Pitch phase diagram

Fig. 11 Phase diagram of a twisted ribbon solution that forms fibrils. The axes represent relative helix pitch of isolated ribbons and relative stacking attraction of ribbons. Reproduced from Aggeli et al. [20]. Copyright 2001 National Academy of Sciences, USA...

Figure 5.24 Model of hierarchical self-assembly of chiral rodlike monomers.109 (a) Local arrangements (c-f) and corresponding global equilibrium conformations (c -f) for hierarchical selfassembling structures formed in solutions of chiral molecules (a), which have complementary donor and acceptor groups, shown by arrows, via which they interact and align to form tapes (c). Black and the white surfaces of rod (a) are reflected in sides of helical tape (c), which is chosen to curl toward black side (c ). (b) Phase diagram of solution of twisted ribbons that form fibrils. Scaled variables relative helix pitch of isolated ribbons h hh /a. relative side-by-side attraction energy between fibrils eaur/e. Reprinted with permission from Ref. 109. Copyright 2001 by the National Academy of Sciences, U.S.A.

Figure 2 Phase diagram of a solution of twisted ribbons which form fibrils, where the relative helix pitch of isolated ribbons hribbom/a is plotted against the relative side-by-side attraction energy between ribbons "ri/ fibnitTibrii = (27r2b2/a2 ktwist. The areas divided by the thick lines reveal the conditions where ribbons, fibrils, and infinite stacks of completely untwisted ribbons are stable. The dotted lines are lines of stability for fibrils containing p ribbons (p are written on the lines) kbend/ktwist = 0.1 (Aggeli et al., 2001b).

The experimental diagram resembles the schematic one except that the decomposition temperature is relatively insensitive to the degree of pyrolysis until the volatile content is reduced below about 10%. This point corresponds approximately to that at which the residue is entirely mesophase, which is also the point at which the Tg of the mesophase equals the decomposition temperature. This means that it is not possible to produce, under these conditions of pyrolysis, a chemically stable single-phase mesophase pitch in the fluid state (although this may be possible by other techniques). 

Figure 9. A pseudo binary phase diagram which explains mesophase formation in a pitch.

Riggs, D. M. Diefendorf, R. J. "A Phase Diagram for Pitches", Preprint, CARBON 80, Baden-Baden, 1980, pp. 326-329. 

Figure 1. Three-dimensional pseudo-phase diagram of a typical pitch.

Fig. 4.8.4. A representative phase diagram calculated from the Landau theory. The normalized ordinate t is proportional toT—T and the normalized abscissa K is proportional to 1 /P, where P is the cholesteric pitch. The diagram illustrates how different BPs can occur by changing the chirality. (From Crooker. )...

The pitch of a cholesteric may vary quite rapidly with temperature, particularly if the phase diagram of the material contains a cholesteric to smectic A transition just below the temperature range of interest since the pitch in this case diverges to infinity as the smectic A phase is approached. Thus, the color of the selective reflection can be used a s a sensitive indicator of temperature. Material for this purpose is incorporated into plastic films with a black backing to absorb the unreflected polarization, or it is encapsulated to apply as a paint and used for a variety of medical, engineering, and consumer applications. 

To complete the characterization of the phases appearing in the measured phase diagrams, typical texture images of the remaining phases are shown in Fig. 5.17. The N phase exhibits a fingerprint texture with the pitch being in the range of a few tm or an oily streak texture as displayed in Fig. 5.17a. Most of the time, the lamellar L phase shows a homeotropic texture with sporadic appearance of oily... 

The predicted phase sequence SmA-TGBA-N was first observed in a mixture of cholesteryl nonanoate and nonyloxybenzoic acid [59], later in a chiral derivative of 4-biphenyl-benzoate [7] and many other pure compounds. According to the theoretical predictions, the occurrence of TGB phases requires a high optical purity and the abilities of the molecules to form a small cholesteric pitch as well as a smectic layer structure. The phase diagrams of chiral-racemic mixtures (Figure 10.8) confirm that the TGB... 

The phase diagram of the HPC-water system, which has a lower critical temperature of mixing, is shown in Fig. 7.7 [34]. When is reached, the system passes into the LC state, which is initially two-phase, and the system then becomes totally liquid crystalline when the concentration of polymer increases above 50% and exhibits the optical properties of the cholesteric mesophase selective reflection of visible light Characteristic alternation of the chromaticity of the preparation—from red to violet— is observed, i.e., the pitch of the cholesteric helix decreases with an increase in the concentration of the polymer, as observed for solutions of polypeptides (cf. curves 1 and 2 in Fig. 7.4). However, in contrast to polypeptides, Ae exponent n in Eq. (7.8) can have values of 0.3 to 3.0 and even up to 6.92 according to the data in the literature [32]. Like Cgp the pitch is a function of the nature of the solvent and decreases with an increase in the acidity of the solvent. 

We can look at an equivalent hardware block diagram. Here we have a wavetable being addressed by what is essentially a counter whose rate is changed to vary the pitch. The term drop sample tuning refers to the fact that samples are either dropped (skipped) or repeated to change the frequency of the oscillator. The phase increment is added to the current value of the phase register every sample, and the integer part of the phase is used as an address to lookup a sample in waveform memory to output to aDAC. 

T0 is the temperature at which weight loss could be detected. Tg was determined by a penetrometry technique that did not allow the separate determination of the values for each phase in the two-phase region consequently only one Tg value for the total pitch is shown in the experimental diagram. This value is characteristic of that phase which forms the continuous matrix in the sample. (Recently, it has been possible ( 5,36 to separate each phase by a hot centrifugation technique, and Tg s for the separate phases have been determined). 

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