3072
J. Phys. Chem. 1980, 84, 3072-3075
increasing pressure, because K1*+ K2 > K1is always fulfilled. The shapes of the curves obtained are quite similar to model calculations from ref 6, although the fine details, due to the simplicity of this approach, will be different from the results of the exact integration with energy-dependent specific rate constants.
-3
Acknowledgment. J.T. thanks the Deutsche Forschungsgemeinschaft for financial support of his work.
t
References and Notes -2
-1
1 log ko/k,-
0
2
3
Flgure 3. Upper channel yield In the falloff range for strong collisions = (Hinshelwood model, eq 41-45; parameters used: (1) f(E,,)lf(E,,) ’I3,K l / ( K 1 ” K2) = 0.05,K2/(K1’ K2) = 0.08; (2) f(Eo2)/f(E,,) = ’/lo, other parameters as (1); (3) f(Eo2)/f(EO1)= ‘1, other parameters as (1); (4) K*/(K,* K ~=) 0.1, f(E,,)/f(E,,) = K,I(K~* K2) = 0.05; (5)K 2 / ( K l * 4- K2) = 0.5, other parameters as (4)).
+
+
+
+
scribed, e.g., in ref 1,2, and 13. For a first orientation, we apply in the following Hinshelwood‘s assumption k,(E) = constant = K1for Eol I E I EO2,kl(E) = constant = K1* for Eo, IE, and k2(E)= constant = K2for Eo, I E. Then, we have
Sm
f(E) dE (45) K1* + K2 + [MI2 E~ The ratio k2/k is illustrated in Figure 3, for a realistic choice of specific rate constants and equilibrium populations, as a function of ko/k,. k2/k rises monotonically with k2
=
(1) J. Troe in “Physlcal Chemistry. An Advanced Treatise”, Vol. VIb, W. Jost, Ed., Academlc Press, New York, 1975. (2) W. Forst, “Theory of Unlmolecular Reactions", Academic Press, New York, 1973. (3) B. J. Gaynor, R. G. Gilbert, and K. D. King, Chem. Phys. Leff., 58, 591 (1978); K. D.King, D. M. Gdden, 0. N. Spokes, and S.W. Benson, Int. J . Chem. Kinet., 3, 411 (1971). (4) Th. Just, P. Roth, and R. Damm, Symp. (Int.) Combust., [Proc.], 18, 961 (1977); G. Rimpel and Th. Just, Ber. Bunsenges. Phys. Chem., in press. (5) I. E. Klein, B. S.Rablnovltch, and K. H. Jung, J. Chem. Phys., 87, 3833 (1977); I. E. Klein and B. S. Rabinovitch, J. Phys. Chem., 82, 243 (1978). (6) N. Chow and D. J. Wllson, J. Phys. Chem., 68, 342 (1962). (71 . . E. V. Waaae and B. S. Rablnovitch. Chem. Rev.. 70. 377 11970): J. phys. Cbm., 78, 1695 (1972); D: C. Tardy and B. S: Rablriovitch; Chem. Rev., 77, 369 (1977). (8) A. P. Penner and W. Forst, Chem. Phys., 11, 243 (1975); 13, 51 (1976). (9) A. P. Penner, Mol. Phys., 38, 155 (1979). (10) A. J. Stace, Mol. Phys., 38, 155 (1979). (11) J. Troe, J . Chem. Phys., 66, 4745 (1977). (12) J. Troe, J . Chem. Phys., 66, 4758 (1977). (13) J. Troe, J . Phys. Chem., 83, 114 (1979). (14) K. Luther and J. Troe, Synp. (It.)Combust., [Proc.],17,535 (1979). (15) fh. Just and J. Troe, J. Phys. Chem., to be published as part 2 of this work. (16) M. Quack and J. Troe, Ber. Bunsenges. phys. Chem., 78,240 (1974). (17) M. Quack and J. Troe, Gas Kinet. Energy Transfer, 2, 125 (1977). (18) D. C. Tardy and B. S.Rabinovitch, J. Chem. phys., 45,3720 (1966); 48, 1282 (1968). (19) J. E. Dove and S. Raynor, J. Phys. Chem., 83, 127 (1979).
Pressure Dependence of Atom Recombination and Photolytic Cage Effect of Iodine in Solution K. Luther, J. Schroeder, J. Tree,* and U. Unterberg Institut fur Physikalische Chemle, Universitiit Gijttlngen, D-3400 Gijttingen, West Germany (Received: April 10, 1980)
The effect of pressures up to 3 kbar on the photodissociation and subsequent atom recombination of iodine was investigated in n-heptane, isooctane, and methylcyclohexane. It was found that the photodissociation quantum yield 4 decreased markedly with increasing density of the solvent as a consequence of the photolytic cage effect, and a linear correlation between 4 and w-~, where q denotes solvent viscosity, was observed. The atom recombination rate constant showed the expected linear dependence on q-’.
