4589
J. Phys. Chem. 1993,97, 4589-4594
Silver Atoms and Clusters in Aqueous Solution: Absorption Spectra and the Particle Growth in the Absence of Stabilizing Ag+ Ions B. G. Ershov,+E. Janata, A. Henglein,' and A. Fojtik Hahn-Meitner-Institur Berlin, Abteilung Photochemie, 1000 Berlin 39, FRG Received: December 10, 1992; In Final Form: February 3, 1993
The absorption spectra of Ago and Ag2+, the first products of silver ion reduction in aqueous solution, are redetermined using pulse radiolysis. Ago absorbs at 360 nm (1.6 X lo4 M-I cm-I), Le., at a longer wavelength than the free atom in vacuo. The great width of 0.91 eV of the absorption band is explained by a strong interaction of the atom in the excited state with the aqueous solvent. The absorption spectrum of A&+ has two peaks (at 310 and 265 nm). The equilibrium Ago Ag+ F? Ag2+ has a free enthalpy < 4 3 6 eV, and from this value the hydration free energy of Ag2+ is calculated to be more negative than -3.6 eV. Approximate values for electrochemical standard potentials of Ag2+ are also given. The reaction 2Agz+ Ag42+ occurs with 2k = 2.6 X 109 M-I s-I. As the absorption band of Ag4,+ disappears, the 355- and 325-nm absorption bands of long-lived oligomeric clusters appear. However, ionic strength studies indicate that Ag42+is not the immediate precursor of these clusters, as an additional step of growth occurs in between. At high doses in the pulse, practically all the silver ions are reduced, when the solution contains formate. Neutral intermediates of the growth of the particles, such as Ag2 and Ag4, can be detected, and the rate of particle growth is not influenced by added electrolytes. The oligomeric clusters are not long-lived under these conditions, and the large silver particles formed tend to agglomerate rapidly.
+
Introduction
Pulse radiolysis is a powerful tool to study the temporal development of metal colloids. A pulse of high-energy electrons is used to generate hydrated electrons and reducing radicals in a metal salt solution. Themetal ions are reducedand agglomerate to form oligomeric clusters and finally colloidal metal particles. In the first part of the present paper, the early steps of the reduction of the silver ion by the hydrated electron, Ag+
+ ea;
-
-
that certain oligomeric silver clustersare long-lived in the presence of excess Ag+ ions and that all agglomeration processes are strongly influenced by the ionic strength of the solution.2 In the second part of the present paper, the reduction of silver ions is carried out under conditions (small Ag+ concentration, very high dose in the pulse) where all silver ions are reduced during the pulse. Under these conditions, only neutral silver clusters are formed; the agglomeration of such neutral particles is studied and compared with the previous findings on the agglomeration in the presence of excess Ag+ ions.
Ago Experimental Section
which have been studied many years ago,l are reinvestigated using more sophisticated equipment. The spectra of Ago and Agz+ are obtained more precisely than in the early studies. In addition, the reduction of Ag+ by the carboxyl radical anion, C02-, is investigated. This radical is generated in the presence of formate via the reactions of the OH radical and the H atom which are also produced in the radiolysis of the aqueous solvent:
HCO;
+ O H (H)
-
C02-
+ H,O (H,)
(3)
It is shown that Ag2+is formed in the reduction of Ag+ by C02as in the reduction by eaq-: thus, Ag2+ can be produced as the only short-lived species in solutions containing both Ag+ and formate ions. In all the previous pulse radiolysis studies, the concentration of hydrated electrons was much smaller than that of the Ag+ ion, the advantage being that reactions 1 and 2 obey first-order kinetics which facilitatesthedeterminationof thespecific rates. Moreover, all the subsequent agglomeration processes occurred in the presence of excess Ag+ ions. It was shown in a preceding paper On leave of absence from the Institute of Physical Chemistry of the Academy of Sciences, Moscow, Russia. * To whom correspondence should be addressed. +
0022-3654/93/2097-4589$04.00/0
The pulse radiolysis equipment has been described previously (3.8-MeVelectrons, 15-nsand 1.5-pspulses; 1.5-cmopticalpath).3 In some of the experiments, the changes in molar conductivity were recorded together with the changes in absorbance. A special computer program for the simulation of sequential reactions was developed which will be published elsewhere.
