velocity of expansion of the plasma cloud exceeds 106 cm/sec. Accordingly, a microsecond after the laser pulse terminates the expanding plasma moves away from the target and charged nanodrops continue their movement in a vacuum, cool down to solidification, and the resulting nanoparticles finally arrive to the substrate surface. The motion trajectory of charged nanoparticles can be corrected with electric field. This opportunity was used to separate the charged nanoparticles from the residues of maternal drops that had not enough time for separation. For this purpose, a steady voltage was applied to the gap between the target and the substrate, so that the corresponding electric field was concentrated near the substrate. The electric field strength was chosen so as to direct nanosize particles to the substrate without disturbing the motion of larger drops. In case of deposition on a dielectric substrate, the trajectories of arriving nanoparticles are additionally disturbed (in the vicinity of the surface) by the Coulomb interaction with nanoparticles deposited in the preceding pulses. As a result, nanoparticles occupy vacant places on the surface and, at short film deposition times, their distribution over the substrate is virtually uniform. At longer deposition, as well as in the case of conducting substrate, particle arrangement on the surface may be more sophisticated, that is

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specific particle self-organization can be observed. Depending on the deposition time and type of substrate, structures composed of sparsely arranged or aggregated particles, densely packed single- or multilayer coatings can be obtained on the substrate. It is also worth noting that laser electrodispersion can produce nanostructured alloy coatings and composite coatings composed of particles of different metals. For these purposes, alloyed targets are used and targets made of different materials are alternately irradiated.

2.2. STRUCTURAL PROPERTIES

OF THE

CATALYST COATINGS

Direct experimental observation of the drop fission in the laser torch plasma would be exceedingly difficult. The main obstacles are associated with the short duration of the fission process (o100 nsec) and the small size and high velocity of the particles. In addition, it should be taken into account that the charging and division of particles occur in high-density and hot laser torch plasma and the presence of this plasma complicates the problem to an even greater extent. Accordingly, the validity of the process scheme we suggested can be only confirmed by indirect data. One of the results indicating that the process of microdrop fission occurs was obtained in an experiment in which the substrate was mounted in a close vicinity of the target surface. As can be seen in Figure 15.3, the surface of the substrate placed near the target is covered with submicrometer particles. It is also to note that part of these

Fig. 15.3. Submicrometer metallic particles on the surface of a substrate mounted near the copper target.

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Fig. 15.4. TEM micrograph of a copper nanostructure on a substrate placed at a distance of 5 cm from the target. Deposition time: 1 min.

particles have projections whose size is approximately 10 times smaller than that of the main particles. The presence of such particles with projections can be interpreted as a consequence of rapid cooling and deposition onto the substrate of drops that are in the initial stage of fission. Figure 15.4 shows a transmission electron microscopy (TEM) micrograph of a granulated copper film deposited by laser electrodispersion. The substrate onto which the structure was deposited was placed at a distance of 5 cm from the target. It is important to note that only nanoparticles of average size equal to 5 nm are seen on the substrate surface, and there are no coarse particles (residues of drops that had not enough time to disintegrate). Additional studies demonstrated that coarse particles of size 100–200 nm also exist, but can only be observed by scanning over a larger substrate area because their number is exceedingly small, about one coarse particle per 106 nanoparticles. This fact can serve as additional evidence in favor of the nanoparticles formation process described above. It can also be seen in Figure 15.4 that, at a comparatively low surface density, the structure is composed of isolated Cu nanoparticles uniformly distributed over the surface. In this film, the particle surface density is on the order of 1012 cm2. If the deposition time is raised from 1 to 5 min, nanoparticles are grouped into ensembles (Figure 15.5), within which particles are in contact with one another. The highest packing density of particles in a single-layer coating is reached at a deposition time of 5 min.At even longer deposition times, a second layer of particles starts to be formed, and particles of the second layer tend to occupy places over gaps between particles of the first layer.

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Fig. 15.5. TEM micrograph of a copper nanostructure. Deposition time: 5 min.

By now, the possibility of deposition of granulated Cu, Ni, Pd, Pt, and Au films by laser electrodispersion has been experimentally verified. The structural parameters of the films being formed were studied by various diagnostic techniques, with the most informative results obtained with TEM, atomicforce microscopy (AFM), and X-ray photoelectron spectroscopy (XPS). TEM micrographs of the structure of Ni and Pd films are shown in Figure 15.6. It can be seen that the arrangement of particles of all the three metals on the substrate is strongly disordered. At the same time, a close comparison of Figures. 15.5 and 15.6 shows that the structures formed by, e.g., Cu and Ni nanoparticles are somewhat different. For example, Cu nanoparticles combine into isolated islands composed of 3–6 particles, while Ni structures exhibit a tendency toward ordering of nanoparticles into chains containing up to 15–20 particles. As shown by the results of processing of the TEM images of the structures, the relative size dispersion of nanoparticles formed by all the metals studied does not exceed 10% and their average size is only determined by the material of which the particles are composed. For example, the average sizes of Ni and Pd particles are 2.5 and 2 nm, respectively. Important data on the structure of the films were obtained in an analysis of electron diffraction patterns recorded directly in the transmission electron microscope. In all cases, the diffraction patterns had the form of diffuse halos, which indicate that nanoparticles are in the amorphous state [30]. The fact that the nanoparticles are amorphous is in all probability due to the exceedingly fast cooling of nanometer drops after the expansion of the plasma cloud. Estimates of the cooling rate of nanodrops at the instant of their hardening give values of up to 107 K/sec.

