J. Phys. Chem. 1982, 86, 3166-3170
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dimer 14. We conclude therefore that (i) CO and COPare produced from FAN and HMF, respectively, and trapped as CO-HCO2H and COz-H2CO or, alternatively, (ii) the precursor decomposes to both CO and COz. The first alternative requires that the vibrations of HCOzH and HzCO are considerably perturbed from those of the monomers. In addition, the bands due to CO and COPwould be expected to show a perturbation and, while the bands at 2158 and 2364 cm-’ satisfy this condition, those at 2140, 2143, and 2344 cm-’ do not. A rationale for the second and more attractive alternative is to assume that either SOZ itself or ground-state HMF can absorb a photon and decompose via a pathway separate from those discussed previously. Formic anhydride might also be included as a possible precursor for photolytic decomposition to COP and CO although with less conviction based on the observations of Story and co-workers.18 Finally, a growth in intensity of absorptions due to H20 between 1590 and 1625 cm-l and at 3710 and 3757 cm-’ is observed. Water or molecular hydrogen are expected to be complementary products to CO and COz on decomposition of SOZ, HMF, or FAN.
Conclusions The reaction of ethylene with ozone in CFJ1 solution at -150 to -130 OC yields SOZ such that CHzCDz gives practically no h4 and d4 ozonides. Oxygen-18 and carbon-13 isotopic substitution complement the deuterium studies of Kuhne et al. and allow a more definite assignment of vibrations involving these atoms. The matrix photolysis and gas-phase pyrolysis of SOZ lead to the isolation of different products. In both cases, however, decomposition of the SOZ is proposed to proceed via intramolecular H-atom transfer to yield a vibrationally excited hydroxymethyl formate (HMF) molecule. Under
the conditions of pyrolysis this activated species decomposes completely, and formic acid and formaldehyde are the major products trapped in the matrix. Carbon dioxide is also detected, probably a product of the decomposition of Yhot”formic acid. There is no evidence for the intermediacy of formic anhydride in SOZ pyrolysis, despite its recent identification among products of the gas-phase ethylene-ozone reaction. In situ photolysis of SOZ encourages rapid vibrational relaxation of “hot” HMF and the molecule is trapped in either the cis or trans conformation. Evidence is presented for the photodecomposition of hydrogen-bonded cis-HMF to a specific formic acid-formaldehyde dimer. The same species is also observed in codeposition of formic acid and formaldehyde and in SOZ pyrolysis experiments. Formic anhydride, probably formed by H2 elimination from vibrationally excited trans-HMF, constitutes the second major photolysis product. The presence of COz,CO, and H20 without detection of monomeric formic acid or formaldehyde implies another mode of decomposition for SOZ, HMF, or FAN in which the former small molecules are the sole products. A brief comparison with results from ethylene-ozone gas-phase studies reveals that some unassigned bands agree closely with several of those identified in this work as due to HMF and the formic acid-formaldehyde dimer. Thus the two sets of experiments are complementary and the present results suggest that ground- or excited-state SOZ may play an important role in the gas-phase ethyleneozone reaction even though it is rarely detected. Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research.
Electrochemical Properties of Small Clusters of Metal Atoms and Their Role in Surface Enhanced Raman Scattering W. J. Plietht Meterlais and W c u l e r Research Divlsbn, Lawrence Berkeley Labofatofy, and Depaftmnt of Chemical Engineering, Universlfy of California, 8&eiey, California 94720 (Received: November 3, 1981; In Final Form: March 29, 1982)
Starting with equations for the shift of the reversible redox potential of small metal particles with size, the electrochemicalproperties of these particles are discussed. Approximate equations are given for the relationship between the particle size and the surface charge, the potential of zero charge, the surface potential, work function and quantities related to this function. The influence of these properties on redox reactions, electrosorption, and chemisorption are discussed. The results are used to explain experimental observation in connection with the surface enhanced Raman effect.
Introduction I t is well known that small particles have properties quite different from the properties of the bulk materials.’ Recently, it was found by Henglein2 that small metal particles possess unusual catalytic properties in radiolysis and this was explained qualitatively by a shift in the redox potential. In a series of papers, Henglein et al.3 investigated the catalyzed reduction of several organic molecules, Institut fiir Physikalische Chemie, Freie Universitiit Berlin, lo00 Berlin 33, West Germany.
