Near order

Indeed, the degree of binding of the counterions to the micellar surface, even in the largest aqueous core, is found to be 12% [2,94]. This means that virtually all counterions are confined in a thin shell near the surface (about 4 A), the concentration of ions in this domain is very high, and a nearly ordered bidimensional spherical lattice of charges is formed at the water/surfactant interface of ionic surfactants. 

In principle, structure analysis can be considered as distribution analysis in atomic dimensions. However, from the practical point of view it makes sense to deal separately with structure analysis and to differentiate between molecular structure analysis and crystal structure analysis. Further structure investigations concern near-orders in solids and liquids (e.g. glass). 

With further increase of the concentration (in p, phase range for H cLii cNb03) many new bands were observed. The fact that the low concentration boundary of the P phases is approximately x = 0.5 leads to the assumption for some kind of ordering of Li and as reported. On one hand, it can be assumed that the protons form a (nearly) ordered sub-lattice. Such a structure would have a phonon spectrum different from that of a pure LiNbOs, see . On the other hand, the PE probably leads to a reduction of the crystal symmetry, i.e. due to the incorporation of H, the two Li sites in the unit cell may become non-equivalent. In such case, the symmetry would be reduced from Csv to C3. As a result, the number of molecules per unit cell would remain the same, but new bands would appear in the vibration spectrum. 

This idea has led long ago [20, 21, 45, 46] to a simple model termed the confined rotator model, where the dielectric response was found due to free planar librations performed without friction during the lifetime of a molecule in a site of near order. These librations occur between two reflective walls, the... 

We recognize that it would be interesting to find a self-consistent form of the well starting from the near-order structure of a liquid. A preliminary attempt was undertaken recently We considered attractive string-like interactions in an ensemble of the H-bonded molecules [12, 12a, 12b] see Section DC. This way of modeling may open new perspective for modeling of dielectric relaxation in aqueous media. 

It is important that the form of the wideband dielectric/FIR spectrum in CH3F resembles that in liquid water and thus could be described in terms of the same hat-curved potential. However, due to a difference between the structures of both fluids and the near-order lifetimes, characterizing them, two important distinctions arise ... 

We remind the reader that the following free parameters are employed in the HC model (a) the reduced potential will depth u = 6 o / ( /tb 7) (b) the angular half-width (3 of the well (c) the mean lifetime x, during which a near-order state exists in a liquid and (d) the form-factor / defined as follows / = (flat part of the well s bottom)/(total well s width 2p). The SD model is characterized by (e) the inhomogeneity-potential parameter p of our self-consistent well, (f) the lifetime xstr, of restricted rotation, and (g) the fraction rvib of dipoles performing RR with respect to their total concentration N. 

Available theoretical and experimental results on electric field induced non-linearities in isotropic dielectrics prove that we have here an effective method for the study of the dectric structure of molecules, as well as of their mutual interactions in dense states, i.e. of the structure of near ordering in liquids. 

DLS profces this motion optically. The particles are illuminated by a coherent light source, typically a laser, creating a diffraction pattern, showing in Fig. 21-12 as a fine structure from the diffraction between the particles, i.e., its near-order. As the particles are moving from impacts of the thermal movement of the molecules of the medium, the particle positions change with the time, t. 

In this case, correlation, or near order, is spoken of. The Bragg-Williams approximation allows for long range only, that is why Q in Equation 65 is called a long-range parameter. 

The first summand defines the intensity of scattering by separate atoms with no interference among them, and the second one the scattering with allowance for interference caused by the near order in the atom location (correlation of density fluctuations). The third term represents the scattering intensity at very small angles and depends on the shape and size of the sample with no dependence on its internal structure. 

Equation (28.9-11) shows the difference between a rubber band and a spring. When a spring is stretched at constant temperature, the energy increases as work is done on the spring. When a rubber band is stretched at constant temperature, doing work on the rubber band, the energy remains constant, so that heat must flow out. Stretching a rubber band at constant temperature must decrease its entropy. This fact seems reasonable from a molecular point of view, because the polymer molecules will be more nearly parallel and more nearly ordered in the stretched state than in the relaxed state. From Eqs. (28.9-8) and (28.9-11) we can derive a relation for this decrease in entropy ... 

Finally, the possibility of some near-order, perhaps due to geometrical packing effects or to non-equilibrium states in the viscous polymer liquid which are trapped... 

For all three collinear antiferromagnetic structures C and G the temperature dependence of separate sub-lattice magnetization near ordering temperature has the form... 

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