Early Reduction hoducts. The rate constant of reaction 1 was determined by recording the pseudo-first-order decay of the 700-nm absorption of the hydrated electron, generated in a deaerated 1 X lo4 M AgC104 solution containing 0.1 M 2-propanol. A value of 4.8 X 1Olo M-I s-I was found, which is noticeably higher than the previous value (3.5 X 10'0 M-1 s-1 1"). To obtain the spectrum of Ago,the solution was pulsed and the absorption changes measured under conditions where practically no Ago atoms had yet been consumed to form Ag,+ (eq 2). A 15-nspulse was used, which produced a concentrationof hydrated electronsof 3 X 1 W M, and the absorptionsignals were measured at 0.1 ps after the pulse. At this time, 36% of the hydrated electrons had reacted. The solution contained also 3.6 X 10-6 M l-hydroxy- l-methylethyl radicals, formed in the reactions of the 0 1993 American Chemical Society
4590 The Journal of Physical Chemistry, Vol. 97, No. 18, 1993
1.8 I
Ershov et al.
1
.=5
aJI
P
I
I
I
‘0-
f 1.0
0 W
time
“200
250
350 X Inml
300
400
Figure 2. Kinetic curves for the buildup and decay of the 360-nm (Ago) and 3 IO-nm (Ag*+) absorptions. Full line: calculated curves. Circles: some experimental points to show the agreement with the theoretical curve. Solution: 1 X l e 4 M AgC104, 0.1 M 2-propanol. Radical concentration: 2 X 10-6 M.
450
Figure 1. Absorption spectra of Ago and Agz+.
OH and H radicals from the radiolysis of water:
OH (H) + (CH,),CHOH
-
H,O (H,)
+ (CH,),COH (4)
The absorption spectrum of this radical is known as it can be generated as the sole transient in solutions containing 2-propanol and nitrous oxide, the latter reacting with hydrated electrons according to eaq-
+ N,O + H,O
-
N,
+ OH- + OH
(5)
to yield additional OH radicals which form organic radicals. (Reactions 4 and 5 occur during the pulse.) The signals of Ago could therefore be corrected for the small contribution of the 1-hydroxy-1-methylethyl radical. Other correctionsincluded the weak absorptionof the hydrated electronsthat had not yet reacted at 0.1 ps and a small absorption decrease due to the consumption of Ag+ ions. The corrected Ago spectrum is shown inzigure 1. It contains a broad unstructured band which peaks at 360 nm. The absorption coefficient (1.6 X lo4 M-I cm-I) is higher by about 10%thanin thefirstdeterminationofthespectrum,Ibwhere no corrections had been made. The width of the band at halfmaximum is 0.91 eV. Thespectrumof Ag2+was obtainedby measuring theabsorption at 10ps after the pulse, i.e., when reactions 1 and 2 werecomplete. The dose in the pulse was low (7 X lo-’ M radicals generated) to avoid second-order reactions of the Ag2+ ions formed. The signals were corrected for the presence of the organic radical and the consumption of Ag+ ions. As can be seen from Figure 1, Ag2+ has an absorption maximum at 310 nm and a weaker maximum at 265 nm. The same spectrum was obtained for solutionscontainingAg+ ions at various concentrations(2 X le5-4 X le4 M) and for various doses in the pulse (up to 2 X le5 M radicals). The rate constant of reaction 2 was obtained by fitting the kinetic curves at 360 and 310 nm with a computer program, knowing the specific rate of reaction 1 and the absorption coefficients of Ago and Ag2+ at these wavelengths. The points in Figure 2 are experimental values; the curves were calculated using a value of 8 X lo9 M-I s-I for the specific rate of reaction 2. This value is substantially higher than the value of 5 X lo9 M-1 s-I reported previously.’b The 310-nm absorption of Ag2+ decays already slightly at longer times in Figure 2; the processes responsible for this decay are the reactions
