Editing Gel

{{short description|Highly viscous liquid exhibiting a kind of semi-solid behavior}}
{{other uses}}
{{TopicTOC-Polymer}}
[[File:Hairgel.JPG|thumb|An upturned vial of [[hair gel]]|241x241px]]
[[File:Silica gel.jpg|thumb|Silica gel]]
A '''gel''' is a [[Quasi-solid|semi-solid]] that can have properties ranging from soft and weak to hard and tough.<ref>{{cite book | author1 = Khademhosseini A. | author2 = Demirci U. | title = Gels Handbook: Fundamentals, Properties and Applications | date = 2016 | publisher = World Scientific Pub Co Inc | isbn = 9789814656108 }}</ref><ref>{{cite book | title = Supramolecular Polymer Networks and Gels | editor = Seiffert S. | publisher = Springer | date = 2015 | asin = B00VR5CMW6 }}</ref> Gels are defined as a substantially dilute [[cross-link]]ed system, which exhibits no flow when in the steady state, although the liquid phase may still diffuse through this system.<ref>{{cite book | last = Ferry | first = John D. | date = 1980 | title = Viscoelastic Properties of Polymers | location = New York | publisher = Wiley | isbn = 0471048941 }}</ref>

[[File:IUPAC definition of a gel.png|thumb|right|550px|link=https://doi.org/10.1351/goldbook.G02600|IUPAC definition for a gel]]

Gels are mostly liquid [[Mass fraction (chemistry)|by mass]], yet they behave like solids because of a three-dimensional cross-linked network within the liquid. It is the cross-linking within the fluid that gives a gel its structure (hardness) and contributes to the adhesive stick ([[Adhesive|tack]]). In this way, gels are a dispersion of molecules of a liquid within a solid medium. The word ''gel'' was coined by 19th-century Scottish chemist [[Thomas Graham (chemist)|Thomas Graham]] by [[clipping (morphology)|clipping]] from ''[[gelatine]]''.<ref>{{cite web |url= http://www.etymonline.com/index.php?term=gel |title=Online Etymology Dictionary: gel |last=Harper |first=Douglas | name-list-style = vanc |author-link=Douglas Harper |website=[[Online Etymology Dictionary]] |access-date=2013-12-09}}</ref>

The process of forming a gel is called [[gelation]].

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== Definitions ==
The [[International Union of Pure and Applied Chemistry]] (IUPAC) defines a ''gel'' and related terms as:
{{glossary}}
{{term|Gel<ref>{{GoldBookRef|title=Gel|file=G02600}}</ref>}}
{{defn|Nonfluid [[colloid|colloidal]] network or polymer network that is expanded throughout its whole volume by a fluid.<ref>{{cite book | vauthors = Jones RG, Kahovec J, Stepto R, Wilks ES, Hess M, Kitayama T, Metanomski WV |title=IUPAC. Compendium of Polymer Terminology and Nomenclature, IUPAC Recommendations 2008 (the "Purple Book")|date=2008|publisher=RSC Publishing, Cambridge, UK|url=https://www.iupac.org/cms/wp-content/uploads/2016/07/ONLINE-IUPAC-PB2-Online-June2014.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.iupac.org/cms/wp-content/uploads/2016/07/ONLINE-IUPAC-PB2-Online-June2014.pdf |archive-date=2022-10-09 |url-status=live}}</ref><ref name = "Slomkowski_2011">{{cite journal | vauthors = Slomkowski S, Alemán JV, Gilbert RG, Hess M, Horie K, Jones RG, Kubisa P, Meisel I, Mormann W, Penczek S, Stepto RF | s2cid = 96812603 | display-authors = 6 |title=Terminology of polymers and polymerization processes in dispersed systems (IUPAC Recommendations 2011)|journal=[[Pure and Applied Chemistry]]|year=2011|volume=83|issue=12|pages=2229–2259|doi=10.1351/PAC-REC-10-06-03 |url=https://www.degruyter.com/downloadpdf/j/pac.2011.83.issue-12/pac-rec-10-06-03/pac-rec-10-06-03.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.degruyter.com/downloadpdf/j/pac.2011.83.issue-12/pac-rec-10-06-03/pac-rec-10-06-03.pdf |archive-date=2022-10-09 |url-status=live }}</ref>}}
{{defn|Note 1: A gel has a finite, usually rather small, yield stress.}}
{{defn|Note 2: A gel can contain:{{ordered list|lost_style_type=lower-roman
| a covalent polymer network, e.g., a network formed by crosslinking polymer
chains or by nonlinear polymerization;
| a polymer network formed through the physical aggregation of polymer chains, caused by hydrogen bonds, crystallization, helix formation, complexation, etc., that results in regions of local order acting as the network junction points. The resulting swollen network may be termed a "thermoreversible gel" if the regions of local order are thermally reversible;
| a polymer network formed through glassy junction points, e.g., one based on block copolymers. If the junction points are thermally reversible glassy domains, the resulting swollen network may also be termed a thermoreversible gel;
| [[Lamella (materials)|lamellar structures]] including [[mesophase]]s, e.g., soap gels, phospholipids, and clays;
| particulate disordered structures, e.g., a [[Flocculation|flocculent]] precipitate usually consisting of particles with large geometrical anisotropy, such as in V<sub>2</sub>O<sub>5</sub> gels and
globular or fibrillar protein gels.}}}}
{{term|[[Hydrogel]]<ref>{{GoldBookRef|title=Hydrogel|file=HT07519}}</ref>}}
{{defn|Gel in which the swelling agent is water.}}
{{defn|Note 1: The network component of a hydrogel is usually a polymer network.}}
{{defn|Note 2: A hydrogel in which the network component is a colloidal network may be referred to as an aquagel.<ref name = "Slomkowski_2011" />}}
{{term|[[Xerogel]]<ref>{{GoldBookRef|title=Xerogel|file=X06700}}</ref><ref>{{cite journal | vauthors = Alemán JV, Chadwick AV, He J, Hess M, Horie K, Jones RG, Kratochvíl P, Meisel I, Mita I, Moad G, Penczek S | s2cid = 97620232 | display-authors = 6 |title=Definitions of terms relating to the structure and processing of sols, gels, networks, and inorganic-organic hybrid materials (IUPAC Recommendations 2007) |journal=Pure Appl Chem |date=2007 |volume=79 |issue=10 |page=1801  |url=https://www.degruyter.com/downloadpdf/j/pac.2007.79.issue-10/pac200779101801/pac200779101801.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.degruyter.com/downloadpdf/j/pac.2007.79.issue-10/pac200779101801/pac200779101801.pdf |archive-date=2022-10-09 |url-status=live|doi=10.1351/pac200779101801 }}</ref>}}
{{defn|Open network formed by the removal of all swelling agents from a gel.}}
{{defn|Note 1: Examples of xerogels include silica gel and dried out, compact macromolecular structures such as gelatin or rubber.}}
{{glossary end}}
-->