D-
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the catalysts being metal clusters of silver, gold, and copper. Another series of experiments, demonstrating the (1)See papers in “Growth and Properties of Metal Clusters”, J. Bourdon, Elsevier, Amsterdam, 1980. (2) A. Henglein, Ber. Bumenges. Phys. Chem., 81,556 (1977). (3) R. Tausch-Treml, A. Henglein, and J. Lilie, Ber. Bunsenges. Phys. Chem., 82, 1335 (1978). (4)J. A. Creighton, C. G. Blatchford, and M. G. Albrecht, J. Chem. SOC.,Faraday Trans. 2, 790 (1979). (5) H. Wetzel and H. Gerischer, Chem. Phys. Lett., 76, 460 (1980). (6)R. M. Hexter and M. G. Albrecht, Spectrochim. Acta, 35A,233 (1979). (7)M. Moskovits, J. Chem. Phys., 69,4159 (1978).
0 1982 American Chemical Society
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Electrochemical Properties of Small Metal Clusters
unusual electrochemid properties of small metal particles, was carried out by Ross.9 He deposited platinum on graphite supports and compared the electrochemical properties of the electrodes with the known behavior of bulk platinum. A deviation from the electrochemical properties of the bulk material was also found for silver nuclei1*12 forming the latent image in photographic layers.lo This deviation was explained more quantitatively by use of Kelvin’s equation.’lJ2 Among the various theories explaining the surface-enhanced Raman scattering is the idea that the surface enhancement is caused by the unusual optical properties of small metal particles. Results of experiments suggesting such a mechanism were carried out with solutions of colloidal gold and silver by Creighton, Blatchford, and Albrecht.4 A similar experiment by Wetzel and Gerischers mainly confirmed the earlier results. Explanations were given by Hexter and Albrecht6 and by Moskovits.’ The cluster explanation suggests that one has to look not only at the optical properties of the small particles but also at their electrochemical behavior. If one understood the deviations of the general electrochemistry of these particles from that of the bulk, one might be able to understand the electrochemical procedures of activation and deactivation of electrodes encountered in Raman studies. For these reasons, we have tried to find a more general description of the electrochemical properties of small metal particles. Starting with equations for the shift of the reversible potential with dispersion, we will discuss various other electrochemical properties such as surface charge, the potential of zero charge, the surface potential, the work function, and related quantities. The approximate relations between these functions and the size will enable us to explain the electrochemical behavior of dispersed metals in more detail.
The Redox Potential of Metal Clusters What is the redox potential of metals in a dispersed state? It was recognized that it is different from the bulk metal and for the special case of a single siver atom in equilibrium with silver ions Henglein2 calculated the dramatic value of -1.8 V for the standard potential, which has to be compared with the standard potential of bulk silver of +0.799 V vs. the NHE. In the attempt to derive the equation for the potential of clusters of more than just one atom we construct an electrochemical cell consisting of two half-cells. One contains a metal in its bulk state, Meb, and the other in the dispersed state, Med. The cell reaction is described by the equations Meb ---* Me2+solv ze(la)
+ ze-Mez+solv
Med
Ob)
(IC) Met, Med The overall electrode reaction is the transference of one mole bulk metal into the dispersed form. The voltage of this electrochemical cell can be calculated from the free energy of the dispersion process -+
(8) (a) R. C. Baetzold, J. Chem. Phys., 68, 555 (1978); (b) R. C. Baetzold and R. E. Mack. ibid.. 62. 1513 (1975). (9)P.Ross, report for Electric Power Research Institute, EM 1553, Project 1200-5. (10)E. Jaenicke in “Advances in Electrochemistry and Electrochemical Engineering”, H. Gerischer and C. Tobias, Ed., Wiley, New York, 1977.Vol. 10. D ~~128. (fl)J. Konstantinov, A. Panov, and G. Malinowski, J. Photogr. S i , 21,250 (1973). (12)J. Konstantinov and J. Malinowski, J.Photogr. Sci., 23,l (1975).