and
The decay of Ag2+ could be accounted for in the computer fit of Figure 2 using a value of 4 X lo9 M-I s-I for these second-order reactions (specific rate of reaction 6, see below). When solutions containing formate and nitrous oxide were used, the absorptions at 360 and 3 10 nm increased after the pulse more slowly than in the solutions containing 2-propanol. C02is the only reducing species in the formate-containing solutions. It was found that the spectrum after 15 ps was that of Agz+ and that thespectrumatshorter timescontainedthe360-nmmaximum of Ago. We therefore formulate the reduction of Ag+ by
CO;
+ Ag+
-
CO, + Ago
(8)
followed by the reaction of eq 2. It has previously been supposedlb that a complex, AgC02, is formed in reaction 8; the present results show that, if formed at all, its lifetime is shorter than 2 ps. The observed kinetic curve at 3 10 nm could be fitted by the computer program using a value of 4 X 1O9 M-I s-I for the specific rate of reaction 8. The driving force of reaction 8 is rather small, Le., AG = -0.1 eV, the respective electrochemical potentials of the systems C02/C02- and Ag+/Ago being -1 .94 and -1.8 V.5 The advantage of using C02- as the reducing agent is that Ag2+is the only product present after a few microseconds. Thus, it is possible to determine the specific rate of reaction 6. It was found that the 3 10-nm absorptionin a solutioncontainingformate and N2O decays via second-order kinetic. A value of 2k = 2.6 X lo9 M-l s-I was obtained for reaction 6. Ag42+has previously been reported to be the product of the self-reaction of Ag2+(eq 6).lb Its spectrum was redetermined, and the number of elementary charges it carries was determined in the present work, Figure 3 shows the absorption spectrum of a solution containing formate and nitrous oxide at various times after the pulse. One can see the 3 10-nm absorption band of A&+ at 8 ps. As this band decays, a new band at 265 nm appears which is attributed to Agd2+. The rate of the second-orderdecay at 310 nm was equal to the rate of the buildup at 265 nm. At longer times, the 265-nm absorption becomes smaller and new bands begin to appear at longer wavelengths. In a preceding paper,2these bands have been ascribed to ‘magic” silver clusters, which are especially long-lived. The 265-nm band of Ag42+is also present in a pulsed solution which contained 2-propanol as can be seen from Figure 4. At 0.4 ms, the 265-nm band is fully developed. The elementary processes occur more slowly than in the presence of formate (Figure 3). The absorption coefficient of Ag42+at 265 nm is (3-4) X lo4 M-l cm-I. The 265-nm band decays within about 1 s. One can also see the buildup of the absorption bands of the “magic” clusters at 290 and 325 nm and at 355 nm. In the preceding paper,2 the sharp 290- and 325-nm bands have been attributed to a chargedcluster which lives for minutes and contains about eight reduced silver atoms, and the broad band at 355 nm
The Journal of Physical Chemistry, Vol. 97, No. 18, 1993 4591
Silver Atoms and Clusters in Aqueous Solution
2-10"
lo-'
5-10"
0.1 [M]
0.06 1000
2 -0.04
-
E
c
vl
W
I-
U
>
c m
e
;0.02 0
100
0.2 0.4 [NaC10,11/2 [M1/z]
0
n 200
300
400
Figure 5. Reciprocal first half-life of the decay of the 265-nm absorption
X lnml Figure 3. Absorption spectrum of a solution containing 1
10-4 M AgClO4,2 X 10-3 M NaHC02, and 2.5 X M N 2 0 at various times after the pulse (4 X 1V M C02- radicals generated in the pulse). X
band as a function of the square root of the concentration of added sodium perchlorate. Other conditions as in Figure 4.
