Anisotropy of mobility

Mobility measurements show that the carriers once created do not have an activated mobility, despite the narrow conduction bands calculated. This, combined with the observed and calculated anisotropy of mobility, suggests that the carriers may be treated as conventional Bloch electrons (39). 

Introduction of the local anisotropy of mobility allows us to specify the matrixes of the extra forces of external and internal resistance and to formulate dynamic equations, which will be discussed in Section 3.4. One can expect that, as a result of the introduction of the local anisotropy, mobility of a particle along the axis of a macromolecule appears to be bigger than mobility in the perpendicular direction, so that the entire macromolecule can move more easily along its contour. The local anisotropy hinders also change of the form of the macromolecular coil, and, by this way, plays a role similar to the role of the term with internal resistance in linear version of the model. 

The system of dynamic equations (3.37) for a chain of Brownian particles with local anisotropy of mobility appears to be rather complicated for direct analysis, and one ought to use numerical methods, described in the next Section,... 

There were different generalisations of the reptation-tube model, aimed to soften the borders of the tube and to take into account the underlying stochastic dynamics. It seems that the correct expansion of the Doi-Edwards model, including the underlying stochastic motion and specific movement of the chain along its contour - the reptation mobility as a particular mode of motion, is presented by equations (3.37), (3.39) and (3.41). In any case, the introduction of local anisotropy of mobility of a particle of chain, as described by these equations, allows one to get the same effects on the relaxation times and mobility of macromolecule, which are determined by the Doi-Edwards model. 

Derived from linear approximation of the equations (3.37), the equilibrium correlation function (4.29), defines two conformation relaxation times r+ and r for every mode. The largest relaxation times have appeared to be unrealistically large for strongly entangled systems, which is connected with absence of effect of local anisotropy of mobility. To improve the situation, one can use the complete set of equations (3.37) with local anisotropy of mobility. It is convenient, first, to obtain asymptotic (for the systems of long macromolecules) estimates of relaxation times, using the reptation-tube model. 

It is important to remember now that there is anisotropy of mobility, which can bring the reptation mode of motion and a different law of mobility of... 

The reptation diffusion is connected with the local anisotropy of mobility of particles, which can be confirmed by investigation of equations (3.37). As an example, Fig. 11 contains the results for displacement of a macromolecule of length M = 25Me (value of parameter x = 0.04) due to numerical integration... 

Abstract The discussion of relaxation and diffusion of macromolecules in very concentrated solutions and melts of polymers showed that the basic equations of macromolecular dynamics reflect the linear behaviour of a macromolecule among the other macromolecules, so that one can proceed further. Considering the non-linear effects of viscoelasticity, one have to take into account the local anisotropy of mobility of every particle of the chains, introduced in the basic dynamic equations of a macromolecule in Chapter 3, and induced anisotropy of the surrounding, which will be introduced in this chapter. In the spirit of mesoscopic theory we assume that the anisotropy is connected with the averaged orientation of segments of macromolecules, so that the equation of dynamics of the macromolecule retains its form. Eventually, the non-linear relaxation equations for two sets of internal variables are formulated. The first set of variables describes the form of the macromolecular coil - the conformational variables, the second one describes the internal stresses connected mainly with the orientation of segments. 

In a liquid crystal, the anisotropy of diffusion results in an anisotropy of mobility and, consequently, conductivity. The corresponding tensor for a uniaxial phase has a standard form ... 

Reinitzer discovered liquid crystallinity in 1888 the so-called fourth state of matter.4 Liquid crystalline molecules combine the properties of mobility of liquids and orientational order of crystals. This phenomenon results from the anisotropy in the molecules from which the liquid crystals are built. Different factors may govern this anisotropy, for example, the presence of polar and apolar parts in the molecule, the fact that it contains flexible and rigid parts, or often a combination of both. Liquid crystals may be thermotropic, being a state of matter in between the solid and the liquid phase, or they may be lyotropic, that is, ordering induced by the solvent. In the latter case the solvent usually solvates a certain part of the molecule while the other part of the molecule helps induce aggregation, leading to mesoscopic assemblies. The first thermotropic mesophase discovered was a chiral nematic or cholesteric phase (N )4 named after the fact that it was observed in a cholesterol derivative. In hindsight, one can conclude that this was not the simplest mesophase possible. In fact, this mesophase is chiral, since the molecules are ordered in... 

