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The Hildebrand solubility parameter (δ) provides a numerical estimate of the degree of interaction between materials and can be a good indication of
solubility In chemistry, solubility is the ability of a substance, the solute, to form a solution with another substance, the solvent. Insolubility is the opposite property, the inability of the solute to form such a solution. The extent of the solubi ...
, particularly for nonpolar materials such as many
polymer A polymer (; Greek '' poly-'', "many" + '' -mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...
s. Materials with similar values of δ are likely to be
miscible Miscibility () is the property of two substances to mix in all proportions (that is, to fully dissolve in each other at any concentration), forming a homogeneous mixture (a solution). The term is most often applied to liquids but also applies ...
.


Definition

The Hildebrand solubility parameter is the
square root In mathematics, a square root of a number is a number such that ; in other words, a number whose '' square'' (the result of multiplying the number by itself, or  ⋅ ) is . For example, 4 and −4 are square roots of 16, because . ...
of the cohesive
energy density In physics, energy density is the amount of energy stored in a given system or region of space per unit volume. It is sometimes confused with energy per unit mass which is properly called specific energy or . Often only the ''useful'' or extrac ...
: : \delta = \sqrt. The cohesive energy density is the amount of
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of ...
needed to completely remove unit volume of
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and b ...
s from their neighbours to infinite separation (an ideal gas). This is equal to the
heat of vaporization The enthalpy of vaporization (symbol ), also known as the (latent) heat of vaporization or heat of evaporation, is the amount of energy (enthalpy) that must be added to a liquid substance to transform a quantity of that substance into a gas. T ...
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 Joel Henry Hildebrand (November 16, 1881 – April 30, 1983) was an American educator and a pioneer chemist. He was a major figure in physical chemistry research specializing in liquids and nonelectrolyte solutions. Education and professor ...
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 (or dissolution) describes the interaction of a solvent with dissolved molecules. Both ionized and uncharged molecules interact strongly with a solvent, and the strength and nature of this interaction influence many properties of t ...
,
miscibility Miscibility () is the property of two substances to mix in all proportions (that is, to fully dissolve in each other at any concentration), forming a homogeneous mixture (a solution). The term is most often applied to liquids but also appl ...
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 nonpolar and slightly polar ( dipole moment < 2
debye The debye (symbol: D) (; ) is a CGS unit (a non- SI metric unit) of electric dipole momentTwo equal and opposite charges separated by some distance constitute an electric dipole. This dipole possesses an electric dipole moment whose value is g ...
s) 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.


Units

The conventional units for the solubility parameter are (
calories The calorie is a unit of energy. For historical reasons, two main definitions of "calorie" are in wide use. The large calorie, food calorie, or kilogram calorie was originally defined as the amount of heat needed to raise the temperature of ...
per cm3)1/2, or cal1/2 cm−3/2. The
SI units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...
are J1/2 m−3/2, equivalent to the
pascal Pascal, Pascal's or PASCAL may refer to: People and fictional characters * Pascal (given name), including a list of people with the name * Pascal (surname), including a list of people and fictional characters with the name ** Blaise Pascal, Frenc ...
1/2. 1 calorie is equal to 4.184 J. 1 cal1/2 cm−3/2 = (4.184 J)1/2 (0.01 m)−3/2 = 2.045 103 J1/2 m−3/2 = 2.045 MPa1/2. Given the non-exact nature of the use of δ, it is often sufficient to say that the number in MPa1/2 is twice the number in 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

From the table, poly(ethylene) has a solubility parameter of 7.9 cal1/2 cm−3/2. Good solvents are likely to be
diethyl ether Diethyl ether, or simply ether, is an organic compound in the ether class with the formula , sometimes abbreviated as (see Pseudoelement symbols). It is a colourless, highly volatile, sweet-smelling ("ethereal odour"), extremely flammable li ...
and
hexane Hexane () is an organic compound, a straight-chain alkane with six carbon atoms and has the molecular formula C6H14. It is a colorless liquid, odorless when pure, and with boiling points approximately . It is widely used as a cheap, relative ...
. (However, PE only dissolves at temperatures well above 100 °C.) Poly(styrene) has a solubility parameter of 9.1 cal1/2 cm−3/2, and thus ethyl acetate is likely to be a good solvent.
Nylon 6,6 Nylon 66 (loosely written nylon 6-6, nylon 6/6, nylon 6,6, or nylon 6:6) is a type of polyamide or nylon. It, and nylon 6, are the two most common for textile and plastic industries. Nylon 66 is made of two monomers each containing 6 carbon atoms ...
has a solubility parameter of 13.7 cal1/2 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

*
Solvent A solvent (s) (from the Latin '' solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a solution. A solvent is usually a liquid but can also be a solid, a gas, or a supercritical fluid. Water is a solvent for ...
* Hansen solubility parameters


References


Notes


Bibliography


External links

* * 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 (δH)) {{DEFAULTSORT:Hildebrand Solubility Parameter Polymer chemistry 1936 introductions