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Pd, 3s 25 nm

25nm nm 25

Ni, 15

Fig. 15.6. TEM micrographs of Ni and Pd structures.

A feature common to all the metals is that nanoparticles do not coagulate on coming in contact with each other. Presumably, this feature is a consequence of the amorphous state of the metal in the particles. It is worth noting that a transition from the amorphous to the polycrystalline state was observed only in copper structures upon heating to above 1501C, with the particles coagulating to form larger polycrystalline grains. Nanoparticles of Ni and Pd demonstrated a considerably higher stability against coagulation, no transition to the polycrystalline state occurred even upon heating to above 4001C. The absence of coagulation under normal conditions makes it possible to deposit densely packed and multilayer coatings composed of separate nanoparticles of the same size.

3. Charge State of Metallic Nanostructures As shown by the results of numerous experiments, the catalytic activity of nanostructured metals, in quite a number of chemical reactions, is closely

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associated with their electrical properties. In turn, the electrical properties of metallic nanostructures depend on a number of structural parameters, such as the size and mutual position of the particles, material of the support (insulator, semiconductor, or metal), etc. Taking into account that the size dispersion of nanoparticles formed by laser electrodeposition is less than 10%, it may be thought, when analyzing the charge state of structures of this kind, that all the particles are identical. We should also take into consideration the fact that, at the instant of time when the structure is formed, nanoparticles tend to be uniformly distributed over the surface because of mutual Coulomb repulsion. This makes it possible to characterize the positions of particles by only a single parameter, surface density of particles on the substrate. At a low surface density of particles, when the average distance between them exceeds 4–5 nm, exchange of electrons between neighboring particles is unlikely. Accordingly, nanoparticles can be charged in this case only via exchange of electrons either with the support, if this is a metal or a semiconductor, or with some external conductor, e.g., with the tip of a tunnel microscope. If such sparse structures are deposited onto an insulator, the density of charged particles is low and the conductivity of the coating is virtually zero. Raising the particle density leads to a decrease in the width of interparticle gaps and to a pronounced increase in the probability of electron tunneling from one particle to another. If, in this case, a structure is deposited onto a dielectric substrate, the number of charged particles and the conductivity of the coating increase dramatically. The conductivity of coatings of this kind is in many regards similar to the hopping conductivity in semiconductors: e.g., the temperature dependence of the conductivity obeys the same law in both cases. Further increase in the density of nanoparticles leads to formation of close contacts between them, which leads to collectivization of electrons in ensembles of contacting particles. In the high-density limit, when each nanoparticle is in contact with all of its neighbors, the nanostructure becomes similar in its electrical properties to a thin metallic film and is characterized by a metallic type of conduction. As shown below, nanostructures with an intermediate density are the most interesting as regards the search for materials with the highest catalytic activity. On one hand, particles in these structures are separated from one another and charge is localized on isolated particles, and, on the other hand, they are situated sufficiently closely for the charge exchange between neighboring particles to become possible. In structures of this kind, the probability of electron tunneling depends on the particle size, height and width of tunneling barriers, and ambient

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temperature [31]. In this case, the ensemble-averaged stationary concentration of charges is primarily determined by the energy spectrum of various charge states and the ambient temperature. Let us first consider the situation in which nanoparticles are deposited onto a dielectric support. At a nottoo-high particle density, when the effects of mutual electrostatic polarization are not important yet, the average number Nz of charged particles with charge Ze (e is the elementary charge) is given by the expression [32]: NZ expðZ2 e2 =r
kTÞ ¼ 1 , P N expðZ2 e2 =r
kTÞ

(2)

Z¼1

where N is the total number of nanoparticles in the system, r the radius of nanoparticles, and e and T the dielectric constant and ambient temperature. This expression gives a time-averaged number of charged particles, whereas the true charge distribution in the system fluctuates with a period on the order of the electron tunneling time. The exponent of the exponential function in formula (2) includes the ratio of the charging energy, Z2e2/re, i.e., the electrostatic energy of an isolated charged particle, to the thermal energy kT. It is also to note that, according to Eq. (2), the average numbers of negatively and positively charged particles with charges of equal magnitudes are the same, i.e., the system of nanoparticles remains, on the whole, electrically neutral. As follows from Eq. (2) for the case of room temperature and e E 1 (i.e., in air or in a vacuum), the fraction of charged particles in nanostructures composed of particles of size 2–5 nm is small, 103, with the particles only singly charged. As the polarity of the environment increases to e E 10–20, a value characteristic of liquid media, the situation changes cardinally. There appear a large number of doubly and triply charged particles, and the fraction of neutral particles does not exceed 40%. To perform a more rigorous calculation of the concentration of charged particles with account of their mutual polarization, which plays a particularly important role in dense structures, a model based on the MonteCarlo procedure has been developed. In this model, electron transitions between particles are taken in accordance with the calculated probabilities of these transitions [33,34]. Figure 15.7 compares the results of such calculations with the data obtained using expression (2). It is to note that the model [34] has been specially developed for describing the charge state of structures composed of identical nanoparticles. The dependences in Figure 15.7 are qualitatively similar for both the models; however, quantitative differences are strong, especially in calculating the densities of doubly and triply charged granules.