0.05
1.5
-5 0.04 c
c
aJ
U aJ
0.03
s 0.5 C
n L 0
4 0.02 0
0.01
O200
10
20
30
40
t H0-6 SI
300
400 200 X [nml
300
Figure 4. Absorption spectrum of a solution containing 1
400 X
lo4 M
AgC104 and 0.1 M 2-propanol at various times after the pulse (4 X 1V M radicals generated in the pulse). Irradiation under argon. Left: decay of Ag2+ absorption (3 10 nm) and buildup of Ag42+absorption (265 nm). Right: decay of absorption (265 nm) and buildup of long-lived cluster absorptions (300, 325, and 355 nm).
has been attributed to another cluster whose lifetime is about 0.1 s. In the experiments of Figure 5 , the kinetic salt effect was investigatedto obtain information about the charge of the species absorbing at 265 nm. The reciprocal half-life of the secondorder decay of the 265-nm absorption is plotted here versus the square root of the concentration of added sodium perchlorate. From the slope of the straight line, and using the BjerrumBrtlnstedt equation, one obtains a value of 4 for the product of the charges of the reacting species. Thus, the species carries two elementary charges. From the value of 1 / at ~ zero NaC104 concentration in Figure 5 a rate constant of 4.8 X lo6M-I s-I was calculated for the second-order disappearance of A g P . Under the conditions of Figure 4, the silver ions are reduced only by the hydrated electrons, and the organic radicals formed via reaction 4 contribute to the reduction only by reacting with Ag2+ions (eq 7). However, the organic radicals can also react among each other, the specific rate being 2k = 1.4 X lo9M-I s-Iq6 Conductivityexperiments were carried out to obtain information about the fraction of radicals that underwent reaction with Ag2+, making use of the fact that a hydrogen ion is formed in reaction 7. It was found that the conductivity is increased by 300 S cm2
Figure 6. Computer calculation of the concentration-time profile of the early products of the reduction of Ag+. The elementary processes considered are compiled in Table I. Solution: 2 X l W M AgC104, 1 X M NaHC02, 2.5 X M N20, pH 5.5. Primary radicals generated: 2 X M eaq-, 2 X lo" M OH, 0.4X lk5M H. 1.5-ps pulse.
mol-' immediately after the pulse, which corresponds to the formation of one hydrogen ion and the consumption of one Ag+ ion. The conductivity then increased by additional 120 S cm2 M-1 as reaction 7 took place. If all organic radicals had reacted, the additional increase would have been about 300 S cm2 mol-'. Thus, it is concluded that about two-thirds of the radicals got lost through self-reaction. Particle Growth in the Absence of Ag+ Ions. To explore the possibility of complete consumption of Ag+ ions in a single pulse of radiation, the computer calculation shown in Figure 6 was carried out. The concentration of Ag+ was rather low in this calculation, i.e., 2 X l t 5M, and the concentration of hydrated electrons and CO2- radicals generated in the 1.5-ps pulse was high, i.e., 4 X 10-5 M. The various elementary reactions which were considered in this calculationare compiled in Table I. Among processes "A" which describe the mutual deactivation of the reducing radicals, the specific rate of the reaction of the hydrated electron with the C02-radical was not known. We obtained an approximate value of 1 X lo9 M-I s-I from experiments on the decayof the 700-nm absorptionof eaq-in a pulsed 1t3 M NaHC02 solution at pH = 11 (taking into account the parallel eaq-+ eaqreaction). The specific rates of all the reactions "B", in which the first reduction products Agoand Ag2+ are formed, are known from the above experiments. The specific rates of two of the following reactions "C", in which the primary products of silver reductionundergo second-order transmutations, have not yet been
Ershov et al.
4592 The Journal of Physical Chemistry, Vol. 97, No. 18, 1993 TABLE I: Compilation of the Elementary Reactions Used in the Computer Calculation of Figure 6
-
+
Reactions A 5.8 x 109 0 1.6 X 10" 1x 109~ 8 X lo8
edq-t eaq-- H2 2OHeaq- H202 OH OH-
+
+
eaq-t C02-- COz2c02- c02- (C02-)2
+
+ Ag+ C02- + Ag+
euq-
+
Ago Ag+
+ +
Reactions B Ago Ago + C02 A&+
0.06 W
4.8 X 4 x 109c 8 X lo9'
4
--
0.08
k [M-I s-I]
reaction
U
C
m
f 0.04 0 v)
Reactions C
Ago Ago --* Ag2O C02- Ag2+ Ag2' t C02 Ag2+ t Ag2+ Ag42+ Ag4' Ag2' + Ag2'
n
m
1.6 X 1O'O 4 x 109d 1.3 x 1 0 9 ~ 5 x 109d
4
0.02
See: Ross, A. B. NSRDS-NBS 43 (Supplement). See: Ross, A. B.; Neta, P. NSRDS-NBS 70. Determined in this paper. Assumed value.
