## 3 Results
### Use of HSDM Formulation for Interpreting Dynamic Adsorption
#### 3.4.3. Implication of the Connectivity of Pores on Ion Diffusivity  
To evaluate the immobilization capacity of a binder toward nuclides, the physical barrier effect of the pore structure on ionic diffusivity ought to be taken into consideration [115]. For cementitious materials like ordinary Portland cement, fly ash-based geopolymers, and slag-blended geopolymers, it has previously been shown that the capillary porosity and connectivity of the capillary pores in porous media play a relevant role in ionic diffusion within these porous materials [115; 120; 121]. The capillary pores with pore diameters rang  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Matrix** & **Caesium(0)** & **Rubidium(I)** & **Cobalt(II)** & **Strontium(II)** \\ \hline
**Portland cement** & \(0.59\times 10^{-11}\) to \(1.70\times\) & —  
ing from 10-50 to 10,000 nm [115; 121] were indeed assumed to dominate the ionic transport processes in cementitious materials. It has previously been suggested that the broad range of \(D_{\mathit{eff}}\) observed in previous studies was mostly attributed to the variability of the porosity, capillary pore volume, and critical pore diameter, which control the ion diffusivity in cementitious materials [115]. In order to describe the connectivity of such porous solids, it was proposed to use the critical pore diameter as a _key_ parameter representative of the highest proportion of interconnected pores, which would be mainly responsible for ion transport characteristics [115; 121; 122]. The critical pore diameter (or continuous pore diameter) was defined as the maximum of the Log differential pore volume, _dV/dlog(diameter)_, versus the pore diameter curve. With this in mind, some investigations permitted us to correlate the critical pore diameter of the binder with the diffusivity behaviour of water-soluble ions such as caesium and strontium [115]. In order to appraise the physical barrier effect of treated brick on the diffusivity of caesium and strontium, we first attempted to attain the critical pore diameter of the brick composite. For this, the calculated _dV/d(log d)_ term was plotted against the pore diameter, and the maximal _dV/d(log d)_ value was determined, as shown in Figure 3c. We found \(\sim\)50 nm (\(\pm\)10 nm). This value was comparable with that obtained for fly ash-based geopolymers (50-151 nm) and lower than those for fly ash/fly ash-based geopolymers (227-249 nm) and ordinary Portland cement (284 nm), but was much lower than that for fly ash/blast furnace slag-blended geopolymers (1567 nm) [115]. Taking into account the empirical linear equation expressing the critical pore diameter of the binder versus the diffusivity of water-soluble ions, which was established by [PERSON] and his co-workers [115], we then evaluated the diffusion coefficient, \(D_{\mathit{soluble}}\), of water-soluble Cs\({}^{+}\) and Sr\({}^{2+}\) ions. We found \(D_{\mathit{soluble}}\) = -4 \(\times\) 10\({}^{-12}\) and -2 \(\times\) 10\({}^{-12}\) m\({}^{2}\cdot\)s\({}^{-1}\), respectively. These values were somewhat lower than those calculated herein using different diffusion-based models (see Table 3). It could, however, be noted that, based either on the results from surface diffusion models (see Section 3.3) or those derived from the dependence of the connectivity of pores in cement-based materials upon the ion diffusion coefficient (as shown in this paragraph), the diffusion of strontium ions was found, in all cases, to be more difficult than that of caesium ions, which is in agreement, in most cases, with the findings of previous studies (see Table 5). Despite the slight discrepancy between the \(D_{\mathit{soluble}}\) and \(D_{\mathit{eff}}\) values determined for Cs\({}^{+}\) and Sr\({}^{2+}\), this study nevertheless permitted us to demonstrate the implication of hydrated entities of nuclides in the diffusion stages.