1013:
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.
365:
492:, 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.
194:
1017:
20:
480:
1012:
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
683:
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
913:
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
430:
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,
395:
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
368:
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
400:
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
378:
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
27:
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
409:
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
426:
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
1319:
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
343:
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
524:
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
373:
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
679:
471:
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
339:
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.
569:
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:
783:
487:
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
274:
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
832:
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.
319:, 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
2151:
1114:
790:
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:
575:
1783:"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
1835:
Jiang, Jingkun; Oberdörster, GĂŒnter; Biswas, Pratim (25 June 2008). "Characterization of size, surface charge, and agglomeration state of nanoparticle dispersions for toxicological studies".
323:, 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
991:
1020:
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.
451:
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
874:
The last model introduces "overlapped DLs". This is important in concentrated dispersions and emulsions when distances between particles become comparable with the Debye length.
1542:
Nakamura, Masashi; Sato, Narumasa; Hoshi, Nagahiro; Sakata, Osami (2011). "Outer
Helmholtz Plane of the Electrical Double Layer Formed at the Solid Electrode-Liquid Interface".
251:
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
566:
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.
502:. 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
866:
817:
447:
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
1246:
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).
410:
region of potential could also involve a partial charge transfer between the ion and the electrode. It was the first step towards understanding pseudocapacitance.
697:
233:
dielectric and stores charge electrostatically. Below the electrolyte's decomposition voltage, the stored charge is linearly dependent on the voltage applied.
1118:
1144:
379:
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.
1198:
563:. In aqueous solutions it is typically on the scale of a few nanometers and the thickness decreases with increasing concentration of the electrolyte.
225:
electrodes immersed in electrolyte solutions repel the co-ions of the charge while attracting counterions to their surfaces. Two layers of opposite
307:
104:
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
1211:
2135:
2114:
2016:"Quantifying electron-transfer and ion-transfer in liquid-solid contact electrification and the formation mechanism of electric double-layer"
1967:
1819:
1757:
1182:
460:
1671:
1082:"Ueber einige Gesetze der Vertheilung elektrischer Ströme in körperlichen Leitern mit Anwendung auf die thierisch-elektrischen Versuche"
533:. It is usually determined by the solution pH value, since protons and hydroxyl ions are the charge-determining ions for most surfaces.
439:
The physical and mathematical basics of electron charge transfer absent chemical bonds leading to pseudocapacitance was developed by
280:
229:
form at the interface between electrode and electrolyte. In 1853, he showed that an electrical double layer (DL) is essentially a
787:
There are several asymptotic models which play important roles in theoretical developments associated with the interfacial DL.
448:
1377:
LĂłpezâOrtiz, Manuel; Zamora, Ricardo A.; Giannotti, Marina InĂ©s; Hu, Chen; Croce, Roberta; Gorostiza, Pau (February 2022).
1379:"Distance and Potential Dependence of Charge Transport Through the Reaction Center of Individual Photosynthetic Complexes"
1046:
2171:
279:
model of the DL. In this model, the charge distribution of ions as a function of distance from the metal surface allows
119:
197:
Simplified illustration of the potential development in the area and in the further course of a
Helmholtz double layer.
293:
Gouy-Chapman layers may bear special relevance in bioelectrochemistry. The observation of long-distance inter-protein
1636:
Conway, B.E. (May 1991), "Transition from 'Supercapacitor' to 'Battery' Behavior in
Electrochemical Energy Storage",
1747:
2166:
1056:
1001:
793:
953:
2181:
1151:
826:
541:
517:. Electric potential difference between the fluid bulk and the surface is called the electric surface potential.
513:
The electric potential on the external boundary of the Stern layer versus the bulk electrolyte is referred to as
271:
177:
2176:
940:
934:
503:
473:
364:
316:
237:
173:
101:
674:{\displaystyle \sigma ^{d}=-{\sqrt {{8\varepsilon _{0}}{\varepsilon _{m}}CRT}}\sinh {\frac {F\Psi ^{d}}{2RT}}}
1186:
871:
This model can be useful for some nano-colloids and non-polar fluids, where the Debye length is much larger.
