May self-diffusion of ions computed from molecular dynamics explain the electrical conductivity of pore solutions in cement-based materials?


Understanding the physical origins of the electrical response of cement-based materials is crucial to enhance the capabilities of non-destructive techniques, especially those based on resistivity or electrochemical measurements deployed in durability assessment and monitoring study of concrete structures. In this article, we show that using the information on the composition-dependent dynamics of ions obtained from molecular dynamics simulations improves the estimates of the electrical conductivity of the pore solutions. The link between ion dynamics and electrical conductivity in aqueous solutions is discussed from the fundamentals of ionic transport at the molecular scale. Also, we quantify the variability of pore solution conductivity. For validation, modeling results are extensively compared to experimental measurements on various cement systems. We show that a dilution effect explains the w/c-dependency of the electrical conductivity of the pore solutions. Also, accounting for the age-dependency of ionic diffusion in the pore solution is crucial to capture the age-dependency of the electrical conductivity of the pore solutions. These results are significant because they allow the prediction of the conductivity for various compositions of interest that may be encountered in cement systems.

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\(c_i\) :

Molar concentration of ion i

\(c_{wc}\) and \(c_{\mathrm{ref}}\) :

Concentration at a given w/c and a given w/c of reference

D :

Diffusion coefficient

\(D_i=D_{ii}\) and \(D_{ij}\) :

Diffusion coefficient of species of type i and mutual diffusion coefficient of species i and j

\(D_{\mathrm{h}}\) :

Homogeneous self-diffusion coefficient

e :

Elementary charge

\({\mathcal {F}}\) :

Faraday constant

\(G_i\) :

Empirical correction factor for the conductivity [1]

I :

Ionic strength

\(\mathbf{J} _{\mathbf{I }}\) :

Ionic current

k :


\(k_\mathrm{B}\) :

Boltzmann constant

N :

Number of ionic species or phases

\({\mathbf{P }}_{\mathbf{I }}\) :

Ionic polarization

\(q_i\) :

Particle charge

\(R_{\mathrm{g}}\) :

Gas constant

\({\mathbf{r }}_{\mathbf{i }}\) :

Position vector of particle i

t :


T :


\({\mathbf{v }}_{\mathbf{i }}\) :

Velocity vector of particle i

V :


w/c :

Water-to-cement mass ratio

\(z_i\) :

Charge number of particle i

\(\alpha\) :

Degree of hydration

\({\varvec{\mu }}_{\mathbf{i }}\) :

Dipole moments of ion i

\(\sigma\) :

Electrical conductivity

\(\sigma ^{\circ }_i\) :

The conductivity of ion type i at infinite dilution

\(\sigma ^{\mathrm{corre}}_i\) :

Empirically corrected electrical conductivity [1]

\(\sigma ^{\mathrm{NE}}_{\mathrm{PS}}\) :

Conductivity obtained by Nernst–Einstein relation

\(\sigma _{\mathrm{PS}}\) :

Electrical conductivity of the pore solution

\(\sigma _\mathrm{s}\) :

Electrical conductivity of the solids at cement paste level

\(\sigma ^{X}_{\mathrm{PS}}\) :

Conductivity due to cross-correlations of dissimilar ion types


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The authors would like to thank the company Eletrobras Furnas and the agency ANEEL - Agência Nacional de Energia Elétrica, from Brazil, for its support in experimental programs concerning the study of electrical resistivity in concretes. O. Cascudo also thanks CNPq – Conselho Nacional de Desenvolvimento Científico e Tecnológico, from Brazil, for the scholarship granted.

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Correspondence to Tulio Honorio.

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Honorio, T., Carasek, H. & Cascudo, O. May self-diffusion of ions computed from molecular dynamics explain the electrical conductivity of pore solutions in cement-based materials?. Mater Struct 53, 67 (2020).

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  • Ion dynamics
  • Electrical conductivity
  • Specific ion effects
  • Composition variability