Excitonic coupling directly revealed on single chains of polyuorene by combined force spectroscopy and uorescence microscopy

Molecular aggregates were discovered in 1930’s, yet, the forces and excitonic coupling energy associated with the aggregate formation have not been detected so far. We directly measure such force and energy on single chains of the conjugated polymer polyfluorene using atomic force and fluorescence microscopes. The polyfluorene chain is attached on either side to a substrate and an AFM tip, respectively, and mechanically stretched under intense laser irradiation. The force – extension curves show force peaks that are attributed to gradual unfolding of the chain. Upon the irradiation, neighboring conjugated segments interact via excitonic coupling when in contact and experience an attractive force which is detected by the AFM. Analysis of the force curves provides excitonic coupling energy which is of same order as theoretically calculated values for a face-to-face fluorene dimer, and in agreement with the energy obtained from single-chain fluorescence spectra. Apart from contributing an essential piece of knowledge in the field of molecular photophysics, the work demonstrates on molecular scale a novel energy conversion mechanism from light to mechanical energy which could be potentially used, e.g., as a driving mechanism for molecular motors.

The exceptional photophysical properties of molecular aggregates continue to fascinate scientists since their discovery 1,2 . Upon mixing in solutions under specific conditions, certain organic dyes can form both J-and H-aggregates, characterized by varying color and distinct spectral and photophysical features [3][4][5] . Over the decades, great effort has been spent on synthesis of novel dyes and utilization of the unique properties of molecular aggregates for functional materials 6.7 . The phenomenon is not restricted to aggregation of small-molecule dyes but has been also observed to cause some of the characteristic properties of light absorbing and emitting conjugated polymers 8 . The signature spectral features of molecular aggregates, the bathochromic (for J-aggregates) and hypsochromic (for H-aggregates) absorption shifts, have been successfully explained by the dye geometrical arrangement in Kasha's theory 3 . The theory itself has roots in the concept of molecular excitons 9 and its application in molecular crystals 10 . The spectral shifts are explained due to splitting of the excited state of the aggregate caused by dipole-dipole interaction between transition dipole moments of neighboring molecules. The amount of the splitting, which provides the exciton coupling energy, depends on the distance between the molecules, their arrangement and on the magnitude of their transition dipoles.
The arrangement of the molecules also determines the allowed or forbidden character of optical transitions into the split states, which in turn determines the H-or J-character of the aggregates. While the Kasha's theory is relatively simple, it has been successfully used to qualitatively describe experimental results on a range of molecular structures over the decades. Still, there has been so far no direct measurement of the energy associated with the exciton coupling, other than by spectroscopic means.
The dipole-dipole interaction between two neighboring molecules is an attractive one, leading to a strongly bound pair in the lower energy level of the split excited state.
Separating such bound state under illumination therefore requires mechanical force that can be, in principle, provided and measured by atomic force microscopy (AFM). The feasibility of such approach has been shown theoretically for force spectroscopy on dimers of perylene and terylene derivatives which were estimated to require forces on the order of pN to tens of pN to break the excitonic bond 11 . Experimentally, force spectroscopy based on stretching of single macromolecular chains with an AFM cantilever has become an established technique that has been used to study conformational changes, nanorheology, mechanical dynamics and function of DNA, proteins as well as synthetic polymers [12][13][14][15][16][17][18] . Further, the single-chain force spectroscopy has been combined with optical microscopy to demonstrate an optomechanical cycle on photochromic dyes 19 or to study and manipulate protein conformations 20,21 .
Synthetic conjugated polymer chains in compact conformations or in films often exhibit spectral properties that can be explained as a result of interactions between individual conjugated segments of the chain. Conjugated segments take a role of individual chromophores and interaction between their transition dipole moments gives rise to phenomena that are well known for aggregates of small molecules, including J-or H-aggregation or excimer formation 22-25 . A good example is the conjugated polymer polyfluorene which is known for its outstanding optoelectronic properties including bright blue emission in solution 26,27 . Under specific conditions the blue emission can be accompanied by a green emission band, the origin of which has been a subject of longstanding debates 28 , but which has recently been shown, on single-molecule level, to arise from intra-chain aggregates 29,30 .
Here, we directly measure the excitonic coupling energy associated with molecular aggregates on single polyfluorene chains using a combination of force spectroscopy and 5 fluorescence microscopy. The polyfluorene chain is mechanically stretched by an AFM cantilever from a self-folded conformation into completely stretched state, and the stretching is accompanied with intense laser irradiation close to the polyfluorene absorption peak. Under such conditions, the force curve of the chain unfolding shows small force peaks that are attributed to excitonic coupling of an intra-chain H-aggregate.

Single PFO chain stretching in dark
Single chain force spectroscopy was performed with poly(9,9-dioctylfluorene) (PFO) terminated at both ends with amino groups. The amino groups react on either ends with epoxy groups on the surface of silane-functionalized quartz substrate and silicon cantilever to form covalent bonds (Fig. 1a). Immobilization of individual amino-   The larger average rupture length value indicates that longer polymer chains are more easily picked up by the AFM cantilever because the amine-terminated free end of the polymer chain diffuses in a hemisphere whose diameter corresponds to chain length, and a larger hemisphere increases the reaction probability.

Single PFO chain stretching under illumination
Typical force spectra in the presence of 14.

