Modern Trends in the ISEs Theory and Applications
This chapter relates to four modern but already well-developed areas in ISEs: real time and space modeling, trace analysis, ISEs under nonzero current, and electronic tongue. Novel materials used in ISEs are discussed in the respective chapters.
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Modern Trends in the ISEs Theory and Applications
This chapter relates to four modern but already well-developed areas in ISEs: real time and space modeling, trace analysis, ISEs under nonzero current, and electronic tongue. Novel materials used in ISEs are discussed in the respective chapters.
7.1 Real Time and Space Modeling of ISEs The multispecies approximation described in Sect. 4.2.5 was among the first approaches to develop ISE theories using computer simulations of the membrane potential. The multispecies approach is limited to a quasi-steady state of the membrane, see Sect. 4.2.5. More recently, a number of attempts have been made aimed at description of the membrane potential in the real time and space. Morf invented a model describing the propagation of ions within an ionophore-based membrane [1]. This description does not account for the non-compensated charges in the double layer at the interface. More advanced theory is developed in Lewenstam’ group [2–7]. This theory does not rely on equilibrium nor on steady state. The core of the Lewenstam’ theory is the numerical solution of the system of the Nernst–Planck and the Poisson equations: oCk ðx; tÞ F Jk ðx; tÞ ¼ Dk zk Ck ðx; tÞ Eðx; tÞ ð7:1Þ ox RT IðtÞ ¼ F
X k
zk Jk ðx; tÞ þ e
oEðx; tÞ ot
ð7:2Þ
Equation (7.1) describes Jk ðx; tÞ the place (x) and time (t)-dependent flux of the species k as a function of Dk ; Ck ðx; tÞ and Eðx; tÞ;—the diffusion coefficient, the species concentration, and the electric field. In Eq. (7.2), the Poisson equation rewritten for IðtÞ the time-dependent total current density, zk stands for the species charge and e for the dielectric permittivity. This allows for tracing the formation of
K. N. Mikhelson, Ion-Selective Electrodes, Lecture Notes in Chemistry 81, DOI: 10.1007/978-3-642-36886-8_7, Ó Springer-Verlag Berlin Heidelberg 2013
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7 Modern Trends in the ISEs Theory and Applications
the boundary and the diffusion potentials in membranes over time and space. Furthermore, the theory provides with guidelines for the optimization of the membrane and of the internal solution compositions for the improvement of the ISE sensitivity. In this way, the theory is applied for the optimization of the membrane and of the internal solution compositions of ISEs for trace analysis (see Sect. 7.2) [6, 7]. The comparative review of different theoretical descriptions of the ISE membrane potential and selectivity is given in [8]. On the other hand, even this very much advanced theory describes the membrane as an ideal system: the species concentration is used instead of activity, the diffusion coefficients are assumed constant, and no local changes of the dielectric permittivity (e.g., close to the interface) are discussed. Furthermore, these advanced theories assume the electrolytes in membranes fully dissociated. Therefore, the effects of the association with membranes, so far, are treated only on the basis of the multispecies approximation described in Sect. 4.5.3.
7.2 ISEs in Trace Analysis For a long time, ISEs c
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