1872
J . Phys. Chem. 1985,89, 1872-1875
tahedrally, and these octahedra share edges making a chain of N a polyhedra as in borax.43 The other two water molecules are held by hydrogen bonding to S042-as in the fifth water molecule of copper sulfate ~ e n t a h y d r a t e The . ~ ~ crystal structure of sodium carbonate decahydrate may be taken as the distorted NaCl type structure with [Na2(H20)lo]2+and C 0 3 2 -ions.44 The [Na2(Hz0)lo]2' ion is formed by sharing one edge of two Na polyhedra. A similar type of dielectric dispersion behavior was found in sodium sulfate decahydrate and s 4 i u m carbonate decah~drate,"~ so that disorder in the configuration may also be possible in sodium carbonate decahydrate." Hence, one of the factors for the higher (43) Morimoto, N. Min. J. 1956, 2, 1. (44) Taga, T. Acta Crystallogr., Secr. B 1969, B25,2656. (45) Kiriyama, R.; Saito, Y . Bull. G e m . SOC.Jpn. 1953, 26, 531.
value of cy, i.e., greater than unity, may be related to the disordered protons in these inorganic crystalline hydrates. The dielectric dispersion behavior found in sodium sulfate decahydrate and sodium carbonate decahydrate has not yet been found in borax.45 It should be mentioned that the average Na-H20 distances in these three crystalline hydrates are in the range 2.42-2.44 The deviation of the a value in borax from those of the other three may be explained by the absence of residual entropy or by the strong isotopic site preference between Na2.8H20 and B,O,(OH),, giving an a value accidentally quite close to unity, the latter being suggested by Pradhananga and Matsuo.14 Registry NO.Al2(S04)ynH20, 17927-65-0;CuS04.5H20, 7758-99-8; CaS04.2H20, 10 101-4 1-4; NiS04.7H20, 10 101-98-1; FeSO4.7H20, 7782-63-0; CoS04.7H20, 10026-24-1; ZnS04-7H20,7446-20-0; MgSO4.7H,O, 10034-99-8; Na2S0,.10H20, 7727-73-3; H2, 1333-74-0.
Solvent Isotope Eftect on Electron-Transfer Processes J. Lee and G . Wilse Robinson* Picosecond and Quantum Radiation Laboratory, Texas Tech University, Lubbock, Texas 79409 (Received: October 25, 1984)
Intermolecular electron ejection from indole is investigated in solvent mixtures of H 2 0 and D20. The activation energy is found to remain constant, 10.8 f 0.6 kcal/mol, for all mixtures. However, the frequency factor decreases linearly as a function of DzOconcentration and is 3 times smaller in pure DzO than in pure HzO.This isotope factor is attributed to a Franck-Condon effect accompanying the transition from neutral to ionized forms, the electron in the latter case being strongly coupled to a cluster of 4 1 water molecules.
*
Introduction Electron ejection has been determined to be a major radiationless deactivation process in the excited state of indole in aqueous solutions. This process has been shown to be sensitive to environmental solvent structure and temperature.',2 The associated large activation energy has been attributed2' to the energy required to reorganize the hydrogen bonding in adjacent water molecules so as to facilitate electron ejection from indole. The importance of a specific water structure, acting as electron acceptor, has been demonstrated quantitatively in water/methanol solvent mixture^.^ Addition of alcohol, which has a different molecular structure and physical properties from water, was found to break the water structure and thus to inhibit the electron ejection process. Theoretical analysis of the decay kinetics using a Markov random walk scheme has successfully been applied to the experimental data. A water cluster of 4 f 1 members was determined to be the effective electron acceptor. In contrast to alcohol, deuterium oxide (D20) has a molecular structure and physical properties close to those of ordinary water. Hence, it is of interest to see how the heavier isotope in the solvent effects the electron ejection process in indole and how the Markov random walk theory applies to this system. Experimental Section Indole was purchased from Eastman Kodak. HPLC grade water and gold label grade deuterium oxide (99.8%) were purchased from Fisher and Aldrich, respectively. All chemicals were used without further purification. H 2 0 / D 2 0 mixtures of 0, 25, (1) Kirby, E. P.; Steiner, R. F. J . Phys. Cfiem. 1970, 74, 4480. (2) Klein, R.; Tatischeff, I. Cfiem. Phys. Leu. 1977, 51, 333. (3) Lee, J.; Robinson,G . W. J . Cfiem. Phys. 1984, 81, 1203.
