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Kinetics of Electron Transfer in Solution Catalyzed by Metal Clusters J. Khatouri, M. Mostafavi, and J. Belloni Laboratoire de Physico-Chimie des Rayonnements associé au Centre National de la Recherche Scientifique, Bât. 350, Université Paris-Sud, Centre d'Orsay, 91405 Orsay Cedex, France

Cluster properties, mostly those that control electron transfer processes such as the redox potential in solution, are markedly dependent on their nuclearity. Therefore, clusters of the same metal may behave as electron donor or as electron acceptor, depending on their size. Pulse radiolysis associated with time-resolved optical absorption spectroscopy is used to generate isolated metal atoms and to observe transitorily the subsequent clusters of progressive nuclearity yielded by coalescence. Applied to sil­ ver clusters, the kinetic study of the competition of coalescence with reactions in the presence of added reactants of variable redox potential allows us to describe the autocatalytic processes of growth or corrosion of the clusters by electron transfer. The results provide the size depen­ dence of the redox potential of some metal clusters. The influence of the environment (surfactant, ligand, or support) and the role of electron relay of metal clusters in electron transfer catalysis are discussed.

T h e increase of the redox potential of a metal cluster in a solvent with its nuclearity is now well established (1-4). The difference between the single atom and the bulk metal potentials is large (more than 2 V, for example, in the case of silver (3)). The size dependence of the redox potential for metal clusters of intermediate nuclearity plays an important role in numerous processes, par­ ticularly electron transfer catalysis. Although some values are available for silver clusters (5, 6), the transition of the properties from clusters (mesoscopic phase) to bulk metal (macroscopic phase) is unknown except for the gas phase (7-9). The redox potential of short-lived metal clusters may be evaluated by the study of the electron transfer kinetics involving a donor-acceptor couple of known redox potential and used as a monitor (5, 6). The metal atoms and the electron donor are generated in the aqueous solution through a short electron pulse. During the coalescence of the clusters, their redox potential increases, ©1998 American Chemical Society

In Photochemistry and Radiation Chemistry; Wishart, James F., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1998.

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as does their nuclearity, n, so that in early steps the potential of the smallest clusters is far below that of the donor and the transfer does not occur (Figure 1). Beyond a certain critical time, t , large enough to enable the growth of clusters and the increase of their potential above the threshold imposed by the donor, the electron transfer from the monitor to the supercritical clusters is allowed and detected by the absorbance decay of the monitor. The observation of an effective transfer therefore implies that the potential of the critical cluster is slighdy more positive than that of the reference system. The values of the nuclearity of this critical cluster allowing the transfer from the monitor and of the transfer rate constant are derived from the fit between the experimental results and the corresponding data calculated by numerical simulation obtained through adjusted parameters (10, 11). By changing the reference potential in a series of redox monitors, the dependence of the cluster potential on the nuclearity was obtained (5, 6). It was also shown that once formed, a critical cluster of silver, for example, behaves as a growth nucleus: alternate reactions of electron transfer and adsorption of surrounding metal ions make the redox potential more and more favorable to the transfer, so that autocatalytic growth is observed (Figure 1). These data enabled us to suggest a new explanation of the photographic development as resulting from (1) the size-dependence of the cluster potential (increasing with η in aqueous solution), and (2) the existence of a potential threshold and therefore a critical size im­ posed by the developer to the electron transfer (5, 12). The aim of this work is to extend the kinetics study of electron transfer to monitor donors of more positive redox potential than previously studied, toward silver clusters, Ag„ , as acceptors and thus to approach the domain where clusters get metal-like properties (13). The selected donor is the naphtazarin hydroquinone, with properties similar to those of the hydroquinone used as a developer in photography. Its redox potential depends on p H , so that different monitor potentials are available through control of p H . Moreover, the reactivity of the donor may be followed by variation of absorbance when naphtazarin hydroquinone, almost transparent in the visible, is replaced by oxidized quinone with an intense absorption band. Rate constants of the process and the nuclearity-redox potential correla­ tion will be compared with corresponding data obtained in another environ­ ment, particularly when a surfactant or an associated ligand is present. The complete analysis of the autocatalytic transfer mechanism will also be compared with the photographic process of electron transfer from hydroquinone devel­ oper to clusters supported on silver bromide.