489:
456:
392:
353:
320:
909:
The primary difference between a double layer on an electrode and one on an interface is the mechanism of
452:
256:
1707:
Russel, W.B., Saville, D.A. and
Schowalter, W.R. "Colloidal Dispersions", Cambridge University Press,1989
918:
218:
210:
115:
2191:
2075:
1844:
1641:
1594:
1333:
1259:
1089:
899:
526:
297:
through the aqueous solution has been attributed to a diffuse region between redox partner proteins (
93:
1888:
1478:
1218:
1041:
842:
549:
545:
241:
226:
1585:
J. Oâm. Bockris; M. A. V. Devanathan; K. MĂŒllen (1963). "On the structure of charged interfaces".
1996:
1929:
1903:
1860:
1618:
1459:
1424:
1301:
903:
891:
530:
419:
284:
267:
154:
1889:"Scalable Surface Area Characterization by Electrokinetic Analysis of Complex Anion Adsorption"
1784:
1668:
2131:
2110:
2091:
2045:
1963:
1921:
1815:
1753:
1610:
1567:
1559:
1524:
1516:
1499:
Grahame, David C. (1947). "The Electrical Double Layer and the Theory of Electrocapillarity".
1416:
1408:
1359:
1293:
1275:
1178:
440:
294:
287:
1960:
Characterization of liquids, nano- and micro- particulates and porous bodies using Ultrasound
1378:
1248:"Long distance electron transfer through the aqueous solution between redox partner proteins"
315:) that is depleted of cations in comparison to the solution bulk, thereby leading to reduced
2083:
2035:
2027:
1988:
1913:
1852:
1687:
1649:
1602:
1551:
1508:
1451:
1398:
1390:
1349:
1341:
1283:
1267:
1097:
1030:
922:
836:
The opposing "thick DL" model assumes that the Debye length is larger than particle radius:
499:
193:
146:
105:
24:
2186:
1675:
822:
537:
514:
423:
375:
222:
135:
77:
33:
821:
This model offers tremendous simplifications for many subsequent applications. Theory of
2079:
1848:
1645:
1598:
1587:
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
1337:
1263:
1093:
396:
the electric field depending on the charge. This orientation has great influence on the
356:
to be constant throughout the double layer, and that fluid viscosity is constant plane.
2040:
2015:
1354:
1321:
1288:
1247:
1187:
Chapter 2, Electrode/electrolyte interfaces: Structure and kinetics of charge transfer.
1061:
1016:
997:
910:
521:
507:
214:
109:
81:
2066:
Stillinger, Frank H.; Kirkwood, John G. (1960). "Theory of the Diffuse Double Layer".
1698:
Dukhin, S.S. & Derjaguin, B.V. "Electrokinetic Phenomena", J.Willey and Sons, 1974
2160:
2000:
1463:
1428:
1177:
Srinivasan S. (2006) Fuel cells, from Fundamentals to Applications, Springer eBooks,
444:
345:
162:
97:
1864:
1800:
Lyklema, J. "Fundamentals of Interface and Colloid Science", vol.2, page.3.208, 1995
1622:
1305:
1933:
1199:
Electrochemical double-layer capacitors using carbon nanotube electrode structures.
1051:
556:
397:
388:
302:
73:
2125:
2104:
1992:
559:, Îș. It is reciprocally proportional to the square root of the ion concentration
2127:
Principles of Colloid and Surface Chemistry, Third Edition, Revised and Expanded
1036:
324:
127:
2031:
1716:
Kruyt, H.R. "Colloid Science", Elsevier: Volume 1, Irreversible systems, (1952)
1345:
1271:
96:. The second layer is composed of ions attracted to the surface charge via the
1856:
496:
336:
298:
252:
131:
65:
2095:
1614:
1563:
1520:
1412:
1279:
1101:
459:
which was derived for reactions with structural changes. Marcus received the
1946:
Hunter, R.J. "Foundations of Colloid Science", Oxford University Press, 1989
276:
139:
2049:
1979:
Wang, Z.L.; Wang, A.C. (2019). "On the origin of contact electrification".
1925:
1606:
1571:
1555:
1528:
1455:
1420:
1394:
1363:
1322:"Phosphorylation disrupts long-distance electron transport in cytochrome c"
1297:
495:
The diffuse layer, or at least part of it, can move under the influence of
112:
rather than being firmly anchored. It is thus called the "diffuse layer".
1877:
V.S. Bogotsky, Fundamentals of Electrochemistry, Wiley-Interscience, 2006.
