Structure transformation from Sierpiński triangles to chains assisted by gas molecules

Reversible transformations between fractals and periodic structures are of fundamental importance for understanding the formation mechanism of fractals. Currently, it is still a challenge to controllably achieve such a transformation. We investigate the effect of CO and CO2 molecules on Sierpiński triangles (STs) assembled from Fe atoms and 4,4″-dicyano-1,1':3',1″-terphenyl (C3PC) molecules on Au surfaces. Using scanning tunneling microscopy, we discover that the gas molecules induce a transition from STs into 1D chains. Based on density functional theory modeling, we propose that the atomistic mechanism involves the transformation of a stable 3-fold coordination Fe(C3PC)3 motif to Fe(C3PC)4 with an axially bonded CO molecule. CO2 causes the structural transformation through a molecular catassembly process.

Assembling Surface Molecular Sierpiński Triangle Fractals via K+-Invoked Electrostatic Interaction

Molecular Sierpiński triangles (STs), a family of elegant and well-known fractals, can be prepared on surfaces with atomic precision. Up to date, several kinds of intermolecular interactions such as hydrogen bond, halogen bond, coordination, and even covalent bond have been employed to construct molecular STs on metal surfaces. Herein a series of defect-free molecular STs have been fabricated via electrostatic attraction between potassium cations and electronically polarized chlorine atoms in 4,4″-dichloro-1,1':3',1″-terphenyl (DCTP) molecules on Cu(111) and Ag(111). The electrostatic interaction is confirmed both experimentally by scanning tunneling microscopy and theoretically by density functional theory calculations. These findings illustrate that electrostatic interaction can serve as an efficient driving force to construct molecular fractals, which enriches our toolbox for the bottom-up fabrication of complex functional supramolecular nanostructures.

Modelling of Electron and Thermal Transport in Quasi-Fractal Carbon Nitride Nanoribbons

In this work, using calculations based on the density functional theory, molecular dynamics, non-equilibrium Green functions method, and Monte Carlo simulation, we study electronic and phonon transport in a device based on quasi-fractal carbon nitride nanoribbons with Sierpinski triangle blocks. Modifications of electronic and thermal conductance with increase in generation g of quasi-fractal segments are estimated. Introducing energetic disorder, we study hopping electron transport in the quasi-fractal nanoribbons by Monte Carlo simulation of a biased random walk with generalized Miller–Abrahams transfer rates. Calculated time dependencies of the mean square displacement bear evidence of transient anomalous diffusion. Variations of anomalous drift-diffusion parameters with localization radius, temperature, electric field intensity, and energy disorder level are estimated. The hopping in quasi-fractal nanoribbons can serve as an explicit physical implementation of the generalized comb model.

Electronic fractal patterns in building Sierpinski-triangles molecular systems

The Sierpinski Triangle (ST) is a fractal mathematical structure that has been used to explore the emergence of flat bands in lattices of different geometries and dimensions in condensed matter....

Packing Biomolecules into Sierpiński Triangles with Global Organizational Chirality

Fractals are found in nature and play important roles in biological functions. However, it is challenging to controllably prepare biomolecule fractals. In this study, a series of Sierpiński triangles with global organizational chirality is successfully constructed by the coassembly of l-tryptophan and 1,3-bi(4-pyridyl)benzene molecules on Ag(111). The chirality is switched when replacing l-tryptophan by d-tryptophan. The fractal structures are characterized by low-temperature scanning tunneling microscopy at the single-molecule level. Density functional theory calculations reveal that intermolecular hydrogen bonds stabilize the Sierpiński triangles.

Sierpiński Structure and Electronic Topology in Bi Thin Films on InSb(111)B Surfaces

Deposition of Bi on InSb(111)B reveals a striking Sierpiński-triangle (ST)-like structure in Bi thin films. Such a fractal geometric topology is further shown to turn off the intrinsic electronic topology in a thin film. Relaxation of a huge misfit strain of about 30% to 40% between Bi adlayer and substrate is revealed to drive the ST-like island formation. A Frenkel-Kontrova model is developed to illustrate the enhanced strain relief in the ST islands offsetting the additional step energy cost. Besides a sufficiently large tensile strain, forming ST-like structures also requires larger adlayer-substrate and intra-adlayer elastic stiffnesses, and weaker intra-adlayer interatomic interactions.

