Broken symmetry and the variation of critical properties in the phase behaviour of supramolecular rhombus tilings

The degree of randomness, or partial order, present in two-dimensional supramolecular arrays of isophthalate tetracarboxylic acids is shown to vary due to subtle chemical changes such as the choice of solvent or small differences in molecular dimensions. This variation may be quantified using an order parameter and reveals a novel phase behaviour including random tiling with varying critical properties as well as ordered phases dominated by either parallel or non-parallel alignment of neighbouring molecules, consistent with long-standing theoretical studies. The balance between order and randomness is driven by small differences in the intermolecular interaction energies, which we show, using numerical simulations, can be related to the measured order parameter. Significant variations occur even when the energy difference is much less than the thermal energy highlighting the delicate balance between entropic and energetic effects in complex self-assembly processes

Nonperturbative Evolution Equation for Quantum Gravity

A scale--dependent effective action for gravity is introduced and an exact nonperturbative evolution equation is derived which governs its renormalization group flow. It is invariant under general coordinate transformations and satisfies modified BRS Ward--Identities. The evolution equation is solved for a simple truncation of the space of actions. In 2+epsilon dimensions, nonperturbative corrections to the beta--function of Newton's constant are derived and its dependence on the cosmological constant is investigated. In 4 dimensions, Einstein gravity is found to be ``antiscreening'', i.e., Newton's constant increases at large distances.Comment: 35 pages, late

Supramolecular heterostructures formed by sequential epitaxial deposition of two-dimensional hydrogen-bonded arrays

Two-dimensional (2D) supramolecular arrays provide a route to the spatial control of the chemical functionality of a surface, but their deposition is in almost all cases limited to a monolayer termination. Here we investigated the sequential deposition of one 2D array on another to form a supramolecular heterostructure and realize the growth—normal to the underlying substrate—of distinct ordered layers, each of which is stabilized by in-plane hydrogen bonding. For heterostructures formed by depositing terephthalic acid or trimesic acid on cyanuric acid/melamine, we have determined, using atomic force microscopy under ambient conditions, a clear epitaxial arrangement despite the intrinsically distinct symmetries and/or lattice constants of each layer. Structures calculated using classical molecular dynamics are in excellent agreement with the orientation, registry and dimensions of the epitaxial layers. Calculations confirm that van der Waals interactions provide the dominant contribution to the adsorption energy and registry of the layers

Supramolecular networks stabilise and functionalise black phosphorus

The limited stability of the surface of black phosphorus (BP) under atmospheric conditions is a significant constraint on the exploitation of this layered material and its few layer analogue, phosphorene, as an optoelectronic material. Here we show that supramolecular networks stabilised by hydrogen bonding can be formed on BP, and that these monolayer-thick films can passivate the BP surface and inhibit oxidation under ambient conditions. The supramolecular layers are formed by solution deposition and we use atomic force microscopy to obtain images of the BP surface and hexagonal supramolecular networks of trimesic acid and melamine cyanurate (CA.M) under ambient conditions. The CA.M network is aligned with rows of phosphorus atoms and forms large domains which passivate the BP surface for more than a month, and also provides a stable supramolecular platform for the sequential deposition of 1,2,4,5-tetrakis(4-carboxyphenyl)benzene to form supramolecular heterostructures

Supramolecular nesting of cyclic polymers

Advances in template-directed synthesis make it possible to create artificial molecules with protein-like dimensions, directly from simple components. These synthetic macromolecules have a proclivity for self-organization that is reminiscent of biopolymers. Here, we report the synthesis of monodisperse cyclic porphyrin polymers, with diameters of up to 21 nm (750 C–C bonds). The ratio of the intrinsic viscosities for cyclic and linear topologies is 0.72, indicating that these polymers behave as almost ideal flexible chains in solution. When deposited on ​gold surfaces, the cyclic polymers display a new mode of two-dimensional supramolecular organization, combining encapsulation and nesting; one nanoring adopts a near-circular conformation, thus allowing a second nanoring to be captured within its perimeter, in a tightly folded conformation. Scanning tunnelling microscopy reveals that nesting occurs in combination with stacking when nanorings are deposited under vacuum, whereas when they are deposited directly from solution under ambient conditions there is stacking or nesting, but not a combination of both

Guest-induced growth of a surface-based supramolecular bilayer

Self-assembly of planar molecules on a surface can result in the formation of a wide variety of close-packed or porous structures. Two-dimensional porous arrays provide host sites for trapping guest species of suitable size. Here we show that a non-planar guest species (C60) can play a more complex role by promoting the growth of a second layer of host molecules (p-terphenyl-3,5,3″,5″-tetracarboxylic acid) above and parallel to the surface so that self-assembly is extended into the third dimension. The addition of guest molecules and the formation of the second layer are co-dependent. Adding a planar guest (coronene) can displace the C60 and cause reversion to a monolayer arrangement. The system provides an example of a reversible transformation between a planar and a non-planar supramolecular network, an important step towards the controlled self-assembly of functional, three-dimensional, surface-based supramolecular architectures.We thank the UK Engineering and Physical Sciences Research Council for financial support under grant EP/D048761/1. M.S.thanks the European Research Council for an Advanced Grant.N.R.C.acknowledges the receipt of a Royal Society Leverhulme Trust Senior Fellowship.S