19:
778:{\displaystyle {\Psi }(r)={\Psi ^{d}}{\frac {a}{r}}\exp({-\kappa }(r-a))}
230:
89:
1763:
1512:
479:
126:
or porous bodies with particles or pores (respectively) on the scale of
1749:
Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices
1403:
895:
349:
245:
145:
DLs play a fundamental role in many everyday substances. For instance,
123:
69:
53:
2087:
1917:
1654:
165:
fluid-based systems, such as blood, paint, ink and ceramic and cement
166:
158:
1442:
Stern, O. (1924). "Zur Theorie der Elektrolytischen Doppelschicht".
1081:
894:
near a surface, and has a significant influence on the behaviour of
1908:
939:
EDLs have an additional parameter defining their characterization:
1015:
363:
192:
61:
57:
1887:
Hanaor, D.A.H.; Ghadiri, M.; Chrzanowski, W.; Gan, Y. (2014).
1812:
Colloidal dispersions : suspensions, emulsions, and foams
335:
The Gouy-Chapman model fails for highly charged DLs. In 1924,
150:
85:
134:. However, DLs are important to other phenomena, such as the
1678:
Central Electrochemical Research Institute, (November, 2008)
1640:(in German), vol. 138, no. 6, pp. 1539â1548,
1088:(in German), vol. 165, no. 6, pp. 211â233,
1667:
A.K. Shukla, T.P. Kumar, Electrochemistry Encyclopedia,
422:
conducted extensive fundamental and development work on
28:
not explicitly show the negative charges of the surface.
1145:"A survey of electrochemical supercapacitor technology"
205:
conductor is brought in contact with a solid or liquid
684:
yields the following expression for electric potential
255:
onto the surface, and the interaction between solvent
956:
845:
796:
700:
578:
240:
independent from the charge density depending on the
1688:
Rudolph A. Marcus: The Nobel Prize in Chemistry 1992
1669:
Pillars of modern electrochemistry: A brief history
153:droplets are covered with a DL that prevents their
2124:Paul C. Hiemenz; Raj Rajagopalan (18 March 1997).
2014:Lin, S.Q.; Xu, L.; Wang, A.C.; Wang, Z.L. (2020).
985:
860:
811:
777:
688:in the spherical DL as a function of the distance
673:
23:Schematic of the electrical double layer (EDL) in
16:Molecular interface between a surface and a fluid
555:The characteristic thickness of the DL is the
118:DLs are most apparent in systems with a large
184:Development of the (interfacial) double layer
80:surrounding the object. The first layer, the
8:
1173:
1171:
1008:Electron transfer in electrical double layer
986:{\displaystyle C={\frac {d\sigma }{d\Psi }}}
209:conductor (electrolyte), a common boundary (
2106:Principles of Colloid and Surface Chemistry
84:(either positive or negative), consists of
1796:
1794:
1792:
1138:
1136:
76:. The DL refers to two parallel layers of
2039:
1954:
1952:
1907:
1653:
1402:
1353:
1287:
963:
955:
844:
795:
749:
730:
723:
718:
701:
699:
651:
641:
617:
612:
605:
597:
595:
583:
577:
290:away from the surface of the fluid bulk.
1741:
1739:
1737:
478:
18:
1810:Morrison, Ian D.; Ross, Sydney (2002).
1072:
943:. Differential capacitance, denoted as
483:detailed illustration of interfacial DL
248:and the thickness of the double-layer.
1638:Journal of the Electrochemical Society
947:, is described by the equation below:
236:This early model predicted a constant
1814:(2nd ed.). New York, NY: Wiley.
1033:(structure of semiconductor junction)
536:Zeta potential can be measured using
56:of an object when it is exposed to a
52:) is a structure that appears on the
7:
1241:
1239:
890:) is the result of the variation of
898:and other surfaces in contact with
825:is just one example. The theory of
431:intercalation and electrosorption.
977:
720:
702:
648:
14:
1837:Journal of Nanoparticle Research
2068:The Journal of Chemical Physics
1958:Dukhin, A. S. and Goetz, P. J.
510:(also denoted as ζ-potential).
383:Bockris/Devanathan/MĂŒller (BDM)
161:. DLs exist in practically all
1752:. Cambridge University Press.
