Insert of
Fig. 3B proposed the possible analysis mechanism scheme of L-lactic acid on the enzyme-free Dy-SCN/FTO PEC electrode. Generally, during the open-circuit potential detection, Fermi energy levels on both sides of the electrode surface are the same since almost no current flows through the surface. That is, the charge is balanced on both sides of the electrode interface. The amount of charge carried by the holes or electrons at the photoelectric semiconductor interface is equal to that carried by the intentionally adsorbed material on the electrode surface (charge shift of polar molecules)
ql =
qs (
ql stands for the amount of charge specifically adsorbed on the semiconductor surface, and
qs is the amount of charge on the semiconductor surface). As the Fermi level inside the semiconductor is higher than that of the solution, part of the electrons move towards the electrode surface. The concentration of the semiconductor carriers on the electrode surface can be calculated according to the formula
pSC =
NA exp[
F(
E −
Efb)/
RT] (
pSC is the concentration of charge carriers at the semiconductor interface,
NA is the total amount of charge carriers inside the semiconductor and it is a constant,
F is Faraday constant,
R represents to the ideal gas constant,
T is the testing temperature, which is 298 K because the laboratory is conducted at room temperature, and
E −
Efb represents the potential drop caused by band bending in the semiconductor). Then the charge amount of the semiconductor surface carrier can be expressed as
qs =
e pSC =
e NA exp[
F(
E −
Efb)/
RT] (
e is the charge of electrons). According to the Freundlich adsorption isothermal equation
Γ =
kf c^(1/
n) (
Γ represents to the amount of adsorbed material on the electrode surface,
kf is the Freundlich adsorption constant, and
n is the adsorption constant of the specific material), the adsorption amount of target molecules on the electrode surface can be calculated according to the concentration of the specific adsorbent in the solution, and the charge of the adsorbent is
ql =
z Γ =
z kf c^(1/
n) (
z is the charge of the adsorbed substance molecule). According to the charge balance, the equation is
e NA exp[
F(
E −
Efb)/(
RT)] =
e pSC =
qs =
ql =
z Γ =
z kf c^(1/
n) and ∆
φ =
E −
Efb = (
RT/
F) ln[
z kf/(
eNA)] + (
RT/
F) ln
c can be obtained (Since the potential drop caused by the bending of the semiconductor energy band is much larger than that in the double layer, the measured value Δ
φ can be considered as
E −
Efb.). When the concentration of the solution is very low, according to the mathematical approximate substitution formula lnx ≈ x, and the constant in the formula is substituted as
a =
RT/
F,
b = (
RT/
F) ln[
zk/(
eNA)], the expression of potential and concentration is ∆
φ =
ac +
b. It can be seen from the derived expression that the photoelectric semiconductor electrode adopts the open-circuit potential method to record the concentration of the target substance (the concentration is low) and the test potential has a linear relationship with the concentration of the analyte. The results obtained in practical performance are in good agreement with the derived expressions.