## 3 Results
### Weber-Morris (W-M) Model
As can be seen in this figure, the \(k_{jpd}\)_(1)_ and \(k_{jpd}\)_(2)_ rate constants exhibited relatively good correlations with R\({}_{\rm H}\) (R\({}^{2}\) = 0.9649 and 0.9735, respectively). The observed hydrated radius (\(R_{H}\)) dependence on diffusion rate constants suggested that the size of the hydrated ion ought to be taken into consideration as a noticeable factor in the diffusional approach of the studied adsorption process. In the diffusion adsorption mechanism, the mobility of the cationic species _first_ toward brick surfaces and _second_ through zeolitic pores/channels should depend on the viscosity of the interfacial medium. The viscosity of the hydrated cation solution (\(\eta\)) was referred to that of the pure water (\(\eta_{o}\)), and could be determined from the Jones-Dole expression [92]:  
\[\frac{\eta}{\eta_{o}}=1+A\cdot C^{1/2}+B\cdot C \tag{12}\]  
where \(C\) (in mol\(\cdot\)L\({}^{-1}\)) is the solute concentration and \(A\) (in L\({}^{1/2}\cdot\)mol\({}^{-1/2}\)) and \(B\) (in L\(\cdot\)mol\({}^{-1}\)) are coefficients depending on the solute, the solvent, and the temperature [92]. Here, we consider the Jones-Dole viscosity coefficient (\(B\)) as a potential indicator of the degree of water structures around the cationic entity, and thereby of the bonding strength of hydration shells covering the element. The B-coefficients of aqueous inorganic ions at 25 \({}^{\circ}\)C in L\(\cdot\)mol\({}^{-1}\) were previously reported by [PERSON] and [PERSON] [92]. Thus, by plotting the intra-particle diffusion rate constants \(k_{jpd}\)_(1)_ and \(k_{jpd}\)_(2)_ against the \(B\) \"viscosity\" parameter (Figure 5), we noticed that the increase in the medium viscosity contributed to a significant inhibition of cationic adsorption kinetics. This suggests that the \(B\)-coefficient also had to be taken into account as a determining parameter regulating cationic diffusion into brick surfaces. In water, the complexation of a cation with H\({}_{2}\)O molecules results in the formation of a hydration shell. This reaction is exothermic, releasing a certain hydration free energy noted here as \"\(\Delta G_{H}\)\". To evaluate the contribution of the molar Gibbs energy of hydration of the cation M\({}^{+}\) or M\({}^{2+}\) (as defined and determined by [PERSON] [91]) to the diffusion behaviour of cationic species inside composite frameworks, we plotted the intra-particle diffusion rate constants, \(k_{jpd}\)_(1)_ and \(k_{jpd}\)_(2)_, against \"\(\Delta G_{H}\)\" (Figure 5). The values of molar Gibbs energy of hydration used for plotting are listed in Table S3. As can be seen in Figure 5, the \(k_{jpd}\)_(1)_ and \(k_{jpd}\)_(2)_ constants exhibited good correlations with the molar Gibbs energy of hydration (R\({}^{2}\) = 0.9923 and 0.9852, respectively). These findings suggest that, for Cs\({}^{+}\) and Cs\({}^{+}\), the \(k_  
Rb\({}^{+}\), which have much softer hydration shells than those of Ni\({}^{2+}\), Cu\({}^{2+}\), Co\({}^{2+}\), Sr\({}^{2+}\), and Zn\({}^{2+}\), the easier rearrangement and loss of the water molecules of hydration around these cations contributed to an enhancement of diffusion kinetics. Globally, the facile kinetic exchange between Na\({}^{+}\) ions on the brick surface and Cs\({}^{+}\) or Rb\({}^{+}\) ions in the solution could be explained in part by the low differences in the ion hydration energies (\(-385\) kJ\(\cdot\)mol\({}^{-1}\) for Na\({}^{+}\), \(-285\) kJ\(\cdot\)mol\({}^{-1}\) for Rb\({}^{+}\), and \(-245\) kJ\(\cdot\)mol\({}^{-1}\) for Cs\({}^{+}\)[91]). These differences were substantially smaller in magnitude than those calculated for the ion exchanges between Na\({}^{+}\) ions and the cationic metals Sr\({}^{2+}\) and Co\({}^{2+}\) (\(-385\) kJ\(\cdot\)mol\({}^{-1}\) for Na\({}^{+}\), \(-1468\) kJ\(\cdot\)mol\({}^{-1}\) for Sr\({}^{2+}\), and \(-2003\) kJ\(\cdot\)mol\({}^{-1}\) for Co\({}^{2+}\)[91]).