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).
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Abbreviations
- 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
- f i :
-
friction coefficient
- F :
-
Faraday constant
- I :
-
total current density
- i 0 :
-
exchange current density
- J :
-
flux of a solution species
- K ext, K ext,i :
-
extraction coefficient (partition coefficient)
- K’:
-
thermodynamic salt extraction coefficient
- K D :
-
concentration ratio salt extraction coefficient
- K ext, or K i/j :
-
thermodynamic ion exchange constant
- K so :
-
solubility product in terms of ion activities
- K s :
-
solubility product in terms of ion concentrations
- K is :
-
formation constant of an ion pair from ion i and ligand s
- K 0 K + 0 K - 0 :
-
standard surface rate constants for slow “activation” surface transfer processes
- k b :
-
surface rate constant for a slow transfer process
- M:
-
Macdonald’s ratio in Eq. (81)
- p:
-
local osmotic pressure
- R:
-
gas constant
- R ∞, R ∞ R R, R F, :
-
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
- μ0 i,μ0 :
-
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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Buck, R.P. (1984). Electrochemistry of Ion-Selective Electrodes. In: White, R.E., Bockris, J.O., Conway, B.E., Yeager, E. (eds) Comprehensive Treatise of Electrochemistry. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2679-3_3
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