1024:
by a two-step process. In the first step, when the molecules in the solution first approach a virgin surface that has no pre-existing surface charges, it may be possible that the atoms/molecules in the solution directly interact with the atoms on the solid surface to form strong overlap of electron clouds. Electron transfer occurs first to make the âneutralâ atoms on solid surface become charged, i.e., the formation of ions. In the second step, if there are ions existing in the liquid, such as H and OH, the loosely distributed negative ions in the solution would be attracted to migrate toward the surface bonded ions due to electrostatic interactions, forming an EDL. Both electron transfer and ion transfer co-exist at liquid-solid interface.
376:
205:
503:, expressed usually in C/m. This surface charge creates an electrostatic field that then affects the ions in the bulk of the liquid. This electrostatic field, in combination with the thermal motion of the ions, creates a counter charge, and thus screens the electric surface charge. The net electric charge in this screening diffuse layer is equal in magnitude to the net surface charge, but has the opposite polarity. As a result, the complete structure is electrically neutral.
1028:
31:
491:
1023:
The formation of electrical double layer (EDL) has been traditionally assumed to be entirely dominated by ion adsorption and redistribution. With considering the fact that the contact electrification between solid-solid is dominated by electron transfer, it is suggested by Wang that the EDL is formed
694:
There is no general analytical solution for mixed electrolytes, curved surfaces or even spherical particles. There is an asymptotic solution for spherical particles with low charged DLs. In the case when electric potential over DL is less than 25 mV, the so-called Debye-Huckel approximation holds. It
924:
formation. With an electrode, it is possible to regulate the surface charge by applying an external electric potential. This application, however, is impossible in colloidal and porous double layers, because for colloidal particles, one does not have access to the interior of the particle to apply a
441:
His "supercapacitor" stored electrical charge partially in the
Helmholtz double-layer and partially as the result of faradaic reactions with "pseudocapacitance" charge transfer of electrons and protons between electrode and electrolyte. The working mechanisms of pseudocapacitors are redox reactions,
406:
proposed the BDM model of the double-layer that included the action of the solvent in the interface. They suggested that the attached molecules of the solvent, such as water, would have a fixed alignment to the electrode surface. This first layer of solvent molecules displays a strong orientation to
379:
Schematic representation of a double layer on an electrode (BMD) model. 1. Inner
Helmholtz plane, (IHP), 2. Outer Helmholtz plane (OHP), 3. Diffuse layer, 4. Solvated ions (cations) 5. Specifically adsorbed ions (redox ion, which contributes to the pseudocapacitance), 6. Molecules of the electrolyte
411:
of the solvent that varies with field strength. The IHP passes through the centers of these molecules. Specifically adsorbed, partially solvated ions appear in this layer. The solvated ions of the electrolyte are outside the IHP. Through the centers of these ions pass the OHP. The diffuse layer is
389:
as they approach the electrode. He called ions in direct contact with the electrode "specifically adsorbed ions". This model proposed the existence of three regions. The inner
Helmholtz plane (IHP) passes through the centres of the specifically adsorbed ions. The outer Helmholtz plane (OHP) passes
38:
at the interface with a negatively-charged surface of a mineral solid. Blue + sphere: cations; red â spheres: anions. The number of cations is larger in the EDL close to the negatively-charged surface in order to neutralize these negative charges and to maintain electroneutrality. The drawing does
420:
Further research with double layers on ruthenium dioxide films in 1971 by Sergio
Trasatti and Giovanni Buzzanca demonstrated that the electrochemical behavior of these electrodes at low voltages with specific adsorbed ions was like that of capacitors. The specific adsorption of the ions in this
437:
electrochemical capacitors. In 1991, he described the difference between 'Supercapacitor' and 'Battery' behavior in electrochemical energy storage. In 1999, he coined the term supercapacitor to explain the increased capacitance by surface redox reactions with faradaic charge transfer between
1330:
Gomila, Alexandre M. J.; PĂ©rez-MejĂas, Gonzalo; Nin-Hill, Alba; Guerra-Castellano, Alejandra; Casas-Ferrer, Laura; Ortiz-Tescari, Sthefany; DĂaz-Quintana, Antonio; Samitier, Josep; Rovira, Carme; De la Rosa, Miguel A.; DĂaz-Moreno, Irene; Gorostiza, Pau; Giannotti, Marina I.; Lagunas, Anna
354:
The Stern layer accounts for ions' finite size and consequently an ion's closest approach to the electrode is on the order of the ionic radius. The Stern model has its own limitations, namely that it effectively treats ions as point charges, assumes all significant interactions in the
535:
is used for estimating the degree of DL charge. A characteristic value of this electric potential in the DL is 25 mV with a maximum value around 100 mV (up to several volts on electrodes). The chemical composition of the sample at which the ζ-potential is 0 is called the
384:
D. C. Grahame modified the Stern model in 1947. He proposed that some ionic or uncharged species can penetrate the Stern layer, although the closest approach to the electrode is normally occupied by solvent molecules. This could occur if ions lose their
690:
482:
There are detailed descriptions of the interfacial DL in many books on colloid and interface science and microscale fluid transport. There is also a recent IUPAC technical report on the subject of interfacial double layer and related
350:
suggested combining the
Helmholtz model with the Gouy-Chapman model: in Stern's model, some ions adhere to the electrode as suggested by Helmholtz, giving an internal Stern layer, while some form a Gouy-Chapman diffuse layer.