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+

Experimental Details A l l reagents were pure: silver salt (Ag2S0 ) and 2-propanol were from Fluka, and naphtazarin (5,8-dihydroxy-l,4-naphthoquinone) (Q) was from Sigma Chemical Co. (see Figure 2) (14, 15). Electron pulses (3-ns duration) were 4

In Photochemistry and Radiation Chemistry; Wishart, James F., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1998.

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KHATOURI ET AL. Kinetics of ET in Solution

n

4

E°[M:/MJ

N I S

) M/M

•a

8 . n+1

n+1

t E °[ S/S"]

S/S

u

r

8C

M*/M '

υ

3

A Ο Ο

3

M /M° +

2 9

2

2

Ο,

A

04

AJ

e" puise

Figure 1. Principle of the determination of short-lived cluster redox potential by kinetics methods. The reference electron donor, S~, of a given potential and the metal atoms are generated by a single puke. During cluster coalescence, the redox potential of the couple E°(M -M ) progressively increases, so that an effective transfer is observed after a critical time when the cluster potential becomes higher than that of the reference, constituting a threshold. Repeatedly, a new adsorption of excess cations, M , onto the reduced cluster, M (n ^ n^), allows another electron transfer from S~ with incrementation of nuclearity. The subcritical clus­ ters M (n n

c

(19)

The general problem of this competition has been solved by numerical simula­ tion for variable values of x , s , n , fca, and k (22). The value of ^ = 2 X 10 L m o l s" for silver clusters is taken as the same as for pure coalescence (reaction 9). The fixation of A g onto Agi is fast and does not interfere with 0

8

- 1

0

c

t

1

+

In Photochemistry and Radiation Chemistry; Wishart, James F., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1998.

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1.2

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0

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i

0.05

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ι

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0.2

t(s) Figure 7. Decay of electron donor concentration as measured at pH 4.8 and as calculated by numencal simulation with dependence on i v Experimental signal: same conditions as in Figure 4. Because the concentration of silver ions after the puke is smaller than that of hydroquinone the ordinate of the experimental plot is ( OD-OD oc)lOD =o- Numbers next to simulation curves correspond to n . The value of k is 2.25 Χ I0 mol L " * " . The best adjustment with numerical simula­ tion is for ric (pH = 4.8) = 85 ± 5. t

c

t

8

t

1

1

the mechanism. For i < n , the coalescence is identical to that in the absence of a donor ( I I ) . W e also assume that the turnover rate constant k (reaction 19) will be the same for both p H values and that at each value the critical nuclearity must depend only on the donor potential and be independent of the initial concentrations of donor s and acceptor x . The best fit between experimental and calculated kinetic data is given by the adjusted values k = (2.25 ± 0.25) Χ 10 L m o l " s" , n (pH = 4.8) = 85 ± 5, and n (pH = 3.9) = 500 ± 30 Figures 7-9). The different features of Q H decay, such as critical time, shape of the curves, and [Ag° ] concentra­ tion dependence, are well reproduced by the numerical simulation for both p H values. It is interesting to observe the sensitivity of the simulation to the adjusted parameters. In Figures 7 and 9, the influence of n is shown for a given value of k , 2.25 Χ 10 L m o l " s" , on the calculated decay at p H 3.9 and 4.8, respectively. The uncertainty is limited because the same k value must account for the decays at both p H values. Note that the increase of n , all other c

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t = 0

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1

t

c

In Photochemistry and Radiation Chemistry; Wishart, James F., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1998.

