Nanoscale π-conjugated ladders

It is challenging to increase the rigidity of a macromolecule while maintaining solubility. Established strategies rely on templating by dendrons, or by encapsulation in macrocycles, and exploit supramolecular arrangements with limited robustness. Covalently bonded structures have entailed intramolecular coupling of units to resemble the structure of an alternating tread ladder with rungs composed of a covalent bond. We introduce a versatile concept of rigidification in which two rigid-rod polymer chains are repeatedly covalently associated along their contour by stiff molecular connectors. This approach yields almost perfect ladder structures with two well-defined π-conjugated rails and discretely spaced nanoscale rungs, easily visualized by scanning tunnelling microscopy. The enhancement of molecular rigidity is confirmed by the fluorescence depolarization dynamics and complemented by molecular-dynamics simulations. The covalent templating of the rods leads to self-rigidification that gives rise to intramolecular electronic coupling, enhancing excitonic coherence. The molecules are characterized by unprecedented excitonic mobility, giving rise to excitonic interactions on length scales exceeding 100 nm. Such interactions lead to deterministic single-photon emission from these giant rigid macromolecules, with potential implications for energy conversion in optoelectronic devices.

their shorter conjugation length. Upon close inspection, one can discern a slight blue shift of the open octamer 10 8 as well, suggestive of slight bending, which may decrease the effective conjugation length.
Also notable is the slight difference in the vibronic contribution between the system containing four repeat units and the larger systems, providing further evidence for a greater conjugation length in the latter. The fact that emission spectra are virtually identical for both open and closed formations points to efficient excitation energy transfer to the longer conjugated segments of the molecules.
Note that, at first inspection, conjugation in the connecting segments between the ladder strands may appear feasible. However, the central phenylene is expected to twist out of the plane of conjugation because of interactions with the NC 6 H 13 groups on either side. There is no indication of an electronic delocalization effect due to conjugation through the ladder rungs in either absorption or fluorescence.
Comparison of the absorption spectrum of the individual "rung" monomer 9 to the rail oligomers in Supplementary Fig. 1 shows that there is an absorption feature in this spectral region for all systems under consideration. However, since this absorption is of high energy, one would expect energy transfer to larger conjugated parts of the molecule to prevent emission from these rung segments, and indeed we see no evidence for such emission. However, we do have preliminary evidence (not shown) that the singlemolecule excitation polarization modulation depth decreases for shorter excitation wavelengths.

Supplementary Note 1.1.2: Transient fluorescence depolarization spectroscopy
To measure the transient fluorescence depolarization shown in Figure 2 of the main text, the so-called Lformat method with a single emission channel is used 1 , as sketched in Supplementary Fig. 2. The analyte is excited by a frequency-doubled Ti:sapphire femtosecond laser system (Chameleon Ultra II, Coherent Inc., and HarmoniXX, APE GmbH), operating at 450 nm. To determine the polarization sensitivity of the setup, a half-wave plate allows to switch between vertically and horizontally polarized excitation. The emission is detected with a Hamamatsu streak-camera system consisting of a spectrograph (Bruker 520IS, Bruker Corporation), a streaking unit (C5680, Hamamatsu Corporation), and an ORCA-ER CCD camera (C4742-95, Hamamatsu Corporation). By measuring vertically (IV(t)) and horizontally polarized (IH(t)) emission components upon vertically polarized excitation, the time resolved anisotropy r(t) is calculated as shown in Supplementary Fig. 2. The vertically and horizontally polarized emission can also be referred to as I || and I Ʇ since it is parallel respectively perpendicular to the vertically polarized excitation. To correct for the polarization sensitivity of the detection setup, vertically and horizontally polarized emission components were also detected under horizontally polarized laser excitation. With these two which limit the single-molecule fluorescence yield. An inverted microscope (Olympus IX71) was used for wide-field as well as for confocal excitation of the samples, and for fluorescence detection.