580:
The theory for a flat surface and a symmetrical electrolyte is usually referred to as the Gouy-Chapman theory. It yields a simple relationship between electric charge in the diffuse layer Ï and the Stern potential Κ:
794:
498:
As stated by
Lyklema, "...the reason for the formation of a "relaxed" ("equilibrium") double layer is the non-electric affinity of charge-determining ions for a surface..." This process leads to the buildup of an
285:
in 1913 both observed that capacitance was not a constant and that it depended on the applied potential and the ionic concentration. The "GouyâChapman model" made significant improvements by introducing a
843:
The thin DL model is valid for most aqueous systems because the Debye length is only a few nanometers in such cases. It breaks down only for nano-colloids in solution with ionic strengths close to water.
330:, electric fields extending several nanometers, and currents decreasing quasi exponentially with the distance at rate ~1 nm. This region is termed "Gouy-Chapman conduit" and is strongly regulated by
2162:
1125:
801:
The first one is "thin DL". This model assumes that DL is much thinner than the colloidal particle or capillary radius. This restricts the value of the Debye length and particle radius as following:
586:
1794:"Measurement and Interpretation of Electrokinetic Phenomena", International Union of Pure and Applied Chemistry, Technical Report, published in Pure Appl.Chem., vol 77, 10, pp.1753-1805, 2005
1846:
Jiang, Jingkun; Oberdörster, GĂŒnter; Biswas, Pratim (25 June 2008). "Characterization of size, surface charge, and agglomeration state of nanoparticle dispersions for toxicological studies".
334:, which adds one negative charge to the protein surface that disrupts cationic depletion and prevents long-distance charge transport. Similar effects are observed at the redox active site of
1002:
1031:
The "two-step" model (Wang model) for the formation of electric double-layer (EDL) at a liquid-solid interface, in which the electron transfer plays a dominant role in the first step.
462:
reactions, in which two chemical species change only in their charge, with an electron jumping. For redox reactions without making or breaking bonds, Marcus theory takes the place of
885:
The last model introduces "overlapped DLs". This is important in concentrated dispersions and emulsions when distances between particles become comparable with the Debye length.
1553:
Nakamura, Masashi; Sato, Narumasa; Hoshi, Nagahiro; Sakata, Osami (2011). "Outer
Helmholtz Plane of the Electrical Double Layer Formed at the Solid Electrode-Liquid Interface".
262:
This model, while a good foundation for the description of the interface, does not consider important factors including diffusion/mixing of ions in solution, the possibility of
577:
The electric field strength inside the DL can be anywhere from zero to over 10 V/m. These steep electric potential gradients are the reason for the importance of the DLs.
513:. There is a conventionally introduced slipping plane that separates mobile fluid from fluid that remains attached to the surface. Electric potential at this plane is called
877:
828:
403:
458:
explains the rates of electron transfer reactionsâthe rate at which an electron can move from one chemical species to another. It was originally formulated to address
1257:
Lagunas, Anna; Guerra-Castellano, Alejandra; Nin-Hill, Alba; DĂaz-Moreno, Irene; De la Rosa, Miguel A.; Samitier, Josep; Rovira, Carme; Gorostiza, Pau (2018-12-04).
421:
region of potential could also involve a partial charge transfer between the ion and the electrode. It was the first step towards understanding pseudocapacitance.
708:
244:
dielectric and stores charge electrostatically. Below the electrolyte's decomposition voltage, the stored charge is linearly dependent on the voltage applied.
1129:
1155:
390:
through the centres of solvated ions at the distance of their closest approach to the electrode. Finally the diffuse layer is the region beyond the OHP.
1209:
574:. In aqueous solutions it is typically on the scale of a few nanometers and the thickness decreases with increasing concentration of the electrolyte.
236:
electrodes immersed in electrolyte solutions repel the co-ions of the charge while attracting counterions to their surfaces. Two layers of opposite
115:
the first layer. This second layer is loosely associated with the object. It is made of free ions that move in the fluid under the influence of
1222:
2027:"Quantifying electron-transfer and ion-transfer in liquid-solid contact electrification and the formation mechanism of electric double-layer"
1682:
1093:"Ueber einige Gesetze der Vertheilung elektrischer Ströme in körperlichen Leitern mit Anwendung auf die thierisch-elektrischen Versuche"
544:. It is usually determined by the solution pH value, since protons and hydroxyl ions are the charge-determining ions for most surfaces.
450:
The physical and mathematical basics of electron charge transfer absent chemical bonds leading to pseudocapacitance was developed by
240:
form at the interface between electrode and electrolyte. In 1853, he showed that an electrical double layer (DL) is essentially a
318:
798:
There are several asymptotic models which play important roles in theoretical developments associated with the interfacial DL.
