J. Phys. Chem. 1985,89, 4569-4574 0 18
well-defined isosbectic point is found at a longer wavelength 1490 nm, and there is a buildup of intensity at 1430-1450 nm-a broader band than in the case of HC104 protonation but still a well-defined one. Clearly the -OH groups released from OH--0 bonds in this titration prefer to form weak bonds with the C1- than to remain “free”. (Lone pairs about C1- can be invoked as the “trap” sites for the free -OH groups for illustrative purposes, although the electron density about the isolated CI- ion is actually spherically symmetric.) In the case of the HClO, titration, the distinction between the -OH--OC103 interaction and the weak interaction between displaced -OH and already fully bonded H 2 0 molecules (e.g., the weak -OH bonds in hot water) is difficult to make. The interactions are almost equally weak and give rise to equally highfrequency -OH overtone frequencies. The isosbestic point at 1442 nm in Figure 2 is to be compared with the range, 1440-1450 nm, of the smeared isosbestic point for the pure water spectrum in the temperature interval 0-80 0C.499
016 014 012
E
In
010
(u
s 008 c
0
2 006 004
a02
aoy
4569
a2
06
04
ae
10
[H’l/[Xl Figure 7. Change of absorbance at 1425 nm from initial value, due to titration of different amine solutions by HC104, as a function of proton:amine concentration ratio. For equal initial concentrationsof -NH bonds, the buildup of ”free” -OH intensity is greatest for methylamine. Insert shows difference between AA in Figure 7 and corresponding AA for NaC104 solution, to normalize for the effect of perchlorate anions alone in disrupting the water structure.
at 1425 nm in Figure 4 (extrapolated where necessary) from the titrated solution intensities in the same figure. The value of AA at the equivalence point for the CH3NH2solution, 0.085, is a little less than the value, 0.048 (1 1.616.0) = 0.093, expected from the N2H4 equivalence point value if only two of the four protons were activated by the first protonation, Le., the charge on one nitrogen weakly activates the protons on the other. To add conviction to the notion that very weak essentially “broken” hydrogen bonds have their overtone intensity at or near 1425 nm we make brief reference to the following study which will be the subject of a separate arti~1e.I~When the protonation of the amine is performed with HCl rather than HC104 a less (13) D. L. Fields and C. A. Angell, to be published.
Conclusion The technique we have described provides a relatively unambiguous way of producing and spectroscopically characterizing weak hydrogen bonds produced by a process of “breaking” or displacing initially intact well-formed hydrogen bonds without temperature change. Observing a close similarity with the spectroscopic consequences of heating water we suggest that the (weak bond) exchange for the temconcept of (strong bond) perature-induced disruption of the water structure is a sound one.
-
Acknowledgment. We are indebted to the Office of Naval Research, Grant No. N0014-78-C-0035, under whose auspices this work was initiated and to the National Science Foundation, Chemistry Grant No. CHE8318416, for support during its conclusion. This work commenced with an attempt to titrate excess -NH protons with excess Hz02lone pairs (at low temperatures). It was E.I. Cooper, now at IBM Research Laboratories, Yorktown Heights, NY, who pointed out that it would be necessary to protonate the amines to make them sufficiently acid to combine with the lone pairs in question. Out of the discussions which followed, the present project developed. Registry No. N,H4, 302-01-2; NH40H, 1336-21-6;CH3NH2,7489-5.
Nonexponential Hole Burning in Organic Glasses R. Jankowiak, R. Richert, and H. Bawler* Fachbereich Physikalische Chemie, Philipps- Universitat, 0-3550 Marburg, FRG (Received: March 26, 1985)
The time evolution of nonphotochemical holes in the absorption profile of tetracene doped into amorphous layers of 2,3dimethylanthracene and 9,lO-diphenylanthracene has been investigated and compared with literature results on tetracene in an alcohol glass. The kinetics can be described in terms of a dispersive first-order reaction of noninteracting reaction centers assuming that site relaxation is a tunnel process, the tunnel parameter X being subject to a Gaussian distribution. Data for hole burning rates have been evaluated via model fits. Successful application of the concept to analysis of literature data for the recovery of photochemical holes suggests that a Gaussian distribution function for the rate-controlling parameter is superior to the conventionally constant distribution function with cutoff condition.
