# Progress of Capillary Flow-Related Hydrovoltaic Technology: Mechanisms and Device Applications
## 2 Current Understandings of Capillary Flow-Related Electricity Generation Mechanisms
### Ion Concentration Gradient  
In addition to evaporation-induced electricity, moisture-induced electricity is another category of capillary flow-related photovoltaic technology. A pioneering work in this field demonstrated electric pulses from a graphene oxide film (GOF), yielding an instant peak voltage of 35 mV and a power density of 4.2 mW/m\({}^{2}\)[14]. The mechanism behind this phenomenon, as proposed by the authors, is based on the ion concentration gradient formed within the moisture-absorbing materials (Figure 2a). Briefly, the GOF is modified to exhibit chemical heterogeneity, in this case, a functional group concentration gradient. When the GOF comes into contact with moisture, or sometimes a water droplet, its functional groups, such as hydroxyl (OH) and carboxyl (COOH), are hydrolyzed to release mobile hydrated hydrogen ions (H\({}^{+}\)). These mobile H\({}^{+}\) then move from regions of high ion concentration to low concentration, creating a potential difference across the GOF. This potential difference, in turn, builds an electric field in the external circuit, resulting in an electric pulse current. The direction and strength of this current are affected by the type of mobile ions (positive or negative), the internal concentration potential, and the volumetric density of ions. Since the electricity is based on the ion concentration gradient, it naturally ceases once the concentration gradient disappears due to ion movement, thereby forming a pulse signal (Figure 2b-e). This electric pulse generation process can be repeated by allowing the GOF to desorb the water moisture and re-establish the functional group concentration gradient. This moisture-induced power generation can be understood in terms of the change in chemical potential as moisture is absorbed by and desorbed from the materials [14]. When moisture is absorbed, the difference in chemical potential between regions of varying humidity creates a driving force for ion movement. The resulting electric potential is induced by the movement of H\({}^{+}\) ions from regions of high chemical potential (high humidity) to low chemical potential (low humidity). To provide a more quantitative perspective, the thermodynamic equilibrium of this system can be described using the Nernst equation and related thermodynamic relationships. In particular, the diffusion current density (J\({}_{\text{diff}}\)) and drift current density (J\({}_{\text{drift}}\)) can be represented by the following equations:  
\[J_{\text{diff}}=-qD\frac{\text{d}c}{\text{d}x} \tag{3}\]  
\[J_{\text{drift}}=\sigma E_{i} \tag{4}\]  
where \(q\) is the elementary charge, \(D\) is the diffusion coefficient, \(c\) is the ion concentration, \(x\) is the distance along the concentration gradient, and \(E_{i}\) is the induced electric field. When thermodynamic equilibrium is achieved, the total current density becomes zero:  
\[J_{\text{diff}}+J_{\text{drift}}=0 \tag{5}\]  
The resulting induced electric field can be expressed as:  
\[E_{i}=\frac{qD}{\sigma}\frac{\text{d}c}{\text{d}x} \tag{6}\]  
Integrating along the length of the gradient gives the induced voltage:  
\[U_{i}=\int\frac{qD}{\sigma}\frac{\text{d}c}{\text{d}x} \tag{7}\]  
These equations highlight how the gradient in hydrogen ion concentration, driven by the change in chemical potential, results in an electric field and consequently generates electrical power. [PERSON] et al. estimated that the energy conversion efficiency for such a MEET  
Figure 2: Ion concentration gradient mechanism. (**a**) Moisture absorption and desorption induce a hydrated ion movement cycle. (**b**) Instantaneous open\(-\)circuit voltage output. (**c**) Instantaneous shortcircuit current output. (**d**) A closer look at the voltage pulse characteristics corresponding to humidity. (**e**) A closer look at the current pulse output characteristics corresponding to humidity. Both of them demonstrate the close relationship between electricity output and moisture. Reproduced from ref.