664:
678:
1405:(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. Simple smooth
650:
669:
667:
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1646:). For the most part, this is a phenomenon associated with diffusive bonding. The more time is given for a pair of surfaces exhibiting diffusive bonding to restructure, the more diffusion will occur, the stronger the adhesion will become. The aforementioned reaction of certain polymer-on-polymer surfaces to ultraviolet radiation and oxygen gas is an instance of hysteresis, but it will also happen over time without those factors.
1486:
668:
1118:
1294:, 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.
1393:
1580:
782:
1106:
1495:
Diffusive bonding in polymer-on-polymer surfaces is the result of sections of polymer chains from one surface interdigitating with those of an adjacent surface. The freedom of movement of the polymers has a strong effect on their ability to interdigitate, and hence, on diffusive bonding. For example, cross-linked polymers are less capable of diffusion and
1703:
this applies very strongly to wetting liquids, but also to gas molecules that could adsorb onto the surface in question, thereby occupying potential adhesion sites. This last point is actually fairly intuitive: Leaving an adhesive exposed to air too long gets it dirty, and its adhesive strength will decrease. This is observed in the experiment: when
1627:). By intermixing periodic breaks into smooth, adhesive surfaces, the interface acquires valuable crack-arresting properties. Because crack initiation requires much greater stress than does crack propagation, surfaces like these are much harder to separate, as a new crack has to be restarted every time the next individual microstructure is reached.
1287:, 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.
1196:. 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
1150:. 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
1702:
This argument can be extended to the idea that when a surface is in a medium with which binding is favorable, it will be less likely to adhere to another surface, since the medium is taking up the potential sites on the surface that would otherwise be available to adhere to another surface. Naturally
1396:
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
1059:
of two separate surfaces form ionic, covalent, or hydrogen bonds. The engineering principle behind chemical adhesion in this sense is fairly straightforward: if surface molecules can bond, then the surfaces will be bonded together by a network of these bonds. It bears mentioning that these attractive
1591:
is perhaps the most crucial of these effects, and is often seen on adhesive tapes. Stringing occurs when a separation of two surfaces is beginning and molecules at the interface bridge out across the gap, rather than cracking like the interface itself. The most significant consequence of this effect
1690:
is high, then each species finds it favorable to cohere while in contact with a foreign species, rather than dissociate and mix with the other. If this is true, then it follows that when the interfacial tension is high, the force of adhesion is weak, since each species does not find it favorable to
1538:
The strength of the adhesion between two materials depends on which of the above mechanisms occur between the two materials, and the surface area over which the two materials contact. Materials that wet against each other tend to have a larger contact area than those that do not. Wetting depends on
1494:
Diffusive forces are somewhat like mechanical tethering at the molecular level. Diffusive bonding occurs when species from one surface penetrate into an adjacent surface while still being bound to the phase of their surface of origin. One instructive example is that of polymer-on-polymer surfaces.
1657:
is true, one can also find evidence of it by performing “stop-start” measurements. In these experiments, two surfaces slide against one another continuously and occasionally stopped for some measured amount of time. Results from experiments on polymer-on-polymer surfaces show that if the stopping
1570:
In concert with the primary surface forces described above, there are several circumstantial effects in play. While the forces themselves each contribute to the magnitude of the adhesion between the surfaces, the following play a crucial role in the overall strength and reliability of an adhesive
1489:
The interface is indicated by the dotted line. A) Non-crosslinked polymers are somewhat free to diffuse across the interface. One loop and two distal tails are seen diffusing. B) Crosslinked polymers not free enough to diffuse. C) "Scissed" polymers very free, with many tails extending across the
1610:
The interplay of molecular scale mechanisms and hierarchical surface structures is known to result in high levels of static friction and bonding between pairs of surfaces. Technologically advanced adhesive devices sometimes make use of microstructures on surfaces, such as tightly packed periodic
1529:
Once across the interface, the tails and loops form whatever bonds are favorable. In the case of polymer-on-polymer surfaces, this means more van der Waals forces. While these may be brittle, they are quite strong when a large network of these bonds is formed. The outermost layer of each surface
1297:
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
1145:
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. Theoretically, the more exact relation between contact
1601:
adhesive agent, and a crack does propagate, it happens by a gradual process called “fingering”, rather than a rapid, brittle fracture. Stringing can apply to both the diffusive bonding regime and the chemical bonding regime. The strings of molecules bridging across the gap would either be the
1425:
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. As a result of this limited motion in both the van der Waals and ionic/covalent bonding situations, practical effectiveness of
1525:
irradiation in the presence of oxygen gas, which suggests that adhesive devices employing diffusive bonding actually benefit from prolonged exposure to heat/light and air. The longer such a device is exposed to these conditions, the more tails are scissed and branch out across the interface.
1433:
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.
665:
1592:
is the restraint of the crack. By providing the otherwise brittle interfacial bonds with some flexibility, the molecules that are stringing across the gap can stop the crack from propagating. Another way to understand this phenomenon is by comparing it to the
1596:
at the point of failure mentioned earlier. Since the stress is now spread out over some area, the stress at any given point has less of a chance of overwhelming the total adhesive force between the surfaces. If failure does occur at an interface containing a
2164:
Vinod, Appu; Reddy
Bhimavarapu, Yagna Valkya; Hananovitz, Mor; Stern, Yotam; Gulec, Semih; Jena, Akash Kumar; Yadav, Sakshi; Gutmark, E. J.; Patra, Prabir K.; Tadmor, Rafael (11 November 2022). "Mucus-Inspired Tribology, a Sticky Yet Flowing Hydrogel".
