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of such a peak would be the singlets present in the system. We have observed signals in this region in two instances when we had access to the appropriate lasers (courtesy of P. R. Carey, National Research Council of Canada). Indeed, in our first c o m m ~ n i c a t i o n we ’ ~ reported a SERS signal from citrate on colloidal silver for 406.7-nm excitation which was about 10% of the signal at 514.5 nm. N o signal was detected at 350.7 nm,
indicating that the enhancement at this wavelength was less than 10% that for 406.7 nm. This red sol was quite coagulated. A similar result was obtained with the azo dye, dabsyl aspartate, where the signal at 413.1 nm was less than 10% of the longer wavelength peak signal. Accordingly, even though a peak SERS signal has not been detected for 400-nm excitation, there is no evidence that such a peak does not exist.
(14) M. Kerker, 0. Siiman, L. A. Bumm, and D.-S. Wang, Appl. Opt., 19, 3253 (1980).
Acknowledgment. This work was supported by NIH Grant GM-30904, by Army Research Office Grant DAAG-29-82-K0062, and by N S F Grant CHE-801144.
Exclton Energy Funnels in ,@Methylnaphthalene-Doped Naphthalene Crystals Stuart T. Gentry+ and Raoul Kopelman* Department of Chemistry, The University of Michigan, Ann Arbor, Michigan 481 09 (Received: March 27, 1984)
Excitation energy funnels, formed by perturbed naphthalene molecules adjacent to BMN @-methylnaphthalene) impurities, are investigated. Our absorption studied document directly the singlet exciton funnel depth and size. Literature singlet energy trapping data, as a function of temperature, are in excellent agreement with a simple model of phonon-assisted detrapping. We also present triplet energy trapping data, as a function of temperature. Fitting them with a funnel model results in a reasonable funnel depth but in an unusually large funnel size. A reasonable interpretation is that exciton-phonon scattering in the bulk crystal (coherence loss) is responsible, in part, for the negative temperature effect. This is consistent with a real negative temperature effect on energy transport (“metallic” energy conduction), as suggested earlier.
A large amount of experimental and theoretical work has been done on elucidating exciton transport and trapping in molecular crystals.’” Due to the uncertainties in knowing the transport parameters which are present in an experimental system, and due to the theoretical approximations which are often made, it is difficult to extract valid conclusions from the comparison of experimental and theoretical data. In this paper we will examine one such parametric ambiguity: the presence of energy funnels surrounding trap sites, with these funnels enhancing the rate of exciton trapping. We will base our conclusions on two different types of experimental data, i.e., on absorption spectra and on the temperature dependence of exciton trapping. In a previous paper6 we presented data on the delayed fluorescence rate constant as a function of temperature for the mixed crystal system consisting of perdeuterionaphthalene (C&8), naphthalene (ClOHg), and P-methylnaphthalene (BMN). We varied the CIoHsconcentration, C,, from 0.20 to 1.0 mole fraction while maintaining the relative BMN concentration, C,, at levels of C,/C, = 10-5-10-3. W e varied the temperature from 1.8 to 16 K. Under these conditions the delayed fluorescence rate constant is proportional to the rate constant for trapping of CloH8 excitons by BMN trap, or supertrap, sites.7 Figure 1 shows the temperature-dependent rate constants for two different crystals: and C, = 0.28, C,/C, = 1 X C, N 1.0, CJC, = 2 X The rate constants are given in terms of the reduced rate constant7 A prominent feature of Figure 1 is that raising the temperature of the C, N 1.O crystal reduces the delayed fluorescence decay rate while raising the temperature of the C, = 0.28 crystal increases the decay rate. (The experimental details for this experiment and for the absorption experiment are given in ref 6, 7, and 8 as well as in the figure captions.) This concentration dependence of the temperature behavior is discussed in ref 6 and 9. For this current paper we only deal with +Present address: Hughes Aircraft Co., 600/F245, P.O. Box 3310, Fullerton, CA 92631.
