The effect of the spacer length on the nature of coupling in side chain liquid crystals polymers and elastomers

Side chain liquid crystal polymers and elastomers exhibit a rich phase behaviour which arises from the antagonistic influences of the entropically disordered polymer chain configuration and the long range orientational ordering of the mesogenic units. This competition arises since the natural macroscopic phase separation is inhibited by the inherent chemical connectivity of the system. At the heart of this connectivity is the spacer link and we consider here its influence on the phase behaviour. In particular we consider a series of elastomers in which the number of alkyl units in the spacer is systematically varied from 2 to 6. The lengthening of the coupling spacer is accompanied by an alternation of the sign of coupling between the polymer chain and the mesogenic unit. These results demonstrate the dominating influence of the so-called hinge effect in determining the phase behaviour. In addition to the alternation of the sign there is some decrease in the magnitude of the coupling with increasing spacer length.

Coupling between mesogenic units and polymer backbone in side-chain liquid crystal polymers and elastomers

The levels of alignment of the mesogenic units and of the polymer backbone trajectory for polyacrylate based nematic side-chain liquid crystal polymers and elastomers were evaluated by using wide angle X-ray and small angle neutron scattering procedures. The X-ray scattering measurements show that substantial levels of preferred orientation of the mesogenic units may be introduced through magnetic fields for uncrosslinked polymers and through mechanical extension for liquid crystal elastomers. Small angle neutron scattering measurements show that for highly aligned samples an anisotropic polymer backbone trajectory is observed in which the envelope is slightly extended by ∼ 10% in the direction parallel to the axis of alignment of the mesogenic units. The sense of this coupling differs from that recorded for other uncrosslinked side-chain liquid crystal polymers. Possible mechanisms to account for this anisotropy and its relationship to the properties of liquid crystal elastomers are discussed. The observed deformation behaviour of the liquid crystal elastomer is non-affine and this appears to confirm the dominating influence of the liquid crystal order of the side chains on the mechanical properties of these novel networks.

A detailed single chain model for molten poly(tetrafluoroethylene) from a novel structure refinement technique on neutron scattering data

We present a new methodology that couples neutron diffraction experiments over a wide Q range with single chain modelling in order to explore, in a quantitative manner, the intrachain organization of non-crystalline polymers. The technique is based on the assignment of parameters describing the chemical, geometric and conformational characteristics of the polymeric chain, and on the variation of these parameters to minimize the difference between the predicted and experimental diffraction patterns. The method is successfully applied to the study of molten poly(tetrafluoroethylene) at two different temperatures, and provides unambiguous information on the configuration of the chain and its degree of flexibility. From analysis of the experimental data a model is derived with CC and CF bond lengths of 1.58 and 1.36 Å, respectively, a backbone valence angle of 110° and a torsional angle distribution which is characterized by four isometric states, namely a split trans state at ± 18°, giving rise to a helical chain conformation, and two gauche states at ± 112°. The probability of trans conformers is 0.86 at T = 350°C, which decreases slightly to 0.84 at T = 400°C. Correspondingly, the chain segments are characterized by long all-trans sequences with random changes in sign, rather anisotropic in nature, which give rise to a rather stiff chain. We compare the results of this quantitative analysis of the experimental scattering data with the theoretical predictions of both force fields and molecular orbital conformation energy calculations.

Side-chain liquid crystalline elastomers: the relationship between the orientational ordering of the polymer backbone and the length of the coupling chain

The influence of cross-linking on the phase behaviour of a series of side-chain liquid crystalline elastomers has been studied. For samples cross-linked in the temperature range corresponding to the nematic phase, the phase transition was shifted compared to that observed when an identical sample was cross-linked in the isotropic phase. This shift represented a stabilisation of the nematic phase in the former case, in line with theoretical expectations. By utilising a novel, slow cross-linking method, which allows the polymer backbone to take up an equilibrium conformation prior to network formation, it proved possible to monitor the shifts in phase transition temperature as a function of the length of the methylene chain coupling the mesogenic units to the polymer backbone. The results obtained are related to the backbone anisotropy and indicate that the level of orientational order of the polymer in the nematic phase backbone increases with a reduction in the length of the coupling chain.

