Editing Friction (section)

===Coefficient of friction===
{{see also|Coefficient of traction}}
{{expand section|explanation of why kinetic friction is always lower|date=August 2020}}
The '''coefficient of friction''' (COF), often symbolized by the Greek letter [[μ]], is a [[dimensionless]] [[scalar (physics)|scalar]] value which equals the ratio of the force of friction between two bodies and the force pressing them together, either during or at the onset of slipping. The coefficient of friction depends on the materials used; for example, ice on steel has a low coefficient of friction, while rubber on pavement has a high coefficient of friction. Coefficients of friction range from near zero to greater than one. The coefficient of friction between two surfaces of similar metals is greater than that between two surfaces of different metals; for example, brass has a higher coefficient of friction when moved against brass, but less if moved against steel or aluminum.<ref name="Air Brake Association-1921">{{cite book|author=Air Brake Association|title=The Principles and Design of Foundation Brake Rigging|url=https://books.google.com/books?id=DoNBAQAAMAAJ&pg=PA5|year=1921|publisher=Air brake association|page=5|access-date=2017-07-27|archive-date=2024-10-07|archive-url=https://web.archive.org/web/20241007090951/https://books.google.com/books?id=DoNBAQAAMAAJ&pg=PA5#v=onepage&q&f=false|url-status=live}}</ref>

For surfaces at rest relative to each other, <math>\mu = \mu_\mathrm{s}</math>, where <math>\mu_\mathrm{s}</math> is the ''coefficient of static friction''. This is usually larger than its kinetic counterpart. The coefficient of static friction exhibited by a pair of contacting surfaces depends upon the combined effects of material deformation characteristics and [[surface roughness]], both of which have their origins in the [[chemical bonding]] between atoms in each of the bulk materials and between the material surfaces and any [[adsorption|adsorbed material]]. The [[fractal]]ity of surfaces, a parameter describing the scaling behavior of surface asperities, is known to play an important role in determining the magnitude of the static friction.<ref name="Hanaor-2016">{{cite journal |last1=Hanaor |first1=D. |last2=Gan |first2=Y. |last3=Einav |first3=I. |year=2016 |title=Static friction at fractal interfaces |journal=Tribology International |volume=93 |pages=229–238 |arxiv=2106.01473 |doi=10.1016/j.triboint.2015.09.016 |s2cid=51900923}}</ref>

For surfaces in relative motion <math>\mu = \mu_\mathrm{k}</math>, where <math>\mu_\mathrm{k}</math> is the ''coefficient of kinetic friction''. The Coulomb friction is equal to <math>F_\mathrm{f}</math>, and the frictional force on each surface is exerted in the direction opposite to its motion relative to the other surface.

[[Arthur Morin]] introduced the term and demonstrated the utility of the coefficient of friction.<ref name="Dowson-1997" /> The coefficient of friction is an [[empirical]] [[measurement]]{{mdash}}it has to be measured [[experiment]]ally, and cannot be found through calculations.<ref name="Valentin L. Popov-2014">{{cite journal |author1=Valentin L. Popov |title=Generalized law of friction between elastomers and differently shaped rough bodies |journal=Sci. Rep. |date=17 Jan 2014 |volume=4 |page=3750 |doi=10.1038/srep03750 |pmid=24435002 |pmc=3894559 |bibcode= 2014NatSR...4.3750P}}</ref> Rougher surfaces tend to have higher effective values. Both static and kinetic coefficients of friction depend on the pair of surfaces in contact; for a given pair of surfaces, the coefficient of static friction is ''usually'' larger than that of kinetic friction; in some sets the two coefficients are equal, such as teflon-on-teflon.

Most dry materials in combination have friction coefficient values between 0.3 and 0.6. Values outside this range are rarer, but [[teflon]], for example, can have a coefficient as low as 0.04. A value of zero would mean no friction at all, an elusive property. Rubber in contact with other surfaces can yield friction coefficients from 1 to 2. Occasionally it is maintained that ''μ'' is always < 1, but this is not true. While in most relevant applications ''μ'' < 1, a value above 1 merely implies that the force required to slide an object along the surface is greater than the normal force of the surface on the object. For example, [[silicone rubber]] or [[acrylic rubber]]-coated surfaces have a coefficient of friction that can be substantially larger than 1.