Introduction A distinguishing feature of a glass is the local fluctuation of the potential energy. It reflects the disorder frozen in during quenching a melt or condensation of a vapor at a cold substrate. Since the system is neither at minimum energy nor at maximum entropy it is subject to a driving force which tends to establish thermodynamic equilibrium. Although macroscopic relaxation is often too slow to be observable on realistic time scales. mi0022-365418512089-4569$01.50/0
croscopic relaxation processes can be probed by various experiments. The example this paper deals with is the local motion of atoms or molecules or clusters thereof within two adjacent potential minima, usually referred to as two-level systems (TLS).1-3 They (1) Anderson, P. W.; Halperin, B. I.; Varma, C. M. Philos. Mag. 1972, 25, 1. (2) Phillips, W.
A. J . Low Temp. Phys.
0 1985 American Chemical Society
1972, 7, 351.
4570 The Journal of Physical Chemistry, Vol. 89, No. 21, 1985
are characterized by their energy splitting E and coupling parameter A. From measurements of the specific heat4 and ultrasonic absorptionSit follows that they are subject to a distribution function which is constant in energy, or, rather, varies smoothly on the scale of kT. On the other hand, there is a wide range of qualities characteristic of amorphous systems, notably organic glasses, which are well described in terms of a Gaussian distribution function for a microscopic parameter. Prominent example is the absorption profile of a molecular electronic transition which can with good accuracy be represented by a Gaussian or a superposition thereof! It documents that ground and excited states are site specific and subject to a Gaussian distribution reflecting the random fluctuation of intermolecular conformation^.^ The implication is that the rate of an elementary electronic process be also site specific, giving rise to dispersion. An example which has been studied in some detail is the diffusion of a charge carrier or an optical excitation. If started at random within the inhomogeneous site distribution the diffusing particle will relax energetically provided that the width of the distribution is >>kT. This can be viewed as a sequence of constraint relaxation e ~ e n t s . ~Both . ~ time-dependent diffusion studies of triplet excitations in benzophenone glasslo and computer simulations” and analytic theory’* revealed a decay law of the type exp[-(t/to)”], consistent with earlier13J4 and recent8s9reasoning regarding relaxation in systems involving hierarchically constrained events. Random fluctuations of the molecular environment in a glass must also affect the rates of chemical reactions. Recently we were able to show that the reversible photochemical transformation of a spiropyran molecule into the merocyanine form in a polymer matrixIs can be understood in terms of a dispersive reaction.I6 The dispersion arises from random variations of the energy barrier controlling molecular rotation. It turned out that the assumption of a Gaussian distribution of activation energies provides an adequate framework for describing the experiment in a quantitative fashion. Quite in analogy, Doba et al.I7 showed that the nonexponential kinetics of hydrogen abstraction in organic glasses18 can also be understood in terms of random fluctuations of a critical reaction parameter, which in this case is the tunnelling distance of a proton within a double-well potential. Anticipating that nonexponential kinetic behavior is a common feature of glasses we investigated the kinetics of burning of a nonphotochemical hole within the inhomogeneously broadened absorption profile of a guest species embedded in an organic glass at a dilution sufficient to ensure that guest molecules are decoupled. Recall that in nonphotochemical hole burning (NPHB) 19-27 molecules that are in resonance with the incident
(3) Jackle, J. 2.Phys. 1972, 257, 212. (4) Zeller, R. C.; Pohl, R. 0. Phys. Rev. B 1971, 4, 2029. ( 5 ) Hunklinger, S. In ‘Festkorperprobleme XVII”; Trensch, J., Ed.; Vieweg: Braunschweig, West Germany, 1977. (6) Jankowiak, R.; Rockwitz, K.-D.; Bassler, H. J . Phys. Chem. 1983,87, 552. (7) Eiermann, R.; Parkinson, G. M.; Bassler, H.; Thomas, J. M. J . Phys. Chem. 1983,87, 544. (8) Palmer, R. G.; Stein, D. L.; Abrahams, E.; Anderson, P. W. Phys. Rev. Lett. 1984, 53, 958. (9) Queisser, H . J. Phys. Rev. Lett. 1985, 54, 234. (10) Richert, R.; Ries, B.; B i d e r , H. Philos. Mug. B 1984, 49, L25. (11) Schonherr, G.; Biissler, H.; Silver, M . , Philos. Mug. E 1981, 44, 47. (12) Griinewald, M.; Pohlmann, B.; Movaghar, B.; Wiirtz, D. Philos. Mug. B 1984, 49, 341. (13) Scher, H.; Montroll, E . W., Phys. Rev. B 1975, 12, 2455. (14) Klafter, J.; Silbey, R. J . Chem. Phys. 1980, 72, 843. (1 5) Smets, G. Adu. Polym. Sci. 1983, 50, 17. (16) Richert, R.; BBssler, H. Chem. Phys. Lett. 1985, 116, 302. (17) Doba, T.; Ingold, K. U.; Siebrand, W.; Wildman, T. A. Chem. Phys. Lett. 1985, 115, 51. (1 8) Vyazkoukin, V. L.; Bol’shakov, B. A,; Tokatchov, V. A. Chem. Phys. 1983, 75, 11. (19) Kharlamov, B. M.; Personov, R. I.; Bykovskaya, L. A. Opt. Commun. 1974, 12, 191. (20) Hayes, J. M.; Small, G. J. Chem. Phys. 1978, 27, 151.