determined directly. The high value of k = 1.6 X 1O1OM-' s-l for the reaction Ago
+ Ago
-
Ag,
(9)
had to be chosen to obtain best agreement between the experimental and calculated time profile of the Ago absorption. This high value can be rationalized as reaction 9 is the combination of two small radicals. The reaction
250
I I I I I I 300 350 400 250 300 350 400 A lnml
Figure 7. Observed absorption spectrum at various times after the pulse. Conditions as in Figure 6. Left: spectra in the microsecond range. Right: spectra in the millisecond range.
TABLE 11: Half-Life Times (in s) for the Appearance and Disappearance of Various Absor tions in the Absence and hesence of Added Electrolytes &Mution: 2 X 10-5 M AgClOd, 1 X lk3M NaHC02, 2.5 X lo-* M N20,S X lo4
Radicals)
1112
was assumed to occur at a diffusion-controlled rate because of its high driving force (AG of reaction 10 is about -1.5 eV; electrochemical potential of the Ag2+/Ag2 system, see below). It can be seen from Figure 6 that only a very low concentration of intermediate Ag4,+ is expected, whereas this cluster plays an important role in the growth of silver particles in the presence of excess silver ions (Figures 3 and 4, and ref 2). Similarly, Ag2+ is accumulated in only a low concentration. The concentration of C02- being rather high for several 10 ps after the pulse, the early reduction products of silver are moving in a strongly reducing environment; thus, there exists little chance that any forms of oxidized silver could reach a significant concentration. The rate constant for the reaction
in Table I was derived from the rate of the decay of the 260-nm absorption band in the 40-250-ps range (Figure 7). Figure 7,left side, shows corrected absorption spectra of the solutionat various times after the pulse up to 40 ps. The measured spectrum at 2 ps contained a very strong band at 350 nm and a weaker one at 235 nm. The latter is due to the excess C02- which decays rather slowly after the pulse according to the calculations in Figure 6. The correction was made by subtracting the contribution of C02- from the observed spectra to obtain the spectra which are shown in Figure 7. All the features of these spectra can be understood in terms of the calculated concentrationtime profiles of Figure 6. The absorption band of Ago disappears during 2-20 ps; the rate of this decay agrees with the one expected from the computer calculation in Figure 6. Note that a weak shoulder at 310 nm can be seen at 10 ps, which is attributed to the small amount of Ag2+ that is expected at this time (Figure 6). At the same time, the Ago band is slightly blue-shifted which is taken as indication for the appearance of a product that has a strong absorption at shorter wavelengths. In fact, a new absorDtion maximum at 270 nm develom is r during ~- --e-10-40 - US: it - - -r - 7
additive none lo4 M Na2S04
lo-) M Na2S04
5X M Na2S04 4 X 10-IM NaC104
t 1 / 2 decay
at 270 nmu
8.6 X 8.2 x 10-5 9.3 x 10-5 8.0 x 10-5 8.8 X
buildup
340 nmb
390 nmc
9.2 X 1.6 X 8.3 X lC5 1.4 X 1 t 2 1.4 X 10-4 1.4 X 10-4 1.0 X lo4 3.2 X le2 8.0 X 1.9 X
Mainly disappearance of Ag2. Mainly appearance of Ag4. Appearance of large particles.
