3620
J. Phys. Chem. 1991, 95, 3620-3626
schemes,24they differ in approach and complexity. The relative success of the present simple scheme is due to the way the combined partition function inversion procedure plus switching function describe-by all accounts fairly correctly-the most complicated event, which is the progressive conversion of a reactant transitional vibrational mode first into a hindered, and then a free, rotor in the products. Admittedly the description of this key event neglects completely the coupling of the angular momentum of transitional rotors with the overall rotational angular momentum to give the conserved total angular momentum, a coupling that by contrast the FTST model treats explicitly. Nevertheless the present simplified treatment yields comparable results, which illustrates that the multiple averaging that leads to a thermal rate constant washes out so much of the microscopic detail that one can make do with limited information and very simple representation. There are, to be sure, adjustable parameters: one in the Gaussian switching function, two in the hyperbolic tangent. The present routine can readily accommodate different switching functions and/or potential functions obtained, e.g., from ab initio calculations, which would eliminate in principle (but perhaps not in practice) all adjustable parameters. (Note that even the FTST cannot do without an adjustable parameter.) The Gaussian switching function (eq 20) has the advantage that it uses a single adjustable parameter, which (in units of A-l) comes close to about 0.25 @(Morse)in the two cases examined so far. It remains to be seen if it is endowed with the same apparent universality as the parameter CY in the exponential switching function of eq 3 used in other variational scheme^.'.^ (24) Greenhill, P. G.; Gilbert, R. G . J . Phys. Chem. 1986, 90,3104.
The two-parameter hyperbolic tangent switching function (eq 19) offers obviously a greater flexibility insofar as modeling experimental results is concerned, but no greater insight into the dynamics of the process since there is no recipe for determining the constants a and b in any particular case,beyond the observation that in general, but only very a proximately, a E O.Z@(Morse), after conversion into units of and b E @(Morse). On the surface, the steepest descents routine described in section 4 does not have much to recommend it for speed since it involves a transcendental equation that must be solved by iteration. However each final z2 serves as input for iteration at the next r, generally 0.1 A or less apart. As a result, the various final z2 are not too different, so that two, or a t most three, iterations are sufficient. The implementation as shown in section 4 is for separable harmonic oscillators, but it can be extended to separable Morse oscillators if the requisite data are available, at a modest increase in complex it^.^^ This partition function inversion approach should be useful primarily for microcanonical variational calculation within the framework of conventional RRKM treatment destined to model the falloff of thermal rate constants, on molecules where available information is limited and/or more sophisticated calculations would be prohibitive. Work on halogen-substituted methanes of atmospheric interest is currently in progress.26
1-l
Registry No. CH3, 2229-07-4; H, 12385-13-6. (25) Forst, W.; Prasil, Z. J. Chem. Phys. 1970, 53, 3065. Huy, L. K.; Forst, W.; Prasil, 2.Chem. Phys. Len. 1971, 9, 476. (26) Forst, W.; Caralp, F. J . Chem. Soe., Furuduy Trunr.,submitted for publication.
One-Dlmensionai Triplet Energy Migration in Columnar Liquid Crystals of Octasubstltuted Phthalocyanines Dimitra Markovitsi,* Isabelle Likuyer, CEA. Centre d’Etudes de Saclay, DSM/SCM/CNRS (IRA 331, Laboratoire de Photochimie, 91 191 sur Yvette Cldex, France
and Jacques Simon ESPCI-CNRS, UA 429, hboratoire de Chimie et Electrochimie des Matlriaux Mollculaires. 10, rue Vauquelin, 75231 Paris Cldex 05, France (Received: July 24, 1990; In Final Form: November 9, 1990)
Time-resolved absorption spectroscopy has been used to study laser-induced triplet excitons of the octakis(alkoxymethy1) metal-free and zinc phthalocyanines ((C120CH2)8P~H2, (C180CH2)8PcH2and (C,20CH2)8PcZnJin their crystalline and columnar liquid-crystalline phases. The triplet states have bem characterized by their absorption spectra and their decay kinetics. At early times, the triplet state population varies as r1I2,which is characteristic of diffusion-limited onedimensional triplet-triplet annihilation. The long-time decays are well described by a model of random walk on a linear chain containing traps. The incoherent exciton path length between two successive defect sites is on the order of a micrometer, and it could be correlated with the size of the microdomains. The values of the exciton hopping time (0.4-68 ps) determined from the short-time decay kinetics are in agreement with those determined independently from the long-time behavior of the triplet decay. The exciton diffusion coefficients determined for the columnar mesophases are found to be higher than those observed in the crystalline phases of the same compounds, consistent with a more efficient energy migration in the liquid crystal than in the crystal.
Introduction One-dimensional energy migration has received considerable attention. Numerous theoretical works describe the properties of quasi-one dimensional incoherent excitons.14 Experimentally, (1) Montroll, E. W. Phys. Soe. Jpn. 1969, 26, 6.
(2) Dlott, D. D.; Fayer, M. D.; Wieting, R. D. J . Chem. Phys. 1978,69, 2752.
