One of the important
parameters in water management of proton exchange
membranes is the electro-osmotic drag (EOD) coefficient of water.
The value of the EOD coefficient is difficult to justify, and available
literature data on this for Nafion membranes show scattering from
in experiments and simulations. Here, we use a classical all-atom
model to compute the EOD coefficient and thermodynamic properties
of water from molecular dynamics simulations for temperatures between
330 and 420 K, and for different water contents between λ =
5 and λ = 20. λ is the ratio between the moles of water
molecules to the moles of sulfonic acid sites. This classical model
does not capture the Grotthuss mechanism; however, it is shown that
it can predict the EOD coefficient within the range of experimental
values for λ = 5 where the vehicular mechanism dominates proton
transfer. For λ > 5, the Grotthuss mechanism becomes dominant.
To obtain the EOD coefficient, average velocities of water and ions
are computed by imposing different electric fields to the system.
Our results show that the velocities of water and hydronium scale
linearly with the electric field, resulting in a constant ratio of
ca. 0.4 within the error bars. We find that the EOD coefficient of
water linearly increases from 2 at λ = 5 to 8 at λ = 20
and the results are not sensitive to temperature. The EOD coefficient
at λ = 5 is within the range of experimental values, confirming
that the model can capture the vehicular transport of protons well.
At λ = 20, due to the absence of proton hopping in the model,
the EOD coefficient is overestimated by a factor of 3 compared to
experimental values. To analyze the interactions between water and
Nafion, the partial molar enthalpies and partial molar volumes of
water are computed from molecular dynamics simulations. At different
water uptakes, multiple linear regression is used on raw simulation
data within a narrow composition range of water inside the Nafion
membrane. The partial molar volumes and partial molar excess enthalpies
of water asymptotically approach the molar volumes and molar excess
enthalpies of pure water for water uptakes above 5. This confirms
the model can capture the bulklike behavior of water in the Nafion
at high water uptakes.