attributed to Ag2. Also at this time, new absorption bands start to develop in the 300-370-nm range. At 250 ps (right side of figure), a broad band peaking at 340 nm is present in this wavelength range. It is built up at the same rate as the 270-nm absorption of Ag2 disappears. The 340-nm absorption is therefore attributed to Ag4. At still longer times, Le., 4 and 40 ms, the absorption maximum lies at 370 nm and moves to 390 nm; i.e., it is positioned in the wavelength range where larger metallic particles absorb. After 40 ms there was no substantial increase in the intensity of this band. In fact, the band started to decrease at much longer times. Note that the intensity of the plasmon band at 40 ms is very low. These features of the plasmon band are interpreted as a fast agglomeration of the larger particles to yield larger aggregates which are known to absorb less intensely in the 400-nm range where single particles strongly absorb. Precipitation of the colloid finally occurs, which is due to the fact that it is not stabilized by excess Ag+ ions. Experiments were also carried out with a solution to which various amounts of sodium sulfate or sodium perchlorate had been added. In Table 11,the observed half-life times of the buildup and decay at various stagesof particle growth are listed for various concentrationsof the added electrolytes. It should be remembered that 1V M Na2S04added to a solution which contains excess silver ions causes an acceleration of the particle growth by a factor of more than 100.2 In the experimentsof Table 11,lW - l w M NaS04 has practically no effect on the rate of growth. Only at the higher concentration of 5 X 1C3M is a small effect observed. NaC104 (0.4 M) also does not noticeably influence the rate.
Silver Atoms and Clusters in Aqueous Solution
The Journal of Physical Chemistry, Vol. 97, No. 18, 1993 4593
Discussion
-
Propertiesof Ago and Ag2+. The first optical transition of the silver atom in the gas phase corresponds to a 5 s 5P transition. It is split by spin-orbit interaction, the wavelengths of the two lines being 338 nm (Pip) and 328 nm (P3/2) (photon energy -3.7 eV). The spectrum of silver atoms trapped in noble gas matrices has been studied intensely.* Three absorption bands due to crystal field interactions with the matrix were observed, which are blue-shifted with respect to the gas-phase lines. The blue shift was explained by a larger perturbation of the more extended excited state than that of the more localized ground state. The silver atom in water has a broad band without significant structure (Figure 1). The band peaks a t 360 nm, Le., at a wavelength much longer than in the gas phase. Contrary to the situation in noble gas matrices, a red shift is observed. The band has been discussed in terms of a 2alg- 2tl, transitionof a hydrated silver atom, which corresponds to electron donation to the hydration shell.9 One may also notice that there exists an important difference with respect to the position of the redox levels of the excited silver atom in the aqueous and noble gas environments. The excited 5P state in the noble gas matrix cannot ionize: the electronic energy of the ground state lies at about -(7.6 - 2.0) = -5.6 eV (taking zero energy for an electron in vacuo; 7.6 eV is the ionization energy of Ago in vacuo; 2.0 eV is the solvation energy of Ag+ in solid argon as calculated from Born's formula). Thus, the absorption of a photon of 3.7 eV by a silver atom leads to an excited state with an electronic energy of -5.6 + 3.7 = -1.9 eV, i.e., far below the conduction band of the matrix which is close to the vacuum level. In the case of water, the excited state could ionize: keeping in mind that the redox potential of a free Ago atom is -1.8 V,5the redox potential of its excited state should be as negative as (-1.8 - 3.7) = -5.5 V, Le., much more negative than the potential of -2.9 V of the hydrated electron. A strong interactionof the excited silver state with the solvent, which could give the excitation the character of a charge-transfer-to-solvent transition, is again conceivable. As other free metal atoms in water have also rather negative redox potentials, this interaction of excited metal atoms with water should be a common phenomenon. The two absorption maxima of Ag2+are energetically 0.67 eV apart from each other. The two bands are possibly due to the u opand u r X ,transitions ) in this diatomic molecule. The fact that the absorption spectrum was not dependent on the Ag+ concentration shows that the equilibrium of eq 1 lies completely on the right-hand side under our concentration conditions: at [Ag+] = 1 X lo4 M, no trace of Ago (360-nm peak) was present; taking [Ag2+]/ [Ago] > 100, onecalculates that the free enthalpy of reaction 2 is more negative than -0.36 eV. The free enthalpy of hydration of Ag2+, AGh(Ag2+), must be more negative by at least 0.36 eV than the hydration free enthalpy of the silver ion, AGh(Ag+)= -4.9 eV, plus the gas-phase dissociation energy of Ag2+,D(Ag2+) = 1.63 eV;lo thus, AGh(Ag2+)< -3.6 eV. This hydration enthalpy for a dimeric ion is remarkably high; one can hardly expect that it is much more negative than -3.6 eV. Knowing the above limiting thermodynamic values of Ag2+, one can calculate approximate values of its electrochemical standard potentials:l3
