The Hildebrand solubility parameter (δ) provides a numerical estimate of the degree of interaction between materials and can be a good indication of solubility, particularly for nonpolar materials such as many polymers. Materials with similar values of δ are likely to be miscible.

Definition[edit]

The Hildebrand solubility parameter is the square root of the cohesive energy density:

The CRC Handbook of Solubility Parameters and Other Cohesion Parameters, Second Edition, which includes 17 new sections and 40 new data tables, incorporates information from a vast amount of material published over the last ten years. The volume is based on a bibliography of 2,900 reports, including 1,200 new citations. The detailed, careful construction of the handbook. The Hildebrand solubility parameter (δ) provides a numerical estimate of the degree of interaction between materials and can be a good indication of solubility, particularly for nonpolar materials such as many polymers. Materials with similar values of δ are likely to be miscible. 'The CRC Handbook of Solubility Parameters and Other Cohesion Parameters, Second Edition', which includes 17 new sections and 40 new data tables, incorporates information from a vast amount of material published over the last ten years. The volume is based on a bibliography of 2,900 reports, including 1,200 new citations. HANDBOOK of SOLUBILITY PARAMETERS and OTHER COHESION PARAMETERS Second Edition Allan E M. Associate Professor of Chemistry Murdoch University Perth, Western Australia CRC Press Boca Raton London New York Washington, D.C.

${\displaystyle \delta =\sqrt{\frac{\mathrm{\Delta }{H}_v-RT}{V_m}}.}$

The cohesive energy density is the amount of energy needed to completely remove unit volume of molecules from their neighbours to infinite separation (an ideal gas). This is equal to the heat of vaporization of the compound divided by its molar volume in the condensed phase. In order for a material to dissolve, these same interactions need to be overcome, as the molecules are separated from each other and surrounded by the solvent. In 1936 Joel Henry Hildebrand suggested the square root of the cohesive energy density as a numerical value indicating solvency behavior.^[1] This later became known as the “Hildebrand solubility parameter”. Materials with similar solubility parameters will be able to interact with each other, resulting in solvation, miscibility or swelling.

Uses and limitations[edit]

Its principal utility is that it provides simple predictions of phase equilibrium based on a single parameter that is readily obtained for most materials. These predictions are often useful for nonpolar and slightly polar (dipole moment < 2 debyes^{[citation needed]}) systems without hydrogen bonding. It has found particular use in predicting solubility and swelling of polymers by solvents. More complicated three-dimensional solubility parameters, such as Hansen solubility parameters, have been proposed for polar molecules.

The principal limitation of the solubility parameter approach is that it applies only to associated solutions ('like dissolves like' or, technically speaking, positive deviations from Raoult's law): it cannot account for negative deviations from Raoult's law that result from effects such as solvation or the formation of electron donor–acceptor complexes. Like any simple predictive theory, it can inspire overconfidence: it is best used for screening with data used to verify the predictions.^{[citation needed]}

Units[edit]

The conventional units for the solubility parameter are (calories per cm³)^1/2, or cal^1/2 cm^−3/2. The SI units are J^1/2 m^−3/2, equivalent to the pascal^1/2. 1 calorie is equal to 4.184 J.

1 cal^1/2 cm^−3/2 = (4.184 J)^1/2 (0.01 m)^−3/2 = 2.045 10³ J^1/2 m^−3/2 = 2.045 MPa^1/2.

Given the non-exact nature of the use of δ, it is often sufficient to say that the number in MPa^1/2 is twice the number in cal^1/2 cm^−3/2.Where the units are not given, for example, in older books, it is usually safe to assume the non-SI unit.

Examples[edit]

From the table, poly(ethylene) has a solubility parameter of 7.9 cal^1/2 cm^−3/2. Good solvents are likely to be diethyl ether and hexane. (However, PE only dissolves at temperatures well above 100 °C.) Poly(styrene) has a solubility parameter of 9.1 cal^1/2 cm^−3/2, and thus ethyl acetate is likely to be a good solvent. Nylon 6,6 has a solubility parameter of 13.7 cal^1/2 cm^−3/2, and ethanol is likely to be the best solvent of those tabulated. However, the latter is polar, and thus we should be very cautions about using just the Hildebrand solubility parameter to make predictions.

