The electronic interactions and excitation energy transfer (EET) processes of a variety of multi-porphyrin arrays with linear, cyclic and box architectures have been explored. Directly meso–meso linked linear arrays (ZN) exhibit strong excitonic coupling with an exciton coherence length of approximately 6 porphyrin units, while fused linear arrays (TN) exhibit extensive π-conjugation over the whole array. The excitonic coherence length in directly linked cyclic porphyrin rings (CZN) was determined to be approximately 2.7 porphyrin units by simultaneous analysis of fluorescence intensities and lifetimes at the single-molecule level. By performing transient absorption (TA) and TA anisotropy decay measurements, the EET rates in m-phenylene linked cyclic porphyrin wheels C12ZA and C24ZB were determined to be 4 and 36 ps−1, respectively. With increasing the size of CNZA, the EET efficiencies decrease owing to the structural distortions that produce considerable non-radiative decay pathways. Finally, the EET rates of self-assembled porphyrin boxes consisting of directly linked diporphyrins, B1A, B2A and B3A, are 48, 98 and 361 ps−1, respectively. The EET rates of porphyrin boxes consisting of alkynylene-bridged diporphyrins, B2B and B4B, depend on the conformation of building blocks (planar or orthogonal) rather than the length of alkynylene linkers.
Excitation energy transfer (EET) processes are the most important function of natural light-harvesting (LH) antenna complexes. Upon absorption of a photon by the antenna complex, many pigments within the complex convey this photon via EET until it encounters a reaction centre. To duplicate these fundamental features in simplified artificial systems, a variety of porphyrin arrays have been explored, which absorb visible light in a wide spectral range and funnel the resulting excitation energy rapidly and efficiently to a designed site. A key parameter for EET is the electronic interactions among neighbouring porphyrin units. The electronic interaction depends on distance and orientation between the neighbouring pigments, both of which can be controlled elaborately according to the linkage motif connecting them.
This paper deals with spectroscopic characterizations both at ensemble and single-molecule level of various types of multi-porphyrin arrays, including directly meso–meso linked linear porphyrin arrays (ZN), meso–meso, β–β, β–β triply linked linear porphyrin arrays (TN), directly meso–meso linked porphyrin rings (CZN), m-phenylene linked cyclic porphyrin wheels (CNZA and CNZB) and self-assembled porphyrin boxes (BNA and BNB). The order in this paper comes from the dimensionality and linkage motif connecting neighbouring porphyrins. Following this sequence, we first illustrate the electronic interactions of the porphyrin arrays based on the steady-state absorption and emission spectra, and the simultaneous measurements of single-molecule fluorescence intensity and lifetime. Then the EET rates and efficiencies are discussed from the results of time-resolved transient absorption (TA) and transient absorption anisotropy (TAA) measurements and coincidence measurement, respectively.
2. Linear porphyrin arrays
(a) Directly meso–meso linked linear porphyrin arrays (ZN)
The molecular design of directly meso–meso linked linear porphyrin arrays (ZN, N=1, 2, 3, 4, 6, 8, 12, 16, 32, 64 and 128) was envisaged to bring the porphyrin units closer for rapid energy transfer (scheme 1) .
The absorption spectra of ZN exhibit split Soret bands owing to exciton coupling between the adjacent porphyrins, while the Q bands remain nearly at the same positions (figure 1a).
The simple point-dipole exciton coupling theory is useful to interpret the spectral features caused by the interchromophoric interactions . As shown in scheme 2, the transition dipole moments of Soret band, Bx and By, which degenerate in a porphyrin monomer, independently interact with those of neighbouring porphyrins.
Bz transition dipole moments along the long molecular axis are excitonically coupled to generate an allowed lower energy transition (Bz+Bz), while the mutual Coulombic interactions between Bx and By (or Bz) transition dipole moments are negligible owing to their orthogonal orientation. Consequently, the Soret band of ZN is split into a red-shifted band and an unperturbed one.
The exciton splitting energy (ΔE) for ZN is given as , where ΔE0 represents the exciton splitting energy of the neighbouring porphyrins and N the number of porphyrin units in the array . For the Soret bands of ZN, ΔE exhibits a good linear correlation against with a slope of ΔE0=2150 cm−1, indicating strong exciton coupling between the neighbouring porphyrin units and good arrangement of the porphyrins as a linear form. In a similar manner, the exciton coupling strength in the S1-state of ZN was determined to be 570 cm−1, which is larger than 280 cm−1 that assumed only point dipole–dipole coupling between the porphyrin units. The short distance between porphyrin units is believed not only to enhance through-space dipole–dipole coupling but also to increase through-bond interaction.
