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{{Short description|Type of paramter}}
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 [[polymer]]s. Materials with similar values of δ are likely to be [[miscible]].
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 [[polymer]]s. Materials with similar values of δ are likely to be [[miscible]].


==Definition==
==Definition==
The Hildebrand solubility parameter is the [[square root]] of the cohesive energy density:
The Hildebrand solubility parameter is the [[square root]] of the cohesive [[energy density]]:


<math>\delta = \sqrt{\frac{\Delta H_v -RT}{V_m}}</math>
: <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]]). This is equal to the [[enthalpy of vaporization|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 Dr. [[Joel Henry Hildebrand]] suggested the square root of the cohesive energy density as a numerical value indicating solvency behavior.<ref name="burke"/> 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.
The cohesive energy density is the amount of [[energy]] needed to completely remove a unit volume of [[molecule]]s from their neighbours to infinite separation (an [[ideal gas]]). This is equal to the [[enthalpy of vaporization|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.<ref name="burke"/> 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==
==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 ([[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 three-dimensional solubility parameters, such as [[Hansen solubility parameters]], have been proposed for polar molecules.
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 ([[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 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|date=October 2015}}
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|date=October 2015}}


==Units==
==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.
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>
1 cal<sup>1/2</sup> cm<sup>−3/2</sup> = (523/125 J)<sup>1/2</sup> (10<sup>−2</sup> m)<sup>−3/2</sup> = (4.184 J)<sup>1/2</sup> (0.01 m)<sup>−3/2</sup> = 2.045483 10<sup>3</sup> J<sup>1/2</sup> m<sup>−3/2</sup> = 2.045483 (10<sup>6</sup> J/m<sup>3</sup>)<sup>1/2</sup>= 2.045483 MPa<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>).
Given the non-exact nature of the use of δ, it is often sufficient to say that the number in MPa<sup>1/2</sup> is about twice the number in 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.
Where the units are not given, for example, in older books, it is usually safe to assume the non-SI unit.


==Examples==
==Examples==
Line 25: Line 26:
|-
|-
! Substance
! Substance
! δ<ref name="burke">{{cite web | url=http://www.cool.conservation-us.org/byauth/burke/solpar/solpar2.html | 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<ref name="burke">{{cite web |author=John Burke |year=1984 |title=Part 2. Hildebrand Solubility Parameter |url=http://www.cool.conservation-us.org/byauth/burke/solpar/solpar2.html |access-date=2013-12-04 |archive-url=https://web.archive.org/web/20110606000004/http://www.cool.conservation-us.org/byauth/burke/solpar/solpar2.html |archive-date=6 June 2011 }}</ref> [cal<sup>1/2</sup> cm<sup>−3/2</sup>]
! δ [MPa<sup>1/2</sup>]
! δ [MPa<sup>1/2</sup>]
|-
|-
Line 50: Line 51:
| [[Dichloromethane]]
| [[Dichloromethane]]
| 9.93
| 9.93
| 19.8
| 20.2
|-
|-
| [[Acetone]]
| [[Acetone]]
Line 65: Line 66:
|-
|-
| [[PTFE]]
| [[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>
| 6.2<ref name="jstoffer">{{cite web | url=http://web.mst.edu/~jstoffer/Solution/solparaexp.html | title=Examples of Solubility Parameters | access-date=2007-11-20}}</ref>
|
|
|-
|-
Line 82: Line 83:
| year = 1999
| year = 1999
| doi = 10.1039/a904631c
| doi = 10.1039/a904631c
⚫
| issue = 11 | bibcode = 1999Ana...124.1707V|display-authors=etal}}
| postscript = <!--None-->
⚫
| issue = 11 |display-authors=etal}}
</ref>
</ref>
| 16.6
| 16.6
Line 98: Line 98:
| 9.5<ref name=vandenburg />
| 9.5<ref name=vandenburg />
| 19.5
| 19.5
⚫
|-
| [[Polyurethane|Polyurethane (PU/PUR)]]
⚫
| 8.9<ref name=vandenburg />
|
|-
|-
| [[Polyethylene terephthalate|PET]]
| [[Polyethylene terephthalate|PET]]
Line 112: Line 116:
|-
|-
| [[(Hydroxyethyl)methacrylate]]
| [[(Hydroxyethyl)methacrylate]]
|
| 25-26<ref name="kwok">{{cite journal | title=Synthetic hydrogels 3. Solvent effects on poly(2-hydroxyethyl methacrylate) networks | vauthors = Kwok AY, Qiao GG, Solomon DH | journal=Polymer | year=2004 | volume=45 | pages=4017–4027 | doi=10.1016/j.polymer.2004.03.104}}</ref>
| 25–26<ref name="kwok">{{cite journal | title=Synthetic hydrogels 3. Solvent effects on poly(2-hydroxyethyl methacrylate) networks |author=Kwok A. Y. |author2=Qiao G. G. |author3=Solomon D. H. | journal=Polymer | year=2004 | volume=45 | issue = 12 | pages=4017–4027 | doi=10.1016/j.polymer.2004.03.104}}</ref>
⚫
|
|-
|-
| [[Polyhydroxyethylmethacrylate|poly(HEMA)]]
| [[Polyhydroxyethylmethacrylate|poly(HEMA)]]
⚫
| 26.93<ref name="kwok"/>
|
|
⚫
| 26.93<ref name="kwok"/>
|-
|-
| [[Ethylene Glycol]]
| [[Ethylene glycol]]
|
⚫
| 29.9<ref name=vandenburg /><ref name="kwok"/>
| 29.9,<ref name="kwok"/> 33.0
| 33.0
|}
|}


