Electric Double Layer

Ir. Yunita Sadeli, Msc Ahmad Ivan Karayan, ST, MengGhiska Ramahdita, ST

Department of Metallurgy and Materias EngineeringUniversity of Indonesia

yunce@metal.ui.ac.id ivan@metal.ui.ac.id ghiska@metal.ui.ac.id

OutlineOutline

IntroIntro Electric Double LayerElectric Double Layer

HelmholtzHelmholtz Gouy-ChapmanGouy-Chapman SternStern GrahameGrahame Bockris, MullerBockris, Muller

MekanismeMekanisme TermodinamikaTermodinamika

Logam - LarutanLogam - LarutanLogam – larutan Logam – larutan Listrik ?? Listrik ?? Diberi perbedaan potensial listrik dari luarDiberi perbedaan potensial listrik dari luar Absorbsi ion pada permukaan logam / arbsorpsi dari permukaan koloidAbsorbsi ion pada permukaan logam / arbsorpsi dari permukaan koloid Perpindahan elektron antara konduktor logam dan elektrolitPerpindahan elektron antara konduktor logam dan elektrolit Ionisasi gugus fungsionalIonisasi gugus fungsional

Kontak lingkungan perbedaan afinitas elektron muatan pada permukaan elektroda special structure = EDL

Electric Double LayerElectric Double Layer Model Helmhotz, beda potensial antara titik tertentu di LRL dgn fasa Model Helmhotz, beda potensial antara titik tertentu di LRL dgn fasa

ruah adalah linear, semakin jauh dari elektroda semakin kecil hingga ruah adalah linear, semakin jauh dari elektroda semakin kecil hingga mencapai nol.mencapai nol.

Gouy Chapman, memperhitungkan adanya gerakan termal dari ion-Gouy Chapman, memperhitungkan adanya gerakan termal dari ion-ion.ion.

Stren =Helmholtz dan Guy-Chapman;Stren =Helmholtz dan Guy-Chapman;

Tegangan permukaan, kerapatanTegangan permukaan, kerapatanmuatan dan kapasitasmuatan dan kapasitas

Daerah antarmuka pada suatu larutan adalah Daerah antarmuka pada suatu larutan adalah daerah yang memiliki harga potensial listrik, daerah yang memiliki harga potensial listrik, ΦΦ, , yang berbeda dibandingkan dengan fasa ruahnya.yang berbeda dibandingkan dengan fasa ruahnya.

Terdapat penataan muatan positif dan negatif dimulai dari Terdapat penataan muatan positif dan negatif dimulai dari permukaan permukaan elektroda hingga ke fasa ruah.elektroda hingga ke fasa ruah. Kapasitas lapis Kapasitas lapis ganda adalah kontanta perbandingan antara potensial ganda adalah kontanta perbandingan antara potensial yang diberikan dengan muatan terhadap spesi dalam yang diberikan dengan muatan terhadap spesi dalam daerah antarmuka.daerah antarmuka.

Double layer terdiri dari :Double layer terdiri dari : Inner layer Inner layer yang padat, dimana potensial menurun secara linear yang padat, dimana potensial menurun secara linear

terhadap jarak dari elektrodaterhadap jarak dari elektroda diffuse layer diffuse layer dimana potensial menurun secara eksponen dimana potensial menurun secara eksponen

Besarnya kapasitas lapis ganda pada berbagai potensial Besarnya kapasitas lapis ganda pada berbagai potensial dapat dilakukan dengan teknik impendasi atau pengukuran dapat dilakukan dengan teknik impendasi atau pengukuran elektrokapilaritas. Metoda ini diperkenalkan oleh Lippmann.elektrokapilaritas. Metoda ini diperkenalkan oleh Lippmann.

HelmholtzHelmholtz Keteraturan muatan positif dan negatif, pola teratur & rigid pada kedua Keteraturan muatan positif dan negatif, pola teratur & rigid pada kedua

interfaceinterface Turunnya potensial dari Turunnya potensial dari ΦΦMM ke ke ΦΦSS bersifat linier, dan Cd , H bukan bersifat linier, dan Cd , H bukan

merupakan fungsi potensial yang diterapkan pada elektrodamerupakan fungsi potensial yang diterapkan pada elektroda

Model Helmholtz untuk lapis rangkap listrik. (a) penataan ion secara kaku. (b) Variasi potensial elektrostatik sebagai fungsi dari jarak (c)variasi Cd terhadap potensial yang di berikan.

Kekurangan dari model Helmholtz Kekurangan dari model Helmholtz pada model ini interaksi ion-ion yang terletak lebih jauh pada model ini interaksi ion-ion yang terletak lebih jauh

tidak diperhitungkantidak diperhitungkan faktor konsentrasi tidak ikut diperhitungkan.faktor konsentrasi tidak ikut diperhitungkan.