The coherence length of a strongly coupled molecular array is important in understanding the photoexcited-state dynamics and collective behaviour of the transition dipole moments. A spectroscopic observable directly related to the exciton coherence length is superradiance. The superradiance can be quantified using a superradiance coherence size, which is defined as the ratio of the radiative decay rate of the array to that of the monomer, because the radiative decay rate of the array increases when the constituent chromophores interact with each other and radiate in phase [5,6]. When the superradiance coherence sizes of ZN were plotted as a function of the number of porphyrin units, a deviation point from the linearity was found to be approximately six porphyrin units, which would be a reasonable estimation for the exciton coherence length of ZN . This result is consistent with the calculated exciton coherence length of six porphyrin units that is based on the equation developed by Kakitani et al. .
At the single-molecule level, the superradiance effect can be examined based on photobleaching dynamics of single molecules . As seen in the fluorescence intensity trajectories (FITs) in figure 2a, ZN photobleaches in a stepwise fashion, where the number of steps for each array is compatible with that of porphyrin units.
To estimate the superradiance coherence size of single molecules, fluorescence lifetimes at the first and last emissive levels in the FIT and fluorescence quantum yield from bulk measurement were employed to calculate the radiative decay rates of the array and the monomer. For the molecules shown in figure 2a, the superradiance coherence sizes were calculated to be 1.8, 2.7, 3.6, 4.4 and 5.0 in going from Z2 to Z6. We carried out a statistical analysis by collecting 64 single-molecule datasets for each array. In figure 2b, distributions of the superradiance coherence size show a progressive shift upward to Z4, after which it becomes saturated at a value around 4.5. Thus, at the single-molecule level, approximately four porphyrin units would be the best estimation of the exciton coherence length of ZN. Not only the covalent direct linkage with a short centre-to-centre distance but also the orthogonal geometry imposed by a large steric hindrance probably minimize static/dynamic disorders of ZN and contribute to preserve coherent excitonic interaction in these arrays even in the solid state at room temperature.
(b) Fused linear porphyrin arrays (TN)
As a straightforward strategy for maximizing π-overlap among the porphyrins, triply meso–meso, β–β, β–β linked linear porphyrin arrays (TN, N=2, 3, 4, 5, 6, 8 and 12) were prepared (scheme 1) . These fully conjugated porphyrin arrays have planar tape-shaped structures and display drastically red-shifted absorption spectra that reach into the far-IR region (figure 1b), reflecting extensive π-conjugation . The absorption bands of the fused porphyrin arrays are roughly categorized into three distinct well-separated bands, which are marked as By, Bx and Qx bands in near-UV, visible and IR regions, respectively, on the basis of their transition properties revealed by the PPP-SCI (Pariser–Parr–Pople (PPP) Hamiltonian-based single-configuration interaction (SCI)) calculations. With an increase in the number of porphyrin units, the By bands retain nearly the same positions as that of the Zn(II) porphyrin monomer, while the Bx and Qx bands are continuously red-shifted along with an increase in their band intensities. The band shift of Bx bands as a function of the number of porphyrin units indicates that the Bx bands exhibit a clear saturation behaviour with the effective conjugation length (ECL) number of ca 8. The Qx bands do not show such saturation behaviour up to T12, i.e. the ECL number of N>12 in the S1-state of TN.
The observed linear plot of the energy difference between By and Bx bands as a function of the number of the porphyrin units indicates that the absorption spectra are actually influenced by the exciton coupling scheme and the constituent porphyrin units are in regular arrangement as a linear form (figure 3a) .
On the contrary, the plot of the Qx bands deviates strongly from the exciton coupling scheme. Instead, as shown in figure 3b, the plot based on a free electron model (a particle in a box model) gives rise to a well-correlated straight line, indicating that the S1-state of TN is characterized by the extensive π-conjugation throughout the entire array.
3. Cyclic porphyrin arrays
(a) Directly meso–meso linked porphyrin rings (CZN)
Inspired by the efficient EET processes in the circularly arranged chromophoric assemblies in natural LH complexes [10–12], cyclic porphyrin arrays have been prepared as artificial photosynthetic antennae. Directly meso–meso linked porphyrin rings (CZN, N=4, 6 and 8) are attractive in view of not only high molecular symmetry but also large and regular electronic interactions that lead to efficient EET (scheme 3) .
The absorption spectra of CZN exhibit broad non-split Soret bands at red-shifted Soret band position. These spectral features are explained by that both of the transition dipole moments Bx and By are excitonically coupled with those of neighbouring porphyrins to cause an excitonically allowed state of the same energy. In CZN, in addition to J-type coupling along the circumference of the ring, H-type coupling is also possible because of the bent structures, where the dihedral angles of neighbouring porphyrin planes are deviated from 90°.
