Understanding Electro-Osmotic Drag Coefficients in Hydrated Polymers

Electro-osmotic drag coefficients (K_drag) are critical parameters in the study of polymeric materials, particularly in the context of hydrated systems like Nafion and sulfonated poly(arylene ether ketones). Recent data highlights two significant trends in the behavior of these coefficients: at low degrees of hydration, K_drag approaches a value of 1 and does not dip below this threshold, while increasing solvent fraction leads to a dramatic rise in the drag coefficient.

As the solvent fraction increases, the electro-osmotic drag coefficient can reach about 50% of its maximum possible value, indicating that all solvent molecules and protonic charge carriers drift at nearly identical velocities. This collective motion of water molecules is particularly pronounced in highly hydrated samples, where the conductivity is primarily supported by structural diffusion. In these conditions, the proton mobility is notably higher than that of water molecules, suggesting that at peak hydration, the transport mechanism is heavily reliant on the interaction between water and protons.

Interestingly, the behavior of K_drag also seems to correlate with the channel diameter of the polymer. A decrease in water content results in a drag coefficient that scales with the fourth power of the channel diameter. This observation is reminiscent of Hagen-Poiseuille-type flow, suggesting that as hydration decreases, the movement of water molecules becomes more restricted, culminating in the “stripping off” of water from the polymer structure.

Further investigations reveal that both water and methanol exhibit virtually identical normalized drag coefficients when analyzed in mixtures. This phenomenon can be attributed to their near-ideal solution behavior, where the interactions between the different species are comparable. However, at lower hydration levels, the preferential solvation of protons by either water or methanol remains an open question, indicating a need for further research into primary hydration effects.

Comparative analyses of Nafion and sulfonated poly(arylene ether ketones) show that the latter generally has a lower electro-osmotic drag coefficient, primarily due to smaller channel sizes. Even with similar channel dimensions, the influence of solvent-polymer interactions plays a significant role in determining the total electro-osmotic drag. Notably, as temperature increases, electro-osmotic drag also tends to rise, reinforcing the notion that thermal conditions can influence polymer behavior in hydrated states.

Overall, while the insights into electro-osmotic drag coefficients are advancing, a comprehensive quantitative model that describes these coefficients as a function of hydration and temperature remains to be developed. Understanding these dynamics is crucial for optimizing the performance of polymeric materials in practical applications, particularly in fuel cells and other electrochemical systems.