Direct hexagonal phase

The closed loop is not the only characteristic of the nonionic surfactant-water binary phase diagram. Like the ionic surfactant-water mixture, nonionic surfactants, at higher concentration in water, exhibit lyotropic mesophases. Figure 3.14 shows a typical binary phase diagram exhibiting the full lyotropic mesophase sequence II, cubic isotropic phase HI, direct hexagonal phase (middle phase) VI, special cubic ( viscous phase) La, lamellar phase (neat phase). Note the presence of the two-phase domains surrounding each mesophase, the critical point on top of each, and the zero-variant three-phase feature. 

Knight et al. investigated the transitions from the micellar phase Li to the lamellar phase L and from the direct hexagonal phase Hi to the micellar phase Li, using the Joule effect T-jump with turbidity or birefringence detection, in Ci2EOg/(water + salt) systems. All transitions were found to occur very rapidly, in about 0.5 s (see Figure 7.3). 

Here, we have shown an "A" ion (shown as a black sphere) which approaches the surface of "AB" and displaces an "A" ion in this solid phase. A series of "hops", i.e.- from "1" to "7", then occurs in the AB-phase with the final "A" ion ending within the B-phase where a displacement in the normally cubic "B" phase occurs. At the same time, the displaced "B" ion is diffusing in the opposite direction by a series of "hops", i.e.- from "a" to "e" to the interface of "AB" with "A". Note that the "A" phase is shown as a hexagonal phase while "B" is a cubic phase (as is the "AB" phase). It should be clear that the rate of diffusion of "A" will differ firom that of "B". 

Suppose we have rhombohedral indices hR kR lR and wish to transform them to hexagonal indices hH IcH iHlH. The c axis of the hexagonal cell is 00 (through the middle of the rhombohedron). Pass from O to O, first of all directly the phase-difference between waves from O and those from O js In. Now go from O to O by way of rhombohedral axial directions-—for instance, via OD, DK, and KO. Waves from D are hR wavelengths ahead of those from 0, those from K are k.R wavelengths ahead of those from D, and those from O are lR wavelengths ahead of those from K. The total is h R- rk R -l r- Thus lH = hRA-kRA lR ... 

Ethanol when added directly to the PTES/TEOS mixture is thus highly favoring the formation of a hexagonal phase with respect to the cubic phase. However, even if ethanol is not directly added to the precursor mixture, it is produced during the synthetic procedure via hydrolysis and condensation reactions of PTES and TEOS. One can now wonder which results will be obtained if methoxysilanes rather than ethoxysilanes are used. 

Figures 4a and 4b depict selected Nitrogen adsorption-desoprtion isotherms and pore size distributions (PSDs) for the same series of samples. As seen here and also in Table 1, all hexagonal phases exhibited pore sizes mostly above 5 nm, while typical pore sizes of MCM-41 silica prepared in the presence of CTAB under more common temperatures, i.e., 80 - 120 °C, have 3.5 to 4 nm pores [5, 19]. Earlier work showed that direct synthesis or postsynthesis hydrothermal restructuring in the mother liquor at high temperature, e.g. 150 °C gave rise to...

Refractive index data are very useful for the quantitation of isotropic (liquid and cubic liquid crystal) phases, and for the calibration of cell thickness and nonflatness. Hovever, the analysis of birefringent phases using refractive index data has been found to be unreliable (9). A problem arises from the fact that the orientation of such phases relative to the direction of the light path, as veil as the system variables, influence refractive indices. In order to use refractive index data for quantitation, a phase must spontaneously orient in a reproducible fashion. Such orientation does occur in the case of fluid lamellar phases (as in short chain polyoxyethylene nonionic systems (7)), but viscous lamellar phases, hexagonal phases, and crystal phases do not orient to a sufficient degree. 

At temperatures above 22.8 °C, the C12E04 interacts with the hexagonal phase of C19 directly. The normalized intensity plots exhibit smoother changes, and an increase in die apparent removal rate as the temperature is increased. The temperature dependence of the removal of C19 is not as sharp as with or C. ... 

The evidence that lamellae 15 nm thick can enter the hexagonal phase came from electron diffraction of specimens annealed as low as 236 °C at 0.54 GPa, 3 K lower than the maximum of the corresponding differential thermal analysis peak recorded for bulk polymer under the same conditions. At this annealing temperature lamellae were still entire, i.e. essentially of unaltered thickness although with some internal variation. No attempt was then made to anneal at lower temperatures and determine the orthorhombic/hexagonal transition temperature for this thickness. Such experiments offer, nevertheless, a direct approach by which the quantities of Eq. 9 may be determined. 

In a similar manner, the ethylene-octene copolymer crystallized directly via the orthorhombic phase without the intervention of the anticipated hexagonal phase as would be anticipated in linear polyethylenes at these high pressures and temperatures (at approximately 3.8 kbar and around 200 °C). At 100 °C, see Fig. 15, the d values for (110) and (200) orthorhombic reflections are 4.08 A and 3.71 A. When the sample is cooled below 100 °C, a new reflection adjacent to the (110) orthorhombic peak appears at 80 °C. The position of the new reflection is found to be 4.19 A and so corresponds to a new phase. No change in the intensity of the existing (110) and (200) reflections is observed, however the intensity of the amorphous halo decreases, which suggests that the appearance of the new reflection (d = 4.19 A) is solely due to the crystallization of a noncrystalline component. On cooling further as the new reflection intensifies, the (110) and (200) orthorhombic reflections shift gradually. However, at 50 °C, the (100) monoclinic reflection appears with a concomitant decrease in the intensity of the (110) orthorhombic reflec-... 

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