772:
769:
757:
746:
712:
706:
449:outer sphere electron transfer
221:was the first to realize that
1:
1444:Zeitschrift fĂŒr Elektrochemie
1115:"The electrical double layer"
1086:Annalen der Physik und Chemie
1047:Interface and colloid science
861:{\displaystyle \kappa a<1}
812:{\displaystyle \kappa a\gg 1}
172:The DL is closely related to
1993:10.1016/j.mattod.2019.05.016
281:MaxwellâBoltzmann statistics
120:surface-area-to-volume ratio
2152:The Electrical Double Layer
1210:Ehrenstein, Gerald (2001).
401:the region beyond the OHP.
2208:
2032:10.1038/s41467-019-14278-9
1346:10.1038/s41467-022-34809-1
1272:10.1038/s41467-018-07499-x
1057:Poisson-Boltzmann equation
1002:electric surface potential
932:
917:EDLs are analogous to the
692:from the particle center:
391:, M. A. V. Devanathan and
1857:10.1007/s11051-008-9446-4
1728:Theoretical Microfluidics
827:electroacoustic phenomena
542:electroacoustic phenomena
463:in 1992 for this theory.
178:electroacoustic phenomena
2103:Paul C. Hiemenz (1986).
1674:August 20, 2013, at the
1477:SMIRNOV, Gerald (2011).
1102:10.1002/andp.18531650603
941:differential capacitance
935:Differential capacitance
929:Differential capacitance
878:Electrical double layers
504:electrokinetic potential
474:electrokinetic phenomena
467:Mathematical description
461:Nobel Prize in Chemistry
325:photosynthetic complexes
283:to be applied. Thus the
238:differential capacitance
174:electrokinetic phenomena
60:. The object might be a
1479:"Electric Double Layer"
884:electrical double layer
490:electric surface charge
457:transition state theory
418:Between 1975 and 1980,
354:dielectric permittivity
288:decreases exponentially
92:onto the object due to
46:electrical double layer
1607:10.1098/rspa.1963.0114
1556:10.1002/cphc.201100011
1456:10.1002/bbpc.192400182
1395:10.1002/smll.202104366
1143:Adam Marcus Namisnyk.
1117:. 2011. Archived from
1080:Helmholtz, H. (1853),
1021:
987:
914:potential difference.
862:
813:
779:
675:
484:
370:
198:
29:
2020:Nature Communications
1326:Nature Communications
1252:Nature Communications
1019:
988:
863:
814:
780:
676:
482:
427:electrodes and ions.
367:
272:David Leonard Chapman
219:Hermann von Helmholtz
196:
94:chemical interactions
22:
1746:Kirby, B.J. (2010).
1224:on 28 September 2011
954:
843:
829:is another example.
794:
698:
576:
527:point of zero charge
149:exists only because
2172:Colloidal chemistry
2080:1960JChPh..33.1282S
1902:(50): 15143â15152.
1849:2009JNR....11...77J
1646:1991JElS..138.1539C
1599:1963RSPSA.274...55B
1513:10.1021/cr60130a002
1338:2022NatCo..13.7100G
1264:2018NatCo...9.5157L
1094:1853AnP...165..211H
1042:Electroosmotic pump
904:fast ion conductors
550:electroosmotic flow
546:streaming potential
259:and the electrode.
244:of the electrolyte
242:dielectric constant
106:electric attraction
1726:Bruus, H. (2007).
1022:
983:
892:electric potential
858:
809:
775:
671:
531:iso-electric point
485:
420:Brian Evans Conway
371:
285:electric potential
268:Louis Georges Gouy
199:
30:
2167:Chemical mixtures
2137:978-0-8247-9397-5
2116:978-0-8247-7476-9
2088:10.1063/1.1731401
1968:978-0-444-63908-0
1962:, Elsevier, 2017
1918:10.1021/la503581e
1821:978-0-471-17625-1
1759:978-0-521-11903-0
1655:10.1149/1.2085829
1183:978-0-387-35402-6
981:
738:
669:
633:
441:Rudolph A. Marcus
405:Trasatti/Buzzanca
295:electron transfer
44:, also called an
2199:
2182:Electrochemistry
2141:
2120:
2099:
2074:(5): 1282â1290.
2054:
2053:
2043:
2011:
2005:
2004:
1976:
1970:
1956:
1947:
1944:
1938:
1937:
1911:
1893:
1884:
1878:
1875:
1869:
1868:
1832:
1826:
1825:
1807:
1801:
1798:
1787:
1781:
1775:
1774:
1772:
1771:
1762:. Archived from
1743:
1732:
1731:
1723:
1717:
1714:
1708:
1705:
1699:
1696:
1690:
1685:
1679:
1665:
1659:
1658:
1657:
1633:
1627:
1626:
1582:
1576:
1575:
1550:(8): 1430â1434.