869:. Another way to view the surface energy is to relate it to the work required to cleave a bulk sample, creating two surfaces. If the new surfaces are identical, the surface energy Îł of each surface is equal to half the work of cleavage, W: Îł = (1/2)W
1658:
time is short enough, resumption of smooth sliding is easy. If, however, the stopping time exceeds some limit, there is an initial increase of resistance to motion, indicating that the stopping time was sufficient for the surfaces to restructure.
1638:, in this case, refers to the restructuring of the adhesive interface over some period of time, with the result being that the work needed to separate two surfaces is greater than the work that was gained by bringing them together (W > Îł
1310:, gold, various polymers and solid gelatin solutions do not stay apart when their separating becomes small enough – on the order of 1–10 nm. The equation describing these attractions was predicted in the 1930s by De Boer and Hamaker:
1561:
Another factor determining the strength of an adhesive contact is its shape. Adhesive contacts of complex shape begin to detach at the "edges" of the contact area. The process of destruction of adhesive contacts can be seen in the film.
1727:
Lateral adhesion is the adhesion associated with sliding one object on a substrate such as sliding a drop on a surface. When the two objects are solids, either with or without a liquid between them, the lateral adhesion is described as
1530:
plays a crucial role in the adhesive properties of such interfaces, as even a tiny amount of interdigitation – as little as one or two tails of 1.25 angstrom length – can increase the van der Waals bonds by an order of magnitude.
1064:. This means in general not only that surfaces with the potential for chemical bonding need to be brought very close together, but also that these bonds are fairly brittle, since the surfaces then need to be kept close together.
2115:
de la Madrid, Rafael; Garza, Fabian; Kirk, Justin; Luong, Huy; Snowden, Levi; Taylor, Jonathan; Vizena, Benjamin (19 February 2019). "Comparison of the
Lateral Retention Forces on Sessile, Pendant, and Inverted Sessile Drops".
978:
and the events that happen at a given surface, but as discussed below, the theory of these variables also yields some interesting effects that concern the practicality of adhesive surfaces in relation to their surroundings.
1278:
1583:
Fingering process. The hatched area is the receiving substrate, the dotted strip is the tape, and the shaded area in between is the adhesive chemical layer. The arrow indicates the direction of propagation for the
987:
There is no single theory covering adhesion, and particular mechanisms are specific to particular material scenarios. Five mechanisms of adhesion have been proposed to explain why one material sticks to another:
1417:
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
1986:
Tadmor, Rafael; Bahadur, Prashant; Leh, Aisha; N'guessan, Hartmann; Jaini, Rajiv; Dang, Lan (21 December 2009). "Measurement of
Lateral Adhesion Forces at the Interface between a Liquid Drop and a Substrate".
1094:, 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 (
1380:
1734:. However, the behavior of lateral adhesion between a drop and a surface is tribologically very different from friction between solids, and the naturally adhesive contact between a flat surface and a
927:. These two energy quantities refer to the energy that is needed to cleave one species into two pieces while it is contained in a medium of the other species. Likewise for a three species system: Îł
1200:
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:
87:
1098:) 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 (
1521:
tails. The heightened concentration of these chain ends gives rise to a heightened concentration of polymer tails extending across the interface. Scission is easily achieved by
1181:
2033:
Tadmor, Rafael; Das, Ratul; Gulec, Semih; Liu, Jie; E. N’guessan, Hartmann; Shah, Meet; S. Wasnik, Priyanka; Yadav, Sakshi B. (18 April 2017). "Solid–Liquid Work of
Adhesion".
1739:
1142:
1470:
in each other. This would be particularly effective with polymer chains where one end of the molecule diffuses into the other material. It is also the mechanism involved in
1695:(relative to the solid), and thus one can extrapolate that cohesion increases in non-wetting liquids and decreases in wetting liquids. One example that verifies this is
1426:
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
1602:
molecules that had earlier diffused across the interface or the viscoelastic adhesive, provided that there was a significant volume of it at the interface.
1086:: 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
766:
1298:
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
1169:
1008:. Other interlocking phenomena are observed on different length scales. Sewing is an example of two materials forming a large scale mechanical bond,
967:
1847:
Vert, Michel; Doi, Yoshiharu; Hellwich, Karl-Heinz; Hess, Michael; Hodge, Philip; Kubisa, Przemyslaw; Rinaudo, Marguerite; Schué, François (2012).
1005:
1699:
rubber, which has a work of self-adhesion of 43.6 mJ/m in air, 74 mJ/m in water (a nonwetting liquid) and 6 mJ/m in methanol (a wetting liquid).
1159:
1056:
1848:
1206:
1137:
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
636:
1588:
1184:. London theorized that attractive forces between molecules that cannot be explained by ionic or covalent interaction can be caused by
1742:(CAB), which uses a combination of centrifugal and gravitational forces to decouple the normal and lateral forces in the problem.