0022-3654/85/2089-1872$01.50/0
50, 75, and 100% were prepared by volume fraction. The concentration of indole in all mixtures was maintained at 5 X M. Details of the apparatus for measuring fluorescence quantum yields, a, and emission lifetimes, 7,were discussed previ~usly.~ Quantum yields at temperatures ranging from 0 to 65 OC were measured for each solvent mixture. Since the radiative rate constant (k,)is insensitive to temperature and to the solvent isotope effect,] only lifetimes in the two pure solvents at room temperature (20 "C) are needed in order to obtain the nonradiative rate constants from the quantum yield data over the whole range of solvent concentrations.
Results Neither the absorption nor the emission spectrum of indole shows a frequency shift upon addition of D20. Fluorescence quantum yields, using indole in H 2 0 (0.3 1) as a reference, are plotted for three different temperatures as a function of D 2 0 concentration in Figure 1. At each temperature, the quantum yield increases as the D 2 0 concentration increases, exhibiting its greatest value in the pure D 2 0 solvent. On the other hand, in all of the solvent mixtures, the quantum yield decreases as the temperature increases. Lifetime measurements at 20 "C give 7 = 5.6 ns for indole in pure D20. The radiative rate (k, = @.?I) is determined to be 8.21 X lo7 s-I, which is comparable to the value 8.29 X lo7 s-I already reported for indole dissolved in H20.3 Hence, a constant value of k, = 8.29 X lo7 s-I was assumed for all H 2 0 / D z 0mixtures. The overall decay rate constant k( 7') H 7-l for indole in solvent mixtures can be expressed by k ( T ) = k, + k,,' + k, exp(-pAE) (1) where k, and k,,' are temperature-independent radiative and 0 1985 American Chemical Society
The Journal of Physical Chemistry, Vol. 89, No. 10, 1985 1873
Charge-Transfer Solvent Isotope Effect
I-
I
1
1
1
20
020
1
l
1
1
1
1
1
1
40 60 80 Volume Fraction (%)
Figure 1. Quantum yields of indole in H 2 0 / D 2 0 mixtures. Solid line, 65 "C (experimental); calculated values; (A)65 "C (experimental);(0) (X)5 "C (experimental).
k
L
I
I
I
20
020
I
I
I
I
I
I
I
I
40 60 80 Volume Fraction (%)
Figure 2. Nonradiative rate constant of indole in H 2 0 / D 2 0 mixtures. (A) 65 "c (experimental); (0)35 "c (experimental); (x) 5 "c (ex-
perimental).
TABLE I: Freauencv Factors for Indole in H,O/D,O Mixtures" [H20Ib 1 .oo 0.75 0.50 0.25 0.00
theor
exptl 9.26 8.99 4.69 4.80 2.88
9.88 7.36 6.24 4.76 2.82
"Assuming AE = 10.8 kcal/mol; knro(mix)= [H20]kn,"(H20)+ lo7 s-I and knr0(D20)= 6.0 X IO7 8. bVolume fraction. [D20]kn,0/(D20),where kn,0(H20) = 7.0 X
nonradiative rate constants, respectively, k, exp(-@As) is the temperature-dependent intermolecular electron-transfer rate constant, in which 0 = (kBT)-',and k, and AE are the frequency factor and the activation energy, respectively, for the process. The total nonradiative rate constant [k,, = kN0 k, exp(-flhE)] thus can be deduced from the value of Q measured at various temperatures together with a knowledge of k,. Figure 2 plots k,, as a function of D 2 0 concentration for three temperatures. At each temperature, this quantity is seen to decrease linearly as the D 2 0 concentration increases, and it tends to its smallest value in pure D 2 0 solvent. A linear least-squares fit for k,, (Figure 3) gives a constant activation energy 10.8 0.6 kcal/mol in all mixtures. This shows that the decrease of the electron-transfer rate upon addition of D 2 0 is caused by a decrease in the frequency factor. The derived frequency factors, assuming AE = 10.8 kcal/mol, are listed in Table I for each solvent composition. At high temperatures, k , = k, exp(-@AE), and the ratio of nonradiative rate constants in H 2 0 and D 2 0 is roughly three. Since AE does not change, this factor is expected to approximate the ratio of the frequency factors [k,(H20)/k,(D20)].