0022-3654/91/2095-3620$02.50/0
such excitons have been detected b studying luminescence from crystals of 1&dibromonaphthalene, !?1 , 2 , 4 , 5 - t e t r a ~ h l o r o b e , ~ ~ ~ (3) Movaghar, B.; Sauer, G. W.; Wilrtz, D. J . Slur. Phys. 1982,27,473. (4) Torney, D. C.; McConnell, H. M. J . Phys. Chem. 1983, 87, 1941. (5) Redner, S.; Kang, K. Phys. Rev. Lea 1983, 51, 1729. ( 6 ) Blumen, A.; Klafter, J.; Zumofen, G. Opricul Specrroscopy of Glp~ses; Zschokke, I., Ed.; D. Reidel Publishing Co.: Dordrecht, Holland, 1986; pp 199-26 5.
0 1991 American Chemical Society
One-Dimensional Energy Migration in Columnar Phases
The Journal of Physical Chemistry, Vo1.95, No. 9, 1991 3621
'compd phase transitions0 ( C I Z O C H ~ ) ~ P C HK ~ 191C.DM I (C120CH2)8PcZn K Db M).C I (C~~OCH~)~PC KH 62.$ ~ Dy 193.C I
a
L,b A
d,c A
31 31 36
3.6
I, K, crystalline phase: DM, hexagonal columnar disordered phase; Db, hexagonal columnar ordered phase; I, isotropic phase. L, intercolumnar distance. ' d , intermolecular distance within the column; d cannot be determined for the metal-free phthalocyanine columnar phases (DM).
DIV&IGENT LENS
Figure 1. Schematic representation of a columnar liquid-crystalline phase. RO
m MONOCHROMATOR RLTERS
OR DIAPHRAGM
'1
TOTOyllOE ENERGY RATIOMETER
p9
R'O 6 R
Figure 2. Octasubstituted phthalocyanine studied: (C120CH2)8P~H2, M = H2, R = C12Ha; (CI20CH2),PcZn, M = Zn, R = C12H2s; (CIIOCH~)$CH~, M H2, R = C I ~ H , ~ .
manganese salts,' 1-13 from p o l y m e r ~ , ' ~and J ~ from some other materials. All these systems consist of linear chains on which energy transport can take place. The one-dimensional character of each system depends onto which extent interchain hopping can occur. It is well-known that the radiationless energy transfer rate is a function of the separation, d, between the chr~mophores:'~.''
k
a
k
exp(-d)
a
l/dJ
Dexter mechanism FBrster mechanism
where s = 6, 8, or 10 respectively for dipole-dipole, dipolequadripole, and quadrupolequadrupole interactions. Therefore, the one-dimensional character of a system greatly depends on the separation distance between the linear chains compared to the intrachain chromophore distance. From this point of view, columnar liquid crystals appear particularly attractive for such studies. Columnar liquid crystals are usually composed of disklike molecules containing a flat and rigid core, surrounded by flexible hydrocarbon chains.Ie2' Their structure corresponds to stacks (7) Opniko, A. I.; Malysheva, L. I.; Zozulenko, I. V. Chem. Phys. 1988, 121,99. (8) Opniko, A. I.; Zozulenko, I. V. J . Lumin. 1989,43, 173. (9) Hochstrasscr, R.M.; Whiteman, J. D. J . Chrm. Phys. 1972,56,5945. (10)Dlott, D. D.; Fayer, M. D.; Wieting, R. D. J . Chem. Phys. 1977.67, 3808. (1 1) Auerbach, R. A.; McPhenon, G. L. Phys. Rev. B 1987,33, 6815. (12)Knochenmuss, R.; GIldel, H. V. J. Chem. Phys. 1987, 11, 1104. (13) Rodrigues, W. J.; Auerbach, R.A.; McPherson, 0. L. J. Chem. Phys. 1986,85,6442. (14)Peterson, K.;Fayer, M. D. J . Chem. Phys. 1986.85, 4702. (IS) Webber, S. E.;Swenberg, C. E.Chem. Phys. 1980,49,231. (16)Farater, T.Discuss. Faraday SOC.1959,27,7. (17) Dexter, D.L.J. Chem. Phys. 1953,21,836. (18) Chandraackhar, S.;Sadashiva, B. K.; Surcsh, K. A. Pramana 1977, 9,471. (19)Levelut, A. M.J . Chim. Phys. 1983,80,149. (20)Destrade, C.;Gasparoux, H.; Foucher, P.; Nguycn, Huu Tihn; Malthete, J. 1.Chlm. Phys. 1983. 80, 137.
Figure 3. Experimental setup used for the study of thin films by timeresolved absorption spectroscopy.