1316:
1518:
1385:
where P is the force (negative for attraction), z is the separation distance, and A is a material-specific constant called the
2395:
N. Maeda; Chen, N; Tirrell, M; Israelachvili, JN (2002). "Adhesion and
Friction Mechanisms of Polymer-on-Polymer Surfaces".
2513:
1482:
powders are pressed together and heated, atoms diffuse from one particle to the next. This joins the particles into one.
1024:
at the joint. The strongest joints are where atoms of the two materials share or swap electrons (known respectively as
629:
1510:), on the other hand are freer to wander into the adjacent phase by extending tails and loops across the interface.
1499:
because they are bonded together at many points of contact, and are not free to twist into the adjacent surface. Un
1666:
Some atmospheric effects on the functionality of adhesive devices can be characterized by following the theory of
1172:, because they do not require either surface to have any permanent polarity. They were described in the 1930s by
43:
2613:
1290:
The additive nature of the dispersion effect has another useful consequence. Consider a single such dispersive
602:
303:
140:
2608:
2526:
A. Majmuder; Ghatak, A.; Sharma, A. (2007). "Microfluidic
Adhesion Induced by Subsurface Microstructures".
769:. In addition to the cumulative magnitudes of these intermolecular forces, there are also certain emergent
622:
343:
229:
1807:
1738:
makes the lateral adhesion in this case, an individual field. Lateral adhesion can be measured using the
298:
207:
90:
2603:
2201:
1856:
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bond to the other. The interfacial tension of a liquid and a solid is directly related to the liquid's
2284:
1192:
could account for attraction between molecules having permanent multipole moments that participate in
757:
responsible for the function of various kinds of stickers and sticky tape fall into the categories of
677:
1193:
1158:
condition with low measured contact angles. Conversely, weak adhesion and strong cohesion results in
214:
20:
1881:
509:
504:
293:
286:
119:
2239:
2494:
1551:
1177:
572:
567:
236:
2071:
Sadullah, Muhammad Subkhi; Xu, Yinfeng; Arunachalam, Sankara; Mishra, Himanshu (11 March 2024).
746:
refers to the tendency of similar or identical particles and surfaces to cling to one another.)
1009:
124:
547:
165:
2073:"Predicting droplet detachment force: Young-Dupré Model Fails, Young-Laplace Model Prevails"
1113:, surface tension causes them to be nearly spherical, and adhesion keeps the drops in place.
2535:
2404:
2299:
2234:
Y. Y. Huang; Zhou, Weixing; Hsia, K. J.; Menard, Etienne; Park, Jang-Ung; Rogers, John A.;
2084:
1996:
1941:
1593:
1402:
1302:. These forces are easily observed through the spontaneous jumping of smooth surfaces into
1147:
877:
754:
743:
385:
202:
182:
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114:
1012:
forms one on a medium scale, and some textile adhesives (glue) form one at a small scale.
8:
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34:
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1965:
1873:
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739:
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241:
197:
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2551:
2469:
2448:"Strength of adhesive contacts: Influence of contact geometry and material gradients"
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2143:
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2012:
1957:
1797:
1777:
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1443:
1303:
1284:
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ionic and covalent forces are effective over only very small distances – less than a
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2008:
2004:
1969:
1949:
1865:
1849:"Terminology for biorelated polymers and applications (IUPAC Recommendations 2012)"
1812:
1767:
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1735:
1547:
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1138:
1110:
1099:
1079:
1029:
963:
is the energy of cleaving species 1 from species 2 in a medium of species 3.
912:
597:
430:
2547:
2416:
1517:
is the cutting up of polymer chains, resulting in a higher concentration of
2555:
2424:
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2319:
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2178:
2147:
2054:
2016:
1961:
1802:
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1543:
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1173:
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1095:
718:: In biology, adhesion reflects the behavior of cells shortly after contact
582:
577:
542:
274:
2359:
1649:
In addition to being able to observe hysteresis by determining if W > Îł
704:
Process of attachment of a substance to the surface of another substance.
1692:
1522:
1513:
Another circumstance under which diffusive bonding occurs is “scission”.
1500:
1419:
649:
592:
495:
2285:"Macroscopic Evidence of the Effect of Interfacial Slippage on Adhesion"
1273:{\displaystyle E=3h\nu -{\frac {3}{4}}{\frac {h\nu \alpha ^{2}}{R^{6}}}}
753:
that cause adhesion and cohesion can be divided into several types. The
1635:
1620:
1615:
technologies inspired by the adhesive abilities of the feet of various
1612:
785:
Diagram of various cases of cleavage, with each unique species labeled.
657:
514:
410:
2258:
2186:
710:: Adhesion requires energy that can come from chemical and/or physical
2163:
1616:
1471:
1466:. This may occur when the molecules of both materials are mobile and
1447:
1442:
Some conducting materials may pass electrons to form a difference in
1299:
1189:
1061:
712:
linkages, the latter being reversible when enough energy is applied.
486:
481:
315:
2130:
1752:
1730:
1503:
1122:
1045:
1037:
1033:
735:
726:: In surgery, adhesion is used when two tissues fuse unexpectedly.
689:
465:
350:
336:
1485:
2283:
Bi-min Zhang Newby, Manoj K. Chaudhury and Hugh R. Brown (1995).