+
*
Figure 3. Arrhenius plots (AE = 10.8) for indole in H 2 0 / D 2 0 mixtures. Solid line, calculated values; (A) D 2 0 (experimental); (0) 50% H 2 0 / D 2 0 (experimental); (X) H 2 0 (experimental).
Markov Model Theoretical calculations using a Markov random walk method were applied earlier to the indole/H20/MeOH s y ~ t e m . ~Good .~ agreement between calculated and observed values suggests a cluster of 4 f 1 water molecules as the effective electron acceptor. A similar type of scheme can be adopted here. In short, an N X 1 row matrix representing the distribution of cluster configurations, including a single configuration representing the ground state, is formulated. This matrix, which describes a binomial distribution initially for the excited-state configurations, changes as the time evolves. A square matrix of order N describes the probabilities per unit time (At) for H 2 0= Di 2 0 solvent exchange and excited-state decay for each configuration. The size (N) of the matrices is related to a critical cluster size ( N - 2 ) , which is the minimum size that can accept an electron. Carrying out an m-fold repetitive multiplication of the second matrix by the first simulates the decay kinetics of the system from time t = 0 to t = mAt. In the case of a CW experiment, where excited species for each configuration are constantly restored by a light source, a small fraction of the initial row matrix is added to the new row matrix after each time interval At. The quantum yields can thus be obtained when this row matrix reaches steady state. Because of the similarities of solvent environment for different cluster configurations, the intermolecular electron-transfer process, unlike the case for H20/MeOH, is expected to occur for all configurations and thus for all H 2 0 / D 2 0 mixtures. According to the Results section, the frequency factor is the only thing affected, the activation energy remaining the same in all H20/D20 solvent mixtures. In fact, because of the linear relationship between k, and D 2 0 concentration shown in Figure 2, the frequency factor for the mixture can simply be written as an average k,(mix) = xk,(D,O)
+ (1 - x)k,(H,O)
(2)
where x is the fraction of deuterium atoms in the solvent mixture and k,(D20) and k,(H20) are the frequency factors for pure D 2 0 and pure H 2 0solvents. This averaged k, is obviously independent of solvent structural considerations. We would thus expect that the Markov method briefly outlined above is unnecessary for H 2 0 / D 2 0solvent mixtures, eq 2 providing an equivalent and much simpler description.
Discussion Our findings in pure H 2 0and D 2 0 solvents are in agreement with those of Kirby and Steiner.' The electron ejection process in indole was found by these workers to have the same activation energy in both solvents but a smaller frequency factor in D20. A new result presented here is the behavior of electron ejection in H 2 0 / D 2 0 mixtures. The k,, of indole in H 2 0 / D 2 0mixtures decreases linearly with D 2 0 concentration, thus maintaining the ~
~~
~
(4) Robinson, G. W.; Lee, J.; Moore, R. A. "Ultrafast Phenomena IV"; Springer-Verlag: West Berlin, 1984, in press.
