Article pubs.acs.org/JPCC
Self-Assembly of Linear Porphyrin Oligomers into Well-Defined Aggregates Joakim Kar̈ nbratt,† Mélina Gilbert,† Johannes K. Sprafke,‡ Harry L. Anderson,‡ and Bo Albinsson*,† †
Department of Chemical and Biological Engineering/Physical Chemistry, Chalmers University of Technology, 412 96 Göteborg, Sweden ‡ Chemistry Research Laboratory, Department of Chemistry, Oxford University, 12 Mansfield Road, Oxford OX1 3TA, U.K. S Supporting Information *
ABSTRACT: Conjugated zinc porphyrin oligomers of various lengths are shown to form well-defined planar aggregates at low temperatures. The aggregation occurs over a narrow temperature interval (170−150 K) and is accompanied by dramatic changes in the electronic absorption and emission spectra. Similar changes are found in J-aggregates in which the transition dipole moments of aggregated chromophores couple to form a new and intense transition in the absorption spectrum, red shifted from the monomeric chromophore band. For the present porphyrin oligomers, the dramatic absorption changes are not associated with the formation of large aggregates, but rather with the dimerization accompanied by planarization of the oligomers. Free oligomers have a broad distribution of porphyrin−porphyrin dihedral angles and show a broad and unstructured absorption spectrum. As the oligomers stack to form aggregates, they planarize and the width of the conformational distribution is reduced to include virtually only the planar conformers, resulting in the observed change of the absorption spectrum. No experimental evidence for the formation of large aggregates was found, while a small aggregate, probably only dimer, is supported by the minor changes of the fluorescence rate constant upon aggregation and the fact that pyridine has no significant effect on the formation of this aggregate, which otherwise is very effective for inhibiting aggregation of zinc porphyrin oligomers. Compared to most porphyrin aggregates, which show broad absorption spectra and quenched fluorescence, these aggregates give sharp absorption and emission spectra with little change in the fluorescence quantum yield. Similar aggregates were also observed for oligomers substituted with both a fullerene electron acceptor and a ferrocene donor. The results presented here will be potentially useful as tools to understand how electron transfer and delocalization processes are influenced by molecular order/disorder transitions.
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INTRODUCTION
shown that the spectral properties of these CPOs are determined by the backbone conformation.12 Planar species, with a fully conjugated system, have red-shifted spectra compared to their twisted counterparts. The ground state is, due to the low barrier for rotation, a broad distribution of different conformations, and the observed absorption spectrum is a weighted average of the individual conformer absorptions and hence, at least for the longer oligomers, is quite broad and unstructured. For the potential applications of the linear porphyrin oligomers, such as extended electronic communication, it is of great importance to be able to control this distribution. It has been shown that the oligomers can be forced into a planar conformation, by coordination to the zinc atoms with multidentate axial ligands to form planar constructs or ladder complexes.13,14 Because we were interested to investigate how temperature influences the conformational distribution, a sample of the porphyrin octamer P8 was slowly cooled in 2-methyltetrahydrofuran (MTHF). Surprisingly, not much happened to the absorption spectrum between room temperature and 170 K,
Conjugated porphyrin oligomers (CPOs) are promising materials in many areas of molecular engineering and have been suggested as building blocks for several diverse applications such as artificial photosynthesis,1 novel optical materials,2−6 photodynamic therapy,7 and molecular scale electronics.8−11 This study focuses on a series of butadiynelinked Zn-porphyrin oligomers spanning from monomer (P1) to octamer (P8) (Figure 1) and their capacity toward the spontaneous formation of well-defined supramolecular aggregates. The individual porphyrin moieties are strongly coupled as seen in the evolution of their ground state spectra going from the monomer to the octamer (Figure 2). It has previously been
Received: February 10, 2012 Revised: August 22, 2012
Figure 1. Porphyrin oligomers studied in this work (Pn, n = 1, 2, 3, 4, 6, 8). The aryl substituents, Ar, are 3,5-di(octyloxy)phenyl. © XXXX American Chemical Society
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Figure 2. Room temperature ground state absorptivities of P1 (black), P2 (red), P3 (green), P4 (blue), P6 (cyan), and P8 (magenta) in chloroform with 1% pyridine added.