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“!” Z = 0 “7” Z = ±2 “,” Z = ±1 “Λ” Z = ±3 100

10-2

10-4 2

4 6 8 Dielectric constant ε

10

Fig. 15.7. Fraction of charged particles vs. the dielectric constant of the medium. Dashed lines, calculation by formula (2); solid lines, numerical simulation.

ε=1

Z = -2

ε = 10

Z = -1 Z=0 Z= 1 Z=2

Fig. 15.8. Distribution of charged particles in dense single-layer coating composed of monodisperse nanoparticles (numerical simulation for dielectric constants e ¼ 1 and e ¼ 10, T ¼ 1001C). Z is the charge multiplicity of nanoparticles.

The calculations also demonstrate that charged granules are mostly arranged in dipoles. Figure 15.8 illustrates this tendency. It can be seen that, at both high and low polarities of the medium, neighboring particles most frequently carry charges of opposite signs. Accordingly, the electric field created by these charges is mainly concentrated in the inter-particle gaps. Because the distances between particles are exceedingly small, the electric field strength is very high: depending on the particle size and polarity of the medium, it varies from 106 to 4  106 V/cm. The models considered give results that account for a large body of experimental data obtained in measurements of the conductivity of nanostructures composed of various metals, deposited onto dielectric substrates

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[35]. However, these models are inapplicable to analysis of the charge state of structures deposited on the surface of a metal or a semiconductor. For example, in the case of a metallic substrate, it is necessary to take into account two additional factors: effect of the conducting substrate on the self-capacitance and mutual capacitance of nanoparticles and the possibility of exchange of electrons between the nanoparticles and the substrate. In this case, the charge state of the system very strongly depends on whether or not an oxide layer is present between a particle and the substrate. In the absence of an oxide layer, the surfaces of particles and substrate are equipotential and charge densities on the surface of particles and substrate are zero. If an oxide layer exists, and just this case most frequently occurs in practice, a charge may be localized on particles and electron transport occurs via tunneling across the oxide layer. In this case, the charge state of the system at a low surface density of particles is described by an expression similar to (2): NZ expððZ  Z eff Þ2 e2 =r
kTÞ ¼ 1 . P N 2 2 expððZ  Z eff Þ e =r
kTÞ

(3)

Z¼1 2

Here, Zeff ¼ Dfre/e is the average charge of the system of nanoparticles, determined by the difference of the work functions of the metals constituting particles and the substrate (Df). Accordingly, the charge state of such a nanostructure becomes dependent on Df and differs from the charge state of a structure deposited onto a dielectric substrate. Figure 15.9 presents the results of calculations of the charge state of Ni nanostructures on metallic substrates with different work functions. It can 0.35 eV

0.7 eV 1.05 eV

Fraction of charged NZ/N

10

0

ε = 10


 = 0

10-1 10

1.4 eV

-2

10-3 10-4 10-5 -2

-1

0 1 2 Charge multiplicity Z

3

4

Fig. 15.9. Fraction of charged Ni particles vs. their charge multiplicity at a varied difference of the work functions of Ni and of the substrate material.

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be seen that, for some substrates, the number of charged particles may be large: e.g., at Df E 0.7 eV, the fraction of singly charged particles is as large as 70%, with the rest of the particles being either neutral or doubly charged. Thus, the charge state of nanostructures can be controlled by an appropriate choice of the materials of a catalyst and a support. When describing the charge state of nanostructures deposited on a semiconducting substrate, it is necessary to take into account that, in contrast to a metal substrate, the charge in a semiconductor is distributed in a relatively thick depletion layer near the surface, and the process of charge exchange between the semiconductor and nanoparticles is largely determined by the state of the semiconductor surface. Let us consider as an example the charge effects that occur in metallic nanostructures deposited on the surface of doped silicon of p- and n-type. It is worth noting that, under common conditions, a 1–2 nm-thick layer of the natural oxide SiO2 is formed on the silicon surface and this layer is tunnel-transparent for electrons. Figure 15.10 shows near-surface band diagrams of p- and n-type silicon with nickel particles deposited onto its surface. A characteristic feature of these diagrams is band bending near the semiconductor surface, which is determined by the so-called pinning of the Fermi level, i.e., by fixation of its energy position at the surface. It is well known that the pinning is due to the formation of specific surface states and the position of the Fermi level at the surface is fixed at d ¼ 0.4 eV from the top of the valence band at any type of doping. The values of energy gap Eg of silicon, electron affinity w and Ni work function f(Ni) are also shown in Figure 15.10. It can be seen that the Fermi level in nickel particles deposited onto p-type silicon lies D ¼ 0.67 eV above the Fermi level in silicon (here, we neglect the difference between the position of the Fermi level and valence band edge, which is a good Energy level of an electron in vacuum χ(Si) = 4.05 eV