Supplementary Note 1.2.2: Excitation polarization modulation depth
To perform the excitation polarization measurements, a fibre-coupled diode laser (PicoQuant LDH-C-440) with a wavelength of 440 nm was operated in continuous mode and the excitation light was passed through a clean-up filter (AHF analysis technology, HC Laser Clean-up MaxDiode 445/10). Subsequently, the linearly polarized excitation laser beam was rotated with an electro-optical modulator (FastPulse Technology Inc., 3079-4PW) and an additional λ/4-wave plate as described elsewhere 2 . The laser beam was expanded and focused via a lens system onto the back focal plane of the oil-immersion objective (Olympus, UPLSAPO 60OX, NA = 1.35) through the back port and a dichroic mirror (AHF analysis technology, RDC 442 nt) in the microscope. An excitation area of ≈ 80 × 80 µm² was generated in the focal plane and the fluorescence of the sample was collected by the same objective, subsequently passing through the dichroic mirror onto an EMCCD camera (Andor iXON3 897). The excitation intensity was set to ≈ 500 mW/cm 2 and the overall magnification resulted in a spatial resolution of approximately 160 nm 2 per pixel, leading to diffraction-limited spots of ≈ 2 × 2 pixels for a single molecule. The polarization was rotated by 180° over periods of 20 s and the fluorescence intensity of each spot was recorded as a function of the polarization angle. A total spot size of ≈ 5 × 5 pixels was assumed to calculate the overall intensity and the local background of the surrounding area was subtracted for each molecule. The data analysis was conducted with a customized software in MATLAB 3 . During data evaluation, it became clear that the measured modulation depth is slightly dependent on the plane of polarization of the molecular absorption, i.e. on the absolute orientation of the transition dipole moment. Such an effect can be caused by a slight polarization artefact of the setup, most probably induced by the dichroic mirror installed, and effectively decreases the apparent modulation depth measured. Such an artefact only becomes apparent in highly polarized absorbers. We therefore sorted the molecules with respect to their absolute phase angle in the modulation experiments, i.e. with respect to their orientation in the laboratory frame, and discarded those single molecules from further evaluation, which were orientated along the less-sensitive detection direction of the setup. This selection procedure was performed analogously for all samples to ensure comparability between the different datasets.