While it is often stated that the COF is a "material property", it is better categorized as a "system property". Unlike true material properties (such as conductivity, dielectric constant, yield strength), the COF for any two materials depends on system variables like [[temperature]], [[velocity]], [[atmosphere]] and also what are now popularly described as aging and deaging times; as well as on geometric properties of the interface between the materials, namely [[surface roughness|surface structure]].<ref name="Hanaor-2016" /> For example, a [[copper]] pin sliding against a thick copper plate can have a COF that varies from 0.6 at low speeds (metal sliding against metal) to below 0.2 at high speeds when the copper surface begins to melt due to frictional heating. The latter speed, of course, does not determine the COF uniquely; if the pin diameter is increased so that the frictional heating is removed rapidly, the temperature drops, the pin remains solid and the COF rises to that of a 'low speed' test.{{Citation needed|date=December 2008}}

In systems with significant non-uniform stress fields, because local slip occurs before the system slides, the macroscopic coefficient of static friction depends on the applied load, system size, or shape; [[Friction#Laws of dry friction|Amontons' law]] is not satisfied macroscopically.<ref>{{Cite journal |last1=Otsuki |first1=M. |last2=Matsukawa |first2=H. |date=2013-04-02 |title=Systematic breakdown of Amontons' law of friction for an elastic object locally obeying Amontons' law |journal=Scientific Reports |volume=3 |pages=1586 |doi=10.1038/srep01586|pmid=23545778 |pmc=3613807 |arxiv=1202.1716 |bibcode=2013NatSR...3.1586O }}</ref>

====Approximate coefficients of friction====
{{Disputed section|date=November 2021}}
{| class="wikitable"
|-
! colspan="2" rowspan="2" data-sort-type="text"|Materials !! colspan="2"|Static Friction, <math>\mu_\mathrm{s}</math> !! colspan="2"|Kinetic/Sliding Friction, <math>\mu_\mathrm{k}\,</math>
|-
|-
!data-sort-type="number"| Dry and clean !!data-sort-type="number"| Lubricated
!data-sort-type="number| Dry and clean !!data-sort-type="number"| Lubricated
|-
! Aluminium
! Steel
| 0.61<ref name="Friction Factors">{{cite web
| url = http://www.roymech.co.uk/Useful_Tables/Tribology/co_of_frict.htm#method
| title = Friction Factors – Coefficients of Friction
| access-date = 2015-04-27
| archive-url = https://web.archive.org/web/20190201171526/http://www.roymech.co.uk/Useful_Tables/Tribology/co_of_frict.htm#method
| archive-date = 2019-02-01