χ(Si) ϕ (Ni) = 4.5 eV

Fermi level in p-Si

Eg =1.12 eV

Fermi level in Ni

e-

ϕ (Ni) 0.4 eV Fermi level in n-Si

e-

Eg

0.4 eV

p-Si

n-Si Layer of native oxide

Fig. 15.10. Band diagrams illustrating the effect of charging of Ni nanoparticles on the surface of silicon. Ni particles are charged positive on p-type silicon and negative on n-type Si.

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approximation in most cases). This quantity is on the order of the charge energy of nickel particles carrying one or two extra electrons. Since D40, the attainment of equilibrium in the system constituted by silicon and Ni particles will be accompanied by electron flow from nickel particles into silicon (as shown by the arrow in Figure 15.10). After the thermodynamic equilibrium in the system is attained, nickel particles will be positively charged, with, on average, one or two lacking electrons per particle. Similarly, the band diagram of n-type Si shows that, in this case, the deposited nickel nanoparticles will be negatively charged on reaching the equilibrium in the system. Thus, the sign and amount of charge appearing on Ni particles depend on the type of doping of the semiconductor. It is to mention that the model considered is valid in the case of relatively low concentration of metallic particles on the semiconductor surface. The point is that the characteristic surface density of built-in charges on the surface of Si is 1012 cm2. If the density of the deposited particles of a catalyst is considerably higher than 1012 cm2, equilibrium in the semiconductor– nanoparticles system will be attained in another way. In this case, a nanostructured film can be regarded as continuous and the situation is closer to that in the so-called Schottky contact, in which there is a thin oxide layer between a semiconductor and metal, but the electric capacitance of the metal is obviously high. As a result, in attainment of equilibrium by charge redistribution, the potential of the metallic layer remains virtually unchanged. A characteristic feature of the systems of nanoparticles deposited on a conducting substrate is that the electric field generated by charged particles is mostly concentrated in the gaps between the particles and the substrate. However, the electric field strength is about the same in both the cases considered (metal and semiconductor substrates) and varies from 106 to 4  106 V/cm. We considered above processes of charge transfer in monodisperse structures composed of identical nanoparticles. If there is a considerable particle size scatter, the description of charge state of such structures becomes much more complicated. This issue has been the subject of several studies (see, e.g., Refs. [35,36]).

4. Effect of Nanoparticle Charging on the Catalytic Properties This section describes a simple model that enables evaluation of the influence of charge effects on the catalytic activity of metallic nanostructures. Also, the results of experiments performed with nanostructured catalysts synthesized by laser electrodispersion are discussed. These results demonstrate a relationship between the catalytic activity and charge density in the

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catalyst structure: in quite a number of reactions, an increase in the charge density leads to a significant rise in the catalytic activity.

4.1. ANALYTICAL ESTIMATES Nanoparticle charging can affect the rate of a catalytic reaction for two reasons. The first is that charged particles create an electric field. As mentioned above, this field is concentrated in gaps between nanoparticles or between the nanoparticles and the substrate. In both cases, the gap width varies within the range 1–3 nm. Because the electric field strength in the gap is 106 V/cm, the potential difference across the molecules of size on the order of 1 nm, present in these gaps, may reach values of 0.1 V. Accordingly, the molecules in the gaps can be excited with a transition to higher energy levels, 0.1 eV above the ground state. The appearance of excited molecules may lead to a significant increase in the rate of chemical reactions [12]. The second charge effect that can affect the catalytic activity of nanostructures is observed for reactions involving electron transfer between the reactant molecules and nanoparticles. If the key stage of the reaction is electron transfer from a metal nanoparticle to an adsorbed molecule, then the presence of a negative charge on the nanoparticle makes the electron transfer energetically more favorable. Owing to this, the catalytic reaction can be accelerated. It is worth noting that, in most of real structures, thin oxide sheaths are formed on the surface of metallic nanoparticles. Therefore, charge transfer should occur via electron tunneling through the potential barrier associated with the presence of an oxide on the surface. It is also to note that the alternative process, transfer of an electron with its excitation into the continuous spectrum, is considerably less probable, because in this case the electron has to overcome a very high potential barrier equal to the work function of the metal. Let us compare the probabilities of tunnel electron transfer from singly and doubly charged metallic nanoparticles (Z ¼ 1 and Z ¼ 2) to an adsorbed molecule. In the general case, tunnel electron transfer occurs in three stages: (i) thermal activation of an electron in the metal, (ii) tunneling of the electron through the barrier to a molecular level, and (iii) transformation of the adiabatic potential of the molecule. If a metallic nanoparticle is singly negatively charged (has one extra electron), the electron leaves behind, upon tunneling through the barrier, a neutral particle, i.e., the tunneling occurs in a zero electric field, as shown in Figure 15.11a. As a result of the tunnel transfer, the electron must find itself at the molecular affinity level (EA), whose energy position is determined by processes of chemisorption of the reactant molecule on the surface of the