2146:
2125:
1978:
1830:
1768:
1193:
1388:
LĂłpezâOrtiz, Manuel; Zamora, Ricardo A.; Giannotti, Marina InĂ©s; Hu, Chen; Croce, Roberta; Gorostiza, Pau (February 2022).
471:
1390:"Distance and Potential Dependence of Charge Transport Through the Reaction Center of Individual Photosynthetic Complexes"
290:
model of the DL. In this model, the charge distribution of ions as a function of distance from the metal surface allows
208:
Simplified illustration of the potential development in the area and in the further course of a
Helmholtz double layer.
304:
Gouy-Chapman layers may bear special relevance in bioelectrochemistry. The observation of long-distance inter-protein
1647:
Conway, B.E. (May 1991), "Transition from 'Supercapacitor' to 'Battery' Behavior in
Electrochemical Energy Storage",
1758:
804:
291:
964:
1162:
528:. Electric potential difference between the fluid bulk and the surface is called the electric surface potential.
524:
The electric potential on the external boundary of the Stern layer versus the bulk electrolyte is referred to as
459:
685:{\displaystyle \sigma ^{d}=-{\sqrt {{8\varepsilon _{0}}{\varepsilon _{m}}CRT}}\sinh {\frac {F\Psi ^{d}}{2RT}}}
1197:
1057:
882:
This model can be useful for some nano-colloids and non-polar fluids, where the Debye length is much larger.
17:
2182:
130:
920:
The primary difference between a double layer on an electrode and one on an interface is the mechanism of
1718:
Russel, W.B., Saville, D.A. and
Schowalter, W.R. "Colloidal Dispersions", Cambridge University Press,1989
2177:
1067:
1012:
2192:
837:
552:
308:
through the aqueous solution has been attributed to a diffuse region between redox partner proteins (
282:
188:
1899:
1489:
1229:
2187:
951:
945:
853:
514:
484:
327:
248:
184:
112:
1596:
J. Oâm. Bockris; M. A. V. Devanathan; K. MĂŒllen (1963). "On the structure of charged interfaces".
500:
467:
364:
331:
1900:"Scalable Surface Area Characterization by Electrokinetic Analysis of Complex Anion Adsorption"
1795:
1679:
463:
267:
1510:
Grahame, David C. (1947). "The Electrical Double Layer and the Theory of Electrocapillarity".
1971:
Characterization of liquids, nano- and micro- particulates and porous bodies using Ultrasound
1389:
1259:"Long distance electron transfer through the aqueous solution between redox partner proteins"
929:
326:) that is depleted of cations in comparison to the solution bulk, thereby leading to reduced
229:
221:
126:
1698:
847:
The opposing "thick DL" model assumes that the Debye length is larger than particle radius:
2202:
2086:
1855:
1652:
1605:
1344:
1270:
1100:
910:
537:
375:
104:
8:
1052:
832:
This model offers tremendous simplifications for many subsequent applications. Theory of
560:
556:
252:
237:
2090:
1859:
1656:
1609:
1598:
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
1348:
1274:
1104:
407:
the electric field depending on the charge. This orientation has great influence on the
367:
to be constant throughout the double layer, and that fluid viscosity is constant plane.
2051:
2026:
2007:
1940:
1914:
1871:
1629:
1470:
1435:
1365:
1332:
1312:
1299:
1258:
1198:
Chapter 2, Electrode/electrolyte interfaces: Structure and kinetics of charge transfer.
914:
902:
541:
430:
295:
278:
165:
2077:
Stillinger, Frank H.; Kirkwood, John G. (1960). "Theory of the Diffuse Double Layer".
1709:
Dukhin, S.S. & Derjaguin, B.V. "Electrokinetic Phenomena", J.Willey and Sons, 1974
2142:
2121:
2102:
2056:
2011:
1974:
1932:
1826:
1764:
1621:
1578:
1570:
1535:
1527:
1474:
1439:
1427:
1419:
1370:
1304:
1286:
1189:
1188:
Srinivasan S. (2006) Fuel cells, from Fundamentals to Applications, Springer eBooks,
451:
305:
298:
1875:
1811:
Lyklema, J. "Fundamentals of Interface and Colloid Science", vol.2, page.3.208, 1995
1633:
1316:
2094:
2046:
2038:
1999:
1944:
1924:
1863:
1660:
1613:
1562:
1519:
1462:
1409:
1401:
1360:
1352:
1294:
1278:
1210:
Electrochemical double-layer capacitors using carbon nanotube electrode structures.
1108:
1041:
933:
510:
157:
116:
35:
2197:
2136:
2115:
2003:
1686:
833:
570:, Îș. It is reciprocally proportional to the square root of the ion concentration
548:
525:
434:
386:
233:
146:
88:
44:
2138:
Principles of Colloid and Surface Chemistry, Third Edition, Revised and Expanded
2042:
1727:
Kruyt, H.R. "Colloid Science", Elsevier: Volume 1, Irreversible systems, (1952)
1356:
1282:
1072:
1008:
921:
532:
518:
225:
120:
107:. The second layer is composed of ions attracted to the surface charge via the
92:
1867:
2171:
2106:
1625:
1574:
1531:
1423:
1290:
1112:
470:
which was derived for reactions with structural changes. Marcus received the
455:
356:
204:
173:
108:
1957:
Hunter, R.J. "Foundations of Colloid Science", Oxford University Press, 1989
2060:
1990:
Wang, Z.L.; Wang, A.C. (2019). "On the origin of contact electrification".
