Residue curve bundles

Points of pure components and azeotropes are stationary or singular points of residue curve bundles. At these points, the value dXi /dt in Eq. (1.11) becomes equal to zero. A stationary point at which all residue curves come to an end is called a stable node (the temperature increases in the direction of this point). A specific point at which all residue curves start is called an unstable node (the temperature... 

The whole concentration space can be filled with one or more residue curve bundles. Each residue curve bundle has its own initial point (unstable node) and its own final point (stable node). Various bundles differ from each other by initial or final points. 

The part of the concentration space filled with one residue curve bundle is called a distillation region Reg°° (Schreinemakers, 1901). A distillation region Reg ) has... 

Residue Curve Bundles of Four-Component Mixtures... 

The structure of residue curve bundles of four-component mixtures is significantly more complex and diverse than that of three-component mixtures. This is due to the fact that each four-component mixture consists of four three-component constituents. Therefore, the number of types of four-component mixtures is enormous. In addition to that, four-component mixtures can have four-component node and saddle azeotropes. In contrast to three-component mixtures, the enormous... 

The totality of all bonds characterizes the mixture s structure. The bond serves as the elementary nonlocal characteristic of the residue curve bundle structure. Bonds form bond chains. The bond chains of maximum length connect the unstable node A and the stable node A+ of the distillation region Reg". Let s call a polyhedron formed by aU stationary points of one maximum-length bond chain and containing aU components of the mixture a distillation subregion Reg. ... 

The structure of the residue curve bundles can be obviously represented only for binary, three-, and four-component mixtures. For mixtures with more components, it is impossible. However, practice needs make necessary the analysis of the bundle structure with any number of components. This problem can be solved by means of a structure matrix description (Petlyuk et al, 1975a, 1975b). 

In Sections 1.3 to 1.5, the residue curve bundles, which characterize the direction of Uquid-vapor tie-lines in each point of the concentration space (i.e., the phase equilibrium field), were considered. As stated previously, such characteristics of the phase equilibrium field and structural elements related to it (bonds, distillation regions, and subregions) are the most important for one of the distillation modes, in particular, for the infinite reflux mode. 

Bonds between the stationary points (points of the components and azeotropes) and distillation subregions Reg j are the structural elements of the distillation regions. Residue curve bundle structure of multicomponent mixtures can be described with the help of a structural matrix that reflects the bonds available between the stationary points. 

Name the stationary points of types of residue curve bundles ... 

Taking into consideration the aforesaid, sections of Chapter 1 referring to residue curves bundles, to the structural elements of these bundles, and to the matrix description of the concentration space structure are completely valid regarding distillation trajectories under the infinite reflux. 

The boundaries separating one bundle from another are specific residue curves that are called the separatrixes of saddle stationary points. In contrast to the other residue curves, the separatrixes begin or come to an end, not in the node points but in the saddle points. A characteristic feature of a separatrix is that in any vicinity of its every point, no matter how small it is, there are points belonging to two different bundles of residue curves. The concentration space for ideal mixtures is filled with one bundle of residue curves. Various types of azeotropic mixtures differ from each other by a set of stationary points of various types and by the various sequence of boihng temperatures in the stationary points. 

Reg°°) region of concentration simplex filled with one bundle of distillation lines (residue curves) at infinite reflux (N => N+). 

Careful work is necessary to remove all preferred orientation from powder samples. Figure 1 shows results obtained with polyethylene terephthalate (PET) fibers. Curve is a typical azimuthal scan of the 010 peak (20 = 17,5°) for a bundle of parallel fibers placed perpendicularly to the x-ray beam. Curve b is the same scan carried out on a "powder" sample, showing that all preferred orientation is removed in our conditions of moulding (350 kg/ m2). For each kind of fiber, it is necessary to do preliminary trials to find the best experimental conditions. For PET fibers, we show on Figure 2 the relative crystallinity index and the residual orientation plotted against the cut-lengh. (5). 

Figure 3. Circular dichroism spectra of Co-Pn-V maquettes, where n = 12,16, and 20 are represented by dotted, solid, and dotted-dashed curves, respectively. As the number of residues increases, the helicity of the bundles is enhanced, as shown by the increased negative elliptidty at 222 nm. All ellipticity measurements are expressed as mean residue ellipticity. The spectra were obtained in 100 mM formate and 50 mM phosphate, pH = 7.0, at 25 V. Peptide quantitation was by amino acid analysis in all cases.

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