Introduction Chemical reactions in the liquid phase are significantly affected by transport processes in the solvent that control the movement of reactants toward or apart from each other. On the one hand there is the uncorrelated statistical molecular motion leading to large overall displacements on a longer time scale that are described as diffusion of the reactants in a quasicontinuous solvent medium with the appropriate boundary conditions at the reaction surface. From this one can obtain a steady-state, diffusioncontrolled reaction rate constant, which, in its simplest approximation, is inversely proportional to the bulk shear 0022-3~54/a0/2084-3072~0 1.oo/o
viscosity of the so1vent.l The homogeneous recombination of halogen atoms in various solvents has been shown in the past to be well described by this On the other hand there is the correlation of molecular motion in the liquid on a short time scale, including multiple collisions of the same partners in a solvent cage, which may alter reaction product yields as compared to the gas phase. A particularly clear-cut example of this is the reduction of the primsy quantum yield of photodissociation for halogens in solution due to geminate recombination of halogen atoms in the solvent cage, known as the “photolytic cage effect”.lOJ1A systematic study of this effect for the iodine 0 1980 American Chemical Society
The Journal of Physical Chemistty, Vol. 84, No.
Pressure Dependence of Atom Recombination
photodissociationwas carried out by Noyes and co-workers using solvents of diffferent viscosities and varying the excitation ~avelength.'"'~ They observed a decrease of the photodissociation quantum yield with increasing wavelength, i.e., decreasing excess kinetic energy of the separating atoms, and increasing viscosity of the solvent. It was not clear, however, whether other solvent parameters were of importance. Therefore it seemed worthwhile to study the effect of changing only one independently variable solvent parameter a t a time on the quantum yield as well as the recombination rate constant. We chose the density as the variable of prime importance to control the viscosity of the solvent. We already reported the observation of a photolytic cage effect for iodine and bromine in the gas phase for various inert gases at sometimes surprisingly low pressures of only a few tens of b a r ~ . ' ~ These J ~ experiments are at present being extended up to pressures of 10 kbar, thus covering the density range up to liquid-phase densities.la Here we wish to report the effect of pressure on the primary quantum yield of iodine photodissociation and the iodine-atom recombination rate constant in liquid n-heptane and isooctane, and some preliminary results in methylcyclohexane, in the pressure range from 1 bar to 3 kbar. Whereav in the earlier experiments by Noyes and co-workers12-15a stationary-state photolysis technique combined with a radical-scavenger method was employed to determine photodissociation quantum yields, we used laser flash photolysis to measure quantum yields and recombination rate constants.
Experimental Section The basic arrangement of the laser flash photolysis apparatus in conjunction with a high-pressure system was as described earlier.lg A Lambda Physik/Zeiss FL 3 B flash-lamp-pumped dye laser was used as the photolysis light source. The laser pulse was characterized by 1.5-ps fwhm and a total energy of 100 mJ at 590 nm with rhodamine 6G dye. An interference filter was used to tune the resonator, resulting in a spectral bandwidth of the pulse of 0.2-0.4 nm. The laser beam was passed through a stainless steel reaction cell of 20-mm length and 5-mm diameter with sapphire windows of 10-mm thickness. The cell contained M iodine solution, whose timethe sample, ca. 5 X dependent concentration was monitored by measuring the iodine-molecule absorbance at 498 nm with a continuous light source (Xe-Hg high-pressure lamp Hanovia 901 B 11 or halogen lamp Osram Halogen Bellaphot 64655) in a beam-in-beam arrangement,ls a double monochromator (2X Oriel type 7244), and a photomultiplier (RCA 1P28A). The laser pulse energy was measured by a calorimeter (Gentec ED 200). The sample solution was separated from the oil-filled high-pressure system by a plastic membrane (Nova Swiss), and pressures of up to 3 kbar were obtained by compressing the oil volume with a hand-operated hydraulic pressure generator (Nova Swiss). Pressures were measured with a Heise manometer (CM 19163, 7-kbar full-scale deflection). Results and Discussion Iodine-atom recombination rate constants in the pressure range from greater than 1bar to 3 kbar were obtained from the rate of increase of the I2 absorbance at 498 nm after the laser flash, which in all cases corresponded to a ~ = ~ we second-order rate law. With A ( t ) = c ~ ( [ I ~-] [I&) therefore have
A(t)-' = A(to)-' + 4kre,t/tZ
(1)
23, 1980 3073
9/10m3 mol ~ r n (heptane) - ~
c
n -heptane 0
E
m
15
9 \
i 10
5
0 0.0
0.5
1.0
1.5
2.0
I
2.5
Figure 1. I-atom recomblnatlon rate constants k, vs. B-' at 300 K In (0)n-heptane and (0)methylcyclohexane: pressure and denslty scales from ref 20; viscosity for methylcyclohexane, ref 21; for nheptane Interpolation between n-hexane and n-octane, ref 20; point (a) from ref 4; point (b) from ref 6. €(I2, 498 nm): In n-heptane, 744 dm3 mol-' cm-'; In methylcyclohexane, 1070 dm3 mol-' cm-'. ~/10-'rnoi cm4
7.1 20 6.9 6 8 6.7
6.6
&5
6.4
6.3 I
I
,
0.4
, Figure 2. I-atom recomblnation rate constants k, vs. 9-l at 300 K in isooctane: density and viscosity from ref 20 e(&, 498 nm) in isooctane = 698 dm3 mol-' cm-'.