1936:
1617:
1595:
1582:
1566:
1539:
1466:
1431:
1405:
1374:
1333:"Phosphorylation disrupts long-distance electron transport in cytochrome c"
1329:
1308:
1256:
1062:
567:
506:
The diffuse layer, or at least part of it, can move under the influence of
408:
399:
313:
123:
rather than being firmly anchored. It is thus called the "diffuse layer".
84:
1888:
V.S. Bogotsky, Fundamentals of Electrochemistry, Wiley-Interscience, 2006.
1047:
1027:
789:{\displaystyle {\Psi }(r)={\Psi ^{d}}{\frac {a}{r}}\exp({-\kappa }(r-a))}
335:
138:
1774:
1523:
137:
or porous bodies with particles or pores (respectively) on the scale of
1760:
Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices
1414:
507:
347:
309:
263:
156:
DLs play a fundamental role in many everyday substances. For instance,
142:
76:
2098:
1928:
1665:
176:
fluid-based systems, such as blood, paint, ink and ceramic and cement
287:
150:
1453:
Stern, O. (1924). "Zur Theorie der Elektrolytischen Doppelschicht".
1092:
905:
near a surface, and has a significant influence on the behaviour of
1919:
950:
EDLs have an additional parameter defining their characterization:
241:
100:
906:
360:
256:
134:
80:
64:
194:
1018:
177:
169:
30:
2134:
1898:
Hanaor, D.A.H.; Ghadiri, M.; Chrzanowski, W.; Gan, Y. (2014).
1823:
Colloidal dispersions : suspensions, emulsions, and foams
490:
346:
The Gouy-Chapman model fails for highly charged DLs. In 1924,
145:. However, DLs are important to other phenomena, such as the
72:
68:
1689:
Central Electrochemical Research Institute, (November, 2008)
1651:(in German), vol. 138, no. 6, pp. 1539â1548,
1387:
1897:
1099:(in German), vol. 165, no. 6, pp. 211â233,
161:
96:
1678:
A.K. Shukla, T.P. Kumar, Electrochemistry Encyclopedia,
433:
conducted extensive fundamental and development work on
39:
not explicitly show the negative charges of the surface.
1552:
1156:"A survey of electrochemical supercapacitor technology"
216:
conductor is brought in contact with a solid or liquid
1845:
695:
yields the following expression for electric potential
266:
onto the surface, and the interaction between solvent
967:
856:
807:
711:
589:
251:
independent from the charge density depending on the
1699:
Rudolph A. Marcus: The Nobel Prize in Chemistry 1992
1680:
Pillars of modern electrochemistry: A brief history
164:droplets are covered with a DL that prevents their
2135:Paul C. Hiemenz; Raj Rajagopalan (18 March 1997).
2076:
2025:Lin, S.Q.; Xu, L.; Wang, A.C.; Wang, Z.L. (2020).
996:
871:
822:
788:
699:in the spherical DL as a function of the distance
684:
393:
34:Schematic of the electrical double layer (EDL) in
1640:
27:Molecular interface between a surface and a fluid
2169:
1546:
1153:
2113:
566:The characteristic thickness of the DL is the
129:DLs are most apparent in systems with a large
2024:
195:Development of the (interfacial) double layer
91:surrounding the object. The first layer, the
1820:
1184:
1182:
1019:Electron transfer in electrical double layer
997:{\displaystyle C={\frac {d\sigma }{d\Psi }}}
220:conductor (electrolyte), a common boundary (
2117:Principles of Colloid and Surface Chemistry
1756:
1503:
939:
888:
477:
95:(either positive or negative), consists of
1807:
1805:
1803:
1220:
1149:
1147:
87:. The DL refers to two parallel layers of
2050:
1965:
1963:
1918:
1736:
1664:
1413:
1364:
1298:
1179:
1090:
301:away from the surface of the fluid bulk.
1989:
1752:
1750:
1748:
1026:
489:
374:
203:
29:
1821:Morrison, Ian D.; Ross, Sydney (2002).
1800:
1509:
1487:
1144:
954:. Differential capacitance, denoted as
494:detailed illustration of interfacial DL
259:and the thickness of the double-layer.
14:
2170:
1960:
1649:Journal of the Electrochemical Society
1646:
958:, is described by the equation below:
247:This early model predicted a constant
1825:(2nd ed.). New York, NY: Wiley.
1745:
1730:
1692:
1452:
1044:(structure of semiconductor junction)
547:Zeta potential can be measured using
67:of an object when it is exposed to a
63:) is a structure that appears on the
1252:
1250:
901:) is the result of the variation of
415:
909:and other surfaces in contact with
836:is just one example. The theory of
442:intercalation and electrosorption.