Analysis of the coupling energy
The force spectroscopy results are further analyzed and interpreted in terms of excitonic coupling between conjugated segments of a folded PFO chain, as schematically shown in Fig. 2a. In the initial phases of stretching under illumination, two conjugated segments are coupled face-to-face in H-aggregate manner. This excitonic coupling is broken as the chain is lifted by stretching (Fig. 2b), resulting in the appearance of the small force peak (Fig. 2c). Integration of the force-extension curve provides energy associated with the excitonic coupling. Further, the extension length along the force peak is related to the coupling length (shown in Fig. 1b).

Comparison with quantum chemical calculations and single-chain fluorescence
Feedback on the values obtained from the force spectroscopy can be provided by quantum chemical calculations and by spectroscopic data. The Fig. 3a shows the molecular aggregate energy scheme as introduced in the Kasha's model. Splitting of the S1 energy level provides the excitonic coupling energy which can be also obtained from a spectral shift between monomer and aggregate fluorescence bands. An example of a fluorescence spectrum of a single PFO chain measured in softened polystyrene matrix during solvent vapor annealing 33 is shown in Fig. 3b. Under such conditions, the PFO spectrum shows dynamic changes between the monomer spectrum peaked around 420 nm and the green band between 530 and 580 nm, due to the chain conformational dynamics 33 .   35 (atomic transition charges, ATC). Since, generally, the excitonic coupling is sufficiently well described by the Coulombic contribution 34 , we follow a previous approach 11 and use the ATC method to calculate the excitonic coupling energy of a faceto-face stacked fluorene dimer as a function of the intermolecular distance. The geometrical arrangement is shown in Fig. 3c, d, and results of the calculation for the S0-S1 transition using DFT and TD-DFT at the B3LYP/6-31G++(d,p) level are shown in Fig.   3e. The calculated coupling energy of a dimer is multiplied by 8 in the Fig. 3e to account for the average length of the PFO conjugated segment 32 . For a realistic range of intermolecular distances between 2 Å and 8 Å the calculated coupling energy ranges from 0.46 eV to 0.023 eV. For the shorter distances in this range, these values are of the same order of magnitude as the excitonic coupling of 0.82 eV obtained from the force spectroscopy. Deviations from the geometry shown in Fig. 3c, d lead to reduced coupling energy, as shown in the calculation results in Supplementary Fig. 3 and Supplementary   Fig. 4. Such effects could be responsible for the deviation from linearity observed in Fig.   2f. A lack of still better agreement between the above calculated and experimental results could be caused by a non-negligible contribution of the short-range interactions or by the size of conjugated segments which could be larger that the 8 monomer units 36 .

Conclusions and outlook
Strong light-induced coupling between molecules in molecular aggregates resulting in an attractive force has been known for decades but direct demonstration of the coupling strength by mechanical means has not been attempted or achieved so far. We succeeded in such demonstration not only qualitatively using atomic force microscopy but to a large extent also quantitatively using single-molecule spectroscopy and quantum chemical calculations as a references. The results contribute an important piece of knowledge in the field of molecular photophysics, and will have an impact in related areas as well. In addition, the work demonstrates on molecular scale a novel energy conversion mechanism from light to mechanical energy, and this fact could have implications, e.g., in development of driving mechanisms of future molecular motors.  dropped onto the functionalized substrate. After THF was completely dried, the substrate was rinsed with toluene to remove the unreacted polymer chains and dried with N2 gas.

Functionalization of AFM cantilever
AFM cantilever was functionalized in almost the same way as the quartz substrate.
First, the cantilever was immersed in ethanol for 1h and transferred into alkaline solution (NH4OH/H2O2/H2O, 1:1:5 v/v) for 1 h. Then, the cantilever was soaked in piranha solution (H2SO4/H2O2, 7:3 v/v) for 30 minutes and thoroughly rinsed with water. Finally, the cleaned cantilever was incubated overnight in 3-Glycidyloxypropyltrimethoxysilane (TCI) and thoroughly rinsed with ethanol and toluene.

Combined confocal and atomic force microscopic setup
The single molecule and AFM measurements were carried out using a home-built setup that combines an inverted fluorescence microscope (IX 73, Olympus) with an AFM head (MFP-3D-SA, Asylum Research). The AFM cantilever used was HQ:CSC38/Al BS (MikroMasch). Nanofishing experiments were performed in toluene. The sample was excited with a 375 nm laser (LDH-D-C375, Pico Quant). Fluorescence from the sample was collected by an oil immersion objective lens (UplanFLN 100×, N.A. 1.3, Olympus) and passed through a dichroic mirror (Dichro 375, Chroma) and a long-pass filter (LP 377, Edmund). The objective lens was mounted on a three-axis piezo stage (PS3L60-030U, NC3311, Nanocontrol) to accurately align its center position with respect to the AFM tip. The fluorescence signal was detected by an electron-multiplying charge-coupled device (EMCCD) camera (iXon, Andor Technology) equipped with an imaging spectrograph (CLP-50LD, Bunkou Keiki) to measure fluorescence spectra. The integration time and gain of EMCCD were 0.2 s and 300, respectively.

Theoretical calculation of excitonic coupling between two PFO segments
Excitonic coupling J is calculated following the same way as reported recently for simulation of force spectroscopy of PDI molecule dimer 11 . The Coulombic interaction is calculated as the interaction between atomic transition charges (ATCs). ATCs for p-th atom in the k-th excited state was expressed as where rij is the distance between atom i and j of molecule I and J and ε0 is the vacuum permittivity. The ATCs of each atom were calculated from isolated fluorene monomer for S0-S1 transition using DFT and TD-DFT at B3LYP / 6-31G++(d,p) level. Because the effective conjugation length of PFO is 8 monomer units 32 , the calculated Jc between the two fluorenes was multiplied by the factor of 8.

Data availability
Data available on request from the authors.