1539:
1533:
1532:
1501:Chemical Reviews
1496:
1490:
1489:
1487:
1485:
1474:
1468:
1467:
1439:
1433:
1432:
1406:
1374:
1368:
1367:
1357:
1316:
1310:
1309:
1291:
1243:
1234:
1233:
1231:
1229:
1223:
1217:. Archived from
1216:
1212:"Surface charge"
1207:
1201:
1196:
1190:
1175:
1166:
1165:
1163:
1162:
1156:
1150:. Archived from
1149:
1140:
1131:
1130:
1128:
1126:
1111:
1105:
1104:
1077:
1031:Depletion region
992:
990:
989:
984:
982:
980:
972:
964:
867:
865:
864:
859:
818:
816:
815:
810:
784:
782:
781:
776:
756:
739:
731:
729:
728:
727:
705:
680:
678:
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672:
670:
668:
657:
656:
655:
642:
634:
623:
622:
621:
611:
610:
609:
596:
588:
587:
213:) among the two
147:homogenized milk
25:aqueous solution
2207:
2206:
2202:
2201:
2200:
2198:
2197:
2196:
2177:Surface science
2157:
2156:
2148:
2138:
2123:
2117:
2102:
2065:
2062:
2060:Further reading
2057:
2013:
2012:
2008:
1981:Materials Today
1978:
1977:
1973:
1957:
1950:
1945:
1941:
1891:
1886:
1885:
1881:
1876:
1872:
1834:
1833:
1829:
1822:
1809:
1808:
1804:
1799:
1790:
1782:
1778:
1769:
1767:
1760:
1745:
1744:
1735:
1725:
1724:
1720:
1715:
1711:
1706:
1702:
1697:
1693:
1686:
1682:
1676:Wayback Machine
1666:
1662:
1635:
1634:
1630:
1593:(1356): 55â79.
1584:
1583:
1579:
1541:
1540:
1536:
1498:
1497:
1493:
1483:
1481:
1476:
1475:
1471:
1441:
1440:
1436:
1376:
1375:
1371:
1318:
1317:
1313:
1245:
1244:
1237:
1227:
1225:
1221:
1214:
1209:
1208:
1204:
1197:
1193:
1176:
1169:
1160:
1158:
1154:
1147:
1142:
1141:
1134:
1124:
1122:
1113:
1112:
1108:
1079:
1078:
1074:
1070:
1027:
1010:
996:where Ï is the
973:
965:
952:
951:
937:
931:
902:or solid-state
880:
841:
840:
823:electrophoresis
792:
791:
719:
696:
695:
658:
647:
643:
613:
601:
579:
574:
573:
538:electrophoresis
515:Stern potential
469:
437:
424:ruthenium oxide
416:
407:
389:J. O'M. Bockris
385:
376:solvation shell
362:
333:
321:phosphorylation
313:
265:
191:
186:
136:electrochemical
100:, electrically
34:surface science
17:
12:
11:
5:
2205:
2203:
2195:
2194:
2189:
2184:
2179:
2174:
2169:
2159:
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2155:
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2147:
2146:External links
2144:
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2121:
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2100:
2061:
2058:
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2006:
1971:
1948:
1939:
1879:
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1758:
1733:
1718:
1709:
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1691:
1680:
1660:
1628:
1577:
1534:
1507:(3): 441â501.
1491:
1469:
1450:(21â22): 508.
1434:
1389:(7): 2104366.
1369:
1320:(2022-11-19).
1311:
1235:
1202:
1191:
1167:
1132:
1121:on 31 May 2011
1106:
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1062:Supercapacitor
1059:
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998:surface charge
994:
993:
979:
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959:
933:Main article:
930:
927:
911:surface charge
879:
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522:zeta potential
508:zeta potential
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384:
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361:
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332:
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257:dipole moments
190:
187:
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110:thermal motion
82:surface charge
15:
13:
10:
9:
6:
4:
3:
2:
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2130:. CRC Press.
2129:
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2109:. M. Dekker.