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parameters being iked, has the effect of delaying the decay, s(t)/s , toward higher values of t (Figure 7). The same s(t) value is reached at times propor­ tional to n . The influence of k is shown in Figure 8. The study of the resolution of kinetics by numerical simulation (II) has shown that the regime of the competition (reactions 18 and 19) must be con­ trolled by the ratio k X 2 X [QH ] =o/&d X [Ag°] = . In the present case, the ratio is much higher than unity. That means that reaction 19 is much faster than reaction 18, so that the total concentration of supercritical clusters remains almost unchanged during the very rapid autocatalytic transfer. From the model, the results of Figures 7 and 9 correspond to a concentration of nuclei of «7 X 10~ mol L " at p H 4.8 and «1.2 X Μ Γ mol L " at p H 3.9. Note that the reservoir of excess silver ions after the pulse is «5 Χ 1 0 " mol L r , so that each nucleus receives about 700 and 4000 supplementary atoms, respectively, through electron transfer. Just after t , the supercritical clusters are still under formation, and the decay rate increases from zero to the turnover value. At long time, the coalescence is no longer negligible relative to the transfer, and the concentration of clusters decreases, so that the decay is slower (Figures 7 and 9). 0

c

t

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t

8

2 #

1

#

8

0

1

5

1

c

Figure 8. Decay of electron donor concentration as measured at pH 4.8 and as calculated by numerical simulation of dependence on k . (Same conditions as in Figure 7.) Numbers next to simulation curves correspond to k . The value of n is 85. The best adjustment is for % = (2.25 ± 0.25) Χ 10 mol h' s' . t

t

c

8

1

In Photochemistry and Radiation Chemistry; Wishart, James F., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1998.

1

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PHOTOCHEMISTRY AND RADIATION CHEMISTRY

t(s) Figure 9. Decay of electron donor concentration as measured at pH 3.9 and as calculated by numerical simulation with dependence on n . Experimental signal, same conditions as in Figure 5. Simulation curves: the same value of k , 2.25 X 10 mol L~ s~ , was selected as at pH = 4.8 The best adjustment is for n (pH = 3.9) = 500 ± 30. c

t

s

1

1

c

Size Dependence o f E°(Agn -Ag^).

The quantum-size effect on metal clusters redox properties in solution is the most important feature for cluster chemistry in solution. Most of data have been obtained on silver clusters suitable as an experimental model (1-4, 22). Assuming in the results just given that the redox potential of the critical cluster is slightly higher than that of the monitor system used, we conclude that: +

E°(Ag&-AgB5) = + 0.22 V

N H E

, and

£°(Ag5 oo-Ag5oo) = +0.33 V +

N H E

(20) Figure 10 shows the nuclearity dependence of silver cluster redox potential in water: together with the data just presented, the previously published values are reported for η = 1 (3), 2 (23), 5 (5), 10 (24), and 11 (25). The E° values for nuclearities η = 1 and η — 2 resulted from thermodynamic calculations. The value for η = 10 was obtained from electron transfer studies where the clusters were the donor and were corroded by H 0 . As a function of the 3

+

In Photochemistry and Radiation Chemistry; Wishart, James F., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1998.

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KHATOURI ET AL. Kinetics of ET in Solution

309

nuclearity (Figure 10), the redox potentials of hydrated silver clusters are seen to increase with N, thus confirming the trend previously observed (5, 6). The density of values available so far is not sufficient to prove the existence of odd-even oscillations like those observed for ionization potentials, I P , of bare silver clusters in the gas phase (26,27). In fact, E° is correlated to the ionization potential of solvated clusters, IP i > by I P [ A g J i = e X E ° [ A g - A g J + 4.5 (5, 28). However, it is obvious that the variations of E° or I P i and I P do exhibit opposite trends versus Η for the solution and gas phase, respectively. The difference between ionization potentials of bare and solvated clusters de­ creases with increasing Η and corresponds fairly well to the solvation free energy deduced from the Born model (29). The redox potential of copper clusters i n aqueous solution also increases with N, and this trend is seemingly general for all metals (13). The redox potential difference between the silver clusters Η = 85 and Η — 500 is not very large (0.11 V). This suggests that we approach an asymptotic value of E° for the bulk metal E°(Ag -Ag o) close to +0.40 V E - Note that the redox potential of the bulk metal E°( Agoo -Agoo ) differs from the well known electrochemical potential E'°(Ag -Aggo) = + 0 . 7 9 6 V E by the adsorption energy of the A g ion on the bulk metal: g

so

v

so

v

n

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oe

+

e

+

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+

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) = E^Ago^-Ag.) - AG

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(21)