where 1 is the length of the reaction cell, E the extinction coefficient of iodine in the particular solvent at 498 nm, and k,, the recombination rate constant as defined by eq 2. The extinction coefficients for all three solvents were d[I2I/dt = krec[I12 (2) found to be pressure independent to within 1% in the pressure range of interest. As halogen atom recombination is a diffusion-controlled reaction in solution, it was expected that k,,, should be inversely proportional to the solvent viscosity 7. The pressure dependence of the viscosity could be obtained from available datamP2' (see figure captions), and Figures 1 and 2 show k, plotted vs. TJ-' for all three solvents. Every point corresponds to an average of several independent measurements. It is evident that the expected linear relationship holds in all cases, a linear least-squares fit to the data yielded for the slope, defined as m = dk,,,/d(s-'), 9.2 f 0.1 kJ mol-' for n-heptane and methylcyclohexane and 14.2 f 0.1 kJ mol-' for isooctane. The extrapolated values for k,,, 0, = 1 bar) agreed well with those measured earlier in n - h e ~ t a n e22 , ~ X lo9 dm3
3074
73e Journal of Physical Chemistry, Vol. 84, No. 23, 1980
Luther et ai.
mol-' s-l, and in methylcyclohexane,6 14 X lo9 dm3 mol-' s-'. The slopes may be compared with an estimate of 10 kJ mol-' at T = 300 K derived from the modified version
9ll0-3 mol cm-3 8.07.8 7.6 plkbar
of the Debye approximation of the stationary diffusioncontrolled reaction rate constant in solution's22
= 4RT/q (3) which applies to the case of solvent and solute molecules of comparable size. The agreement is surprisingly good for n-heptane and methylcyclohexane,but somewhat worse for isooctane. 12-photodissociationquantum yields 4, Le., the yield of atom pairs that do not undergo geminate recombination in the "solvent cage", were determined from the observed initial transient minimum of the I2 absorbance Aminjust after the laser pulse and from the number of photons absorbed at the laser wavelength AL of 590 nm. As the laser pulse duration was comparable to the rate of change of absorbance in most cases, one had to allow for dissociation and recombination contributions to the total signal according to the equation kD
Figure 3. Iz-photodissochtion quantum yields 4 vs. q-' at 300 K and an excitation wavelength of 590 nm in nheptane. &, 590 nm) = 256 dm3 mol-' cm-'. Density and viscosity as in Figure 1.
(4)
from which one could derive the expression for the quantum yield
10 6.8 6.7 1
/
1
I
1
3.0 2.0 1.5 I I I
I
P 110-3 mol cm-3 6.6 6.5 6.4 I
1.0 !
