Hansen’s three-component

Beerbower (36) has correlated solubility parameter with emulsifier selection with some success. Following Winsor (37), he calculates a ratio of the lyophobic to hydrophilic portions of emulsifiers using Hansen s three-component solubility parameter values. In the one test reported, there seems to be excellent correlation of the optimum ratio with stability of the emulsion. 

The polarity of the oil can be estimated from Hansen s three-dimensional solubility parameters. Hansen separated Hildebrand s solubility parameter into three independent components < d for the dispersion contribution, polar contribution, and 51, for the H-bonding contribution. As an estimation of the oil polarity, we define Dpi, as the square root of the square of the polar component plus the... 

The quantities Cjj and C221 by this interpretation, thus become directly measurable experimentally through the Internal pressures of the pure components at total system pressures not too far removed from atmospheric. Furthermore, from this interpretation, a two-dimensional solubility parameter concept emerges. One of these, 6y, is a solubility parameter evaluated from and includes the volume dependent terms in the total liquid state energy expression the second is termed a residual solubility parameter, 6j-, evaluated as the difference between for a component and AE. Both 6y and 61-are thus directly measured on the pure components (25) and are related to Hansen s three-dimensional solubility parameters by Equations 15 and 16. 

Miscible blends are most commonly formed from elastomers with similar three-dimensional (Hansen, 1967a,b Hansen and Beerbower, 1971) solubility parameters. An example of this is blends from copolymer elastomers (e.g., ethylene-propylene or styrene-butadiene copolymers) of slightly different composition, or microstructure. When the forces between the components of the polymer blend are mostly dispersive, miscibility is only achieved in neat polymers with a very close match in Hansen s three-dimensional solubility parameter (Hansen, 1967a,b Hansen and Beerbower, 1971), such that small combinatorial entropy for high molecular weight elastomers can drive miscibility. 

Three-component systems. Crowley et. al. proposed the three-dimensional solubility volumes (Figure 4.1.3). Better known are Hansen s three-dimensional solubility volumes (Figure 4.1.4). In Hansen s approach, the components of solubility parameters for mixed solvents are calculated from Eq. [4.1.56] ... 

Much attention has been given to quantifying the hydrogen bonding energies. This was reviewed in 1968 (2). The most satisfactory approach is Hansen s (3). He proposed a three-component parameter such that... 

In a further refinement Hansen (1967a,b) and Hansen and Beerbower (1971) have further elaborated the concept and have shown that S can be described in terms of three components Sd the contribution from dispersion interaction, Sp the contribution from polarity, and Sh the contribution from hydrogen bonding, and the total solubility parameter 8t is the root mean square of the three components ... 

The interactions of small solvent molecules are short range. However, the polymer molecules are much larger and they do not have sharply defined solubility parameters. The region of solubility can be drawn as a rough sphere in the three-dimensional space of partial solubility parameters. The description of a polymer s solubility characteristics by Hansen has four components - three partial... 

In an effort to retain the three components in a two-dimensional description, Teas (Gardon and Teas, 1976) proposed a triangular graph (Appendix 3), using reduced solubility parameters, derived from Hansen s partial solubility... 

Hansen [5] extended Hildebrand s concept by considering three components for the solubility parameter, a dispersion component 8polar component 8p, and a hydrogen bonding component 8,j,... 

The Hildebrandt parameter St can be calculated with the three Hansen solubility parameters in consideration of the dispersive Sj, polar 5p, and hydrogen S bonding components. Thus, the interaction between the fatty acids (FA) used as pure substances and bonded onto the magnetite surface (FA Fe304) could be characterized [15, 22]. The calculated values are presented in Table 1 and the following correlation applies The smaller the value, the more soluble is the surfactant in the solvent. 

According to Hansen s theory [13], 5, the Hildebrand parameter, can be calculated using the three components 5, which represents the energy from dispersion bonds 5i which represents the energy from hydrogen bonds between molecules and 8p, which represents the energy from dipolar intermolecular forces ... 

A good correlation is obtained if the results of Vincent and Raha are plotted in a f)v f)h, diagram. The results for the three polymers can be made to coincide if 8V <5vp and f)hs <5hp are used as parameters, where the capital subscripts S and P denote solvent and polymer. The difficulty in this approach is that the solubility parameter components of the polymers are not readily available. For poly(methyl methacrylate) and poly(vinyl chloride), values of 8V and <5h, as determined by Hansen (1969) have been mentioned in Chap. 7 these values are used here. For polysulphone the values of Sv and f)h have been chosen in such a way that a good correlation was obtained. The solubility parameter components used are mentioned in Table 26.7. 

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