Jankowiak et ai.
IC
0 0
0.E
4
1.-
URUELENGTH (NR)
URUELENGTH (Nll)
-
Figure 1. Hole profiles burnt into the inhomogeneously broadened So SI 0-0 profile of tetracene doped into amorphous 2,3-dimethylanthracene (A, = 491.5 nm): (a) 4-min burning time, (b) 45-min burning time (the burn intensity was 3 m W cm-2).
laser line leave their absorption position by structural site conversion and reappear as antiholes in different spectral regions. When studying the time evolution of the hole shape as a function of C W irradiation one usually notices a fast initial change followed by gradual levelling off in the long time limit. At first glance, such a behavior appears characteristic of a reversible first-order reaction, the rate constants for forth and back reaction being comparable. However, this simple picture leads to an inconsistency. Since the burnt hole remains more or less stable after terminating the burning process, the back reaction had also to be photostimulated, although the burnt molecules are usually no longer in resonance with the laser. Therefore hole recovery, if important at all, should occur at greatly reduced rate. In this paper we argue that NPHB is a highly dispersive process. The dispersion arises from the fact, that molecules absorbing resonantly at a given energy sit in configurationally inequivalent environments, since the photon field couples the whole manifold of ground and excited states that accidently have the same energy differences.28 Therefore the double-well parameters that control site conversion, notably the A-parameter, must also be subject to a distribution. As a consequence “easy” sites will burn first, the long time behavior being dominated by the more resistant ones. This effect turns out to be the dominant source for the apparent hole saturation observed in the long burning time limit, photostimulated spectral diffusion playing only a minor role. Experimental Section Photophysical hole burning experiments were carried out on tetracene (TC) incorporated in amorphous matrices of 9,lO-diphenylanthracene (DPA) and 2,3-dimethylanthracene (DMA). mol/mol of the dopant Vitreous layers containing (1-3) X were laid down onto a glass slide by vapor condensation. The substrate was kept in thermal contact with a temperature controlled cold stage (Cryo tip, Model WMA-1) attached to the cold finger of a He flow cryostat (Heli-Tran LT-3-110 system). The (21) Cuellar, E.; Castro, G. Chem. Phys. 1981, 54, 217. (22) Rebane, K. K.; Avarma, R. A. Chem. Phys. 1982, 68, 191. (23) Jankowiak, R.; Bassler, H. Chem. Phys. Lett. 1983, 95, 124; 1983, 101, 274. J. Mol. Electron., in press. (24) Small, G. J. In ‘Spectroscopy and Excitation Dynamics of Condensed Molecular Systems”; Panovitch, V. M., Hochstrasser, R. M., Eds.; NorthHolland: Amsterdam, 1983; p 515. (25) Fearey, B. L.; Carter, T. P.; Small, G. J. J . Phys. Chem. 1983, 87, 3590. (26) Carter, T. P.; Fearey, B. L.; Hayes, J. M.; Small, G. J. Chem. Phys. Lett. 1983, 102, 272. (27) Bogner, U.; Schatz, P.; Seel, R.; Maier, M . Chem. Phys. Lett. 1983, 102, 267. (28) Lee, H. W. H.; Walsh, C. A,; Fayer, M. D. J . Chem. Phys., in press.