1822:
1787:
1479:
1467:
1427:
1406:
1151:
866:
219:
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1146:
angle and work of adhesion is more involved and is given by the
1117:
1392:
1291:
1162:
conditions with high measured contact angles and poor wetting.
1041:
360:
1413:– are commonly used for these dispersive adhesive properties.
1985:
1624:
1475:
1414:
750:
697:
264:
1579:
2224:
F. London, "The
General Theory of Molecular Forces" (1936).
2070:
1704:
1558:
are difficult to bond without special surface preparation.
1375:{\displaystyle {\frac {P}{area}}=-{\frac {A}{24\pi z^{3}}}}
1307:
781:
2446:
Popov, Valentin L.; Pohrt, Roman; Li, Qiang (2017-09-01).
2114:
1105:
2233:
653:
400:
1932:
K. Kendall (1994). "Adhesion: Molecules and
Mechanics".
2525:
1446:
at the joint. This results in a structure similar to a
904:
are the surface energies of the two new surfaces, and Îł
1319:
1209:
1141:
is used to evaluate adhesiveness indirectly, while a
46:
1846:
1401:The effect is also apparent in experiments where a
1168:forces are particularly useful for the function of
673:
Adhesion of a frog on a wet vertical glass surface.
2110:
2108:
1715:, is smaller than the cleavage energy in vacuum, W
1374:
1272:
865:that is required to build an area of a particular
81:
2032:
2595:
2486:
1036:atom in one molecule is attracted to an atom of
2105:
1903:
1901:
2588:Adhesion and Adhesives: Science and Technology
2340:
2066:
2064:
1176:, and have been observed by many researchers.
1004:of the surfaces and hold surfaces together by
2583:, Royal Society of Chemistry Paperbacks, 1997
1661:
911:This methodology can also be used to discuss
630:
2490:Science friction: Adhesion of complex shapes
2445:
2028:
2026:
1981:
1979:
1898:
966:A basic understanding of the terminology of
2159:
2157:
2061:
1911:(Academic Press, New York, 1985). chap. 15.
82:{\displaystyle J=-D{\frac {d\varphi }{dx}}}
1931:
637:
623:
2463:
2368:
2358:
2129:
2096:
2023:
1976:
1927:
1925:
1923:
1921:
1919:
1917:
1707:is cleaved in air, its cleavage energy, W
1462:Some materials may merge at the joint by
1048:in another molecule, a phenomenon called
2519:
2390:
2388:
2278:
2276:
2154:
1578:
1484:
1391:
1116:
1104:
780:
688:
676:
662:
648:
2516:Tribology International 2016, Volume 93
2341:von Fraunhofer, Anthony (21 Feb 2012).
1397:energetically favorable for PDMS stamp.
2596:
2218:
1914:
1422:that use adhesive chemical compounds.
1078:In dispersive adhesion, also known as
974:is very helpful for understanding the
2514:Static Friction at Fractal Interfaces
2385:
2273:
2227:
2202:"What is required for good adhesion?"
1542:Low surface energy materials such as
1539:the surface energy of the materials.
1082:, two materials are held together by
2240:"Stamp Collapse in Soft Lithography"
1722:
1283:While the first term is simply the
1125:flower which shows better adhesion.
13:
2573:
2347:International Journal of Dentistry
2199:
1605:
1055:Chemical adhesion occurs when the
14:
2625:
1909:Intermolecular and Surface Forces
1430:nature of the interfacial bonds.
915:that happens in another medium: Îł
876:If the surfaces are unequal, the
861:is conventionally defined as the
776:
1565:
1437:
1121:Water droplets are flatter on a
1032:). A weaker bond is formed if a
2507:
2497:from the original on 2021-12-21
2487:Friction Physics (2017-12-06),
2480:
2439:
2334:
2193:
2009:10.1103/PhysRevLett.103.266101
1840:
1109:Cohesion causes water to form
734:is the tendency of dissimilar
1:
2312:10.1126/science.269.5229.1407
2167:ACS Applied Polymer Materials
1954:10.1126/science.263.5154.1720
1834:
1630:
1454:force between the materials.
1182:statistical quantum mechanics
1067:
991:
982:
2140:10.1021/acs.langmuir.8b03780
2047:10.1021/acs.langmuir.6b04437
1740:centrifugal adhesion balance
1574:
1457:
1143:Centrifugal Adhesion Balance
996:Adhesive materials fill the
7:
1808:Pressure-sensitive adhesive
1745:
1533:
1015:
908:is the interfacial energy.
10:
2630:
2098:10.1038/s42005-024-01582-0
1857:Pure and Applied Chemistry
1662:Wettability and absorption
1450:and creates an attractive
1071:
742:to cling to one another. (
685:is caused due to adhesion.
18:
2465:10.1007/s40544-017-0177-3
2206:blog.biolinscientific.com
1194:electrostatic interaction
1020:Two materials may form a
21:Adhesion (disambiguation)
2590:, Chapman and Hall, 1987
1870:10.1351/PAC-REC-10-12-04
1090:with respect to average
141:Clausius–Duhem (entropy)
91:Fick's laws of diffusion
2548:10.1126/science.1145839
2417:10.1126/science.1072378
2343:"Adhesion and Cohesion"
1989:Physical Review Letters
1552:polytetrafluoroethylene
1409:surfaces – without any
299:Navier–Stokes equations
237:Material failure theory
2179:10.1021/acsapm.2c01434
2077:Communications Physics
1585:
1491:
1398:
1376:
1274:
1126:
1114:
970:, surface energy, and
855:
728:
693:
686:
674:
660:
83:
2614:Intermolecular forces
1907:J. N. Israelachvili,
1719:, by a factor of 13.