Boronic ester Sierpiński triangle fractals: from precursor design to on-surface synthesis and self-assembling superstructures

Herein, we designed and synthesized a precursor with a three-fold node and successfully constructed covalent Sierpiński triangle (ST) fractals with boronic ester linkages both at the liquid/solid interface at room temperature and by thermal annealing in a water atmosphere under ambient conditions. Remarkably, large-scale ordered superstructures of covalent STs are constructed by thermal annealing, which paves the way for property investigation of STs.

Packing Sierpiński Triangles into Two-Dimensional Crystals

Fractals are of fundamental importance in science and technology. Theoretical simulations indicate that Sierpiński triangles (STs) possess specific optical and electronic properties. To study their properties and uncover their potential applications, it is necessary to pack STs into large-scale two-dimensional crystalline structures. Here, a series of ordered structures consisting of ST units are successfully constructed on gold surfaces through coordination between 1,3-bis(4-pyridyl) benzene molecules and Fe atoms. Crystals of STs are characterized by scanning tunneling microscopy. K-map analysis explains the structural formation mechanism, which is further verified by density functional theory calculations. The molecular free diffusion and nice structure matching between STs and gold surfaces play important roles in the formation of crystals of STs.

Programming and simulating chemical reaction networks on a surface

Models of well-mixed chemical reaction networks (CRNs) have provided a solid foundation for the study of programmable molecular systems, but the importance of spatial organization in such systems has increasingly been recognized. In this paper, we explore an alternative chemical computing model introduced by Qian & Winfree in 2014, the surface CRN, which uses molecules attached to a surface such that each molecule only interacts with its immediate neighbours. Expanding on the constructions in that work, we first demonstrate that surface CRNs can emulate asynchronous and synchronous deterministic cellular automata and implement continuously active Boolean logic circuits. We introduce three new techniques for enforcing synchronization within local regions, each with a different trade-off in spatial and chemical complexity. We also demonstrate that surface CRNs can manufacture complex spatial patterns from simple initial conditions and implement interesting swarm robotic behaviours using simple local rules. Throughout all example constructions of surface CRNs, we highlight the trade-off between the ability to precisely place molecules and the ability to precisely control molecular interactions. Finally, we provide a Python simulator for surface CRNs with an easy-to-use web interface, so that readers may follow along with our examples or create their own surface CRN designs.

Multicomponent Metallo-Supramolecular Nanocapsules Assembled from Calix[4]resorcinarene-Based Terpyridine Ligands

Tetrafunctionalized calix[4]resorcinarene cavitands commonly serve as supramolecular scaffolds for construction of coordination-driven self-assembled capsules. However, due to the calix-like shape, the structural diversity of assemblies is mostly restricted to dimeric and hexameric capsules. Previously, we reported a spontaneous heteroleptic complexation strategy based on a pair of self-recognizable terpyridine-based ligands and Cd^II ions. Building on this complementary ligand pairing system, herein three types of nanocapsules, including a dimeric capsule, a Sierpiński triangular prism, and a cubic star, could be readily obtained through dynamic complexation reactions between a tetratopic cavitand-based ligand and various multitopic counterparts in the presence of Cd^II ions. The dimeric capsular assemblies display the spacer-length-dependent self-sorting behavior in a four-component system. Moreover, the precise multicomponent self-assembly of a Sierpiński triangular prism and a cubic star possessing three and six cavitand-based motifs, respectively, demonstrates that such self-assembly methodology is able to efficiently enhance architectural complexity for calix[4]resorcinarene-containing metallo-supramolecules.