Figure 3. Temperature dependent absorption of P8 (upper), P6 (middle), and P4 (lower) in MTHF. The displayed temperature intervals are 170−150 K for P8 and P6 and 165−135 K for P4. A weak baseline distortion at 900 nm is observed at lower temperature and is attributed to changes in the solvent absorptivity (vibrational overtone absorption).
but between 170 and 150 K a dramatic change was observed. This sudden change is interpreted as a signature of the formation of spectroscopically well-defined aggregates accompanied by a planarization of the oligomers. We here show how temperature can be used to form highly structured, apparently monodisperse aggregates with remarkable photophysical properties. Similar dramatic spectroscopic changes have been observed for various cyanine dyes15,16 and also for charged monomeric porphyrins in aqueous solutions,17 and in these cases a so-called J-aggregate formation has been advocated as the model.18 In this paper, we show that for the porphyrin oligomers much smaller aggregates can give rise to J-aggregatelike absorption changes due to the strong dependence of the electronic absorption spectrum on backbone conformation. We also show that similar aggregates can be formed with appended electron acceptor and/or donor units to the porphyrin oligomers and this is envisioned to provide some interesting novel systems for investigating charge migration.
cooling the oligomers from room temperature to liquid nitrogen temperature, this transformation can be avoided completely (see Figure S1 in the Supporting Information) although, when the temperature is raised again, the samples start to equilibrate once permitted by the viscosity. Note that that these transformations occur well above the glass transition for MTHF (≈90 K) and that the viscosity at 170 K is about 20 times higher than at room temperature.19 Other solvents were also tested and similar behavior was seen with the oligomers dissolved in decalin with 5% pyridine added (see Figure S2 in the Supporting Information). The transition temperature is then increased to approximately 240 K and the transition is also much slower compared to MTHF. The process is though much more complicated in decalin since other less defined aggregates are present even at room temperature, and the increased light scattering observed, point to formation of larger constructs in addition to the ones observed in MTHF. Two State Model. The series of absorption spectra in Figure 3 all show nice isosbestic points during the formation of the aggregates and the process can be very well described by a two state model between free oligomer and aggregate. Singular value decomposition (SVD) analysis was applied on the series of absorption spectra to extract the two most significant spectral components. These were then further fitted to a simple equilibrium model in which the apparent enthalpy and entropy changes were optimized (see Supporting Information for details). Shown in Figure 4 are the extracted spectral components as well as concentration profiles of free octamer and aggregates, in units of monomer concentration. Table 1 shows the optimized thermodynamic parameters along with empirically determined melting temperatures (Tm's) for P8, P6, and P4. The presented thermodynamic values represent the case where only the dimer is formed, but an analysis assuming that the aggregates can grow to infinite sizes was also done which did not improve the fit significantly (Table S1 in Supporting Information). The results indicate higher melting temperatures for the longer oligomers and the enthalpy and
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RESULTS Figure 3 shows the spectral changes of P8, P6, and P4 in MTHF as a function of temperature. Each spectrum represents a fully equilibrated sample at its corresponding temperature. The changes from room temperature down to 170 K did not affect the spectra significantly and are hence omitted from Figure 3. Below 170 K the systems undergo major transformations. For P8 as an example, a new peak, red-shifted from the Q-band is growing in at 850 nm and dominates the spectrum at 150 K. In addition to this, several underlying peaks are revealed compared to the unstructured Q-band found at 170 K. In the Soret-band much less dramatic changes are observed; the main peak decreases while the shoulder at 495 nm is increasing slightly. The same features are seen for P6 and P4 although slightly less dramatic and the transition temperatures are also somewhat lower (see Figure 3 and Supporting Information). Shorter oligomers (P3 and P2) also show indications of the same transformation, but the extremely slow equilibration rates due to the high viscosity of the solvent at the transition temperatures (below 140 K) prevented any thorough investigation. The process is fully reversible but equilibration is slow: it takes hours for the system to completely change from its monomeric state to the fully aggregated form. By quickly B
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Figure 5. Absorption changes of P6 at 849 nm after a step change in temperature from 163 to 161 K. The concentrations are 0.3 (black), 1.6 (red), 3.7 (green), and 16 μM (blue). The temperature jump was applied at time zero, and there was a slight induction time of 1−2 min before the cryostat reached the new temperature.
