Biomedical Engineering Reference
In-Depth Information
There are two main factors that infl uence the selectivity of a sensor: limits in dis-
crimination of an interfering ion and upper limits in stability constant of an analyte-
ionophore complex. While an ideal ionophore does not form complexes with interfering
ions, too strong complexation with the primary ion leads to a massive extraction of ana-
lyte into membrane phase coupled with a coextraction of sample counter-ions, known as
Donnan exclusion failure. In such cases, at high activities and lipophilicities of sample
electrolytes,
a
I
(org) increases and a breakdown of membrane permselectivity prevents
the Nernst equation to hold.
Often, however, the PBP model can be used to describe the infl uence of key membrane
parameters on the selectivity with a simplifi ed equation after making certain assumptions.
It is here given for cation-selective electrodes based on neutral carriers [30]:
zz
I
/
⎛
⎞
n
J
⎢
⎥
⎟
⎜
zz
/
zL
nRz
R
(/
)
J
(
β
)
R
I
J
pot
J
T
J
TJ
JL J
n
T
(9)
KK
IJ
IJ
β
n
⎡⎡
⎢
⎥
zL
nRz
(
/
)
I
IL I
n
T
⎝
⎠
I
T
I
TI
where
K
IJ
is the equilibrium constant for the ion exchange between uncomplexed pri-
mary and interfering ions between the sample and organic phase,
β
JL
n
J
are the
overall complex formation constants for ions I and J with stoichiometric factors
n
I
and
n
J
,
L
T
and
R
T
are the total membrane concentrations of ionophore and cation exchanger,
correspondingly. A similar equation may be derived for charged-carrier-based ISEs (not
shown). As the membrane selectivity depends on the concentrations of the carrier and
ionic sites, the modifying effect of the ionophore-ion exchanger ratio can be predicted,
which allows one to tune the selectivity of the sensor when the primary and interfering
ions are of different charge and/or form complexes with ionophores of different stoichi-
ometry. Although ionophores in some cases may simultaneously form complexes of dif-
ferent stoichiometry, making calculations of the optimal ratio much more complicated,
this approach remains useful. For the simplest case where the primary and interfering
ions are of the same charge and form complexes of the same stoichiometry, the selectiv-
ity coeffi cient does not depend on ionophore and ion exchanger concentration and the
selectivity coeffi cient reduces to the equilibrium constant, which can be expressed by:
β
IL
n
I
and
β
β
pot
KK
n
n
JL J
(10)
IJ
IJ
IL I
The selectivity here is directly proportional to complex formation constants and can be
estimated, once the latter are known. Several methods are now available for determina-
tion of the complex formation constants and stoichiometry factors in solvent polymeric
membranes, and probably the most elegant one is the so-called sandwich membrane
method [31]. Two membrane segments of different known compositions are placed into
contact, which leads to a concentration polarized sensing membrane, which is measured
by means of potentiometry. The power of this method is not limited to complex for-
mation studies, but also allows one to quantify ion pairing, diffusion, and coextraction
processes as well as estimation of ionic membrane impurity concentrations.
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