Editing Adhesion (section)

===Dispersive===
{{Main|Dispersive adhesion}}

In dispersive adhesion, also known as [[physisorption]], two materials are held together by [[van der Waals force]]s: the attraction between two molecules, each of which has a region of slight positive and negative charge. In the simple case, such molecules are therefore [[Chemical polarity|polar]] with respect to average [[charge density]], although in larger or more complex molecules, there may be multiple "poles" or regions of greater positive or negative charge. These positive and negative poles may be a permanent property of a molecule ([[Keesom force]]s) or a transient effect which can occur in any molecule, as the random movement of electrons within the molecules may result in a temporary concentration of electrons in one region ([[London forces]]).

[[File:Drops I.jpg|thumb|Cohesion causes water to form [[Drop (liquid)|drops]], surface tension causes them to be nearly spherical, and adhesion keeps the drops in place.]]
[[File:Hibiscus pink.jpg|thumb|Water droplets are flatter on a [[Hibiscus]] flower which shows better adhesion.]]

In [[surface science]], the term ''adhesion'' almost always refers to dispersive adhesion. In a typical solid-liquid-gas system (such as a drop of liquid on a solid surrounded by air) the [[contact angle]] is used to evaluate adhesiveness indirectly, while a [[Centrifugal Adhesion Balance]]<ref name="Tadmor2009">{{cite journal |last1=Tadmor |first1=Rafael |last2=Bahadur |first2=Prashant |last3=Leh |first3=Aisha |last4=N'guessan |first4=Hartmann |last5=Jaini |first5=Rajiv |last6=Dang |first6=Lan |title=Measurement of Lateral Adhesion Forces at the Interface between a Liquid Drop and a Substrate |journal=Physical Review Letters |date=21 December 2009 |volume=103 |issue=26 |pages=266101|doi=10.1103/PhysRevLett.103.266101 |pmid=20366322 |bibcode=2009PhRvL.103z6101T }}</ref><ref name="Tadmor2017">{{cite journal |last1=Tadmor |first1=Rafael |last2=Das |first2=Ratul |last3=Gulec |first3=Semih |last4=Liu |first4=Jie |last5=E. N’guessan |first5=Hartmann |last6=Shah |first6=Meet |last7=S. Wasnik |first7=Priyanka |last8=Yadav |first8=Sakshi B. |title=Solid–Liquid Work of Adhesion |journal=Langmuir |date=18 April 2017 |volume=33 |issue=15 |pages=3594–3600 |doi=10.1021/acs.langmuir.6b04437 |pmid=28121158 }}</ref><ref name="Sadullah2024">{{cite journal |last1=Sadullah |first1=Muhammad Subkhi |last2=Xu |first2=Yinfeng |last3=Arunachalam |first3=Sankara |last4=Mishra |first4=Himanshu |title=Predicting droplet detachment force: Young-Dupré Model Fails, Young-Laplace Model Prevails |journal=Communications Physics |date=11 March 2024 |volume=7 |issue=1 |page=89 |doi=10.1038/s42005-024-01582-0 |bibcode=2024CmPhy...7...89S |doi-access=free }}</ref><ref name="de la Madrid2019">{{cite journal |last1=de la Madrid |first1=Rafael |last2=Garza |first2=Fabian |last3=Kirk |first3=Justin |last4=Luong |first4=Huy |last5=Snowden |first5=Levi |last6=Taylor |first6=Jonathan |last7=Vizena |first7=Benjamin |title=Comparison of the Lateral Retention Forces on Sessile, Pendant, and Inverted Sessile Drops |journal=Langmuir |date=19 February 2019 |volume=35 |issue=7 |pages=2871–2877 |doi=10.1021/acs.langmuir.8b03780 |pmid=30724570 |arxiv=1902.06721 }}</ref><ref name="Vinod2022">{{cite journal |last1=Vinod |first1=Appu |last2=Reddy Bhimavarapu |first2=Yagna Valkya |last3=Hananovitz |first3=Mor |last4=Stern |first4=Yotam |last5=Gulec |first5=Semih |last6=Jena |first6=Akash Kumar |last7=Yadav |first7=Sakshi |last8=Gutmark |first8=E. J. |last9=Patra |first9=Prabir K. |last10=Tadmor |first10=Rafael |title=Mucus-Inspired Tribology, a Sticky Yet Flowing Hydrogel |journal=ACS Applied Polymer Materials |date=11 November 2022 |volume=4 |issue=11 |pages=8527–8535 |doi=10.1021/acsapm.2c01434 |osti=1922923 }}</ref> allows for direct quantitative adhesion measurements. Generally, cases where the contact angle is low are considered of higher adhesion per unit area. This approach assumes that the lower contact angle corresponds to a higher surface energy.<ref>{{Cite web|url=https://blog.biolinscientific.com/what-is-required-for-good-adhesion|title=What is required for good adhesion?|last=Laurén|first=Susanna|website=blog.biolinscientific.com|language=en-us|access-date=2019-12-31}}</ref> Theoretically, the more exact relation between contact angle and work of adhesion is more involved and is given by the [[Young-Dupre equation]]. The contact angle of the three-phase system is a function not only of dispersive adhesion (interaction between the molecules in the liquid and the molecules in the solid) but also cohesion (interaction between the liquid molecules themselves). Strong adhesion and weak cohesion results in a high degree of [[wetting]], a [[Lyophilicity|lyophilic]] condition with low measured contact angles. Conversely, weak adhesion and strong cohesion results in [[Lyophobicity|lyophobic]] conditions with high measured contact angles and poor wetting.

