Mechanical Stiffening of Porphyrin Nanorings through Supramolecular Columnar Stacking

Solvent-induced aggregates of nanoring cyclic polymers may be transferred by electrospray deposition to a surface where they adsorb as three-dimensional columnar stacks. The observed stack height varies from single rings to four stacked rings with a layer spacing of 0.32 ± 0.04 nm as measured using scanning tunneling microscopy. The flexibility of the nanorings results in distortions from a circular shape, and we show, through a comparison with Monte Carlo simulations, that the bending stiffness increases linearly with the stack height. Our results show that noncovalent interactions may be used to control the shape and mechanical properties of artificial macromolecular aggregates offering a new route to solvent-induced control of two-dimensional supramolecular organization.


Further Images and Analysis of Crossing Polymer Nanorings
The height of two overlapping single rings (see Fig. 1A) is 0.40 nm and is consistent with our observation of two stacked rings. Also, the bright overlapping region between the single and the double ring is consistent with the measured ring height of a triple stack. Figure S1: Overlapping arrangement of one double ring (left) and two single rings. Scale bar length is 5 nm. The height profiles indicate that a double stacked ring is consistent with two overlapping single rings. Figure S2 shows a stacked nanoring with the 24 porphyrin sub-units identified. Figure S3 shows a low coverage of c-P24. Figure S2: STM image of triple stack ring. Scale bar length is 6 nm. Tunnel current, 30 pA, sample voltage -2.0 V. Figure S3: STM images that indicate the preferential adsorption at gold step edges. Tunnel current, 30 pA, sample voltage -2.0 V. The rings were deposited from toluene/methanol. The Scale bar lengths are 40 nm.

Solution-Phase UV-visible-near infrared Titrations
When pyridine is added to a solution of c-P24 in chloroform, there is a noticeable colour change from red to green. The evolution of the UV-vis-NIR spectrum with increasing pyridine concentration is shown in Figure S4. The blue-shift of the Q band and the narrowing 4 of the B band are typical indications of a dissagregation process [H. L. Anderson, Inorg. Chem. 1994, 33, 972 and T. E. O. Screen, et al., J. Mater. Chem. 2003, 13, 2796. The spectra in Figure S3 were acquired with a equilibration time of 1 hour after each addition of pyridine, however even with this long delay, the system did not completely reach equilibrium during the early stages of the titration. The slow kinetics is another indication of a disaggregation process because coordination of pyridine to a zinc porphyrin is normally very rapid. Figure S4: UV-vis-NIR absorption spectra of c-P24 (concentration: 0.15 µM) in toluene at increasing concentrations of pyridine (concentration: 0 to 7 mM). Spectra recorded at 298 K is a 10 mm quartz cuvette with a 1 hour equilibration delay after addition of each aliquot of pyridine.

Computational Model and Monte-Carlo Simulations
The discrete form of the energy functional describing the elastic energy of deformation may be written as, where C i and ∆s i are the local curvature and segment length at the i th bending point, κ S is the stretching stiffness, and L is the equilibrium separation between bending points. The second term in the functional is a term which describes the energy due to bond stretching. This is introduced for computational reasons in order to access the available configurations of the nanorings more efficiently. Since the interest here is in nanorings governed by bending rather than stretching we use κ S >>2κ B /L 3 .
Local curvatures and segment lengths may be expressed purely in terms of vectors {s} to give the total energy expression which is expressed in a manner such that the summation prefactors represent characteristic bending (κ B /L) and stretching (κ S L 2 /2) energies respectively.
One final consideration of nanoring energetics relates to their physical size, and the bending limitations imposed by the unfavourable overlapping of porphyrin macrocycles. This behaviour can be modelled by placing hard discs (overlapping of which costs an infinite energy penalty) at the midpoints between bends; the size of these discs controls the maximum bending angle to limit the bending angle to 60°. Hard discs of diameter √3L/2 are used throughout to impose this bending restriction (see inset of Figure 4A), which also prevents any parts of a ring from overlapping.