The physical dimensions and dynamics of calmodulin have also been investigated by tyrosine fluorescence. To learn about the internal mobility of calmodulin, Lambooy et al 1 and Steiner et al measured the steady-state fluorescence anisotropy of the tyrosine. Since the average correlation... 

The mobility of tyrosine in Leu3 enkephalin was examined by Lakowicz and Maliwal/17 ) who used oxygen quenching to measure lifetime-resolved steady-state anisotropies of a series of tyrosine-containing peptides. They measured a phase lifetime of 1.4 ns (30-MHz modulation frequency) without quenching, and they obtained apparent rotational correlation times of 0.18 ns and 0.33 ns, for Tyr1 and the peptide. Their data analysis assumed a simple model in which the decays of the anisotropy due to the overall motion of the peptide and the independent motion of the aromatic residue are single exponentials and these motions are independent of each other. 

In practice, the emission anisotropy of luminescent molecules in solution is considered to be proportional to the viscosity of the medium, except in the case where structural reasons arise, for instance helix-coil transition, cross-linking in polymer systems etc... (18-21). Therefore, if there is only the effect in viscosity, the mobility of the marker must be higher in the case of the compact complex system which have a very low viscosity. 

The second possibility (the direct magnetic effect of currents in Y) is shown to depend on the anisotropy of the magnetic susceptibility of Y. Quantitatively this shift is usually small, although it may account for the shift to high screening when some protons associate with an aromatic system, which has a large anisotropy due to the mobile electrons,... 

Steady-state measurements of the fluorescence anisotropy of fluorescein derivatives form the basis of a sensitive analytical technique also used to detect and quantitate proteins [36], steroids [37-39], therapeutic drugs, and narcotics [40-42], In a different approach, the anisotropy of the fluorescein conjugate is measured as a function of the medium viscosity to determine the segmental mobility of the chains that cover the binding site [43-45],... 

Reticulum ATPase [105,106], Owing to the long-lived nature of the triplet state, Eosin derivatives are suitable to study protein dynamics in the microsecond-millisecond range. Rotational correlation times are obtained by monitoring the time-dependent anisotropy of the probe s phosphorescence [107-112] and/or the recovery of the ground state absorption [113— 118] or fluorescence [119-122], The decay of the anisotropy allows determination of the mobility of the protein chain that cover the binding site and the rotational diffusion of the protein, the latter being a function of the size and shape of the protein, the viscosity of the medium, and the temperature. 

Several molecular properties can be measured using emission and excitation spectra. These include fluorescence lifetime, efficiency, anisotropy of the emitted light, mobility of chromophores, rates of quenching, and energy transfer to other chromophores. 

In description of effects observed in extension of molten polymers, the determinant is the phenomenon of anisotropy of the mobility of macromolecules. In the Doi-Ed-vards reptation theory the anisotropy of the mobility of macromolecules is taken into account topologically by means of placing a macromolecule into a certain hypothetical tube. In this case large-scale movements are allowed only along the macromolecule and are totally inhibited in the lateral direction. This, indeed, is a limiting case of mobility anisotropy. 

The popcom formation tendency is enhanced by addition of suitable liquids. In a system with 20 volume % butanone, the first popcom particles are visible after 16 hours at a bulk conversion of 8.5 in a mobile liquid. The optical anisotropy of these polymers disappears in dimethyl-formamide, where they swell but do not dissolve. On the contrary, when a popcom polymer is formed from a similar feed but with additional glycol dimethacrylate, this material—which contains a high amount of chemical crosslinks—retains its optical anisotropy also after swelling in dimethylformamide for a long time. 

Abstract We use Nuclear Magnetic Resonance relaxometry (i.e. the frequency variation of the NMR relaxation rates) of quadrupolar nucleus ( Na) and H Pulsed Gradient Spin Echo NMR to determine the mobility of the counterions and the water molecules within aqueous dispersions of clays. The local ordering of isotropic dilute clay dispersions is investigated by NMR relaxometry. In contrast, the NMR spectra of the quadrupolar nucleus and the anisotropy of the water self-diffusion tensor clearly exhibit the occurrence of nematic ordering in dense aqueous dispersions. Multi-scale numerical models exploiting molecular orbital quantum calculations, Grand Canonical Monte Carlo simulations, Molecular and Brownian Dynamics are used to interpret the measured water mobility and the ionic quadrupolar relaxation measurements. 

Figure 3. Anisotropy of the water mo- Figure 4. Water transverse mobilities...

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