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the C, 1.O case. Reference 6 interpreted the nominally pure CloH8 crystal data as being consistent with a bandlike transport model. Increasing the temperature increases the phonon scattering of exciton wave packets; consequently, the rate of exciton transport is slowed This interpretation is still consistent with the data; however, it is not the only interpretation which is. The temperature data can also be explained by an energy funnel model. Supertrap-Induced Energy Funnels. A major contribution to the trapping efficiency may be the potential presence of energy funnels surrounding the BMN sites.13 An example of such an energy funnel is the situation where the supertrap molecule perturbs the crystal lattice so as to decrease the excitation energies of the surrounding host and guest molecules. These perturbed sites are similar to the X-traps induced by antitrap impurities,14 except that the molecules perturbed by a supertrap have their (1) V. M. Agranovich and M. D. Galanin in “Electronic Excitation Energy Transfer in Condensed Matter”, Vol. 3, V. M. Agranovich and A. A. Maradudin, Eds., North-Holland Publishing Co., Amsterdam, 1982. (2) N. E. Geacintov and C. E. Swenberg, “Luminescence Spectroscopy”, M.Lumb, Ed., Academic Press, London, 1978. (3) R. Kopelman in “Spectroscopyand Excitation Dynamics of Condensed Molecular Systems”, Vol. 4, V. M. Agranovich and R. M. Hochstrasser, Eds., North-Holland Publishing Co., Amsterdam, 1983, p 139. (4) V. M. Kenhe in “Electronic Excitations and Interaction Processes in Organic Molecular Aggregates”, P. Reineker, H. Haken, and H. C. Wolf, Eds., Springer-Verlag, West Berlin, 1983, Springer Ser. Solid-state Sci. No. 49, p 193. (5) P. Argyrakis, D. Hooper, and R. Kopelman, J . Phys. Chem., 87, 1467 (1983). (6) S. T. Gentry and R. Kopelman, Phys. Rev. B Condens. Mutter, 27, 2579 (1983). (7) S. T. Gentry and R. Kopelman, J . Chem. Phys., in press. (8) S. T. Gentry and R. Kopelman, J . Chem. Phys. 7 8 , 373 (1983). (9) S. T. Gentry, Doctoral Dissertation, The University of Michigan, 1983. (IO) G. G. Roberts, N. Apsley, and R. W. Munn, Phys. Rep., 60, 59 (1980). (11) R. W. Munn and R. Silbey, Mol. Cryst. Liq. Cryst., 57, 131 (1980). (12) V. Ern, A. Suna, Y.Tomkiewicz, P. Avakian, and R. P. Groff, Phys. Rev. B Solid State, 5, 3222 (1972). (13) D. P. Craig and S . H. Walmsley, “Excitons in Molecular Crystals”, W. A. Benjamin, Inc., New York, 1968. (14) H. C. Wolf and K. W. Benz, Pure Appl. Chem., 27, 439 (1971).
0 1984 American Chemical Society
The Journal of Physical Chemistry, Vol. 88, No. 15, 1984 3171
Letters
TABLE I: X-trap Energy Funnel Analysis
+
singlet absorption data singlet2’ transport vs. temp data triplet transport vs. temp data
0
0 0
0 0
no6
“1
o
0
4
o
e
12
16
Temp(K)
Figure 1. Reduced trapping rate constant as a function of temperature for low and high guest concentration crystals. fi is defined in eq 1. The measurements were made by using a dye laser to provide direct excitation of the naphthalene first triplet state. The laser was switched on and off by an electrooptic modulator with a 20-11s transition time. Reference 7 shows that the decay rate in the delayed fluorescence intensity when the laser is turned off is proportional to the triplet exciton trapping rate. Note the 3 orders of magnitude scale change between top and bottom.
