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Samenvatting
Double layer effects in computational electrochemistry
S. Van Damme, L. Hotoiu, C. Albu, G. Weyns, D. Deconinck, J. Deconinck
Vrije Universiteit Brussel, Research Group SURF Pleinlaan 2, 1050 Brussels, Belgium,
tel.: +32 2 6291820, email: stvdamme@vub.ac.be
INTRODUCTION
The interfacial region between a metal electrode and an electrolyte solution is called the double layer and is depicted in figure 1 (13). Because metals are good conductors, the charge of the metal is located on its surface and gives rise to a surface charge density . Adsorbed ions or molecules form the compact layer. As the thickness of this layer is of molecular dimensions, it can be regarded as a plane with a surface charge density . The total surface charge density is balanced by a charge density distribution in the diffuse layer, the thickness of which is on the order of the Debye length.
Figure 1: Structure of the double layer.
The double layer structure affects the electrode kinetics in two ways. Firstly, when the potential of an electrode is varied, the current that flows is partly consumed to charge the double layer capacity. Secondly, the driving force for the faradaic reactions is the difference between the electrode potential, , and the solution potential at the inner limit of the diffuse layer, (13).
MODEL
The proposed model for computational electrochemistry consists of the balance equations for each dissolved species,
, [1]
and Gauss' law,
. [2]
is the charge number, the diffusion coefficient and the concentration of species . is the massaverage velocity, is the solution potential, the temperature and the permittivity. is Faraday's constant and the ideal gas constant. is the rate of homogeneous reaction and the stoichiometric constant of species in this reaction.
Balance equations are also written for the adsorbed species, but without considering surface diffusion,
, [3]
where is the surface concentration of species .
BOUNDARY CONDITIONS
At an electrode the perpendicular flux is related to the rates of the electrode reactions,
, [4]
where is the external unit normal. The rate of an electrode reaction is assumed to follow ButlerVolmer kinetics (1,2), which may depend on both the volume concentrations and the surface concentrations.
The electric field at the interface is related to the total surface charge density,
. [5]
The compact layer is regarded as a capacitor, such that the surface charge density on the metal is given by
, [6]
where is the specific capacitance and the potential of zero charge. The surface charge density due to adsorbed ions is simply related to the surface concentrations,
. [7]
IMPLEMENTATION
The model consists of two sets of partial differential equations, equations 1 and 2 being defined in the electrolyte solution and equation 3 on the interface. To solve these equations simultaneously, a simulation framework "MuPhyS" that can handle multidomain problems was developed.
APPLICATION
The present model opens the possibility to study electrochemical processes in more detail. As an example, the VolmerHeyrovskýTafel mechanism of hydrogen evolution from acidic electrolyte solutions is simulated on a rotating disc electrode for different hypothetical kinetic constants reflecting different types of metals.
REFERENCES
1. J. Newman, K. E. ThomasAlyea, Electrochemical Systems, 3rd ed., John Wiley & Sons, 2004.
2. J. O'm. Bockris, A. K. N. Reddy, Modern Electrochemistry. An Introduction to an Interdisciplinary Area, Vol. 2, Springer, 1995.
3. A. Frumkin, Zeitschrift für physikalische Chemie, 164, 121 (1933).
S. Van Damme, L. Hotoiu, C. Albu, G. Weyns, D. Deconinck, J. Deconinck
Vrije Universiteit Brussel, Research Group SURF Pleinlaan 2, 1050 Brussels, Belgium,
tel.: +32 2 6291820, email: stvdamme@vub.ac.be
INTRODUCTION
The interfacial region between a metal electrode and an electrolyte solution is called the double layer and is depicted in figure 1 (13). Because metals are good conductors, the charge of the metal is located on its surface and gives rise to a surface charge density . Adsorbed ions or molecules form the compact layer. As the thickness of this layer is of molecular dimensions, it can be regarded as a plane with a surface charge density . The total surface charge density is balanced by a charge density distribution in the diffuse layer, the thickness of which is on the order of the Debye length.
Figure 1: Structure of the double layer.
The double layer structure affects the electrode kinetics in two ways. Firstly, when the potential of an electrode is varied, the current that flows is partly consumed to charge the double layer capacity. Secondly, the driving force for the faradaic reactions is the difference between the electrode potential, , and the solution potential at the inner limit of the diffuse layer, (13).
MODEL
The proposed model for computational electrochemistry consists of the balance equations for each dissolved species,
, [1]
and Gauss' law,
. [2]
is the charge number, the diffusion coefficient and the concentration of species . is the massaverage velocity, is the solution potential, the temperature and the permittivity. is Faraday's constant and the ideal gas constant. is the rate of homogeneous reaction and the stoichiometric constant of species in this reaction.
Balance equations are also written for the adsorbed species, but without considering surface diffusion,
, [3]
where is the surface concentration of species .
BOUNDARY CONDITIONS
At an electrode the perpendicular flux is related to the rates of the electrode reactions,
, [4]
where is the external unit normal. The rate of an electrode reaction is assumed to follow ButlerVolmer kinetics (1,2), which may depend on both the volume concentrations and the surface concentrations.
The electric field at the interface is related to the total surface charge density,
. [5]
The compact layer is regarded as a capacitor, such that the surface charge density on the metal is given by
, [6]
where is the specific capacitance and the potential of zero charge. The surface charge density due to adsorbed ions is simply related to the surface concentrations,
. [7]
IMPLEMENTATION
The model consists of two sets of partial differential equations, equations 1 and 2 being defined in the electrolyte solution and equation 3 on the interface. To solve these equations simultaneously, a simulation framework "MuPhyS" that can handle multidomain problems was developed.
APPLICATION
The present model opens the possibility to study electrochemical processes in more detail. As an example, the VolmerHeyrovskýTafel mechanism of hydrogen evolution from acidic electrolyte solutions is simulated on a rotating disc electrode for different hypothetical kinetic constants reflecting different types of metals.
REFERENCES
1. J. Newman, K. E. ThomasAlyea, Electrochemical Systems, 3rd ed., John Wiley & Sons, 2004.
2. J. O'm. Bockris, A. K. N. Reddy, Modern Electrochemistry. An Introduction to an Interdisciplinary Area, Vol. 2, Springer, 1995.
3. A. Frumkin, Zeitschrift für physikalische Chemie, 164, 121 (1933).
Originele taal2  English 

Titel  The 219th ECS meeting 
Status  Published  3 mei 2011 
Evenement  Unknown  Duur: 3 mei 2011 → … 
Conference
Conference  Unknown 

Periode  3/05/11 → … 
Vingerafdruk
Duik in de onderzoeksthema's van 'Double Layer Effects in Computational Electrochemistry'. Samen vormen ze een unieke vingerafdruk.Projecten
 1 Afgelopen

GOA57: An integrated experimental and modelling approach for the reliable determination of characteristic electrochemical parameters.
Hubin, A., Deconinck, J., Tourwe, E., Van Damme, S., De Wilde, D. & Albu, C.
1/01/08 → 31/12/12
Project: Fundamenteel

The 219th ECS Meeting
Eugen Lucian Hotoiu (Speaker)
1 mei 2011 → 5 mei 2011Activiteit: Talk or presentation at a conference

The 219th ECS Meeting
Steven Van Damme (Speaker)
1 mei 2011 → 5 mei 2011Activiteit: Talk or presentation at a conference

The 219th ECS Meeting
LeventeCsaba Abodi (Participant)
1 mei 2011 → 5 mei 2011Activiteit: Participation in conference