Hole Burning Kinetics in Organic Glasses 0
The Journal of Physical Chemistry, Vol. 89, No. 21, 1985 4571
*5
W
U w W
1 0 I
0
I.
s Ly
L 0
0 L
0
0'
0
10
20
30
1
40
u 10
20
30
0
10
20
TlnE (RIN)
deposition rate was 50-90 A s-l, and the substrate temperature during deposition was varied between 2.5 and 4.2 K. Holes were burnt by a N z pumped dye laser operated at 491.5 nm and 50 Hz. (Continuing earlier NPHB studiesz3we meanwhile found that T C can occupy two different sites in the glasses under study, only one of these being subject to hole burning. Details are being published elsewhere.) The laser bandwidth was 0.1 cm-', the time-averaged intensity was =3 mW/cmz. Time evolution of the hole was inferred from the temporal decay of the T C fluorescence excited by the burn beam. In separate runs hole profiles were recorded after various burning times. Typical burn experiments are carried out on a time scale of minutes.
Results As an example for a NPHB spectrum in an aromatic glass we present in Figure 1 hole profiles burnt at Ab = 491.5 nm into the inhomogeneously broadened So -,SI 0-0 band of TC in DMA after various burning times tb. Only the zero phonon (ZP) hole and a discrete real and pseudo phonon satellite, probably reflecting a molecular libration, are shown. With increasing burning time the hole depth grows and the hole width increases. Figure 2a portrays the time evolution of both the maximum depth of the ZP hole and the normalized hole area evaluated on the basis of a Lorentzian line shape. The decrease in sample absorbance at Ab is shown in Figure 2b together with the sample absorbance corrected for hole broadening, obtained by multiplying the optical density of the normalized hole area with A ( t b ) / A ( t b + O ) . Examples for growth of the ZP hole in the DPA/TC system at 2.5 and 4.2 K are presented in Figure 3. Discussion Following common practice we assume that the guest molecules couple to two-level of the amorphous matrix which in turn couple to the phonon bath of the s y ~ t e m .After ~ ~ ~optical ~~ excitation tunnelling occurs within the double-well potential with rate constant v,,e(-X) where uo is a phonon frequency of order 1Ol2 s-I and X is a measure of the wave function overlap through the tunnel barrier. The vast majority of tunnelling processes occurs under conservation of the environment of the guest molecule. They manifest themselves via their contribution to the dephasing of the excited state monitored by the (homogeneous) width of the zero phonon line. Photophysical hole burning requires that the environment of an excited molecule relaxes irreversibly to a new conformation with modified van der Waals interaction energy of the excited guest molecule. Then the guest molecule is removed
I
I
20
30
111111111111
40
Figure 2. (a) Normalized depth and area of holes in DMA/TC as a function of burning time. (b) Optical density at Ab as a function of burning time (dashed curve). The full curve is the optical density corrected for the increase of the hole area in course of the burn process. Dots represent the fit by eq 4.
1
I
10
30
40
50
TIME (SEC) Figure 3. Time evolution of the maximum hole depth in the system 9,10-diphenylanthracene/tetracene. The burning temperature was 4.2 K (a) and 2.5 K (b). Dots represent the fit by eq 4.
from its original absorption site and appears at a remote place within the inhomogeneous absorption profile. Assuming that site relaxation is the consequence of an inelastic tunnelling process we characterize it by a rate constant
k, = k,O exp(-X) (1) The hole burning process can be written as a consecutive first-order reaction of the type M&M*-P
kt
kf
where qZ is the rate of photon absorption by M, q being the absorption cross section and Z the photon flux, k f is the reciprocal lifetime of the excited sensor molecule M*, and P denotes the photophysical product. Bearing in mind that (i) ground-state conversion P M is a slow process on the time scale of a typical burn e ~ p e r i m e n t ~and ~ v ~(ii) ~ the absorbance of the product molecules at the burn wavelength is small, if not zero (in the case of high energy antiholes), hole filling has been ignored in the above scheme. We shall return to this problem later in the discussion. Solution of the rate equations describing the above system under the condition of small NPHB yield, Le., k, Rdn. Within this framework that Xfin < X < ha,, a logarithmic decay law is recovered, the slope of the decay function being -[ln Rl/Rmin]-' where Rl is the fastest rate observable within the time frame of the experiment. We have analyzed the Breinl et al. data in terms of a dispersive tunnel reaction with rate constant k," exp(-A) assuming that the rate determining tunnel parameter X is distributed according to a Gaussian with width u, centered around b,, making the straightforward assumption that the tunnelling particle is the proton/deuteron. The resulting constraint is that the ratio of the (38) Gorokhovskii, A. A.; Kikas, J. V.; Palm, V. V.; Rebane, L. A. Fir. Tuerd. Tela 1981, 23, 1140.