ACD =
‘d
- +, = -AGD/zF
(3)
AtD is thus the difference in equilibrium oxidation potentials between the dispersed (Ed) and the bulk metal (eb). One way to find AGD is to look for the change of free energy associated with the change in surface area. As a first approximation one can consider a small particle as a sphere of radius r. The change of free energy with surface area A is given by
dG = y dA where y is the surface tension. We substitute dA = 87rr dr
(4)
(5)
UM
dr = - dn (6) 4ar2 where U M is the molar volume and n is the number of moles dispersed. Integrating between n = 0 and n = 1, we get the free surface energy of one mole of metal dispersed into particles of radius r. The free surface energy of the bulk can be neglected and we obtain (7)
This is an analogous expression to the Kelvin equation. If, in addition, we take the crystallography of the particles into account we have to apply Wulf s law,2O substituting yi/ri for y / r . For crystallites in their crystallographic equilibrium y i / r ishould be constant. So while eq 7 is not changed in principle, separation into y and r would give mean values y and r. For growing nuclei, of course, the condition of equilibrium will rarely be satisfied and in general we have to expect nonequilibrium values of y and r, but in all these cases eq 7 will be a good approximation as long as the size of particles is not less than 100 atoms, equal to approximately 7 8, of radius. For a long period of time, eq 7 was considered as too simple a model to be applied for the sophisticated photographic process. However, recently the validity of eq 7 was demonstrated for silver clusters deposited on silver bromide layers.l1J2 Inserting eq 7 into eq 3 we obtain the following relationship for the potential difference AtD
One thus expects a cathodic shift in the redox potential of small metal particles compared to the redox potential of the bulk which is proportional to the ratio y / z and the reciprocal radius l/r. Some values of y for a number of metals obtained mainly by the zero-creep method13 are listed in Table I. These values refer to vacuum and will be different in an electrolyte depending on the properties of the double layer. One can therefore use only approximate values for y / r in calculations of AED. The results of one such calculation is shown in Figures l a and b. The data show that the shift of the redox potential is significant for particles with radius as large as 100 A. While eq 8 will describe the potential shift for particle sizes above 10 A with sufficient accuracy, it becomes inaccurate for the interesting small particles consisting of only a few atoms (Figure 2). A more general way to obtain AGD is therefore described using the following cycle (Figure 2). In a vacuum, AGD must be equal to the sum of the free
~
(13)R. G. Linford in ‘Solid State Surface Science”, M. Green, Ed., Marcel Dekker, New York, 1973.
Plieth
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TABLE I : Values of Surface Energy 7 (Ref 13),Lowest Valence State 2,and Molar Volume V, for Some Common Electrode Materials
~
Ag Au
1140 930 1370 1040 Cu 1750 900 1710 1000 Pt 2300 1310 Fe 2170 1380 Fe 2320 1410 Co 1970 1350 Ni 1860 1220 Cr 2200 1550 Ti 1700 1600 Calculated with -ar/aT =
1590 1880 2190
10.28 10.21 7.12 3240 2 9.10 2930 7.11 2640 2 6.62 2460 2 6.60 2690 (2) 7.22 2490 (2) 10.64 0.5 erg cm-2 grad". 1 1
BUCK SOLID
Flgure 2. Cycle to relate the free energy for dispersion AGD to the calculated free energy of cluster formation AGa; AGd and AGare free energy of subllmation and solvation, respectively.
a
-
Meb
' \
O -01
Ii i l li ii
OJ
a
Flgure 3. Cycle to discuss the dependence of the free energy of dispersion AGD on the surface charge.
a
ILL/!-
mensional shape. In this case, instead y, the boundary free energy 6 has to be u~ed.'~J' Then the differential free energy change is given by the equation
-0.2
50
150
100
200
dG = 6 dl
r /A
?
