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Intrapore energy barriers govern ion transport and selectivity of desalination membranes

A fundamental study elucidates the mechanisms underlying selective ion transport through desalination membranes.


Pore hindrance transport model
The membrane average pore radius was estimated based on the pore hindrance transport model where membranes are considered to have a bundle of cylindrical pores with the same radius (73,74). The membrane real (intrinsic) rejection of neutral organic solutes, r , can then be described where c is the hydrodynamic hindrance coefficient for convective flow and is the Peclect number. The partition coefficient, Φ, describes the solute distribution at the pore mouth when only steric interactions are considered: where < ′ >is the average solute concentration within the pore, is the concentration just outside the pore, and is the ratio of the solute radius, s , to the pore radius, p .
According to the thin-film theory, the real rejection can be related to the observed rejection, o , by accounting for the concentration polarization (75): where f is the mass transfer coefficient and V is the membrane permeate water flux.
To estimate the average pore radius, we first utilized Equation S3 to calculate the membrane real rejections of each organic solute (erythritol, xylose, and ethylene glycol) from the experimentally obtained observed rejections. The parameters Φ c and were then solved by fitting the real rejection data to Equation S1 using an optimization process (Solver, Microsoft Excel). The obtained parameter Φ c , which is only a function of the ratio of the solute to pore radius, enables us to calculate the average pore radius. Additional details on this process can be found in our previous work (76).

Ion transport in an electro-driven process
The overall membrane conductance for ion transport in an electro-driven process can be described where m is the membrane area, is the elementary charge, A is the Avogadro number, ∆Φ is the voltage across the membrane, is the Faraday constant, and i and i are the flux and the valence of ionic species i, respectively. For the 1:1 electrolytes considered in this study, where m is the membrane thickness and ± is the transport number for cations or anions.
According to Nernst-Plank equation, the ionic flux for an electro-driven process is given by ( ) 78 where and are the diffusion coefficient inside the membrane and partition coefficient at membrane-solution interface, respectively, is the electrolyte molar concentration in the bulk solution, and is the Boltzmann constant. The subscript ± indicates a parameter assigned for either anions or cations.
Combining Equations S5 and S6 gives where is the ion permeability, is the absolute temperature (K), and is a temperatureindependent parameter.
The overall energy barrier for ion transport through the membrane ( P,± ) can be calculated using an Arrhenius-type equation: where ±,o is a pre-exponential factor and is the gas constant. Substituting Equation S7 into Equation S8 yields: where ± is the pre-exponential factor.

Determination of overall ion conductance
The membrane ion conductance was obtained using a linear sweep voltammetry (LSV) technique.
A membrane coupon was assembled into a homemade two-chamber diffusion cell and an Ag/AgCl reference electrode (CHI111, CH Instruments, Austin, TX) was inserted in each chamber (Fig. 1C).
During the LSV measurement, current was recorded while sweeping the voltage difference between the two reference electrodes from -50 to 50 mV at a scan rate of 2 mV s -1 . Reciprocal of the slope of the obtained I-V curve indicates the charge transfer resistance of the system with the membrane. The LSV measurement was repeated after removing the membrane coupon for the estimation of charge transfer resistance of the system without the membrane (Fig. S3A). The difference between the two obtained resistances is the resistance for ion transport through the membrane (i.e., reciprocal of the overall ion conductance).

Determination of ion-pore interaction energy using density functional theory (DFT) simulation
In the DFT simulation, we used a continuum solvation model to probe the interaction energy changes between ions and the pore during their transport through a pristine 0. ( , ) can be used as the potential energy surface (PES) of ion entering the pore along the Y and Z coordinates.