of molecular disks forming segregated columns (Fi ure 1). In such mesophases the intercolumnar distance is 2 W ,depending on the flexible alkyl chain length (not to confuse with the energy transport chain, which is the column axis), while the intermolecular distance within the column is smaller than 4.5 A. The above structural properties make these phases ideal one-dimensional systems with promising applications as energy guides in the field of molecular data processing. The first photophysical studies of the columnar liquid crystals appeared in 1987.22*23 It has been demonstrated that energy migration can take place in triphenylene,22phthalo~yanine,~~-~' triarylpyrylium,*" and porphyrin29columnar mesophases. The present paper deals with laser-induced incoherent triplet excitons observed with octasubstituted phthalocyanines in their crystalline and liquid-crystalline phases by time-resolved absorption spectroscopy. Particular attention is focused on the decay kinetics which are related to the dimensionality of the exciton migration. Three different discogens are studied (Figure 2): octakis((dodecy1oxy)methyl) metal-free phthalocyanine, (C120CH2)8PcH2,octakis((dodecy1oxy)methyl)zinc phthalocyanine, (C120CH2)8PcZnand the octakis(octadecyloxymethy1) metal-free phthalocyanine, (C180CH2)8P~H2. The synthesis and the structural characterization of their organized phases have been reported p r e v i ~ u s l y . ~ 'The * ~ ~crystal ~ to liquid crystal transitions
1
(21)Picchocki, C.;Simon, J. N. J . Chim. 1985,9, 159. (22)Markovitsi, D.; Rigaut, F.; Mouallem, M.; MalthZte, J. Chem. Phys. Lett. 1987. 135. 236. (23)Blanzat, B.; Barthou, C.; Tercier, N.; AndrQ J. J.; Simon, J. J. Am. Chem. Soc. 1987,109,6193. (24)Markovitsi, D.; Tran-Thi, T. H.; Briois, V.; Simon, J.; Ohta, K.J. Am. Chem.-Soc. 1988.110.2001. (25)Markovitsi, D.'; Wuyer, I. Chem. Phys. Lett. 1988,149,330. (26)Blassc, G.; Dirben, G. J.; Meijerink, A,; Van Der Pol, J. F.; Neeleman, E.;Drcnth, W. Chrm. Phys. Lett. 1989,154,420. (27)Markovitsi, D.; Lkuyer, I.; Simon, J. Chrm. Phys. Leu. 1990, 167, 467. (28)Markovitsi, D.; Lfmyer. I.; Clergwt, B.; Jallabert, C.; Strzelecka, H.; Veber, M. Liq. Crysr. 1989,6, 83. (29)Gregg, B. A.; Fox, M. A.; Bard, A. J. J. Phys. Chem. 1989,93,4227. (30)Picchocki,C.; Simon, J.; Skoulios, A.; Guillon, D.; Weber, P. J. Am. Chem. Soc. 1982,104,5245. (31) Guillon, D.; Skoulios, A,; Piechocki, C.; Simon, J.; Weber, P. Mol. Cryst. Liq. Cryst. 1983,100, 215. (32) Guillon, D.; Weber, P.; Skoulios. A.; Piechocki, C.; Simon, J. Mol. Crysr. Lis. Cryst. 1985,130, 223.
3622 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 take place at 79,78, and 62 OC, respectively, for (C120CH2)8P~H2, (C120CH2)8PcZn,and (C180CH2)~PcH2,and the mtsophases are stable in a very large temperature range (Table I). In the mesophases the distance between two neighboring columns is 31 A for the dodecyl derivatives and 36 A for the octadecyl derivative. The mean stacking distance is found to be 3.6 A for the zinc complex (Dh: ordered mesophase), while it cannot be determined for the metal free compounds (Du: disordered mesophase). In the solid phases at room temperature, the columnar structure is preserved; X-ray diffraction patterns obtained with (C120CH2)8P~H2 show that a tilting angle of about 24O between the macrocycle planes, and the column axis induces an orthorhombic structure (a = 24.6 A, b = 19.4 A, c = 4.3 A).33 When the (CI80CHJ8PcH2is heated to the liquid-crystal temperature domain and then cooled down to 20 "C, it forms a metastable phase whose structure is similar to the mesomorphic one.
Markovitsi et al.
wavelenpth
Apm)
Figure 4. Steady-state absorption spectra of (C120CH2)8PcH2 in (-) homogeneous solution ( lod M, toluene), (-- -) crystalline phase, and liquid-crystalline phase; (a) macrocycle plan- perpendicular to the column axis (hexagonal lattice); (b) macrocycle planes tilted (monoclinic form). (-e-)
Experimental Part The organized phase spectroscopic cells used for the time-resolved measurements consisted of a quartz slide on which a few milligrams of powder compound were deposited; the slide was then heated to 200 OC and pressed on the surface of a quartz flow cell. The sample thickness (1, = 9-20 pm) was measured with a micrometer. For steady-state absorption studies a small quantity of compound was spread on the heated flow cell; in this case the sample thickness was smaller than 1 pm, and it was evaluated by comparing its optical density at several wavelengths to that observed with cells of a known thickness. Temperature control was achieved via water circulation in the flow cell using a Haake N2-B circulator. The time-resolved absorption spectrometer used as exciting light the second harmonic of a Nd:YAG laser (532 nm, 9 4 s fwhm, single shot). To obtain uniform excitation on thin-film samples, the laser beam passed through a divergent lens (six dioptries) before arriving at the sample holder whose aperture surface (20-30 mm2) determined the excited area, S (Figure 3). The probing light (xenon arc, Osram XBO 450W/1) was perpendicular to the sample, and it formed an angle of 30° with the laser beam; it was dispersed in a Huet M25 monochromator and analyzed by a Hamamatsu R928T photomultiplier and a Tektronix 7834 memory ascilloscope. Adequate filters were used to avoid sample excitation with the probing light, in particular when the latter was intensified (Schott BG23 and WG series) and to eliminate stray light from the laser (MTO DA429a). The laser pulse energy was measured with two different Rj 7200 energy ratiometers (Laser Precision Instruments); it was varied by using neutral optical density filters (Schott NG series). For the determination of the incident energy, the spectroscopic cell was replaced by a quartz slide (Figure 3), and the average of 10 values was used. The laser pulse intensity was kept lower than 3 X 10l6 photons cm-2. The fluorescence lifetimes of the homogeneous solutions have been measured with a single-photon-counting spectrometer described in detail elsewhere.28
M)o
(102)
3
2
1
,I
A'
A!