Cinnamate ester containing liquid crystalline side chain polymers

The synthesis of methacrylate esters of 4-cyanophenyl-(4-(ω-hydroxyalkyloxy)) cinnamates, with spacer lengths of 2 and 6 methylene units and the synthesis of the corresponding acrylate ester with a spacer of 2 methylene units are described. The methacrylate monomers were polymerized by free radical polymerization, both as homopolymers and as copolymers with the analogous benzoate monomer of spacer length 6. The acrylate ester could not be polymerized successfully under the same reaction conditions. Polymers were characterized by NMR spectroscopy, gel permeation chromatography, differential scanning calorimetry, and thermo-optic observations. Of the monomers prepared, only the cinnamate with a hexamethylene spacer shows a mesophase, seen on supercooling of the melt. All of the polymers prepared were liquid crystalline, with smectic behavior predominating in the polymethacrylates with the longer spacer group. A narrow nematic region is seen just below the clearing temperature with a range of 3–9°C, nematic character is increased in the copolymer series with the degree of incorporation of the cinnamate monomer with the spacer group of length 2.

Approaches to the synthesis of novel photoactive side chain liquid crystalline polymers containing analogues of the cinnamate ester group

A series of chain liquid crystalline copolymers of 4-cyanophenyl 4′-(6-methacryloyloxyhexyloxy)benzoate and 2-methacryloyloxyethyl β-(1-naphthyl)-propenoate were prepared by free radical polymerization. The corresponding polyacrylates could not be prepared in the same way and an alternative method was used for their preparation involving the synthesis of copolymers of the mesogenic monomer and 2-hydroxyethyl acrylate followed by treatment of the resulting polymers with β-(1-naphthyl)propenoyl chloride. The materials are of interest as photoactive liquid crystalline polymers. The effect of introducing a bulky nonmesogenic group into a liquid crystalline copolymer generally lowers the clearing temperature and raises Tg but also gives rise to contrasting phase behaviour in these two series of polymers. Polymethacrylates which show mesomorphism have sharp transitions and continue to exhibit a highly ordered smectic phase over the bulk of their liquid crystal range. Polyacrylates, on the other hand, exhibit a weakening and broadening-out of their thermal transitions consistent with a lowering of order. These results emphasize the effect of the polymer backbone on phase behaviour.

A search for invariant relative satellite motion

This report presents the canonical Hamiltonian formulation of relative satellite motion. The unperturbed Hamiltonian model is shown to be equivalent to the well known Hill-Clohessy-Wilshire (HCW) linear formulation. The in°uence of perturbations of the nonlinear Gravitational potential and the oblateness of the Earth; J2 perturbations are also modelled within the Hamiltonian formulation. The modelling incorporates eccentricity of the reference orbit. The corresponding Hamiltonian vector ¯elds are computed and implemented in Simulink. A numerical method is presented aimed at locating periodic or quasi-periodic relative satellite motion. The numerical method outlined in this paper is applied to the Hamiltonian system. Although the orbits considered here are weakly unstable at best, in the case of eccentricity only, the method ¯nds exact periodic orbits. When other perturbations such as nonlinear gravitational terms are added, drift is signicantly reduced and in the case of the J2 perturbation with and without the nonlinear gravitational potential term, bounded quasi-periodic solutions are found. Advantages of using Newton's method to search for periodic or quasi-periodic relative satellite motion include simplicity of implementation, repeatability of solutions due to its non-random nature, and fast convergence. Given that the use of bounded or drifting trajectories as control references carries practical di±culties over long-term missions, Principal Component Analysis (PCA) is applied to the quasi-periodic or slowly drifting trajectories to help provide a closed reference trajectory for the implementation of closed loop control. In order to evaluate the e®ect of the quality of the model used to generate the periodic reference trajectory, a study involving closed loop control of a simulated master/follower formation was performed. 2 The results of the closed loop control study indicate that the quality of the model employed for generating the reference trajectory used for control purposes has an important in°uence on the resulting amount of fuel required to track the reference trajectory. The model used to generate LQR controller gains also has an e®ect on the e±ciency of the controller.

Time complexity analysis of the stochastic diffusion search

The Stochastic Diffusion Search algorithm -an integral part of Stochastic Search Networks is investigated. Stochastic Diffusion Search is an alternative solution for invariant pattern recognition and focus of attention. It has been shown that the algorithm can be modelled as an ergodic, finite state Markov Chain under some non-restrictive assumptions. Sub-linear time complexity for some settings of parameters has been formulated and proved. Some properties of the algorithm are then characterised and numerical examples illustrating some features of the algorithm are presented.