-10 O
where 1 is the boundary length of the two-dimensional clusters. If we assume disks as the approximate form of the two-dimensional nuclei, dl is related to dn, the differential of the mole number of metal present as clusters, by the relation dl = (AM/r) dn
-
0
5
15
IO
r
20
25
/I
energy of sublimation AGsub, the free energy associated with the clustering of single metal atoms AGcl, and the energy of interaction of the surface atoms with the solvent molecules AGwlv. Thus, one obtains
+ AGci + AG,l,
(11)
Here, AM is the molar area of the cluster forming atoms and r is the mean radius of the disks. Substituting eq 11 into eq 10 and integrating over one mole gives the change of free energy which is inserted into eq 3 and we obtain for the shift of the redox potential
Flgure 1. Cathodic shift of the reversible redox potential of a metal electrode with decreasing particle radius (after eq 8) for three selected values of surface energy: (a) for particle size r < 250 A; (b) for particle size r < 25 A. Cuve 1,500 erg cm-2; curve 2,1500 erg cm-2; curve 3, 2500 erg cm-*.
AGD = AG,b
(10)
(9)
The equation allows AGD to be obtained from quantum chemical first principle calculations, taking .hG,,b from experiments and neglecting AGmlv. Calculations for the clustering energy have recently been carried out for Ag for Cu c1usters,16*8b and others.8b These calculations show an oscillating behavior of the energy with the number of atoms.
Small Metal Clusters on Surfaces Metal clusters formed on surfaces can have two-di(14) S. Traasntti in "Advances in Electrochemistryand Electrochemical Engineering",H. Gerischer end C. W. Tobias,Ed.,Wiley, New York, 1977, Vol. 10,p 258. (15) R.Matejec and E. Moisar, Ber. Bunsenges. Phys. Chen.,69,566 (1965). (16) A. B. Anderson, J. Chem. Phys., 68, 1744 (1978).
where r is now the radius of the cluster disk on the surface. The energy 6 will depend considerably on the structure of the surface of the supporting material.
The Charge of the Particles and the Potential of Zero Charge In this section we will discuss the role of the surface charge in the dispersion process. We ask the question: what is the free energy of dispersion if we carry out the dispersion at a surface charge different from the surface charge a t the redox potential of the bulk? We will find the answer by carrying out the dispersion process in a way illustrated in Figure 3. For reasons of comparison it is assumed that the bulk metal (one mole) forms a sphere of radius R. First we discharge the bulk metal. The work to discharge a compact sphere of charge q b and radius R in a medium with the dielectric constant e is given by the equation w b = -qb2/8?rto& (134 where tois the dielectric permittivity of the vacuum. After (17) J. P. Bernard, A. de Haan, and H. van de Porten, C.R. Acad. Sci., Part C,276, 588 (1973). (18)J. Billmann, G. Kovacs, and A. Otto, Surf. Sci., 92, 153 (1980).
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Electrochemical Properties of Small Metal Clusters
dispersion of the now uncharged bulk metal into N particles of radius r, we have to recharge these particles. The work for this process is qd2 Wd=+N 8?reoer I t follows (Figure 3) that AGDPq= w
b
+ AGD + wd
(14)
The values for AG are equal if wb
= -wd
(154
N is determined from the requirement that the total mass of the dispersed spheres equals that of the initial bulk sphere (4/3)rr3pN= (4/3)?rR3p,where N = R3/r3. Substituting into (13) and rearranging (15a) can be brought into the form qd/47V2 = qb/4?rR2
(15b)
The free energy of dispersion AGD is independent of the surface charge of the bulk under the condition; the surface charge density has to be constant during the dispersion process. It follows that the whole electrochemical potential scale of the dispersed metal is shifted namely by the same value as the reversible potential. In particular, the point of zero charge is shifted by epzc,d
(16)
- Cpzc,b =
Comparing bulk and dispersed metal at equal potentials the dispersed metal is characterized by a more positive surface charge density. This one-to-one relationship between the potential scale of the bulk and of the dispersed metal will have to be modified by considering the dependence of AG on y (eq 7). According to the Lipmann equation y varies with the potential. For the liquid mercury it decreases by about 10 to 20% at both sides of the electrocapillary maximum. For solid metals this dependence will be less significant and the one-to-one relationship will be a good approximation.
