Nernstian responses

Myoglobin is a classic example of a protein with a single Fe /Fe redox centre that exhibits a reversible Nernstian response. The kinetics of homogeneous electron transfer are reasonably rapid in a myoglobin system despite the tertiary globin structure surrounding the heme iron. Additionally, the porphyrin 

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Figure 16(a) (O) shows the EMF responses of a 1,2-dichloroethane membrane containing anionic sites (KT/ C1PB). A Nernstian response was obtained. An SHG response to KCl was observed at activities of the latter above 10 M [Fig. 16(b), O]-These results can be interpreted in the same way as for ionophore-incorporated PVC liquid membranes, for which we have shown that the concentration of oriented cation complexes at the liquid-liquid interface can explain both the observed SHG signal and EMF response. The present SHG responses thus suggest primary ion concentration dependent charge separation at the interface of the 1,2-dichloroethane membranes incorporated with ionic sites. 

Sol-gel-derived membranes encapsulating a bis(crown ether) derivative [bis(12-crown-4-ylmethyl) 2-dodecyl-2-methylmalonate] [28] were also fabricated with an initial DEDMS/TEOS ratio of 3 for Na -ISFETs. The Na -ISFETs showed a Nernstian response to Na+ activity changes in the activity range of 1 x 10 " to 1 M and a short response time of 2 s. Employment of a polythiophene interlayer improved the potential instability and the lower detection limit in both of the K - and Na -ISFETs based on the sol-gel-derived membranes with the initial DEDMS/TEOS ratio of 3 (Fig. 8). 

Typical profiles for the potential response of Na -ISFETs based on the sol-gel-derived membranes modified chemically by alkoxysilylated 16-crown-5 (7) and bis(12-crown-4) (11), together with anion excluder (9) show that both of the Na -ISFETs have high sensitivity with a Nernstian response to Na activity changes in wide activity ranges of 3 x 10 to 1 M (Fig. 12). The potential response is quite fast in the Na -ISFETs in spite of the covalent bonding of the neutral carriers to the ion-sensing membranes, as exemplified in the membrane system of the bis(12-crown-4) (11). Some mobility of the chemically bonded neutral carriers can probably be maintained in the present sol-gel-derived membranes. The response time ( 9o) is several seconds for both of the Na -... 

Useful experimental parameters in cyclic voltammetry are (i) the value of the separation of the potentials at which the anodic and cathodic peak currents occur, A = Pia — PiC, and (ii) the half wave potential, 1/2, the potential mid-way between the peak potentials. A value of AE of c. 0.057 V at 25°C is diagnostic of a Nernstian response, such as that shown in Figure 2.87. More generally, if n electrons are transferred from R, then the separation will be 0.057/n V. It should be noted that the expected value for AE of 0.57/nV has no relationship to the usual Nernstian slope of RT/nF = 0.059/n V at 25UC. 

Silver halide and thiocyanate membranes would respond in a similar way to a silver sulphide membrane, Ag+ ions being the mobile species, but by themselves make unsuitable membrane materials. A Nernstian response is, however, retained when they are incorporated into a Ag2S matrix, the membrane behaving as if it were a pure halide or thiocyanate conductor, i.e. 

Figure 4- Response of an lead-selective electrode based on a calix[6]arene hexaphosphene oxide to sequential 10-fold dilutions of a sample solution demonstrating a very rapid Nernstian response down to sub-nanomolar concentrations of lead. The inset shows a linear Nernstian plot is obtained with almost theoretical slope (25.7 mV per decade) down to 10-10 M.

Fig. 18a. 13. Schematic representation of ion-selective electrode selectivity as determined by the separation solution method (SSM). E I) is the potential of the electrode in primary-ion solution and E(J) the electrode potential in the interfering ion solution. Both primaiy and interfering ions show Nernstian response.

In this method, an entire calibration curve is measured for the primary ion in a constant background of interfering ion. aj(BG) is the activity of the constant interfering ion in the background. afiDL) is the low detection limit (LDL) of the Nernstian response curve of the electrode as a function of the primary-ion activity. In the mixed interference method the selectivity is calculated from the following equation ... 

For both methods, a Nernstian response of both interfering ion and primary ion is required [9,67,68]. 

Conversely, the fundamentals for the UDL he on the coextraction of counterions into the membrane therefore, the membrane is no longer permselective (Donnan failure) [9]. Ideally, when the ionophores are saturated by ions, the ion-ionophore complex functions as an ion-exchanger and the membrane shows an anion Nernstian response. The UDL can be estimated from the membrane composition, formation constant and coextraction coefficients obtained from the so-called sandwich membrane method [73]. 

When Afh -a oo, a Nernstian response is obtained. The half-wave potential is equal to the standard potential. Conversely, when Afh —> 0, the electrode electron transfer is irreversible. In the case of a Butler-Volmer kinetic law, the half-wave potential is expressed as... 

In addition to this, and in contrast with the homogeneous case discussed in Section 5.2.2, the diffusion of P and Q is therefore not perturbed by any homogeneous reaction. If, furthermore, the P/Q electron transfer at the electrode is fast and thus obeys Nernst s law, the diffusive contribution to the current in equations (5.11) and (5.12) is simply equal to the reversible diffusion-controlled Nernstian response, idif, discussed in Section 1.2. The mutual independence of the diffusive and catalytic contributions to the current, expressed as... 

In the following section, it is shown that mathematical methods which have been used to interpret adsorption data bias the interpretation towards chemical and electrostatic properties which lead to a significantly sub-Nernstian response this bias arises out of the need for mathematical simplifications, not from physical considerations. 

The fonnation of ion pairs in the membrane thus has no effect on the Nernstian response of the membrane. 

The membrane potential is again given by (3.2.3). Limitation of the Nernstian response occurs in both systems if the analyte contains a salt of with rather hydrophobic anion B , which can dissolve in the membrane to form a further complex. 

Consider a liquid membrane that exhibits a Nernstian response for ions and is immersed in a solution with a K ion activity of flK (5)- A reference calomel electrode is connected with this solution by a saturated KCl liquid bridge. The whole system is depicted schematically in fig. 4.9. The gate voltage, Vq, is given by... 

Characteristics of the fluoride ion-selective electrode The LaFj ISE exhibits Nernstian response to the activity of fluoride ions in the concentration range 1 M to 10" M [31, 53,325]. When the solution is buffered for fluoride ions using ZiO and Th " salts, Baumann [28] has demonstrated that Nernstian response can be obtained down to a free fluoride ion concentration of 10" ° moldm". In solutions with an ionic strength of 2 moldm", the detection limit is 0.2 ppm, i.e. about 10" moldm", while in pure NaF solutions it may be as low as 10" moldm ... 

ISEs with both these groups of systems exhibit Nernstian response to the Ca activity in the range 10" to 10 M in metal buffers with a slope of d isE/d log flca = 0.029 V. They can be used in the presence of 50 mM Na" for down to micromolar concentrations of Ca. The potentials of these ISEs do not depend on the hydrogen ion activity in the pH range 5.5 to 9 [146]. 

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