24:
2070:
1118:
988:
731:
713:
659:
25:
2214:
2156:
1247:
1848:Journal of Nanoparticle Research
2079:The Journal of Chemical Physics
2018:
1983:
1969:Dukhin, A. S. and Goetz, P. J.
1951:
1891:
1882:
1839:
1814:
1788:
1721:
1712:
1703:
1672:
1589:
1481:
1446:
521:(also denoted as ζ-potential).
394:Bockris/Devanathan/MĂŒller (BDM)
273:
172:. DLs exist in practically all
1763:. Cambridge University Press.
1381:
1323:
1214:
1203:
1084:
783:
780:
768:
757:
723:
717:
460:outer sphere electron transfer
232:was the first to realize that
13:
1:
1455:Zeitschrift fĂŒr Elektrochemie
1126:"The electrical double layer"
1097:Annalen der Physik und Chemie
1078:
1058:Interface and colloid science
872:{\displaystyle \kappa a<1}
823:{\displaystyle \kappa a\gg 1}
183:The DL is closely related to
2004:10.1016/j.mattod.2019.05.016
292:MaxwellâBoltzmann statistics
199:
131:surface-area-to-volume ratio
7:
2163:The Electrical Double Layer
1221:Ehrenstein, Gerald (2001).
1035:
412:the region beyond the OHP.
10:
2219:
2043:10.1038/s41467-019-14278-9
1357:10.1038/s41467-022-34809-1
1283:10.1038/s41467-018-07499-x
1068:Poisson-Boltzmann equation
1013:electric surface potential
943:
928:EDLs are analogous to the
703:from the particle center:
402:, M. A. V. Devanathan and
370:
1868:10.1007/s11051-008-9446-4
1739:Theoretical Microfluidics
838:electroacoustic phenomena
553:electroacoustic phenomena
474:in 1992 for this theory.
445:
424:
189:electroacoustic phenomena
2114:Paul C. Hiemenz (1986).
1685:August 20, 2013, at the
1488:SMIRNOV, Gerald (2011).
1113:10.1002/andp.18531650603
952:differential capacitance
946:Differential capacitance
940:Differential capacitance
889:Electrical double layers
515:electrokinetic potential
485:electrokinetic phenomena
478:Mathematical description
472:Nobel Prize in Chemistry
341:
336:photosynthetic complexes
294:to be applied. Thus the
249:differential capacitance
185:electrokinetic phenomena
71:. The object might be a
1490:"Electric Double Layer"
895:electrical double layer
501:electric surface charge
468:transition state theory
429:Between 1975 and 1980,
365:dielectric permittivity
299:decreases exponentially
103:onto the object due to
57:electrical double layer
1618:10.1098/rspa.1963.0114
1567:10.1002/cphc.201100011
1467:10.1002/bbpc.192400182
1406:10.1002/smll.202104366
1154:Adam Marcus Namisnyk.
1128:. 2011. Archived from
1091:Helmholtz, H. (1853),
1032:
998:
925:potential difference.
873:
824:
790:
686:
495:
381:
209:
40:
2031:Nature Communications
1337:Nature Communications
1263:Nature Communications
1030:
999:
874:
825:
791:
687:
493:
438:electrodes and ions.
378:
283:David Leonard Chapman
230:Hermann von Helmholtz
207:
105:chemical interactions
33:
1757:Kirby, B.J. (2010).
1235:on 28 September 2011
965:
854:
840:is another example.
805:
709:
587:
538:point of zero charge
160:exists only because
2183:Colloidal chemistry
2091:1960JChPh..33.1282S
1913:(50): 15143â15152.
1860:2009JNR....11...77J
1657:1991JElS..138.1539C
1610:1963RSPSA.274...55B
1524:10.1021/cr60130a002
1349:2022NatCo..13.7100G
1275:2018NatCo...9.5157L
1105:1853AnP...165..211H
1053:Electroosmotic pump
915:fast ion conductors
561:electroosmotic flow
557:streaming potential
270:and the electrode.
255:of the electrolyte
253:dielectric constant
117:electric attraction
1737:Bruus, H. (2007).
1033:
994:
903:electric potential
869:
820:
786:
682:
542:iso-electric point
496:
431:Brian Evans Conway
382:
296:electric potential
279:Louis Georges Gouy
210:
41:
2178:Chemical mixtures
2148:978-0-8247-9397-5
2127:978-0-8247-7476-9
2099:10.1063/1.1731401
1979:978-0-444-63908-0
1973:, Elsevier, 2017
1929:10.1021/la503581e
1832:978-0-471-17625-1
1770:978-0-521-11903-0
1666:10.1149/1.2085829
1194:978-0-387-35402-6
992:
749:
680:
644:
452:Rudolph A. Marcus
416:Trasatti/Buzzanca
306:electron transfer
55:, also called an
16:(Redirected from
2210:
2193:Electrochemistry
2152:
2131:
2110:
2085:(5): 1282â1290.