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>
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&nbsp;°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.
, 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 ==
== See also ==
* [[Solvent]]
* [[Solvent]]
* [[Hansen Solubility Parameters]]
* [[Hansen solubility parameters]]


==References==
==References==
Line 139: Line 142:
{{cite book
{{cite book
| last = Barton
| last = Barton
| first = AFM
| first = A. F. M.
| title = Handbook of Solubility Parameters and Other Cohesion Parameters, 2nd edition
| title = Handbook of Solubility Parameters and Other Cohesion Parameters
| edition = 2nd
| publisher = CRC Press
| publisher = CRC Press
| year = 1991}}
| year = 1991
}}
{{cite book
{{cite book
| last = Barton
| last = Barton
| first = AFM
| first = A. F. M.
| title = Handbook of Polymer Liquid Interaction Parameters and Other Solubility Parameters
| title = Handbook of Polymer Liquid Interaction Parameters and Other Solubility Parameters
| publisher = CRC Press
| publisher = CRC Press
| year = 1990}}
| year = 1990
}}


==External links==
==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]-->
* <!--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>))
* 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}}
{{DEFAULTSORT:Hildebrand Solubility Parameter}}

Latest revision as of 22:35, 27 November 2024

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 cohesive energy density is the amount of energy needed to completely remove a 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 cal1/2 cm−3/2. The SI units are J1/2 m−3/2, equivalent to the pascal1/2. 1 calorie is equal to 4.184 J.

1 cal1/2 cm−3/2 = (523/125 J)1/2 (10−2 m)−3/2 = (4.184 J)1/2 (0.01 m)−3/2 = 2.045483 103 J1/2 m−3/2 = 2.045483 (106 J/m3)1/2= 2.045483 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 about 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

[edit]
Substance δ[1] [cal1/2 cm−3/2] δ [MPa1/2]
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 19.9
2-propanol 11.6 23.8
Ethanol 12.92 26.5
PTFE 6.2[2]
Poly(ethylene) 7.9[2]
Poly(propylene) 8.2[3] 16.6
Poly(styrene) 9.13[2]
Poly(phenylene oxide) 9.15[2]
PVC 9.5[3] 19.5
Polyurethane (PU/PUR) 8.9[3]
PET 10.1[3] 20.5
Nylon 6,6 13.7[3] 28
Poly(methyl methacrylate) 9.3[3] 19.0
(Hydroxyethyl)methacrylate 25–26[4]
poly(HEMA) 26.93[4]
Ethylene glycol 29.9,[4] 33.0

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 and hexane. (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 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

[edit]

References

[edit]

Notes

[edit]
  1. ^ a b John Burke (1984). "Part 2. Hildebrand Solubility Parameter". Archived from the original on 6 June 2011. Retrieved 2013-12-04.
  2. ^ a b c d "Examples of Solubility Parameters". Retrieved 2007-11-20.
  3. ^ a b c d e f Vandenburg, H.; et al. (1999). "A simple solvent selection method accelerated solvent extraction of additives from polymers". The Analyst. 124 (11): 1707–1710. Bibcode:1999Ana...124.1707V. doi:10.1039/a904631c.
  4. ^ a b c Kwok A. Y.; Qiao G. G.; Solomon D. H. (2004). "Synthetic hydrogels 3. Solvent effects on poly(2-hydroxyethyl methacrylate) networks". Polymer. 45 (12): 4017–4027. doi:10.1016/j.polymer.2004.03.104.

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.

[edit]
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