Supporting Information: Photochemical Control of Exciton Superradiance in Light Harvesting Nanotubes

Transcription

1 Supporting Information: Photochemical Control of Exciton Superradiance in Light Harvesting Nanotubes Sandra Doria, 1,2,3 Timothy S. Sinclair, 1 Nathan D. Klein, 1 Doran I. G. Bennett, 4 Chern Chuang, 1 Francesca Stefania Freyria, 1 Colby P. Steiner, 1 Paolo Foggi, 2,5,6 Keith Nelson, 1 Jianshu Cao, 1 Alán Aspuru-Guzik, 4 Seth Lloyd, 7 Justin Ryan Caram, 1,8* Moungi G. Bawendi, 1* 1 Department of Chemistry, 7 Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States 2 European Laboratory for Non Linear Spectroscopy (LENS), Università degli studi di Firenze, via Nello Carrara 1, Sesto Fiorentino, Florence, Italy 3 Dipartimento di Chimica Ugo Schiff, Università degli Studi di Firenze, via della Lastruccia, 3-13, Sesto Fiorentino, Florence, Italy 4 Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, Massachusetts 02138, USA 5 INO CNR, Istituto Nazionale di Ottica Consiglio Nazionale delle Ricerche, Largo Fermi 6, Florence, Italy 6 Dipartimento di Chimica, Biologia e Biotecnologie, Università di Perugia, Via Elce di Sotto 8, Perugia, Italy 8 Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, CA 90095, United States *Co-Corresponding Authors

2 Supporting Figure 1. Fluorescence integrated area as a function of irradiation time in case of CW excitation at 532 nm. The inset shows the same curves, where the horizontal axis is scaled by number of excitations.

3 Supporting Figure 2. a) Streak camera collected lifetime of the monomer in solution and the aggregate in sugar matrix, showing lifetime shortening from the monomer to the LHNs.b) Fluorescent decay rate during irradiation of the sample, derived from a single exponential fit of the lifetime trace.

4 Supporting Figure 3. Two dimensional rephasing spectra of LHNs in sugar matrix in conditions initial exposure (a) and after 60 minutes exposure (b). c) Inhomogeneous linewidth, calculated as the diagonal section of the map in figure (a). The black curve show Gaussian fits of inner and outer wall features. d) Two dimensional rephasing spectra of LHNs in sugar matrix after 90 minutes exposure. e) Additional two-dimensional rephasing spectra collected after the sample was being left 90 mins in the dark. f) Inhomogeneous linewidth, calculated as the diagonal section of the map in figure (d). The black curve shows Gaussian fits of inner and outer wall features. The dashed lines indicate the blueshift of the IW peak during illumination.

5 Supporting Figure 4 Schematic illustration of instrument used to collect power dependent fluorescent intensity and lifetimes. Supporting Figure 5. Spectra of the four laser beams used to record 2D electronic spectra in the plotted on top of the sample absorption spectrum.

6 Fitting Peak Shape. A clear sign of exciton delocalization in aggregates is feature narrowing. Absorption and emission linewidths result from static (inhomogeneous) and dynamic (homogeneous) mechanisms of line-narrowing. We fit the emission spectrum (figure 1c of main text) using two Pseudo-Voigt functions centered around and cm -1, that represent the inner and outer wall contributions respectively: a 0 [(1 a)exp ( ln(2) ( E E 1 ) 2 ) + σ 1 a 1+( (E E 1 ) σ1 ) 2 ] + (S1) +b 0 [(1 b)exp ( ln(2) ( E E 2 ) 2 ) + σ 2 b 1+( (E E 2 ) ) 2 ] σ2 Where the two terms of the sum are the two weighted Voigt functions: a 0 (b 0 ) is the feature height, E 1 (E 2 ) is the feature position, σ 1 (σ 2 ) is the FWHM of the Gaussian as well as of the Lorentzian function, a (b) is the Lorentzian fraction used, 1-a (1-b) is the Gaussian fraction used, and E is the variable representing the energy on the x-axis. Table 1 of S.I. shows the range of fitting parameters in case of 22.4 W/cm 2 excitation power. The following table shows the of fitting parameters in case of 22.4 W/cm 2 excitation power per unit area, at three delay times: as soon as sample illumination starts, after 60 seconds (when the QY reaches its maximum) and after 600 s of irradiation. Fitting parameters Initial value After 60 s of irradiation After 600 s of irradiation a 0 (a.u.) (4.54±0.2)x10 8 (5.62±0.3)x10 8 (3.67±0.1)x10 8 E 1 (cm -1 ) 16689± ± ±1 σ 1 (cm -1 ) 62.83± ± ±0.2 a (a.u.) 0.436± ± ±0.003 b 0 (a.u.) (3.66±0.1)x10 4 (4.14±0.2)x10 4 (3.31±0.1)x10 4 E 2 (cm -1 ) 16951± ± ±1 σ 2 (cm -1 ) 74.23± ± ±0.05 b (a.u.) 1.478± ± ±0.001 Table 1. Fitting parameters resulting from the Pseudo-Voigt fit (equation 4 of the main text) of the fluorescence spectra collected during sample irradiation with illumination power per unit area 22.3 W/cm 2. Fitting lifetimes. In figure S2 we show time resolved fluorescence traces recorded for matrix-stabilized C8S3 J-aggregates and monomer on a streak camera. We fit the monomer lifetime to two exponentials, obtaining a weighted average lifetime of 240 ps. The aggregate lifetime fits to a single exponential with a lifetime of 90 ps, similar to prior studies. 1 From the QY and the total decay rate k tot, it is straightforward to separate the contributions of radiative and non radiative components k r and k nr : k tot = k r + k nr (S2)

