## 3 Mathematical Model
\begin{array}{c}\text{Linear}:\ C_{\rm b}=a\ C_{\rm f},\ \text{Langmuir}:\ C_{\rm b}=\frac{a_{\rm f}C_{\rm f}}{1+b_{\rm L}C_{\rm f}},\\ \text{ BET}:\ C_{\rm b}=\frac{a_{\rm BET}\ b_{\rm BET}\ C_{\rm f}}{(C_{\rm f} \max-C_{\rm f})\bigl{(}1+(b_{\rm BET}-1)\ \frac{c_{\rm f}}{C_{\rm f}\max}\bigr{)}},\ \text{ Freundlich}:\ C_{\rm b}=a_{\rm F}C_{\rm f}^{k},\end{array}  \tag{20}\]  
where: \(a\), \(a_{\rm L}\), \(a_{\rm BET}\), \(a_{\rm F}\), \(b_{\rm L}\), \(b_{\rm BET}\), \(k<1\)--parameters characterizing the process, \(C_{\rm f}\max\)--maximum concentration of free chlorides in solution (mol/m\({}^{3}\)). The first is simply a convenient form of approximating the physical relationship, the second and the third assume that the gas-phase adsorbate layer on the solid adsorbent is a monolayer [9] or poly-layer [12], and the fourth is empirical [10]. The Langmuir and BET ones are originally formulated for the physical process of different nature in comparison to the binding chlorides by the cement matrix, and they should be used in the description of the considered process with some restrictions concerning its interpretation. The BET isotherm has an inflection point from negative to positive curvature where the curvature is negative for lower concentrations and positive for higher concentrations, however, the isotherm itself may significantly overestimate the result in the area of \(C_{\rm f}\) concentrations close to \(C_{\rm f}\max\), which results from the term \((C_{\rm f}\max-C_{\rm f})\) in its denominator. The course of the Langmuir and Freundlich isotherms is characterized by a negative curvature in the entire range of the \(C_{\rm f}\) variability under consideration, which agrees quite well with a number of experimental data for different types of concrete available in the literature (e.g., [29; 30; 32]). These data, in order to be representative for cement matrix materials, are obtained from tests of chloride binding by material taken from the internal parts of samples [29; 32] or from fully ground samples [30]. In this way, the influence of a different structure of the boundary layer of the samples on the results, in which the proportion of cement paste and aggregate or porosity may be changed, is compensated. For example, interesting structural studies of the external layer of concrete samples with different surface treating methods are presented in [33]. Dueto the fact that in practical conditions, the external parts of concrete elements are obviously not removed and mediate the transport of chlorides to the interior of the concrete, the determination of the chloride binding isotherms taking into account the influence of the near-surface layers is an important issue. In the literature, this phenomenon is referred to as the \"skin effect\", which was described in more detail at the beginning of the article. An appropriate correction of the mathematical model from this point of view is of great importance in correctly predicting the progress of chloride transport in reinforced concrete structures, the more so as the typical thicknesses of the concrete cover of steel reinforcement are up to 5 cm, and the thicknesses of the surface zones with changed properties may be of the order of the thickest aggregate fraction radius. Thus, it follows that the thicknesses of the zones affecting the \"skin effect\" may be of the same order as the thickness of the reinforcement cover. With the above in mind, the authors limited themselves to analyzing the \"skin effect\" under the following extent and simplifying assumptions:  
1. The conditions of the experiment should emphasize in the transport of chlorides only the influence of the change in the composition and structure of concrete in the near-surface part in relation to the bulk part (i.e., due to the increase in the volume of cement paste in relation to the aggregate and/or the change in porosity). 2.