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Electron energy in vacuum

∆ET EA E'T

EA ET Fermi level

d

R

R (b)

d

Fig. 15.11. Band diagrams illustrating electron transfer from the surface of negatively charged nanoparticle to adsorbed molecules of the reactant: (a) singly charged particle, and (b) doubly charged particle.

oxide sheath. It can be seen in the figure that, for charge transfer to occur, it is necessary that an electron in the metal should be thermally activated. In this case, an electron at the Fermi level must acquire an additional energy equal to ET, and this value is the activation energy of this process. In case the nanoparticle is doubly negatively charged, an electron tunnels through the potential barrier to a molecule, leaving behind one extra electron, i.e., the tunneling occurs in a repulsive electric field (Figure 15.11b). Let us now assume that the electric field of charged particle does not affect the molecule affinity EA (energy EA is reckoned from the potential level at the particle surface). Then, it can be seen from the figure that the electron activation energy decreases by a value equal to the potential drop across the oxide sheath. This value can be readily estimated to be [37]: DE T ¼

e2 d .
d R R þ d

(4)

Here, ed and d are the dielectric constant and the thickness of the oxide sheath of the metal, and R the radius of a metallic core of nanoparticle. Similar analysis can be made for particles with an arbitrary initial charge multiplicity Z. If, in particular, a particle is originally neutral, tunneling will occur in an attractive electric field. It can be readily seen that, in the general case, the activation energy is ET+(Z+1)DET. The assumption that the molecular affinity EA is independent of the electric field of charged particles is quite reasonable, because at|Z|r 3 this field is still considerably weaker than the local electric fields associated with the chemisorption process. Let us now evaluate the influence exerted by the particle charge on the specific (per unit mass of the metal) catalytic activity of nanostructures. Let

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us compare the specific activity of low-density structures, in which the charge effects are unimportant, with that of high-density structures, in which a considerable part of particles is charged (NZ/N is the fraction of particles with a charge Z ). To obtain the estimate of interest, it is necessary to take into account that the catalytic activity exponentially depends on the activation energy. Further, to account for the contribution of particles with different original charges, it is necessary to take a sum of exponentials with different activation energies dependent on Z, i.e., to sum over charge multiplicities Z. Thus, the ratio of the specific activity of a high-density structure (A) to that of a sparse structure (A0) is equal to
 X NZ A E T þ ðZ þ 1ÞDE T exp  ¼ . (5) A0 N kT Z In a particular case of copper nanostructures, nanoparticles have the form of metallic nuclei of radius R ¼ 1.7 nm coated with a Cu2O sheath of thickness d ¼ 0.7 nm with ed E 4 [38]. For structures of this kind, the dependence of the fraction of charged particles on the dielectric constant of the solution is presented in Figure 15.7. Substitution of these values in expression (5) gives A/A0 E 10. This value is in reasonable agreement with the experimental data presented below. It should be emphasized once more that, in addition to the average number of charged particles, an important characteristic of the system is the lifetime of the ‘‘instantaneous’’ distribution of charges or the existence time of dipoles formed by neighboring charged particles. Estimates show that this time is 1010 sec for copper nanostructures composed of 5 nm particles. This time is considerably longer than the characteristic time of a chemical reaction and, more so, than that of tunnel transfer of an electron from particles to reactant molecules. Thus, in analysis of the catalytic activity of nanostructures the charge distribution and the electric fields created by charged particles can be regarded as stationary. 4.2. EXPERIMENTAL RESULTS

AND

DISCUSSION

Originally, the effect of charge state of nanostructures on their catalytic activity was recognized from analysis of the experimental data on the catalytic properties of metallic nanoparticles immobilized in the matrix of a polyparaxylylene polymer [13–15,24]. It was found that the dependence of the catalytic activity (and, in some cases, of the selectivity) of copper, palladium, and iron nanoparticles on the metal content of these structures has a maximum. This maximum exists not only for the specific (related to unit weight) activity, but also for the absolute activity. More specifically, for copper and