The exciton coherence length of CZ4 was evaluated at the single-molecule level . In the case of cyclic structures, because the coherence can propagate in both directions owing to the absence of terminal unit, it is necessary to assume that the coherence regions from both directions do not collide. In figure 4, the exciton coherence length of the molecule is calculated to be 2.84 by employing the fluorescence lifetimes at the first and fourth emissive levels in the FIT of 1.65 and 2.28 ns, respectively, and the fluorescence quantum yield of 0.071 of CZ4.
The average exciton coherence length of CZ4 was determined to be 2.74 from 20 single-molecule datasets. This value is shorter than four of the linear array Z4 . The cyclic structure of CZ4 probably cannot cause an exciton to be fully delocalized among all four porphyrins, because the transition dipoles of the porphyrins are arranged nearly orthogonal to one another, which reduces the excitonic interactions among the four porphyrin units. In CZ6 and CZ8, the exciton coherence length could not be examined because their FITs did not show clear stepwise photobleaching behaviours.
(b) m-Phenylene linked cyclic porphyrin wheels (CNZA and CNZB)
Two types of a series of extremely large yet discrete cyclic porphyrin wheels were also prepared to explore EET processes. The directly meso–meso linked porphyrin dimer Z2 and tetramer Z4 are bridged by m-phenylene spacers, respectively, to form cyclic structures CNZA (N=10,12,16,18,24 and 32) and CNZB (N=24; scheme 4) [15,16].
The absorption spectra of C12ZA and C24ZB are similar to those of dimer Z2 and tetramer Z4 subunits, respectively, while the further split Soret bands of C12ZA indicate additional dipole–dipole interaction between Z2 subunits via the m-phenylene spacer. These data indicate that the electronic interactions are predominated by the exciton coupling within meso–meso linked porphyrin subunits. In the absorption spectra of CNZA, the peak positions of low-energy Soret bands converge into a single position, which originates from exciton couplings among non-unidirectional transition dipole moments in circular geometries. According to this feature, it can be conceived that three-dimensional orientations between two adjacent Z2 subunits remain relatively the same in all CNZA [17–19].
To explore the fast EET processes at the ensemble level, femtosecond TA and TAA measurements were conducted on Z2, 2Z2 and C12ZA [20,21]. In the TA decays, Z2 and 2Z2 reveal no power dependence and show only single decay components that are in agreement with the S1-state lifetimes. On the other hand, the TA decay of C12ZA appears to be very sensitive to the pump power; when the pump power is increased, the contributions of relatively fast components, τ1 and τ2, are enhanced relative to the slowest component, τ3 (figure 5a). The pump power dependence of the TA decays is a strong indication of exciton–exciton annihilation, because the excitation with high density of photons may generate two or more excitons in one cyclic array, followed by recombination between the excitons, which give rise to fast deactivation channels. Figure 5b shows TAA decay profiles of Z2, 2Z2 and C12ZA. While Z2 exhibits the single decay component with a time constant of 0.17 ps, 2Z2 and C12ZA exhibit two decay components: 0.18 and 4.70 ps for 2Z2 and 0.16 and 1.22 ps for C12ZA. Since the time constants of fast components are well matched with that of Z2, these components are thought to arise from the depolarization within Z2. On the other hand, we consider that the slow components result from the depolarization owing to the EET between Z2 subunits via m-phenylene spacer.
When the Förster-type incoherent energy hopping model is employed by assuming a migration-limited character of exciton–exciton annihilation and a random walk formalism of anisotropy decay [22–25], the analytical exciton–exciton annihilation and depolarization times are connected with EET time by equations (3.1) and (3.2): 3.1and 3.2where N is the number of effective hopping sites, α the angle between the adjacent transition dipoles, τannihilation the slowest exciton–exciton annihilation time and τhopping the inverse of the nearest neighbour energy hopping rate. Equation (3.1) assumes that the exciton–exciton annihilation reflects the migration-limited exciton–exciton recombination along the whole cyclic array and how many hops are required for this recombination to be accomplished. On the other hand, equation (3.2) is understood by considering that the depolarization is complete when the transition dipole migrates through 90° and that how many hops are required for this rotation to be accomplished. As C12ZA consists of six Z2 subunits, the number of hopping sites would be N=6. Introducing N=6 and α=60° in equations (3.1) and (3.2), the EET rates between neighbouring Z2 subunits are calculated to be 3.66 and 4.25 ps−1, respectively. It is noteworthy that the two different experimental observables, exciton–exciton annihilation and anisotropy depolarization times, result in a consistent EET rate of 4.0±0.4 ps−1 within a small error range.1
The EET rate between neighbouring Z4 subunits in C24ZB was determined similarly by TAA measurements to be 36 ps−1 (scheme 4), which is almost the same as that of the reference molecule 2Z4 [15,17]. A large difference between the EET rates of C12ZA and C24ZB is explained in terms of a large difference in the centre-to-centre distance of meso–meso linked porphyrin subunits: the distance of C24ZB is ca 1.5-fold longer than that of C12ZA, which, on the basis of the distance factor of R−6 in the Förster EET equation, explains well the approximately 10 times difference in the observed EET rates.
