Liquid crystal properties of some substituted pyrazines

A number of biphenyl, terphenyl analogues and ethynes which contain a pyrazine ring have been made and their liquid crystal transition temperatures, together with examples of birefringence measurements, are reported. All the 2,5-disubstituted pyrazine systems are liquid crystalline showing high birefringence values for the biphenyl and terphenyl analogues, whereas the 1,5-disubstituted systems are not liquid crystalline. The pyrazine ethyne systems exhibit very high birefringence values. X-ray diffraction has been used to identify the liquid crystal phases of 2-n-nonyloxy-5-(4'-propylbiphenyl-4-yl)pyrazine.     

Generalized Born scattering in anisotropic media

The Born scattering approximation has been widely used in seismology to study scattered waves, and to linearize the propagation problem for inversion. The standard Born theory requires the model be separated into a smooth, reference model and a perturbation. Scattering occurs from the pertubation. In the distorted Born approximation, when the reference model is inhomogeneous, the reference Green's functions are normally not known exactly, but the error in these Green's functions is rarely quantified. In this paper, we generalize Born scattering theory to include the errors in the Green's functions explicitly, and obtain scattering integrals from these errors. For forward modelling, there is no need to separate the model into a reference and perturbation part - approximate Green's functions in the true model can be used to calculate the scattered signals.

The theory is developed for inhomogeneous, anisotropic media. Asymptotic ray theory results are suitable approximate Green's functions for the generalized Born scattering theory. The error terms are simple, easily calculated and included in the scattering integrals. Various applications of generalized Born scattering theory have already appeared in the literature, e.g. quasi-shear ray coupling, and this paper is restricted to an improved and more complete theoretical development. Further applications will appear elsewhere.     

Sobolev Spaces with only Trivial Isometries

We will give some conditions for Sobolev spaces on bounded Lipschitz domains to admit only trivial isometries.     

Stereochemistry of lactide polymerization with chiral catalysts: new opportunities for stereocontrol using polymer exchange mechanisms

The synthesis of chiral aluminum and yttrium alkoxides and their application for lactide polymerization are reported. The complexes (SalBinap)MOR [4, M = Al, R = (i)Pr; 5, M = Y, R = (CH(2))(2)NMe(2)] are synthesized by reacting the ligand (SalBinap)H(2) [2,2'-[(1,1'-binaphthalene)-2,2'-diylbis(nitrilomethylidyne)]bisphenol] with the appropriate metal trisalkoxide. While enantiomerically pure yttrium complex 5 did not effect stereocontrol in the polymerization of either meso- or rac-lactide, homochiral 4 was found to exhibit excellent stereocontrol in a range of lactide polymerizations. Enantiomerically pure 4 polymerizes meso-lactide to syndiotactic poly(lactic acid) (PLA), while rac-4 polymerizes meso- and rac-lactide to heterotactic and isotactic stereoblock PLA, respectively. On the basis of the absolute stereochemistry of ring-opening of meso-lactide using (R)-4, a polymer exchange mechanism is proposed to account for the PLA microstructures resulting from rac-4.     

Catalysts for the living insertion polymerization of alkenes: access to new polyolefin architectures using Ziegler-Natta chemistry

Coordination-insertion polymerization systems have long been superior to their anionic, cationic, and radical polymerization counterparts with regard to stereochemical control. However, until five years ago, these metal-based insertion methods were inferior to ionic and radical mechanisms in the category of living polymerization, which is simply a polymerization that occurs with rapid initiation and negligible chain termination or transfer. In the last half decade, the living insertion polymerization of unactivated olefins has emerged as a powerful tool for the synthesis of new polymer architectures. Materials available today by this route range from simple homopolymers such as linear and branched polyethylene, to atactic or tactic poly(alpha-olefins), to end-functionalized polymers and block copolymers. This review article summarizes recent developments in this rapidly growing research area at the interface of synthetic and mechanistic organometallic chemistry, polymer chemistry, and materials science. While special emphasis is placed on polymer properties and novel polymeric architectures, most of which were inaccessible just a decade ago, important achievements with respect to ligand and catalyst design are also highlighted.     

Darboux transformations for higher-rank Kadomtsev-Petviashvili and Krichever-Novikov equations

It is shown that the action of a special rank 2 or rank 3 Darboux transformation, calledtransference, upon a pair of commuting ordinary differential operators of orders 4 and 6 implements the Abelian sum on their elliptic joint spectrum. A consequence of this is that, under the deformation of these commuting operators by the KP flow, every rank 2 KP solution corresponds to a solution of the Krichever-Novikov (KN) equation, and vice versa, with the transference process providing the correspondence between (2+1) and (1+1) dimensions. For a singular joint spectrum, it is further shown that transference at the singular point produces a correspondence between solutions of the singular KN equation and those of the KdV equation. These correspondences are illustrated by considering examples of a nondecaying rational KdV or Boussinesq solutions and the corresponding rational, singular-KN and rational KP solutions which the transference process generates.     

Disordered ground states for classical discrete-state problems in one dimension

It is known that one-dimensional lattice problems with a discrete, finite set of states per site generically have periodic ground states (GSs). We consider slightly less generic cases, in which the Hamiltonian is constrained by either spin (S) or spatial (I) inversion symmetry (or both). We show that such constraints give rise to the possibility ofdisordered GSs over a finite fraction of the coupling-parameter space—that is, without invoking any nongeneric fine tuning of coupling constants, beyond that arising from symmetry. We find that such disordered GSs can arise for many values of the number of statesk at each site and the ranger of the interaction. The Ising (k=2) case is the least prone to disorder:I symmetry allows for disordered GSs (without fine tuning) only forr5, whileS symmetry never gives rise to disordered GSs.     

Ultraviolet protection factors for clothing: an intercomparison of measurement systems

In recent years the need to standardize measurement protocols for quantifying the degree of ultraviolet radiation (UVR) protection provided by clothing has led to the introduction of a number of standards around the world. To date, these standards have specified spectral measurements of UVR transmission by clothing and fabrics. Development of a standard test method has become an important part of the testing process, and this article presents results from an intercomparison involving 10 independent testing laboratories and 11 different UVR transmission measurement instruments. In addition to comparing the measured ultraviolet protection factors (UPF), this intercomparison also incorporates detailed scan results from all 10 laboratories and highlights differences in performance of the various instruments in different wavelength regions. Careful examination of these differences can indicate where changes to the systems could be made to allow improvements both in equipment performance and in agreement of the final results. The variability in the measurements of UPF in this study suggest that the protection categories in standards may need to be broadened.     

An experimental and theoretical study of competitive adsorption at the n-heptane/water interface

A model to calculate the interfacial concentration of competing surface active species in a two-phase oil/water system was developed. To enable the calculation of the surface excess of 2-hydroxy-5-nonylacetophenone oxime (HNAPO, active ingredient of LIX 84) in the presence of surfactants competing for interfacial area, an interfacial adsorption competition model was derived for noninteracting surface active species in a n-heptane/aqueous system, assuming ideal enthalpy and entropy of mixing. The model was found to be valid for HNAPO in the presence of sodium dodecyl sulfate (SDS) or dodecyldimethyl(3-sulfopropyl)ammonium (DDSA). In the case of dodecyltrimethylammonium chloride (DTAC) or octa(ethylene glycol) mono-n-dodecyl ether (C12E8) as the competing surfactants with HNAPO, the predicted surface excess values from the model fit less favorably. The difference was shown to not be due to nonideal entropy of mixing.