-
-
Ag, e 2Ag+ + 2e-
Eo = -0.97 V
(12c)
Ion and Oligomeric Clusters. It was found in the The investigation of the kinetic salt effect of Figure 5 that the species absorbing a t 265 nm carries two elementary charges which is in agreement with the formula Ag4*+for the product of reaction 6. This ion can be considered to be a dimer of silver, complexed by two Ag+ ions; in other words, the equilibrium
lies on the right-hand side. If dimeric silver, Ag2, is formed in the presence of excess Ag+ ions, for example via reaction 9, one may expect that Ag42+is again produced through the equilibrium of eq 13. The two charges on Ag42+also make it understandable that this ion can be stabilized for a long time even under air when formed in the presence of a p01yanion.I~ The investigation of the ionic strength effect on the buildup of the 325-nm absorption has revealed that the precursor of Ags carries threecharges? It is thereforeconcluded that Agd2+,which carries only two charges, is not the immediate precursor of the 325-nm cluster but that there exists an intermediate step of particle growth, in which a particle carrying three charges is formed. A mechanism for this was proposed in the preceding paper.* The ionic strength effect is also invoked to explain the fact that the growth processes are faster in the presence of formate than in its absence (Figures 3 and 4, respectively). Complete Ag+ Reduction: Growth of Neutral Particles. The experiments of Figure 7 confirm the computer calculations in Figure 6 that complete reduction of silver ions is possible using a strong pulse which produces twice as many hydrated electrons plus C02- radicals within 1.5 ps than silver ions are present. Thus, the growth of neutral metallic particles can be studied. The great efficiency of complete silver reduction is due to the exceptionally high specific rate of the reaction of eaq-with Ag+; thus, this reaction can successfully compete with the reactions of the hydrated electron with itself and with C02-. The few silver ions that survive the pulse and which are mainly present as Ag2+ and Ag42+are efficiently reduced by the excess C02- radicals, which create a reducing environment some 10 ps after the pulse. In the establishment of the equilibrium of eq 13, intermediate Ag3+may be formed which can also be reduced by C02- to yield Ag,. However, such a process can also not be of great importance because of the low concentration of Ag+ shortly after the pulse. The present studies on the complete silver ion reduction are considered the basis for similar studies with other metal ions, the goal being to increase our knowledge about the absorption spectra of atoms and clusters in solution and to observe the transition from the nonmetallic clusters to larger metallic particles. It is interesting to compare the essential features of particle growthin theabsenceof excessAg+ions with thosein the presence of excess Ag+ ions as described previously.2 It was pointed out that the formation of colloidal silver from the atom via oligomeric clusters and growing metallic particles may be compared to the coagulation of colloids, which has been investigated for over half a century. In the presence of excess Ag+ ions and a t low ionic strength, the formation of the silver colloid requires sometimes many minutes, as intermediate oligomeric clusters of long lifetime exist under these conditions and the growing particles are stabilized by Ag+ ions. This situation is comparable to slow coagulation. However, added Na2S04causes the formation of the colloid to occur within about 10 ms, as a result of the neutralization of positively charged particles, a process which may be compared to fast coagulation or neutralization coagulation in colloid chemistry.2-15 The rate of growth of the neutral particles was not influenced by added electrolytes (Table 11). In fact, the growth is about as fast as in the case studied in ref 2, where both excess Ag+ ions and Na2S04are present. Thus, the colloid formation via the growth of neutral particles is another example that can be discussed in terms offast coagulation. The colloidal particles
4594
The Journal of Physical Chemistry, Vol. 97, No. 18, 1993
formed under these conditions are not stabilized by Ag+, the result being that they already start to coagulate during their formation. Note that this fast coagulation is also the result of a neutralization, Le., the reduction of all Ag+ ions and other positively charged growing particles by the COZ- radical.