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palladium nanocomposites used as catalysts in isomerization of chloro-olefins the maximum of catalytic activity was attained at an average distance between neighboring particles equal to several nanometers. This distance is small enough to permit tunnel electron transfer between metal nanoparticles. It was also shown that a steep rise in the conductivity of these structures occurs at the same metal content at which the activity is at a maximum. This coincidence qualitatively confirmed the assumption that charge redistribution between nanoparticles affects their catalytic properties. However, a more rigorous analysis of these effects requires a model catalytic system in which the size, shape, and composition of particles would remain unchanged on widely varying the degree of surface coverage (or volume filling) by these particles. Nanostructures formed by laser electrodispersion considered above proved to be the most appropriate for this purpose. In fabrication of the catalysts by laser electrodispersion, thermally oxidized silicon wafers with a thickness of SiO2 oxide layer of 1 mm were used as a substrate. A substrate with so thick an oxide layer can be regarded as an insulator. In some cases, wafers of crystalline (1 0 0) Si were used, which had on their surface only a thin (1–2 nm) layer of a natural oxide. This layer is tunnel-transparent for electrons, and, therefore, charge exchange between supported nanoparticles and silicon is possible. In the study, a certain type of chemical reaction, sensitive to the charge state of a catalyst, was chosen. As test reactions for copper and nickel films, the following chlorohydrocarbons conversions were selected [30,34,39]:  allyl isomerization of 3,4-dichlorobutene-1 into trans-1,4-dichlorobutene-2:

CH2 C1  CHC1  CH ¼ CH2 $CH2 C1CH ¼ CHCH2 CL;  addition of carbon tetrachloride at the double bond of octane-1:

CC14 þ CH3 ðCH2 Þ5 CH ¼ CH2 ! CH3 ðCH2 Þ5 CHC1-CH2 ðCC13 Þ;  joint metathesis of C–H and C–Cl bonds in decane and carbon tetra-

chloride: RH þ CC14 ! RC1 þ CHC13 ; where R ¼ C10H21. Active ion–radical or radical intermediates of these processes are formed upon electron transfer from catalyst particles to the reactant [40]: d  þ d Mn þ RCl ! Mþ n þ RCl ! Mn ðCl Þ þ R .

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This key stage of catalysis is exceedingly sensitive to the charge state of the catalyst. The catalytic activity of nickel and palladium films was studied in hydrogenation of nonene-1 and chlorobenzene [41]: C9 H18 þ H2 ! C9 H20 ; Cl Pd, H2

Pd, H2

- HCl

The reactions mentioned above can also be of practical importance, e.g., as model reactions for processing of organochlorine wastes. All the metallic nanostructures deposited by laser electrodispersion on both types of silicon substrates were found to be exceedingly active in the above processes. The activity was orders of magnitude higher than that of typical supported catalysts prepared by the standard techniques. Such a high activity is presumably due not only to the small size and amorphous state of nanoparticles, but also to the influence exerted by the charge effects discussed above. Let us first consider the case of substrates of thermally oxidized silicon (dielectric support). Figure 15.12 shows several examples of how the specific catalytic activity of copper nanoparticles produced by laser electrodispersion depends on the particle density in the above three reactions involving chlorohydrocarbons. It can be seen that, in all cases, the catalytic activity has a maximum at virtually the same particle density of 3–4  1012 cm2. Here, the presence of the maximum cannot be due to the ordinary size effect in which a dependence on the particle size is manifested because all the films are composed of metal particles of the same size and shape. The presence of such a maximum can hardly be attributed to anything other than interparticle interaction. It is important to note that the maximum catalytic activity is observed at the surface particle densities at which there occurs a steep rise in the film conductivity (by nine orders of magnitude!) and a film passes from the dielectric state to the conducting state. In our opinion, the data obtained can serve as clear evidence in favor of the existence of a size effect of the second kind, which consists in that the properties of the structures vary with the surface particle density or average width of the gap between neighboring particles. In this case, the size effect of the second kind is, in the end, manifested in that the catalytic properties of a nanostructure strongly depend on its charge state. An even more clearly pronounced manifestation of the influence exerted by the charge of nanoparticles on their catalytic properties was observed in a

Specific activity x 10-3, Mole of product /(mole of Cu h)

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1 2 3 4 5

10 8 6 4 2 0 0

2 4 6 8 10 12 Surface particle density x 10-12, cm-2

Fig. 15.12. Specific catalytic activity vs. surface density of copper nanoparticles on thermally oxidized silicon in reactions involving chlorohydrocarbons: (1) CCl4+C8H16 at 1501C, (2) the same at 1301C and e ¼ 10, (3) isomerization of dichlorobutenes at 1101C, (4) isomerization of dichlorobutenes at 1301C, and (5) CCl4+C10H22 at 1301C.

