Ultrafast delocalization of excitation in synthetic light-harvesting nanorings

When light is absorbed by a nanoring consisting of 6–24 porphyrin units, the excitation delocalizes over the whole molecule within 200 fs. Highly symmetric nanorings exhibit thermally enhanced super-radiance.

: Detailed chemical structures of the porphyrin oligomers used in this study. The sidechain (R) has no significant effect on the absorption or photoluminescence spectra of the compounds, but it influences the solubility, aggregation behaviour and ease of purification. Versions of the oligomers with R = t-Bu or R = OC 8 H 17 were used, as indicated above. In the case of the linear octamer l-P8, material with R = t-Bu was used for photoluminescence anisotropy experiments whereas octamer with R = OC 8 H 17 was used in temperature-dependent photoluminescence experiments.
All photoluminescence experiments were carried out using solutions of zinc porphyrin oligomers in toluene containing 1% by volume of pyridine, except in the cases of c-P6·T6 and c-P8·T8 which were studied in pure toluene. The pyridine ligand coordinates to the zinc centres of the porphyrin units, increasing the solubility and preventing aggregation. The chemical structures of the zinc porphyrin oligomers used in this study are shown in Figure 1. These materials were synthesised and characterised using previously published procedures. [1][2][3][4][5][6][7][8][9] All samples were rigorously purified by gel permeation chromatography (GPC), and their purity was checked by 500 MHz 1 H NMR, MALDI-TOF mass spectrometry and analytical GPC. The cyclic hexamer and its template complex, c-P6 and c-P6·T6, were prepared directly from the porphyrin monomer l-P1 as described in Ref. 4. The cyclic octamer and its template complex, c-P8 and c-P8·T8, were prepared from l-P2 using the T8 template, using the method described in Ref. 3.
Monodisperse linear oligomers l-P6 and l-P8 were synthesised by coupling mono-silylated precursors as described in references 2,6-9. The synthesis and characterisation of l-P18 is described as follows; l-P10 emerged as a by-product of the process but was not used in the study reported here.

Steady-state Absorption and Emission Spectra
!"" #"" $"" %""" %&"" "'" ) ) ) *+ ) ) ) ) *+ ) ) ) ) *+ ) ) ) ) *+ ) ) ) ) *+ ) ) ) ) *+ ) ) ) ) *+ ) ) ) ) *+ ,-,-! ) ) ) ) *+ ) ) ) ) *+ ) ) ) ) *+ ) ) ) ) *+ ) ) ) ) *+ ) ) ) ) *+ ,-,-   where the former two are in agreement with a previous study on identical molecules which also determined an initial anisotropy of 0.36 for the linear tetramer (l-P4) of the same series. 10 This study demonstrated that only for short oligomers a PL anisotropy close to 0.4 was found, the theoretically expected value for a randomly oriented distribution of non-interacting linear dipoles. 11 For longer oligomers, the early-time anisotropy (following light absorption and nuclear relaxation) was observed to be smaller, the longer the porphyrin oligomer. 10 These effects were shown to be related to the "worm-like" nature of longer molecules which may be substantially bent, and hence an ultrafast reorientation of the oscillating dipole moment may originate from excitation self-trapping following fast vibrational relaxation of the molecule. The PL anisotropy dynamics for the "linear" porphyrin molecules can hence be understood in terms of dynamic exciton self-localization that leads to an ultrafast re-orientation of the emitting dipole. Such depolarization effects will be more pronounced the more curved the conjugated segments are that sustain the excitation, as described previously. 10   Time-dependent PL intensity decay transients were determined from the two measured intensity components (I , with polarization parallel, and I ⊥ with polarization perpendicular to the excitation polarization) as I = I + 2I ⊥ and are plotted in Fig. 10 for cyclic and Fig. 11 for linear porphyrins. From monoexponential fits to these data (I = I 0 exp(−k total t)) the overall decay rate k total was determined, which is composed of both radiative (k r ) and non-radiative (k nr ) parts.

Quantum Yield
Calculation of the fluorescence quantum yield of porphyrin compounds is complicated by the lack of well-characterized quantum yield standards in the near-infrared region. Accordingly, two mutually complementary techniques were used to ensure an accurate determination of the quantum yield of one compound (l-P6) to be used as a reference material. Accordingly, the yield of l-P6 was determined using both: A) An Integrating Sphere Approach. An absolute measurement of quantum yield may be made using a broadband integrating sphere and spectrally corrected spectrometer, following an approach as described by de Mello et al. 12 Briefly: three spectral measurements are made, one without a sample present (referred to as I las ), one with the sample in the sphere and directly in the laser beam (I in ) and one with the sample in the sphere but removed from the direct beam and illuminated by scattered laser light only (I out ). The concentration of the sample is carefully controlled to have less than ∼10% absorption at any wavelength to avoid self-absorption effects. The single-pass absorption of the sample can be calculated by where λ laser indicates the number of photons in the spectral region of the exciting laser. From this, the quantum yield may be calculated using where λ PL is the number of photons in the spectral region of the photoluminescence. Under excitation into the Soret band using a 450 nm LED source, a quantum yield of 0.263 was calculated, while excitation into the Q X band using a 770 nm laser diode resulted in a quantum yield of 0.256.
This technique can provide high systematic accuracy, but -due to the direct comparision of laser and photoluminescence on a single scan -can be challenging for low quantum yield samples.

B) A Relative Approach. A relative measurement of quantum yield can be made by comparison
of the absorption and emission of a sample in comparison to that of a reference standard, using the relationship From the integrated area of the emission spectra (I(λ PL )) and the absorbance at the excitation wavelength (ABS(λ laser )) the quantum yield of sample may be determined. Two dilute fluorescence standards were used; Rhodamine-6G in ethanol for excitation at 475 nm (QY=0.95 13 Table 1 for the investigated range of cyclic and linear porphyrin compounds.