2065:
2064:
2054:
2022:
2016:
2015:
1987:
1981:
1967:
1958:
1955:
1949:
1948:
1922:
1904:
1895:
1889:
1886:
1880:
1879:
1843:
1837:
1836:
1818:
1812:
1809:
1798:
1792:
1786:
1785:
1783:
1782:
1773:. Archived from
1754:
1743:
1742:
1734:
1728:
1725:
1719:
1716:
1710:
1707:
1701:
1696:
1690:
1676:
1670:
1669:
1668:
1644:
1638:
1637:
1593:
1587:
1586:
1561:(8): 1430â1434.
1550:
1544:
1543:
1512:Chemical Reviews
1507:
1501:
1500:
1498:
1496:
1485:
1479:
1478:
1450:
1444:
1443:
1417:
1385:
1379:
1378:
1368:
1327:
1321:
1320:
1302:
1254:
1245:
1244:
1242:
1240:
1234:
1228:. Archived from
1227:
1223:"Surface charge"
1218:
1212:
1207:
1201:
1186:
1177:
1176:
1174:
1173:
1167:
1161:. Archived from
1160:
1151:
1142:
1141:
1139:
1137:
1122:
1116:
1115:
1088:
1042:Depletion region
1003:
1001:
1000:
995:
993:
991:
983:
975:
878:
876:
875:
870:
829:
827:
826:
821:
795:
793:
792:
787:
767:
750:
742:
740:
739:
738:
716:
691:
689:
688:
683:
681:
679:
668:
667:
666:
653:
645:
634:
633:
632:
622:
621:
620:
607:
599:
598:
224:) among the two
158:homogenized milk
36:aqueous solution
21:
2218:
2217:
2213:
2212:
2211:
2209:
2208:
2207:
2188:Surface science
2168:
2167:
2159:
2149:
2128:
2073:
2071:Further reading
2068:
2023:
2019:
1992:Materials Today
1988:
1984:
1968:
1961:
1956:
1952:
1902:
1896:
1892:
1887:
1883:
1844:
1840:
1833:
1819:
1815:
1810:
1801:
1793:
1789:
1780:
1778:
1771:
1755:
1746:
1735:
1731:
1726:
1722:
1717:
1713:
1708:
1704:
1697:
1693:
1687:Wayback Machine
1677:
1673:
1645:
1641:
1604:(1356): 55â79.
1594:
1590:
1551:
1547:
1508:
1504:
1494:
1492:
1486:
1482:
1451:
1447:
1386:
1382:
1328:
1324:
1255:
1248:
1238:
1236:
1232:
1225:
1219:
1215:
1208:
1204:
1187:
1180:
1171:
1169:
1165:
1158:
1152:
1145:
1135:
1133:
1124:
1123:
1119:
1089:
1085:
1081:
1038:
1021:
1007:where Ï is the
984:
976:
974:
966:
963:
962:
948:
942:
913:or solid-state
891:
855:
852:
851:
834:electrophoresis
806:
803:
802:
760:
741:
734:
730:
729:
712:
710:
707:
706:
669:
662:
658:
654:
652:
628:
624:
623:
616:
612:
608:
606:
594:
590:
588:
585:
584:
549:electrophoresis
526:Stern potential
480:
448:
435:ruthenium oxide
427:
418:
400:J. O'M. Bockris
396:
387:solvation shell
373:
344:
332:phosphorylation
324:
276:
202:
197:
147:electrochemical
111:, electrically
45:surface science
28:
23:
22:
15:
12:
11:
5:
2216:
2206:
2205:
2200:
2195:
2190:
2185:
2180:
2166:
2165:
2158:
2157:External links
2155:
2154:
2153:
2147:
2132:
2126:
2111:
2072:
2069:
2067:
2066:
2017:
1982:
1959:
1950:
1890:
1881:
1838:
1831:
1813:
1799:
1787:
1769:
1744:
1729:
1720:
1711:
1702:
1691:
1671:
1639:
1588:
1545:
1518:(3): 441â501.
1502:
1480:
1461:(21â22): 508.
1445:
1400:(7): 2104366.
1380:
1331:(2022-11-19).
1322:
1246:
1213:
1202:
1178:
1143:
1132:on 31 May 2011
1117:
1082:
1080:
1077:
1076:
1075:
1073:Supercapacitor
1070:
1065:
1060:
1055:
1050:
1045:
1037:
1034:
1020:
1017:
1009:surface charge
1005:
1004:
990:
987:
982:
979:
973:
970:
944:Main article:
941:
938:
922:surface charge
890:
887:
880:
879:
868:
865:
862:
859:
819:
816:
813:
810:
785:
782:
779:
776:
773:
770:
766:
763:
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756:
753:
748:
745:
737:
733:
728:
725:
722:
719:
715:
678:
675:
672:
665:
661:
657:
651:
648:
643:
640:
637:
631:
627:
619:
615:
611:
605:
602:
597:
593:
533:zeta potential
519:zeta potential
479:
476:
447:
444:
426:
423:
417:
414:
395:
392:
372:
369:
343:
340:
322:
275:
272:
268:dipole moments
201:
198:
196:
193:
121:thermal motion
93:surface charge
26:
9:
6:
4:
3:
2:
2215:
2204:
2201:
2199:
2196:
2194:
2191:
2189:
2186:
2184:
2181:
2179:
2176:
2175:
2173:
2164:
2161:
2160:
2150:
2144:
2141:. CRC Press.
