# The Role of Surface Texture on the Photocatalytic H\({}_{2}\) Production on TiO\({}_{2}\)
## 1 Introduction
### Semantics and Thermodynamics  
Many different processes can be listed under the banner of hydrogen photoproduction. First, considerations about the reaction products suggest a subdivision into two main groups: (_i_) hydrogen production via water photosplitting, where O\({}_{2}\) is the product of the anodic semireaction; (_ii_) hydrogen production via photoreforming, where CO\({}_{2}\) instead of O\({}_{2}\) is yielded. The reaction involved in (_i_), for liquid and vapor water, is associated to a positive Gibbs free energy variation [6]:  
\[2\;\mathrm{H}_{2}\mathrm{O}_{\mathrm{(I)}}\to 2\;\mathrm{H}_{2\mathrm{(g)}}+ \mathrm{O}_{2\mathrm{(g)}}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \Delta\mathrm{G}^{0}=237\;\mathrm{kJ}\;\mathrm{mol}^{-1} \tag{1}\]  
\[2\;\mathrm{H}_{2}\mathrm{O}_{\mathrm{(g)}}\to 2\;\mathrm{H}_{2\mathrm{(g)}}+ \mathrm{O}_{2\mathrm{(g)}}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; \Delta\mathrm{G}^{0}=229\;\mathrm{kJ}\;\mathrm{mol}^{-1} \tag{2}\]  
This means that the reaction is not spontaneous at room temperature, but requires a significant energy input, which can be chemical, electrochemical or electromagnetic (Figure 1). To perform water photosplitting, the energy required will be provided in the form electromagnetic energy, i.e., light. Considering that two electrons are required to oxidize one water molecule to O\({}_{2}\), the energy required is to be delivered by two photons, then the minimum photon energy will be 1.23 eV, i.e., \(\approx\)1010 nm:  
\[\textit{photon energy}\;(eV)=\frac{\Delta G^{0}}{2N_{A}e}\]  
where \(N_{A}\) is the Avogadro constant and \(e\) is the electron's elementary charge. But, because O\({}_{2}\) is the product of water oxidation, the whole process is actually a _four_-photon, _four_-electron process. Consequently, to promote water cleavage in an electrolyzer, the energy constraint will be overcome thanks to an external bias, which must be larger than 1.23 V, because of the standard potentials of the couples:  
\[2\;\mathrm{H^{+}}_{\mathrm{(aq)}}+2\;\mathrm{e^{-}}\rightarrow\mathrm{H_{2(g)}} \mathrm{E^{0}}=0.000\;\mathrm{V} \tag{3}\]  
\[4\;\mathrm{H^{+}}_{\mathrm{(aq)}}+\mathrm{O_{2(g)}}+4\;\mathrm{e^{-}} \to 2\;\mathrm{H_{2}O_{(g)}} \mathrm{E^{0}}=1.229\;\mathrm{V} \tag{4}\]  
Considering that  
\[\Delta\mathrm{G^{0}}=\mathrm{nFE^{0}} \tag{5}\]  
with n = 2 in the case of water, Equation (5) further demonstrates how the thermodynamic requirements of Equations (1)-(4) are linked together [7]. Due to its positive Gibbs energy variation, water photosplitting is a photosynthetic reaction. For this reason, it could be legitimately considered a form of artificial photosynthesis, and, in fact, the anodic semireaction involves the oxidation of water and the formation of molecular oxygen, while on the cathodic side there is the formation of a fuel, H\({}_{2}\), finalizing the transformation of electromagnetic energy into chemical energy. In the case of hydrogen production from photoreforming, a hydrogen-containing organic compound--such as methanol--produces hydrogen and carbon dioxide:  
\[\mathrm{CH_{3}OH_{(l)}+H_{2}O_{(l)}\to 3\;H_{2(g)}+CO_{2(g)}} \Delta\mathrm{G^{0}}=8\;\mathrm{kJ}\;\mathrm{mol^{-1}} \tag{6}\]  
In this latter case the Gibbs free energy variation is still positive, but its value is almost two orders of magnitude less than in the case of Equation (1). The reason is the great stability of carbon dioxide, which has Gibbs' free energy of formation, \(\Delta\mathrm{G^{0}}_{f}\), of \(-394\;\mathrm{kJ}\;\mathrm{mol^{-1}}\)[8]. On the other hand, water also has a quite large \(\Delta\mathrm{G^{0}}_{f}\) (water formation reaction is the reverse of Equation (1)). Therefore, depending on the particular organic compound, its reforming could be either endergonic or exergonic, according to the number of water and carbon dioxide molecules involved in the reaction.