Yn .-ln
L
b
E
.D-
E
a
I‘
dk e
- O
Frequency Icm-’1
Figure 2. Absorption spectrum for BMN in naphthalene. Peak a is the BMN 0-0 first singlet transition. The first singlet naphthalene band begins at peak e and extends to higher energies, with e being the lowenergy Davydov component. Peak f corresponds to the 438-cm-’ BMN vibronic peak. Peaks b, c, and d are respectively the 17-,8-, and 4-cm-’ X-traps. The spectrum was recorded at 1.8 K by using steady-state xenon lamp excitation. Note: highly purified naphthalene spectra9do not show peaks a, b, c, d, and f [includingthe photon side band built on peak a], but only the two Davydov components [peak e and the broad peak at high
energy]. luminescence quenched by the supertrap; Le., they are dark X traps. Presumably the crystal perturbation and the consequent depth of the X-traps are largest for the guest and host sites closest to a supertrap. The overall result is that once an exciton lands on a site within an energy funnel (a set of X-traps resulting from one supertrap), it has a large probability of energetically cascading down to the supertrap. In ref 8 we demonstrated that an energy funnel exists for singZet excitons in the CloD8/CloHs/BMNcrystal system. An extended trapping region of this sort had been claimed previously for anthracene-doped naphthalene ~ r y s t a l s . ’ ~ JOur ~ , ~evidence for the presence of a BMN-induced energy funnel consisted of optical (15) 2.G. Soos and (,-1 977) -I.
R. C. Powell, Phys. Reu. B: Solid State, 6, 4035
(16) H. Auweter, A. Braun, U. Mayer, and D. Schmid, 2. Naturforsch., A , 34A, 761 (1979).
AE,. cm-’ -10 (4, 8, 17) 7fl 6 f l
(AR R)/R 2 f 0.5 2 f 0.5 7f2
absorption spectra. We studied the first singlet transitions of nominally 100% C&8 with and without trace amounts of BMN present as well as 100% C&g with and without BMN. Figure 2 shows typical spectra taken on a mole fraction BMN in CloH, crystal. The 0-0 BMN peak is located at 31 063 cm-l. There are five peaks visible in the 3 1 450-3 1 500-cm-’ region. The peak at 3 1 499 cm-’ corresponds to the 438-cm-l BMN vibronic transition. (This is an in-band pseudo-localized vibron.) Its position remains constant when switching from a BMN-doped CloHs crystal to a doped CloDscrystal. The low-energy C10H8 crystal Davydov component is located at 31 475 cm-’. The remaining peaks located at 4, 8, and 17 cm-’ to the low-energy side of the naphthalene peak are visible only when BMN is present in the crystal. In addition, their position relatiue to the concomitant low-energy Davydov peak is constant when one switches from a doped C10H8 crystal to a doped CI0D8crystal. (The Davydov peak shifts 99 cm-’ to higher energy when going from a C,oH8 to a CloDs crystal.) Reference 8 assigns these peaks as being BMN-induced X-traps. By comparing the relative X-traps and BMN absorbances to the CloHsand BMN absorption coefficients, and by considering the Rashba absorption e f f e ~ t , ~ we ~J~J~ that the BMN-induced energy funnel is limited in size to the nearest-neighbor lattice sites of the BMN molecule. Temperature-Dependent Trapping Efficiency. The presence of energy funnels surrounding the supertrap sites can significantly enhance the rate at which a free exciton is trapped by BMN molecules. This is due to the increase in the effective collisional cross section of the supertrap. Auweter, Braun, Mayer, and Schrnidl6 have proposed a model whereby this increase in the trapping efficiency depends on temperature. The parameter of interest is the transfer rate from an X-trap back to the guest quasi-lattice as compared to the rate from that X-trap to the neighboring supertrap. If the transfer rate from the X-trap to the guest quasi-lattice approaches the transfer rate between normal guest sites, then the energy funnel will have very little effect on the overall trapping rates: the trapping cross section is that of a “bare” supertrap site. This condition is met at moderately high temperatures, Le., high with respect to the 17-cm-’ X-trap depth but low with respect to the 478-cm-’ singlet,19or 240-cm-’ triplet,” BMN trap