Physical Chemistry Third Edition

13.5 Nonequilibrium Electrochemistry 597

other and move to the surface of the electrode in order to be as far from each other

as possible. Similarly, any excess positive charges will be found at the surface of

a positively charged electrode. Ions and neutral molecules can be adsorbed on an

electrode surface. Adsorbed ions are divided into two classes. If an ion is adsorbed

directly on the surface, it is said to bespecifically adsorbed. Specifically adsorbed

ions are generally adsorbed without a complete “solvation sphere” of attached solvent

molecules. Every electrolyte solution contains at least one type of cation and one type

of anion, and the cations will generally not be adsorbed to the same extent as the anions,

so that adsorbed ions contribute to the charge at the surface. In addition to specifically

adsorbed ions, a charged electrode surface will attract an excess of oppositely charged

ions in the solution near the electrode. Thesenonspecifically adsorbed ionsare fully

solvated and will not approach so closely to the surface as specifically adsorbed ions.

The region near an electrode surface thus contains two layers of charge. The electrode

surface (including specifically adsorbed ions) has a charge of one sign. This charge

attracts a more diffuse layer of ions of the opposite charge, as shown schematically in

Figure 13.14a. These two regions are called theelectrical double layeror sometimes

thediffuse double layer. The layer of specifically adsorbed ions is called thecompact

layer, theinner Helmholtz layer, or theStern layer. The location of the nonspecifically

adsorbed ions is sometimes called theouter Helmholtz planeor theGuoy plane.

Guoy and Chapman developed a theory of the charge distribution in the double layer

about 10 years before Debye and Hückel developed their theory of ionic solutions, which

is quite similar to it.^29 If one neglects nonelectrostatic contributions to the potential

energy of an ion of typeiwith valencezi, the concentration of ions of typeiin a region

of electric potentialφis given by the Boltzmann probability formula, Eq. (9.3-41):

cici 0 e−zieφ/kBTci 0 e−ziF φ/RT (13.5-1)

whereciis the concentration of ions of typeiand whereci 0 is the concentration at a

location whereφ0. In the second version of the equation,Fis Faraday’s constant,

equal toNAve96485 C mol−^1.

Guoy and Chapman combined Eq. (13.4-1) with the Poisson equation of electro-

statics and found that if the potential is taken equal to zero at large distances, the electric

potential in the diffuse double layer is given as a function ofx, the distance from the

electrode, by

φφ 0 e−κx (13.5-2)

whereφ 0 is the value of the potential at the surface of the electrode. The parameterκ

is given by

κe

(

2 NAvρ 1 I

εkBT

) 1 / 2

(13.5-3)

whereεis the permittivity of the solvent,ρ 1 is the density of the solvent,Iis the

ionic strength as defined in Chapter 7,eis the charge on a proton,kBis Boltzmann’s

constant, andTis the absolute temperature. Figure 13.14b shows this potential as a

function of distance from the electrode surface for an ionic strength of 0.010 mol kg−^1

and a temperature of 298.15 K. TheDebye lengthis defined equal to 1/κ.Itisthe

distance from the surface of the electrode to the location at which the potential is

equal to 1/e(about 0.368) of its value at the surface and is a measure of the effective

thickness of the diffuse double layer.

(^29) G. Guoy,J. Phys. (Paris), 9 , 457 (1910); D. L Chapman,Phil. Mag., 25 , 475 (1913).