## 2 Theoretical Background  
pH Sensing Aspects: Considerations for Global Industry 4.0 Applications  
The term _Potentia Hydrogenii_, commonly known as pH, was originally proposed by [PERSON] to describe the solution pressure of hydrogen-ions in aqueous solutions. Nowadays, the pH is conceived as a metric to quantify the activity of hydrogen-ions, \(a_{H+}\), in any solution. Mathematically, the pH is defined as shown in Equation (1) [34]:  
\[\mathrm{pH}=-\log a_{H+} \tag{1}\]  
The most common materials utilized for constructing electrochemical pH sensors include: 1. Glass Electrodes, 2. Metal Oxides, 3. Polymer/Carbon, and 4. Metal/Metal Oxide-Metal Composites [35]. The suitability of any of the aforementioned sensors to address global _Industry 4.0_ challenges, including _Vertical Farming_, depends on worldwide availability, accessibility, and cost-efficiency of the constituting materials. Unquestionably, the _Glass Electrode_ is a front-runner by fulfilling the requirements needed for global adoption of pH sensing. Glass electrodes [36], including the well-known _silver \(|\)silver-chloride_ (AgIAgClI) arrangement, implement a two electrode setup. These potentiometric systems consist of working and reference electrodes. Furthermore, the main working concept of these pH sensors relies on measuring equilibrium conditions at the surface of the working electrode. Under equilibrium conditions, _Nernst's Law_, shown in Equation (2) applies, and describes the (half) cell potential in terms of the activity of the electroactive species [37]:  
\[E_{eq}=E^{0}+\left(\frac{\mathrm{R}T}{n\mathrm{F}}\right)\ln\left(\frac{a_{0} }{a_{R}}\right)=E^{0}+2.303\left(\frac{\mathrm{R}T}{n\mathrm{F}}\right)\log \left(\frac{a_{0}}{a_{R}}\right) \tag{2}\]  
where  
\(E_{eq}\) represents the electric potential at equilibrium [V],  
\(E^{0}\) denotes standard potential [V],  
\(\mathrm{R}\) is the universal gas constant; 8.314 [J mol\({}^{-1}\) K\({}^{-1}\)],  
\(T\) represents the temperature [K],  
\(n\) denotes the electrons number,  
\(\mathrm{F}\) is the Faraday constant; 96,485 [C mol\({}^{-1}\)],  
\(a_{0}\) represents the activity of the oxidizing agent,  
\(a_{R}\) denotes the activity of the reducing agent. In a practical setting, on one side of the sensor, the reference electrode is exposed to a well-known and constant solution of hydrogen-ion activity, e.g., a buffer solution. On the other side of the sensor, the electrode is in contact with the pH solution under study. Due to the aforementioned sensor design, the contribution of one (i.e., the reference) of the electrodes is known, and Equation (2) can be rewritten as a function of the pH under study, as expressed in Equation (3):  
\[E=E^{0}-\left(\frac{2.303\times\mathrm{R}T}{n\mathrm{F}}\right)\mathrm{pH} \tag{3}\]  
Detection electronics, signal conditioning and acquisition, as well as wireless communications of the electrical signal are critical aspects in sensing (pH) variables for global VF (and _Industry 4.0_) applications, especially due to the fact that a majority of the (farming) operations occur in places with scarce access to technology. Therefore, the instrumentation required to accurately measure pH for global _Industry 4.0_ applications is far from trivial, requiring accurate characterization of the expected signals and a suitable design that is applicable to the setting where the technology will be implemented. Taking these considerations for global VF applications into account, an accurate characterization of the expected signal is indispensable. For a standard and globally available _silver \(|\)silver-chloride_ reference electrode configuration, the electrochemical redox response is well known (AgIAgClI standard potential being 220 mV [38]) and involves thegeneration of only one electron. Consequently, the relationship between electric potential and pH is linear, and the slope is a function of temperature (refer to Equation (3)).