depth. Lowering the temperature tends to “freeze” the exciton in the energy funnel long enough to allow the exciton to jump to the supertrap. In summary, lowering the temperature raises the energy funnel dependent trapping efficiency. To test whether our triplet trapping rate vs. temperature data (C, = 1.0; Figure 1) are consistent with our X-trap spectra and with the Auweter et al. model, we have extended their model slightly. If AEx is the trap depth of an X-trap, then the rate constant for back-transfer from the X-trap to the guest sites, kbt, will be given by kbt(T) a exp(-AEx/kBT) (2) where kBis Boltzmann’s constant. The overall rate constant, k(T), for trapping from the guest two-dimensional3 quasi-lattice to a supertrap site will depend on temperature as
k(T)/k(O) = R + AR(l - eXp(-AE,/kBT)) (3) where R is the bare-site trapping radius. AR is the change in the
(17) (1963). (18) (1974). (19) 1977. (20)
E. I. Rashba, Sou. Phys.-Solid
State (Engl. Transl.), 4, 2417
F. W. Ochs, P. N. Prasad, and R. Kopelman, Chem. Phys.; 6, 253 E. M. Monberg, Doctoral Dissertation, The University of Michigan, H. Port and H. C. Wolf, Z . Nuturforsch. A , 23a, 315 (1968).
J. Phys. Chem. 1984,88, 3172-3174
3172
trapping radius when X-traps are added in the low-temperature limit. Equation 3 is based on a crude model where all of the supertrap-induced X-traps have the same activation energy. The equation is useful, however, in demonstrating the magnitude of the temperature effect that an energy funnel has on exciton trapping. Our interpretation of eq 3 also assumes that we are in the low-temperature limit with respect to the supertrap depth; Le., R is temperature independent when compared to the temperature dependence of the X-trap back-transfer. We fit eq 3 to the experimental data in Figure 1. The triplet results are listed in Table I along with out absorption singlet X-trap data. We obtained comparable X-trap depths for the triplet temperature and singlet absorption data: 6 and 10 cm-’, respectively. On the other hand, our temperature data predicted an energy funnel radius 3-4 times larger than the nearest-neighbor funnel found by the absorption data. It is difficult, however, to see how perturbations due to one extra CH3group (on the BMN molecule) will significantly perturb naphthalene molecules that are seven nearest-neighbor distances away (or, equivalently, a shell of 112 naphthalene molecules around the supertrap12). There are several possible explanations: ( 1 ) The model which was used to derive eq 3 is too crude. (2) We are comparing triplet exciton data to singlet exciton data, which is not necessarily valid. (3) The X-trap absorption data pertain to an actual radius on the lattice while the temperature data depend on the effective trapping radius which includes other trapping efficiency considerations. As an example, the effective trapping efficiency of a BMN site in the absence of an energy funnel may be significantly reduced by the 240-cm-I energy mismatch20for guest-to-supertrap pairwise transfer. Confining an exciton to an energy funnel will help overcome the subsequent slow X-trap to BMN transfer. (4) Our parametrization in terms of a cross section may also include effects which are actually due to the loss of coherence as discussed in the Introduction. As a further test of the temperature-dependent energy funnel model, we looked at the data reported by Braun, Pfisterer, and Schmid.21 They studied the temperature dependence of singlet exciton trapping by BMN in naphthalene. They analyzed their data with respect to the Agranovich and KonobeevZ2band theory. If we reanalyze their data using eq 3, we find that AEx 7 cm-’ and the energy funnel radius would be approximately 2 times larger than a bare BMN site (cf. Table I). These values are in good agreement with our absorption data. One problem with the energy funnel model is that it does not explain the naphthalene and anthracene triplet transport tem(21) A. Braun, H. Pfisterer, and D. Schmid, J. Lumin., 17, 15 (1978). (22) V. M. Agranovich and Yu. V. Konobeev, Phys. Status Solid, 27,435 (1968).