forward and unimolecular in the reverse direction) assuming small perturbations from equilibrium leads to a single exponential relaxation kinetics and the rate constant for relaxation is given by 1 = k+[Pn]eq + k − (1) τ where k+ is the forward (association) rate constant, k− is the reverse (dissociation) rate constant, and [Pn]eq is the monomer concentration at the new equilibrium (161 K). From the equilibrium analysis the equilibrium constant is estimated to be K = 2.11 × 105 M−1 at 161 K and fitting the relaxation times at several oligomer concentrations (Figure 5, Figure S6 in the Supporting Information, eq 1) leads to k+ = 670 s−1 M−1 and k− = 0.0030 s−1. It is satisfying that the kinetic analysis gives an equilibrium constant (k+/k− = 2.23 × 105 M−1) which is of the same order of magnitude as the one estimated from the equilibrium analysis. A stepwise temperature rise gives similar relaxation kinetics supporting the assumption behind eq 1. The slow association constant cannot be addressed to the high viscosity present in the sample at this temperature. The viscosity of MTHF at 161 K was calculated to be 0.0109 kg m−1 s−1.19 This gives a rate constant for a diffusion limited reaction of about 108 M−1 s−1, much higher than the fitted association rate constant.22 This indicates the importance of finding the right conformation for dimerization which greatly slows down the process. For shorter oligomers (P2, P3), the probability of having the right conformation is expected to be higher due to the narrower distribution of conformers. However, we do not observe the formation of aggregates for the short oligomers in MTHF due to the reaction rate limitations. It can be seen in Table 1 that the apparent melting temperature decreases with the size of the oligomers (from 163 K for P8 to 146 K for P4). Thus melting temperatures below 140 K are expected for P3 and P2. At the high viscosities expected for transition temperatures below 140 K, the slow diffusion will prevent the observation of aggregate formation in P2 and P3. In poor solvents such as decalin (vide supra), which do not solvate the porphyrins as well as MTHF, the transition occurs at higher temperatures, whereas better solvents such as THF
Figure 4. (top) The two most significant spectral components extracted from SVD analysis of the P8 dimerization and (bottom) the corresponding concentration profiles of the monomer (squares) and the dimer (triangles). The spectral profiles and concentration variations correspond to the optimized enthalpy (ΔH) and entropy (ΔS) values in Table 1. The concentration of the dimer is displayed as the concentration of P8 units.
Table 1. Optimized Enthalpy (ΔH) and Entropy (ΔS) Changes of the Porphyrin Oligomer Dimerization Extracted from the Fita tetramer hexamer octamer
ΔH (kJ/mol)
ΔS (J/mol K)
Tm (K)
−86 −137 −168
−459 −749 −906
146 158 163
a
Tm is the apparent melting temperature where 50% of the oligomers have formed aggregates. The total oligomer concentration is 0.19 μM for P4, 0.48 μM for P6, and 0.29 μM for P8.
entropy change scale almost proportionally with the oligomer size. The magnitude of the aggregation enthalpy increases with around (−)20 kJ/mol per added porphyrin monomer unit in the oligomers, a number that is slightly lower than the value reported by Hunter et al., who estimated ππ-stacking interaction between two zinc porphyrin units to be 48 ± 10 kJ mol−1.20,21 These interactions are very solvent dependent and are affected by the geometry of the porphyrin−porphyrin interaction, but the large negative entropies of aggregation point toward the formation of highly ordered aggregates. Kinetics. In order to study the kinetics of the aggregation/ dimerization reaction, a sample of P6 in MTHF was subjected to small temperature changes and the relaxation toward a new equilibrium was investigated. As can be seen in Figure 5, increasing the concentration of P6 also increases the rate of relaxation. For a dimerization reaction (bimolecular in the C
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porphyrin aggregate. The dramatic spectral change unambiguously suggests a planar conformation of the oligoporphyrins. Furthermore, all strong electronic transitions of the oligomers in the visible region are long axis polarized.12,25 Close packing of stacked oligomers but with their planes displaced could hence lead to an attractive coupling of the individual dipole moments in a J-aggregated fashion.15 There are several results that support the formation of a J-aggregate, for instance, the formation of a new red-shifted absorption band and a very small Stokes-shifted emission. On the other hand, absorption from planar conformers is also expected to give rise to a sharp band at the red-most end of the Q-band.12 The effects of dipole−dipole coupling between individual oligomers and the spectral shift due to planarization are hence similar and the question is to what extent they are contributing to the spectral changes seen. The properties of a large aggregate would be dominated by the dipole−dipole coupling, while a small aggregate is more influenced by intramolecular oligomer planarization. Several experiments have been performed in order to shed light on the structure or size of