+

The free energy, Δ G j (Ag ), is therefore equal to -0.4 V, which is a reasonable value. The results of Fig. 10 indicate that, at least concerning the redox propera(

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-2

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1 11



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1 1 1



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1 1 1 1

I • • ι

15

Π '* ι 1

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200

Nuclearity

ι ι ι I> » ι ι

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Figure 10. Size dependence of the redox potential of silver clusters in water (Φ). Data previously published are reported: η = 1 (3), 2 (23), 5 (Β), 10 (24), and 11 (25); η = 85 and 500 (this work).

In Photochemistry and Radiation Chemistry; Wishart, James F., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1998.

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[A/A-J

acceptor

[M / M].

catalyst

[D+/D]

donor

n

+

1

^

,

M+

M„

n

Figure 11. Mechanism of catalytic electron transfer involving metal clusters as relay. The thermodynamic conditions to he fulfilled are that the cluster redox potential he higher than the donor D and lower than the acceptor A potential, which implies that the cluster itself is in a size range that offers the efficient redox potential.

ties of silver clusters, the transition between the mesoscopic and the macro­ scopic phase occurs around the nuclearity η = 500 (diameter « 0.8 nm). The size-dependence of redox properties of metal clusters is crucial for their catalytic efficiency in electron transfer processes (30,31 ). Actually, a metal cluster acting as a catalytic relay behaves alternatively as an acceptor and a donor of electrons (Figure 11). Therefore, the thermodynamics imply that the value of the redox potential of the couple E ° ( M - M ) would be intermediate between that of the donor system as the lower threshold and that of the acceptor system as the upper threshold. The reaction between these systems, negligible in the absence of the catalyst, becomes efficient because of the double electron transfer through the metal cluster (32). The strong efficiency of ultradivided metals is thus due not only to their high specific area but essentially to their appropriate thermodynamic properties. Note that the local roughness on even large clusters also creates variable potentials, which when selected by the double threshold are favorable to the transfer. n

+

n

I n f l u e n c e o f t h e E n v i r o n m e n t . In contrast with the ionization po­ tential of clusters in the gas phase, which depends only on the nuclearity and

In Photochemistry and Radiation Chemistry; Wishart, James F., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1998.

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Kinetics of ET in Solution

KHATOURI E T AL.

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the metal considered, the redox or the ionization potential of clusters in solution depends not only on the nuclearity but also strongly on all interactions with surrounding molecules: solvent, surfactant, ions, ligand, and support. The data are still more scarce than for just hydrated clusters. However, some optical absorption spectra of single silver atoms in different solvents suggest the influ­ ence of the environment (30). Surfactant. It has been found that silver clusters generated in the pres­ ence of the surfactant polyacrylate (PA) (33) or of some other polyanions such as polyphosphate (PP) (34) coalesce slowly [Jfc (2Ag4 )(PA) = 10 L mol s" ] and are stabilized at very small nuclearity, of only a few units. Scanning tunnel­ ing microscopy (STM) techniques have confirmed the stability of oligomeric species i n the presence of P A (η ^ 7) (35). The kinetics study of electron transfer from the donor sulfonatopropylviologen anion to A ^ ( P A ) showed that the transfer starts effectively at the critical size, n , of 4, which is similar to clusters without surfactant. However, the rate constant for the electron transfer is 2 Χ 10 and 5 Χ 10 L mol s i n neutral and acidic media, respectively, instead of 7 Χ 10 L m o l without surfactant (36). Moreover, the clusters Ag4(PA) are not oxidized by molecular oxygen, so that their redox potential would be higher than -0.33 V E - These differences in behavior are assigned to the complexing properties of polyacrylate, which stabilizes and protects small clusters from coalescence and corrosion (37). 2+