perature dependence presented in ref 12 and 23. These papers report that the rate of triplet transport in pure crystals becomes slower as the temperature is increased for T > 77 K. This is similar to our low-temperature data. Their data, however, are based on homofusion (exciton annihilation) and therefore should not depend on energy funnels. Conclusions. In a previous paper6 we presented data on the triplet exciton transport temperature dependence as a function of guest concentration in mixed naphthalene crystals. We interpreted the results as showing a transition from hopping transport at low CloH8concentrations to bandlike transport at high CloHg concentrations. We have reanalyzed these results and have now shown that the decrease in the trapping rate constant with increasing temperature in nominally pure CloHs crystals is also consistent with a temperature-dependent energy funnel model. This latter interpretation is consistent in part with X-trap absorption data. This X-trap funnel effect would not be evident at lower CloHs concentrations where the random clusterization of naphthalene sites has the same effect on trapping as X-trap energy funnels. We should also note that either interpretation leads to the conclusion that triplet exciton transport is inchoherent in “pure(neat) naphthalene crystals for temperatures above 1.8 K. The energy funnel model is an incoherent transport model. If the bandlike transport interpretation is correct, then the magnitude of the trapping rate constant indicates a scattering length which is much less than a lattice i.e., incoherent band transport. Furthermore, if we assume that the energy funnel model is responsible, in part, for the temperature effect, it probably is small enough that the trapping efficiency is only enhanced by a factor of 2 or 3. The rate of exciton trapping will still be limited by the rate at which an exciton moves through the CloHg quasi-lattice and finds a BMN site. The singlet exciton data of Braun et alaz1fit extremely well with the energy funnel that we observed directly via the absorption experiment. Thus, the interpretation in terms of an Agranovich and Konobeev coherence (band) model22is probably unjustified.6 We conclude that a very careful analysis is required in order to separate funnel effects from coherence effects, as was also concluded by Kenkre and S ~ h m i d . ~ ~ Acknowledgment. This work was supported by N I H Grant NO. R01 NS80116-16. (23) K. von Burg, L. Altwegg, and I. Zschokke-Granacher, Phys. Reu. B Condens. Matter, 22, 2037 (1980). (24) D. Schmid in “Electronic Excitations and Interactions Processes in Organic Molecular Aggregates”, P. Reineker, H. Haken, and H. C. Wolf, Eds., Springer-Verlag,West Berlin, 1983, Springer Ser. Solid-state Sci. No. 49, p 184; V. M. Kenkre and D. Schmid, Chem. Phys. Lett., 94,603 (1984).
Cyclic Voltammetry of Bilayer Lipid Membranes H.Ti Tien Membrane Biophysics Lab, Department of Physiology, Michigan State University, East Lansing, Michigan 48824 (Received: March 28, 1984) Planar bilayer lipid membranes (BLM) have been extensively employed as models of biomembranes. This paper reports a new type of BLM containing TCNQ (7,7’,8,8’,-tetracyano-p-quinodimethane)whose electrical properties have been investigated by a voltammetric technique. A voltammogram of quinhydrone (BQ/H,Q) is reported for the first time by using the TCNQ-containing BLM. Thus, it is shown that a suitably modified BLM can function as an electronic conductor in aqueous media partaking in redox reactions at the membrane/solution interface. Electron-transfer chains are involved in a number of biomembranes such as the cristae membrane of the mitochondrion and the thylakoid membrane of the chloroplast in energy transduction and utilization.1,2 These electron-transfer systems or redox chains,
made of protein moiety, are embedded in a matrix of lipids in the form of a bilayer and are the functional entities whose active investigations occupy a central domain in membrane bioenerg e t i c ~ . One ~ approach to the study of these complex systems has
(1) Metzler, D. E. “Biochemistry: The Chemical Reactions of Living Cells”; Academic Press: New York, 1977; Chapter 5.
(2) Gregory, R. P. F. “Biochemistry of Photosynthesis”;Wiley: New York, 1978; pp 126-65.
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0 1984 American Chemical Society