1
10
lo2
103
toL
time ( m i d Figure 7. Decay of the hole area at 4.21 K for quinizanin in C2D50D/CD30D(open circles) and in C2HSOH/CH30H(full circles). The upper half shows the data and logarithmic fit taken from Breinl et al." The lower part displays the same data together with a fit using eq = 20, uD = 6 , XoH = 4. The resulting parameters are K: = 1 s-', ioD 14.2, and uH = 4.3. Note that bD/bH N uD/uH E 21/2= m(D)/m(H) as proposed by X = (2mc)Il2.
Xo values for protonated and deuterated host has to be XoD/XoH = 21/2. Figure 7 compares the original data of ref 31 with fitting curves according to eq 4. The fitting parameters are K," = 1 s-l, XoD = 20, XoH = 14.2, uD = 6 , uH = 4.3, Le., uD/XoD= uH/XoH = 0.42. The small value of k," compared to a zero point frequency
reflects the extremely low probability that a tunnel process moves a guest absorber from an arbitrary place within the spectrum into resonance with the hole. We believe that the quality of this fit is at least as good if not better than the logarithmic fit chosen by Breinl et aL3' Nevertheless we do not claim this to be a stringent test for the uniqueness of the analyzing procedure suggested herein. We rather wish to point out that the quality of a fit is not a sufficient criteria for discriminating among various models. The reason is that a logarithmic decay law is barely distinguishable from a plot according to eq 4 or a time extended exponential of the form exp[-(t/to)"]. This is because on the time scale of a quasi-static measurement only a small fraction of all possible events are sampled, Le., only a small section of the distribution function of the rate-controlling parameter is actually probed. On the other hand we believe that a Gaussian distribution function for, say, the X-parameter is a physically more sensible choice than a rectangular distribution function requiring cutoff conditions for normalization purposes which are specific for a certain experimental situation. The conceptual disadvantage of the Gaussian distribution function is that it relates the time dispersion of a kinetic process to a statistical variable which cannot be calculated ab initio, yet nevertheless is the fundamental kinetic quantity of the system. In the following we derive the distribution for the tunnelling rates consistent with a Gaussian distribution function for the tunnelling matrix element X. By substitution of R ' = e-', eq 4 transforms into [M(t)l =
represents the modified distribution function. Ro' is the average rate determined by Xo. Plots of P'(R? in linear and log/log representation are presented in Figure 8. In the relevant range
J . Phys. Chem. 1985,89, 4574-4571
4574
Figure 8. Distribution of rates R’normalized to P’(R,? = 1. The range 0 I R’ 5 3000 s-] is associated with the variation exp[-2u] I X I exp[2u]. The parameters are Ro’=4.5 X (X,= lo), u = 4 and a frequency factor of 1 s-’. The insert shows that P’(R’) is in accord with a power law (P’ Re*,”).
Conclusions By studying nonphotochemical hole burning in organic glasses we have shown that hole formation is a dispersive first-order reaction. Experimental results can be rationalized in terms of a tunnel model for the site relaxation process with only one kinetic parameter being subject to a Gaussian distribution function. Formally this is the tunnelling parameter A. However, its standard deviation (r contains the contribution of the random fluctuation of other kinetically relevant system parameters as well. Comparison with the results of hole recovery studies of Breinl et suggests that the Gaussian distribution function can profitably be used to explain the dynamic behavior of two-level systems. It is consistent with a diversity of features characteristic of organic glasses and alleviates the problem of introducing somewhat arbitrary cutoff conditions when specifying the distribution of rates and reaction parameters, respectively.
of rates the deviation from a hyperbolic law are small as expected. The essential differences between eq 8 and 6 are that the pole at large rates is absent and that [ M ( t ) ]converges although P’(R9 is divergent at R‘ = 0.