2140:
2139:
2133:
2129:
2123:
2120:. M. Dekker.
2119:
2118:
2112:
2108:
2104:
2100:
2096:
2092:
2088:
2084:
2080:
2075:
2074:
2062:
2058:
2053:
2048:
2044:
2040:
2036:
2032:
2028:
2021:
2013:
2009:
2005:
2001:
1997:
1993:
1986:
1980:
1976:
1972:
1966:
1964:
1954:
1946:
1942:
1938:
1934:
1930:
1926:
1921:
1916:
1912:
1908:
1901:
1894:
1885:
1877:
1873:
1869:
1865:
1861:
1857:
1853:
1849:
1842:
1834:
1828:
1824:
1817:
1808:
1806:
1804:
1797:
1791:
1777:on 2019-04-28
1776:
1772:
1766:
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1761:
1753:
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1611:
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1603:
1599:
1592:
1584:
1580:
1576:
1572:
1568:
1564:
1560:
1556:
1549:
1541:
1537:
1533:
1529:
1525:
1521:
1517:
1513:
1506:
1491:
1484:
1476:
1472:
1468:
1464:
1460:
1456:
1449:
1441:
1437:
1433:
1429:
1425:
1421:
1416:
1411:
1407:
1403:
1399:
1395:
1391:
1384:
1376:
1372:
1367:
1362:
1358:
1354:
1350:
1346:
1342:
1338:
1334:
1326:
1318:
1314:
1310:
1306:
1301:
1296:
1292:
1288:
1284:
1280:
1276:
1272:
1268:
1264:
1260:
1253:
1251:
1231:
1224:
1217:
1211:
1206:
1200:(769 kB)
1199:
1195:
1191:
1185:
1183:
1168:on 2014-12-22
1164:
1157:
1150:
1148:
1131:
1127:
1121:
1114:
1110:
1106:
1102:
1098:
1094:
1087:
1083:
1074:
1071:
1069:
1066:
1064:
1061:
1059:
1056:
1054:
1051:
1049:
1046:
1043:
1040:
1039:
1029:
1025:
1016:
1014:
1011:and Ï is the
1010:
985:
980:
977:
971:
968:
961:
960:
959:
957:
953:
947:
937:
935:
931:
926:
923:
918:
916:
912:
908:
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900:
896:
886:
883:
866:
863:
860:
857:
850:
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845:
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839:
835:
830:
817:
814:
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720:
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641:
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635:
629:
625:
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613:
609:
603:
600:
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591:
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573:
569:
564:
562:
558:
554:
550:
545:
543:
539:
534:
529:
527:
522:
520:
516:
512:
509:
504:
502:
492:
488:
486:
475:
473:
469:
465:
461:
457:
456:Marcus Theory
453:
443:
439:
436:
432:
422:
413:
410:
405:
401:
391:
388:
377:
368:
366:
362:
358:
357:diffuse layer
352:
349:
339:
337:
333:
329:
325:
321:
316:
315:
311:
307:
302:
300:
297:
293:
289:
284:
280:
271:
269:
265:
260:
258:
254:
250:
245:
243:
239:
235:
231:
227:
223:
219:
215:
206:
192:
190:
186:
181:
179:
175:
174:heterogeneous
171:
167:
163:
159:
154:
152:
149:behaviour of
148:
144:
140:
136:
132:
128:
124:
122:
118:
114:
110:
109:Coulomb force
106:
102:
98:
94:
90:
86:
82:
78:
74:
70:
66:
62:
58:
54:
50:
46:
37:
32:
19:
18:Diffuse layer
2137:
2116:
2082:
2078:
2034:
2030:
2020:
1995:
1991:
1985:
1970:
1953:
1910:
1906:
1893:
1884:
1854:(1): 77â89.
1851:
1847:
1841:
1822:
1816:
1790:
1779:. Retrieved
1775:the original
1759:
1738:
1732:
1723:
1714:
1705:
1694:
1674:
1648:
1642:
1601:
1597:
1591:
1558:
1555:ChemPhysChem
1554:
1548:
1515:
1511:
1505:
1493:. Retrieved
1483:
1458:
1454:
1448:
1397:
1393:
1383:
1340:
1336:
1325:
1266:
1262:
1237:. Retrieved
1230:the original
1216:
1205:
1170:. Retrieved
1163:the original
1134:. Retrieved
1130:the original
1120:
1096:
1086:
1063:Nanofluidics
1022:
1006:
955:
949:
930:double layer
927:
919:
898:
894:
892:
884:
881:
846:
842:
831:
800:
797:
705:
700:
696:
693:
583:
579:
576:
571:
568:Debye length
565:
546:
530:
523:
505:
497:
481:
464:Henry Eyring
449:
440:
428:
419:
409:permittivity
404:Klaus MĂŒller
397:
383:
353:
345:
319:
312:
303:
281:in 1910 and
277:
274:GouyâChapman
261:
246:
217:
213:
211:
182:
155:
133:, such as a
125:
75:particle, a
60:
56:
52:
49:double layer
48:
42:
2203:Soft matter
1415:2445/191184
1343:(1): 7100.