Impact of oxygen (O -) functionalization on simulated ion transport
As shown in Fig. S7, the minimum energy pathway calculated by DFT indicates that the intrapore diffusion pathway for both Na + and Fions was significantly affected by the -Ogroup in the sub-nanometer pore. After entering the pore, both ions are preferably translocated along the pore center in pristine, unfunctionalized pore. However, in the presence of intra-pore -Ofunctionalization, an off-centered path near the -Ogroup is observed for both ions due to the steric repulsion of the -O -. Importantly, when ions leave the -Ogroup and the steric effect is diminished, it is clearly shown that Na + and Fions are electrostatically attracted and repulsed by the Ogroup, respectively.
The effect of the -Ogroup on the PES of ion transport is shown in Fig. S8. For the pristine, unfunctionalized sub-nanometer pore (grey filled squares), the PES of both Na + and Fshowed a monotonically increasing trend when the ion enters the pore (Z coordinate = 12 Å), and no further energy barrier can be observed during the intra-pore diffusion process. In comparison, after anchoring an -Ogroup on the inner pore wall (Z coordinate = 6 Å in Fig. S8), the energy barrier for Na + ions to enter the pore was lowered to 9.8 kcal mol -1 (the barrier near pore entrance in the Contribution of partition and intra-pore diffusion to the overall energy barrier for salt transport. In the solution-diffusion model, intrinsic salt permeability ( ) is defined as the product of partition coefficient ( ) and diffusion coefficient ( ): For salt transport through the membrane, the salt needs to overcome energy barriers both during partitioning into pores and diffusion inside the pores: where D and ∆ K are the energy barriers for intra-pore diffusion and the energy change in the partition step, respectively, and o and o are the pre-exponential factors. Substituting Equations S8, S12, and S13 into Equation S11 yields: Therefore, the overall energy barrier for salt transport in sub-nanometer pores in the polyamide layer is the sum of the contributions from both the energy change in the partition step and the energy barrier of intra-pore diffusion:

QCM sample preparation
The protocol for isolating the polyamide layer from the RO membrane is well described in the literature (53,79,80). Specifically, the polyester support layer of the RO membrane was first peeled off using tweezer, leaving a composite of the polysulfone and polyamide layers. Next, the polysulfone and polyamide composite was placed on the QCM sensor with the polyamide layer facing the surface of the sensor. Following this step, the polysulfone layer was dissolved by dropwise addition of dimethylformamide (DMF), leaving only the polyamide layer on the QCM sensor. Last, the QCM sensor coated with the polyamide layer was air dried, rinsed with DI water, and dried again with nitrogen gas.

Determination of the volume of polyamide layer
To determine the volume of the polyamide layer on the QCM sensors, the mass of the polyamide layer was first measured by running QCM tests with the sensors before and after being coated with the polyamide layers in air. With the resulting resonance frequency change in the QCM tests, ∆ , the mass of the polyamide layer ( ) can be calculated by the Sauerbrey relationship (5  ): where is the overtone number ( = 3 in this study) and is the crystal constant (17.7 ng Hz -1 cm -2 ). With the mass ( ) and density ( ) of the polyamide layer, the volume of the polyamide layer ( ) can be determined: The experimental results are summarized in Table S2.