study of the activity of Cu nanoparticles in the reaction of dichlorobutene isomerization at different dielectric constants of a solvent. Analysis of the dependences obtained (see Figure 15.13) shows that at a low surface particle density n ¼ 1.6  1011 cm2, when charge exchange between nanoparticles is virtually impossible, the rate of the catalytic reaction is independent of the solvent polarity. An increase in the particle density to n ¼ 8  1011 cm2, accompanied by a decrease in the width of gaps between nanoparticles to 1.5–2.5 nm, leads to a strong dependence of the activity on the solvent polarity. This result is not unexpected and is in good agreement with the estimates made above. Indeed, raising the solvent polarity leads to an increase in the fraction of charged nanoparticles (see Figure 15.7), which, in turn, causes, in accordance with formula (5), a rise in the gain coefficient of catalytic activity, A/A0. As can be seen in Figure 15.13, the ten-fold increase in activity is attained at a particle density n ¼ 4  1012 cm2 and e ¼ 10, which is in good agreement with the above estimate A/A0 E 10. Another specific feature of the catalytic behavior of the structures under study consists in that the chemical nature of a metal becomes a factor less important for catalysis as the surface nanoparticles density increases. This is well seen in Figure 15.14, which shows the results obtained in measurements of the activity of copper- and nickel-based catalysts in the reaction of carbon tetrachloride addition to olefins. Presented in this figure are the activities of catalysts prepared by laser electrodispersion and the conventional deposition techniques. Two important features are worth noting. First, the activity

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Activity x10-2, Mole /l•h

8

ET AL.

n=4.0 1012 cm-2 n=8.0 1011 cm-2 n=1.6 1011 cm-2

6 4 2 0 2

4 6 8 Dielectric constant of the solution

10

Fig. 15.13. Activity of Cu nanoparticles in the reaction of dichlorobutene isomerization vs. the dielectric constant of the solvent at different nanoparticle densities.

Laser electrodispersion Impregnation and reduction

Specific activity, Mole of product / (mole of metal h)

100000

10000

1000

100

10

1

Ni

Cu

Fig. 15.14. Comparison of specific catalytic activities of Ni and Cu nanoparticles deposited onto a thermally oxidized silicon by laser electrodispersion (n E 5  1012 cm2) with those of catalysts prepared by the method of impregnation and reduction (1% Ni/SiO2, 1% Cu/SiO2). Reaction of carbon tetrachloride addition to olefins.

of the conventional catalysts is many orders of magnitude lower than that of films prepared by laser electrodispersion. Second, and exceedingly important, is that the conventional nickel-based catalysts are considerably less active in the given reaction than those based on copper. At the same time, equally high activities are observed at close surface particle densities for

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Specific activity x 10-3 Mole of product /(mole of Cu h)

copper and nickel structures deposited by laser electrodispersion. The highly active catalysts synthesized by this method also exhibited unusually low effective activation energy of carbon tetrachloride addition to olefins. The value of 50 kJ/mol, obtained for the reaction with octane-1, is substantially lower than the commonly observed activation energies of 80–100 kJ/mol [42]. The possible reason is that the appearance of highly active charged states in a catalyst makes different metals closer in their catalytic properties. Passing to conducting substrates markedly changes the situation. Figure 15.15 shows dependences of the catalytic activities of copper nanoparticles on the particle density, measured in the reaction of isomerization of dichlorobutenes with the particles deposited onto the surface of oxidized and unoxidized silicon. Similar results were obtained with nickel nanostructures under the identical process conditions. On both types of substrates, the activity of nanoparticles is exceedingly high, but the dependence of the catalytic activity on the particle density exhibits fundamentally different types of behavior. In deposition of particles onto a dielectric substrate (thermally oxidized silicon), this dependence shows a sharp maximum. At the same time, in the case of deposition onto a conducting substrate, a gradual decrease in activity is observed as the degree of coverage of the support surface with particles increases. Again, this behavior is in good agreement with the results obtained in modeling of the charge state of nanostructures. Calculations show that the maximum density of charged copper particles is reached on the dielectric substrate at a density n E 4  1012 cm2, at which the catalytic activity is the highest. On conducting substrates, the density of charged Cu particles is virtually constant

10 9 8 7 6 5 4 3 2 1 0

2 1

0

1

2

3

Surface particle density

4 x10-12,

5

6

cm-2

Fig. 15.15. Specific catalytic activity vs. surface density of copper nanoparticles in dichlorobutene isomerization at T ¼ 1101C: (1) oxidized silicon support and (2) silicon support.

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at no3  1012 cm2 and decreases as the density increases further, i.e., the run of this dependence is similar to that of curve 2 in Figure 15.15. The dissimilarities between the charge states of nickel nanostructures deposited onto substrates of well-conducting p- and n-type silicon (unoxidized) were manifested in different catalytic activities in the reaction of carbon tetrachloride addition to olefins. It was shown that negatively charged nanoparticles on an n-type Si substrate have a two times higher activity, compared with positively charged particles on a p-type Si substrate (see Figure 15.10). The specific property of nickel nanoparticles deposited onto silicon substrates of different types of doping was also clearly manifested in another reaction we studied, hydrogenation of multiple bonds. It is known that the optimal situation for catalysis of processes of this kind is presence of a positive charge on metallic particles [43]. This can be achieved upon deposition of Ni nanoparticles onto p-type silicon. Indeed, experiments did show that the activity of Ni nanoparticles onto p-type silicon exceeds by nearly two orders of magnitude the activity of catalysts based on ultra-dispersed platinum and palladium, prepared by other methods. Application of charge effects in catalysis may also prove highly useful in practical regard. As an example of this kind can serve the results obtained in a study of the catalytic activity and stability of palladium nanoparticles produced by laser electrodispersion in a practically important process of hydrodechlorination of chlorobenzene. It was shown that using a catalyst with the optimal degree of surface coverage makes it possible to raise the activity by three orders of magnitude, compared with the conventional catalyst. It is also important that the catalyst deposited by laser electrodispersion retains its high activity during a sufficiently long time. The operational stability of a catalyst is a difficultly solved problem of key importance in processes of hydrodechlorination in the gas phase. It is worth noting that catalytic hydrodechlorination is the only truly ecologically safe technique for elimination of toxic polyorganochlorine wastes of technological origin. This method has not found wide use solely because of the high expenditure of the precious metal and low stability of the catalysts. Here, an opportunity to tackle with these problems can be foreseen.