[[London dispersion]] forces are particularly useful for the function of [[adhesive device]]s, because they do not require either surface to have any permanent polarity. They were described in the 1930s by [[Fritz London]], and have been observed by many researchers. [[London dispersion force|Dispersive force]]s are a consequence of [[statistical quantum mechanics]]. London theorized that attractive forces between molecules that cannot be explained by ionic or covalent interaction can be caused by [[polar moment]]s within molecules. [[Multipole]]s could account for attraction between molecules having permanent multipole moments that participate in [[electrostatic interaction]]. However, experimental data showed that many of the compounds observed to experience van der Waals forces had no multipoles at all. London suggested that momentary dipoles are induced purely by virtue of molecules being in proximity to one another. By solving the quantum mechanical system of two electrons as [[harmonic oscillator]]s at some finite distance from one another, being displaced about their respective rest positions and interacting with each other's fields, London showed that the energy of this system is given by:

:<math>E = 3 h \nu - \frac{3}{4} \frac{h \nu \alpha^2}{R^6}</math>

While the first term is simply the [[zero-point energy]], the negative second term describes an attractive force between neighboring oscillators. The same argument can also be extended to a large number of coupled oscillators, and thus skirts issues that would negate the large scale attractive effects of permanent dipoles cancelling through symmetry, in particular.

The additive nature of the dispersion effect has another useful consequence. Consider a single such dispersive [[dipole]], referred to as the origin dipole. Since any origin dipole is inherently oriented so as to be attracted to the adjacent dipoles it induces, while the other, more distant dipoles are not correlated with the original dipole by any phase relation (thus on average contributing nothing), there is a net attractive force in a bulk of such particles. When considering identical particles, this is called cohesive force.<ref name=London>F. London, "The General Theory of Molecular Forces" (1936).</ref>

When discussing adhesion, this theory needs to be converted into terms relating to surfaces. If there is a net attractive energy of cohesion in a bulk of similar molecules, then cleaving this bulk to produce two surfaces will yield surfaces with a dispersive surface energy, since the form of the energy remain the same. This theory provides a basis for the existence of van der Waals forces at the surface, which exist between any molecules having [[electrons]]. These forces are easily observed through the spontaneous jumping of smooth surfaces into [[Contact mechanics|contact]]. Smooth surfaces of [[mica]], gold, various polymers and solid [[gelatin]] solutions do not stay apart when their separating becomes small enough – on the order of 1–10&nbsp;nm. The equation describing these attractions was predicted in the 1930s by De Boer and Hamaker:<ref name=Kendall/>

:<math>\frac{P}{area} = -\frac{A}{24 \pi z^3}</math>

where P is the force (negative for attraction), z is the separation distance, and A is a material-specific constant called the [[Hamaker constant]].

[[File:Roofcollapse.jpg|thumb|left|The two stages of PDMS microstructure collapse due to van der Waals attractions. The PDMS stamp is indicated by the hatched region, and the substrate is indicated by the shaded region. A) The PDMS stamp is placed on a substrate with the "roof" elevated. B) Van der Waals attractions make roof collapse energetically favorable for PDMS stamp.]]

The effect is also apparent in experiments where a [[polydimethylsiloxane]] (PDMS) stamp is made with small periodic post structures. The surface with the posts is placed face down on a smooth surface, such that the surface area in between each post is elevated above the smooth surface, like a roof supported by columns. Because of these attractive dispersive forces between the PDMS and the smooth substrate, the elevated surface – or "roof" – collapses down onto the substrate without any external force aside from the van der Waals attraction.<ref name=Huang>{{cite journal|url=http://rogers.matse.illinois.edu/files/2005/sagginglangmuir.pdf|author=Y. Y. Huang|title=Stamp Collapse in Soft Lithography|doi=10.1021/la0502185|year=2005|last2=Zhou|first2=Weixing|last3=Hsia|first3=K. J.|last4=Menard|first4=Etienne|last5=Park|first5=Jang-Ung|last6=Rogers|first6=John A.|last7=Alleyne|first7=Andrew G.|author-link7=Andrew G. Alleyne |journal=Langmuir|volume=21|issue=17|pages=8058–68|pmid=16089420}}</ref> Simple smooth [[polymer]] surfaces – without any [[microstructure]]s – are commonly used for these dispersive adhesive properties. [[Decal]]s and stickers that adhere to glass without using any chemical adhesives are fairly common as toys and decorations and useful as removable labels because they do not rapidly lose their adhesive properties, as do [[sticky tape]]s that use adhesive chemical compounds.

These forces also act over very small distances – 99% of the work necessary to break van der Waals bonds is done once surfaces are pulled more than a nanometer apart.<ref name=Kendall/> As a result of this limited motion in both the van der Waals and ionic/covalent bonding situations, practical effectiveness of adhesion due to either or both of these interactions leaves much to be desired. Once a crack is initiated, it propagates easily along the interface because of the [[brittle]] nature of the interfacial bonds.<ref name=Newby>{{cite journal|url=http://www.lehigh.edu/~mkc4/our%20papers/Bimin_slippage_science.pdf|author= Bi-min Zhang Newby, Manoj K. Chaudhury and Hugh R. Brown|title=Macroscopic Evidence of the Effect of Interfacial Slippage on Adhesion|doi=10.1126/science.269.5229.1407|year=1995|journal=Science|volume=269|issue=5229|pages=1407–9|pmid=17731150 |bibcode= 1995Sci...269.1407Z|s2cid= 29499327}}</ref>

As an additional consequence, increasing surface area often does little to enhance the strength of the adhesion in this situation. This follows from the aforementioned crack failure – the stress at the interface is not uniformly distributed, but rather concentrated at the area of failure.<ref name=Kendall/>