I
plkbar
6.3
I
I
0.5 I
IO
n,(t) is the rate of absorption of photons per unit volume that was approximated by fitting a function of the type g(t) = at exp(-bt) (6) where a and b are fitting parameters, to the laser pulse time profile, such that n,(t) = a constant X g(t), and by applying the normalization condition
o x I
0
1
1
(7)
which gave the total number of photons absorbed per unit volume. AF is the absorbed energy fluence, and the other symbols are as defined previously or have their usual meaning. AF could be determined with the calorimeter by laser pulse energy measurement behind the sample cell either filled with neat solvent or the corresponding solution. This could be checked against the absorbance at the laser wavelength calculated from the Beer-Lambert law with the appropriate extinction coefficients, and the agreement between the two methods was within error limits at the laser light intensities employed in our experiments. The quantum yields deduced in this way were found to decrease by almost two orders of magnitude from their normal pressure value in both solvents when the pressure was raised to 3 kbar, which was equivalent to an increase in solvent density by 1 X mol cm-3above its value at 1 bar. The extrapolated quantum yields at atmospheric pressure were somewhat lower than those reported earlier. Thus we found in n-heptane and isoodane 4 (1bar) = 0.15 f 0.01 and 0.18 f 0.05, respectively, whereas Strong and Willard gave 4 = 0.43 f 0.32 in nheptane,' and Meadows and Noyes 4 = 0.36 f 0.04 in n-hexane,15which are greater by more than a factor of 2. The reason for this is not clear, but it seems that the better time resolution combined with a more accurate method to estimate the number of photons absorbed in our experiments gave a more reliable value of 4. As I-atom recombination is a diffusion-controlledprocess in solution and consequently strongly influenced by the viscosity of the solvent, one would expect a comparable influence on
-
Figure 4. I,-photodissochtiin quantum yields 4 vs. q-' at 300 K and an excitation wavelength of 590 nm in isooctane. e(&, 590 nm) = 199 dm3 mol-' cm-'. Density and viscosity as in Figure 2.
the complementary dissociation process. Noyes has proposed a simple continuum which contains the proportionality 4 q-' for small quantum yieldsa2' For our results, however, we found a linear dependence of 4 and q-2, as evident from Figures 3 and 4. For n-heptane this correlation is very good, while for isooctane it is still noticeable, though scatter is considerable. At the moment, we have no explanation in terms of a model or theory to offer for this observation, but we are presently extending our investigations to different solvents.
-
Conclusion Our results demonstrate that the approach to change solvent density and thus viscosity by the application of high pressures to investigate diffusion-controlled processes in solution is promising, because the number of variables can be kept small. The 7-' dependence of atom recombination rate constants was as expected, almost conforming to the simple Debye approximation. The empirical linear correlation between 4 and q-2 requires further substantiation but nevertheless might help to improve existing models for the cage effect. We believe that these investigations of the overall cage effect are a valuable supple-
J, Phys. Chem. 1980, 84, 3075-3079
(12) (13) (14) (15) (16)
ment to the study of the picosecond dynamics of this phenomenon.2s>26 Acknowledgment. We are grateful to the Deutsche Forschungsgemeinijchaft for financial support within Sonderforschungsbereich 93 “Photochemistry with Lasers”.
(17) (18) (19)
References and Notes (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (1 1)
. ,
P. Debye, Trans. Electrochem. Soc., 82, 265 (1942). H. Rosmari and R. M. Noyes, J. Am. Chem. Soc., 80,2410 (1958). S.Aditya and J. E. Willard, J . Am. Chem. Soc., 79, 2680 (1957). R. Marshall and N. Davidson, J. Chem. Phys., 21, 2086 (1953). S. R. Logan, R. Bonineau, J. Joussot-Dubien, and P. Fomler de Violet, J . Chem. SOC.Fnraday Trans. 7, 71, 2148 (1975). A. M. Halpern and K. Weiss, J . Phys. Chem., 72, 3863 (1968). R. L. Strong and J. 1E. Willard, J. Am. Chem. Soc.,79, 2098 (1957). R. L. Strong, J . Phys. Chem., 86, 2423 (1962). R. L. Strong, J. Am. Chem. Soc., 87, 3563 (1965). J. Frank and E. Rabinowitch, Trans. Faraday Soc., 30, 120 (1934). E. Rabinovvitch and W. C. Wood, Trans. Faraday Soc., 32, 1381 (1936).
