Potentiometric sensors

Potentiometric sensors have been traditionally defined as a zero current method and the most extensively used in practical applications for many decades due to their simplicity, low cost, great selectivity and sensitivity.^5–8 There

are three general groups of potentiometric devices; i) ion-selective electrodes (ISEs), ii) coated wire electrodes (CWEs) and iii) field effect transistors (FETs).⁹ While the ISEs based on different matrices, potentiometric sensors based on polymeric or liquid membrane materials are the most widely used as the sensing layer, which physically separates the liquids between an aqueous inner filling solution and sample solution. The ion-selective membranes (ISMs) are employed in the polymeric membrane (e.g. poly(vinylchloride) (PVC)^10–12, polyurethanes (PU)^13–15, polystyrene (PS)^16,17, silicone rubbers^18,19) and are utilized to construct the ISE. The ISEs have been widely exploited for being capable of selective ionic species including cations (e.g. potassium, sodium, calcium, pH)^20–25, anions (e.g. chloride, nitrite, nitrate, thiocyanate, bicarbonate/carbonate)20,21,26–29 and polycation (e.g. heparin^30,31 and protamine^32–34). The ISM must be permselective toward the target analyte or primary ion. Examples of the ISEs based on different matrices include the glass membranes for pH measurement, solid state membranes (e.g. LaF3

membrane for fluoride detection), precipitates of insoluble salts in polymer matrices (e.g. AgCl, AgBr, AgI, Ag2S, CuS, CdS, PbS).³⁵ More typically, the polymeric-based ISM contains a selective receptor (ionophore) (e.g.

tridodecylamine for measurement of pH value^36,37, valinomycin for potassium detection), an ionic additive (e.g.

sodium tetrakis[3,5-bis(trifluoromethyl)phenyl]borate (NaTFPB), tridodecylmethylammonium chloride (TDMACl) and a plasticizer (e.g. 2-nitrophenyl octyl ether (o-NPOE), dioctyl sebacate (DOS)). A lipophilic inert electrolyte (e.g. tetradodecylammonium tetrakis(4-chlorophenyl)borate (ETH500)) is alternatively used to reduce membrane resistance³⁸ and improve the selectivity by influence of activity coefficient in the membrane phase.³⁹

Figure 1. Galvanic cell (left), two-electrode system used for potentiometry (right).^7,40,41

The potentiometric technique is based on measuring the potential difference (electromotive force, EMF) between the ISE and a reference electrode (e.g. an Ag/AgCl element, double junction reference electrode (Ag/AgCl/KCl, 3M), Hg/Hg2Cl2).⁴¹ The potential at the reference electrode must be constant and independent of sample concentration/composition. This is based on a galvanic cell, where the reactions spontaneously occur at the electrodes when they are externally coupled by a conductor (Figure 1, left).⁴¹ A determination in potentiometry is conducted in a two electrode galvanic cell under zero current conditions. Potentiometric sensors basically contain the ISE (cathode, indicator electrode) and reference electrode (anode) (Figure 1, right).^7,8 The potential difference at the membrane/sample interface is measured using a high impedance voltmeter in order to ensure there is no

current flow in the electrochemical cell.^7,8,40,41 Since the potential of the reference electrode remains constant, the potential difference (cell potential) is correlated to the activity of the target analyte or the ion of interest. The ideal relationship between the EMF response and the ion activity is described by the Nernst equation (eq. 1)^7,8,41 as shown below:

𝐸!= 𝐸^"+_%^#$

!&𝑙𝑛𝑎! eq. 1

where Ei is the potential or EMF readout. R, T and F are the universal gas constant (8.314 J mol^-1 K^-1), absolute temperature (K) and the Faraday constant (96,485 C mol^-1), respectively. ai is an activity of primary ion i in sample solution, zi is a charge of the primary ion i, E⁰ is a constant potential value. At room temperature (298 K), eq. 1 may be written as follows (eq. 2):

𝐸!= 𝐸^"+_%^'

!𝑙𝑜𝑔𝑎! eq. 2

where s is the Nernstian slope, typically is 59.2 mV for monovalent cation and 29.6 mV for divalent cation in the absence of interfering ion. If the sample contains other interfering ions with the same charge as the primary ion, these ions may be replaced the primary ion in the ion-selective membrane.^7,8 This results in a deviation from the Nernstian equation. The Nicolsky equation is used as extension of eq. 2 to describe this behavior, as shown in eq.

3.^7,8,40

𝐸_!= 𝐸^"+_%^'

!𝑙𝑜𝑔)𝑎_!+ ∑_)-!𝐾_!,)^*+,𝑎₎, eq. 3 where 𝐾_!,)^*+, is the selectivity coefficient. ai and aj are the activities of primary ion i and interfering ion j in the mixed sample solution, respectively. The smaller value of 𝐾_!,)^*+, gives better selectivity of the primary ion over the interfering ion. If the primary and interfering ion have different charges. The eq. 3 is expanded in a semi-empirical manner and to describe the potential change. Eq. 4 is called the Nicolsky-Eisenman equation:^7,8,40

𝐸!= 𝐸^"+_%^'

!𝑙𝑜𝑔 -𝑎!+ ∑)-!𝐾_!,)^*+,𝑎₎^%!/%". eq. 4 The most important characteristic of ISEs is its selectivity. The selectivity coefficients can be measured experimentally by the separate solution method (SSM) and the fixed interference method (FIM) method. The SSM requires individual calibration curves of primary and interfering ion in separate solutions. The selectivity coefficient is calculated by using potential readouts and two activities of primary and interfering ions, which lie on the Nernstian slope of each curve. The selectivity coefficient can be measured based on Nicolski equation, which may be written as shown by eq. 5.^7,40,42

𝐾_!,)^*+,= −^%!/0!_'^10"2+ 𝑙𝑜𝑔 ^3!

3_"^#!/#" eq. 5

Figure 2. Measurement of upper and lower detection limits of the ion-selective electrode, according to the IUPAC recommendations.⁴³

The FIM, however, is the technique where the calibration curve of the primary ion is established in a fixed concentration of interfering ion in the sample solution. The selectivity coefficient can be obtained from the lower detection limit (LDL) of the calibration curve. According to the recommendation of the IUPAC, the lower or upper detection limits are given by the intersection of the two extrapolated linear segments of the calibration curve (Figure 2).^7,42,43

𝐾_!,)^*+, =^3!(565)

3_"^#!/#" eq. 6

The lowest detection limit of the polymeric membrane-based ISEs is often observed around 1 µM.^7,44–46 This may be caused by limited selectivity or because the ion flux in the inner filling solution (e.g. 10 – 100 mM primary ion) is introduced to the membrane side, resulting in the primary ion leaching into the sample solution. This can be improved by using a small amount of ion exchange in the membrane, which may be the origin of the primary ion leaching into the sample⁴⁷ and using a diluted concentration of the primary ion in the inner filling solution or with ion buffers.^25,41,44 The primary ion flux can also be reduced by applying a bias current that counteracts the ion flux, which helps to improve the detection limit to ultra-trace levels.⁴⁸ The upper detection limit of the ISEs is defined similarly to the lower detection limit. This may be caused by a breakdown in permselectivity of the ISE membrane (i.e. Donnan exclusion failure).^49–51 An increase of analyte concentration, or an excessive binding affinity between ionophore and analyte, increases the concentration of complexed ionophores in the membrane. Eventually, the membrane begins to act as ion-exchanger and results in a co-extraction of counter ions into the sensing membrane.