Electrochemistry and capillary condensation theory reveal the mechanism of corrosion in dense porous media

Corrosion in carbonated concrete is an example of corrosion in dense porous media of tremendous socio-economic and scientific relevance. The widespread research endeavors to develop novel, environmentally friendly cements raise questions regarding their ability to protect the embedded steel from corrosion. Here, we propose a fundamentally new approach to explain the scientific mechanism of corrosion kinetics in dense porous media. The main strength of our model lies in its simplicity and in combining the capillary condensation theory with electrochemistry. This reveals that capillary condensation in the pore structure defines the electrochemically active steel surface, whose variability upon changes in exposure relative humidity is accountable for the wide variability in measured corrosion rates. We performed experiments that quantify this effect and find good agreement with the theory. Our findings are essential to devise predictive models for the corrosion performance, needed to guarantee the safety and sustainability of traditional and future cements.


Supplementary Table 1. Mesured electrical and electrochemical paparemetrs. Compilation of average measured
values (out of minimum 4 measurements for corrosion rate and electrical resistivity, 2 measurements for cathodic limiting current density) and relative standard deviations. The data are reported divided per type of binder, water to binder ratio and exposure condition used. The same data are reported graphically in Figures 1c and 1d Table 1) of the same electrical/electrochemical parameter changing one variable (with the higher value amongst the two always as numerator), keeping the other experimental variables constant. As an example, the sensitivity of corrosion rate to the water to binder ratio is reported as ratios between average corrosion rates of samples of the same binder, stored in the same exposure condition, but realized with different water to binder ratios.
It clearly appears that the exposure RH is by far the most influencing experimental variable for every measured parameter, followed by the type of binder used and the water to binder ratio, these latter two having an overall comparable influence on electrical / electrochemical properties.

Supplementary Figure 4. Comparison between cathodic limiting current and corrosion rate, sample by sample.
Corrosion rate and cathodic limiting current data, the x axis represents each single sample on which both cathodic current and corrosion rate were measured. By comparing the measured cathodic limiting current to the corrosion rate for the different samples it is possible to establish if the corrosion rate is limited by the cathodic reaction rate.
It appears that the cathodic limiting current, regardless of the experimental variables, is always one order of magnitude higher than the corrosion rate, ruling out the possibility of cathodic control of the corrosion process. It also looks like the values of the two parameters vary with great consistence one with the other, sample by sample.
This can be explained by the two processes having very much in common: both are electrochemical processes and both are strictly taking place at the electrode (embedded steel) surface.

Supplementary Note 1 Potential influence of oxygen concentration, iron concentration and pH on the corrosion rate
In electrochemical systems such as corrosion, the final reaction rate can be defined by the mixed potential theory [1,2,3]. The common representation of these systems is called Evans diagram (Supplementary The equations describing cathodic and anodic straight lines (Supp. Fig. 5) can be written: The theoretical corrosion rate can be, at this point, calculated as the intersection between cathodic and anodic functions, isolating first the intersection corrosion potential (Ecorr) from both (6) and (7): Now it is possible to discuss the impact of species concentration in the pore solution on the corrosion rate and calculate what would be necessary to reach the experimentally measured corrosion rate span (factor 200). As it can be seen from equation (5), Tafel slopes do not depend on the species in solution so they will be considered constant. Equation (4) is a theoretical expression that cannot be used in practice because a single reaction can be composed of many steps [4,5,6], and typically the rate limiting step is unknown. Anyways this is a second order effect because the variation of experimentally measured exchange current densities was shown to impact on final corrosion rate of a maximum factor 0.3 [7].
Therefore the only parameter we can really evaluate, from a theoretical point of view, is the dependence of the reversible potentials on the species concentration in solution and their impact on the corrosion rate.
Starting with the cathodic reaction showed in eq. (1) the dependence of the cathodic reversible potential on the oxygen concentration is The pH variation needed to have a 200 times different corrosion rate is Evaluating now the impact of iron concentration in the pore solution The expression of the anodic reaction reversible potential is Concentration of metallic iron is considered as 1, the calculations proceed as previously shown The pore solution composition can explain the variation of corrosion rate from a relative humidity of 50% to 99% only by absurd variations of species concentration, such as:  An oxygen concentration difference of 34.9 orders of magnitude;  A pH difference of 8.7;  An iron concentration difference of 17.5 orders of magnitude.
In conclusion the 200 factor of corrosion rate variation depending on the relative humidity, cannot be explained by an influence of the pore solution composition on the electrochemical process.