The Surface Potential With the properties so far derived we can look at more specific properties of the double layer of the small particles. The potential across the double layer is separated into two contributions: the surface potential x and the Volta POtential +. The Volta potential is determined by the charge on the surface already discussed in the foregoing chapter. The surface potential x represents the dipole structure of the surface and is mainly dependent on the dipole dentisy N p x =f(Nd (17) The dipole layer between the metal atoms and the electrolyte will in general be a closely packed layer of solvent molecules and their images in the metal. It is postulated that this layer is, as a first approximation, independent of the particle size. To illustrate this reasoning we will form the ratio between the number of metal atoms N Mon a sphere of radius r (surface area per atom: A M )and the number of dipole molecules ND on a sphere with the radius increased by the diameter of the metal atoms a (surface area per molecule: AD). The ratio is given by N D AM (r + a)2 (18) 1 2 N M AD r2 AD A closely packed dipole layer is, in general, bound by co-=--
"(
+
;)
valent forces between surface atoms and dipole molecules. Additional dipoles need a full size space between the present dipoles only available if this ratio is doubled. For clusters r 1 10 A the dipole density N p = AD-' will be approximately constant, regardless of the size of the particles. Thus, x will become independent of r. It follows that Xd
- Xb
0
(19)
The potential difference AeD is mainly determined by the difference of the Volta potential A+.
The Work Function and the Chemical Potential of Electrons Changes of the potential of zero charge can, according to the literature,14 be related to changes in the work function @, We can write for the differences between dispersed and bulk metal (20) @ d - @b = F(cpzc,d - epzc,b)
It follows using eq 16 @d
- @b = F A ~ D 0 (22) The chemical potential of electrons in dispersed metals is higher than in the bulk metal. The chemical potential of electrons in a metal is also related to the concept of electronegativity. We can deduce from eq 22 that the electronegativity is increased with decreasing particle size.
Conclusions for the Electrochemical Behavior The result of the foregoing discussion can be summarized in three points which, as we have tried to show, have one common origin: metal atoms in a small array are in energetically less favorable positions compared to bulk positions. ( a )Negative Shift of the Equilibrium Potential. This point determines the equilibrium properties as well as the capability for reduction or oxidation. The results by Henglein3 can be explained qualitatively by these properties. The experiments with silver clusters on silver bromide by Malinowski et a1.l1J2 gave quantitative evidence for the prediction that a particle in a special redox environment will grow or decrease in size depending on the equilibrium condition. The stabilization of the latent image in photographic layers with a particle size between 4 and 40 silver atoms15 is another example. ( b )Negative Shift of the Potential of Zero Charge epW. Electrosorption on a surface depends on the position of the potential with respect to the potential of zero charge epzc. Because of the shift of this potential for small particles, we expect a change in the electrosorption properties. An experimental confirmation for this prediction is given by the results of Ross.g A negative shift of -50 mV was measured for the formation of the oxide electrosorption layer on graphite-supported platinum clusters compared to bulk platinum. The particle size was approximately 20 A. The shift would predict a ratio y / z between 200 and 300 erg cm-' rather low compared with the values for the surface energy of platinum in Table I. ( c ) The Decrease of the Work Function W . The decrease of the work function can be considered as a reduced
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J. Phys. Chem. 1982, 86, 3170-3172
electron affinity of small particles. This will be observable in photoelectron emission spectra. With regard to the electron donor properties of metals this means also a stronger ability to form charge-transfer complexes.
The Electrochemical Properties of Small Metal Particles and the Surface Enhanced Raman Effect In the observation of the so-called surface enhanced Raman effect (SERS) some of the most fundamental experimental results have not yet found reasonable explanations. This included the following points: Why is the oxidation reduction cycle important? Why does silver deposition at moderate negative potentials result in no enhancement but deposition at high negative potentials18 does? Why does the enhancement effect irreversibly disappear after the polarization is increased above a limiting negative p ~ t e n t i a l ? ' ~ The answers to these questions may be found by considering the Outstanding electrochemical properties of microparticles especially of smallest size (e.g., 4-40 A for Ag15). The explanations described are further support for the idea that these particles are also responsible for the optical process of e n h a n ~ e m e n t . ~ , ~ The formation of clusters and microcrystallites on surfaces in metal deposition is favored (especially for silver) by rather rough electrochemical conditions with regard to the electrode potential as well as with regard to diffusion limitations. Special deposition forms (whisker, powder deposition) are obtained under very similar conditions as are necessary to activate an electrode for enhanced Raman scattering. No enhancement is found when the silver is deposited under moderate deposition conditions, regardless of the electrode roughness. In this case a fairly smooth deposit is, in general, obtained. Nevertheless, the fresh deposit strongly absorbs molecules and ions of the electrolyte. Thus, adsorption on a blank surface cannot explain the (19) W. J. Plieth, B. Roy, and H. Bruckner, Ber. Bunsenges. Phys. Chem., 85, 273 (1981). (20) B. Honigmann, "Gleichgewichta- und Wachstumsformen von Kristallen", D. Steinkopf Verlag, Darmstadt, 1958.
