Hildebrand solubility parameter
Encyclopedia
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 non polar materials such as many polymer
s. Materials with similar values of δ are likely to be miscible.
of the cohesive energy density:
The cohesive energy density is the amount of energy
needed to completely remove unit volume of molecule
s from their neighbours to infinite separation (an ideal gas
), which is equal to the heat of vaporization divided by molar volume
. 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. Dr. Joel Henry Hildebrand
suggested the square root of the cohesive energy density as a numerical value indicating solvency behavior. 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.
<2 debye
s) systems without hydrogen bonding. It has found particular use in predicting solubility and swelling of polymers by solvents. More complicated, 3 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.
SI units
are (MPa)1/2 (The unit is one of pressure as one pascal
is a joule per cubic meter.)
Conversion from the two is by δ (MPa1/2) = 2.0455 δ (cal1/2 cm-3/2)
sqrt(4.184) = 2.04548283
Given the non-exact nature of the use of δ, it is often sufficient to say the number of MPa 1/2 is twice the number of (cal1/2 cm-3/2).
Where the units are not given, for example in older books, it is usually safe to assume the non SI unit.
From the table, poly(ethylene)
has a solubility parameter of 7.9 cal1/2 cm3/2. Good solvents are likely to be diethyl ether
and hexane
. Poly(styrene) has a solubility parameter of 9.1 cal1/2 cm3/2
, and thus ethyl acetate is likely to be a good solvent. Nylon 6,6 has a solubility parameter of 13.7 cal1/2 cm3/2, 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.
Solubility
Solubility is the property of a solid, liquid, or gaseous chemical substance called solute to dissolve in a solid, liquid, or gaseous solvent to form a homogeneous solution of the solute in the solvent. The solubility of a substance fundamentally depends on the used solvent as well as on...
, particularly for non polar materials such as many polymer
Polymer
A polymer is a large molecule composed of repeating structural units. These subunits are typically connected by covalent chemical bonds...
s. Materials with similar values of δ are likely to be miscible.
Definition
The Hildebrand solubility parameter is the square rootSquare root
In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x...
of the cohesive energy density:
The cohesive energy density is the amount of energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
needed to completely remove unit volume of molecule
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
s from their neighbours to infinite separation (an ideal gas
Ideal gas
An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.At normal conditions such as...
), which is equal to the heat of vaporization divided by molar volume
Molar volume
The molar volume, symbol Vm, is the volume occupied by one mole of a substance at a given temperature and pressure. It is equal to the molar mass divided by the mass density...
. 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. Dr. Joel Henry Hildebrand
Joel Henry Hildebrand
Joel Henry Hildebrand was an American educator and a pioneer chemist. He was a major figure in chemistry research specializing in liquids and nonelectrolyte solutions.-Education and professorship:...
suggested the square root of the cohesive energy density as a numerical value indicating solvency behavior. 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
Solvation
Solvation, also sometimes called dissolution, is the process of attraction and association of molecules of a solvent with molecules or ions of a solute...
, miscibility
Miscibility
Miscibility is the property of liquids to mix in all proportions, forming a homogeneous solution. In principle, the term applies also to other phases , but the main focus is usually on the solubility of one liquid in another...
or swelling.
Uses and Limitations
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 non-polar and slightly polar (dipole momentBond dipole moment
The bond dipole moment uses the idea of electric dipole moment to measure the polarity of a chemical bond within a molecule. The bond dipole μ is given by:\mu = \delta \, d....
<2 debye
Debye
The debye is a CGS unit of electric dipole momentElectric dipole moment is defined as charge times displacement: Historically the debye was defined as the dipole moment resulting from two charges of opposite sign but an equal magnitude of 10-10 statcoulomb10-10 statcoulomb is approximately 0.2083...
s) systems without hydrogen bonding. It has found particular use in predicting solubility and swelling of polymers by solvents. More complicated, 3 dimensional solubility parameters, such as Hansen Solubility Parameters
Hansen Solubility Parameters
Hansen Solubility Parameters were developed by Charles Hansen as a way of predicting if one material will dissolve in another and form a solution...
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.
Units
Conventional units are (calories / cm3)1/2, or cal1/2 cm-3/2SI units
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...
are (MPa)1/2 (The unit is one of pressure as one pascal
Pascal (unit)
The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre...
is a joule per cubic meter.)
Conversion from the two is by δ (MPa1/2) = 2.0455 δ (cal1/2 cm-3/2)
sqrt(4.184) = 2.04548283
Given the non-exact nature of the use of δ, it is often sufficient to say the number of MPa 1/2 is twice the number of (cal1/2 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
| Substance | δ | δ (SI) |
|---|---|---|
| n-Pentane | 7.0 | 14.4 |
| n-hexane | 7.24 | 14.9 |
| Diethyl Ether | 7.62 | 15.4 |
| Ethyl Acetate | 9.1 | 18.2 |
| Chloroform | 9.21 | 18.7 |
| Dichloromethane | 9.93 | 20.2 |
| Acetone | 9.77 | 19.7 |
| 2-propanol | 11.6 | 23.8 |
| Ethanol | 12.92 | 26.2 |
| PTFE3 | 6.2 | |
| Poly(ethylene)3 | 7.9 | |
| Poly(propylene)2 | 8.2 | 16.6 |
| Poly(styrene)3 | 9.13 | |
| Poly(phenylene oxide)3 | 9.15 | |
| PVC2 | 9.5 | 19.5 |
| PET2 | 10.1 | 20.5 |
| Nylon 6,62 | 13.7 | 28 |
| PMMA2 | 9.3 | 19.0 |
| HEMA 2 | 25-26 | |
| poly(HEMA) 2 | 26.93 | |
| Ethylene Glycol 2 | 29.9 | Data from except, |
From the table, poly(ethylene)
Polyethylene
Polyethylene or polythene is the most widely used plastic, with an annual production of approximately 80 million metric tons...
has a solubility parameter of 7.9 cal1/2 cm3/2. Good solvents are likely to be diethyl ether
Diethyl ether
Diethyl ether, also known as ethyl ether, simply ether, or ethoxyethane, is an organic compound in the ether class with the formula . It is a colorless, highly volatile flammable liquid with a characteristic odor...
and hexane
Hexane
Hexane is a hydrocarbon with the chemical formula C6H14; that is, an alkane with six carbon atoms.The term may refer to any of four other structural isomers with that formula, or to a mixture of them. In the IUPAC nomenclature, however, hexane is the unbranched isomer ; the other four structures...
. Poly(styrene) has a solubility parameter of 9.1 cal1/2 cm3/2
, and thus ethyl acetate is likely to be a good solvent. Nylon 6,6 has a solubility parameter of 13.7 cal1/2 cm3/2, 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.