7 QY = k r k tot We measured QY of the C8S3 monomer and matrix stabilized aggregates of and 0.15 respectively. k r and k nr are determined to be to be (6.25 ± 0.01)x10 7 s -1 and ( ± 0.01)x10 7 s -1 for the monomer and (1.69 ± 0.02)x10 9 s -1 and (9.41 ± 0.01)x10 9 s -1 for the aggregate respectively. The presence of two exponentials in the fluorescence decay of the monomer suggest either emission from multiple states, or multiple species. Nevertheless, the radiative rate estimated is consistent with other cyanine dyes such as Cy3 (~14x10 7 s -1 ) (derived from data in (S3) Temperature Dependence Supporting Figure 6. Temperature dependent photoluminescent spectra show increasing blueshift and narrowing consistent with photobrightening. Calculating couplings and comparison to the absorption spectra. We use the atomic transition charges method to calculate the matrix element of the Frenkel exciton model. 2 4 This method has been well established for such task and is known to reproduce accurate coupling magnitudes compared to, for example, those calculated from direct diabatization of dimer model onto the monomer basis that can be considered exact in the current context. This is a crucial ingredient for our purpose of modeling the effect of static disorder since the traditional simple dipole or even the extended dipole models strongly overestimate the exciton coupling magnitudes when the molecules are in close proximity. This is illustrated in figure S7, where we plotted the excitonic couplings between two neighboring C8S3 dye molecules in the 2-D brick layer model adopted in this study. The horizontal axis corresponds to the offset in the direction of the long axis of the molecules, such that when the offset is zero the two molecules are in a face-to-face configuration. It is

8 clear that the overestimation of the two dipole-based models is most severe for nearest neighbors, and all the methods converge in the long-range regime. In figure S8 we show that this model reproduces the 5K inner wall parrellel absorption spectrum with σ 2 =350 cm -1 of static gaussian disorder. We chose of 582cm -1 in the main text to conform with the 2DES data. With either starting poing, the magnitude of the observed changes are similar, corresponding to 5% site deletion and 50 cm -1 of change in static disorder. Supporting Figure 7. Coupling as a function of horizontal shift for two monomers spaced at 1nm for three models of excitonic coupling.

9 Supporting Figure 8. Modeled fit spectra for the inner wall parrallel. Plotted against the 5K absorption spectrum. The feature at 16650cm -1 arises due to contamination of C8S3 bundles. 5 Estimating Delocalization. To estimate exciton delocalization as a function of static disorder we will use an oscillator strength inverse participation ratio (IPR), defined as follows: N I k = 1 n=1 N φ k,n 4 f k = φ k,n n=1 N I f = 1 N f k I k k=1 (4) 2 (5) Where φ k,n is coefficient at each site which arises from diagonalizing the Hamiltonian described equation 4 in the main text. (6) Supporting Figure 9. The Oscillator Strength weighted IPR for varying levels of disorder and site deletion. References (1) Pugžlys, A.; Augulis, R.; Van Loosdrecht, P. H. M.; Didraga, C.; Malyshev, V. A.; Knoester, J. Temperature-Dependent Relaxation of Excitons in Tubular Molecular Aggregates: Fluorescence Decay and Stokes Shift. J. Phys. Chem. B 2006, 110, (2) Chang, J. C. Monopole Effects on Electronic Excitation Interactions between Large

10 Molecules. I. Application to Energy Transfer in Chlorophylls. J. Chem. Phys. 1999, 67, (3) Beljonne, D.; Cornil, J.; Silbey, R.; Millie, P.; Bre das, J. L. Interchain Interactions in Conjugated Materials: The Exciton Model versus the Supermolecular Approach. J. Chem. Phys. 2000, 112, (4) Kistler, K. A.; Spano, F. C.; Matsika, S. A Benchmark of Excitonic Couplings Derived from Atomic Transition Charges. J. Phys. Chem. B 2013, 117, (5) Eisele, D. M.; Arias, D. H.; Fu, X.; Bloemsma, E. A.; Steiner, C. P.; Jensen, R. A.; Rebentrost, P.; Eisele, H.; Tokmakoff, A.; Lloyd, S.; et al. Robust Excitons Inhabit Soft Supramolecular Nanotubes. Proc. Natl. Acad. Sci. U. S. A. 2014, 111,