New trends in ion-selective electrodes - Electrochemical Sensors, Biosensors and Their Biomedical Applications - page 90

simplicity that only sodium and protamine ions may be extracted into the membrane
phase, the relationship between current i is a sum of the fl uxes of sodium, J Na , and
protamine, J PA :

i FA ( J Na z PA J PA ) (12)

where A is the exposed membrane area. Equations for the sensor response function can
be derived on the basis of a steady-state diffusion model similar to that employed for
the theoretical description of the potentiometric polyion-selective electrode [52]. If no
protamine is present in the solution an equation resembling the Nernst equation can
be obtained, but when protamine is present in the sample it will compete with sodium
in the extraction process (Eq. (12)). Assuming that the applied current imposes a fl ux
that is always larger than the fl ux that can be sustained by polycation diffusion alone
and that electromigration is neglected, the sensor response function can be written as
follows [51]:

⎛ ⎞

a

EE RT
F

⎜ ⎟

0 Na

ln (13)

PB

⎛ ⎞

D

δ ⎟

⎜ i

FA

aq,PA

m

z c

PA PA, bulk

D δ

⎝ ⎠

⎝ ⎠

m,Na aq

In comparison to Eq. (11) if the activity of sodium ions is constant for a current pulse
of fi xed duration and magnitude the phase boundary potential is a function of pro-
tamine concentration in the sample.
A baseline potential pulse followed each current pulse in order to strip extracted
ions from the membrane phase and, therefore, regenerated the membrane, making it
ready for the next measurement pulse. This made sure that the potentials are sampled
at discrete times within a pulse that correspond to a δ m that is reproducible from pulse

to pulse. This made it possible to yield a reproducible sensor on the basis of a chemi-
cally irreversible reaction. It was shown that the duration of the stripping period has
to be at least ten times longer than the current pulse [53]. Moreover the value of the
baseline (stripping) potential must be equal to the equilibrium open-circuit potential
of the membrane electrode, as demonstrated in [52]. This open-circuit potential can be
measured prior to the experiment with respect to the reference electrode.
Figure 4.10 shows the applied current (upper plot) and resulting potential (bottom
plot) for a protamine-selective sensor [54]. Upon application of current the observed
potential decreased, indicating the arising diffusion gradient of ions in the membrane.
Sampled potentials that represent the sensor response were obtained as the average
value during the last 100 ms of each current pulse. The observed current during the fol-
lowing baseline potential pulse continuously decreased to zero and was indicative of
ions diffusing back from the membrane into the sample.
This method was further modifi ed to eliminate any excessive iR drop across the ion-
selective membrane when the current was applied. The modifi ed setup (termed pul-
strodes) allows one to set the current to zero after the current pulse and to measure the
potential, which in this mode does not contain any undesirable iR component [55].