the aggregates, such as resonance light scattering, dynamic light scattering, and steady state anisotropy, but none of these methods give evidence for large aggregates in these samples. There is no increased turbidity of the samples after the formation, dynamic light scattering could not detect any changes in signal when comparing a sample before (170 K) and after (150 K) aggregation, and the fluorescence anisotropy signal was also virtually unchanged between these temperatures. Furthermore, a comparison between the fluorescence rate constants of the free octamer and those of the aggregates (Table 2) showed that their transition moments are comparable in size. Large aggregates that show a dramatic change in their absorption spectra, such as the J-aggregates, usually have huge absorptivities compared to their constituent monomers. A rough estimate of the aggregate size can be made by comparing the measured rate constants to calculated ones using the Strickler−Berg relation which relates the fluorescence rate constant of a chromophore to its molar absorptivity.26
and pyridine do not show any aggregation at temperatures above their freezing points (Figure S7 in the Supporting Information). Steady State Emission. Figure 6 shows the normalized absorption and emission spectra excited at 864 nm of P8 after
Figure 6. Normalized absorption (solid) and emission (dashed) spectra of the porphyrin octamer at 150 K. The excitation wavelength was 864 nm.
equilibration at 150 K. As seen in Figure 6, there is an exceptionally small Stokes shift and the structured emission mirrors the absorption very well. A similar, but less dramatic, spectral change and concomitant small Stokes shift is also observed for the so-called ladder complexes.23 A small amount of a second blue-shifted emission band is visible when exciting at shorter wavelengths. This resembles the emission observed for the nonaggregated sample at 172 K with similar excitation spectra and is therefore attributed to emission from small amounts of free octamer still present at 150 K. The fluorescence lifetimes were also measured at 163 K (Figure S9 in the Supporting Information). At this temperature there is an equal amount of aggregated and nonaggregated oligomers according to the equilibrium model (Figure S3 in the Supporting Information). The fluorescence lifetimes are shown in Table 2 together with the fluorescence quantum yields for the aggregates and free octamer.
∫
k f = (2.88 × 10−9)ν 2 ε(ν) dν
In eq 2 ν is the transition wavenumber and ε is the molar absorptivity. By scaling the absorptivity extracted from the two state model (Figure 4 and Figures S3−S5 in the Supporting Information) with the number of oligomers in the aggregate to match the calculated rate constant with the measured one, an estimate of the aggregate size can be made.27 Due to the rough assumptions made and the limitations of the Strickler−Berg relation, the results should not be considered quantitatively, but they clearly indicate that the aggregate consists of only a few oligomer molecules, probably not more than two or three units. This strongly suggests a small aggregate size, but the effect cannot merely be due to the planarization of individual oligomers free in solution since thermodynamically this would not occur in the sharp and narrow temperature interval observed here and, additionally, an intramolecular process would show much faster kinetics than observed. Furthermore, the aggregation can be made with or without pyridine present without any significant change in melting temperature. An excess of pyridine would probably prevent the formation of large aggregates but may permit an oligomer dimerization. Furthermore, coordination of pyridine to the zinc centers of the porphyrin oligomers is associated with a distinct red shift of the
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DISCUSSION The results presented here all show indications of the formation of highly structured and spectroscopically well-defined Table 2. Fluorescence Quantum Yields (Φf) and Lifetimes (τf) and Radiative Rate Constant (kf) of the Porphyrin Octamer Measured at 163 K, Where Approximately Half the Oligomers Have Converted to Aggregatesa compound
Φfb (%)
τfc (ps)
kf (ns−1)
free octamer aggregate
10 7
930 575
0.107 0.122
(2)
The fluorescence decays and deconvoluted spectra are shown in the Supporting Information (Figure S9). bThe optical densities of the two species at the excitation wavelength were scaled with their corresponding absorptivities, and their individual emission spectra were obtained by subtracting the contribution from the other species. The quantum yield of P6 in toluene was used as reference.24 cThe sample was excited at 495 nm and the emission decay was measured at 800 and 867 nm for the free octamer and aggregates, respectively. a
D
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absorption spectrum; in particular, the strong “aggregate” peak is red-shifted by 12 nm as seen in Figure 7. A large stacked
Figure 7. Absorption spectra of P8 in 2MTHF showing the spectral shift associated with pyridine coordination. The solid line shows the spectrum measured at 160 K with 1% pyridine, and the dashed line shows the spectrum at 155 K without pyridine.
