Anisotropic conformation

In the isotropic phase, differential Equation 2.106 is simplified to the Legendre equation with eigenfunctions, the Legendre polynomials Pn(cos9) and the eigenvalues n(n +1). 

The mean square end-to-end distance component parallel to the director is given by 

The three components of the mean square end-to-end distances are the same. 

If the chain is long enough, the chain conformation is of random walk 

For nematic polymers, their conformation is no longer spherical, but a prolate ellipsoid. The mean square end-to-end distance of the chain at its nematic phase is anisotropic. 

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Here, tg is the energy difference between a trans and a gauche link and the number of gauche links in the spacer is g. The term g g=F g g=F is the additional energy resulting from the so-called pentane effect produced by a g g=F sequence in the spacer. Within the nematic phase the more anisotropic conformers are favored, as we have seen, and the conformational distribution becomes [66]... 

Significantly greater anisotropy of the coil is observed in the smectic mesophase (a 4 1 for polymer XXXV and a = 1.6 for polymer XXXVI). This means that the macromolecular chain has a very anisotropic conformation, stretched in the direction perpendicular to the direction of the effect of the magnetic field. Based on neutron-scattering and x-ray data, a model was proposed in [48] in which the macromolecular chain is positioned in one smectic layer, passing through it many times, as Fig. 6.19a indicates. 

In a gedanken experiment, a polymer is swollen with a liquid crystal and crosslinked. By swelling with the LC polymer chains lose their isotropic conformation due to the anisotropic environment. This leads to an anisotropic conformation of the network chains as well. The respective coil dimensions differ parallel and perpendicular to the director of the LC phase. Upon heating, the LC phase will lose its anisotropy and turn isotropic. The polymer network will follow this change, but due to the crosslinks, the adaption of an isotropic conformation will lead to a deformation of the elastomer (Figure 19). 

If the amount of the sample is sufficient, then the carbon skeleton is best traced out from the two-dimensional INADEQUATE experiment. If the absolute configuration of particular C atoms is needed, the empirical applications of diastereotopism and chiral shift reagents are useful (Section 2.4). Anisotropic and ring current effects supply information about conformation and aromaticity (Section 2.5), and pH effects can indicate the site of protonation (problem 24). Temperature-dependent NMR spectra and C spin-lattice relaxation times (Section 2.6) provide insight into molecular dynamics (problems 13 and 14). 

Anisotropic behaviour is also exhibited in optical properties and orientation effects can be observed and to some extent measured by birefringence methods. In such oriented materials the molecules are in effect frozen in an unstable state and they will normally endeavour to take up a more coiled conformation due to rotation about the single bonds. If an oriented sample is heated up the molecules will start to coil as soon as they possess sufficient energy and the mass will often distort. Because of this oriented materials usually have a lower heat distortion temperature than non-oriented polymers. 

A modification of the united-atom approach, called the anisotropic united-atom (AUA) model was the focus of extensive work by Karabomi et al. [362-365]. As in the other models of hydrocarbon chains described so far, the AUA approach to monolayers was preceded by work on alkanes [367]. hi the AUA model the interaction site is located at the geometrical mean of the valence electrons of the atoms it represents, while the pseudoatom itself is located at the carbon atom position. The movement of each interaction center depends on the conformation of the molecule as a whole. 

Our first exploration of property space was focused on acetylcholine. This molecule was chosen for its interesting structure, major biological role, and the abundant data available on its conformational properties [15]. The behavior of acetylcholine was analyzed by MD simulations in vacuum, in isotropic media (water and chloroform) [16] and in an anisotropic medium, i.e. a membrane model [17]. Hydrated n-octanol (Imol water/4mol octanol) was also used to represent a medium structurally intermediate between a membrane and the isotropic solvents [17]. 

Conversely, in a membrane model, acetylcholine showed mean log P values very similar to those exhibited in water. This was due to the compound remaining in the vicinity of the polar phospholipid heads, but the disappearance of extended forms decreased the average log P value somewhat. This suggests that an anisotropic environment can heavily modify the conformational profile of a solute, thus selecting the conformational clusters more suitable for optimal interactions. In other words, isotropic media select the conformers, whereas anisotropic media select the conformational clusters. The difference in conformational behavior in isotropic versus anisotropic environments can be explained considering that the physicochemical effects induced by an isotropic medium are homogeneously uniform around the solute so that all conformers are equally influenced by them. In contrast, the physicochemical effects induced by an anisotropic medium are not homogeneously distributed and only some conformational clusters can adapt to them. 

This chapter considers the distribution of spin Hamiltonian parameters and their relation to conformational distribution of biomolecular structure. Distribution of a g-value or g-strain leads to an inhomogeneous broadening of the resonance line. Just like the g-value, also the linewidth, W, in general, turns out to be anisotropic, and this has important consequences for powder patterns, that is, for the shape of EPR spectra from randomly oriented molecules. A statistical theory of g-strain is developed, and it is subsequently found that a special case of this theory (the case of full correlation between strain parameters) turns out to properly describe broadening in bioEPR. The possible cause and nature of strain in paramagnetic proteins is discussed. 

When a strong static electric field is applied across a medium, its dielectric and optical properties become anisotropic. When a low frequency analyzing electric field is used to probe the anisotropy, it is called the nonlinear dielectric effect (NLDE) or dielectric saturation (17). It is the low frequency analogue of the Kerr effect. The interactions which cause the NLDE are similar to those of EFLS. For a single flexible polar molecule, the external field will influence the molecule in two ways firstly, it will interact with the total dipole moment and orient it, secondly, it will perturb the equilibrium conformation of the molecule to favor the conformations with the larger dipole moment. Thus, the orientation by the field will cause a decrease while the polarization of the molecule will cause an... 

From these overall profiles, it is not easy to extract conformational properties, other than that it will be clear that the lipid molecules are strongly anisotropically oriented in the bilayer. For this, other characteristics are much more appropriate. It is possible to define an order parameter which indicates how much the lipid tails are oriented normal to the membrane ... 

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