1697:polydimethyl siloxane
1582:
1488:
1395:
1377:
1306:. Smooth surfaces of
1275:
1180:are a consequence of
1120:
1108:
784:
755:intermolecular forces
702:
692:
680:
672:
652:
294:Bernoulli's principle
287:Archimedes' principle
84:
1674:. It is known that Îł
1594:stress concentration
1403:polydimethylsiloxane
1317:
1207:
1198:harmonic oscillators
1148:Young-Dupre equation
1084:van der Waals forces
878:Young-Dupré equation
656:drops adhering to a
386:Cohesion (chemistry)
208:Infinitesimal strain
44:
19:For other uses, see
2609:Chemical properties
2540:2007Sci...318..258M
2409:2002Sci...297..379M
2360:10.1155/2012/951324
2304:1995Sci...269.1407Z
2089:2024CmPhy...7...89S
2001:2009PhRvL.103z6101T
1946:1994Sci...263.1720K
1672:interfacial tension
1074:Dispersive adhesion
763:dispersive adhesion
304:Poiseuille equation
35:Continuum mechanics
29:Part of a series on
2236:Alleyne, Andrew G.
1783:Fracture mechanics
1586:
1492:
1399:
1372:
1270:
1188:within molecules.
1127:
1115:
856:
771:mechanical effects
767:diffusive adhesion
694:
687:
675:
661:
510:Magnetorheological
505:Electrorheological
242:Fracture mechanics
79:
16:Molecular property
2604:Materials science
2259:10.1021/la0502185
2200:Laurén, Susanna.
2173:(11): 8527–8535.
2041:(15): 3594–3600.
1778:Contact mechanics
1763:Bacterial adhesin
1611:posts. These are
1444:electrical charge
1370:
1339:
1285:zero-point energy
1268:
1236:
1178:Dispersive forces
1166:London dispersion
759:chemical adhesion
670:
647:
646:
522:
521:
456:
455:
225:Contact mechanics
148:
147:
77:
2621:
2581:Adhesion Science
2568:
2567:
2534:(5848): 258–61.
2523:
2517:
2511:
2505:
2504:
2503:
2502:
2484:
2478:
2477:
2467:
2443:
2437:
2436:
2403:(5580): 379–82.
2392:
2383:
2382:
2372:
2362:
2338:
2332:
2331:
2298:(5229): 1407–9.
2289:
2280:
2271:
2270:
2244:
2231:
2225:
2222:
2216:
2215:
2213:
2212:
2197:
2191:
2190:
2161:
2152:
2151:
2133:
2124:(7): 2871–2877.
2112:
2103:
2102:
2100:
2068:
2059:
2058:
2030:
2021:
2020:
1983:
1974:
1973:
1940:(5154): 1720–5.
1929:
1912:
1905:
1896:
1895:
1893:
1892:
1886:
1880:. Archived from
1853:
1844:
1768:Capillary action
1758:Adhesive bonding
1723:Lateral adhesion
1556:polyoxymethylene
1387:Hamaker constant
1381:
1379:
1378:
1373:
1371:
1369:
1368:
1367:
1348:
1340:
1338:
1321:
1279:
1277:
1276:
1271:
1269:
1267:
1266:
1257:
1256:
1255:
1239:
1237:
1229:
1170:adhesive devices
1050:hydrogen bonding
1026:covalent bonding
720:to the surface.
671:
639:
632:
625:
471:
470:
436:Gay-Lussac's law
426:Combined gas law
376:Capillary action
261:
260:
104:
103:
88:
86:
85:
80:
78:
76:
68:
60:
26:
25:
2629:
2628:
2624:
2623:
2622:
2620:
2619:
2618:
2594:
2593:
2576:
2574:Further reading
2571:
2524:
2520:
2512:
2508:
2500:
2498:
2485:
2481:
2444:
2440:
2393:
2386:
2339:
2335:
2287:
2281:
2274:
2253:(17): 8058–68.