Supplementary Note 1.2.3: Single-molecule photon-correlation spectroscopy
For this measurement, the samples were excited by a frequency-doubled Ti:sapphire oscillator (Spectra Physics MaiTai BB) with laser pulses of approximately 80 fs duration and a repetition rate of 80 MHz. The wavelength was set to 440 nm and the beam was expanded to a diameter of ~1 cm with a lens system before being coupled into the oil-immersion objective. An excitation intensity of ≈ 200 W/cm 2 was used for the tetramers (10 4 , 12 4 ) and octamers (10 8 , 12 8 ) and an intensity of ≈ 40 W/cm 2 for the polymers (10 n , 12n). To obtain fluorescence images, an area of 20 × 20 μm 2 was scanned using a piezo stage (Physik Instrumente (PI) GmbH & Co. KG). Using the piezo stage and the fluorescence images, the laser beam was focused on one single molecule at a time and its emission was collected by the objective and subsequently spatially and spectrally filtered by a 50 μm pinhole and a fluorescence filter (AHF Analysentechnik AG, Edge basic LP 442 long-pass filter). The filtered fluorescence was split with a 50:50 beam splitter into two equivalent detection channels. Two avalanche photodiodes (APD) from PicoQuant (τ-SPAD-20), connected to a time-correlated single-photon counting module (TCSPC, PicoQuant GmbH, HydraHarp 400) were used as detectors. A Hanbury Brown and Twiss 4 arrangement was used to measure the time difference ∆τ between photon arrival times. The TCSPC data was correlated and evaluated using a LabView program. An example histogram of correlation events for a closed octamer 12 8 is shown in Supplementary Fig. 3. The central peak counts the occurrence of photons recorded on both detectors after one laser pulse whereas the lateral peaks count how often there is a difference of one, two or three laser pulse periods between incident photons. Following Ref. (5), the central and mean lateral values of the photon coincidence histogram can then be used to calculate the number of independent emitters as shown in Supplementary   Fig. 3. For the histogram in Figure 4 of the main text, this analysis was performed for each molecule individually. To correct for the background, the signal-to-background ratio S/B for each molecule was determined from the fluctuations in the intensity time traces, and a theoretical limit for the number of emitters present was calculated as explained in detail in Ref. 5. As the S/B ratio ranges between 75 and 600 for all single molecules, the theoretical minimum of the number of emitters extracted from the photon antibunching dip in the correlation is below 1.05 for the case of one emitter and below 2.11 for the case of two emitters as shown in Supplementary Fig. 3. Figure 3. Photon antibunching measurement to determine the number of independent emitters in a molecule. Left: an example of a photon correlation histogram obtained for one single closed octamer molecule 12 8 , as extracted from the PL intensity trace. The correlation events for each shift in time ∆τ between two laser pulses in intervals of the laser period TLaser = 12.5 ns are counted, and the resulting histogram is normalized to the mean value of occurrences on the lateral peaks NL. This value describes the amplitude of correlations for photon arrival times with a time lag larger than one excitation pulse period. The probability of measuring two photons at the two detectors for one and the same laser pulse is given by the central peak value NC, which is 0.011 for the example of a closed octamer molecule depicted. The central-to-lateral peak value ratio, NC/NL, can be evaluated for each molecule measured individually, as was done in Figure 4 of the main text. For each individual ratio N C /N L , the number of independent emitting units can be computed. To correct for the influence of the fluorescence background in the measurement of the photon correlation, the signal-to-background (S/B) ratio of the measurement must be accounted for. This value ranges between 75 for dark molecules and 600 for bright ones. Following the analysis in Ref. 6, the theoretical minimum of NC/NL, and therefore the effective number of independent emitters, can be calculated as shown on the right-hand side of the figure. For dark molecules with a low S/B ratio of 75, the number of emitters determined from the photon antibunching dip rises from 1 to 1.05 for the case of one single emitter present, and from 2 to 2.11 for the case of two. In bright molecules with a large S/B ratio these values converge to 1 and 2, respectively.

Supplementary Note 1.2.4: Bimodal distribution of polarization modulation-depth histogram
We note that the distribution histogram of polarization modulation-depth values for the ladder polymer 12n contains a substantial number of low values. Interestingly, the statistical distribution in this low-value range appears to closely match the distribution observed for the open polymer structures 10n, as shown in Supplementary Fig. 4. We proposed that the distribution for 12 n is bimodal in nature and that the distribution in the range of low values arises from polymers for which a defect is present so that a kink occurs in the chain. An example of such a defect is discussed in more detail in the STM image in

Supplementary Note 1.3: Cryogenic single-molecule spectroscopy: sample preparation and setup
To measure the spectra at cryogenic temperatures shown in Fig. 4 of the main text, the analyte molecule samples were prepared as explained in section 1.2 except that sapphire glass was used instead of borosilicate glass for the cover slips. The substrate was mounted in a cold-finger helium-flow cryostat and cooled to a temperature of approximately 5 K. Excitation of the sample was carried out by a frequencydoubled Ti:sapphire femtosecond laser system (Chameleon Ultra II, Coherent Inc., and HarmoniXX, APE GmbH), operating at 440 nm. The laser was focused on the back focal plane of the objective (Olympus, LUCPLFLN40X) with a lens, resulting in parallel illumination of around 70 × 70 µm² on the sample. The redshifted fluorescence was subsequently transmitted through a dichroic mirror (AHF Analysentechnik, RDC 442 nt) onto a sCMOS-Camera (ORCA-Flash), which allows the inspection of all emitting molecules in the illuminated area. A fluorescence filter (AHF Analysentechnik AG, Edge basic LP 442 long-pass filter) blocks scattered laser radiation. The fluorescence of selected spots could then be focused on the entrance slit of a grating spectrometer (Princeton Instruments, Acton SP2300) with a lens. A grating of 600 grooves/mm was used to disperse the signal before the spectrum was recorded with a cooled CCD camera (Princeton Instruments, PIXIS 100). An integration time of 2 s or 1 s was used for the octamers and polymers, respectively, at an excitation power of approximately 800 W/cm 2 .

