Sharpness of the phase transition in percolation models

The equality of two critical points — the percolation thresholdp _H and the pointp _T where the cluster size distribution ceases to decay exponentially — is proven for all translation invariant independent percolation models on homogeneousd-dimensional lattices (d1). The analysis is based on a pair of new nonlinear partial differential inequalities for an order parameterM(,h), which forh=0 reduces to the percolation densityP — at the bond densityp=1–e ^– in the single parameter case. These are: (1)MhM/h+M ²+MM/, and (2) M/|J|MM/h. Inequality (1) is intriguing in that its derivation provides yet another hint of a ³ structure in percolation models. Moreover, through the elimination of one of its derivatives, (1) yields a pair of ordinary differential inequalities which provide information on the critical exponents and . One of these resembles an Ising model inequality of Fröhlich and Sokal and yields the mean field bound 2, and the other implies the result of Chayes and Chayes that . An inequality identical to (2) is known for Ising models, where it provides the basis for Newman's universal relation and for certain extrapolation principles, which are now made applicable also to independent percolation. These results apply to both finite and long range models, with or without orientation, and extend to periodic and weakly inhomogeneous systems.Research supported in part by the NSF Grant PHY-8605164Also in the Physics Department     

Substitution and condensation reactions with poly(anilineboronic acid): reactivity and characterization of thin films

Poly(anilineboronic acid) thin films are treated under various conditions to achieve substitution or condensation reactions involving the boronic acid moiety. These reactions are studied with polarization modulated infrared reflection absorption spectroscopy, cyclic voltammetry, and UV-vis spectroscopy. The results suggest the single-step formation of substituted polyanilines, such as poly(hydroxyaniline), halogenated polyanilines, and mercury chloride-substituted polyaniline. A condensation reaction of poly(anilineboronic acid) with cis-diol compounds in aqueous solution, as well as with phenylenebisboronic acid and salycilamide in THF, indicates the formation of boronic esters. The latter reactions appear to be a good entry point for the formation of complex or supramolecular polymer structures.     

A novel synthetic route to substituted pyranoanthocyanins with unique colour properties

Anthocyanins, isolated from natural sources by countercurrent chromatography, were reacted with cinnamic acids bearing at least one electron-donating substituent at the para-position. The resulting pyranoanthocyanins obtained by this simple one-step reaction were much less susceptible to pH shifts and retained their original colour over a wide pH-range. Through reaction with p-dimethylamino cinnamic acid, synthetic malvidin- and cyanidin-based anthocyanins with a unique violet hue were prepared.     

A CNDO/INDO crystal orbital model for transition metal polymers of the 3d series—basis equations

The crystal orbital formalism in the tight-binding approximation is combined with a recently developed CNDO/INDO model for transition metal species of the 3d series in order to allow band structure calculations on the Hartree-Fock (HF) SCF level for one-dimensional (1D) chains with organometallic unit cells. The band structure approach based on the CNDO and INDO approximation can be used for any atom combination up to bromine under the inclusion of the 3d series. The matrix elements for the tight-binding Hamiltonian are derived for an improved CNDO and INDO framework. The total energy of the 1D chain is partitioned into one-center contributions and into two-center increments of the intracell and intercell type. Semiempirical band structure calculations on simple model systems are compared with available ab initio data of high quality.     

Solution structure of a beta-peptide ligand for hDM2

We recently reported a beta-peptide foldamer, beta53-1, that folds into a 14-helix in aqueous solution, binds the oncoprotein hDM2 with submicromolar affinity, and potently inhibits the interaction of hDM2 with a peptide derived from the activation domain of p53 (p53AD). Here, we present the solution structure of beta53-1 in methanol. Details of the structure illustrate fundamental and novel elements of beta-peptide folding and recognition. These elements include the detailed arrangement of a complex, 14-helix-stabilizing salt bridge on one helical face, and a unique "wedge into cleft" packing interaction along a second. The structure also reveals how a subtle distortion in the beta53-1 14-helix geometry alters the presentation of its recognition epitope, rendering it particularly well suited for alpha-helix mimicry. The solution structure of beta53-1 demonstrates that well folded beta-peptide oligomers can effectively present an extended, highly variable surface that could be used as a general platform for targeting critical protein-protein interfaces.     

Homoatomic P --> P coordination: a versatile synthetic approach to polyphosphorus dications

Polyphosphorus dications have been synthesised and comprehensively characterised as diphosphine (dppe, dmpe and dpph) linked Ar2P+ Lewis acids (Ar = C6H5); this application of unique homoatomic coordination chemistry provides important building blocks for extended systems.     

Reactions of methyltris(triarylphosphine)cobalt : I. Formation of biaryls

Methyltris(triarylphosphine)cobalt (Ar₃P)₃CoCH₃, decomposes in solutions of THF, benzene or chlorobenzene to yield biaryls. Coupling to biaryls occurs at the ring carbon originally bonded to phosphorus. Mixed biaryls are obtained from crossover reactions of complexes bearing different triarylphosphine ligands and reactions of complexes with free triarylphosphines.     

Bistable ferroelectric liquid crystal photoswitch triggered by a dithienylethene dopant

The spontaneous polarization (PS) of a ferroelectric liquid crystal is modulated reversibly by photocyclization of the dopant 1,2-bis[5'-(4' '-heptyloxyphenyl)-2'-methylthien-3'-yl]perfluorocyclopentene. The magnitude of PS photomodulation increases with dopant concentration up to 3 mol %, and the resulting photoswitch is fatigue resistant and bistable. To the best of our knowledge, this is the first example of a bistable ferroelectric liquid crystal photoswitch to be reported in the literature.     

Molecular potential-energy surfaces for chemical reaction dynamics

This paper reviews the construction of molecular potential-energy surfaces by an interpolation method which has been developed over the last several years. The method uses ab initio quantum chemistry calculations of the molecular electronic energy in an automated procedure to construct global potential- energy surfaces which can be used to simulate chemical reactions with either classical or quantum dynamics. The methodology is explained and several applications are presented to illustrate the approach. Received: 22 February 2002 / Accepted: 2 May 2002 / Published online: 6 November 2002 Correspondence to: M. A. Collins e-mail: collins@rsc.anu.edu.au Acknowledgements. The methods described in this overview are the result of collaborations with former members of my group, in particular with Josef Ischtwan, Meredith Jordon, Keiran Thompson and Ryan Bettens. I am also indebted for inspiration gained from many discussions with my colleagues Leo Radom and Donghui Zhang (National University of Singapore). This work has been supported by the Supercomputer Facility of the Australian National University and the Australian Partnership for Advanced Computing.