1269:(1): 5157.
1048:DLVO theory
310:cytochromes
166:coagulation
139:micrometres
127:Interfacial
85:porous body
79:, a liquid
2172:Categories
2037:(1): 399.
1920:2106.03411
1781:2010-01-15
1172:2012-12-10
1079:References
508:tangential
363:, assumes
348:Otto Stern
264:adsorption
214:electronic
151:electrodes
143:nanometres
99:which are
77:gas bubble
2107:0021-9606
2012:189987682
1626:2053-9169
1575:1439-4235
1532:0009-2665
1475:138033996
1440:244922892
1424:1613-6810
1291:2041-1723
989:Ψ
981:σ
911:solutions
858:κ
815:≫
809:κ
775:−
765:κ
762:−
755:
732:Ψ
714:Ψ
660:Ψ
650:
626:ε
614:ε
604:−
592:σ
398:In 1963,
361:Coulombic
328:screening
242:molecular
228:appears.
222:interface
200:Helmholtz
113:screening
2061:31964882
1937:25495551
1907:Langmuir
1876:95536100
1683:Archived
1634:94958336
1583:21557434
1540:18895519
1495:23 April
1432:34874621
1375:36402842
1317:54444826
1309:30514833
1136:23 April
1036:See also
907:colloids
531:Usually
238:polarity
212:When an
101:adsorbed
2087:Bibcode
2052:6972942
1945:4697498
1856:Bibcode
1653:Bibcode
1606:Bibcode
1366:9675734
1345:Bibcode
1300:6279779
1271:Bibcode
1101:Bibcode
540:or the
380:solvent
371:Grahame
288:diffuse
257:solvent
234:charged
135:colloid
83:, or a
81:droplet
65:surface
2198:Matter
2145:
2124:
2105:
2059:
2049:
2010:
1998:: 34.
1977:
1943:
1935:
1874:
1829:
1767:
1632:
1624:
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1573:
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1530:
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1438:
1430:
1422:
1373:
1363:
1315:
1307:
1297:
1289:
1239:30 May
1192:
934:plasma
559:, and
511:stress
446:Marcus
425:Conway
226:phases
178:slurry
170:butter
89:charge
2008:S2CID
1941:S2CID
1915:arXiv
1903:(PDF)
1872:S2CID
1796:(pdf)
1630:S2CID
1471:S2CID
1436:S2CID
1394:Small
1313:S2CID
1233:(PDF)
1226:(PDF)
1166:(PDF)
1159:(PDF)
342:Stern
218:ionic
168:into
73:solid
69:fluid
2143:ISBN
2122:ISBN
2103:ISSN
2057:PMID
1975:ISBN
1933:PMID
1827:ISBN
1765:ISBN
1622:ISSN
1579:PMID
1571:ISSN
1536:PMID
1528:ISSN
1497:2013
1428:PMID
1420:ISSN
1371:PMID
1305:PMID
1287:ISSN
1241:2011
1190:ISBN
1138:2013
893:The
864:<
647:sinh
359:are
317:and
187:and
119:and
97:ions
47:, a
2095:doi
2047:PMC
2039:doi
2000:doi
1925:doi
1864:doi
1661:doi
1614:doi
1602:274
1563:doi
1520:doi
1463:doi
1410:hdl
1402:doi
1361:PMC
1353:doi
1295:PMC
1279:doi
1109:doi
932:in
899:EDL
752:exp
517:or
466:'s
162:fat
141:to
61:EDL
43:In
2174::
2101:.
2093:.
2083:33
2081:.
2055:.
2045:.
2035:11
2033:.
2029:.
2006:.
1996:30
1994:.
1962:^
1939:.
1931:.
1923:.
1911:30
1909:.
1905:.
1870:.
1862:.
1852:11
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1747:^
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1628:.
1620:.
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1600:.
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1469:.
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1369:.
1359:.
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1339:.
1335:.
1311:.
1303:.
1293:.
1285:.
1277:.
1265:.
1261:.
1249:^
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1181:^
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936:.
917:.
563:.
555:,
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454:.
338:.
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180:.
153:.
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2130:.
2109:.
2097::
2089::
2063:.
2041::
2014:.
2002::
1947:.
1927::
1917::
1878:.
1866::
1858::
1835:.
1784:.
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1663::
1655::
1636:.
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1542:.
1522::
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1273::
1267:9
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1175:.
1140:.
1111::
1103::
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978:d
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969:C
956:C
897:(
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778:a
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758:(
747:r
744:a
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721:r
718:(
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677:T
674:R
671:2
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642:T
639:R
636:C
630:m
618:0
610:8
601:=
596:d
572:C
323:1
320:c
314:c
51:(
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