Persistence of UK Real Estate returns: a Markov chain analysis

The persistence of investment performance is a topic of perennial interest to investors. Efficient Markets theory tells us that past performance can not be used to predict future performance yet investors appear to be influenced by the historical performance in making their investment allocation decisions. The problem has been of particular interest to investors in real estate; not least because reported returns from investment in real estate are serially correlated thus implying some persistence in investment performance. This paper applies the established approach of Markov Chain analysis to investigate the relationship between past and present performance of UK real estate over the period 1981 to 1996. The data are analysed by sector, region and size. Furthermore some variations in investment performance classification are reported and the results are shown to be robust.

The type and quantity of dietary fat and carbohydrate alter faecal microbiome and short-chain fatty acid excretion in a metabolic syndrome ‘at-risk’ population syndrome.

An obese-type human microbiota with an increased Firmicutes:Bacteroidetes ratio has been described that may link the gut microbiome with obesity and metabolic syndrome (MetS) development. Dietary fat and carbohydrate are modifiable risk factors that may impact on MetS by altering the human microbiome composition. We determined the effect of the amount and type of dietary fat and carbohydrate on faecal bacteria and short chain fatty acid (SCFA) concentrations in people ‘at risk’ of MetS.

Synthesis and phase behaviour of a homologous series of polymethacrylate-based side-chain liquid crystal polymers

The homologous series of side chain liquid crystal polymers, the poly[x-(4-methoxyazobenzene- 40-oxy)alkyl methacrylate]s, has been prepared in which the length of the flexible alkyl spacer has been varied from 3 to 11 methylene units. All the polymers exhibit liquid crystalline behaviour. The propyl and butyl members show exclusively nematic behaviour. The pentyl, hexyl, octyl and decyl members show a nematic and a smectic A phase while the heptyl, nonyl and undecyl homologues exhibit only a smectic A phase. The smectic A phase has been studied using X-ray diffraction and assigned as a smectic A1 phase in which the side chains are fully overlapped and the backbones are confined to lie between the smectic layers. For the nonyl member an incommensurate smectic phase is observed. The dependence of the transition temperatures on the length of the flexible spacer is understood in terms of the average shapes of the side chains.

Spectrally invariant approximation within atmospheric radiative transfer

Certain algebraic combinations of single scattering albedo and solar radiation reflected from, or transmitted through, vegetation canopies do not vary with wavelength. These ‘‘spectrally invariant relationships’’ are the consequence of wavelength independence of the extinction coefficient and scattering phase function in veg- etation. In general, this wavelength independence does not hold in the atmosphere, but in cloud-dominated atmospheres the total extinction and total scattering phase function vary only weakly with wavelength. This paper identifies the atmospheric conditions under which the spectrally invariant approximation can accu- rately describe the extinction and scattering properties of cloudy atmospheres. The validity of the as- sumptions and the accuracy of the approximation are tested with 1D radiative transfer calculations using publicly available radiative transfer models: Discrete Ordinate Radiative Transfer (DISORT) and Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART). It is shown for cloudy atmospheres with cloud optical depth above 3, and for spectral intervals that exclude strong water vapor absorption, that the spectrally invariant relationships found in vegetation canopy radiative transfer are valid to better than 5%. The physics behind this phenomenon, its mathematical basis, and possible applications to remote sensing and climate are discussed.

The p85 subunit of phosphatidylinositol 3-kinase associates with the Fc receptor gamma-chain and linker for activitor of T cells (LAT) in platelets stimulated by collagen and convulxin.

There is extensive evidence to show that phosphatidylinositol 3-kinase plays an important role in signaling by the immune family of receptors, which has recently been extended to include the platelet collagen receptor, glycoprotein VI. In this report we present two potential mechanisms for the regulation of this enzyme on stimulation of platelets by collagen. We show that on stimulation with collagen, the regulatory subunit of phosphatidylinositol 3-kinase associates with the tyrosine-phosphorylated form of the adapter protein linker for activator of T Cells (LAT) and the tyrosine-phosphorylated immunoreceptor tyrosine-based activation motif of the Fc receptor gamma-chain (a component of the collagen receptor complex that includes glycoprotein VI). The associations of the Fc receptor gamma-chain and LAT with p85 are rapid and supported by the Src-homology 2 domains of the regulatory subunit. We did not obtain evidence to support previous observations that the regulatory subunit of phosphatidylinositol 3-kinase is regulated through association with the tyrosine kinase Syk. The present results provide a molecular basis for the regulation of the p85/110 form of phosphatidylinositol 3-kinase by GPVI, the collagen receptor that underlies activation.