==Composition==
Gels consist of a solid three-dimensional network that spans the volume of a liquid medium and ensnares it through [[surface tension]] effects. This internal network structure may result from physical bonds such as polymer chain entanglements (see [[polymer]]s)  (physical gels) or [[chemical bond]]s such as [[disulfide]] bonds (see [[thiomer]]s) (chemical gels), as well as [[crystallite]]s or other junctions that remain intact within the extending fluid. Virtually any fluid can be used as an extender including water ([[hydrogel]]s), oil, and air ([[aerogel]]). Both by weight and volume, gels are mostly fluid in composition and thus exhibit densities similar to those of their constituent liquids. Edible jelly is a common example of a hydrogel and has approximately the density of water.

===Polyionic polymers===
Polyionic polymers are polymers with an ionic functional group. The ionic charges prevent the formation of tightly coiled polymer chains. This allows them to contribute more to [[viscosity]] in their stretched state, because the stretched-out polymer takes up more space. This is also the reason gel hardens. See [[polyelectrolyte]] for more information.

==Types==

===Colloidal gels===

A [[colloid]]al gel consists of a [[Percolation theory|percolated]] network of particles in a fluid medium,<ref>{{cite journal | vauthors=((Zaccarelli, E.)) | journal=Journal of Physics: Condensed Matter | title=Colloidal gels: equilibrium and non-equilibrium routes | volume=19 | issue=32 | pages=323101 | date=15 August 2007 |  doi=10.1088/0953-8984/19/32/323101| arxiv=0705.3418 | bibcode=2007JPCM...19F3101Z | s2cid=17294391 }}</ref> providing [[Rheology|mechanical properties]],<ref>{{cite journal | vauthors=((Tsurusawa, H.)), ((Leocmach, M.)), ((Russo, J.)), ((Tanaka, H.)) | journal=Science Advances | title=Direct link between mechanical stability in gels and percolation of isostatic particles | volume=5 | issue=5 | pages=eaav6090 | date= May 2019 | doi=10.1126/sciadv.aav6090| pmid=31172025 | pmc=6544450 | arxiv=1804.04370 | bibcode=2019SciA....5.6090T }}</ref> in particular the emergence of elastic behaviour.<ref>{{cite journal | vauthors=((Whitaker, K.)), ((Varga, Z.)), ((Hsiao, L.)), ((Solomon, M.)), ((Swan, J.)), ((Furst, E.))  | journal=Nature Communications | title=Colloidal gel elasticity arises from the packing of locally glassy clusters | volume= 10 | date= May 2019 | issue=1 | page=2237 | doi=10.1038/s41467-019-10039-w | pmid=31110184 | pmc=6527676 | bibcode=2019NatCo..10.2237W }}</ref> The particles can show attractive interactions through [[Depletion force|osmotic depletion]] or through polymeric links.<ref>{{cite journal | vauthors=((Howard, M. P.)), ((Jadrich, R. B.)), ((Lindquist, B. A.)), ((Khabaz, F.)), ((Bonnecaze, R. T.)), ((Milliron, D. J.)), ((Truskett, T. M.)) | journal=The Journal of Chemical Physics | title=Structure and phase behavior of polymer-linked colloidal gels | volume=151 | issue=12 | pages=124901 | date=28 September 2019 | doi=10.1063/1.5119359| pmid=31575167 | arxiv=1907.04874 | bibcode=2019JChPh.151l4901H | s2cid=195886583 }}
</ref>

