Abstract
In this chapter, we will discuss the formalism of the practically relevant representation of the signals obtained from an “ideal” electrode. We will do this using a macroscopic, thermodynamic approach. We will not go into the microscopic details on why and when the electrodes respond in this particular way, leaving this discussion, and also the discussion of the “real-world electrodes”, which are not that ideal, for subsequent chapters.
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Notes
- 1.
Except of a phase with a gradient of an electrolyte, see Sect. 2.3.
- 2.
Charge number (valency) is an integer indicating the number of elementary charges carried by the species. One elementary charge equals 1.60 × 10−19 C. For instance, an electron carries an electric charge of −1.60 × 10−19 C, and a calcium cation carries an electric charge of +3.20 × 10−19 C, so the respective charge numbers are −1 and +2. Rigorously speaking, we must use term “charge number” to characterize the electric charge of the species. In practice, however, we never do so, and instead of “charge number”, we just say “charge,” like charge of electron is −1 and charge of calcium cation is +2. Therefore, throughout the text, the term “charge” will be used for “charge number.”
- 3.
Due to thermal movement, some random, chaotic charge separation always exists on short distances. However, being averaged over space and time, it produces zero effect.
- 4.
Some local fluctuations and local fluxes always exist except at absolute zero; however, they do not produce any macroscopic effect due to averaging over space and time.
- 5.
This equation appears very different from Eq. 2.11. The difference comes from the procedure of the measurements of the transference numbers. These are performed in a uniform solution (no activity gradients, so \( {{\text{d}\ln a_{I} } \mathord{\left/ {\vphantom {{\text{d}\ln a_{I} } {\text{d}x}}} \right. \kern-0pt} {\text{d}x}} = 0 \)), and the results are normalized to 1 unit of the electric field: \( {{\text{d}}\varphi \mathord{\left/ {\vphantom {{\text{d}\varphi } {\text{d}x}}} \right. \kern-0pt} {\text{d}x}} = 1, \) for example, 1 V/m, or 1 V/cm, or whatever. In fact, this normalization does not really matter because in Eq. 2.28, the respective terms eliminate anyway.
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Mikhelson, K.N. (2013). The Basics of the ISEs. In: Ion-Selective Electrodes. Lecture Notes in Chemistry, vol 81. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36886-8_2
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