1874 The Journal of Physical Chemistry, Vol. 89, No. 10, 1985
same activation energy throughout the entire concentration range (see Figure 2). This result supports the idea2' that the activation energy for the electron ejection process is a reflection of solvent structure. Addition of D 2 0 to H 2 0does not disturb the normal liquid structure appreciably. As a result, the indole molecule sees a similar hydrogen-bonded network in H 2 0 / D 2 0 mixture environments. The same amount of energy is required to break up this structure and re-form it to activate the electron ejection channel. The constant activation energy ensures that the dependence of the decay rates on D 2 0 concentration is linear. On the contrary, both the activation energies and frequency factors in H20/MeOH mixtures (Table I of ref 3) decrease nonlinearly upon addition of methanol, converging to zero activation energy and zero electron ejection rate in pure methanol. The theoretical values for CP and k,, are shown as solid lines in Figures 1 and 2 . Although, as remarked earlier, agreement between calculated and observed results is consistent with the four-cluster random walk theory of electron ejectiori in H 2 0 / D 2 0 mixtures, the calculated result, unlike the case for H20/MeOH solvent mixtures, is unable to distinguish cluster sizes from one another. Different compositions of H 2 0 and D 2 0 in the cluster give identical @ and k,,, as shown by eq 2 in the last section. Table I lists the frequency factors obtained from the linear least-squares fit of the calculated values. Interestingly, the roughly factor of 3 ratio H20:D20for the frequency factors seems to be present in other charge transfers. For instance, in the case of anilinonaphthalenesulfonate derivative^,^ where the activation energy for electron transfer is near zero, a frequency factor ratio H 2 0 : D 2 0of about 3 has been observed.
Conclusions The larger frequency factor in the case of H 2 0 in comparison to D 2 0 probably reflects the fact that 0-H vibrations of the solvent are sensitively involved in the electron-transfer process. If the final caged electron state and initial neutral molecule state do not possess the same amount of vibrational energy, the excess vibrational excitation in the final state is accompanied by Franck-Condon factors in the radiationless rate expression. These are known6*' to be more favorable for hydrogen vibrations than for deuterium vibrations. The observed factor of 3 is small, for example, compared with the factors usually observed for rare-earth deactivation processes in H 2 0 vs. D 2 0 solvents.s A recent study of the proton-transfer process in the 2naphthol/H,O/MeOH system' indicates that solvent structural considerations for electron and proton transfers in water are very similar. A water cluster [H20]4flis the effective acceptor in each case. It is probable then, as for the proton cage,1° that hydrogen bonding within the electron cage is stronger than in normal water. Thus, present in these charged systems is the appropriate change in vibrational coordinate necessary for the existence of a measurable 0-H Franck-Condon effect on the radiationless chargetransfer process. It is possible to compare further the electron- and protontransfer processes. Studies" of the proton-transfer process from 8-hydroxy- 1,3,6-pyrenetrisulfonate(HPTS) in H 2 0 and D 2 0 solvents under high-pressure conditions have shown that the rate increases as the pressure increases. Furthermore, there is roughly a factor of 3 difference between the proton-transfer rate constants for H,O and D 2 0 solvents over the whole pressure range studied, 1 atm to -8.5 kbar. Pressure is known to weaken the hydrogen-bond network in water.12 According to our views, then, these (5) Robinson, G. W; Robbins, R. J.; Fleming, G . R.; Morns, J. M.; Knight, A. E. W.; Morrison, R. J. S. 1.Am. Chem. SOC.1978, 100, 7145. (6) Robinson, G . W. J . Mol. Spectrosc. 1961, 6, 58. Robinson, G. W.; Frosch, R. P. J . Chem. Phys. 1962, 37, 1962. (7) Siebrand, W.; Williams, D. F. J . Chem. Phys. 1967, 46, 403. (8) Haas, Y . ; Stein, G. Chem. Phys. Lett. 1972, 15, 12. Kropp, J. L.; Windsor, M. W. J . Chem. Phys. 1965, 42, 1599. (9) Lee, J.; Griffin, R. D.; Robinson, G. W. J . Chem. Phys., in press. (10) Triolo, R.; Narten, A. H. J . Chem. Phys. 1975, 63, 3624. (11) Huppert, D. H.; Jayaraman, A.; Maines, Sr.,R. G . ;Steyert, D. W.; Rentzepis, P. M. J . Chem. Phys. 1984, 81, 5596. (12) Kamb, B. In "Structural Chemistry and Molecular Biology"; Rich, A.; Davidson, N., Eds.; W.H. Freeman: San Francisco, 1968; pp 507-542.