To calculate the EET rates in CNZA, an appropriate modelling is important because it is thought that, for all cyclic arrays, numerous conformational isomers could exist in solution . If all cyclic arrays have ideal circular structures (regular polygon model), we can obtain the values of αflat and Nflat from equation (3.2) as shown in table 1. On the other hand, if we assume that the geometrical structure of 2Z2 would be similar to those in CNZA as supported by the absorption spectra, we can regard the EET time τhopping in all CNZA as that of 2Z2 (5.4 ps). Hence, equation (3.2) substituted by the observed depolarization time τdepolarizatin and the fixed EET time τhopping provides the calculated values of and for CNZA (table 1). Although a different approach is applied, values of C12ZA, C16ZA and C18ZA are in good accordance with the ideal Nflat values, indicating that these arrays exist as circular polygon structures. In a sharp contrast, C10ZA, C24ZA and C32ZA show a large discrepancy not only between and Nflat values but also between and αflat values. These features reveal that the constituent motif of m-phenylene linked 2Z2 is not ideal to form cyclic porphyrin arrays without structural distortions in C10ZA, C24ZA and C32ZA mainly due to the interchromophoric angle of 120° between the neighbouring subunits.
At the single-molecule level, the EET efficiencies of individual cyclic porphyrin arrays were examined by carrying out coincidence measurement [17,18]. This measurement allows for the observation of singlet–singlet annihilation processes occurring in a single molecule (figure 6a) [26,27].
Note that efficient EET mediates the collision of two or more excitons that are generated by single intense laser pulse to bring one exciton to a higher excited state, followed by relaxation of this exciton in the form of fluorescent emission of a photon. In such a case, a time interval between two consecutive detected photons conforms to a multiple of the laser repetition rate (NL in figure 6b). On the other hand, if photon pairs induced by the same laser pulse are emitted simultaneously owing to the absence of this process, the interphoton time would be zero (NC in figure 6b). Thus, a NC/NL value obtained from interphoton arrival time distribution of a single molecule can directly be related to the EET efficiency. In figure 6b, the NC/NL value of C12ZA is calculated to be 0.15, which implies that singlet–singlet annihilation readily occurs owing to the efficient EET within the array. For a statistical analysis, histograms of the NC/NL values were constructed. The distribution of NC/NL values of C24ZB is slightly shifted to higher values relative to that of C12ZA (figure 6c), which reveals less efficient EET in the larger array. Similarly, in the histograms of NC/NL values of C10ZA, C12ZA and C16ZA, the distributions are shifted to higher values in the order of C12ZA (0.24), C10ZA (0.34) and C16ZA (0.38) (figure 6c). The smallest NC/NL value found for C12ZA among the investigated arrays reveals that the overall structure of C12ZA is rigid enough without any significant distortion in the solid state.
4. Self-assembled porphyrin boxes
(a) Porphyrin boxes consisting of directly meso–meso linked diporphyrins (BNA)
Three-dimensional Zn(II) porphyrin boxes BNA (N=1, 2 and 3) were constructed by self-assembly of meso–meso pyridine-appended Zn(II) diporphyrins DNA (scheme 5), where the size of BNA is controlled by inserting one or two phenyl groups between the porphyrin and pyridyl substituents .
Owing to the different meso–aryl substituents, D1A–D3A are all chiral. Accordingly, the spontaneous box formation is achieved through homochiral self-sorting association of the respective (R) and (S) isomers of D1A–D3A. The absorption spectra of BNA show much smaller split Soret bands than those of DNA. In addition, the extent of split also exhibits a systematic change depending on the size of box ; while the high-energy Soret band remains at the same position, the low-energy Soret band shifts to blue in the order of B3A<B2A<B1A. The complicated Soret band splitting observed in BNA arises from various dipole–dipole excitonic interactions among eight mutually perpendicular porphyrin units. The low-energy Soret state indicates excitonic dipole–dipole interactions among eight parallel transition dipole moments along the x-axis, whereas the high-energy Soret state implies excitonic dipole–dipole interaction among four parallel transition dipole moments along the y- or z-axis (scheme 5).
