Biphasic region

Lyotropic liquid crystals are those which occur on the addition of a solvent to a substance, or on increasing the substance concentration in the solvent. There are examples of cellulose derivatives that are both thennotropic and lyotropic. However, cellulose and most cellulose derivatives form lyotropic mesophases. They usually have a characteristic "critical concentration" or "A point" where the molecules first begin to orient into the anisotropic phase which coexists with the isotropic phase. The anisotropic or ordered phase increases relative to the isotropic phase as the solution concentration is increased in a concentration range termed the "biphasic region." At the "B point" concentration the solution is wholly anisotropic. These A and B points are usually determined optically. 

The lattice theory deals with rod-like particles which do not have interactions with their neighbors except, of course, repulsions occur when the particles overlap. Above a certain criticsd concentration (V2 ) that depends on the axi d ratio x the theory predicts the system will adopt a state of partial order (biphasic region). Below V2 the system... 

Fig. 7. Comparison of experimental phase boundary concentrations between the isotropic and biphasic regions for various liquid-crystalline polymer solutions with the scaled particle theory for wormlike hard spherocylinders. ( ) schizophyllan water [65] (A) poly y-benzyl L-glutamate) (PBLG)-dimethylformamide (DMF) [66-69] (A) PBLG-m-cresoI [70] ( ) PBLG-dioxane [71] (O) PBLG-methylene chloride [71] (o) po y(n-hexyl isocyanate) (PHICH°Iuene at 10,25,30,40 °C [64] (O) PHIC-dichloromethane (DCM) at 20 °C [64] (5) a po y(yne)-platinum polymer (PYPt)-tuchIoroethane (TCE) [33] ( ) (hydroxypropyl)-cellulose (HPC)-water [34] ( ) HPC-dimethylacetamide (DMAc) [34] (N) (acetoxypropyl) cellulose (APC)-dibutylphthalate (DBP) [35] ( ) cellulose triacetate (CTA)-trifluoroacetic acid [72]...

The ternary phase diagram shown in Fig. 9b for the schizophyllan-water system has two more phase regions the isotropic-anisotropic (cholesteric)-anisotropic triphasic region (IAA) and the anisotropic-anisotropic biphasic region (AA). This was the first observation of the complex phase diagram as had been predicted by Abe and Flory, but the diagram quantitatively departs from their prediction in the positions and sizes of the regions [76]. 

Fig. 22. Plot of In [(H,1 2 — 1)/LjC ] vs L c constructed from the q0 data of aqueous xanthan presented in Fig. 20a. The vertical segments in the upper panel indicate the phase boundary concentration ct between the isotropic and biphasic regions...

Fig. 35. Effect of phase behavior on palladium-catalyzed oxidation of benzyl alcohol to benzaldehyde in supercritical CO2 characterized by transmission- and ATR-IR spectroscopy combined with video monitoring of the reaction mixture (102). The figure at the top shows the pressure dependence of the reaction rate. Note the strong increase of the oxidation rate between 140 and 150 bar. The in situ ATR spectra (middle) taken at 145 and 150 bar, respectively, indicate that a change from a biphasic (region A) to a monophasic (B) reaction mixture occurred in the catalyst surface region in this pressure range. This change in the phase behavior was corroborated by the simultaneous video monitoring, as shown at the bottom of the figure.

It has been found for some systems, and may be true for all, that there is no transition directly from the isotropic to the nematic phase as the critical condition is attained. Instead, a narrow biphasic region is found in which isotropic and nematic phases co-exist. This behaviour was predicted by Flory 2), even although his initial calculations related to monodisperse polymers. It is accentuated by polydispersity (see Flory s review in Vol. 59 of Advances in Polymer Science), and indeed for a polydisperse polymer the nematic phase is found to contain polymer at a higher concentration and of a higher average molecular weight than the isotropic phase with which it is in equilibrium. 

Fig. 6.35 Calculated constant y N ( = 12) phase diagram for a binary blend of a diblock and homopolymer with equal degree of polymerization (/ = 1) as a function of the volume fraction of homopolymer, 0h, and the composition of the diblock (/) (Matsen 1995ft). For clarity, only the largest biphasic regions are indicated.

Fig. 638 Calculated constant %N (=11) phase diagram for a symmetric diblock blended with high-molecular-weight homopolymers (Janert and Schick 1997b). Biphasic regions are unlabelled. Note the large region of three-phase coexistence between the lamellar and the A-rich and B-rich disordered phases, (a) Both homopolymers have 0 = 1.5 (b) ft = 1.0, ft = 1.5.

Fig. 6.50 Phase diagram for the same blend as Fig. 6.47(b) also calculated using SCFT, by Matsen and Bates (1995), but allowing for biphasic regions.

Miller et al. have initiated studies to elucidate the kinetics of forming the ordered phase in the polypeptide solutions. When the isotropic solution is temperature-jumped across the biphasic region into the region in which the ordered phase is stable, the kinetics can be described by a nucleation and growth mechanism with many similarities to the kinetics of polymer crystallization. They have also shown that the kinetic process can be divided into two time scales the conversion of the randomly oriented rods to a random array of locally oriented rod domains, followed by growth of some domains at the expense of others. 

When the temperature is adjusted so that the final state is in the narrow biphasic region of the phase diagram, ordered spherulites appear in the disordered phase. Although the time scale becomes long as the driving force to form the ordered phase becomes small, the appearance of spherulites suggests a nucleation mechanism. 

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