Colloidal gels have three phases in their lifespan: gelation, aging and collapse.<ref>{{cite journal | vauthors=((Lu, P. J.)), ((Zaccarelli, E.)), ((Ciulla, F.)), ((Schofield, A. B.)), ((Sciortino, F.)), ((Weitz, D. A.)) | journal=Nature | title=Gelation of particles with short-range attraction | volume=453 | issue=7194 | pages=499–503 | date= May 2008 | doi=10.1038/nature06931| pmid=18497820 | bibcode=2008Natur.453..499L | s2cid=4409873 }}</ref><ref>{{cite journal | vauthors=((Zia, R. N.)), ((Landrum, B. J.)), ((Russel, W. B.)) | journal=Journal of Rheology | title=A micro-mechanical study of coarsening and rheology of colloidal gels: Cage building, cage hopping, and Smoluchowski's ratchet | volume=58 | issue=5 | pages=1121–1157 | date= September 2014  | doi=10.1122/1.4892115| bibcode=2014JRheo..58.1121Z }}
</ref> The gel is initially formed by the assembly of particles into a space-spanning network, leading to a phase arrest. In the aging phase, the particles slowly rearrange to form thicker strands, increasing the elasticity of the material. Gels can also be collapsed and separated by external fields such as gravity.<ref>{{cite journal | vauthors=((Manley, S.)), ((Skotheim, J. M.)), ((Mahadevan, L.)), ((Weitz, D. A.)) | journal=Physical Review Letters | title=Gravitational Collapse of Colloidal Gels | volume=94 | issue=21 | pages=218302 | date=3 June 2005 | doi=10.1103/PhysRevLett.94.218302| pmid=16090356 | bibcode=2005PhRvL..94u8302M | s2cid=903595 | url=http://nrs.harvard.edu/urn-3:HUL.InstRepos:41417294 | url-access=subscription }}</ref> Colloidal gels show linear response rheology at low amplitudes.<ref>{{cite journal | vauthors=((Johnson, L. C.)), ((Zia, R. N.)), ((Moghimi, E.)), ((Petekidis, G.)) | journal=Journal of Rheology | title=Influence of structure on the linear response rheology of colloidal gels | volume=63 | issue=4 | pages=583–608 | date= July 2019 | doi=10.1122/1.5082796| bibcode=2019JRheo..63..583J | s2cid=189985243 | doi-access= }}</ref> These materials have been explored as candidates for a drug release matrix.<ref>{{cite journal | vauthors=((Meidia, H.)), ((Irfachsyad, D.)), ((Gunawan, D.)) | journal=IOP Conference Series: Materials Science and Engineering | title=Brownian Dynamics Simulation of Colloidal Gels as Matrix for Controlled Release Application | volume=553 | pages=012011 | date=12 November 2019 | issue=1 | doi=10.1088/1757-899X/553/1/012011| bibcode=2019MS&E..553a2011M | s2cid=210251780 | doi-access=free }}</ref>

===Hydrogels===
{{Main|Hydrogel}}
{{see also|Superabsorbent polymer|Self-healing hydrogels|Hydrogel agriculture}}
[[File:Superabsorber Hydrogel KSG 2917 pK.jpg|thumb|Hydrogel of a superabsorbent polymer]]

A [[hydrogel]] is a network of polymer chains that are hydrophilic, sometimes found as a [[colloid]]al gel in which water is the dispersion medium. A three-dimensional solid results from the hydrophilic polymer chains being held together by cross-links.{{clarify|reason=What is the nature of the cross-links? Covalent? Hydrogen bonds?|date=March 2019}} Because of the inherent cross-links, the structural integrity of the hydrogel network does not dissolve from the high concentration of water.<ref>{{Cite journal| vauthors = Warren DS, Sutherland SP, Kao JY, Weal GR, Mackay SM |date=2017-04-20|title=The Preparation and Simple Analysis of a Clay Nanoparticle Composite Hydrogel|journal=Journal of Chemical Education|language=EN|volume=94|issue=11|pages=1772–1779|doi=10.1021/acs.jchemed.6b00389|issn=0021-9584|bibcode=2017JChEd..94.1772W}}</ref> Hydrogels are highly [[absorption (chemistry)|absorbent]] (they can contain over 90% water) natural or synthetic polymeric networks.
Hydrogels also possess a degree of flexibility very similar to natural tissue, due to their significant water content. As responsive "[[smart materials]]," hydrogels can encapsulate chemical systems which upon stimulation by external factors such as a change of pH may cause specific compounds such as glucose to be liberated to the environment, in most cases by a [[sol-gel|gel-sol transition]] to the liquid state.<ref>{{cite journal | vauthors = Bordbar-Khiabani A, Gasik M | title = Smart hydrogels for advanced drug delivery systems | journal = International Journal of Molecular Sciences | date = 2022 | volume = 23 | issue = 7 | pages = 3665 | doi = 10.3390/ijms23073665 | pmid = 35409025 | pmc = 8998863 | doi-access = free }}</ref> Chemomechanical polymers are mostly also hydrogels, which upon stimulation change their volume and can serve as [[actuators]] or [[sensors]]. The first appearance of the term 'hydrogel' in the literature was in 1894.<ref>{{cite journal | vauthors = Bemmelen JM |s2cid=197928622|doi=10.1007/BF01830147|title=Der Hydrogel und das kristallinische Hydrat des Kupferoxydes|journal=Zeitschrift für Chemie und Industrie der Kolloide |volume=1 |issue=7 |pages=213–214 |year=1907 }}</ref>

