Molecular dynamics of a liquid-crystalline polymer with laterally fixed mesogenic side groups

Abstract

The long range molecular dynamical behaviour of liquid-crystalline side chain polymers with the mesogenic groups linked laterally to the backbone have been studied by using dielectric relaxation spectroscopy over a broad temperature and frequency range. The samples were oriented homeotropically and homogenously by electric and magnetic fields and the relaxations were recorded during alignment and with the fully aligned samples. By fitting the data to theoretical relaxation curves, accurate relaxation parameters could be determined, allowing us to perform a comparison with end-fixed liquid-crystalline side chain polymers on the one hand and with low molecular weight liquid crystals on the other. The relaxation in homeotropic alignment for the laterally fixed compound has more analogies in some aspects, for example, the relaxation time distribution, with low molecular weight liquid crystals than with the corresponding end-fixed compounds, though the activation energy is very large (241 kJ/mol). We relate this to the length of the rigid mesogenic unit and the resulting stronger repulsion by the neighbouring side chains during reorientation. In homogeneous alignment the relaxation is very broad and also has a large activation energy. Different molecular processes are related to this relaxation regime. The relationship between the different relaxation processes and the molecular structure is discussed.     

An easy-to-use estimate of the energy-release rate for crack arrays

Formation of crack arrays plays an increasing role in several fields of applied physics. The energy-release rate of the cracks controls the development of the array. Therefore, following the concept of configurational forces, a simplified analytical expression is provided for the energy-release rate, which is based both on numerical studies and on a specially adapted beam model. Comparisons of this easy-to-use estimate of the energy-release rate with established results from the literature as well as detailed numerical results are presented. The provided estimate of the energy-release rate can easily be extended to non-equidistant cracks and an anisotropic material.     

On square roots of the Haar state on compact quantum groups

The paper is concerned with the extension of the classical study of probability measures on a compact group which are square roots of the Haar measure, due to Diaconis and Shahshahani, to the context of compact quantum groups. We provide a simple characterisation for compact quantum groups which admit no non-trivial square roots of the Haar state in terms of their corepresentation theory. In particular it is shown that such compact quantum groups are necessarily of Kac type and their subalgebras generated by the coefficients of a fixed two-dimensional irreducible corepresentation are isomorphic (as finite quantum groups) to the algebra of functions on the group of unit quaternions. An example of a quantum group whose Haar state admits no nontrivial square root and which is neither commutative nor cocommutative is given.     

Cheating as a dynamic marketing strategy in monopoly,cartel and duopoly

In 2015 it was discovered that Volkswagen had manipulated the exhaust emissions of its (diesel) cars. Since then, numerous other automotive car manufacturers were strongly suspected to violate against the same emission standards. This paper investigates how and why firms (monopoly, cartel and duopoly) engage in cheating, more precisely, promising attributes that are actually not part of the product. Firms make claims in order to better market their product but risk damaging their future reputation. The upshot of the paper is the stark difference between open loop and Markov perfect oligopolistic equilibrium outcomes. More precisely, the latter mitigates cheating substantially even below the levels attained by monopolies and cartels (unless consumers have a very short memory), which is contrary to the outcome in the limiting static version of the game. Therefore, revealing the true state (e.g., by mandating strict inspections) could force firms to use this information and play in Markov instead of open loop strategies.

     

A mixed hp FEM for the approximation of fourth‐order singularly perturbed problems on smooth domains

We consider fourth‐order singularly perturbed problems posed on smooth domains and the approximation of their solution by a mixed Finite Element Method on the so‐called Spectral Boundary Layer Mesh. We show that the method converges uniformly, with respect to the singular perturbation parameter, at an exponential rate when the error is measured in the energy norm. Numerical examples illustrate our theoretical findings.     

Gold-surface binding of molecular switches studied by M?ssbauer spectroscopy

The nonanuclear coordination compound [Mo^IV{(CN)Fe^III(3-methyl-saldptn)}₈]Cl₄ exhibits multiple spin transitions (3-methyl-saldptn = N,N′-bis(3′′-methyl-2′′-hydroxy-benzyliden)-1,7-diamino-4-azaheptane). This spin crossover cluster is bound via a self-assembled monolayer onto a two dimensional array gold surface. M?ssbauer spectroscopy indicates that the thermally and optically induced spin crossover of the compound is maintained. Thereby, the foundation for its potential practical application (e.g. in the field of information storage) was laid.