Helmholtz layer modelHelmholtz layer model

Electrical Double LayerElectrical Double Layer

Gouy-Chapman ModelGouy-Chapman Model

Considers the applied potential and electrolyte concentration influence Considers the applied potential and electrolyte concentration influence the value of the double layer capacity. So the double layer would have the value of the double layer capacity. So the double layer would have variable thickness (diffuse double layer).variable thickness (diffuse double layer).

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Gouy-Chapman ModelGouy-Chapman Model

This model explains why This model explains why measurements of the measurements of the dynamics of electrode dynamics of electrode processes are almost processes are almost always done using a large always done using a large excess of supporting excess of supporting electrolyte. electrolyte.

Electrical Double LayerElectrical Double LayerStern ModelStern Model

Combined the Helmholtz and G-C models – where the double layer Combined the Helmholtz and G-C models – where the double layer was formed by a compact layer of ions next to the electrode and a was formed by a compact layer of ions next to the electrode and a diffuse layer extending into the bulk.diffuse layer extending into the bulk.

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The Stern model of the electrode-The Stern model of the electrode-solution interfacesolution interface

The Helmholtz model The Helmholtz model overemphasizes the overemphasizes the rigidity of the local solution.rigidity of the local solution.

The Gouy-Chapman The Gouy-Chapman model underemphasizes model underemphasizes the rigidity of local solution.the rigidity of local solution.

The improved version is The improved version is the Stern model. the Stern model.

Electrical Double LayerElectrical Double LayerGrahame ModelGrahame Model

Added a third region to the Stern model. An adsorbed ion loses its solvation and Added a third region to the Stern model. An adsorbed ion loses its solvation and bonding is strong. The IHP passes through the center of these ions. The OHP bonding is strong. The IHP passes through the center of these ions. The OHP passes through the center of solvated ions, and the region outside the OHP is passes through the center of solvated ions, and the region outside the OHP is the diffuse region.the diffuse region.

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Electrical Double LayerElectrical Double LayerBockris, Devanathan, and Muller ModelBockris, Devanathan, and Muller Model

Takes into account the physical nature of the interfacial region, i.e. Takes into account the physical nature of the interfacial region, i.e. water also interacts with the electrode. Since solvent concentration is water also interacts with the electrode. Since solvent concentration is much higher than the solute, there must be predominately solvent much higher than the solute, there must be predominately solvent molecules near the interface. Also introduced the shear plane – zeta molecules near the interface. Also introduced the shear plane – zeta potential.potential.

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Models of Interface Charge DistributionModels of Interface Charge Distribution• Helmholtz Model

– Sharp Electrode-Electrolyte interface– No Debye layer ( = 0)– Voltage jump at interface (“dipole layer”)– Constant differential capacitance

• Gouy-Chapman Model– Sharp Electrode-Electrolyte interface– Finite Debye length (“double layer”)– Voltage continuous across interface– “Parabolic” differential capacitance

• Gouy-Chapman-Stern Model– Linear voltage adjacent to electrode–“Parabolic” differential capacitance with “wings”

MekanismeMekanisme

Electrical Double LayerElectrical Double LayerThere is a charge on the metal electrode, qThere is a charge on the metal electrode, qM M and a and a

charge in the solution, qcharge in the solution, qSS. .

This is the electrical double layer. This is the electrical double layer.

The charge density, The charge density, – ( – (C/cmC/cm22))

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To easily understand the structure of theTo easily understand the structure of the EDL, we introduce three types EDL, we introduce three types of ions in the solution; potential-determining, specificallyof ions in the solution; potential-determining, specifically adsorbedadsorbed and and indifferent ions [6]. indifferent ions [6].

Potential-determining ions are adsorbed at the surface directly.Potential-determining ions are adsorbed at the surface directly. Their Their equilibrium distribution between the surface and the solution equilibrium distribution between the surface and the solution determines the surfacedetermines the surface potential relative to potential in bulk solution.potential relative to potential in bulk solution.

Indifferent ions are affected by Coulomb force of the surface charge.Indifferent ions are affected by Coulomb force of the surface charge. Specifically-adsorbed ions are strongly interacted with the surface Specifically-adsorbed ions are strongly interacted with the surface

through all interactionsthrough all interactions other than purely Coulomb forceother than purely Coulomb force

IHP = specifically adsorbed ions, OHP = indifferent ionsIHP = specifically adsorbed ions, OHP = indifferent ions

Simple model that contains two planes.Simple model that contains two planes. One plane = charged surfaceOne plane = charged surface Second plane = layer of adsorbed ionsSecond plane = layer of adsorbed ions No other ions presentNo other ions present e.g. if the surface is negative, the counter ions aree.g. if the surface is negative, the counter ions are cations in a single layercations in a single layer The charge potential drops linearly with distanceThe charge potential drops linearly with distance from the surface. from the surface. Does not work for soils—charged surfaces areDoes not work for soils—charged surfaces are not strong enough to adsorb a monolayer.not strong enough to adsorb a monolayer.