aggregate would have just a few Zn centers accessible to pyridine coordination, and most of the oligomers would only show little or no change in the transition energies (absorption peak positions). Instead, the observed shift in the aggregate transitions with and without pyridine present is comparable to the shift of a free oligomer when pyridine is added (Figure 7). Hypothetically, it would be possible to observe such a shift if the aggregates are arranged in a wormlike structure, where most of the porphyrin units in the oligomers are accessible to pyridine coordination, but we cannot see how such an arrangement could be consistent with planarization of the oligomer. Finally, peripheral substituents such as a fullerene electron acceptor and/or a ferrocene donor do not affect the aggregate formation as shown by the similar dramatic absorbance changes of Fc-P6-C60 in Figure 8. This similarity in behavior would be surprising for larger constructs, whereas a dimer could easily accommodate these molecular alterations of the oligomer structure. It is interesting to compare the observed aggregates to solutions of oligomers dissolved in noncoordinating solvents such as dichloromethane, chloroform, and toluene. The oligomers aggregate strongly in these solvents at room temperature, but these aggregates are different in that (a) they dissociate in the presence of pyridine, (b) they have broader absorption spectra, and (c) they have much lower fluorescence quantum yields (the fluorescence quantum yield of P8 in toluene at room temperature is 0.7% compared to 8.0% when disaggregated in THF). The extremely slow kinetics would normally not be intuitive for a dimerization process, but with the fairly high viscosity and the large number of different dihedral conformations present even at low temperatures, this seems more likely. Out of the huge number of oligomer encounters, only the ones with a planar or very close to a planar conformation will undergo dimerization due to the close packing of the large substituents needed in order to provide a sufficient π-stacking. In summary, we have observed the formation of a well-defined small aggregate of linear porphyrin oligomers that might be useful in applications where the electronic communication is influenced by the structural heterogeneity. Over a very small temperature
Figure 8. (top) Molecular structure of the fullerene and ferrocene appended hexamer oligomer, Fc-P6-C60. (bottom) Absorption spectra of Fc-P6-C60 in MTHF measured at 180 (black), 170 (red), 166 (green), 162 (blue), and 158 K (cyan).
range (170−150 K) the oligomer goes from being totally randomized with respect to its dihedral angles (i.e., the porphyrin planes) to becoming structurally very well-defined with an expected high degree of electronic delocalization.
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ASSOCIATED CONTENT
S Supporting Information *
Experimental section, low temperature absorption of P8 in MTHF after quick cooling, low temperature absorption of P8 in decalin, two-state model, kinetics, low temperature absorption of P8 in THF, steady state emission, time-resolved fluorescence decays. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the Swedish Research Council (VR) and the Swedish Energy Agency. Louisa J. Esdaile is acknowledged for the synthesis of the fullerene and ferrocene appended hexamer oligomer.
