Lecture 21.ppt

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    2 Structure of electrified interface

    1. The electrical double layer

    2. The Gibbs adsorption isotherm

    3. Electrocapillary equation

    4. Electrosorption phenomena

    5. Electrical model of the interface

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    2.1 The electrical double layer

    Historical milestones-The concept electrical double layer Quincke 1862-Concept of to parallel layers of opposite char!es Helmholt" 18#$ and

    Stern 1$2%-Concept of diffuse layer &ouy 1$1'( Chapman 1$1)-*odern model &rahame 1$%#

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    Presently accepted model of the electrical double layer

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    2.2 &ibbs adsorption isotherm

    +efinitions

    G total Gibbs function of the system

    G,G,G- Gibbsfunctions of phases ,,

    Gibbs function of the surface phase :

    G! G " G + G#

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    Gibbs $odel of the interface

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    %oncentration

    &istance

    'urface e(cess

    )ypothetical surface

    The amount of species * in the surface phase+

    n*= n* " n*, n*}

    Gibbs surface e(cess *

    * ! n*s

    surface area

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    Gibbs adsorption isotherm

    %han/e in G brou/ht about by chan/es in T0p0 and n*

    dG!-'dT , dp , d , *dn*

    surface ener/y or needed to create a unit area by cleaa/e

    jinpTj

    jnG

    =

    ,,

    - chemical potential

    dG!-'dT , dp , , *dn*

    dG

    !-'

    dT ,

    dp , , *dn*

    and

    dG! dG "dG + dG}= 'dT , d , , *dn*

    npTA

    G

    ,,

    =

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    &eriation of the Gibbs adsorption isotherm

    dG! -'dT , d , , *dn*

    nte/rate this e(pression at costant T and p

    G! , *n*

    &ifferentiate G

    dG! d, d , n*d*, *dn*

    The first and the last equations are alid if+

    d, n*d*! 6 or

    d ! - *d*

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    &ibbs model of the interface , Summary

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    2.3 The electrocapillary equation

    %u7 / /%l 8%l0 )290: )/ %u77

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    $ ! ;

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    :ippmann equation

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    &ifferential capacity of the interface

    2

    2

    dE

    d

    dE

    dC M

    ==

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    %apacity of the diffuse layer

    Thicness of the diffuse layer

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    2.4 Electrosorption phenomena

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    2.- lectrical properties of the

    interfacen the most simple case ideally polari>able electrode the

    electrochemical cell can be represented by a simple ?% circuit

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    mplication electrochemical cell has a time constant that

    imposes restriction on inesti/ations of fast electrode process

    Time needed for the potential across the interface to reachThe applied alue +

    Ec - potential across the interface

    E - potential applied from an e(ternal /enerator

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    Time constant of the cell

    = ?u%d

    =

    dudu

    cCR

    t

    CR

    EE exp1

    Typical alues ?u!56;%!2; /ies !166s

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    %urrent floin/ in the absence of a redo( reaction nonfaradaic current

    n the presence of a redo( reaction faradaic impedance is connected in parallel

    to the double layer capacitance. The scheme of the cell is+

    The oerall current floin/ throu/h the cell is +

    i ! if, inf

    9nly the faradaic current ifcontains analytical or inetic information