Growth axial ratio

Phillips EM, Byron PR, Dalby RN. Axial ratio measurements for early detection of crystal growth in suspension-type metered dose inhalers. Pharm Res 1993 10 454-456. 

Deviations from spherical shape can be modeled as a growth into prolate or oblate shapes. The area enclosed volume ratio constraint implies a constraint in the possible values of the two semiaxes describing the particle size. Halle [62] calculated the correlation functions for the combined particle tumbling and surface diffusion of prolate and oblate particles. His results have, for example, been applied to microemulsion systems [48,58], focusing on the ratio yVpr(0)// 5,sph(0). where the subscripts pr and sph refer to prolate and spherical particles, respectively. For a given ratio of interfacial area to enclosed volume, which specifies the radius R of the sphere, y, pr(0)//. sph(0) is a function of the prolate axial ratio, Diat, and R. Knowing Djat and R from other experiments, it is possible to determine the aggregate axial ratio from the relaxation experiment. 

From all the results presented above, it can be concluded that the droplets grow with temperature and that they do not grow to axial ratios >4-6 before they either reach the phase boundary or the system become bicontinuous. The growth increases with the oil length, but the axial ratio when system of discrete droplets... 

FiS- Mechanism of collagen fibril growth in sea cucumber dermis and sea urchin ligament, based on literature descriptions (Trotter et al 1998, 2(XX)a). The mechanism ensures a tapered shape and a consistent axial ratio. 

The closed SLC is exemplified in Figure 14(b) by a class B system when sites are internally compensated and no further growth accompanies the formation of the mesophase. The behavior of the closed SLC is thus indistinguishable from that of a molecular LC (Figure 14(a)). Relevant cases are DNA [146], adequately described by the theory of the molecular LC (Section II.C.2), and poly(p-benzamide) (PBA) in AA -dimethylacetamide/LiCl solutions. An assembly of seven PBA molecules with a side-by-side shift of one fourth the molecular length was detected in both isotropic and lyotropic solutions. Even the axial ratio of the assembly ( 104) was undistinguishable from the axial ratio ( 100) of molecularly dispersed PBA [147]. 

Cases in which equilibria constants are rather weak (exemplified by folic acid tetramers. Table 1, polymer 7, cf. Section III.C.2) show complete uncoupling between growth and liquid crystallinity. Data in Figure 18 evidence no cooperative growth producing large (>1) axial ratios. Themesophase appears at 40% concentration and DP is 10 when the axial ratio is still <1. 

Quaternary ammonium bromides and hydroxides (quats) are applied as templates in the synthesis of zeolites with relatively high Si/Al ratio. Examples will be given of the use of mon-, di-, poly- and associated quats as templates in zeolite growth. Templated zeolites of the MFI-type can be grown in a lateral or in an axial way onto metal supports, providing promising composite systems, for separation and catalysis, respectively. 

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