2242:
2232:
2228:
2223:
2219:
2210:
2208:
2198:
2194:
2162:
2155:
2113:
2106:
2069:
2062:
2031:
2024:
1984:
1977:
1930:
1915:
1906:
1899:
1890:
1888:
1884:
1851:
1845:
1841:
1837:
1832:
1828:Cohesion number
1818:Synthetic setae
1793:Insect adhesion
1748:
1725:
1718:
1714:
1710:
1689:
1685:
1681:
1677:
1664:
1656:
1652:
1645:
1641:
1633:
1623:(most notably,
1608:
1606:Microstructures
1577:
1568:
1536:
1497:interdigitation
1460:
1440:
1411:microstructures
1363:
1359:
1352:
1347:
1325:
1320:
1318:
1315:
1314:
1262:
1258:
1251:
1247:
1240:
1238:
1228:
1208:
1205:
1204:
1131:surface science
1076:
1070:
1018:
994:
985:
972:surface tension
968:cleavage energy
962:
958:
954:
950:
946:
942:
938:
934:
930:
926:
922:
918:
907:
903:
899:
895:
891:
887:
883:
872:
853:
849:
845:
841:
837:
830:
829:
825:
821:
814:
813:
809:
805:
801:
794:
793:
786:
779:
729:
719:
711:
701:
663:
643:
614:
613:
612:
532:
524:
523:
477:Viscoelasticity
468:
458:
457:
445:
395:
391:Surface tension
355:
258:
256:Fluid mechanics
248:
247:
246:
160:
158:Solid mechanics
150:
149:
101:
93:
69:
61:
59:
45:
42:
41:
24:
17:
12:
11:
5:
2627:
2617:
2616:
2611:
2606:
2592:
2591:
2586:A.J. Kinloch,
2584:
2575:
2572:
2570:
2569:
2518:
2506:
2479:
2458:(3): 308–325.
2438:
2384:
2333:
2272:
2226:
2217:
2192:
2153:
2104:
2060:
2022:
1995:(26): 266101.
1975:
1913:
1897:
1864:(2): 377–410.
1838:
1836:
1833:
1831:
1830:
1825:
1820:
1815:
1810:
1805:
1800:
1795:
1790:
1785:
1780:
1775:
1770:
1765:
1760:
1755:
1749:
1747:
1744:
1724:
1721:
1716:
1712:
1708:
1687:
1683:
1679:
1675:
1668:surface energy
1663:
1660:
1654:
1650:
1643:
1639:
1632:
1629:
1607:
1604:
1576:
1573:
1567:
1564:
1535:
1532:
1515:Chain scission
1508:thermoplastics
1459:
1456:
1439:
1436:
1383:
1382:
1366:
1362:
1358:
1355:
1351:
1346:
1343:
1337:
1334:
1331:
1328:
1324:
1281:
1280:
1265:
1261:
1254:
1250:
1246:
1243:
1235:
1232:
1227:
1224:
1221:
1218:
1215:
1212:
1092:charge density
1072:Main article:
1069:
1066:
1017:
1014:
993:
990:
984:
981:
976:physical state
960:
956:
952:
948:
944:
940:
936:
932:
928:
924:
920:
916:
905:
901:
897:
893:
889:
885:
881:
870:
859:Surface energy
851:
847:
843:
839:
835:
827:
823:
819:
811:
807:
803:
799:
791:
778:
777:Surface energy
775:
696:
695:
645:
644:
642:
641:
634:
627:
619:
616:
615:
611:
610:
605:
600:
595:
590:
585:
580:
575:
570:
565:
560:
555:
550:
545:
540:
534:
533:
530:
529:
526:
525:
520:
519:
518:
517:
512:
507:
499:
498:
492:
491:
490:
489:
484:
479:
469:
464:
463:
460:
459:
454:
453:
447:
446:
444:
443:
438:
433:
428:
423:
418:
413:
407:
404:
403:
397:
396:
394:
393:
388:
383:
381:Chromatography
378:
373:
367:
364:
363:
357:
356:
354:
353:
334:
333:
332:
313:
301:
296:
284:
271:
268:
267:
259:
254:
253:
250:
249:
245:
244:
239:
234:
233:
232:
222:
217:
212:
211:
210:
205:
195:
190:
185:
180:
179:
178:
168:
162:
161:
156:
155:
152:
151:
146:
145:
144:
143:
135:
134:
130:
129:
128:
127:
122:
117:
109:
108:
102:
99:
98:
95:
94:
89:
75:
72:
67:
64:
58:
55:
52:
49:
38:
37:
31:
30:
15:
9:
6:
4:
3:
2:
2626:
2615:
2612:
2610:
2607:
2605:
2602:
2601:
2599:
2589:
2585:
2582:
2578:
2577:
2565:
2561:
2557:
2553:
2549:
2545:
2541:
2537:
2533:
2529:
2522:
2515:
2510:
2496:
2492:
2491:
2483:
2475:
2471:
2466:
2461:
2457:
2453:
2449:
2442:
2434:
2430:
2426:
2422:
2418:
2414:
2410:
2406:
2402:
2398:
2391:
2389:
2380:
2376:
2371:
2366:
2361:
2356:
2352:
2348:
2344:
2337:
2329:
2325:
2321:
2317:
2313:
2309:
2305:
2301:
2297:
2293:
2286:
2279:
2277:
2268:
2264:
2260:
2256:
2252:
2248:
2241:
2237:
2230:
2221:
2207:
2203:
2196:
2188:
2184:
2180:
2176:
2172:
2168:
2160:
2158:
2149:
2145:
2141:
2137:
2132:
2127:
2123:
2119:
2111:
2109:
2099:
2094:
2090:
2086:
2082:
2078:
2074:
2067:
2065:
2056:
2052:
2048:
2044:
2040:
2036:
2029:
2027:
2018:
2014:
2010:
2006:
2002:
1998:
1994:
1990:
1982:
1980:
1971:
1967:
1963:
1959:
1955:
1951:
1947:
1943:
1939:
1935:
1928:
1926:
1924:
1922:
1920:
1918:
1910:
1904:
1902:
1887:on 2015-03-19
1883:
1879:
1875:
1871:
1867:
1863:
1859:
1858:
1850:
1843:
1839:
1829:
1826:
1824:
1821:
1819:
1816:
1814:
1813:Rail adhesion
1811:
1809:
1806:
1804:
1801:
1799:
1796:
1794:
1791:
1789:
1786:
1784:
1781:
1779:
1776:
1774:
1773:Cell adhesion
1771:
1769:
1766:
1764:
1761:
1759:
1756:
1754:
1751:
1750:
1743:
1741:
1737:
1733:
1732:
1720:
1717:mica/vac/mica
1713:mica/air/mica
1706:
1700:
1698:
1694:
1673:
1669:
1659:
1647:
1637:
1628:
1626:
1622:
1618:
1614:
1603:
1600:
1595:
1590:
1581:
1572:
1566:Other effects
1563:
1559:
1557:
1553:
1549:
1548:polypropylene
1545:
1540:
1531:
1527:
1524:
1520:
1516:
1511:
1509:
1505:
1502:
1498:
1487:
1483:
1481:
1477:
1473:
1469:
1465:
1455:
1453:
1452:electrostatic
1449:
1445:
1438:Electrostatic
1435:
1431:
1429:
1423:
1421:
1416:
1412:
1408:
1404:
1394:
1390:
1388:
1364:
1360:
1356:
1353:
1349:
1344:
1341:
1335:
1332:
1329:
1326:
1322:
1313:
1312:
1311:
1309:
1305:
1301:
1295:
1293:
1288:
1286:
1263:
1259:
1252:
1248:
1244:
1241:
1233:
1230:
1225:
1222:
1219:
1216:
1213:
1210:
1203:
1202:
1201:
1199:
1195:
1191:
1187:
1186:polar moments
1183:
1179:
1175:
1171:
1167:
1163:
1161:
1157:
1153:
1149:
1144:
1140:
1139:contact angle
1136:
1132:
1124:
1119:
1112:
1107:
1103:
1101:
1100:London forces
1097:
1096:Keesom forces
1093:
1089:
1085:
1081:
1080:physisorption
1075:
1065:
1063:
1058:
1057:surface atoms
1053:
1051:
1047:
1043:
1039:
1035:
1031:
1030:ionic bonding
1027:
1023:
1013:
1011:
1007:
1003:
999:
989:
980:
977:
973:
969:
964:
914:
909:
879:
874:
868:
864:
860:
833:
817:
797:
789:
783:
774:
772:
768:
764:
760:
756:
752:
747:
745:
741:
737:
733:
727:
725:
721:
717:
713:
709:
705:
699:
691:
684:
679:
659:
655:
651:
640:
635:
633:
628:
626:
621:
620:
618:
617:
609:
606:
604:
601:
599:
596:
594:
591:
589:
586:
584:
581:
579:
576:
574:
571:
569:
566:
564:
561:
559:
556:
554:
551:
549:
546:
544:
541:
539:
536:
535:
528:
527:
516:
513:
511:
508:
506:
503:
502:
501:
500:
497:
494:
493:
488:
485:
483:
480:
478:
475:
474:
473:
472:
467:
462:
461:
452:
449:
448:
442:
439:
437:
434:
432:
429:
427:
424:
422:
421:Charles's law
419:
417:
414:
412:
409:
408:
406:
405:
402:
399:
398:
392:
389:
387:
384:
382:
379:
377:
374:
372:
369:
368:
366:
365:
362:
359:
358:
352:
349:
345:
342:
338:
335:
330:
329:non-Newtonian
327:
323:
319:
318:
317:
314:
312:
309:
305:
302:
300:
297:
295:
292:
288:
285:
283:
280:
276:
273:
272:
270:
269:
266:
263:
262:
257:
252:
251:
243:
240:
238:
235:
231:
228:
227:
226:
223:
221:
218:
216:
215:Compatibility
213:
209:
206:
204:
203:Finite strain
201:
200:
199:
196:
194:
191:
189:
186:
184:
181:
177:
174:
173:
172:
169:
167:
164:
163:
159:
154:
153:
142:
139:
138:
137:
136:
132:
131:
126:
123:
121:
118:
116:
113:
112:
111:
110:
107:Conservations
106:
105:
97:
96:
92:
73:
70:
65:
62:
56:
53:
50:
47:
40:
39:
36:
33:
32:
28:
27:
22:
2587:
2580:
2579:John Comyn,
2531:
2527:
2521:
2509:
2499:, retrieved
2489:
2482:
2455:
2451:
2441:
2400:
2396:
2350:
2346:
2336:
2295:
2291:
2250:
2246:
2229:
2220:
2209:. Retrieved
2205:
2195:
2170:
2166:
2121:
2117:
2080:
2076:
2038:
2034:
1992:
1988:
1937:
1933:
1908:
1889:. Retrieved
1882:the original
1861:
1855:
1842:
1803:Mucoadhesion
1729:
1726:
1701:
1665:
1648:
1634:
1609:
1599:viscoelastic
1587:
1569:
1560:
1544:polyethylene
1541:
1537:
1528:
1512:
1493:
1461:
1441:
1432:
1424:
1420:sticky tapes
1400:
1384:
1296:
1289:
1282:
1174:Fritz London
1164:
1134:
1128:
1077:
1054:
1019:
1006:interlocking
995:
986:
965:
910:
875:
857:
831:
815:
795:
790:: Îł = (1/2)W
787:
748:
731:
730:
723:
722:
715:
714:
707:
706:
703:
496:Smart fluids
441:Graham's law
370:
347:
340:
325:
311:Pascal's law
307:
290:
278:
133:Inequalities
1736:liquid drop
1693:wettability
1621:vertebrates
1523:ultraviolet
1501:crosslinked
1133:, the term
515:Ferrofluids
416:Boyle's law
188:Hooke's law
166:Deformation
2598:Categories
2501:2017-12-30
2353:: 951324.