5

1

r

8

7

- 1

8

- 1

N H

Ligand. The redox potential of the single silver atom solvated in water was calculated with the aid of a thermodynamic cycle including the electro­ chemical potential of the bulk metal in aqueous solution and the sublimation energy of the metal (3). The hydration energy of the neutral species is consid­ ered negligible relative to that of the cation. In the presence of a strong complexing agent such as the ligand C N ~ , the metal-ligand binding energy must be taken into account. A recent study (38) has calculated the redox potential of the couple A g i ( C N ) 2 ~ - A g i ( C N ) " using the self-consistent field method for the determination of the electronic structure of the gaseous species and the cavity model for the solvation energy. The results showed that the redox potential of the complexed atom is very negative, E° (Ag (CN) --Ag° (CN) -) = -2.6 V , and is lower by 0.8 V than the uncomplexed hydrated atom (3). The equilibrium constant of complexation of Ag° by 2 C N " has been evaluated to 10 at 298 K, which implies that the cyano complex is stable relative to dissociation. However, it is highly reactive as an electron donor. The results for the ligand C N ~ illustrate again the influence of the local environment on cluster properties (39, 40). In the case of cyano complexation, the redox potential of the complexed atom at least decreases markedly relative to that of free solvated atoms. Recent results on the ligand N H also lead to the conclusion of a more negative redox potential, £ (Ag (NH3)2 -Ag (NH )2), than £°(Ag -Ag°i) (41, 42). I

I

1

2

1

2

2

0

2

2

N H E

7

3

o

I

1

+

0

1

3

+

Support. It is noteworthy to compare the potential of electron donors able to transfer electrons to unsupported clusters compared with the potential

In Photochemistry and Radiation Chemistry; Wishart, James F., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1998.

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of a photographic developer able to develop AgBr-supported clusters of the same critical nuclearity. For instance, free clusters solvated in water of nucle­ arity n = 4 are developed by an electron donor of E° = -0.41 V E (5), whereas a weaker reducing agent, such as hydroquinone (p-dihydroxybenzene) is able to develop clusters supported on an AgBr emulsion from the same critical nuclearity n = 4 (43). As discussed above in the case of naphtazarin hydroquinone, the dielectronic donor hydroquinone ( Q ' H ) induces a two-step reduction via the semiquinone ( Q " ~ - Q ) with two standard redox potential values. Under the basic p H conditions of photographic development, successive potential values involved in the usual hydroquinone developer are E°(Q'~-Q'H ) = +0.024 V (or - 0 . 2 0 V i ) and E ° ( Q ' - Q ' - ) = +0.078 V N H E (or - 0 . 1 4 4 V i ) . Note that in this system the second step from the semiquinone corresponds to a potential higher than from Q ' H . The first elec­ tron transfer from the hydroquinone determines the threshold potential for developability, that is, the potential of the critical cluster, here of nuclearity n = 4. Thus, we may conclude that the reduction of the free cluster Ags requires a potential of the donor more negative by [0.024-(-0.41)] = 0.43 V than the same AgBr-supported cluster, the difference being induced by the stabilizing effect of the support. The difference is likely dependent on the nuclearity. However, it is expected that the redox potential of AgBr-supported clusters is systematically more positive than the potential of free clusters measured in water, as shown for this first evaluation at size η = 4. c

N

H

c

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2

2

N H E

A g C

A g C

2

c

+

Stabilizing effects have been directly observed by pulse radiolysis studies of silver cluster coalescence supported on 4-nm silica colloidal particles (44). Very small oligomeric clusters absorbing at 290 nm and 330 nm are stable in the presence of oxygen and even C u or R u ( N H ) C l 3 ( £ ° = 0.2 V E ) These supported the exhibition of higher redox potentials than for free oligo­ meric clusters. 2 +

3

6

N H

Conclusions The redox potentials of short-lived silver clusters have been determined through kinetics methods using reference systems. Depending on their nuclearity, the clusters change behavior from electron donor to electron acceptor, the thresh­ old being controlled by the reference system potential. Bielectronic systems are often used as electron donors in chemistry. When the process is controlled by critical conditions as for clusters, the successive steps of monoelectronic transfer (and not the overall potential), of which only one determines the thresh­ old of autocatalytical electron transfer (or of development) must be separately considered. The present results provide the nuclearity dependence of the silver cluster redox potential in solution close to the transition between the mesoscopic phase and the bulk metal-like phase. A comparison with other literature data allows emphasis on the influence of strong interaction of the environment (surfactant, ligand, or support) on the cluster redox potential and kinetics. Rela-

In Photochemistry and Radiation Chemistry; Wishart, James F., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1998.