[[File:IUPAC definition for a polymer gel.png|thumb|right|550px|link=https://doi.org/10.1351/goldbook.PT07187|IUPAC definition for a polymer gel]]

===Organogels===
{{See also|Organogels}}

An '''organogel''' is a [[crystallinity|non-crystalline]], [[glass|non-glassy]] thermoreversible ([[thermoplastic]]) solid material composed of a [[liquid]] [[organic compound|organic]] phase entrapped in a three-dimensionally cross-linked network. The liquid can be, for example, an [[organic solvent]], [[mineral oil]], or [[vegetable oil]]. The [[solubility]] and [[wikt:Particle|particle]] dimensions of the structurant are important characteristics for the [[Elasticity (physics)|elastic]] properties and firmness of the organogel. Often, these systems are based on [[self-assembly]] of the structurant molecules.<ref>Terech P. (1997) "Low-molecular weight organogelators", pp. 208–268 in: Robb I.D. (ed.) ''Specialist surfactants''. Glasgow: Blackie Academic and Professional, {{ISBN|0751403407}}.</ref><ref>{{cite book | vauthors = Van Esch J, Schoonbeek F, De Loos M, Veen EM, Kellogg RM, Feringa BL | date =  1999 | chapter = Low molecular weight gelators for organic solvents | pages = 233–259 | veditors = Ungaro R, Dalcanale E | title = Supramolecular science: where it is and where it is going | publisher = Kluwer Academic Publishers | isbn = 079235656X}}</ref> (An example of formation of an undesired thermoreversible network is the occurrence of wax crystallization in [[petroleum]].<ref>{{cite journal | vauthors = Visintin RF, Lapasin R, Vignati E, D'Antona P, Lockhart TP | title = Rheological behavior and structural interpretation of waxy crude oil gels | journal = Langmuir | volume = 21 | issue = 14 | pages = 6240–9 | date = July 2005 | pmid = 15982026 | doi = 10.1021/la050705k }}</ref>)

Organogels have potential for use in a number of applications, such as in [[pharmaceutics|pharmaceuticals]],<ref>{{cite journal | vauthors = Kumar R, Katare OP | title = Lecithin organogels as a potential phospholipid-structured system for topical drug delivery: a review | journal = AAPS PharmSciTech | volume = 6 | issue = 2 | pages = E298-310 | date = October 2005 | pmid = 16353989 | pmc = 2750543 | doi = 10.1208/pt060240 }}</ref> cosmetics, art conservation,<ref>{{cite journal | vauthors = Carretti E, Dei L, Weiss RG |doi=10.1039/B501033K|title=Soft matter and art conservation. Rheoreversible gels and beyond|year=2005|journal=Soft Matter|volume=1|issue=1|pages=17 |bibcode = 2005SMat....1...17C }}</ref> and food.<ref>{{cite journal|vauthors=Pernetti M, van Malssen KF, Flöter E, Bot A |doi=10.1016/j.cocis.2007.07.002|title=Structuring of edible oils by alternatives to crystalline fat|year=2007|journal=Current Opinion in Colloid & Interface Science|volume=12|issue=4–5|pages=221–231}}</ref>

===Xerogels===

[[File:IUPAC definition for a xerogel.png|550px|thumb|right|alt=IUPAC definition for a xerogel|link=https://doi.org/10.1351/goldbook.X0670|https://doi.org/10.1351/goldbook.X06700.]]

A '''xerogel''' {{IPAc-en|ˈ|z|ɪər|oʊ-|ˌ|dʒ|ɛ|l}} is a solid formed from a gel by drying with unhindered shrinkage. Xerogels usually retain high porosity (15–50%) and enormous surface area (150–900 m<sup>2</sup>/g), along with very small [[Porosity|pore]] size (1–10&nbsp;nm). When [[solvent]] removal occurs under [[supercritical fluid|supercritical]] conditions, the network does not shrink and a highly porous, low-density material known as an ''[[aerogel]]'' is produced. Heat treatment of a xerogel at elevated temperature produces viscous [[sintering]] (shrinkage of the xerogel due to a small amount of viscous flow) which results in a denser and more robust solid, the density and porosity achieved depend on the sintering conditions.