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1766:on 2019-04-28
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1188:
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1180:
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1172:
1168:
1157:on 2014-12-22
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1000:and Ï is the
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969:
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491:
481:
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475:
466:
464:
462:
458:
454:
450:
446:
445:Marcus Theory
442:
434:
432:
428:
425:
421:
413:
411:
404:
402:
399:
394:
390:
382:
380:
377:
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359:
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351:
347:
346:diffuse layer
341:
338:
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183:
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138:behaviour of
137:
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98:Coulomb force
95:
91:
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1984:
1980:
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1959:
1942:
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1830:
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1764:the original
1748:
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1543:
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1472:
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1226:. Retrieved
1219:the original
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1194:
1159:. Retrieved
1152:the original
1123:. Retrieved
1119:the original
1109:
1085:
1075:
1052:Nanofluidics
1011:
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944:
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919:double layer
916:
908:
887:
883:
881:
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685:
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557:Debye length
554:
535:
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494:
486:
470:
453:Henry Eyring
438:
429:
417:
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398:permittivity
393:Klaus MĂŒller
386:
372:
342:
334:
308:
301:
292:
270:in 1910 and
266:
263:GouyâChapman
250:
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206:
202:
200:
171:
144:
122:, such as a
114:
64:particle, a
49:
45:
41:
38:double layer
37:
31:
2192:Soft matter
1404:2445/191184
1332:(1): 7100.
1258:(1): 5157.
1037:DLVO theory
299:cytochromes
155:coagulation
128:micrometres
116:Interfacial
74:porous body
68:, a liquid
2161:Categories
2026:(1): 399.
1909:2106.03411
1770:2010-01-15
1161:2012-12-10
1068:References
497:tangential
352:, assumes
337:Otto Stern
253:adsorption
203:electronic
140:electrodes
132:nanometres
88:which are
66:gas bubble
2096:0021-9606
2001:189987682
1615:2053-9169
1564:1439-4235
1521:0009-2665
1464:138033996
1429:244922892
1413:1613-6810
1280:2041-1723
978:Ψ
970:σ
900:solutions
847:κ
804:≫
798:κ
764:−
754:κ
751:−
744:
721:Ψ
703:Ψ
649:Ψ
639:
615:ε
603:ε
593:−
581:σ
387:In 1963,
350:Coulombic
317:screening
231:molecular
217:appears.
211:interface
189:Helmholtz
102:screening
2050:31964882
1926:25495551
1896:Langmuir
1865:95536100
1672:Archived
1623:94958336
1572:21557434
1529:18895519
1484:23 April
1421:34874621
1364:36402842
1306:54444826
1298:30514833
1125:23 April
1025:See also
896:colloids
520:Usually
227:polarity
201:When an
90:adsorbed
2076:Bibcode
2041:6972942
1934:4697498
1845:Bibcode
1642:Bibcode
1595:Bibcode
1355:9675734
1334:Bibcode
1289:6279779
1260:Bibcode
1090:Bibcode
529:or the
369:solvent
360:Grahame
277:diffuse
246:solvent
223:charged
124:colloid
72:, or a
70:droplet
54:surface
2187:Matter
2134:
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1999:
1987:: 34.
1966:
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1228:30 May
1181:
923:plasma
548:, and
500:stress
435:Marcus
414:Conway
215:phases
167:slurry
159:butter
78:charge
1997:S2CID
1930:S2CID
1904:arXiv
1892:(PDF)
1861:S2CID
1785:(pdf)
1619:S2CID
1460:S2CID
1425:S2CID
1383:Small
1302:S2CID
1222:(PDF)
1215:(PDF)
1155:(PDF)
1148:(PDF)
331:Stern
207:ionic
157:into
62:solid
58:fluid
2132:ISBN
2111:ISBN
2092:ISSN
2046:PMID
1964:ISBN
1922:PMID
1816:ISBN
1754:ISBN
1611:ISSN
1568:PMID
1560:ISSN
1525:PMID
1517:ISSN
1486:2013
1417:PMID
1409:ISSN
1360:PMID
1294:PMID
1276:ISSN
1230:2011
1179:ISBN
1127:2013
882:The
853:<
636:sinh
348:are
306:and
176:and
108:and
86:ions
36:, a
2084:doi
2036:PMC
2028:doi
1989:doi
1914:doi
1853:doi
1650:doi
1603:doi
1591:274
1552:doi
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1452:doi
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1391:doi
1350:PMC
1342:doi
1284:PMC
1268:doi
1098:doi
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506:or
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151:fat
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