Supplementary Notes 3: Scanning-tunnelling microscopy Supplementary Note 3.1: Experimental setup and methods
Scanning tunnelling microscopy (STM) of 12 4 , 12 8  which is used as a calibration grid. Data processing, also for image calibration and noise filtering, was performed using the SPIP 5 (Image Metrology) software package. Molecular and supramolecular modelling was performed using Wavefunction Spartan '18.

Supplementary Notes 3.2: Additional scanning-tunnelling microscopy images
In addition to the STM images shown in Figure 7). Similar to the STM image of 12 4 , the STM image of 12 8 shows submolecularly resolved features, therefore allowing clear insights into the adsorbate pattern. In accordance with the reduced surface mobility related to the increased contact area of the adsorbed species with the substrate, the lamellae of not randomly adsorbed, but the backbones are rather shifted along the normal direction of the lamellae.
The intermolecular distances (determined by the interdigitating hexyloxy side-chain periphery) as well as the intramolecular rail-rail distance remain unaltered within the scope of measurement accuracy.
However, an example of one defective molecule is seen in Supplementary Fig. 7B. This defect, comprising one interrupted rail and the rotation of the ladder segments around the uninterrupted rail axis is marked by the arrow. Such a single defect would result in a kinked but otherwise rigid polymer chain. In solution, such a kinked chain of 12 n would then more closely resemble the conformation of the open polymer 10 n , offering an explanation for the seemingly bimodal appearance of the polarization modulation depth histogram in Supplementary Fig. 4. However, we found no evidence for such defect formation in GPC, MALDI or NMR of any of the compounds, suggesting that such defects are quite rare.

Supplementary Note 3.3: Comment on STM image resolution and visibility of defects
The resolution of the polymer strands, and that of the small molecules, achievable with the STM depends not only on the molecule-surface interactions, but also to a great extent on the intermolecular interactions.
Densely packed 2D crystalline monolayers of small molecules, even at the solid/liquid interface at room temperature, usually lead to very high resolution down to the level of individual CH2 groups (for densely packed alkanes), whereas disordered films, such as those made of polydisperse polymers, are typically visible only with significantly lower resolution. Examples of other STM images of single-stranded arylenealkynylene polymers have been published by Lei et al. 16 and Samorí et al. 17 , with a rather similar resolution to what we can achieve.
For the case of 12 4 , 12 8 , and 12 n this limitation implies the following: (1) In the 2D crystals or in the densely packed ordered monolayers formed by 124 and 128, respectively, the molecules are very well localized and immobile, which translates to a rather high image resolution.
(2) 12 n packs with a significantly lower degree of order, which translates to a higher degree of residual molecular mobility on the surface at room temperature. This thermal motion of the molecules is faster than the timescale of STM measurements, and therefore leads to lower image resolution. In particular, considering the densely packed image region of Supplementary Fig. 8A and Figure 1C   The pale-yellow precipitate was suspended in toluene and filtered again. The final filtrate was concentrated under reduced pressure. After adding EtOH, a yellow solid precipitated and was collected by filtration. 14 was obtained in the form of yellow crystals (4.25 g; 10.9 mmol; 54%).

