Self-assembly of hydrogen-bonded two-dimensional quasicrystals

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The process of molecular self-assembly on solid surfaces is essentially one of crystallization in two dimensions, and the structures that result depend on the interplay between intermolecular forces and the interaction between adsorbates and the underlying substrate1. Because a single hydrogen bond typically has an energy between 15 and 35 kilojoules per mole, hydrogen bonding can be a strong driver of molecular assembly; this is apparent from the dominant role of hydrogen bonding in nucleic-acid base pairing, as well as in the secondary structure of proteins. Carboxylic acid functional groups, which provide two hydrogen bonds, are particularly promising and reliable in creating and maintaining surface order, and self-assembled monolayers of benzoic acids produce structure that depends on the number and relative placement of carboxylic acid groups2,3,4,5,6. Here we use scanning tunnelling microscopy to study self-assembled monolayers of ferrocenecarboxylic acid (FcCOOH), and find that, rather than producing dimeric or linear structures typical of carboxylic acids, FcCOOH forms highly unusual cyclic hydrogen-bonded pentamers, which combine with simultaneously formed FcCOOH dimers to form two-dimensional quasicrystallites that exhibit local five-fold symmetry and maintain translational and rotational order (without periodicity) for distances of more than 400 ångströms.

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Figure 1: STM images of FcCOOH and FcCH2COOH.
Figure 2: Calculations and proposed structures for FcCOOH dimers and pentamers.
Figure 3: Comparison of a FcCOOH monolayer structure to a P1 Penrose tiling.


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This work was supported by the US National Science Foundation under grant NSF CHE-1124762. The authors acknowledge high-performance computing resources and support from the Center for Research Computing at the University of Notre Dame.

Author information

N.A.W. and R.C.Q. performed STM measurements and made the initial experimental discovery. R.P.F., C.S.L. and S.A.C. designed the computational approach, and R.P.F. performed the calculations. J.A.C. and K.W.H. provided the molecules used, as well as several others used as tests and controls. All authors participated in analysis and interpretation of the results. N.A.W. drafted the manuscript. S.A.K. prepared extended data figures, edited the manuscript and coordinated the efforts of the research team.

Correspondence to S. Alex Kandel.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Images of isolated and densely packed pentamers, and measured orientational distributions.

a, 915 Å × 860 Å image of FcCOOH adsorbed at lower density. Molecules are dispersed over the surface in a wide variety of structures, including two-row rectangular features that may correspond to FcCOOH dimers. Isolated pentamers are evident and are outlined using pentagons, with colour indicating the direction of each pentamer’s symmetry axes, as shown in the colour wheel at the upper right. Tick marks around the colour wheel’s circumference show the in-plane orientation of each pentamer, and the distribution of angles is indistinguishable from random. b, 470 Å × 555 Å image of FcCOOH at near-complete coverage. Orientations of the pentamers are strongly peaked around two angles.

Extended Data Figure 2 Pentamer-to-pentamer orientational correlation function.

Correlation function for pentamer orientations for the image in Extended Data Fig. 1b, once again showing that pentamer orientation is strongly peaked around two angles, but also that the orientational order is constant over the entire area imaged. Blue lines mark the standard deviation, σ, as a function of distance between pentamer centres. Integrating over all distances produces the histogram shown at the left.

Extended Data Figure 3 Two-dimensional Fourier transform and two-dimensional spatial correlation function showing five- and ten-fold symmetry of FcCOOH monolayers.

a, Expanded version of the two-dimensional FFT from Fig. 3c, with overlaid polygons in red and blue showing five- and ten-fold symmetry. Data were low-pass-filtered to remove the d.c. signal and to enhance the contrast of sharp features. b, Two-dimensional spatial correlation function from Fig. 3d, displayed to longer distances to show the persistence of translational order. Red, blue, and black patterns are overlaid, and are based on identical data, except the red and blue point sets are rotated ±36°; the overlap of all three colours demonstrates the long-range ten-fold symmetry of the data.

Extended Data Figure 4 Section of the two-dimensional spatial correlation function, with frequency analysis.

a, Line section of the spatial correlation function from Fig. 3d and Extended Data Fig. 3b (also inset), showing translational order over the entire observed range of over 400 Å. b, Fourier transform of a. The frequency f0 corresponds to periodicity with a wavelength of 34.7 Å. Additional frequencies are equal to f0 times powers of the golden ratio, φ = (1 + √5)/2. The combination of frequencies with irrational ratios is characteristic of quasiperiodic order.

Extended Data Figure 5 Two adjacent FcCOOH monolayer domains, showing periodic and aperiodic packing as well as a change in overall chirality.

a, 675 Å × 365 Å image of FcCOOH showing two packed domains with a grain boundary down the centre of the image. The domain at the left of the image has an extended region where pentagons are packed in a periodic (crystalline) fashion, whereas the domain at the right appears quasicrystalline. b, c, The orientation of the pentagons differs between the two domains, as does the chirality; b is taken from the left-hand side of a and c is taken from the right-hand side of a. d, Raw data for Fig. 3, unfiltered and without overlaid pentagons.

Extended Data Table 1 Calculated energies for FcCOOH clusters, from dimers to hexamers

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Wasio, N., Quardokus, R., Forrest, R. et al. Self-assembly of hydrogen-bonded two-dimensional quasicrystals. Nature 507, 86–89 (2014) doi:10.1038/nature12993

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