Double Layer

+

+

+

+

+

-

-

electrode electrolyte

+

+

+

+

The influence of net charge decreases with distance and so the number of oppositely charged ions, equaling the number of ions of both charges prevailing electro neutrality.

The difference in potential between the surface of shear plane and electro neutral region of solution is called Zeta potential (ζ), which is given by Helmholtz- Smoluchowski equation. ζ = 4πηu/εr

where η = viscosity of dispersion medium εr = relative permittivity of dispersion medium u = mobility of colloidal particle

Electrical Double LayerElectrical Double LayerInner Layer – solution closest to electrode, adsorbed Inner Layer – solution closest to electrode, adsorbed

ions.ions.

Also called the Also called the compactcompact, , HelmholtzHelmholtz, or , or SternStern Layer Layer

SS = = ii + + dd = - = -MM

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Electrical Double LayerElectrical Double LayerStructure of double layer can effect the rate of Structure of double layer can effect the rate of

electrode processes, since the potential electrode processes, since the potential varies throughout the layers.varies throughout the layers.

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Electrical Double LayerElectrical Double Layer

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The electric potential at the interfaceThe electric potential at the interface

1. Outer potential2. Inner potential3. Surface potential

The potential difference between the points in the bulk metal (i.e. electrode) and the bulk solution is the Galvani potential difference which is the electrode potential discussed in chapter 7.

Length Scales in Length Scales in ElectrochemistryElectrochemistry

a)a) Thickness of Electrode-Electrolyte interfaceThickness of Electrode-Electrolyte interface

b)b) Charge separation distance (Debye layer); related to Charge separation distance (Debye layer); related to concentrations and dielectric constantconcentrations and dielectric constant

c)c) Long range concentration decay length due to Long range concentration decay length due to diffusion/convection in electrolytediffusion/convection in electrolyte

Phase Field ModelPhase Field Model• Add a new phase variable,

and equation • Solve over entire domain:

• Phase field equation• Poisson's equation• Transport equations

• No boundary conditions at interface• Treat complex interface shape / topology changes• Avoid approximations

t,x

concentration

distance

• Phase-Field Model– Diffuse Electrode-Electrolyte interface– Finite Debye length– Differential capacitance appears realistic– Long-range diffusion possible

Electrode Electrolyte

Diffuse Interface

Example of Components in PhasesExample of Components in Phases

• Mole Fractions

• Molar Volume

• Concentrations

• Assume

• Constraint

iX

mii VXC /

i

n

iim XVV

1

SOHSOCu

e

VVVV

V

22

42

1 0

1

/1ei

Si VC

• Ion Charge zi

Electrode is solid solution of CuElectrode is solid solution of Cu+2+2 and interstitial e and interstitial e--.. Electrolyte is aqueous solution of CuElectrolyte is aqueous solution of Cu+2+2, SO, SO44

-2 -2 and Hand H22O.O.

Free EnergyFree Energy

t coefficienenergy gradient field phase

density charge

potential ticelectrosta

species ofion concentrat

field phase

eunit volumper energy free Helmholtz

energy free Helmholtz

22

1,,,

2

Njj

j

V

V

jVj

FCz

jC

f

F

dVCfCF

0.20

0.15

0.10

0.05

0.00

-0.05

/(J

/m2 )

-0.3 -0.2 -0.1 0.0 0.1 0.2°/V

-1.0

-0.5

0.0

0.5

1.0

S/(

C/m

2 )

7

6

5

4

3

Cd/

(F

/m2 )

0.25 mol/L

1 mol/L

Spectral ComputationSpectral Computation

surface energy

surface charge

differential capacitance

Traditional Double-Layer Theory Traditional Double-Layer Theory (Gouy-Chapman)(Gouy-Chapman)

Boltzmannn Distribution

Poisson Equation

C j C j0 exp

z jF RT

Cj zjF N

d2dx 2

ddx

8RTC 0

1/ 2

sinhzF 2RT

for z : z electrolyte

(more generally, there is a first integral …)

•Electrolyte voltage profile

• is the voltage/concentration decay length (Debye length)•Surface energy, surface charge, differential capacitance, etc. all related to voltage across interface, i.e.,

•Nernst relation

Double Layer (cont.)Double Layer (cont.)

tanh zF /4RT tanh zF 0 / 4RT

exp x

2C0z 2F 2

RT

1/ 2

1

0 RT

nFlnCO

CR

S

Ref d

S

C

Ref

Numerical Solution in Outer VariablesNumerical Solution in Outer Variables

Interface width:

= 0.1

/2, /4, /8, /16

Numerical Solution in Inner VariablesNumerical Solution in Inner Variables

Interface width:

, /2, /4, /8, /16