=== Nanocomposite hydrogels ===
[[Nanocomposite hydrogels]]<ref name="ReferenceA">{{cite journal | vauthors = Gaharwar AK, Peppas NA, Khademhosseini A | title = Nanocomposite hydrogels for biomedical applications | journal = Biotechnology and Bioengineering | volume = 111 | issue = 3 | pages = 441–53 | date = March 2014 | pmid = 24264728 | pmc = 3924876 | doi = 10.1002/bit.25160 }}</ref><ref>{{cite journal|last1=Carrow|first1=James K.|last2=Gaharwar|first2=Akhilesh K. | name-list-style = vanc |title=Bioinspired Polymeric Nanocomposites for Regenerative Medicine|journal=Macromolecular Chemistry and Physics|volume=216|issue=3|pages=248–264|date=November 2014|doi=10.1002/macp.201400427}}</ref> or hybrid hydrogels, are highly hydrated polymeric networks, either physically or covalently crosslinked with each other and/or with nanoparticles or nanostructures.<ref>{{cite journal | vauthors = Kutvonen A, Rossi G, Puisto SR, Rostedt NK, Ala-Nissila T | s2cid = 26096794 | title = Influence of nanoparticle size, loading, and shape on the mechanical properties of polymer nanocomposites | journal = The Journal of Chemical Physics | volume = 137 | issue = 21 | pages = 214901 | date = December 2012 | pmid = 23231257 | doi = 10.1063/1.4767517 | arxiv = 1212.4335 | bibcode = 2012JChPh.137u4901K }}</ref> Nanocomposite hydrogels can mimic native tissue properties, structure and microenvironment due to their hydrated and interconnected porous structure. A wide range of nanoparticles, such as carbon-based, polymeric, ceramic, and metallic [[nanomaterials]] can be incorporated within the hydrogel structure to obtain nanocomposites with tailored functionality. Nanocomposite hydrogels can be engineered to possess superior physical, chemical, electrical, thermal, and biological properties.<ref name="ReferenceA"/><ref>{{cite journal | vauthors = Zaragoza J, Babhadiashar N, O'Brien V, Chang A, Blanco M, Zabalegui A, Lee H, Asuri P | display-authors = 6 | title = Experimental Investigation of Mechanical and Thermal Properties of Silica Nanoparticle-Reinforced Poly(acrylamide) Nanocomposite Hydrogels | journal = PLOS ONE | volume = 10 | issue = 8 | pages = e0136293 | date = 2015-08-24 | pmid = 26301505 | pmc = 4547727 | doi = 10.1371/journal.pone.0136293 | bibcode = 2015PLoSO..1036293Z | doi-access = free }}</ref>

==Properties==
Many gels display [[thixotropy]] – they become fluid when agitated, but resolidify when resting.
In general, gels are apparently solid, jelly-like materials. It is a type of [[non-Newtonian fluid]].
By replacing the liquid with gas it is possible to prepare [[aerogel]]s, materials with exceptional properties including very low density, [[specific surface area|high specific surface areas]], and excellent thermal insulation properties.

=== Thermodynamics of gel deformation ===
A gel is in essence the mixture of a polymer network and a [[solvent]] phase. Upon stretching, the network [[Cross-link|crosslinks]] are moved further apart from each other. Due to the polymer strands between crosslinks acting as [[Entropic force|entropic springs]], gels demonstrate elasticity like [[Rubber elasticity#Polymer chain theories|rubber]] (which is just a polymer network, without solvent). This is so because the [[Thermodynamic free energy|free energy]] penalty to stretch an [[Ideal chain|ideal polymer]] segment <math>N</math> monomers of size <math>b</math> between crosslinks to an [[End-to-end vector|end-to-end distance]] <math>R</math> is approximately given by<ref name=":0">{{Cite book |last1=Rubinstein |first1=Michael |last2=Colby |first2=Ralph H. |url=https://www.worldcat.org/oclc/50339757 |title=Polymer physics |date=2003 |publisher=Oxford University Press |isbn=0-19-852059-X |location=Oxford |oclc=50339757}}</ref>

: <math>F_\text{ela} \sim kT \frac{R^2}{Nb^2}.</math>

This is the origin of both gel and [[rubber elasticity]]. But one key difference is that gel contains an additional solvent phase and hence is capable of having significant volume changes under [[Deformation (physics)|deformation]] by taking in and out solvent. For example, a gel could swell to several times its initial volume after being immersed in a solvent after equilibrium is reached. This is the phenomenon of gel swelling. On the contrary, if we take the swollen gel out and allow the solvent to evaporate, the gel would shrink to roughly its original size. This gel volume change can alternatively be introduced by applying external forces. If a uniaxial compressive [[Stress (mechanics)|stress]] is applied to a gel, some solvent contained in the gel would be squeezed out and the gel shrinks in the applied-stress direction.