Construction and Properties of Sierpiński Triangular Fractals on Surfaces

Fractal structures are of fundamental importance in science, engineering, mathematics, and aesthetics. Construction of molecular fractals on surfaces can help to understand the formation mechanism of fractals and a series of achievements have been acquired in the preparation of molecular fractals. This review focuses on Sierpiński triangles (STs), representatives of various prototypical fractals, on surfaces. They are investigated by Monte Carlo simulations and ultra-high vacuum scanning tunneling microscopy. STs are bonded through halogen bonds, hydrogen bonds, metal-organic coordination bonds and covalent bonds. The coexistence of and competition between fractals and crystals are realized for a hydrogen-bonded system. Electronic properties of two types of STs are summarized.

Symmetrically backfolded molecules emulating the self-similar features of a Sierpinski triangle

We synthesized self-similar molecules (G3 and G2; based on phenylalkynyl backbones) with symmetrically backfolded shapes inspired by the famous fractal of a Sierpinski triangle. Unlike the more traditional, starburst dendrimers, the centripetal-shaped Sierpinski molecules feature side branches symmetrically bent away from the growth direction of the main branch, thus contrasting the natural-tree shape. Molecule G3 exhibits three distinct levels of the structural hierarchy comprising the primary, secondary and tertiary branches, while the smaller G2 contains only features of the 1^st and 2^nd orders. In spite of the much larger conjugated backbone of G3, its solution UV-vis absorption and fluorescence exhibit no red shift relative to G2. In a test of nitrobenzene sensing, a thin film of G3 deposited from THF was more sensitively quenched in fluorescence than the smaller G2.

Supramolecular Assemblies on Surfaces: Nanopatterning, Functionality, and Reactivity

Understanding how molecules interact to form large-scale hierarchical structures on surfaces holds promise for building designer nanoscale constructs with defined chemical and physical properties. Here, we describe early advances in this field and highlight upcoming opportunities and challenges. Both direct intermolecular interactions and those that are mediated by coordinated metal centers or substrates are discussed. These interactions can be additive, but they can also interfere with each other, leading to new assemblies in which electrical potentials vary at distances much larger than those of typical chemical interactions. Earlier spectroscopic and surface measurements have provided partial information on such interfacial effects. In the interim, scanning probe microscopies have assumed defining roles in the field of molecular organization on surfaces, delivering deeper understanding of interactions, structures, and local potentials. Self-assembly is a key strategy to form extended structures on surfaces, advancing nanolithography into the chemical dimension and providing simultaneous control at multiple scales. In parallel, the emergence of graphene and the resulting impetus to explore 2D materials have broadened the field, as surface-confined reactions of molecular building blocks provide access to such materials as 2D polymers and graphene nanoribbons. In this Review, we describe recent advances and point out promising directions that will lead to even greater and more robust capabilities to exploit designer surfaces.

One-dimensional molecular chains formed by Sierpiński triangles on Au(111)

One-dimensional molecular chains with Sierpiński triangles as building blocks were prepared on Au(111) and studied by low-temperature scanning tunneling microscopy.

Non-intuitive clustering of 9,10-phenanthrenequinone on Au(111)

The direct injection of a 9,10-phenanthrenequinone in tetrahydrofuran solution on a Au(111) substrate in high vacuum results in the formation of metastable clusters with a non-intuitive structure. Metastable, rectangular tetramers of this molecule form in which the net molecular dipoles all orient toward the center of the cluster. This structure does not allow for additional hydrogen bonding and thus the origin of its metastability is not clear. We compare this feature to other structures observed on this surface, as well as those formed during the deposition of 9-fluorenone, which does not exhibit this anomalous clustering behavior.

Construction of Sierpiński triangles with the coexistence of C60or MnPc molecules

Sierpiński triangles up to the fourth order were successfully prepared using 4,4′′-dicyano-1,1′:3′,1′′-terphenyl molecules and Fe or Co atoms with the coexistence of the third molecules (C₆₀or MnPc) on a reconstructed Au(111) substrate.