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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]], particularly for non polar materials such as many [[polymer]]s. Materials with similar values of δ are likely to be [[miscible]].
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==Definition==
The Hildebrand solubility parameter is the [[square root]] of the cohesive energy density:
 
<math>\delta = \sqrt{\frac{\Delta H_v -RT}{V_m}}</math>
 
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 [[enthalpy of vaporization|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.
 
==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 ([[bond dipole moment|dipole moment]] <2 [[debye]]s{{Citation needed|date=September 2009}}) 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.
 
==Units==
The conventional units for the solubility parameter are ([[calories]] per cm<sup>3</sup>)<sup>1/2</sup>, or cal<sup>1/2</sup> cm<sup>-3/2</sup>. The [[SI units]] are J<sup>1/2</sup> m<sup>-3/2</sup>, equivalent to the [[pascal (unit)|pascal]]<sup>1/2</sup>. 1 calorie is equal to 4.184 J.
 
1 cal<sup>1/2</sup> cm<sup>-3/2</sup> = (4.184 J)<sup>1/2</sup> (0.01 m)<sup>-3/2</sup> = 2.045 × 10<sup>3</sup> Pa<sup>1/2</sup>
 
Given the non-exact nature of the use of δ, it is often sufficient to say the number of MPa<sup>1/2</sup> is twice the number of (cal<sup>1/2</sup> cm<sup>-3/2</sup>).
Where the units are not given, for example in older books, it is usually safe to assume the non SI unit.
 
==Examples==
{| class="wikitable sortable"
|-
! Substance
! δ<ref name="burke">{{cite web | url=http://www.cool.conservation-us.org/byauth/burke/solpar/ | title=Part 2.  Hildebrand Solubility Parameter | accessdate=2013-12-04 | author=John Burke | year=1984}}</ref> [cal<sup>1/2</sup> cm<sup>-3/2</sup>]
! δ [MPa<sup>1/2</sup>]
|-
| [[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
|-
| [[PTFE]]
| 6.2<ref name="jstoffer">{{cite web | url=http://web.mst.edu/~jstoffer/Solution/solparaexp.html | title=Examples of Solubility Parameters | accessdate=2007-11-20}}</ref>
|
|-
| [[Poly(ethylene)]]
| 7.9<ref name=jstoffer />
|
|-
| [[Poly(propylene)]]
| 8.2<ref name="vandenburg">{{Cite journal
  | last = Vandenburg
  | first = H. ''et al.''
  | coauthors = et al.  
  | title = A simple solvent selection method accelerated solvent extraction of additives from polymers
  | journal = The Analyst
  | volume =  124
  | pages = 1707–1710
  | url = http://www.rsc.org/Publishing/Journals/AN/article.asp?doi=a904631c
  | year = 1999
  | doi = 10.1039/a904631c
  | postscript = <!--None-->
  | issue = 11 }}
</ref>
| 16.6
|-
| [[Poly(styrene)]]
| 9.13<ref name=jstoffer />
|
|-
| [[Poly(phenylene oxide)]]
| 9.15<ref name=jstoffer />
|
|-
| [[PVC]]
| 9.5<ref name=vandenburg />
| 19.5
|-
| [[Polyethylene terephthalate|PET]]
| 10.1<ref name=vandenburg />
| 20.5
|-
| [[Nylon 6,6]]
| 13.7<ref name=vandenburg />
| 28
|-
| [[Poly(methyl methacrylate)]]
| 9.3<ref name=vandenburg />
| 19.0
|-
| [[(Hydroxyethyl)methacrylate]]
| 25-26<ref name="kwok">{{cite journal | title=Synthetic hydrogels 3. Solvent effects on poly(2-hydroxyethyl methacrylate) networks | last=Kwok | first=Alan Y. | coauthors=Greg G. Qiao David H. Solomon | journal=Polymer | year=2004 | volume=45 | pages=4017–4027}}</ref>  
|
|-
| [[Polyhydroxyethylmethacrylate|poly(HEMA)]]
| 26.93<ref name="kwok"/>  
|
|-
| [[Ethylene Glycol]]
| 29.9<ref name=vandenburg /><ref name="kwok"/>
|
|}
 
From the table, [[polyethylene|poly(ethylene)]] has a solubility parameter of 7.9 cal<sup>1/2</sup> cm<sup>-3/2</sup>. 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<sup>1/2</sup> cm<sup>-3/2</sup>
, and thus ethyl acetate is likely to be a good solvent. [[Nylon 6,6]] has a solubility parameter of 13.7 cal<sup>1/2</sup> cm<sup>-3/2</sup>, 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]]
* [[Hansen Solubility Parameters]]
 
==References==
 
===Notes===
{{reflist}}
 
===Bibliography===
{{cite book
  | last = Barton
  | first = AFM
  | title = Handbook of Solubility Parameters and Other Cohesion Parameters, 2nd edition
  | publisher = CRC Press
  | year = 1991}}
{{cite book
  | last = Barton
  | first = AFM
  | title = Handbook of Polymer Liquid Interaction Parameters and Other Solubility Parameters
  | publisher = CRC Press
  | year = 1990}}
 
==External links==
* <!--http://scrub.lanl.gov/pdf/williams/04_chapter_04.pdf Information on theory and derivation of Hildebrand solubility parameters by Laurie L. Williams]-->
* Abboud J.-L. M., Notario R. (1999) [http://old.iupac.org/publications/pac/1999/71_04_pdf/abboud.pdf 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<sub>H</sub>))
 
{{DEFAULTSORT:Hildebrand Solubility Parameter}}
[[Category:Polymer chemistry]]

Latest revision as of 22:41, 9 April 2014

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