Ershov et al. equilibrium 12a: Ag,
-
-
Ag;(g)
References and Notes (1) (a) Pukies, J.; Roebke, W.; Henglein, A. Ber. Bunsen-Ges. Phys. Chem. 1968, 72, 842. (b) Tausch-Treml, R.; Henglein, A.; Lilie, J. Ber. Bunsen-Ges. Phys. Chem. 1978,82, 1335. (2) Ershov, B. G.; Janata, E.; Henglein, A. J . Phys. Chem. 1993,97,339. (3) (a) Kumar, A.; Janata, E.; Henglein, A. J . Phys. Chem. 1988, 92, 2587. (b) Janata, E. Radiat. Phys. Chem. 1992,40,437. (4) Schwarz, H. A,; Dodson, R. W. J . Phys. Chem. 1980, 15, 603. ( 5 ) Henglein, A. Ber. Bunsen-Ges. Phys. Chem. 1990, 94, 600. (6) Ross, A. B.; Neta, P. Natl. Stand. Ref. Data Ser. (US., Natl. Bur. Stand.) 1982, NSRDS-NBS 70. (7) The shape of the absorption band of CO2- was redetermined in our laboratory. It essentially agrees with the one found in: Buxton, G. V.; Sellers, R. M. J . Chem. SOC.Faraday Trans. I 1973,69, 5 5 5 . The band described by Hug (Hug, G. S.Natl. Stand. Ref. Data Ser. (US., Natl. Bur. Stand.) 1981, NSRDS-NBS 69) was found to be too narrow. (8) Kolb, D. M.; Forstmann, F. In Matrix IsolationSpectroscopy; Barnes, A. J., Orville-Thomas, W. J., Miiller, A., Gaufrb, R., Eds.; D. Reidel Publishing: Dordrecht, 1981; p 347. (9) (a) Ershov, B. G.; Sukhov,N. L.; Ionova, G. B.;Spitsin, V. I. J. Inorg. Chem. (Moscow) 1986, 31, 1363. (b) Aleksandrov, A. I.; Ionova, G. V.; Ershov, B. G. Radiat. Phys. Chem. 1979, 13, 199. (10) ThedissociationenergyofAg2is1.66eV.I' Theionization potentials ofAgoandAg! are 7.57 and 7.60, respe~tively.~~ From thesedata onecalculates D(Ag:+) = 1.63 eV. (1 1) Bauschlicher, C. W.; Langhoff, S.R.; Partridge, H. J . Chem. Phys. 1990, 93, 8133. (!2) (a) Morse, M. D. Chem. Rev. 1986,86, 1049. (b) Jackschath, C.; Rabin, I.; Schulze, W. Z . Phys. D 1992, 22, 517. (13) In writing the following cycles it is assumed that the hydration free energies of the neutral particles, Agn and Ag,, are practically zeros (g = gas phase).
Ag,+(g) + e-(g)
net: Ag,
-
AG = 7.6 eV AG < -3.6 eV
Ag;(aq)
AG = -4.5 eV
e-(g)
e-
Ag;(aq)
+ e-
= x A G / e = 0.36 eV
= x A G / e = >-1.44 V
equilibrium 12c:
2Ag0
net: Ag,
2Ag'
Ag,
2Ag0
2Ag'
2e-
2e-
AG = -3.6 eV
AG = 1.66 eV E O
= x A G / 2 e = 4.91 V
(14) (a) Mulvaney, P.; Henglein, A. J . Phys. Chem. 1990,94,4182. (b) Henglein, A.; Linnert, T.; Mulvaney, P. Ber. Bunsen-Ges. Phys. Chem. 1990, 94,1449. (c) Henglein, A.; Mulvaney, P.; Linnert, T. J . Chem. Soc., Faraday Discuss. 1991, 92, 31. (15) (a) Ershov. B.G.;Sukhov. N. L.:Troitskii. D.A. High Enerw Chem. 1991, 25, 176. (b) Ershov, B. G.; Sukhov, N. L.; Troitsk;, D. AyRadiat. Phys. Chem. 1992, 39, 127.