Radiative and Non-radiative Decay Rates
Using the extracted Quantum Yield QY , the overall decay rate k total extracted from the timedependent PL intensity decay was separated into its radiative (k r ) and non-radiative (k nr ) parts through k r = QY × k total and k total = k r + k nr .
The resulting non-radiative and radiative decay rates are shown in Figure 12 for cyclic and linear porphyrins as a function of the number of porphyrin monomers incorporated in the molecule. For all compounds, the non-radiative decay rates is at a factor of two larger than the radiative rate. The observed PL transients are hence dominated by the non-radiative contribution to the overall decay.  c-P24 and l-P6 as a function of solution temperature between 220 K and 360 K. The inset shows the respective integral over these spectra (which are proportional to the total number of photons emitted across the spectrum) as a function of inverse absolute temperature. Fitting these data with an Arrhenius function allows the extraction of the shown activation energies E A for temperatureactivated photon emission rates. For c-P6 and c-P6·T6 (as well as c-P8 and c-P8·T8 -see main manuscript) sizeable activation energies are observed, while for the larger nanorings and for the linear molecules, E A is comparatively small. For the 6-nanorings, templating leads to an increase in activation energy, similar to observations made for the 8-nanorings (see main manuscript). Note however, that for the 6-rings, this increase is smaller, which we attribute to the presence of a peak (at 920 nm) in the emission of c-P6·T6 that shows opposite trends to the rest of the spectrum (i.e. an decrease in PL efficiency with increasing temperature). This peak has been identified in a previous study 4 as arising from an impurity emission. Hence the correct activation energy for an impurity-free solution of c-P6·T6 is likely to be larger than the stated value of E A = 20.5 meV.
No. of Photons emitted per unit time and wavelength (arb. units)

Spectral
Integral (arb. units) Integral (arb. units) Figure 13: Steady-state photon emission intensity spectra for (a) c-P6 in toluene/ 1% pyridine, (b) c-P6·T6 in toluene, (c) c-P12 in toluene/ 1% pyridine, and (d) c-P24 in toluene/ 1% pyridine at sample temperatures of 220 K (black line), 240 K (red), 260 K (green), 320 K (blue) and 360 K (cyan). The insets show the spectral integral over these spectra (which is proportional to the total number of photons emitted from the sample) as a function of inverse temperature. From these data, the shown activation energy E A for thermally enhanced emission was extracted through exponential fitting.  Figure 14: Steady-state photon emission intensity spectra for l-P6 in toluene/1% pyridine at sample temperatures of 220 K (black line), 240 K (red), 260 K (green), 320 K (blue) and 360 K (cyan). The insets show the spectral integral over these spectra (which is proportional to the total number of photons emitted from the sample) as a function of inverse temperature. From these data, the shown activation energy E A for thermally enhanced emission was extracted through exponential fitting. Figure 15 displays the PL emission decay curves for l-P8, c-P8 and c-P8·T8 as a function of solution temperature. For the cyclic molecules, no change in decay dynamics is observed. As shown above, the PL decay for cyclic compounds is dominated significantly by non-radiative decay channels and hence the observed increase in PL emission intensity with increasing temperature can only be caused by an increase in the radiative emission rate.

Monte Carlo Simulation of Porphyrin Nanoring Conformations
A Monte Carlo model was used to generate thermally-equilibrated nanoring configurations to simulate the average non-circularity g in an ensemble of nanorings containing n porphyrins. 16 The expression for the bending energy of a nanoring is a discretised analogue of the elastic bending energy of a continuous closed loop, where κ B is the bending rigidity, C is the local curvature, and s is the loop coordinate.
where C i and ∆s i are local curvature and segment length at the i th bending point, κ s is stretching stiffness, and L is equilibrium separation between bending points. Local curvatures and segment lengths may be expressed in terms of vectors {s i } to give written such that summation prefactors represent characteristic bending (κ B /L) and stretching (κ S L 2 /2) energies. For nanoring configurations to be governed by bending (rather than stretching), κ S 2κ B /L 3 is used. Bending limitations (imposed to prevent the overlapping of neighbouring, and distant, porphyrin macrocycles) are achieved by placing hard discs of diameter √ 3L/2 at the midpoints between bends. Overlapping of these discs results in an infinite energy penalty.
To generate thermally-equilibrated nanorings obeying by the energetics described above, Monte Carlo simulations are run using the Metropolis algorithm. The characteristic bending, κ B /L, and thermal, k B T energies are the only relevant energy scales. The ratio of these defines a dimensionless rigidity R = κ B /Lk B T ; the sole parameter controlling the energetics of the model.
The departure from circularity of a nanoring is characterised by a single parameter, g (see main text). To find an average nanoring non-circularity, g, for a particular set of parameters, R and n, a nanoring is initially set in a circular configuration. The system evolves via the Metropolis algorithm and equilibrium is reached after an initial transient period. Equilibrium non-circularity values are recorded for an extensive time period, and a time-averaged value g can be obtained.
For complete rigor, time-averaged values are obtained from many independent simulations (using different random seeds) and subsequently averaged. By correlating g values obtained from simulations with those measured from STM images, it was shown in Ref. 16 that R ≈ 6 accurately reproduces nanoring configurations for both c-P12 and c-P24 nanorings adsorbed on an Au (111) surface at room temperature (T = 290 K), i.e. the bending rigidity κ B (and porphyrin periodicity L) is inherently common to all rings. ring size, increasing temperature increases the average distortion from circularity of a nanoring.
One can also see that for a given temperature, increasing ring size increases the average distortion from circularity (the five data points at T = 290 K are shown in Figure 3(c) of the main text).