k, 'L,
L
Photophysical Characterizations Homogeneous Solutions. The steady-state absorption spectra of (C120CH2)gPcH2, (C120CH2)8P~Znr and (C180CH2)8P~H2, obtained with dilute toluene solutions ( 5 X lod M) are identical with those observed with the corresponding unsubstituted metal-free (PcH,) and zinc (PcZn) phthalocyanines.u The same similarity is observed for the triplet-triplet absorption spectra obtained following laser excitation at 532 nm with outgassed toluene solution^.^^^^ Moreover, the triplet lifetimes { 125 f 15 ps for ( C 1 2 0 C H 2 ) 8 P ~ and H 2 (C180CH2)8PcH2, 230 f 10 ps for (33) Ohta,K.; Jacquemin, L.; Sirlin, C.; Bosio, L.;Simon, J. N e w / . Chem. 1988, 12, 751. (34) Lever, A. B. P. Adu. Inorg. Chem. Radiochem. 1965, 7 , 27. (35) Pyatosin, V. E.; Tsvirko. M.P. Zh. Prikl. Spcrrosc. 1980,33,320. ( 3 6 ) McVie, J.; Sinclair, R.S.;Truscott, T. G. J. Chem. Sac., Faraday Trans. 2 1978, 1870. (37) Jacques, P.; Braun, A. M.Helv. Chim. Acta 1981. 61, 1800.
~~
(38) Harriman, A.; Richoux, M.C. J. Chem.Soc., Faraday nuns. 2 IW,
76, -16 18.
(39) Than-Thi, T.-H.; Dcsforge, C.; Thiec, C.; Gasprd, S. J. Phys. Chem.
1989, 93,
1226.
(40)Stadelmann, H.R. J. Lumin. 1972,5, 171.
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3623
One-Dimensional Energy Migration in Columnar Phases bOD(I:o)
1
I
TABLE 11: Sample Characteristics
.-•
OD ~
r
ym
ChbM (532 nmY
c0,d
M-'
cm-'
I'.
ym
20 OC 85 oc
20
0.51 0.46
2.7 2.5
2600 2700
8 8
20 90
16
0.51 0.46
1.7 1.6
2100 2200
10 10
0.45 0.40
1.0 1.0
2800 2800
9 9
(C,@CH2)8PCZn O C
oc
(CI~OCHZ)~PCH~
I
P 0
comd I,! (C,zOCHz)*PcHT ~~
2
4
6
1.
(lO'*photons / c d )
Figure 6. Zero-time differential optical density variation as a function of the absorbed laser pulse intensity; (C1z0CHz)8PcH2 at 20 OC.
20 OC 71 O C
9
OI,, measured thickness of the sample. bCo,ground-state conccntration, evaluated on the basis of density measurements and the structural parameters of the various phases. OD, ground-state optical density at 532 nm. molar extinction coefficient at 532 nm. *le, effective optical path length, corresponding to the sample thickness for which the optical density at 532 nm is equal to 1.
mensional linear stacks at van der Waals distances and are also observed in the case of oxygen-linked polymeric phthalocyanines.41 the (C180CH2)8PcH2 at 20 OC. On the contrary, the existence of a split band is observed in at 20 obliquely stacked structures of phthalocyanine ~ r y s t a l s . ~ ~ . ~ ~Similar experiments performed with (C120CH2)8P~Zn OC have revealed that saturation occurs even at very low laser Therefore, the changes observed in the absorption spectra at the pulse intensities (I = 0.8 X lOI5 photons cm-2). In this case, the transition temperatures are in agreement with the structural plot of AODo versus I, does not display any linear part and Ae changes from a hexagonal columnar phase, in which the column cannot be determined by this method. The maximum tripletaxes are perpendicular to the macrocycle planes (Figure 4a) to triplet absorption coefficients, €T,-T., of unsubstituted PcZn and a tilted conformation (monoclinic form, Figure 4b); the PcH2 are respectively 2.9 X lo4 and 3.0 X lo4 M-' cm-' in ho(C180CH2)8PcH2 solid state obtained by cooling the mesophase mogeneous soluti0ns.4~It can be assumed that the metal-free and retains the hexagonal structure. zinc octasubstituted phthalocyanines have practical1 the same Figure 5 shows the differential absorption spectra obtained with ~T,-T,. Therefore, the value Ac = (5.5 f 1.5) X 1 O Y W cm-l (C120CH2)8P~H2 at 0.2 ps following laser excitation (532 nm, determined for (C120CH2)8P~H2 and (C180CH2)8PcH2at 20 OC 9 ns) of the Q band; similar spectra are obtained with both of the will be used also for (C120CH2)8PCZn.Moreover, the crystal to other compounds. All of them peak at 5 W 5 1 0 nm, which is characteristic of the phthalocyanine triplet-triplet a b s o r p t i ~ n ? ~ ~ ' mesophase transition is not expected to cause a large change in the absorption coefficient (see Figure 4). The differential spectra obtained with the liquid crystals are slightly blue-shifted with respect to those observed with the solid Incoherent Triplet Exciton Decay Kinetics phases. Theoretical Models. In nonisotropic media, the experimental Figure 6 shows the variation of the zemtime differential optical kinetic data can be fitted to various theoretical models, greatly density, AODo, which is proportional to the triplet-state concendepending on the dimensionality of the studied system. Nonotration, at 500 nm, as a function of the absorbed light intensity, riented