Three-component solubility parameters

Hansen proposed that all types of bonds holding liquid molecules are broken during vaporization, and he divided the cohesive energy, A Uv into three parts  

The polar contribution, 5P, was calculated using a slight modification of Bottcher s equation in terms of measurable dipole moment, fl, refractive index, nD, molar volume, V and relative permittivity, e. 

For many solvents the above physical data are not available and Beerbower developed a much simpler and somewhat reliable equation for such cases  

Beerbower related 5d, 5p, 5 solubility parameters to the surface tension of organic solvents  

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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. 

Originally intended for application to substances whose cohesion arose from dispersion forces, the parameter seem to be of limited use with polymers, which generally decompose before vaporization enthalpies can be determined. The concept now has been greatly expanded. The overall 6 can be divided into dispersion and polar contributions. Often non-polar homomorphs of polar molecules can provide values of 5, and polar contributions, can then be obtained from differences between 6 and Further refinements due to Hansen " have introduced a three-component solubility parameter, which separates non-dispersive contributions into polar and hydrogen bond components. This has been applied to organic liquids, and to some polymers. Calculations of b for macromolecules also can be made from tabulated values of molar attraction constants, and extensive summaries of b and of other cohesion parameters are readily available to the potential user. Ultimately, however, the application of b to polymer systems is impeded for the following reasons ... 

There have been many attempts to divide the overall solubility parameter into components corresponding to the several intermolecular forces. For example, a so-called three-dimensional solubility parameter concept is built on the assumption that the ced is an additive function of contributions from dispersion (d), polar (p), and H-bonding (h) forces. It follows that... 

Hansen CM (1967) The Three Dimensional Solubility Parameter - Key to Paint Component Affinities I. J Paint Technol 39 104... 

While the solubility parameter can be used to conduct solubility studies, it is more informative, in dealing with charged polymers such as SPSF, to employ the three dimensional solubility parameter (A7,A8). The solubility parameter of a liquid is related to the total cohesive energy (E) by the equation 6 = (E/V) 2, where V is the molar volume. The total cohesive energy can be broken down into three additive components E = E j + Ep + Ejj, where the three components represent the contributions to E due to dispersion or London forces, permanent dipole-dipole or polar forces, and hydrogen bonding forces, respectively. This relationship is used... 

Hansen, C. M. 1967. The three dimensional solubility parameter. Key to paint component af nities I. Solvents, plasticizers, polymers, and resiials.PaintTechnol39 104-117. 

To improve further on this equation, three-dimensional solubility parameters were proposed [45-47] to account for more speciLc interactions that can occur, such as hydrogen bonding. The solubility parameter was divided into three components ... 

Here 6d, <5p, and <5h are the contributions to the solubility parameter from dispersive forces, dipole-dipole forces, and hydrogen bonding forces, respectively. Since the three forces can occur to varying degrees in different components and can be represented on a three dimensional diagram, this theory is termed the three-dimensional solubility parameter. Barton (1983, 1990) tabulates the contributions to the three dimensional solubility parameter for a variety of solvents and polymers. 

Hansen CM. The three-dimensional solubility parameter— key to paint component affinities. J. Paint Tech. 1967 39(505) 104—117. Rogers CE. Permeation of gases and vapors in Polymers. In Comyn J. ed.. Polymer Permeability. New York Elsevier Applied... 

Lo used the three-term solubility parameter (Barton, 1983) and a graphical procedure to identify solvents for liquid-liquid extraction. In a 2D space constructed from the polar component of the solubility parameter 6p and the hydrogen bonding component of the solubility parameter 6, the distribution coefficient of the solute B, mg, is given by... 

BurreU, H., Solubility parameters for film formers, Off. Dig., 27(369), 726-758, 1972 BurreU, H., A solvent formulating chart. Off. Dig., 29(394), 1159-1173, 1957 Burrell, H., The use of the solubility parameter concept in the United States, VI Federation d Associations de Techniciens des Industries des Peintures, Vemis, Emawc et Encres d Imprimerie de VEurope Continentale, Congress Book, 1962, 21-30. Hansen, C.M., The three dimensional solubility parameter-key to paint component affinities 1, J. Paint TechnoL, 39(505), 104-117, 1967. 

Hansen, C.M., The three dimensional solubility parameter — key to paint component affinities II, J. Paint TechnoL, 39(511), 505-510, 1967. 

The most comprehensive approach to resin solubilities has been that of Hansen [19] in which the solubility parameter is divided into three components. The basis of this three-dimensional solubility parameter system is the assumption that the energy of evaporation, i.e., the total cohesive energy AjEJt which holds a liquid together, can be divided into contribution from dispersion (London) forces ABd, polar forces AEp, and hydrogenbonding forces AEh- Thus,... 

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. 

Hansen CM. 1967. The three-dimensional solubility parameter—Key to paint component affinities. J. Paint Technol 39(505) 104-117. 

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