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tive to free solvated clusters, these interactions may either lower (CN~, N H ) or increase (surfactants PA and PP; support) the reactivity and therefore control the cluster efficiency in the electron transfer catalysis. 3

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Acknowledgment We are indebted to A. J. Swallow for fruitful suggestions and discussions during this work.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.

Delcourt, M . O.; Belloni, J. Radiochem.Radioanal.Lett. 1973, 13, 329. Basco, N.; Vidyarthi, S. K. Walker, D. C. Can. J. Chem. 1973, 51, 2497. Henglein, A. Ber. Bunsen Ges. Phys. Chem. 1977, 81, 556. Henglein, A. Chem. Rev. 1989, 89, 1861. Mostafavi, M.; Marignier, J. L.; Amblard, J.; Belloni, J. Radiat.Phys. Chem. 1989, 34, 605. Mostafavi, M.; Marignier, J. L.; Amblard, J.; Belloni, J. Ζ. Phys. D: At. Mol. Clusters 1989, 12, 31. Morse, M . D. Chem. Rev. 1986, 86, 4049. Schumacher, E. Chimia 1988, 42, 357. Haberland, H . Clusters of Atoms and Molecules; Springer-Verlag, Berlin, Germany, 1994; Vols. 1, 2. Khatouri, J.; Mostafavi, M . Ridard, J.; Amblard, J.; Belloni, J. Ζ. Phys. D: At. Mol. Clusters 1995, 34, 47. Khatouri, J.; Ridard, J.; Mostafavi, M.; Amblard, J.; Belloni, J. Ζ. Phys. D: At. Mol. Clusters 1995, 34, 57. Belloni, J.; Mostafavi, M.; Marignier, J. L.; Amblard, J. J. Imaging Sci. 1991, 35, 68. Khatouri, J.; Mostafavi, M.; Amblard, J.; Belloni, J. Proc. 6th Int. Symp. Small Part. Inorg. Clusters,Ζ.Phys. D: At. Mol. Clusters 1993, 26, S82. Land, E.; Mukherjee, T.; Swallow, A. J.; Bruce, J. M. J. Chem. Soc. Faraday Trans. I 1983, 79, 391. Land, E.; Mukherjee, T.; Swallow, A. J.; Bruce, J. M. J. Chem. Soc. Faraday Trans. 1989, 79, 405. Belloni, J. Billiau, F. Cordier, P.; Delaire, J. Α.; Delcourt, M . O. J. Phys. Chem. 1978, 82, 532. Saito, E. Belloni, J. Rev. Soc. Inst. 1976, 47, 629. Schwarz, Η. Α.; Dodson, R. W. J. Phys. Chem. 1989, 93 409. Buxton, G. V. J. Phys. Chem. Ref. Data 1988, 17, 513. Von Pukies, J.; Roebke, W.; Henglein, A. Ber. Bunsen Ges. Phys. Chem. 1968, 72, 842. Janata, E.; Henglein, Α.; Ershov, B. G. J. Phys. Chem. 1994, 98, 10888. Henglein, A. Ber. Bunsen Ges. Phys. Chem. 1995, 99, 903. Tausch-Treml, R.; Henglein, Α.; Lilie J. Ber. Bunsen Ges. Phys. Chem. 1978, 82, 1335. Platzer, O.; Amblard, J. Marignier, J. L.; Belloni, J. J. Phys. Chem. 1992, 96, 2334. Henglein, A. Tausch-Treml, R. J. Colloid Interface Sci. 1981, 80, 84. Jackschath, C.; Rabin, I.; Schulze, W. Z. Phys. D: At. Mol. Clusters 1992, 22, 517. ;

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In Photochemistry and Radiation Chemistry; Wishart, James F., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1998.

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