3-dimensional solubility plot

The three-dimensional solubility parameler concept defines the limits of compatibility as a sphere. Values of these parameters for some of the solvents listed earlier in Table 12-3 are given in Table 12-4. More complete lists are available in handbooks and technological encyclopedias. The recommended procedure in conducting a solubility parameter study is to try to dissolve the polymeric solute in a limited number of solvents that are chosen to encompass the range of subsolubility parameters. A three-dimensional plot of solubility then reveals a solubility volume for the particular polymer in 5d, 5p, space. 

Figure 12.26. Typical plots of three dimensional solubility parameters in 8 - 8, 8 - 8 j and 8 - 8j planes for PC/ABS (90/10) blend.

FIGURE 3.3 Hansen solubility plot (three-dimensional) for cellulose acetate (Hansen, 2007), with Hansen partial solubility parameters, 8, 8p and 8h, in MPa. See Figure A3.28 for the same data plotted in a ternary Teas chart. 

Three-Component SSTs. SST also has been separated into three components usually y , and These can be established by measuring contact angles with three pure liquids (23,39-42) or by wetting smdies with a series of liquids (43,44). Note that the d, p, h notation (dispersion, polar, hydrogen bonding) is the same as that used for three-dimensional solubility parameters (8, S ", s "). There is a good reason for this as there is a close relationship between these material properties (45-48) and a solubility parametCT plot can be converted to surface units (43-47). 

It should be pointed out at this juncture that strict thermodynamics treatment of the film-covered surfaces is not possible [18]. The reason is difficulty in delineation of the system. The interface, typically of the order of a 1 -2 nm thick monolayer, contains a certain amount of bound water, which is in dynamic equilibrium with the bulk water in the subphase. In a strict thermodynamic treatment, such an interface must be accounted as an open system in equilibrium with the subphase components, principally water. On the other hand, a useful conceptual framework is to regard the interface as a 2-dimensional (2D) object such as a 2D gas or 2D solution [ 19,20]. Thus, the surface pressure 77 is treated as either a 2D gas pressure or a 2D osmotic pressure. With such a perspective, an analog of either p- V isotherm of a gas or the osmotic pressure-concentration isotherm, 77-c, of a solution is adopted. It is commonly referred to as the surface pressure-area isotherm, 77-A, where A is defined as an average area per molecule on the interface, under the provision that all molecules reside in the interface without desorption into the subphase or vaporization into the air. A more direct analog of 77- c of a bulk solution is 77 - r where r is the mass per unit area, hence is the reciprocal of A, the area per unit mass. The nature of the collapsed state depends on the solubility of the surfactant. For truly insoluble films, the film collapses by forming multilayers in the upper phase. A broad illustrative sketch of a 77-r plot is given in Fig. 1. 

The validity of the approach based on (6.2) was proven when the fraction of dose absorbed, Fa, was found to increase with AP for several drugs with a wide variety of physicochemical properties and various degrees of extent of absorption [156]. Additional support for the AP concept was provided by a 3-dimensional plot of Fa as a function of the ionization-solubility/dose term (fun/9) and the octanol/water partition coefficient Pc [157]. In fact, because of the recent interest in the apparent permeability estimates Papp measured in the in vitro Caco-2 monolayer system, it was suggested that Papp can replace the octanol/water partition coefficient Pc in (6.2) [157]. 

FIG. 26.16 The same kind of view as Fig. 26.15, but now two-dimensionally plotted as functions of the solubility parameter <5d and the hydrogen bonding parameter r)h. The cross in the closed areas depicts the parameters of the polymer. 

However, what if we had more than one variable to consider In other words, we have multivariate data. For example, what if we want to identify trends in the properties of a range of organic molecules The variables we might want to consider could be melting point, boiling point, M, solubility in a solvent and vapour pressure. We can, of course, tabulate the data, as before, but this does not allow us to consider any trends in the data. To do this we need to be able to plot the data. However, once we exceed three variables (which we need to be able to plot in three dimensions) it becomes impossible to produce a straightforward plot. It is in this context that chemometrics offers a solution, reducing the dimensionality to a smaller number of dimensions and hence the ability to display multivariate data. The most important technique in this context is called principal component analysis (PCA). 