Lee and Robinson weakened hydrogen bonds would present less of an obstacle when breaking up and re-forming around the electron or the proton. Pressure therefore should reduce the activation energy for these charge-transfer processes, while the frequency factors should remain fairly constant with increasing pressure. The ratio of H 2 0 : D 2 0rates indicates that the frequency factor ratio of approximately 3 is maintained over the entire pressure range studied. Direct evidence pertaining to the effect of high pressure in lowering the activation energy of proton conductance has already been presented by Nakahara and 0 ~ u g i . l Pressure ~ effects are also known in electrochemical rea~ti0ns.l~These may be at least partly caused by this activation energy decrease. It would be interesting to have combined pressure/temperature data on electron and proton transfers in aqueous systems so that the activation energies and frequency factors can be separately determined. In conclusion, it should be remarked here that the 4-cluster concept for the hydration of H+ in aqueous solutions has been discussed desultorily in the literature since its inception in 1954.15 Various hypotheses about the hydration of OH- and e- have also been presented in general A recent paperI8 compares the kinetics of cathodic H2evolution from H30+and H904+and concludes that frequency factor changes, with their attendant t~nneling'~ characteristics, can be as important as activation energy differences in determining the rates of proton discharge from diferent proton sources. The Franck-Condon effect is an integral part of the tunneling process.6*zoObserved deuterium effects may very well implicate 0-H bond changes in the 4-cluster and the participation of these bonds in the transition from initial to final state of charge-transfer and charge-mobility processes in aqueous media. The apparent obstacle holding back more intensive discussion of these important charged entities in aqueous media is the question of their specificity. For example, the dimer HS02+has been suggested2] as an alternate form for the hydrated proton. Reading various papers in the literature leads to the general feeling that an entire range of intervariable structures has always to be considered, of which H30+,HS02+,and H904+are but three. One is advised16that there is no need, in general, to indicate the extent of hydration, as in H904+. In all but the most concentrated of H+ solutions, where there is a stoichiometric shortage of water, our work' has now seemed to rule out the importance of H30+ or H502+.Such small charged water clusters are not only unable to survive as distinct entities in the presence of other water molecules but more importantly single or paired water molecules refuse to accept a charge (electron or proton) in an aqueous or mixed aqueous liquid environment. Schematically, equilibria in the reactions
+ H A A- + (H+.nH20) n H 2 0 + B * B+ + (e-.nH20)
nH20
(3)
have a much greater tendency to lie to the right for n = 4 but to the left for n C 4. In addition, our work has indicated that the 4-cluster can be considered a distinct entity for the purpose of kinetic discussions. It furthermore has shown that interactions beyond the first coordination shell can be fulfilled equally well (or nearly so) by alcohol molecules as by water molecules. Thus, our current view is that the [H2O], cluster has a sufficiently high stability relative to other structures to be considered a specific entity in electron (13) Nakahara, M.; Osugi, J . Rev. Phys. Chem. Jpn. 1980, 50, 66. ( 1 4) Conway, B. E.; Currie, J. C. Can J . Chem. 1978, 56, 9 15.
(1 5) Wicke, E.; Eigen, M.; Ackermann, Th. 2.Phys. Chem. Wiesbaden 1954, I , 340. Eigen, M.; De Maeyer, L. Proc. R. SOC.London, Ser. A 1958, 247 505. (16) Gigute, P. A. J . Chem. Ed. 1979, 56, 571.
(17) Kenney-Wallace, G.A . In "Photoselective Chemistry"; Part 2; Jortner, J., Ed.; Wiley: New York, 1981; pp 535-577. (18) Conway, B. E.; Tessier, D. F. In?. J . Chem. Kine?. 1981, 13, 925. (19) Conway, B. E. Can. J . Chem. 1959, 37, 178. (20) Hunt, G . R.; McCoy, E. G.;Ross, I. G . Aust. J . Chem. 1962,15, 591. (21) Huggins, M. L. J . Phys. Chem. 1936, 40, 723.
