Separation ordered

The time-dependent structure factor S k,t), which is proportional to the intensity I k,t) measured in an elastic scattering experiment, is a measure of the strength of the spatial correlations in the ordering system with wavenumber k at time t. It exliibits a peak whose position is inversely proportional to the average domain size. As the system phase separates (orders) the peak moves towards increasingly smaller wavenumbers (see figure A3.3.3. 

The interactions between solute and the pha.ses are exactly the same as those present in LC separations, namely, dispersive, polar and ionic interactions. At one extreme, the plate coating might be silica gel, which would offer predominately polar and induced polar interactions with the solute and, con.sequently, the separation order would follow that of the solute polarity. To confine the polar selectivity to the stationai y phase, the mobile phase might be -hexane which would offer only dispersive interactions to the solute. The separation of aromatic hydrocarbons by induced polar selectivity could be achieved, for example, with such a system. 

C. TDGL and CHC Models for Phase Separating/Ordering Systems... 

The computation of the curvatures from the bulk field differential geometry has proven to be rather imprecise. The errors produced by the use of the approximate formulas (100)-(104) are especially big if the spatial derivatives of the field sharp peaks at the phase interface. This is a common situation in the late-stage kinetics of the phase separating/ordering process, when the order parameter is saturated and the domains are separated by thin walls. Here, to calculate the curvatures, we propose a much more accurate method. It is based on the observation that the local curvatures are quantities that can be inferred solely from the shape of the interface, without appealing to the properties of the bulk field [Pg.212]

Finally we return to monolayers at surfaces again and consider wetting phenomena at inter ces separating ordered domains For example,... 

If the system is nearly commensurate, discommensurations will naturally form and separate ordered commensurate phases. These discommensurations have a gapless excitation spectrum [60]. This subject has been reviewed in Ref. 61. 

The major disadvantage of all early investigations on chromatographic crossfractionation was related to the fact that both separation modes were connected to each other either off-line or in a stop-flow mode. Regardless of the separation order, SEC vs. HPLC or HPLC vs. SEC, in the first separation step fractions were collected, isolated, and then subjected to the second separation step. This procedure, of course, is very time-consuming and the reliability of the results at least to a certain extent depends on the skills of the operator. 

Figure 21 Longitudinal and vertical faults separating ordered regions in a crystal fragment containing mostly the phase (Ba3Nb6Si4026)6. BajNb Ti Oii (Reproduced by permission from Phys. Status Solidi, 1978, 49, 189)...

Based on microscopic structural details liquid crystals form three separate ordered phases nematic, smectic, and cholesteric. 

Here Qm and Q can be separate order parameters or order parameter components. In combination, Equations (4) and (5) provide a means of predicting the elastic constant variations associated with any phase transition in which the relaxation of Q in response to an applied stress is rapid relative to the time scale of the experimental measurement. A classic example of the success that this approach can have for describing the elastic behaviour of real materials is provided by the work of Errandonea (1980) for the orthorhombic monoclinic transition in LaPsOi4 (Fig. 4). 

For high symmetry systems, strain coupling needs to take account of the separate components of the order parameter. For example, cubic tetragonal, cubic < orthorhombic and tetragonal orthorhombic transitions in perovskites are associated with the M3 and R25 points of the reciprocal lattice of space group Pm3m and there are two separate order parameters, each with three components. The full Landau expansion is (from Carpenter et al. 2000b). 

Grating with prism showing separated orders... 

Comprehensive Periodicals Subscription Service offers combined annual subscription to all UNESCO periodicals for 10. An over-all standing book order scheme also exists. Separate orders for individual items are possible. Subject lists are obtainable from I.D.S. One of publications of wider interest is Index Translationum now in Vol. 3 (1952). 

Hermanek and co-workers (6) first reported the general importance of liquid phase hydrogen-bonding effects for adsorption on alumina. These workers cited several examples of the inversion of sample separation order... 

Sample retention volumes in GSC and liquid-solid chromatography (ESC) are obviously interrelated. Numerous experimental studies have demonstrated a general similarity of separation order in corresponding GSC and LSC systems [for a review see Ref. (5)]. Since liquid phase interactions have been shown to be unimportant in most LSC systems, insofar as sample K" values are concerned, the relationship between retention volumes in GSC and LSC should assume a relatively simple form. At first glance it might appear that Eq. (8-3) is directly applicable... 

Equation (9-2) can be recast into a form which facilitates comparison of separation order in corresponding GSC and LSC systems ... 

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