Concentration units phase diagrams

Fig. 16. Electric field/concentration phase diagrams separating the homogeneous (acentric or ferroelectric) phase region from phase-separated regions for various values of host dielectric constant (curves 1 through 5 correspond respectively to dielectric constant values ol 2, 3, 5, 7, and 10). Field (e or ,) and concentration (x) are in dimensionless units as described in the text...

Fig. 14 a, b. Phase diagrams of polyfmethycrylic acid) (PMAA)-ionene-type polycation (2X) complex, (a) and (b) Ionic strength (jn) as a function of the concentration of the complex at the degree of neutralization of PMAA (a) = 0 and 5 = 1, respectively, (e) Dependence of pH on fi at constant concentration of the complex (5 x 10-3 mol of repeating unit/1) at 25 "C, Solution1 = complex is formed (soluble under this condition) Solution2 = complex is not formed... 

The concentration of the polymer is important Decreasing the concentrations brings the system closer to the critical point (in the phase diagram), smoothing K values toward the unit value and finally decreasing the selectivity. 

For any case in which F is zero, a definite reproducible solubility equilibrium can be reached. Complete representation of the solubility relations is accomplished in the phase diagram, which gives the number, composition, and relative amounts of each phase present at any temperature in a sample containing the components in any specified proportion. Solubilities may therefore be expressed in any appropriate units of concentration, such as the quality of the solute dissolved (defined mass, number of moles) divided by the quantity either of the solvent (defined mass, volume, or number of moles) or of the solution (defined mass, volume, or number of moles). Jacques et al. (1981) have provided a compilation of the expressions for concentration and solubility. 

Thomas and co-workers used Raman spectroscopy to generate a phase diagram of antiparallel and parallel G-quadruplex structures as controlled by concentrations of Na and K " ions. Both alkali ions facilitate the formation of an antiparallel diagonal-loop G-quadruplex by four units of the telomere repeat sequence of O. nova, d(T4G4)4, at low concentrations. An extended, parallel-stranded tetramolecular G-quadruplex is formed at higher cation concentrations. However, K " is more effective than Na in inducing the parallel strand association. The midpoints of the Na " and K concentrations required for the structural transition are 225 and 65 mM, respectively. ... 

Four different types of two-component system will now be considered. Detailed attention is paid to the first type solely to illustrate the information that can be deduced from a phase diagram. It will be noted that the concentration of a solution on a phase diagram is normally given as a mass fraction or mass percentage and not as mass of solute per unit mass of solvent , as recommended for the solubility diagram (section 3.3). Mole fractions and mole percentages are also suitable concentration units for use in phase diagrams. 

In all the phase diagrams presented above, mole fractions x or mass fractions w were used to characterize compositions. In separation processes, however, concentrations in mol/volume (in the unit mol m ) or mass/volume (kg m ) are more important, since partition coefficients, capacity ratios, etc. are normally defined using concentrations instead of mole fractions (see Equations (2) and (6)). The differences between the isothermal p(x) and p(c) phase diagrams are very important, especially at low pressures [10-14]. 

Fig. 2. Commonly observed electronic phase diagram of the high-temperature superconductors. The superconducting (SC) region spreads over the hole concentration p per CuOj unit from 0.05 to 0.28, showing the maximum at 0.15. Below p=0.02, the antiferromagnetic (AF) phase is obtained. To is die temperature below vshich various properties show anomalies with respect to the Fermi hquid, while below T a gap is thought to open up in the spin excitation spectrum.

The solid-liquid phase diagrams for tetrabutylammonium unsaturated carboxylate-water binary systems are shown in Figures 1 and 2. In these figures the logarithm of the concentration expressed in mole fraction(X) is plotted against the reciprocal of the absolute temperature. The temperature expressed in ordinary Celsius units is shown on the upper side of the figure. Because of the similarity of the data with one another, some of the results are not shown in these figures. 

The second example is a system composed of water and an ionic amphiphile which incorporates several ethylene imine units and hydroxyl groups [26]. The phase diagram is shown in Fig. 1.8. The lyotropic SmC analog phase is stabilized over a quite broad concentration range. To prove the correct phase assignment of the lyotropic SmC analog phase, the authors provided X-ray dififaction data as well as texture images, which exhibit the characteristic schlieren texture known from thermotropic SmC phases cf. inset of Fig. 1.8). 

The construction of phase diagrams of poly(oxyethylene) materials e.g., compound 7) in water reveals the generation of lyotropic liquid crystal phases. Compound 7 is a non-ionic surfactant where the polar head group comprises the oxyetltylene units and, as usual, the hydrophobic alkyl chain is the non-polar unit. At high concentrations (70-90%) of compound 7 in water the lamellar (L ) phase is generated up to moderate temperatures... 

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