2211:2019-12-31
2131:1902.06721
1891:2013-07-16
1835:References
1636:Hysteresis
1631:Hysteresis
1617:arthropods
1613:biomimetic
1490:interface.
1190:Multipoles
1068:Dispersive
992:Mechanical
983:Mechanisms
880:applies: W
700:definition
658:spider web
568:Gay-Lussac
531:Scientists
431:Fick's law
411:Atmosphere
230:frictional
183:Plasticity
171:Elasticity
2474:2223-7690
2083:(1): 89.
1589:Stringing
1584:fracture.
1575:Stringing
1472:sintering
1464:diffusion
1458:Diffusive
1448:capacitor
1357:π
1345:−
1300:electrons
1249:α
1245:ν
1226:−
1223:ν
1160:lyophobic
1156:lyophilic
1062:nanometer
959:, where W
896:, where Îł
736:particles
608:Truesdell
538:Bernoulli
487:Rheometer
482:Rheometry
322:Newtonian
316:Viscosity
66:φ
54:−
2564:19769678
2556:17932295
2495:archived
2452:Friction
2433:32153774
2425:12130780
2379:22505913
2328:29499327
2320:17731150
2267:16089420
2247:Langmuir
2238:(2005).
2148:30724570
2118:Langmuir
2055:28121158
2035:Langmuir
2017:20366322
1962:17795378
1878:98107080
1798:Meniscus
1753:Adhesive
1746:See also
1731:friction
1682:= (1/2)W
1678:= (1/2)W
1571:device.
1534:Strength
1504:polymers
1135:adhesion
1123:Hibiscus
1046:fluorine
1038:nitrogen
1034:hydrogen
1022:compound
1016:Chemical
923:= (1/2)W
919:= (1/2)W
913:cleavage
826:= (1/2)W
822:= (1/2)W
744:Cohesion
740:surfaces
732:Adhesion
683:meniscus
681:Concave
466:Rheology
371:Adhesion
351:Pressure
337:Buoyancy
282:Dynamics
120:Momentum
2536:Bibcode
2528:Science
2405:Bibcode
2397:Science
2370:3296218
2300:Bibcode
2292:Science
2187:1922923
2085:Bibcode
1997:Bibcode
1970:1525799
1942:Bibcode
1934:Science
1823:Wetting
1788:Galling
1480:ceramic
1474:. When
1468:soluble
1428:brittle
1407:polymer
1304:contact
1152:wetting
867:surface
553:Charles
361:Liquids
275:Statics
220:Bending
2562:
2554:
2472:
2431:
2423:
2377:
2367:
2326:
2318:
2265:
2185:
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2053:
2015:
1968:
1960:
1876:
1686:. If Îł
1625:geckos
1519:distal
1415:Decals
1292:dipole
1042:oxygen
1010:velcro
765:, and
751:forces
724:Note 3
716:Note 2
708:Note 1
603:Stokes
598:Pascal
588:Navier
583:Newton
573:Graham
548:Cauchy
451:Plasma
346:
344:Mixing
339:
324:
306:
289:
277:
265:Fluids
198:Strain
193:Stress
176:linear
125:Energy
2560:S2CID
2429:S2CID
2324:S2CID
2288:(PDF)
2243:(PDF)
2126:arXiv
1966:S2CID
1885:(PDF)
1874:S2CID
1852:(PDF)
1476:metal
1111:drops
1088:polar
1044:, or
1002:pores
998:voids
900:and Îł
698:IUPAC
578:Hooke
558:Euler
543:Boyle
401:Gases
2552:PMID
2470:ISSN
2421:PMID
2375:PMID
2351:2012
2316:PMID
2263:PMID
2183:OSTI
2144:PMID
2051:PMID
2013:PMID
1958:PMID
1711:or W
1705:mica
1670:and
1619:and
1554:and
1308:mica
1154:, a
863:work
749:The
593:Noll
563:Fick
115:Mass
100:Laws
2544:doi
2532:318
2460:doi
2413:doi
2401:297
2365:PMC
2355:doi
2308:doi
2296:269
2255:doi
2175:doi
2136:doi
2093:doi
2043:doi
2005:doi
1993:103
1950:doi
1938:263
1866:doi
1709:121
1684:212
1680:121
1653:+ Îł
1642:+ Îł
1478:or
1129:In
1102:).
1028:or
1000:or
961:132
957:132
955:= W
951:– W
947:– W
943:+ W
939:= W
935:– γ
931:+ Îł
925:212
921:121
892:– γ
888:+ Îł
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850:= W
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842:– W
838:+ W
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818:: Îł
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