(20) (21) (22) (23) (24) (25) (26)
3075
J. Zlmmerman and R. M. Noyes, J . Chem. Phys., 18,658 (1949). F. W. Lamp and R. M. Noyes, J. Am. Chem. Soc., 78,2140 (1954). D. Booth and R. M. Noyes, J . Am. Chem. Soc., 82, 1668 (1960). L. Meadows and R. M. Noyes, J. Am. Chem. Soc., 82, 1872 (1960). K. Luther and J. Troe, Chem. Phys. Left., 24,85 (1974); C.Dupuy and H. van den Bergh, IbM., 57, 348 (1978): H. Hippler, K. Luther, M. Maler, J. Schroeder, and J. Troe In “Laser Induced Processes In Molecules”, Vd. 6, Springer-Vedag, West Berlin, 1979, p 286. H. Hlppler, V. Schubert, and J. Troe, to be submitted. H. HiDDler. K. Luther, and J. Troe, Ber. Bunsenges. Phys. Chem., 77, i i 0 4 (1973). D. W. Brazier and G. R. Freeman, Can. J . Chem., 47, 893 (1969). J. Jonas, D. Hasha, and S. 0. Huang, J . Chem. Phys., 71, 3996 (1979). A. D. OsborneandG. Porter, Proc. R. SOC.London, Ser. A , 284, 32 (1965). R. M. Noyes, Z . Elektrochem., 84, 153 (1960). J. Schroeder, J. Troe, and U. Unterberg, Nachr. Akad. WIss. Bttlnaen. Math.-Phvs. KI., 2, 1 (1980). T. J. ehuang, G. W. Hoffmann, and K. E. Eisenthal, Chem. Phys. Left., 25, 201 (1974). C.A. Langhoff, K. GnBdig, and K. B. Elsenthal, Chem. Phys., 46, 117 (1980).
Infrared Spectroscopy of Some Chemisorbed Molecules on Tungsten Oxide-Silica A. J. van Roosmalen,” D. Koster, and J. C. Mol Unlverslty of Amsterdam, Institute of Chemlcd Technology, Plantage Muklergracht 30, 1018 TV Amsterdam, The Netherhnds (Received March 4, 1980)
Transparent plates of a tungsten oxidesilica metathesis catalyst were prepared by hydrolyzing a WC&-Si(OC2H& mixture. From the infrared spectra of adsorbed pyridine and ammonia, it is concluded that the chemisorption sites on the catalyst surface are of the Lewis type. Strong Bransted acid sites could not be observed the surface hydroxyls appear to resemble the weakly Bransted-acidichydroxyls on dry silica gel. Temperature-programmed reduction showed that -95% of the tungsten on the calcined catalyst is present as surface compounds and less than 5% as metathesis-inactive“free” oxide. The Lewis acidity is ascribed to these surface compounds, which are thought to be coordinativelyunsaturated species resulting from the dehydration of W06 octahedra shariing edges or planes with the silica lattice.
Introduction Tungsten oxide-silica is a well-known catalyst for the metathesis of alkene!J.1v2 In recent years, much work has been done to elucidate the nature of the active sites on this and other oxidic metathesis catalysts by using a large variety of techniques.”“ From the results of laser-Raman spectroscopy and temperature-programmed reduction of tungsten oxide-silica systems, Thomas et ah6 concluded that the precursor for the active site in metathesis is a surface compound and not the “free” oxide as such. However, no details of this surface compound could be given. More knowledge about the surface structure of tungsten oxide-silica might be obtained from infrared spectroscopy, being a straightforward, nondestructive method that can be applied easily in situ. Unfortunately, tungsten oxidesilica is opaque below 1350 cm-l (transmission less than 1%)owing to the strong lattice vibrations of the support. As a result, the interesting surface modes v(W-0) and v(W-0-Si) are obscured. Infrared studies will, therefore, yield only indirect injformation. In this paper, we present the results of a study on the interaction of some probe molecules, viz., pyridine, ammonia, and hexamethyldisilazane, with the surface of tungsten oxide--silica. One reason for this study was the
-
0022-3654/80/2084-3075$01 .OO/O
suggestion made by Laverty et aL7that strong Brernsted acid sites play an important role in the heterogeneously catalyzed metathesis. Because the force constants in ammonia and pyridine are strongly dependent on protonation and complex formation: the infrared spectra of these molecules adsorbed on the catalyst surface can prove or disprove the presence of such Brernsted acid sites. A second reason was the observation that ammonia and amines can greatly enhance the catalytic activity of tungsten oxide-silica in the metathesis of propeneagJO Hexamethyldisilazane was used as it is known to react almost quantitatively with the hydroxyl groups on dry silica gel.l1 Conventional catalysts are, in general, not easy to study by infrared spectroscopy: scattering usually reduces the transparency of pressed catalyst wafers considerably. Moreover, most tungsten oxide-silica catalysts hold substantial amounts of “free” tungsten oxide. Here, we will show that it is possible to prepare a catalyst with an excellent transparency and a low “free” oxide content. Temperature-programmed reduction12 was used to compare this catalyst with tungsten oxide-silica catalysts from other preparations in order to quantify the bonding strength between the tungsten and the support and to calculate the amount of “free” tungsten oxide. All catalysta 0 1980 American Chemical Society