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REFERENCES
(1) Lin, V. S.-Y.; DiMagno, S. G.; Therien, M. J. Science 1994, 264, 1105−1111. (2) Anderson, H. L.; Martin, S. J.; Bradley, D. D. C. Angew. Chem., Int. Ed. 1994, 33, 655−657. (3) Beljonne, D.; O’Keefe, G. E.; Hamer, P. J.; Friend, R. H.; Anderson, H. L.; Bredas, J. L. J. Chem. Phys. 1997, 106, 9439−9460. E
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(4) Kuebler, S. M.; Denning, R. G.; Anderson, H. L. J. Am. Chem. Soc. 2000, 122, 339−347. (5) Priyadarshy, S.; Therien, M. J.; Beratan, D. N. J. Am. Chem. Soc. 1996, 118, 1504−1510. (6) LeCours, S. M.; Guan, H. W.; DiMagno, S. G.; Wang, C. H.; Therien, M. J. J. Am. Chem. Soc. 1996, 118, 1497−1503. (7) Collins, H. A.; Khurana, M.; Moriyama, E. H.; Mariampillai, A.; Dahlstedt, E.; Balaz, M.; Kuimova, M. K.; Drobizhev, M.; Yang, V. X. D.; Phillips, D.; Rebane, A.; Wilson, B. C.; Anderson, H. L. Nat. Photonics 2008, 2, 420−424. (8) Anderson, H. L. Chem. Commun. 1999, 2323−2330. (9) Ostrowski, J. C.; Susumu, K.; Robinson, M. R.; Therien, M. J.; Bazan, G. C. Adv. Mater. 2003, 15, 1296−1300. (10) Fenwick, O.; Sprafke, J. K.; Binas, J.; Kondratuk, D. V.; Di Stasio, F.; Anderson, H. L.; Cacialli, F. Nano Lett. 2011, 11, 2451− 2456. (11) Mai, C.-L.; Huang, W.-K.; Lu, H.-P.; Lee, C.-W.; Chiu, C.-L.; Liang, Y.-R.; Diau, E. W.-G.; Yeh, C.-Y. Chem. Commun. 2010, 46, 809−811. (12) Winters, M. U.; Karnbratt, J.; Eng, M.; Wilson, C. J.; Anderson, H. L.; Albinsson, B. J. Phys. Chem. C 2007, 111, 7192−7199. (13) Anderson, H. L. Inorg. Chem. 1994, 33, 972−981. (14) Taylor, P. N.; Anderson, H. L. J. Am. Chem. Soc. 1999, 121, 11538−11545. (15) Harrison, W. J.; Mateer, D. L.; Tiddy, G. J. T. J. Phys. Chem. 1996, 100, 2310−2321. (16) Kirstein, S.; Daehne, S. Int. J. Photoenergy 2006, No. 20363, DOI: doi:10.1155/IJP/2006/20363 . (17) Ribo, J. M.; Crusats, J.; Farrera, J. A.; Valero, M. L. J. Chem. Soc., Chem. Commun. 1994, 681−682. (18) Würthner, F.; Kaiser, T. E.; Saha-Möller, C. R. Angew. Chem., Int. Ed. 2011, 50, 3376−3410. (19) Brocklehurst, B.; Young, R. N. J. Chem. Soc., Faraday Trans. 1994, 90, 2001−2001. (20) Hunter, C. A.; Meah, M. N.; Sanders, J. K. M. J. Am. Chem. Soc. 1990, 112, 5773−5780. (21) Hunter, C. A.; Sanders, J. K. M. J. Am. Chem. Soc. 1990, 112, 5525−5534. (22) Eng, M. P.; Ljungdahl, T.; Andreasson, J.; Mårtensson, J.; Albinsson, B. J. Phys. Chem. A 2005, 109, 1776−1784. (23) Chang, M.-H.; Hoffmann, M.; Anderson, H. L.; Herz, L. M. J. Am. Chem. Soc. 2008, 130, 10171−10178. (24) Hoffmann, M.; Karnbratt, J.; Chang, M. H.; Herz, L. M.; Albinsson, B.; Anderson, H. L. Angew. Chem., Int. Ed. 2008, 47, 4993− 4996. (25) Drobizhev, M.; Stepanenko, Y.; Dzenis, Y.; Karotki, A.; Rebane, A.; Taylor, P. N.; Anderson, H. L. J. Phys. Chem. B 2005, 109, 7223− 7236. (26) Strickler, S. J.; Robert, A. B. J. Chem. Phys. 1962, 37, 814−822. (27) Figure 4 shows the absorptivity of an aggregate consisting of two monomers. If the aggregate were four monomers large, the absorptivity would be twice as high. The integrated absorptivities of aggregates with different numbers of included oligomers were then used in eq 2 to calculate the estimated fluorescence rate constant. The calculated values of kf were, for a dimer, 7.6 × 108 s−1, for a tetramer, 1.5 × 109 s−1, and, for a decamer, 3.79 × 109 s−1. These should then be compared to the measured fluorescence rate constants shown in Table 2.
F
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