Anisotropy ratios, diffusion

Fig. 7. Arrhenius plots of diffusion constants of nematic and isotropic pentyl-alkyl-cyano-biphenyl SCB (upper) and pentyl-alkyloxy-cyano-biphenyl 50CB (lower) to illustrate the quality of the Arrhenius law, the anisotropy ratio and the changes due to the slightly different side-groups of the two cyano-biphenyls. The data cannot be interpreted with existing theories. ...

Assuming the validity of Fick s laws for liquid crystals, various theories [7-15] have been developed to describe the diffusion constants D and in particular their anisotropy ratio a, in terms of the mesophase order and other adequate macroscopic and microscopic material parameters. However, in view of the unsatisfactory agreement with experimental data, so far this has only achieved limited success. By transforming the diffusion tensor from a local (cluster) to the laboratory director frame and by taking the orientational ensemble average, Blinc et al. [7] showed that the two tensor components of D for thermotropic N, S, and Sc phases should be coupled to the order parameter S, the average diffusion constant (D), and the limiting values D, of a perfectly ordered cluster (S = 1) in the... 

Hence the predicted macroscopic anisotropy ratio C7 is independent of (D), and for S=1 is equal to ltd)l AL) for 5=0.6 with dlL=3, Eq. (6) gives cr=0.5. Relations equivalent to Eqs. (6a) and (6b) have been reported by Leadbetter et al. [10]. In smectic phases the final expression for 7 becomes more complicated and lengthy, since a periodic potential barrier, hindering the diffusion process perpendicular to the smectic layers (i.e. D ) must be included [9-12] this is often done by using an additional Boltzmann-factor for D in Eq. (6b), so that despite the fact that dobserved ratios o and 7 even considerably larger than unity can be explained by such a modification of the theoretical concept. Hess et al. [ 13] have more recently developed expressions rather different from Eqs. (5a, 5b) by an affine transformation of the isotropic diffusion law... 

Diffusivities of binary, ternary and multi-component liquid crystalline mixtures, e.g. of soap (potassium laurate (PL), water [25, 58], and lipid (dipalmitoylphosphatidylcho-line (DPPC) [25, 59] systems in lamellar, hexagonal, cubic, nematic and micellar mesophases [25,60,61] have been studied extensively by pulsed-field-gradient NMR [25] and optical techniques [62], partly because of their intimate relation to the structure and dynamical performance of biological membranes [18]. The main distinction from thermotropic phases is that for layered structures a noticeable diffusion occurs only within the layers (i.e. lateral, frequently written as Dl, but in our notation DjJ, whereas it is negligibly small and difficult to detect across the layers [60-62] (transverse migration, for bilayers denoted by flip-flop ) so the mobility is essentially two dimensional, and the anisotropy ratio is so great that it is seldom specified explicit-... 

Table 1. Diffusion constants and anisotropy ratios of typical thermotropic and lyotropic liquid crystals considered in the text (Extensive data and references are collected in Kruger 24], Lindblom et al. [25], and Karger et al. [38],...

Fundamental theories of diffusion for low-molecular weight liquid crystals in the nematic phase have been studied by Franklin [103-105] based on Oseen-Kirkwood hydrodynamic theory for isotropic liquids. Further theories of diffusion for low-molecular weight liquid crystals have been developed. These theories explained partially the experimental data on Dy and D. Chu and Moroi [106], and Leadbetter [107] have obtained that the anisotropy ratio of the diffusion coefficients, Dy/Dj, for low-molecular weight liquid crystals are expressed by [2y(l - S) + 2S -b 1]/[7(S + 2) -b 1 — S], where y = Ttd/Al in which I is the length and d of the diameter of the... 

Above roughening (see Figure 6), the decay of the gratings is well described by the classical continuum theory for sufficiently small ratios amplitude/wavelenght, with g = 2 for evaporation, and 4 for surface diffusion. Deviations, observed otherwise, can be explained mostly by the anisotropy of the surface tension. ... 

The factor R may be called a diffusion anisotropy factor for the surface. For diffusion of a W on the W (110), Tsong Casanova find a diffusion anisotropy factor of 1.88 from a set of data taken at 299 K, and of 2.14 from a set of data taken at 309 K. The average is 2.01, which agrees with the theoretical value, 2, to within 0.5%. A more detailed general analysis has since then been reported,137 and diffusion anisotropy on the W (110) surface has also been observed in field emission experiments.138 It should be noted, however, that the same ratio can be expected if an adatom jumps instead in the [001] and [110] directions with an equal frequency. Thus a measurement of surface diffusion anisotropy factor alone does not establish uniquely the atomic jump directions. The atomic jump directions can, of course, be established from a measurement of the displacement distribution function in two directions as discussed in the last section. Such measurements can only be done with atomic resolution field ion microscopy. 

In their study of the NMR T2 and T2 of crosslinked cis-polyisoprene sheets under extension, von Meerwall and Ferguson 65) found that T2 of the rubber had much smaller anisotropy ( magic angle effect) than that of trace penetrants at the same extension ratio X < 3. However, the penetrant diffusion (referred to the strained dimensions) was within experimental error isotropic these findings are equally valid for C6F6 and n-hexadecane as penetrant. The authors concluded that segment orien-... 

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