Determination of the partition coefficient
By definition, the partition coefficient ( ) can be calculated as = (S18) where and are the salt concentrations in the membrane (polyamide layer) and bulk solution, respectively. Since the bulk solution concentration is known, can be obtained by determining . As the volume of the polyamide layer ( ) has been determined, can be determined after the mass of salt partitioning into the membrane ( , ) is measured: where is the molecular weight of the salt.
The mass of the partitioned salt, , , was measured using a QCM (Fig. 3B) with protocols adopted from the literature (53,81). In the QCM test, three coated sensors (i.e., samples) and one uncoated sensor (i.e., control) were used in four parallel modules, resulting in three replicate experimental results. As the pump is continuously drawing solution from the feed tank and evenly distributing the solution to the modules, all the sensors were exposed to the same solution throughout the test. The resonance frequency of each sensor was in-situ monitored and recorded by a computer connected to the QCM instrument.
During the QCM tests, the sensors were first exposed to DI water for about 2 hours to establish stable baselines of the resonance frequencies. Then, the sensors were exposed to the test salt solution (or solutions with increased concentrations) for about 20 minutes to achieve new stabilized frequency readings. The changes of resonance frequency between DI water and the test solution can be obtained for both the sample sensor (∆ ) and the control sensor (∆ ). After running the test solution (or solutions), DI water was used again to rinse the system for another two hours and check the frequency baselines. Representative QCM results with increased NaCl solutions can be found in Fig. S9.
For data analysis, as the control sensor served to account for the frequency change resulting from the change of the physical properties of salt solutions (e.g., density and viscosity), the frequency change resulting from the salt partitioning into the polyamide layer (∆ , ) can be obtained as the difference between ∆ and ∆ (i.e., ∆ , = ∆ − ∆ ). Based on the Sauerbrey relationship, , can be calculated from ∆ , . Thus, knowing , , the partitioning coefficient can be determined by Equations S18 and S19.
In our QCM experiments, we have used 0.5 M as the solution concentration of the investigated salts for the determination of K . Such high concentration was applied because low solution concentration (i.e., < 0.1 M) can lead to large variations (>50 %) in the QCM measurements due to the limited resolution of the instrument (Table S3). Notably, remains constant as the solution concentration changes (Fig. S9 and Table S3), as also observed in a previous study (53). Figure S1. Example of concentration increase in the middle chamber as cations (Na + ) and anions (I -) diffuse from the side chambers over time. Figure S2. Arrhenius plots for salt transport through membranes with three electrolytes: (A) NaF, (B) NaBr, and (C) NaI. Two membrane coupons, with their active polyamide layers facing the solution chambers, were assembled into a custom-made three-chamber diffusion cell (Fig. 1A). The two side chambers were filled with a single salt solution ( s =10 mM) and middle chamber was filled with DI water. Salt flux ( salt ) was measured at five different temperatures (22, 26, 30, 33, 37 °C) by monitoring the conductivity change in the middle chamber over time. Solution pH was maintained at 5.7 in all experiments. Error bars represent standard deviations from duplicate measurements. The fitted slope is 0.0257 V and the transport number of Na + was estimated to be 1.0 for this CEM according to Equation 6. Considering the highly linear dependence of membrane potential on concentration ratio (R 2 = 0.999), only concentration ratios of 5:1, 2:1, and 1:1 were used for transport number measurements with the RO membrane. Figure S4. Transport number of Na + ions with RO membranes. (A) Transport number of Na + ( Na + ) with RO membranes for four electrolytes (NaF, NaCl, NaBr, and NaI) at pH 5.7 as calculated from the measured membrane potentials. (B) Dependence of membrane potential on the concentration ratio between the two chambers ( Fig. 1C) for NaF at pH 9.5, 5.7, and 4.5. The slopes of the curves were used to calculate the corresponding transport numbers of Na + and F -. Experimental conditions: salt concentration was maintained constant in one chamber ( h =10 mM), and the concentration in the other chamber ( l ) was gradually increased from 2 to 5 and 10 mM to obtain concentration ratios of 5:1 , 2:1, and 1:1, respectively. Solution pH was adjusted using 0.1 M H2SO4 and 0.1 M KOH. Error bars represent standard deviations from triplicate measurements. Figure S5. Arrhenius plots for decoupled anion and cation transport through membranes with three electrolytes: (A) NaF, (B) NaBr, and (C) NaI. The overall membrane conductance was obtained using linear sweep voltammetry (-50 -50 mV) with 10 mM of electrolytes in both chambers (Fig. 1C) at temperatures of 22, 26, 30, 33, and 37 °C. The transport number ( ± ) was calculated using the membrane potential (∆Φ mbr ) measured at the same temperatures mentioned above. For membrane potential measurement, at each temperature salt concentration was maintained constant in one chamber ( h =10 mM), and the concentration in the other chamber ( l ) was gradually increased from 2 to 5 and 10 mM to obtain concentration ratios of 5:1 , 2:1, and 1:1, respectively. Solution pH was maintained at 5.7 in all experiments. Error bars represent standard deviations from duplicate measurements.