5. Summary Considered in this chapter are specific features of the catalytic behavior of metallic nanostructures of new type, produced by laser electrodispersion of metals. This method makes it possible to obtain Cu, Ni, or Pd nanoparticles whose sizes are specific to each particular metal, with the relative particle size scatter being exceedingly narrow, r10%. An important distinctive

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feature of these catalysts consists in that metallic particles are amorphous. A consequence of the amorphous state of the metal is the high stability of nanoparticles against coagulation. This made it possible to form catalytic coatings with high particle density on the support surface, including those in which neighboring particles are in close contact with one another. Experiments show that the catalytic activity of these structures in quite a number of reactions of chlorohydrocarbon conversion is exceedingly high and surpasses that of the conventional catalysts by orders of magnitude. Also, a strong dependence of the catalytic activity on the particle density in a structure was observed. These dependences were found to be fundamentally different for coatings deposited onto various, conducting (e.g., p- and n-type silicon) and dielectric substrates. These new manifestations of the catalytic behavior of nanostructured metallic catalysts are, in all probability, due to specific charge effects, which are the most important in high-density structures. It was shown that charge fluctuations in high-density structures, which occur owing to tunnel transitions of electrons between particles, result in, at temperatures close to room temperature, a considerable fraction of nanoparticles in the structure being charged. The quantitative estimate of this effect is in good agreement with the experimental data. The results obtained, as well as the developed concept of the influence of nanoparticle density on the catalytic activity (size effect of the second kind), may be the most useful in the following cases:  in development of catalysts based on precious and rare metals, when

the content of such a metal can be lowered by orders of magnitude without changing the basic parameters of a catalyst;  in obtaining the necessary selectivity, when the process temperature can be lowered without any loss of catalytic activity, with milder conditions of the process thereby provided;  in intensifying the already existing technologies, with the working load on a catalyst substantially raised at the same apparatus volume, without any decrease in the conversion of reactants. It is to note that some of the issues touched upon in this chapter still require a more detailed experimental study and theoretical interpretation. In particular, the model considered above, which makes it possible to relate an increase in the catalytic activity to appearance of charge on nanoparticles, undoubtedly needs refinement and a more thorough experimental verification. A clear understanding of the important issue of how the electrical properties of conducting supports affect the catalytic activity of deposited structures requires that, in the first place, experiments with a larger number of reactions and a wide variety of metallic and semiconducting substrates

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should be performed. It is also necessary to develop a model that could describe the dependence of the catalytic activity of metallic nanostructures on the strength of the electric fields that exist in the gaps between charged nanoparticles or in those between the particles and the support. It is beyond any doubt, however, that the concepts concerning the influence exerted by the charge state of metallic nanostructures on their catalytic activity and the role of the support in catalysis can be used in purposeful development of new catalytic systems and in optimization of the properties of the existing catalysts. These opportunities open up new prospects for technological catalysis. These are the questions for repeating the content of the chapter: 1. Estimate the temperature of laser torch plasma corresponding to the threshold of capillary instability of liquid 100 nm copper drop. This estimate can be done using the instability threshold condition (1) rewritten in the form:  1=2 aR RD kT e 40:4  e ,
0 R þ RD where k is the Boltzmann’s constant, e the electron charge, RD the Debye radius in laser torch plasma. The value of surface tension of copper is a ¼ 1.3 N/m and Debye radius is RD ¼ 100 nm. 2. Estimate the surface density of 5 nm Cu particles tightly packed in one layer covering on smooth support surface. Make this estimation for cubic and hexagonal particle arrangement. 3. Using the expression (2), calculate the ratio of the numbers of singly and doubly charged 5 nm copper particles taking the dielectric constant e ¼ 10 and ambient temperature T ¼ 300 K. 4. Using formula (4), compare the value of the potential drop across the oxide sheath of copper nanoparticle with the thermal energy kT. In calculation, use the value of copper nuclei radius R ¼ 1.7 nm, the thickness of Cu2O sheath d ¼ 0.7 nm, and the dielectric constant of the sheath ed E 4.

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