Correlation length apparent

The lack of this correlation is apparently due to the fact that the Cspiro-0(1) bond length in the ground transition state (the region of thermochromic cleavage)40... 

Apparently from the plots of log10 K (Fig. 47a) and log10 p (Fig. 47b) of the fractal ensemble versus the iteration step, number n, all these elastic properties behave like fractals before an eventual levelling off. The latter is obviously associated with the upper limit of fractal-like asymptotics, above which the elastic properties of a system are no longer p dependent on the scale—that is, on the iteration number (the loss of the self-similarity property occurs at iteration step n q = logc/log/o which defines the correlation length c at the given concentration, p). 

Dependence of apparent viscosity on concentration Extent of shear rate thinning Correlation length... 

The apparent hydrodynamic diameters of the droplets (or the correlation length), as calculated using the Stokes-Einstein equation for a number of different systems, are given in Table 2. These early findings showed that the micelle sizes measured in near-critical and supercritical solutions were similar to those found for conventional water-in-oil microemulsions in liquid alkane. At lower fluid densities, DLS probes the combined effect of the collective diffusion coefficient of the micelle cluster and that of the individual micelles. 

For those systems near a phase transition, the apparent hydrodynamic diameter of the droplets (or the correlation length), as calculated using the Stokes-Einstein equation, appears to decrease as pressure increases [2,4,39]. For example, the apparent hydrodynamic diameter of a microemulsion droplet (for [surfactant] = 150 mM and 5) in supercritical xenon [2] decreases from 6.5 to 4.5 nm as pressure is increased from 350 to 550 bar (10 bar = 1 MPa). This effect is due to the change in the extent of micelle clustering rather than an actual change in the micelle size. 

The definition of this apparent correlation length can be extended to dilute regimes, in which case app gives g/V3 (see eqn (2.72)). The behaviour of app is entirely different in dilute solutions and concentrated solutions. In dilute solutions, lapp dincreases with the molecular weight and the excluded volume, while in concentrated solutions app — I is independent of the molecular weight and decreases as a function of concentration and excluded volume (see eqn (5.36)). The reason can be easily understood from Fig. 5.1 once polymers overlap each other, the excluded volume interaction tends to make the concentration homogeneous. 

As an example, let us consider flie apparent correlation length defined by eqn (5.41). We can take the same line of argument as given in Section 2.6. 

The morphological observations of the Sq phase under PLM and TEM are apparently the same as those in the Sp phase. For example, TEM morphology of TPP(n=7) shown in Figure 13 is actually taken at room temperature and therefore, it is in the Sq phase. The correlation length of 11 nm corresponds well with the observation of the lamellar-like spacing in Figure 13 ( -15 nm). Note that the correlation length of the layer structure in the Sp phase in TPP(n=7) is only 5 nm. 

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