}}</ref>
|
| 0.47<ref name="Friction Factors"/>
|
|-
!Aluminium
!Aluminium
|1.05–1.35<ref name="Friction Factors"/>
|0.3<ref name="Friction Factors"/>
|1.4<ref name="Friction Factors"/>–1.5{{cn|date=March 2024}}
|-
!Gold
!Gold
|
|
|2.5{{cn|date=March 2024}}
|
|-
!Platinum
!Platinum
|1.2<ref name="Friction Factors"/>
|0.25<ref name="Friction Factors"/>
|3.0{{cn|date=March 2024}}
|
|-
!Silver
!Silver
|1.4<ref name="Friction Factors"/>
|0.55<ref name="Friction Factors"/>
|1.5{{cn|date=March 2024}}
|
|-
! Alumina ceramic
! Silicon nitride ceramic
|
|
|
| 0.004 (wet)<ref name="Ferreira-2012">{{cite journal
| title = Ultra-low friction coefficient in alumina–silicon nitride pair lubricated with water
| doi=10.1016/j.wear.2012.07.030
| volume=296
| issue = 1–2
| journal=Wear
| pages=656–659| date = 2012-08-30
| last1 = Ferreira
| first1 = Vanderlei
| last2 = Yoshimura
| first2 = Humberto Naoyuki
| last3 = Sinatora
| first3 = Amilton
}}</ref>
|-
! [[Aluminium magnesium boride|BAM (Ceramic alloy AlMgB<sub>14</sub>)]]
! [[Titanium boride]] (TiB<sub>2</sub>)
| 0.04–0.05<ref name="Tian-2003">{{cite journal|doi=10.1063/1.1615677|title=Superhard self-lubricating AlMgB[sub 14] films for microelectromechanical devices|year=2003|last1=Tian|first1=Y.|last2=Bastawros|first2=A. F.|last3=Lo|first3=C. C. H.|last4=Constant|first4=A. P.|last5=Russell|first5=A.M.|last6=Cook|first6=B. A.|journal=Applied Physics Letters|volume=83|issue=14|page=2781|bibcode=2003ApPhL..83.2781T|url=http://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1004&context=mse_pubs|access-date=2019-01-31|archive-date=2024-10-07|archive-url=https://web.archive.org/web/20241007090944/https://dr.lib.iastate.edu/handle/20.500.12876/55639/|url-status=live}}</ref>
| 0.02<ref name="Kleiner, Kurt-2008">{{cite web
| url = https://www.newscientist.com/article/dn16102-material-slicker-than-teflon-discovered-by-accident.html
| title = Material slicker than Teflon discovered by accident
| author = Kleiner, Kurt
| date = 2008-11-21
| access-date = 2008-12-25
| archive-date = 2008-12-20
| archive-url = https://web.archive.org/web/20081220162702/http://www.newscientist.com/article/dn16102-material-slicker-than-teflon-discovered-by-accident.html
| url-status = live
}}</ref><ref name="Higdon-2011">{{cite journal|doi=10.1016/j.wear.2010.11.044
| title=Friction and wear mechanisms in AlMgB14-TiB2 nanocoatings
| year=2011|last1=Higdon|first1=C.|last2=Cook|first2=B.|last3=Harringa|first3=J.
| last4=Russell|first4=A.|last5=Goldsmith|first5=J.|last6=Qu|first6=J.|last7=Blau|first7=P.|journal=Wear|volume=271|issue=9–10
| pages=2111–2115}}</ref>
|
|
|-
! Brass
! Steel
| 0.35–0.51<ref name="Friction Factors"/>
| 0.19<ref name="Friction Factors"/>
| 0.44<ref name="Friction Factors"/>
|
|-
! Cast iron
! Copper
| 1.05<ref name="Friction Factors"/>
|
| 0.29<ref name="Friction Factors"/>
|
|-
! Cast iron
! Zinc
| 0.85<ref name="Friction Factors"/>
|
| 0.21<ref name="Friction Factors"/>
|
|-
! Concrete
! Rubber
| 1.0
| 0.30 (wet)
| 0.6–0.85<ref name="Friction Factors"/>
| 0.45–0.75 (wet)<ref name="Friction Factors"/>
|-
! Concrete
! Wood
| 0.62<ref name="Friction Factors"/><ref name="Coefficient of Friction Archived March 8"/>
|
|
|
|-
! Copper
! Glass
| 0.68<ref name="Barrett-1990" />
|
| 0.53<ref name="Barrett-1990" />
|
|-
! Copper
! Steel
| 0.53<ref name="Barrett-1990" />
|
| 0.36<ref name="Friction Factors"/><ref name="Barrett-1990" />
| 0.18<ref name="Barrett-1990" />
|-
! Glass
! Glass
| 0.9–1.0<ref name="Friction Factors"/><ref name="Barrett-1990" />
| 0.005–0.01<ref name="Barrett-1990" />
| 0.4<ref name="Friction Factors"/><ref name="Barrett-1990" />
| 0.09–0.116<ref name="Barrett-1990" />
|-
! Human synovial fluid
! Human cartilage
|
| 0.01<ref name="Coefficients of Friction of Human Joints">{{cite web
| url = http://hypertextbook.com/facts/2007/ConnieQiu.shtml
| title = Coefficients of Friction of Human Joints
| access-date = 2015-04-27
| archive-date = 2024-10-07
| archive-url = https://web.archive.org/web/20241007090943/https://hypertextbook.com/facts/2007/ConnieQiu.shtml
| url-status = live
}}</ref>
|
| 0.003<ref name="Coefficients of Friction of Human Joints"/>
|-
! Ice
! Ice
| 0.02–0.09<ref name="The Engineering Toolbox"/>
|
|
|
|-
! [[Polyethene]]
! Steel
| 0.2<ref name="Friction Factors"/><ref name="The Engineering Toolbox"/>
| 0.2<ref name="Friction Factors"/><ref name="The Engineering Toolbox"/>
|
|
|-
! [[PTFE]] (Teflon)
! PTFE (Teflon)
| 0.04<ref name="Friction Factors"/><ref name="The Engineering Toolbox">{{cite web
| url = http://www.engineeringtoolbox.com/friction-coefficients-d_778.html
| title = The Engineering Toolbox: Friction and Coefficients of Friction
| access-date = 2008-11-23
| archive-date = 2013-12-03
| archive-url = https://web.archive.org/web/20131203000601/http://www.engineeringtoolbox.com/friction-coefficients-d_778.html
| url-status = live
}}</ref>
| 0.04<ref name="Friction Factors"/><ref name="The Engineering Toolbox"/>
|
| 0.04<ref name="Friction Factors"/>
|-
! Steel
! Ice
| 0.03<ref name="The Engineering Toolbox"/>
|
|
|
|-
! Steel
! PTFE (Teflon)
| 0.04<ref name="Friction Factors"/>−0.2<ref name="The Engineering Toolbox"/>
| 0.04<ref name="Friction Factors"/>
|
| 0.04<ref name="Friction Factors"/>
|-
! Steel
! Steel
| 0.74<ref name="Friction Factors"/>−0.80<ref name="The Engineering Toolbox"/>
| 0.005–0.23<ref name="Barrett-1990" /><ref name="The Engineering Toolbox"/>
| 0.42–0.62<ref name="Friction Factors"/><ref name="Barrett-1990" />
| 0.029–0.19<ref name="Barrett-1990" />
|-
! Wood
! Metal
| 0.2–0.6<ref name="Friction Factors"/><ref name="Coefficient of Friction Archived March 8"/>
| 0.2 (wet)<ref name="Friction Factors"/><ref name="Coefficient of Friction Archived March 8"/>
| 0.49<ref name="Barrett-1990" />
| 0.075<ref name="Barrett-1990" />
|-
! Wood
! Wood
| 0.25–0.62<ref name="Friction Factors"/><ref name="Coefficient of Friction Archived March 8">[http://www.engineershandbook.com/Tables/frictioncoefficients.htm Coefficient of Friction] {{webarchive |url=https://web.archive.org/web/20090308124246/http://www.engineershandbook.com/Tables/frictioncoefficients.htm |date=March 8, 2009 }}. EngineersHandbook.com</ref><ref name="Barrett-1990">{{cite journal |last1=Barrett |first1=Richard T. |title=(NASA-RP-1228) Fastener Design Manual |url=http://hdl.handle.net/2060/19900009424 |website=NASA Technical Reports Server |publisher=NASA Lewis Research Center |access-date=3 August 2020 |page=16 |date=1 March 1990 |hdl=2060/19900009424 |archive-date=7 October 2024 |archive-url=https://web.archive.org/web/20241007091010/https://ntrs.nasa.gov/citations/19900009424 |url-status=live }}</ref>
| 0.2 (wet)<ref name="Friction Factors"/><ref name="Coefficient of Friction Archived March 8"/>
| 0.32–0.48<ref name="Barrett-1990" />
| 0.067–0.167<ref name="Barrett-1990" />
|}