columnar liquid crystals are locally anisotropic, and I., obtained for (C120CH2)8P~H2 at 20 O C . For low intensities one-dimensional models seem appropriate to describe exciton (I, < 1 X 10I6photons cm-2), AODo is approximtely proportional decays. However, on a macroscopic scale, the material shows no to I,. As I, increases, a saturation effect is observed, at triplet anisotropy; from this point of view, a three-dimensional model concentrations much lower than the ground-state concentration can be tentatively used. (-l'%), indicating a decrease in the triplet quantum yield, &. In transient absorption experiments, the well-known exponential This is probably due to singlet-singlet annihilation,& which, at and second-order decay laws, corresponding respectively to mohigh excitation intensities, may constitute an additional pathway nomolecular and bimolecular triplet deactivation, are valid only for the singlet deactivation competing with the intersystem in the conditions of a well-stirred reactor, Le., when the spatial crossing. distribution of the triplet states remains homogeneous during the From the slope AODo/I, of the quasi-linear part of the curve whole course of the reaction. The above kinetic models may also in Figure 6, it is possible to evaluate the differential molar exbe applied when triplet migration is taking place in three ditinction coefficient: Ae = +,-Tn - e-,. The Beer-Lambert law mensions. For onedimensional systems, the exact monomolecular gives and bimolecular decays have been calculated through computer simulations; under certain conditions, analytical approximations At = AODo/l,CT (1) are also available (reviewed in detail in refs 6 and 7). These where CTis the triplet concentration in mol L-' and le the effective analytical expressions are presented below. path length (cm, see Table 11). C, can be expressed by means Pseudomonomoleculardecay: An exciton performing a random of the absorbed light intensity, I, (photons cm-2) and the triplet walk on a linear chain may encounter a trap (a chemical impurity quantum yield, &; hence or a structural defect) and be rapidly deactivated. For randomly distributed traps, the exciton long-time decay is described by the Ac = 6 X 1020A0Do/t#TI, (2) equationV-7.I 3 Taking for h the value determined for the phthalocyanine dilute solutions (& = 0.17)," Ae is found to be (5.5 i 1.5) X l e M-1 cm-I at 500 nm. The same value has also been determined for (41) Dirk,C. W.; Tamotsu, I.; Schoch, K.F.;Marks, T. J. J . Am. Chem.
Soc. 1983, 105, 1539.
(42) Sharp, J. H.; Lardon, M. J. Phys. Chem. 1968, 72, 3230. (43) Sharp, J. H.; Abkowitz, M. J . Phys. Chem. 1973, 77,477. (44) Carmichael, 1.; Hug, G. L. J . Phys. Chcm. Ref. Dora 1986, 15, 1. (45) Carmichael,I.; Helman, N. P.;Hug, G. L.J. Phys. Chem. Ref.Dora 1987, 16, 239. (46)Ho, Z. Z.; Peyghambarian, N. Chcm. Phys. Lcrr. 1988. 148. 107.
n ( t ) / n ( o ) = xt,(t/T)1/2 e ~ p ( - l . g ( * ~ x , , 2 t / ~-) ~@t} / ~ (3) for t > T/*~X,~, where n(t) and n(0) are the exciton concentration respectively at time t and time zero (mol ~ m - ~ ) , is 8 'the exciton lifetime in the absence of traps (SI), x, is the trap molar fraction, and T is the exciton hopping time. Assuming that the lifetime 8' is very long compared to the observation time scale and replacing the exciton concentration by the transient optical density (AOD(t) = 103Aen(t)le], eq 3 is rewritten In AOD(t) = In (at)'/2- 4.05(~1r)~/~ +b (4)
3624 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991
Markovitsi et al.
TABLE 111: Experimental Triplet Decay Cluncteristics io-'k:
"pd
~ 1 / 2
(CIZOCHZ)~PCHZ 20 OC 1.6 f 0.1 85 OC 4.1 f 0.3 (C120CHz)IPcZn 20 OC 1.2 f 0.1 90 OC 14.4f 1.0 (ClsOCHZ)8PcHz 20
oc
77 o
1.5 f 0.1
1.4f 0.1
c
I O ~ A O D ~icra: ~
s-1
9.0 f 0.5 9.0 f 0.5
2.3 f 0.3 8.5 f 1.0
10.0 f 0.5 6.5 f 0.5
1.2 f 0.3 65 f 15
28 f 2 34 f 2
20
*2
17f 1
"k,slope of the linear plot I/AOD a f l / l (Figure 7). "OD&, differential optical density at the threshold between the two kinetic schemes. parameter giving the best fit for the plots In AOD versus t , according to the function In (ur)1/2- ( ~ t ) l(Figure /~ 8); u = x ~ / T , where x, is the trap molar fraction and T is the exciton hopping time. 0 0
A
50
100
Ln (Am) I
1'
150
200
I
1
t (ps)
I
I
01
0
t
2
1
$12 (10.3
s'h )
Short-time triplet decay kinetics observed with the (CIzOCH2),PcH2at 500 nm following laser excitation (532 nm, 6 ns); the average of 10 independent ex riments is shown. 20 OC: (m)0.9 X 10" photons c d , (0)1.1 X IO1 photons 85 OC: (0)1.2 X 10l6 photons cM2, (A) 2.5 X IO1* photons cm-'.
Figure 7.