To study the gel mechanical state in equilibrium, a good starting point is to consider a cubic gel of volume <math>V_{0}</math> that is stretched by factors <math>\lambda_1</math>, <math>\lambda_2</math> and <math>\lambda_3</math> in the three orthogonal directions during swelling after being immersed in a solvent phase of initial volume <math>V_{s0}</math>. The final deformed volume of gel is then <math>\lambda_1\lambda_2\lambda_3V_{0}</math> and the total volume of the system is <math>V_{0}+V_{s0}</math>, that is assumed constant during the swelling process for simplicity of treatment. The swollen state of the gel is now completely characterized by stretch factors <math>\lambda_1</math>, <math>\lambda_2</math> and <math>\lambda_3</math> and hence it is of interest to derive the [[Deformation (physics)|deformation free energy]] as a function of them, denoted as <math>f_\text{gel}(\lambda_1,\lambda_2,\lambda_3)</math>. For analogy to the historical treatment of [[rubber elasticity]] and mixing free energy, <math>f_\text{gel}(\lambda_1,\lambda_2,\lambda_3)</math> is most often defined as the free energy difference after and before the swelling normalized by the initial gel volume <math>V_{0}</math>, that is, a free energy difference density. The form of <math>f_\text{gel}(\lambda_1,\lambda_2,\lambda_3)</math> naturally assumes two contributions of radically different physical origins, one associated with the [[Elastic Deformation|elastic deformation]] of the polymer network, and the other with the [[Entropy of mixing|mixing]] of the network with the solvent. Hence, we write<ref name=":1">{{Cite book |last=Doi |first=M. |url=https://www.worldcat.org/oclc/851159840 |title=Soft matter physics. |date=2013 |publisher=Oxford University Press USA |isbn=978-0-19-150350-4 |location=Oxford |oclc=851159840}}</ref>

: <math>f_\text{gel}(\lambda_1, \lambda_2, \lambda_3) = f_\text{net}(\lambda_1, \lambda_2, \lambda_3) + f_\text{mix}(\lambda_1, \lambda_2, \lambda_3).</math>

We now consider the two contributions separately. The polymer elastic deformation term is independent of the solvent phase and has the same expression as a rubber, as derived in the Kuhn's theory of [[rubber elasticity]]:

: <math>f_\text{net}(\lambda_1,\lambda_2,\lambda_3) = \frac{G_0}{2} (\lambda_1^2 + \lambda_2^2 + \lambda_3^2 - 3),</math>

where <math>G_0</math> denotes the [[shear modulus]] of the initial state. On the other hand, the mixing term <math>f_\text{mix}(\lambda_1,\lambda_2,\lambda_3)</math> is usually treated by the [[Flory–Huggins solution theory|Flory-Huggins free energy]] of [[Polymer solution|concentrated polymer solutions]] <math>f(\phi)</math>, where <math>\phi</math> is polymer volume fraction. Suppose the initial gel has a polymer volume fraction of <math>\phi_0</math>, the polymer volume fraction after swelling would be <math>\phi=\phi_0/\lambda_1\lambda_2\lambda_3</math> since the number of monomers remains the same while the gel volume has increased by a factor of <math>\lambda_1\lambda_2\lambda_3</math>. As the polymer volume fraction decreases from <math>\phi_0</math> to <math>\phi</math>,  a polymer solution of concentration <math>\phi_0</math> and volume <math>V_{0}</math> is mixed with a pure solvent of volume <math>(\lambda_1\lambda_2\lambda_3-1)V_{0}</math> to become a solution with polymer concentration <math>\phi</math> and volume <math>\lambda_1\lambda_2\lambda_3V_{0}</math>. The free energy density change in this mixing step is given as

: <math>V_{g0} f_\text{mix}(\lambda_1 \lambda_2 \lambda_3) = \lambda_1 \lambda_2 \lambda_3 f(\phi) - [V_0 f(\phi_0) + (\lambda_1 \lambda_2\lambda_3 - 1) f(0)],</math>

where on the right-hand side, the first term is the [[Flory–Huggins solution theory|Flory–Huggins]] energy density of the final swollen gel, the second is associated with the initial gel and the third is of the pure solvent prior to mixing. Substitution of <math>\phi = \phi_0/\lambda_1\lambda_2\lambda_3</math> leads to

: <math>f_\text{mix}(\lambda_1, \lambda_2, \lambda_3) = \frac{\phi_0}{\phi} [f(\phi) - f(0)] - [f(\phi_0) - f(0)].</math>

Note that the second term is independent of the stretching factors <math>\lambda_1</math>, <math>\lambda_2</math> and <math>\lambda_3</math> and hence can be dropped in subsequent analysis. Now we make use of the [[Flory–Huggins solution theory|Flory-Huggins]] free energy for a polymer-solvent solution that reads<ref>{{Cite book |last=Doi |first=M. |url=https://www.worldcat.org/oclc/59185784 |title=The theory of polymer dynamics |date=1986 |others=S. F. Edwards |isbn=0-19-851976-1 |publisher=Clarendon Press |location=Oxford |oclc=59185784}}</ref>

: <math>f(\phi) = \frac{kT}{v_c} [\frac{\phi}{N} \ln\phi + (1 - \phi) \ln(1 - \phi) + \chi \phi (1 - \phi)],</math>

where <math>v_c</math> is monomer volume, <math>N</math> is polymer strand length and <math>\chi</math> is the [[Flory–Huggins solution theory|Flory-Huggins]] energy parameter. Because in a network, the polymer length is effectively infinite, we can take the limit <math>N\to\infty</math> and <math>f(\phi)</math> reduces to

: <math>f(\phi) = \frac{kT}{v_c} [(1 - \phi) \ln(1 - \phi) + \chi \phi(1 - \phi)].</math>