J . Phys. Chem. 1985,89, 1875-1879
1875
mobility problems. The work should also allow the design and analysis of better directed experiments on these varied effects, using simultaneous temperature and pressure variations.
or proton charge-transfer and charge-mobility processes, providing that the picture22of rapid and concomitant dissociation and association of hydrogen bonds in such clusters is retained. The work presented here using solvent isotope dilution should clear the way for a better understanding of the origins of frequency factors and activation energies appearing in all these charge-
Acknowledgment. Financial support of the charge-transfer Program at the PQRL has been shared jointly by the National Institutes of Health (Grant GM23765) and the National Science Foundation (Grant CHE8215447). Registry No. Indole, 120-72-9; D1,7782-39-0.
(22) Eigen, M.; De Maeyer, L. In ‘The Structure of Electrolytic Solutions”; Hamer, J., Ed.; Wiley: New York, 1959; pp 64-85.
Bolometric Evidence for Cluster Formation In Supersonlc Molecular Beams of COP and C4F8 Garry B. Spector, Brian B. Brady, and George W. Flynn* Department of Chemistry and Columbia Radiation Laboratory, Columbia University, New York, New York 10027 (Received: November 26, 1984; In Final Form: January 28, 1985)
A bolometer/mass spectrometer/flux meter technique was used to study the effect of cluster formation on adsorption energy in molecular beams of C02and C4F8. In beams of COz,which are known to contain large clusters at high backing pressures, the experimentally measured adsorption energy per molecule drops effectively to zero at backing pressures above 50 psi, in agreement with a simple model for adsorption energy at various cluster sizes. In C4F8,the beam is heavily clustered at all backing pressures and the apparent adsorption energy is found to decrease significantly.
Introduction Cluster formation in molecular beams or free-jet expansions of various species has been a subject of interest for a number of years. Molecular beams can be used to study such van der Waals molecules that form with condensation during supersonic expansion. Both the optimum conditions for forming clusters in beams and the optimum conditions for avoiding them are reasonably well-known.14 A description and analysis of the spectra of many of these van der Waals molecules has been given in detail5v6and the bond strength^,'.^ s t r u c t ~ r e , ~synthetic *’~ conditions,” and energy-transfer rates12 of many clusters have been obtained by supersonic expansion techniques. Experiments have also been performed to investigate the importance of clusters in chemical reaction^'^-'^ and their interactions with surfaces.16
Quantitative methods for the determination of the distribution of van der Waals molecules in supersonic expansions are still being deve1oped.l’ Mass spectrometry provides only limited information concerning the cluster content of a beam or jet, as electronbombardment ionization can easily dissociate the weak van der Waals bond in many clusters. Thus, absolute percentages of clusters cannot be determined in this way. In the past few years, the technique of vibrational predissociation, where a laser predissociates clusters in the near collisionless or collisionless region of a beam, has been used with both mass spe~trometers’~J~ and liquid helium cooled bolometers2b23as detectors. The predissociation leads to an attenuation of the molecular beam signal; this “negative” signal can be related to the cluster percentage in a beam. In the present experiments we have used a bolometer to detect clusters in molecular beams of C 0 2 and C4F8.The bolometer measures total energy flux, which is composed of translational, internal, and adsorption energies. Adsorption energy is simply the energy released to the bolometer when a particle condenses on its surface. The translational energy is determined simultaneously with the total energy flux by using a mass spectrometer for time-of-flight (TOF) measurements. Thus, the sum of internal and adsorption energies can be determined by difference. An upper limit for the internal energy can be obtained from the isenthalpic expansion equation for a free jet. In previous exp e r i m e n t ~ , ~the ~ -adsorption ~~ energy was approximated by the
(1) J. B. Anderson, R.P. Andres, and J. B. Fenn, Adu. Chem. Phys., 10, 275 (1966). (2) 0. F. Hagena and W. Obert, J. Chem. Phys., 56, 1793 (1972). (3) D. Golomb, R.E. Good, and R. F. Brown, J . Chem. Phys., 52, 1545 ( 1970). (4) D. Golomb, R.E. Good, A. B. Bailey, M. R.Busby, and R.Dawborn, J. Chem. Phvs.. 57. 3844 (1972). (5) D. H.