The Hansen Plots Extension to Polar and Hydrogen Bonding Systems Hansen observed that when the solubility parameter increments of the solvents and polymers are plotted in three-dimensional plots, then the good solvents lie approximately within a sphere of radius R (with the polymer located in the center). Because three-dimensional plots are a bit cumbersome to use, two alternative simplihed ways are often employed. 

Solubility data can be plotted in a three-dimensional system using the 8D, 8p, and SH parameters as coordinates. The solubility regions for various polymers will be spherical if the 8D axis is expanded with a unit distance equal to twice that of the unit distances on the other axes. This effect is attributed to the directional nature of the molecular forces involved in 8P and 8H vs. the omnidirectional nature of the atomic dispersion forces. Description of solubility in terms of a geometrically simple model has many advantages, particularly in computer processing. 

If the three solubility parameter components for dispersion forces 5, dipole forces p, and hydrogen bonds plotted on a three-dimensional space diagram (Fig. 2), a system is obtained in which a vector S is defined for each solvent. The vector describes the solvent s solubility and miscibility behavior [14.28], [14.29]. Solvents that lie close to one another in this space diagram (i.e., whose vector difference is small) have similar solution properties and often a similar chemical structure. Solvents that are far apart on the diagram differ greatly in their chemical and physical characteristics they are generally immiscible [14.30]-[14.32], The solubility parameters as well as their components are shown for some solvents in Table 15. 

A three-dimensional model is used to plot polymer solubilities by giving the coordinates of the centre of a solubility sphere based on dispersion force components, hydrogen bonding and polar components, and by plotting a radius of interaction of around 2 SI units. A sphere of solution is plotted from the coordinates and radius. Liquids whose parameters lie within the sphere for a particular polymer are likely to be suitable solvents for it (Hansen, 1971). While extensive data has been published for liquids, the number of Hansen solubility parameters for polymers is more limited (Barton, 1983). From tbe selected solubility parameters for liquids and polymers in Table 4.1, it is clear tbat the high value for water excludes it as a solvent for polymers and that polystyrene and poly (methyl methacrylate) should be soluble in acetone. 

A three-dimensional plot is always preferable to a two-dimensional plot because of the influence of molar mass on solubility, which is invariably encountered. In such a plot, the molar mass distribution for each mean monomeric unit composition is drawn in, such that a graph in relief (Figure 2-2) is obtained. The effort involved in producing such a graph is quite large, however. 

When a soluble third component is added to two partially miscible liquids, we obtain a ternary system in which the third component (solute) is partitioned between the two liquid phases (solvents). The phase behavior of such systems is important in liquid-liquid extraction, a process that takes advantage of the differences in solubility to transfer a solute from one solvent into another. Since two mole fractions are required to represent composition in ternary systems, it is not possible to present temperature-composition or pressure-composition graphs in a two-dimensional plot. Instead, we map out the composition of the phases at constant pressure and temperature. This is done in triangular diagrams such... 

For this reason two-dimensional plots are generally made when using the Nelson, Hemwall and Edwards parameter system. In the first instance solubility maps were constructed of the fractional polarity against the Hildebrand solubility parameter, as shown in Figure 2.9. 

In a later stage it appeared to be more convenient to plot the hydrogen bond index against the Hildebrand solubility parameter as demonstrated in Figure 2.10. In this way of presentation contours of the maximum permissible fractional polarity can be indicated, which gives a good, and in practice very satisfactory, presentation of the three-dimensional case. 

A set of 43 features was derived from physical and chemical data CIR-, UV-, NMR-spectra, molecular weight, melting point, boiling point, density, specific rotation, solubility in water and alcohol) for each of a total of 47 compounds. Feature selection and eigenvector plots indicate that there are only two meaningful axes in the 43-dimensional data space. The axes were found to relate to the molecule s electron donor ability and its directed dipole. 

Hansen solubility properties are usually plotted in a three-dimensional coordinate system with the Hansen parameters as x, y, z axes. The coordinates of a solute can be determined by analyzing the solubility of a solute in a series of solvents with known Hansen parameters. By fitting a spheroid into the solubility space, the solubility volume of this solute can be identified. The solubility space of a solute is defined by the origin of a spheroid, resulting from the three coordinates, and the three radii in each dimension, with solvents inside the spheroid and nonsolvents outside. The radius of the sphere, Rq, indicates the maximum difference for solubility. Generally, good solvents are within the sphere, and bad ones are outside of it. Furthermore, the solubility distance ... 

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