Conformational landscapes of bimesogenic compounds and their implications for the formation of modulated nematic phases

ABSTRACT

The twist-bend phase (N_TB) is most commonly observed in materials with a gross-bent shape: dimers; bent-cores; bent-oligomers. We had suggested previously that the bend-angle of such systems effectively dictates the relative thermal stability of the N_TB phase. However, our earlier paper relied on the use of a single energy-minimum conformer and so failed to capture any information about flexibility and conformational distribution. In the present work, we revisit our hypothesis and examine a second set of dimers with varying linking groups and spacer composition. We have improved on our earlier work by studying the conformational landscape of each material, allowing average bend-angles to be determined as well as the conformer distribution. We observe that the stability of the N_TB phase exhibits a strong dependence not only on the Boltzmann-weighted average bend-angle (rather than just a static conformer), but also on the distribution of conformers. To a lesser extent, the flexibility of the spacer appears important. Ultimately, this work satisfies both theoretical treatments and our initial experimental study and demonstrates the importance of molecular bend to the N_TB phase.     

Separation properties in the primitive ideal space of a multiplier algebra

We use recent work on spectral synthesis in multiplier algebras to give an intrinsic characterization of the separable C*-algebras A for which Orc(M(A)) = 1, i.e., for which the relation of inseparability on the topological space of primitive ideals of the multiplier algebra M(A) is an equivalence relation. This characterization has applications to the calculation of norms of inner derivations and other elementary operators on A and M(A). For example, we give necessary and sufficient conditions on the ideal structure of a separable C*-algebra A for the norm of every inner derivation to be twice the distance of the implementing element to the centre of M(A).     

Strength of convergence in non-free transformation groups

Let $(G,X)$ be a transformation group where the group G does not necessarily act freely on the space X. We investigate the extent to which the action of G may fail to be proper. Stability subgroups are used to define new notions of strength of convergence in the orbit space and of measure accumulation along orbits. By using the representation theory of the associated crossed product $C^{?}$-algebra, we show that these notions are equivalent under certain conditions.     

Measurement of the flux of ultrahigh energy cosmic rays from monocular observations by the High Resolution Fly's Eye experiment

We have measured the cosmic ray spectrum above 10(17.2) eV using the two air-fluorescence detectors of the High Resolution Fly's Eye observatory operating in monocular mode. We describe the detector, phototube, and atmospheric calibrations, as well as the analysis techniques for the two detectors. We fit the spectrum to a model consisting of galactic and extragalactic sources.     

Extensions of Pure States and Projections of Norm One II

It is shown that if a C*-algebra A contains a semi-scatteredC*-algebra B such that the pure states of B and the zero functionalextend uniquely to A, and the canonical mapping B^ Âis injective, then there exists a (unique) projection of normone R: A B. In certain circumstances, the conditional expectationR can be effected by a unitary averaging process using unitaryelements in the centre of the multiplier algebra M(B).     

Strength of convergence and multiplicities in the spectrum of a C*-dynamical system

We consider separable C*-dynamical systems (A, G,) for whichthe induced action of the group G on the primitive ideal spacePrim A of the C*-algebra A is free. We study how the representationtheory of the associated crossed product C*-algebra A G dependson the representation theory of A and the properties of theaction of G on Prim A and the spectrum Â. Our main toolsinvolve computations of upper and lower bounds on multiplicitynumbers associated to irreducible representations of A G. Weapply our techniques to give necessary and sufficient conditions,in terms of A and the action of G, for AG to be (i) a continuous-traceC*-algebra, (ii) a Fell C*-algebra and (iii) a bounded-traceC*-algebra. When G is amenable, we also give necessary and sufficientconditions for the crossed product C*-algebra AG to be (iv)a liminal C*-algebra and (v) a Type I C*-algebra. The resultsin (i), (iii)–(v) extend some earlier special cases inwhich A was assumed to have the corresponding property.     

Effect of the linking unit on the twist-bend nematic phase in liquid crystal dimers: a comparative study of two homologous series of methylene- and ether-linked dimers

ABSTRACT

Two series of bimesogens with phenyl benzoate mesogenic units were prepared: one series having a heptamethylene spacer and the other a pentamethylene spacer with two ether-linking groups. These materials were prepared to provide experimental backing to the widely held hypothesis that methylene-linked bimesogens are more likely to exhibit the twist-bend nematic mesophase than their ether-linked counterparts. Several of the methylene-linked materials exhibited nematic and N_TB mesophases, whereas the analogous ether-linked materials gave only nematic phases albeit with significantly higher clearing points. Virtual N–N_TB transition temperatures for both methylene- and ether-linked bimesogens were extrapolated by constructing binary phase diagrams with the well-studied twist-bend material CB9CB. Contrary to our expectations these virtual transition temperatures were in most cases higher for the ether-linked bimesogens than in the analogous methylene compounds, this runs counter to reported theories and hypotheses that the incorporation of ether-linking groups should serve to destabilise the N_TB phase.     

Limit sets and strengths of convergence for sequences in the duals of thread-like Lie groups

We consider a properly converging sequence of non-characters in the dual space of a thread-like group and investigate the limit set and the strength with which the sequence converges to each of its limits. We show that, if (π _k ) is a properly convergent sequence of non-characters in , then there is a trade-off between the number of limits σ which are not characters, their degrees, and the strength of convergence i _σ to each of these limits (Theorem 3.2). This enables us to describe various possibilities for maximal limit sets consisting entirely of non-characters (Theorem 4.6). In Sect. 5, we show that if (π _k ) is a properly converging sequence of non-characters in and if the limit set contains a character then the intersection of the set of characters (which is homeomorphic to ) with the limit set has at most two components. In the case of two components, each is a half-plane. In Theorem 7.7, we show that if a sequence has a character as a cluster point then, by passing to a properly convergent subsequence and then a further subsequence, it is possible to find a real null sequence (c _k ) (with ) such that, for a in the Pedersen ideal of C ^*(G _N ), exists (not identically zero) and is given by a sum of integrals over .     

Stable rank and real rank for some classes of group -algebras

We investigate the real and stable rank of the -algebras of locally compact groups with relatively compact conjugacy classes or finite-dimensional irreducible representations. Estimates and formulae are given in terms of the group-theoretic rank.