enhancement mechanism. Ad-atoms are also expected on the surface under these conditions. The lack of enhancement despite the presence of these ad-atoms is a strong argument against the simple ad-atom theory for the enhancement. Clusters, especially silver clusters, have to be stabilized after formation. Otherwise they could not exist in equilibrium with the smoother, less energetic surfaces. The stabilization may be caused by complex formation with the substance under investigation (pyridine, CN-, etc.). The cluster properties will result in much stronger chemisorption bonds than on the bulk metal surface. The stabilization is lost after cleavage of the chemisorption or electrosorption bond when surpassing a limiting negative potential. The unstable cluster will rapidly transform into a stable surface form, that means it disappears from the surface and the enhancement effect is lost. Thus, in addition to discussing the optical properties of metal particles it seems helpful also to look at the electrochemical properties to derive a more complete understanding of the enhancement mechanism. As was pointed out by one reviewer, a formalism of the thermodynamics of small systems was developed by Hi1121 and was recommended to be used for the thermodynamic analysis of this paper. A reformulation of our analysis is in progress. Acknowledgment. The present paper was partly formulated and written during a sabbatical leave at the Lawrence Berkeley Laboratory of the University of California. I would like to thank my colleagues who made my stay such an enjoyable experience. I appreciate especially discussions with Rolf Muller, Phil Ross, Charles Tobias, Joe Farmer, and Felix Schwager. I appreciate also the funding by the German Research Foundation who made this stay financially possible. Preparation of the manuscript was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Materials Sciences Division of the US. Department of Energy under contract No. W-7405-ENG-48. (21) T. L. Hill,"Thermodynamics of Small Systems", W. A. Benjamin, New York, 1964, Vol. 1, 2.
Pressure Effect on the Krafft Points of Ionic Surfactants Nagamune Nlshikldo,' Hldekl Kobayashl, and Mltsuru Tanaka Depaftment of Chemistry, Facutty of Science, Fukuoka University, Fukuoka 814-01, Japan (Received: December 8, 1981; I n Final Form: March 29, 1982)
The pressure dependence of the Krafft temperature (or point) of typical anionic and cationic surfactants (sodium alkyl sulfates and cetyltrimethylammoniumbromide) has been determined at pressures up to 400 MPa by means of the electroconductivitymethod. The Krafft temperatures increased rapidly with pressure, and hence the range of temperature and pressure in which micelles can exist is rather restricted. In order to establish a rule describing the pressure dependenceof the Krafft temperature, the volume changes of transition from the hydrated surfactant solid to micellar state for sodium alkyl sulfates at atmospheric pressure have been calculated according to the model that a Krafft temperature is a melting point of the hydrated surfactant solid. Comparison of the calculated value with the directly determined one in the literature gave reasonable agreement, suggesting that the model is useful for describing the rule.
Introduction With increasing concentration of an ionic surfactant in water, the solid precipitates as a result of the limit of solubility at low temperatures at constant pressure. However, the solubility increases very rapidly at a certain temperature, called a Krafft point or temperature,' and 0022-365418212086-3 170$01.2510
consequently the solutions of almost any composition become homogeneous at temperatures about 4O above the Krafft temperature. This phenomenon characteristic of (1) (a) F. Krafft and H. Wiglow, Ber., 28, 2566 (1895). (b) Recently, the Krafft temperature has been found for the aqueous solutions of nonionic surfactants under high pressure; see ref 9.
0 1982 American Chemical Society
