Calculated electrolyte conductivity
_{calc}
can be expressed as a weighted sum of the equivalent conductivity
_{i}
of each ionic species [11]:

The quantities *z _{i}* and

While a number of highly accurate equations containing numerous coefficients
exist for estimating the equivalent conductivity [8],
a new single-parameter model is proposed for its simplicity, with the
objective that the equation should be accurate to within 10 %
for typical pore solutions.
Previous work [6] indicates that the uncertainty in
estimating the bulk conductivity _{b} can be less than a few percent.
From Eqn. 1, an uncertainty of 10 % in pore solution
conductivity _{p} would translate into a similar uncertainty in
the calculated formation factor .
Such a level of uncertainty would be difficult to improve upon using
existing diffusion cell experiments.

The concentration dependence of the individual equivalent conductivities at 25 ºC is approximated using the following single-parameter model that characterizes low concentration data well, and remains reasonably accurate at concentrations near 1 mol/L:

The quantity º is the equivalent conductivity of an
ionic species at infinite dilution, and is only a function of temperature;
the values of º for Na, K, OH, Ca, Cl, and SO
at 25 ºC can be found in the literature[8],
and are shown in
Table 1.
The quantity *I*_{M} is the ionic strength (molar basis), and
has the following definition [11]:

(4) |

The empirical coefficients
*G _{i}*
are chosen to best agree with published data
for the electrical conductivity of solutions. In principle, the coefficient

The algebraic form of Eqn. 3 is based on previous
work on the conductivity of electrolytes. It is known that the
leading term in the correction should be
proportional to *c*^{½} [13]. At higher
concentrations, however, this is an overcorrection. Onsager and Fuoss (OF)
[14] gave additional terms that are
proportional to *c* log *c* and *c*. Although rigorous, using
the OF
equation would require multiple coefficients for each species, which
violates the objective of simplicity desired here. As a compromise,
Eqn. 3 is a modification of a relationship (for
binary salts) by Walden [15] that is a function of the salt
concentration and requires an empirical coefficient for each salt.
The extension to electrolytes containing many ionic species was achieved
by changing the salt concentration to the molar ionic strength *I*_{M
} .
This change is motivated by similar relationships for estimating the
activity of ionic species in concentrated electrolytes [8].

Based on Eqn. 2, the most significant contributor to the pore solution conductivity of a cementitious system is the OH ion; its equivalent conductivity is a factor of two greater than that for sodium or potassium (see Table 1), and it is present at the highest concentration. Because the equivalent conductivity of the remaining ionic species in the pore solution of a well hydrated specimen are all of the same magnitude, the Na and the K should be secondary contributors due to their relatively high concentrations after 1 d [12].

Two other species to consider are calcium and sulfate.
Due to high alkalinity,
the equilibrium calcium concentration
in pore solution is typically on the order of 0.001 mol/L [10].
The corresponding calcium
contribution to the overall conductivity (assuming *I*_{M} 1.0
mol/L and _{p} = 20 S/m)
is on the order of 0.003 S/m, and so can be neglected.
Using the pore solution speciation model by Taylor [9],
the concentration of sulfate can be roughly approximated by the
potassium and sodium concentrations:

(5) |

( = 0.06 L/mol) Using this approximation, sulfate will make the greatest relative contribution when the sum of the potassium concentration and the sodium concentration approaches 1 mol/L (it is unlikely they will be significantly greater). The corresponding sulfate contribution to the pore solution conductivity is approximately 0.25 S/m, or less than 2 % of the anticipated total conductivity.

Therefore, the electrical conductivity of most pore solutions of well-hydrated cement-based materials could be accurately estimated from the contribution of the Na, K, and OH ions alone. In those cases where other species are present at significant concentrations, additional coefficients are provided in Table 1, but are not part of the validation experiment.

Species |
zº (cm^{2} S/mol) |
G (mol/l)^{-½} |

OH | 198.0 | 0.353 |

K | 73.5 | 0.548 |

Na | 50.1 | 0.733 |

Cl | 76.4 | 0.548 |

Ca | 59.0 | 0.771 |

SO | 79.0 | 0.877 |