A Method for Incorporating Transcendentally Small Terms into the Method of Matched Asymptotic Expansions

The essential ideas behind a method for incorporating exponentially small terms into the method of matched asymptotic expansions are demonstrated using an Ackerberg–O'Malley resonance problem and a spurious solutions problem of Carrier and Pearson. One begins with the application of the standard method of matched asymptotic expansions to obtain at least the leading terms in outer and inner (Poincaré-type) expansions; some, although not all, matching can be carried out at this stage. This is followed by the introduction of supplementary expansions whose gauge functions are transcendentally small compared to those in the standard expansions. Analysis of terms in these expansions allows the matching to be completed. Furthermore, the method allows for the inclusion of globally valid transcendentally small contributions to the asymptotic solution; it is well known that such terms may be numerically significant.     

Directed assembly and reactivity of olefins within a one-dimensional ladder-like coordination polymer based on a dinuclear Zn(II) platform

A ladder-like coordination polymer involving a dinuclear Zn Schiff-base complex possesses organic linkers that undergo [2+2] photodimerisation in the solid state.     

A test for homology: photoactive crystalline assemblies involving linear templates based on a homologous series of phloroglucinols

[reaction: see text] Cocrystallization of trans-1,2-bis(4-pyridyl)ethylene (4,4'-bpe) with eight members of a homologous series of phloroglucinols 1a-h yields molecular solids 2(1a-h).2(4,4'-bpe) with components held together by four O-H...N hydrogen bonds. In each case, the molecules assemble to form a discrete four-component assembly with olefins preorganized for a [2 + 2] photodimerization. UV irradiation of each member in the series of solids produces rctt-tetrakis(4-pyridyl)cyclobutane (4,4'-tpcb), stereospecifically, in up to 100% yield.     

Coplanar recognition by a Rebek cleft is provided by cooperative structural effects involving a combination of O-H...O, O-H...N, and C-H...O forces

Reaction of 2,7-di-tert-butyl-9,9-dimethyl-4,5-xanthenedicarboxylic acid (1), a Rebek cleft, with 1,2-trans-bis(2-pyridyl)ethylene (2) yields a three-component organic assembly, 2(1).2 (3), of nanoscale dimensions that is held together by 10 cooperative O-H.N, O-H.O, and C-H.O hydrogen bonds. The cleft adopts a planar conformation, by forming an intramolecular O-H.O hydrogen bond, which enables the host to recognize the guest in a coplanar orientation that facilitates the cooperativity displayed by the multiple forces.     

Crystal and molecular structure of 2,7-di-tert-butyl-9,9-dimethyl-4,5-xanthenedicarboxylic acid

The crystal and molecular structure of molecular cleft 2,7-di-tert-butyl-9,9-dimethyl-4,5-xanthenedicarboxylic acid (1) is reported. Crystal data for 1: triclinic, space group P, a = 7.934(2), b = 10.387(2), c = 14.084(3) Å, = 96.049(3), = 101.231(4), = 95.635(4)°, V = 1123.7(4) ų, and D _c = 1.21 g/cm³, for Z = 2. The molecule crystallizes as a cyclic, hydrogen-bonded dimer held together by four O–H······O hydrogen bonds involving four carboxyl groups each of which interact by way of a cyclic hydrogen-bonded motif. The complex organizes in the solid state to form a 2D layered structure.     

Metal-mediated reactivity in the organic solid state: from self-assembled complexes to metal-organic frameworks

The purpose of this tutorial review is to address the use of metal ions to mediate reactions in the organic solid state. We describe metal complexes and coordination networks that facilitate dimerizations, oligomerizations and polymerizations of olefins and acetylenes via irradiation (e.g. ultraviolet (UV) and (60)Co gamma-rays) and thermal annealing. We show how metal ions can be utilized to direct the formation of polymers and molecules. We also describe how supramolecular chemistry has recently influenced dimerization processes in self-assembled metal-organic solids.     

Coding a coordination-driven self-assembly via a hydrogen bond-directed solid-state synthesis: an unexpected chiral tetrahedral capsule

An achiral ligand, synthesized in the solid state via a coded hydrogen bond-directed organic synthesis, self-assembles with Cu(II) ions to form a chiral tetrahedral capsule that hosts an anion as a guest.     

On the concept of a transmission absorber to suppress internal resonance

Internal resonances within vibration isolators have been shown to increase force transmission and consequently radiated noise from supporting structures. Previous research has successfully used dynamic vibration absorbers to attenuate internal resonances. This paper introduces the term transmission absorber to describe a system that exerts both restoring and inertial forces proportional to relative motion. A novel uni-axial vibration isolator concept incorporating transmission absorbers to suppress internal resonance is proposed and theoretically compared with an isolator including dynamic vibration absorbers. The designs are optimised by using a combination of particle swarm and gradient-based optimisation algorithms. It is shown that the proposed isolator concept, incorporating transmission absorbers, has the potential to outperform previous designs, demonstrating force transmissibility levels approaching those of an ideal isolator.     

Onion-shell metal-organic polyhedra (MOPs): a general approach to decorate the exteriors of MOPs using principles of supramolecular chemistry

Metal-organic polyhedra with surface-exposed organic groups have been designed. The polyhedra are based on concentric shells of alternating negative-positive-negative charges and have been used to design homochiral hosts.