,
gc
Liquid Crystal
for r > 1/r2a, with a = x,,Z/r and b = constant. Bimolecular decay: The one-dimensional diffusion-limited triplet-triplet annihilation is described by a Smoluchowski-type eq~ation:~.~**
n(t)/n(O) = I1
+ n(0)/dNo(32Dt/?r)1/2)-'
(5)
where d is the one-dimensional lattice constant (cm), No and C, are the ground-state concentration respectively in mol cm-3 and mol L-' (No = lW3 Co),and D is the exciton diffusion coefficient (cm2 d). Replacing the exciton concentration by the differential optical density, eq 5 can be written l/AOD = l/AODo
+ kr1i2
(6)
with
k = (AcdleCo)-1(32D/r)1/2 The exciton hopping time, 7
T,
(7)
which is given by the formula
= &/2D
(8)
can then be determined as follows: 7
= 16/r(AckleCo)2
(9)
The experimental results have to be fitted to the most appropriate models (1-D or 3-D).At low excitation intensities, only a few triplet states are generated, and monomolecular decay takes place. Such a low triplet concentration is also obtained when mast of the triplet states have already been annihilated, i.e., a long time after the laser excitation. At shorter times the bimolecular process (triplet-triplet annihilation) can be observed if the excitation intensity is high enough. The threshold between the monomolecular and bimolecular proceses depends on both triplet migration efficiency and the trap molar fraction.
0
10
20
30
40
t
(PSI
Longtime triplet decay kinetics observed with the (Cl,0CHz)8PcH2at 500 nm following laser excitation (532 nm, 9 ns), and 85 OC (1.2 X 10l6photons cm-z). at 20 (1.1 X 10I6photons The dashed lines correspond to the function In ( u t ) 1 / 2- ( U ~ ) I / u~ ;= 2.3 X IO4 s-l at 20 OC and u = 8.5 X lo's-' at 85 OC. The average of 15 independent experiments is shown. Figure 8.
Results and Discussion Figure 7 represents the reciprocal differential optical density, observed with (C120CH2)8PcH2 at early times of the triplet exciton decay, plotted versus f1/2 (bimolecular diffusion-limited 1-D model). Two different temperatures are shown corresponding to the solid crystalline (20 "C) and the liquid crystalline (85 "C) phases. For laser intensities of -1 X 10l6photons cm-2, the 1/AOD versus plots are approximately linear up to a certain threshold differential optical density, AOD*. The slope, k,of the above linear plots and the AOD* values are listed in Table 111. With increasing laser intensity the AOD* value remains constant, but it is observed at longer times. A further increase of the laser intensity may deteriorate the organized phase structure; this is detected by a change in the decay for the same triplet concentration. When the laser intensity is too weak, the plots are no more linear. Two representative examples depicting the variation
One-Dimensional Energy Migration in Columnar Phases TABLE I V Orgadzed P Exciton Decay Klnetics
h Roperties Determined from Triplet
comd 104x,,,# (C~OCHZMCHZ 20 *c 85 OC
(C lzOCH2)8PcZn 20 OC 90 OC (CI8OCH2)8PCH2 ~~
20 O
C
77 "C
I~x,,"
IO-'NC t,"pm
4.0 4.5
8.0 9.0
2.5 2.2
3.6 2.6
7.1
2.8
5.1
3.8
13 17
26 34
The Journal of Physical Chemistry, Vol. 95, NO. 9, 1991 3625 TABLE V Properties of the One-Mmdonal Triplet Exciton (Orders of Magnitude) 1'10 p Q,( ps 10"; cmz s-I "Pd
(CI zOCHZ~PCH z 20 OC
0.9-1.1O
85 OC
0.8-1.W
40 1.4
28
45 0.4
42 0.4
46 66
34 68
9.5
1.6-2.5' 8-14.
(C120CH2)8PcZn
0.8
0.6
20 o c 90 OC
1.0 1.4
(Cl8OCHz)8PcHz 20 "C 77 OC
0.3-0.4' 0.2-0.3'
Oxtb,triplet exciton molar fraction at the threshold between the two kinetic schemes I/AOD a f1I2and In (AOD)a In (uf)'12 - (ut)Il3. b ~ t ,trap , molar fraction: x,, = 2xtb. N,average number of molecules in the column between two traps; N = 2/x,. d L , mean column length between two traps; L = Nd. 'Postulating an intermacrocyclic distance, d, of 3.5-4.5 A.33
of the decay with the exciting light intensity are shown in Figure 7. Similar experiments were carried out in the long-time range, where the monomolecular decay process is expected to be predominant. The experimental points have been fitted to eq 4 (Figure 8); the dashed lines correspond to the function In - 4 . 0 5 ( ~ ? ) ' / ~The . a values giving the best fits with the experimental decay curves are listed in Table 111. From these values it can be checked that the time scale of our observations is situated within the validity domain of eq 4 t > 1/&. Another assumption that has to be checked is related to the inherent lifetime of the triplet exciton, PI, neglected in eq 4. The studied organized phases cannot be oriented, and consequently they always contain structural defects. For this reason it is impossible to determine experimentally. However, it is expected to increase as the mobility of the molecules decreases. For example, the anthracene triplet lifetime is 0.9 ms in hexane and 85 ms in PMMA solutions." Therefore, it seems reasonable to assume that the phthalocyanine triplet state in the crystalline and liquid-crystalline phases decays in the millisecond time scale since in toluene solutions the triplet , for the lifetime is found to be 125 and 240 ~ s respectively, metal-free and the zinc derivative. The triplet decay curves obtained with (C120CH2)8PcZnand (C,80CH2)8PcH2can be fitted to the same functions as those used for (C120CH2)8P~H2 (Table 111). These results show that the early behavior of the triplet exciton decay is consistent with one-dimensional annihilation and its long-time behavior can be fitted with a kinetic model describing a random walk on a linear chain containing traps. The exciton molar fraction at the threshold between the two decay modes, x&, is determined according to the equation Xth = AODth/AtI,Co (10) Considering that annihilation cannot occur any longer if there is one exciton left per linear chain, the trap concentration, xtrrcan be related to xth:
xtr = 2xth (11) The average number of molecules in the column contained between two traps, N , and the corresponding column length, L, are given respectively by N = 2/xtr (12) L = Nd (13) Table IV gives the xth, xtr,N , and L values determined for the phthalocyanine organized phases. The column length between two traps corresponding to the dodecyl derivatives, for both the crystalline and the liquid-crystalline phases, is the order of a micrometer. The monodomains formed in nonoriented liquid crystals may have this size; therefore, it seems that the column ends in each monodomain could behave as traps for the triplet excitons, in particular if oxygen molecules are confined in this region. It is interesting to note that the number of molecules in
1.5 170 1.3-2.2'
0.9-1 -5'
q, exciton hopping time determined from the short-time decay curves (eq 9, Figure 7). b12,exciton hopping time determined from the long-time decay curves (eq 4, Figure 8). D, exciton diffusion coefficient (eq 7). 'Postulating an intermacrocyclic distance, d, of 3.5-4.5 A.33
the stack (4OOO) evaluated for the (C120)8PcH2ordered columnar phase on the basis of steady-state fluorescence experiments26 is very close to the N value (3800) determined here for the ordered mesophase of the (C120CH2)8PcZn. It is possible to determine an order of magnitude for the exciton hopping time by two independent methods, based either on the short-time or on the long-time decay kinetics. In the first case, T, is obtained through eq 9, using the slope k of the 1/AOD versus plots (Figure 7). In the second case, the parameter a giving the best fit in the long-time decay (Figure 8) and the trap molar fraction (Table IV) yield T~ (eq 4). The values of T~ and 7 2 determined for each of the organized phases studied (Table V) are very similar. The triplet exciton hopping times determined for molecular crystals (anthracene, naphthalene, stilbene, etc.) are of the same order of m a g n i t ~ d e . 4 ' ~ ~ The values of the trap molar fractions, the hopping times, and the exciton diffusion coefficients, listed in Tables IV and V, indicate only an order of magnitude. This is due to the uncertainty in the determination of the optical path length, I, and of the differential extinction coefficient, At, resulting from two assumptions: I, corresponds to the sample thickness for which the optical density at the excitation wavelength is equal to 1 (Table 11) and Ae is taken to be the same for all the samples. The hopping time is found to be shorter in the liquid crystal than in the crystal by at least a factor 5 for the (C120CH2)8P~H2 and a factor of 110 for the (CI20CH2),PcZn. Moreover, the exciton diffusion coefficient is found to be higher in the liquid crystal than in the crystal. These results are consistent with a more efficient energy migration in the mesophase than in the solid state. Steady-state fluorescence experiments, performed with mixtures of metal-free and copper phthalocyanine columnar phases led to the same conclusion for the migration of the singlet exciThe D values determined for the (C120CH2)8PcZna t 90 OC indicate that energy migration is more efficient in an ordered columnar phase. The fact that no significant difference has been detected between the decays of (C180CH2)8PcH2at 20 and 77 OC is attributed to the structural similarity of the mesophase and the metastable crystalline phase. Finally, the comparison of the hopping times determined for (CI20CH2)8PcH2 and (C,80CH2)8PcH2could suggest that the lengthening of the lateral chains is rather unfavorable for the triplet exciton migration. The long-time triplet decays can also be fitted with the sum of a classical 3-Dsecond-order law and an exponential term.24*25 This decay mode should correspond to a three-dimensional t r i p let-triplet annihilation and triplet migration (intercolumnar h ~ p p i n g ) . ' ~However, *~~ such a kinetic model is not valid at short times and does not permit the determination of a triplet-triplet annihilation constant, YT-T (YT-T = 1.7 X 1C2'k'Atle), since YT-T (47) Kepler, R. G.; Switendick, A. C. Phys. Rev. Lett. 1965, 15, 56. (48) Yokoi, K.; Ohba, Y. Chem. Phys. Lett. 1986, 129, 240. (49) Wolf, H. K. In Advances in Atomic and Molecular Physics; Bates, D. R., Ed.; Academic Press: New York, 1967; Vol. 311, pp 119-142. (50) Efremov, N. A.; Kulikov, S.G.; Personov, R. I.; Romanovskii, Y. V. Chem. Phys. 1988, 128,9.