Substitution of this expression into <math>f_\text{mix}(\lambda_1,\lambda_2,\lambda_3)</math> and addition of the network contribution leads to<ref name=":1" />

: <math>f_\text{gel}(\lambda_1, \lambda_2, \lambda_3) = \frac{G_0}{2} (\lambda_1^2 + \lambda_2^2 + \lambda_3^2) + \frac{\phi_0}{\phi} f(\phi).</math>

This provides the starting point to examining the swelling equilibrium of a gel network immersed in solvent. It can be shown that gel swelling is the competition between two forces, one is the [[osmotic pressure]] of the polymer solution that favors the take in of solvent and expansion, the other is the restoring force of the polymer network [[Elasticity (physics)|elasticity]] that favors shrinkage. At equilibrium, the two effects exactly cancel each other in principle and the associated <math>\lambda_1</math>, <math>\lambda_2</math> and <math>\lambda_3</math> define the equilibrium gel volume. In solving the force balance equation, graphical solutions are often preferred.

In an alternative, scaling approach, suppose an [[Isotropy|isotropic]] gel is stretch by a factor of <math>\lambda</math> in all three directions. Under the [[Affine transformation|affine network]] approximation, the mean-square [[End-to-end vector|end-to-end distance]] in the gel increases from initial <math>R_0^2</math> to <math>(\lambda R_0)^2</math> and the elastic energy of one stand can be written as

: <math>F_\text{ela} \sim kT \frac{(\lambda R_0)^2}{R_\text{ref}^2},</math>

where <math>R_\text{ref}</math> is the mean-square fluctuation in end-to-end distance of one strand. The modulus of the gel is then this single-strand elastic energy multiplied by strand number density <math>\nu=\phi/Nb^3</math> to give<ref name=":0" />

: <math>G(\phi) \sim \frac{kT}{b^3} \frac{\phi}{N} \frac{(\lambda R_0)^2}{R_\text{ref}^2}.</math>

This modulus can then be equated to [[osmotic pressure]] (through differentiation of the free energy) to give the same equation as we found above.

=== Modified Donnan equilibrium of polyelectrolyte gels ===
Consider a [[hydrogel]] made of [[polyelectrolyte]]s decorated with [[weak acid]] groups that can ionize according to the reaction

: <math>\text{HA} \rightleftharpoons \text{A}^- + \text{H}^+</math>

is immersed in a salt solution of physiological concentration. The degree of [[ionization]] of the [[polyelectrolyte]]s is then controlled by the <math>\text{pH}</math> and due to the charged nature of <math>\text{H}^+</math> and <math>\text{A}^-</math>, [[electrostatic interactions]] with other ions in the systems. This is effectively a reacting system governed by [[Acid dissociation constant|acid-base equilibrium]] modulated by electrostatic effects, and is relevant in [[drug delivery]], sea water [[desalination]] and [[Dialysis (chemistry)|dialysis]] technologies. Due to the elastic nature of the gel, the dispersion of <math>\text{A}^-</math> in the system is constrained and hence, there will be a partitioning of salts ions and <math>\text{H}^+</math> inside and outside the gel, which is intimately coupled to the [[polyelectrolyte]] degree of ionization. This ion partitioning inside and outside the gel is analogous to the partitioning of ions across a semipemerable membrane in classical [[Gibbs–Donnan effect|Donnan]] theory, but a membrane is not needed here because the gel volume constraint imposed by network elasticity effectively acts its role, in preventing the macroions to pass through the fictitious membrane while allowing ions to pass.<ref name=":2">{{Cite journal |last1=Landsgesell |first1=Jonas |last2=Hebbeker |first2=Pascal |last3=Rud |first3=Oleg |last4=Lunkad |first4=Raju |last5=Košovan |first5=Peter |last6=Holm |first6=Christian |date=2020-04-28 |title=Grand-Reaction Method for Simulations of Ionization Equilibria Coupled to Ion Partitioning |url=https://pubs.acs.org/doi/10.1021/acs.macromol.0c00260 |journal=Macromolecules |language=en |volume=53 |issue=8 |pages=3007–3020 |doi=10.1021/acs.macromol.0c00260 |bibcode=2020MaMol..53.3007L |issn=0024-9297}}</ref>