The EET processes in BNA were examined by performing TAA measurements . While DNA reveal only slow TA decays without any anisotropy decays in the time region of tens of picoseconds, BNA show a relatively fast TAA rise (12, 25 and 89 ps for B1A–B3A). The EET rates were calculated to be 48, 100 and 356 ps−1 for B1A–B3A by introducing α=90° in equation (3.2). On the other hand, the slowest exciton–exciton annihilation times of 30, 60 and 228 ps were observed for B1A–B3A from the TA measurements. Using equation (3.1) with N=4 gives rise to the EET rates of 48, 96 and 365 ps−1 for B1A–B3A. The number of hopping sites of four seems to be reasonable because, in BNA, directly meso–meso linked diporphyrin is likely to act as a single hopping site. The obtained exciton hopping rates from the two separate measurements are consistent with each other.
(b) Porphyrin boxes consisting of conjugated diporphyrins (BNB)
Another type of three-dimensional Zn(II) porphyrin boxes, B2B and B4B, were also prepared by self-assembly of alkynylene-bridged diporphyrins, D2B and D4B . Because of the rotational conformational heterogeneities of DNB along the alkynylene linkers, two kinds of self-assembled porphyrin boxes are constructed by planar or orthogonal conformers, respectively (scheme 6).
Using the alkynylene-bridged diporphyrins as building blocks is advantageous in that the alkynylene linkers provide extended π-conjugation between porphyrin units, resulting in new, low energy and strong electronic transitions of Q-bands. These features ensure enhanced solar spectral absorption and efficient EET processes.
To reveal fast EET processes in B2B and B4B, TA measurements were performed . The planar and orthogonal conformers were selectively excited to explore the effect of the dihedral angle between porphyrin units in alkynylene-bridged diporphyrins on the EET processes in BNB. In the case of porphyrin boxes comprising planar conformers, introducing N=4 and the observed time component of 1.1 ps in equation (3.1) reveals the EET rate of approx. 1.2 ps−1 (scheme 6). Because the time component related to this process does not become slower as the distance between two porphyrin units within a dimer changes, we can directly assign this annihilation component as the exciton hopping time among the four building blocks. In a similar manner, the time component of 0.7 ps of porphyrin boxes that are constructed by orthogonal conformers also can be related to the EET rate of approx. 1 ps−1 among the four constituents. For these porphyrin boxes, additional slow time component of 10 ps was observed and this component gives rise to the EET rate of 12 ps−1 by assuming N=4 (scheme 6). On the basis of the analysis of the calculated Förster energy transfer rates, it is suggested that the dihedral angle of 90° causes additional EET processes among exciton states localized on porphyrin monomers within the orthogonal dimer.
The EET processes of various forms of porphyrin arrays have been explored for the purpose of applications in molecular photonics and electronics. It has been proved that the mechanisms and rates of EET processes are modulated by the electronic interactions of porphyrin arrays, which range from excitonic dipole–dipole interaction to extensive π-conjugation and a proper combination of these two as well. The fundamental information on the EET processes presented here will serve as a platform in designing novel porphyrin arrays with tuned electronic couplings to elicit desired photophysical properties.
We express our sincere gratitude to the colleagues with whom we have been collaborating over the years on this subject, in particular, Prof. Atsuhiro Osuka (Kyoto University) and his skilled graduate students and postdoctoral fellows. This research was financially supported by World Class University (R32-2010-000-10217) and Mid-career Researcher (2010-0029668) Programmes from the Ministry of Education, Science, and Technology of Korea, and by AFSOR/AOARD grant no. FA2386-10-1-4080.
One contribution of 14 to a Theo Murphy Meeting Issue ‘Quantum-coherent energy transfer: implications for biology and new energy technologies’.
↵1 Based on the Förster EET equation, we have calculated the EET rate between neighbouring Z2 subunits in 2Z2 to be 251 ps−1. The details of the calculation are presented in Yoon et al. . The large discrepancy between the experimental and the calculated EET rates might be interpreted in two ways: (i) significant participation of through-bond energy transfer processes in the overall energy transfer processes and (ii) failure of the point-dipole approximation of Förster's resonance energy transfer model in the case of a relatively short distance between donor and acceptor. Since Förster's model overestimates the EET rate in the latter case, the observed fast hopping rate of 2Z2 is more likely elucidated by the contribution of the through-bond energy transfer processes.
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