## 1 Introduction
In general, K can be characterized in the following way for these specific types of reactions: the complexation constant (K) for complex formation/dissolution reactions, the stability constant (K) for redox reactions, the solubility-product constant (Ksp) for dissolution/precipitation reactions, and the distribution coefficient (Kd) and selectivity coefficient (Kx) for sorption reactions. Surface complexation theory describes sorption phenomena based on the surface reaction equilibrium. Such phenomena occur on the surface of materials such as iron, aluminum, silica and manganese hydroxides, as well as on those of humic substances. Accordingly, four models have been proposed, namely the constant capacitance model, the diffuse double-layer model, the triple-layer model, and the charge distribution multisite complexation model. Surface complexation models are still being developed for the description of the adsorption/desorption reactions of nuclides. For example, [PERSON] [2] reported that cesium can be adsorbed on the surface of silica, and that a surface complexation model (SCM) can describe the adsorption of cesium on the surface of silica. Moreover, [PERSON] et al. [3] indicated that cesium tends to bind to silica particles in cement hydration minerals. [PERSON] et al. [4] observed that cesium can be adsorbed on the silicate chain (C-S-H) of cement. In addition to cesium nuclides, [PERSON] and [PERSON] [5; 6] reported that the adsorption of radionuclides is a major concern in water-mineral geochemical reactions with regard to the safety assessment of radioactive waste. They have developed a surface complexation model based on diffusion layer theory to assess the cations (such as Am\({}^{3+}\), Pu\({}^{4+}\), Pu\({}^{5+}\) and Np\({}^{5+}\)) and anions (such as I\({}^{-}\), IO\({}_{3}\)\({}^{-}\), SeO\({}_{3}\)\({}^{2-}\), SeO\({}_{4}\)\({}^{2-}\) and TeO\({}_{4}\)\({}^{-}\)) of radionuclides in clay and various minerals by using chemical thermodynamic and equilibrium constant data. For equilibrium reactions, the equilibrium constant is temperature-dependent, and can be calculated using the Van't Hoff equation, as follows: [1]  
\[\mathrm{K_{T}}\mathrm{=K_{T}}\exp\left[\frac{\mathrm{\Delta H_{T}}}{\mathrm{R }}\left(\frac{\mathrm{T-T_{r}}}{\mathrm{T_{r}}}\right)\right] \tag{3}\]  
where K\({}_{T}\) and K\({}_{T}\) are the equilibrium constants for equilibrium reactions at the temperature of interest, T, and the referenced temperature, T\({}_{r}\) (298.15 K), respectively; \(\mathrm{\Delta H_{T}}\), is the enthalpy of the associated equilibrium reactions; and R is the ideal gas constant (8.315 J mol\({}^{-1}\) K\({}^{-1}\)). The equilibrium constant is also pressure-dependent, and can be expressed as follows:  
\[\mathrm{lnK_{P}}\mathrm{=lnK_{P_{S}}-\frac{\mathrm{\Delta V_{T,P_{S}}}}{ \mathrm{T\cdot R\cdot\beta}}\ln\frac{\rho_{P}}{\rho_{P_{S}}}} \tag{4}\]  
where K\({}_{P}\) and K\({}_{P_{S}}\) are the equilibrium constants for the equilibrium reactions at the pressure of interest, P, and the reference pressure, P\({}_{N}\) (i.e., the saturated vapor pressure), respectively; \(\mathrm{\Delta V_{T,P_{S}}}\) is the volume change of the dissociation reaction at the temperature T and reference pressure P\({}_{N}\); \(\beta\) is the isothermal compressibility coefficient of water at the temperature T and the pressure of interest, P; and \(\rho_{P}\) and \(\rho_{P_{S}}\) are the densities of water at the pressure of interest, P, and reference pressure, P\({}_{N}\), respectively.