Solubility sphere

Calculated Solubility Sphere for Cholesterol Solubility — RED Order (see Equation 10.5)... 

When plotted in three dimensions, the Hansen parameters provide an approximately spherical volume of solubility for each polymer in Sj, Sp, 6h space. The scale on the dispersion axis is usually doubled to improve the spherical nature of this volume. The distance of the coordinates (6j, 6p, 61) of any solvent i from the center point (6, 5, S ) of the solubility sphere of polymer j is... 

This distance can be compared with the radius R of the solubility sphere of the polymer (Table 3.6), and if... 

As this value is less than the radius of the polymer solubility sphere (6.2 cal / cm-2/ ), the polymer is expected to be soluble. This is found to be the case in a 10% w/w solution. 

This distance can be compared with the radius R of the solubility sphere of the polymer (Table 3.6), and if d < R, the likelihood of the solvent i dissolving the polymer j is high. This works well, despite the limited theoretical justification of the method. 

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. 

Hansen gave a visual interpretation of his method by means of three-dimensional spheres of solubility, where the eenter of the sphere has eoordinates eorresponding to the values of components of solubility parameter of polymer. The sphere can be coupled wifli a radius to characterize a polymer. All good solvents for particular polymer (each solvent has been represented as a point in a three-dimensional space with coordinates) should be inside the sphere, whereas all non-solvents should be outside the solubility sphere. An example is given in Section 4.1.7. 

The separation of the cohesion energy into contributions of various forces implies fliat it is possible to substitute energy for parameter and sum contributions proportional to the second power of a difference of corresponding components. Hansen s treatment permits evaluation of the dispersion and polar contribution to cohesive energy. The fitting parameter of the approach (the solubility sphere radius) reflects on the supermolecular structure of polymer-solvent system. Its values should be higher for amorphous polymers and lower for glass or crystalline polymers. 

Where such a program is available, in principle the following steps have to be taken. For the design of a completely new solvent system, the solubility sphere within a three-dimensional solubility parameter system should either be known or has to be constructed for the solute in question. As a simplification, a solubility map described in the chapter on solvent power (Figure 2.10) may be used [10]. For many polymeric materials these data already exist for the Nelson, Hemwall and Edwards or the Hansen solubility parameter concepts. Alternatively as described in section 2.2 a sphere or map can be constructed. Once the area of solubility is known, suitable solvent blends can be designed with solubility parameters falling within this area. When one has to choose one of the above concepts it should be noted that the idea of a sphere of... 

Some solubility parameters and molar volume values for the main plasticizers chemical families are given in Table 5.2. Regarding the Hansen parameters data table, the relative energy difference (RED) between PLA and molecules has been calculated by dividing the distance by the PLA solubility sphere radius. Therefore, the lower the difference value is, the better is the miscibility. Furthermore, a distance value higher than 1 means that the... 

Just as with the single parameter above, the method may be illustrated using the example of a xylene-butanol mixture. We calculate the dissolving power of individual solvents from the separation between the centre of the resin s solubility sphere and the solvent s value, relative to the calculated sphere radius (i ), using the equation for 5 rel... 

For non-solvents, 5 1 will be greater than 1, while for good solvents, 5 1 will be less than 1, and hence the solvent s parameter will be inside the solubility sphere. Thus for an epoxy resin, the centre of the sphere is 8d = 19.8, 8p = 10.6 and 6h = 10.3, with R = 9.6. For xylene, 5rei = 1.24 and -butanol = 1.09, and both would be poor solvents if used alone. However, a blend of 62% xylene and 38% n-butanol has 5rei = 0.80, and the solubility parameter of this blend lies inside the solubility sphere of the... 

In Equation 4.2 the i terms correspond to the parameters of the resin and the j terms to the parameters of the solvent. This equation measures the distance in three-dimensional space between the total solubility parameters of the solvent and resin. The total solubility parameter, 5, is a point in space where the three partial solubility parameter vectors meet. If the calculated radius of interaction, of the solvent and resin combination is less than the radius of the resin solubility sphere then the solvent will probably dissolve the resin and the solvent s solubility point will fall within the solubility sphere of the resin (Figure 4.1). A poor resin solvent would have a solubility point outside the resin envelope. Calculation of the radius of interaction for solvents and resins can be made easy through the use of the computer spreadsheet described in Chapter 19. 

The center point coordinates and radius of the solubility sphere of the epoxy resin were available from a laboratory solubility study and are ... 

Visually, compatibility is recognized by the intersection (overlap) or separation of solubility spheres, each representing one material. 

FIGURE 7.1 Finding the center and radius of the PLA solubility sphere. 

Hansen solubility parameters in MPa dp, 5/, at the centre of the polymer s solubility sphere. R is the radius of the sphere (Hansen, 2007). 

In Equation (2) the i terms correspond to the parameters of the resin, and the j terms to the parameters of the solvent. The three-dimensional envelop for a polymer or resin is determined by measuring the solubility behavior of the resin in a number of solvents that have a range of varying nonpolarity, polarity, and hydrogen-bonding character. Computer models exist that can take resin solubility data and compute the three solubility parameters of the resin along with the radius of the resin solubility sphere. Resin values for many solvents can be found in the literature. This handbook provides values for a few hundred chemicals. 

Figure 4.15 Solubility sphere in three-dimensional solubility parameter space.

Solution. No. The solvent point lies in the 8p—8 plane (i.e., 8h = Q). The closest approach the polymer solubility sphere makes to this plane is 5.0—3.0 = 2. Thus, despite nearly identical 8 s the solvent will not dissolve the polymer. 

Figure 7.4 shows the solubility sphere for polystyrene (5i — 8.6, d, = 3.0, 5 = 2.0, R = 3.5, aU in hildebrands). Note that parts of the polyst3 rene sphere lie outside the first octant. The physical significance of these areas is questionable, at best. 

---