Under certain conditions some materials have very low friction coefficients. An example is (highly ordered pyrolytic) graphite which can have a friction coefficient below 0.01.<ref>{{cite journal |last=Dienwiebel |first=Martin |title=Superlubricity of Graphite |display-authors=etal |journal=Phys. Rev. Lett. |volume=92 |page=126101 |year=2004 |doi=10.1103/PhysRevLett.92.126101 |url=http://www.physics.leidenuniv.nl/sections/cm/ip/group/PDF/Phys.rev.lett/2004/92(2004)12601.pdf |issue=12 |bibcode=2004PhRvL..92l6101D |pmid=15089689 |s2cid=26811802 |access-date=2011-09-01 |archive-date=2011-09-17 |archive-url=https://web.archive.org/web/20110917120623/http://www.physics.leidenuniv.nl/sections/cm/ip/group/PDF/Phys.rev.lett/2004/92(2004)12601.pdf |url-status=live }}</ref>
This ultralow-friction regime is called [[superlubricity]].<ref>{{Citation |last=Müser |first=Martin H. |title=Theoretical Studies of Superlubricity |date=2015 |work=Fundamentals of Friction and Wear on the Nanoscale |pages=209–232 |editor-last=Gnecco |editor-first=Enrico |url=https://link.springer.com/10.1007/978-3-319-10560-4_11 |access-date=2025-04-25 |place=Cham |publisher=Springer International Publishing |language=en |doi=10.1007/978-3-319-10560-4_11 |isbn=978-3-319-10559-8 |editor2-last=Meyer |editor2-first=Ernst}}</ref>