Formula: C6H2I2N2S
Mol weight: 387.97 g mol -1 .        The number of carbon signals in the spectrum is less than expected, highly probably a result of signal broadening due to the imine-enamine tautomerism. piperidine (20 mL) were saturated with argon for 30 min and then added to the solids. The reaction mixture was stirred at ambient temperature for 3 d. The reaction was diluted with aq. hydrochloric acid (10%) and dichloromethane. The layers were separated and the aqueous layer was extracted with dichloromethane.
The combined organic layers were washed with water and brine, dried (Na 2 SO 4 ) and the solvent was evaporated. The crude product was purified by column chromatography (dichloromethane/ethyl acetate: 40/1, Rf = 0.47) to yield 4 (970 mg; 786 µmol; 55 %) as a yellow oil which solidified upon storing.

Formula: C78H104N4O5Si2
Mol weight: 1233.88 g mol -1 .   Due to the imine-enamine tautomerism the signals in the proton and carbon NMR spectra are significantly broadened, so that an analysis of the spectra is not possible. Therefore, it is not possible to make any statement on the purity of the compound. For this reason, no yield is given in this step.

Formula: C146H204N6O8Si4
Mol weight: 2283.61 g mol -1 .         The degree of polymerization was determined by GPC after 3 h, before 3,5-di-tert-butyl phenylacetylene was added in a large excess to terminate the reaction.   The overestimation factor of 1.4 for the tetramer 10 4 explains quantitatively the higher average degree of oligomerization determined by GPC (P n = 6.6) compared to the end-group analysis (P n = 4.8).  104 (4.8 mg, 535 nmol) was dissolved in dichloromethane (6 mL) and tetra-n-butylammonium fluoride (1 mL, 1 M in THF) was added. The reaction mixture was stirred at 35 °C for 3 h. Dichloromethane and water were added, and the layers were separated. The aqueous layer was extracted with dichloromethane, the combined organic layers were washed with water, dried (Na 2 SO 4 ) and the solvent was evaporated. The crude product was purified by recGPC. The product was obtained as a yellow film.

MS
Due to the small amount of substance, the product was not further purified as usual by precipitation following recGPC. For this reason, no exact weight was determined and no yield is given in this step.  1 M), and water, dried (Na2SO4), and the solvent was evaporated. The crude product was subjected to a short filter column (dichloromethane) and recGPC. The pre-purified product was diluted in dichloromethane and precipitated with methanol. After filtration, the product was obtained as a yellow solid (2.5 mg, 315 nmol, 59 % for two steps).

Formula: C544H668N16O32
Mol weight: 7943.41 g mol -1 . The crude polymer was purified coarsely by recGPC and separated into five fractions with low polydispersity. One of the fractions was dissolved in dichloromethane and precipitated with methanol.
After filtration, the polymer fraction was obtained as a yellow film. The peak molecular weight of the GPC analysis M p = 151.8•10 3 g mol -1 can be used to calculate the real molecular weight when divided by 1.78, the overestimation factor extrapolated for a degree of polymerization of 40. This gives the actual peak molecular weight of approximately 85.3 •10 3 g mol -1 which agrees well the MALDI-TOF results.
11n 10 n (approximately 10 mg) was dissolved in dichloromethane (10 mL) and tetra-n-butylammonium fluoride (1 mL, 1M in THF) was added. The reaction mixture was stirred at 35 °C for 1 h. Dichloromethane and water were added, and the layers were separated. The aqueous layer was extracted with dichloromethane, the combined organic layers were washed with water, dried (Na2SO4) and the solvent was evaporated. The crude product was purified via recGPC. The product was obtained as a yellow film.
Due to the small amount of substance, the product was not further purified as usual by precipitation following recGPC. For this reason no exact weight was determined and no yield is given in this step.  and by subsequent recGPC. The prepurified product was diluted in dichloromethane and precipitated with methanol. After filtration, the product was obtained as a yellow solid (1.9 mg, 23 %). Due to the small amount of product, no 1 H-NMR spectrum could be obtained.