See also[edit]

References[edit]

Notes[edit]

1. ^ ^abJohn Burke (1984). 'Part 2. Hildebrand Solubility Parameter'. Retrieved 2013-12-04.CS1 maint: discouraged parameter (link)
2. ^ ^abcd'Examples of Solubility Parameters'. Retrieved 2007-11-20.CS1 maint: discouraged parameter (link)
3. ^ ^abcdefVandenburg, H.; et al. (1999). 'A simple solvent selection method accelerated solvent extraction of additives from polymers'. The Analyst. 124 (11): 1707–1710. doi:10.1039/a904631c.
4. ^ ^abcKwok A. Y., Qiao G. G., Solomon D. H. (2004). 'Synthetic hydrogels 3. Solvent effects on poly(2-hydroxyethyl methacrylate) networks'. Polymer. 45: 4017–4027. doi:10.1016/j.polymer.2004.03.104.CS1 maint: uses authors parameter (link)

Bibliography[edit]

Barton, A. F. M. (1991). Handbook of Solubility Parameters and Other Cohesion Parameters (2nd ed.). CRC Press.

Barton, A. F. M. (1990). Handbook of Polymer Liquid Interaction Parameters and Other Solubility Parameters. CRC Press.

External links[edit]

• Abboud J.-L. M., Notario R. (1999) Critical compilation of scales of solvent parameters. part I. pure, non-hydrogen bond donor solvents – technical report. Pure Appl. Chem. 71(4), 645–718 (IUPAC document with large table (1b) of Hildebrand solubility parameter (δ_H))

Hansen Solubility Sphere

Hansen solubility parameters were developed by Charles M. Hansen in 1967 to predict the solubility of polymers in solvents. They are widely used in the paint and coatings industry. The method is based on the idea that like dissolves like. This is the case when the solvent and the solute have similar Hansen Solubility Parameters.
The three Hansen parameters can be considered the coordinates of a point in the so-called Hansen space. The closer two points are, the more likely the compounds are to dissolve into each other. In the case of a polymer, only solvents within a certain range will dissolve the polymer. This range is usually an ellipsoid and only solvents within this space are likely to dissolve the polymer in question.

Hansen Solubility Sphere

Occasionally, the scale of the dispersion axis is doubled, providing approximately a spherical volume of solubility. Then the distance of the solvent coordinates (δ_d2, δ_p2, δ_h2) from the center point (δ_d1, δ_p1, δ_h1) of the solute sphere is given by

R_a² = 4(δ_d2 - δ_d1)² + (δ_p2 - δ_p1)² + (δ_h2 - δ_h1)²

The distance R_a in the equation above can be compared with the solubility radius of the polymer, R₀. If R_a < R₀ then there is a high likelihood of the solvent to dissolve the polymer. The radius of the solubility sphere is often called the interaction radius and the ratio R_a / R₀ the relative energy difference (RED) of the system.

R_a / R₀ > 1 → the compound is a non-solvent

R_a / R₀ < 1 → the compound is a solvent

R_a / R₀ = 0 → the compound may cause swelling

Hansen¹ and Barton² have tabulated the interaction radius and partial solubility parameters for many polymers and solvents.

Barton Handbook Of Solubility Parameters Free

To give an example, we calculate R_a / R₀ of polystyrene (PS) and acetone. According to Hansen¹, PS has an interaction radius of approximately 12.7 and its partial solubility parameters are (δ_d, δ_p, δ_h) = (21.3, 5.7, 4.3) and those of acetone are (15.5, 10.4, 7.0). This gives

Barton Handbook Of Solubility Parameters Pdf

R_a = {(2·15.5 - 2·22.3)² + (10.4 - 5.8)² + (7.0 - 4.3)²}^1/2 = 12.8

→ R_a / R₀ = 12.8 / 12.7 ≈ 1.0

This result indicates that acetone is not a solvent for polystyrene but might cause some swelling of the polymer.

Barton Handbook Of Solubility Parameters 2

Barton Handbook Of Solubility Parameters

References

Barton Handbook Of Solubility Parameters Class

1. Charles M. Hansen, Hansen Solubility Parameters: A User's Handbook, 2nd Edition, 2007
2. Allan F.M. Barton, CRC Handbook of Solubility Parameters and Other Cohesion Parameters, 2nd ed., 1991