Acknowledgment. We are grateful to Professor J. Friedrich for a stimulating discussion. This work was supported by the Stiftung Volkswagenwerk and the Fonds der Chemischen Industrie.
0
2
1
3
R,nO3s-’)
-
Ab Initio MO Calculations on Cyclodisiloxanes and Other Si-X-Si-X Problem of “Silica-w
Rings and the
”
M. O’Keeffe* Department of Chemistry, Arizona State University, Tempe, Arizona 85287
and G. V. Gibbs Department of Geological Sciences, Virginia Polytechnic Institute, Blacksburg, Virginia 24061 (Received: April 3, 1985)
Ab initio SCF MO calculations have been performed for molecules containing Si-X-Si-X rings (X = S, 0, N, or C). The strain energy in the cyclodisiloxane ring is estimated to be 177 kJ mol-’ and in the cyclodisilathianering, 15 kJ mol-]. Calculated geometries are in general agreement with observation with the exception of the ring structure reported for silica-w. The short S i 4 3 distance in silicon-oxygen rings does not correspond to Si-Si bonding.
Introduction In the immense variety of silicate minerals, four-membered Si-0-Si-0 rings are unknown although larger (6, 8, etc.) rings are very common. However, a synthetic polymorph of S O 2 , generally referred to as “silica-w”, has been reported] and its structure found to be similar to that of SiS2, Le., to consist of infinite chains of edge-sharing S O 4 tetrahedra, or, alternatively put, infinite chains of spiro Si-0-Si-0 rings. In a recent paper2 we reported the calculated geometry of tetrahydroxycyclodisiloxane and remarked that the ring dimensions calculated for the molecule were very different from those found for the crystal. Since that work the synthesis and structure of tetramesitylcyclodisiloxane has been reported3 -this has ring geometry closer to that calculated. As our previous experience4 with silicates and phosphates has been that S C F calculated geometries of model molecules reproduced the local structures of molecules and crystals accurately, we have further investigated the discrepancy between calculated and observed structures in silica-w. We have also investigated the analogous siliconsulfur compounds and compared (1) Weiss, A.; Weiss, A. Z . Anorg. Allg. Chem. 1954, 276, 95. (2) OKeeffe, M.; Gibbs, G. V. J . Chem. Phys. 1984, 81, 876. (3) Fink, M. J.; Haller, K. J.; West, R.; Michl, J. J. Am. Chem. SOC.1984, 106,822. (4) O’Keeffe,M.; DomengEs, B.; Gibbs, G. V. J . Phys. Chem. 1985.89, 2304 and references therein.
TABLE I: Observed and Calculated Dimensions (A and deg) of Si-0-Si-0 Rinns
H Si 0
H4Si40I O
SizOza
6-3 1G’ 6-31G’(*) STO-3G STO-3G, inner ring STO-3G, outer ring 6-31G’
tetramesitylcyckodisiloxaneb silica-w‘ a
Si-.Si 2.420 2.375 2.422 2.419
O...O
Si-0-Si
2.303 2.320 2.314 2.316
92.7 91.3 92.6 92.5
1.670 1.660 1.675 1.674
2.429 2.311
92.8
2.469 2.249 2.31 2.47
94.3 86
2.58
87
1.684, 1.669 ,683 .66, 1.72 .87
Reference 19. Reference 3. e Reference
2.70
Si-0
1.
observed and calculated geometries in Si-X-Si-X (X = N or C) rings. Calculations have been made with the GAUSSIAN-80 computer program5 using the STO-3G minimal basis set and the 6-31G split valence basis set6 with polarization functions. When polarization ( 5 ) Binkley, J. S.; Whiteside, R. A.; Krishnan, R.; Schlegel, H. B.; Seeger, A. Quantum Chemistry Program Exchange,
R.; DeFrees, D. J.; Pople, J.
Indiana University, Bloomington, IN. (6) Francl, M. M.; Pietro, W. J.; Hehre, W. H.; Binkley, J. S.; Gordon, M. S.; DeFrees, D. J.; Pople, J. A. J . Chem. Phys. 1982, 77, 3654 and references therein.
0022-3654185 12089-4574%01.50/0 0 1985 American Chemical Societv
