Electrochemistry of Ion-Selective Electrodes

  • Richard P. Buck

Abstract

Ion-Selective Electrodes (ISEs) for measurement of activities of species in aqueous and mixed solvents, or partial pressures of dissolved gases in water, are mainly membrane-based devices, involve permselective, ion-conducting materials. The electrodes are generally used in the potentiometric (zero-current) mode, and they superficially resemble classical redox electrodes of Types 0 (inert), 1 (Ag/Ag+), 2 (Ag/AgCl/CP), and 3 (Pb/PbC2O4/ CaC2O4/Ca2+). The latter, while ion selective, depends on a redox couple (electron exchange), rather than solely on ion exchange as the principal origin of interfacial potential differences (pd’s).

Keywords

Permeability Foam Rubber Fluoride Beach 

Auxiliary Notation

A

area

ai

activity of an ion in exterior, bathing solution

a+,a_

activities of cations and anions

aba_

bulk activity in exterior bathing solution where electro-neutrality applies

asa_

“surface” activity as determined by mass transport but outside the space-charge region

asa_

“surface” activity as determined by mass transport but outside the space-charge region

a(0)

activity of a species at a surface within the space-charge region

a(x)

activity of a species as a function of position x

b

parameter in the power-law activity coefficient expression

ci, ck, etc.

concentration of a species in a bathing solution

cs, cs,0, cs,d

bulk species concentration where electroneutrality applies, typically side “0” or “d”

cs, cs,0, cs,d

surface species concentration determined by mass transport, but outside the space-charge region

c’

concentration is equivalent units rather than molar, molal

c(x)

concentration of a species as a function of position x

c+,c_

concentrations of a cation and an anion

Cd,1or CRCF

double-layer capacitance at low frequencies for interfaces contacting permeable and nonpermeable ions. Subscripts R and F are used for time constant expressions involving resistive surface layers and films

C0,ror CW

capacitances, often called “pseudo” for low-frequency time constants involving nonequilibrium and steady-state transport. W is given to the Warburg capacitance

Cgor CB

capacitance, geometric or bulk

d

membrane thickness

D

diffusion coefficient

E

electric field

fi

friction coefficient

F

Faraday constant

I

total current density

i0

exchange current density

J

flux of a solution species

Kext,Kext,i

extraction coefficient (partition coefficient)

K

thermodynamic salt extraction coefficient

KD

concentration ratio salt extraction coefficient

Kext, or Ki/j

thermodynamic ion exchange constant

Kso

solubility product in terms of ion activities

Ks

solubility product in terms of ion concentrations

Kis

formation constant of an ion pair from ion i and ligand s

K0K+0K-0

standard surface rate constants for slow “activation” surface transfer processes

kb

surface rate constant for a slow transfer process

M

Macdonald’s ratio in Eq. (81)

p

local osmotic pressure

R

gas constant

R∞,RRR,RF,

resistances; high frequency, “activation”, surface layer

and Rw

surface film, and Warburg

and R0

dc resistance

s

Laplace transform variable

s

subscript for neutral carrier or univalent anion exchanger

s

temperature

t

transference number

ui,u*i,

mobilities of ions

υi

partial molar volume of an ion

υi

velocity of a species

V,V,c,VDC

cell voltage

x

running distance variable for one-dimensional transport

X

membrane charged sites concentration

z or zi

membrane charged sites concentration

Z

impedance function

δ

Nernst diffusion layer thickness

δ’

Nernst diffusion layer thickness at left membrane interface

δ”

Nernst diffusion layer thickness at right membrane interface

ε

dielectric permittivity = εrε0

ε0

dielectric permittivity of free space (rationalized)

εr

conventional dielectric constant

εr

yi,,y, y mean activity coefficient

k

reciprocal Debye thickness

Ø

local inner potential of a phase

Ø

local inner potential of a phase, specifically bulk where electroneutrality applies

Ø s, Ø b

local inner potential values near the surface but outside the space-charge region, similarly in the bulk A Δ Ø m, Δ Øoverall membrane potential difference

p

space-charge density

ω

frequency in radian/sec

ω

charge with sign for sites

μih μ

chemical potential of a species

μih μ

electrochemical potential of a species

μ0i0

standard chemical potential of a species

т

time cpnstant

т∞ or tB

time constant for the high-frequency bulk transport process

тR or т F

surface rate time constants (from “activation”, surface resistance, or surface film) Bars over symbols indicate quantities for the membrane or metal phase

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Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • Richard P. Buck
    • 1
  1. 1.Department of ChemistryUniversity of North CarolinaChapel HillUSA

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