# Properties of the Iron Bacteria Biofouling on Ni-P-rGO Coating
## 4 Discussion  
Though there have been some reports about iron bacteria biofouling on electroless plating coatings, their reaction mechanisms have rarely been discussed [4; 5]. [PERSON] et al. [18] stated that there were four interaction energy components that were involved in the mechanism: the interaction between the bacteria and the substrate, the one between the bacteria and the solution, the one between the substrate and the solution, and biofouling adhesion, which consists of the combination of the three interactions, \(\Delta E_{132}^{TOT}\). In other words, bacterial adhesion occurs if the total interaction energy \(\Delta E_{132}^{TOT}\) is negative; furthermore, with the decrease of the \(\Delta E_{132}^{TOT}\) value, bacterial adhesion increases. \[\Delta E_{132}^{TOT}\ =\ \Delta E_{132}^{LW}+\Delta E_{132}^{EL}+\Delta E_{132}^{ AB}+\Delta E_{132}^{Br} \tag{6}\]  
From Equation (6), it can be seen that the four kinds of interaction energy among bacteria (1), substrates (2) and solutions (3) are the Lifshitz-van der Waals (LW) component, the electrostatic double-layer (EL) component, the Lewis acid-base component (AB), and the Brownian motion (Br) component. The four kinds of interaction energies are calculated as follows, respectively:  
\[\Delta E_{132}^{LW}\ =\ -\frac{24\pi H_{0}^{2}\Big{(}\sqrt{\gamma_{1}^{LW}}- \sqrt{\gamma_{3}^{LW}}\Big{)}\Big{(}\sqrt{\gamma_{2}^{LW}}-\sqrt{\gamma_{3}^ {LW}}\Big{)}R}{6H} \tag{7}\]  
\[\Delta E_{132}^{EL}\ =\ \pi\varepsilon_{0}\cdot\varepsilon_{r}R\cdot\Big{(} \zeta_{1}^{2}+\zeta_{2}^{2}\Big{)}\times\Bigg{[}\frac{2\zeta_{1}\cdot\zeta_{2 }}{\zeta_{1}^{2}+\zeta_{2}^{2}}\cdot ln\frac{1+\exp(\kappa\cdot H)}{1-\exp( \kappa\cdot H)}+ln[1-exp(-2\cdot\kappa\cdot H)]\Bigg{]} \tag{8}\]  
\[\Delta E_{132}^{AB}\ =\ 2\Big{[}\sqrt{\gamma_{3}^{+}}\Big{(}\sqrt{\gamma_{1}^{ -}}+\sqrt{\gamma_{2}^{-}}-\sqrt{\gamma_{3}^{-}}\Big{)}+\sqrt{\gamma_{3}^{-}} \Big{(}\sqrt{\gamma_{1}^{+}}+\sqrt{\gamma_{2}^{+}}-\sqrt{\gamma_{3}^{+}}\Big{)} -\sqrt{\gamma_{1}^{+}\gamma_{2}^{-}}-\sqrt{\gamma_{1}^{-}\gamma_{2}^{+}}\Big{]} \tag{9}\]  
\[\Delta E_{132}^{Br}\ =\ 0.414\times 10^{-20}J \tag{10}\]  
where \(\gamma^{LW}\), \(\gamma^{-}\), and \(\gamma^{+}\) are the surface energy components of the Lifshitz-van der Waals forces, the electron-acceptor, and the electron-donor, which can be calculated via the contact angles; \(H\), which is the separation distance between the bacteria and the substrate [20], is assumed to be around 4 nm; \(H_{0}\) is the minimum equilibrium distance and is 0.157 nm [20]; \(R\) is the radius of the bacteria and is 0.65 \(\upmu\)m [20]; \(\varepsilon_{0}\) is the electrical permittivity under the vacuum and is \(8.85\times 10^{-12}\) J\(\cdot\)m\({}^{-2}\).V\({}^{-2}\); \(\varepsilon_{r}\) is the relative dielectric permittivity of water, which is 78.54 [20]; \(\kappa\) is the Debye-Huckel parameter (with 1/\(\kappa\) = 1.1 nm) [20]; \(\zeta_{1}\) and \(\zeta_{2}\) are the zeta potentials of the bacteria (\(-15\) mV) and substrate (\(-25\) mV), respectively [20]; and \(\lambda\) is the correlation length of the molecules of the liquid medium, which is in the range of 0.2-1.0 nm [20; 30]. Figure 7: Effect of the surface energy component on the weight of the iron bacteria biofouling. According to the experimental and modeling results, \(\Delta E_{132}^{TOT}\) had a high correlation to the ratio of \(\gamma_{2}^{LW}\) to \(\gamma_{2}^{-}\). The ratio of \(\gamma_{2}^{LW}\) to \(\gamma_{2}^{-}\) was defined as the CQ ratio by [PERSON] and [PERSON] [19; 20], and it can be used to estimate whether biofouling more easily deposits. When the \(\gamma_{1}^{LW}\) and \(\gamma_{2}^{LW}\) values are both higher than \(\gamma_{3}^{LW}\), the \(\Delta E_{132}^{TOT}\) value increases with a decreasing CQ ratio.