The Donnan potential revealed

Abstract

Selective transport of solutes across a membrane is critical for many biological, water treatment and energy conversion and storage systems. When a charged membrane is equilibrated with an electrolyte, an unequal distribution of ions arises between phases, generating the so-called Donnan electrical potential at the solution/membrane interface. The Donnan potential results in the partial exclusion of co-ion, providing the basis of permselectivity. Although there are well-established ways to indirectly estimate the Donnan potential, it has been widely reported that it cannot be measured directly. Here we report the first direct measurement of the Donnan potential of an ion exchange membrane equilibrated with salt solutions. Our results highlight the dependence of the Donnan potential on external salt concentration and counter-ion valence, and show a reasonable agreement with current theoretical models of IEMs, which incorporate ion activity coefficients. By directly measuring the Donnan potential, we eliminate ambiguities that arise from limitations inherent in current models.

Fig. 1. Overview of direct Donnan potential measurement using tender APXPS.

a A schematic of the experimental setup during data acquisition from the CR-61 membrane equilibrated in aqueous salt solution. b Equilibrium ion-partitioning between a membrane in contact with a monovalent electrolyte solution. At equilibrium, electroneutrality requires an equivalent number of counter-ions (which, for a monovalent system, is equal to the fixed charge concentration) to balance the fixed charge groups. The co-ions sorbing into the membrane are accompanied by an equivalent number of counter-ions, leading to significantly higher concentrations of counter-ions than co-ions in the membrane. c Illustration of the potential drop at the membrane/solution interface. d Corresponding binding energy (BE) shifts in the membrane related core levels. e Relationship between the measured BE of membrane related core levels and the Donnan potential as a function of external solution concentration.

Fig. 2. Experimental measurements of the Donnan potential.

Representative a O 1s and b S 1s core level spectra collected from CR-61 membranes equilibrated with different concentrations of NaCl solutions (GPW: gas phase water, LPW: liquid phase water). The binding energy is calibrated using bulk liquid phase water. The effects of the EDL on the binding energy position of the LPW peak are considered, and corrections are made during the calibration process. (Details of the energy calibration process are set forth in Supplementary Note 4) Circles represent raw experimental data, and lines indicate the sum of fits. Representative spectra not provided here for three other concentrations of NaCl solutions are presented in Supplementary Fig. 6 for visual inspection. c Averaged S 1s binding energy and the corresponding Donnan potential values as a function of the external solution concentration. Note that the S 1s binding energy shift versus Donnan potential shows a linear dependence of ∼1 eV/V. Error bars that represent the experimental uncertainty in S 1s binding energy were determined from the standard deviation of repeated measurements of a minimum of five different locations in each case. The binding energy values of fitted core level components for each individual analysis position are provided in Supplementary Table 6. The dashed line represents the best fit to a linear dependence. The fitted line was extrapolated to the equivalent concentration of counter-ions (3.2 M), where the Donnan potential approaches 0 V.

Fig. 3. Comparison between the experiment and theory.

Comparison of experimentally measured Donnan potential values obtained from binding energy shifts in membrane related core levels with the Manning/Donnan model predictions as a function of external a NaCl and b MgCl₂ solution concentration. Error bars represent experimental uncertainty and are the standard deviation of repeated measurements of a minimum of four different locations in each case. Dashed lines are the linear fits of ambient pressure X-ray photoelectron spectroscopy (APXPS) experimental data for external NaCl and MgCl₂ solutions with slopes of 0.049$\pm$0.004 and 0.026$\pm$0.002, respectively. (Brief discussion and further analysis of experimental uncertainties and statistical significance are provided in Supplementary Note 7). Details on Donnan potential calculations using the Manning/Donnan models are given in Supplementary Note 8. The absolute difference between the linear fit of the experimental data and predictions from the analytical model is provided to better capture the comparison between theory and experiment for each electrolyte concentration.