J , Phys. Chem, 1991, 95,3626-3630
3626
The transient differential absorption spectra obtained following laser excitation in the Q band with the thin films show the formation of a triplet state in the crystalline and liquid-crystalline phases. Both the 1-D and the 3-D models have been used to analyze the triplet decay curves. In the first case, at early times, the exciton population varies as f which is characteristic of diffusion-limited one-dimensional triplet-triplet annihilation, and the longtime decays are well described by a random walk on a linear chain containing traps. In the second case, the decays are fitted with the sum of an exponential term and a classical second-order law (C, a t-l); the triplet-triplet annihilation %onstant+' determined in this way greatly depends on the excitation intensity. On the contrary, the variation of the excitation intensity has no influence on the parameters determined with the 1-D model; therefore, the 1-Dmodel is more appropriate to describe the triplet migration in the examined organized phases. The exciton path length between two successive traps is on the order of a micrometer, and it could be correlated with the size of the microdomains. The values of the exciton hopping time (0.4-68 ps) determined from the short-time decay kinetics are in agreement with those Summary and Conclusions determined independently from the long-time behavior of the The most important findings of the photophysical studies of triplet decay. the octasubstituted phthalocyanines ( C 1 2 0 C H 2 ) 8 P ~ H 2 , The exciton diffusion coefficients determined for the columnar (C120CH2)8PcZn,and (C180CH2)sPcH2can be summarized as mesophases are found to be higher than those observed in the follows: crystalline phases of the same compounds. Moreover, triplet In dilute homogeneous solutions the alkoxy chains, attached migration seems to be favored by the ordering of the mesophase. to the phthalocyanine ring through a methylene group a t the 3 In conclusion, this work has revealed the one-dimensional and 4 positions, have no significant influence on the photophysical character of the triplet migration in both the crystalline and the properties (absorption and fluorescence spectra; fluorescence and columnar liquid-crystalline phases of the phthalocyanine derivatives triplet lifetimes) of the phthalocyanine chromophore. and has shown that energy migration is more efficient in the liquid The changes in the thin-films absorption spectra observed in crystal than in the crystal of the same compound. the crystal to liquid crystal temperature are in agreement with Acknowledgment. We are highly indebted to Dr.Ross Brown a modification of the molecular arrangement from a monoclinic for fruitful discussions. structure to a hexagonal stacking. greatly depends on the excitation light intensity. For exam le, in the case of (C120CH2)8PcH2 a t 85 "C, 7T-T = IS X lo-' Ps-' when I = 1.1 X 10I6photons cm-l and 7T-T = 6 X cm3 s-I when I = 2.6 X 10l6 photons On the contrary, for the same variation of the light intensity, the parameter a, corresponding to eq 4, remains constant. This remark and the good agreement between the short-time and long-decays prove that the 1-D model is more appropriate to fit the experimental results. Comment: Our first findings concerning the triplet states in the (C180CH2)8PcH2and (C120CH2)8P~Zn columnar phases were published in two short communication^.^'*^^ The decays reported in these papers were observed within only a decade of time; the time scale was chosen so that a 90% decrease in the differential optical density could be detected. The later improvement of our experimental method allowed us to avoid artifacts related to strongly absorbing samples (triplet exciton formation due to the probing light, local fusion of the samples, etc.) and to detect the decays on a longer time scale (about 3 decades of time). Therefore, the present work is based on more complete and reliable experimental data, and it takes into account more appropriate kinetic models.
Kinetics of Reactions of Halogenated Methyl Radicals with Hydrogen Iodide Jorma A. Seetulat and David Gutman* Department of Chemistry, Catholic University of America, Washington, D.C. 20064 (Received: August 6. 1990; In Final Form: November 9, 1990)
The kinetics of the reactions of CH21, CH2Br,CH2CI,and CHCI2 with HI were studied in a tubular reactor coupled to a photoionization mass spectrometer. Rate constants were measured as a function of temperature (typically between 294 and 552 K) to determine Arrhenius parameters. For these and other R + HI reactions studied to date (Le,, those involving alkyl radicals), a linear free energy relationship was discovered which correlates the large differences in reactivity among all these R + HI reactions with the inductive effect of the substituent atoms or groups on the central carbon atom.
+
The reactions of polyatomic free radicals (R)with hydrogen iodide are of considerable interest in the fields of chemical kinetics and thermochemistry. This is due largely to the fact that a significant portion of our current knowledge of the thermochemistry of polyatomic free radicals has been derived from kinetic studies of the equilibriumI4
R
+ HI =RH + I
the exothermic R H I reactions are rapid and they replace an active intermediate (R)with a relatively inactive one (I). Golden and Benson have succinctly pointed out that the radical-trapping ability of HI derives from the fact that the bond dissociation energy of H I (71 kcal mol-') represents the strongest bond an I atom can make and one of the weakest that an H atom makes.' (This fact further implies that a radical R will always abstract H from HI and never the reverse.)
(A)
A second interest in these reactions arises from the fact that HI can be used as a radical trap for polyatomic free radicals in
reacting system^.^.^ Its use for this purpose is effectual because Permanent address: Department of Physical Chemistry, University of Helsinki, Helsinki, Finland.
0022-3654/91/2095-3626$02.50/0
(1) Golden, D. M.; Benson, S. W. Chem. Reo. 1969, 69, 125. (2) O'Neal, H. E.; Benson, S.W. In Free Rodicols; Kochi, J. K., Ed.; wiley: NCW York, 1973; vol. 2, Chapter 17. (3) Walsh, R. Acc. Chem. Res. 1981, 14, 246. (4) Soctula, J. A.; Russell, J. J.; Gutman, D. J. Am. Chem. Soc. 1990,112, 1347. (5) Benson, S.W.; ONeal, E. J . Chem. Phys. 1%1,31, 514. (6) O'Neal, E.; Benson, S. W. J . Chem. Phys. 1962.36, 2196.
0 1991 American Chemical Society