The coupling between the ion partitioning and polyelectrolyte ionization degree is only partially by the classical [[Gibbs–Donnan effect|Donnan]] theory. As a starting point we can neglect the electrostatic interactions among ions. Then at equilibrium, some of the weak acid sites in the gel would dissociate to form <math>\text{A}^-</math>that electrostatically attracts positive charged <math>\text{H}^+</math> and salt cations leading to a relatively high concentration of <math>\text{H}^+</math> and salt cations inside the gel. But because the concentration of <math>\text{H}^+</math> is locally higher, it suppresses the further ionization of the acid sites. This phenomenon is the prediction of the classical Donnan theory.<ref>{{Cite book |url=https://www.worldcat.org/oclc/48383405 |title=Electrostatic effects in soft matter and biophysics |date=2001 |publisher=Kluwer Academic Publishers |others=Christian, Ph. D. Holm, Patrick Kékicheff, Rudolf Podgornik, North Atlantic Treaty Organization. Scientific Affairs Division, NATO Advanced Research Workshop on Electrostatic Effects in Soft Matter and Biophysics |isbn=1-4020-0196-7 |location=Dordrecht [Netherlands] |oclc=48383405}}</ref> However, with electrostatic interactions, there are further complications to the picture. Consider the case of two adjacent, initially uncharged acid sites <math>\text{HA}</math> are both dissociated to form <math>\text{A}^-</math>. Since the two sites are both negatively charged, there will be a charge-charge repulsion along the backbone of the polymer than tends to stretch the chain. This energy cost is high both elastically and electrostatically and hence suppress ionization. Even though this ionization suppression is qualitatively similar to that of Donnan prediction, it is absent without electrostatic consideration and present irrespective of ion partitioning. The combination of both effects as well as gel elasticity determines the volume of the gel at equilibrium.<ref name=":2" /> Due to the complexity of the coupled acid-base equilibrium, electrostatics and network elasticity, only recently has such system been correctly recreated in [[Computer simulations of fluids|computer simulations]].<ref name=":2" /><ref>{{Cite journal |last1=Blanco |first1=Pablo M. |last2=Madurga |first2=Sergio |last3=Mas |first3=Francesc |last4=Garcés |first4=Josep L. |date=2019-11-12 |title=Effect of Charge Regulation and Conformational Equilibria in the Stretching Properties of Weak Polyelectrolytes |url=https://pubs.acs.org/doi/10.1021/acs.macromol.9b01160 |journal=Macromolecules |language=en |volume=52 |issue=21 |pages=8017–8031 |doi=10.1021/acs.macromol.9b01160 |bibcode=2019MaMol..52.8017B |hdl=2445/156380 |s2cid=208747045 |issn=0024-9297|hdl-access=free }}</ref>

== Animal-produced gels ==
Some species secrete gels that are effective in parasite control. For example, the [[long-finned pilot whale]] secretes an enzymatic gel that rests on the outer surface of this animal and helps prevent other organisms from establishing colonies on the surface of these whales' bodies.<ref>{{cite book | vauthors = Dee EM, McGinley M, Hogan CM | date = 2010 | chapter-url = http://www.eoearth.org/article/Long-finned_pilot_whale?topic=49540 | chapter = Long-finned pilot whale | veditors = Saundry P, Cleveland C | editor-link2 = Cutler J. Cleveland | title = [[Encyclopedia of Earth]] | publisher = [[National Council for Science and the Environment]] | location = Washington DC }}</ref>

[[Hydrogels]] existing naturally in the body include [[mucus]], the [[vitreous humor]] of the eye, [[cartilage]], [[tendons]] and [[blood clots]]. Their viscoelastic nature results in the soft tissue component of the body, disparate from the mineral-based hard tissue of the skeletal system. Researchers are actively developing synthetically derived tissue replacement technologies derived from hydrogels, for both temporary [[Implant (medicine)|implants]] (degradable) and permanent implants (non-degradable). A review article on the subject discusses the use of hydrogels for [[nucleus pulposus]] replacement, cartilage replacement, and [[synthetic tissue]] models.<ref>{{cite web |url=https://www.orthoworld.com/site/index.php/publications/view_article/221558 |archive-url=https://archive.today/20121217235511/https://www.orthoworld.com/site/index.php/publications/view_article/221558 |url-status=dead |archive-date=December 17, 2012 |title=Injectable Hydrogel-based Medical Devices: "There's always room for Jell-O"1 |publisher=Orthoworld.com |date=September 15, 2010 |access-date=2013-05-19 }}</ref>

==Applications==
Many substances can form gels when a suitable [[Thickening agent|thickener or gelling agent]] is added to their formula. This approach is common in the manufacture of a wide range of products, from foods to paints and adhesives.

In fiber optic communications, a soft gel resembling [[hair gel]] in viscosity is used to fill the plastic tubes containing the fibers. The main purpose of the gel is to prevent water intrusion if the buffer tube is breached, but the gel also buffers the fibers against mechanical damage when the tube is bent around corners during installation, or flexed. Additionally, the gel acts as a processing aid when the cable is being constructed, keeping the fibers central whilst the tube material is extruded around it.

== See also ==
* [[Aerogel]]
* [[2-Acrylamido-2-methylpropane sulfonic acid]]
* [[Agarose gel electrophoresis]]
* [[Food rheology]]
* [[Gel electrophoresis]]
* [[Gel filtration chromatography]]
* [[Gel pack]]
* [[Gel permeation chromatography]]
* [[Hydrocolloid]]
* [[Ouchterlony double immunodiffusion]]
* [[Paste (rheology)]]
* [[Polyacrylamide gel electrophoresis]]
* [[Radial immunodiffusion]]
* [[Silicone gel]]
* [[Two-dimensional gel electrophoresis]]
* [[Void (composites)]]
* [[Soft matter]]
* [[Equilibrium gel]]

== References ==
{{Reflist|30em}}

== External links ==
{{commons category|Gels}}
{{wiktionary|gel}}
* {{GoldBookRef |title=xerogel |file=X06700 }}

{{Dosage forms|state=expanded}}

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