Electroneutrality Breakdown and Specific Ion Effects in Nanoconfined Aqueous Electrolytes Observed by NMR

Ion distribution in aqueous electrolytes near the interface plays critical roles in electrochemical, biological and colloidal systems and is expected to be particularly significant inside nanoconfined regions. Electroneutrality of the total charge inside nanoconfined regions is commonly assumed a priori in solving ion distribution of aqueous electrolytes nanoconfined by uncharged hydrophobic surfaces with no direct experimental validation. Here, we use a quantitative nuclear magnetic resonance approach to investigate the properties of aqueous electrolytes nanoconfined in graphitic-like nanoporous carbon. Substantial electroneutrality breakdown in nanoconfined regions and very asymmetric responses of cations and anions to the charging of nanoconfining surfaces are observed. The electroneutrality breakdown is shown to depend strongly on the propensity of anions toward the water-carbon interface and such ion-specific response follows generally the anion ranking of the Hofmeister series. The experimental observations are further supported by numerical evaluation using the generalized Poisson-Boltzmann equation


Abstract
Ion distribution in aqueous electrolytes near the interface plays critical roles in electrochemical, biological and colloidal systems and is expected to be particularly significant inside nanoconfined regions. Electroneutrality of the total charge inside nanoconfined regions is commonly assumed a priori in solving ion distribution of aqueous electrolytes nanoconfined by uncharged hydrophobic surfaces with no direct experimental validation. Here, we use a quantitative nuclear magnetic resonance approach to investigate the properties of aqueous Electric double layer (EDL) near the interface is of fundamental importance in various applications ranging from redox reactions in electrochemistry to colloidal particles assembly 1 and DNA sequencing 2 . The neutrality of the total charge is an important condition in deriving the ion distribution near the interface in the EDL theory. For an uncharged hydrophobic surface such as the water/air interface, positive and negative ions can still be separated in the interfacial region (~10 Å) due to different propensities toward the interface between cations and anions 3,4,5,6 ; such effect is called specific-ion effect 7,8,9,10,11 since it is driven by nonelectrostatic interactions that varies significantly between different ions even for ions with the same electrovalency (e.g., Fand I -). In the scenario of aqueous electrolytes confined by hydrophobic surfaces where the pore size is comparable in size to the interfacial region determined by the specific-ion effect, a natural question raised is how the tendency of charge separation near the interface reconciles with electroneutrality inside nanoconfined regions. Could electroneutrality of the total charge in fact be violated substantially inside nanoconfined regions driven by the specific-ion effect?
Theoretical studies nearly always take the total charge neutrality inside nanoconfined regions for granted and experimental evaluation of electroneutrality inside nanoconfined regions is lacking.
Such evaluation could contribute significantly to our understandings of some very important processes such as energy storage in supercapacitor 12 , ion transport through nanochannels 13 , and ionic processes in proteins 7 .
Nanoporous carbon with graphitic-like internal surfaces provides an ideal model system for investigating the electroneutrality in nanoconfined aqueous electrolytes using nuclear magnetic resonance (NMR). Previous studies showed that fluid inside carbon nanopores exhibits a different NMR chemical shift from that outside the nanopores due to the ring current effect, which gives rise to a nucleus independent chemical shift (NICS) 14,15,16,17,18 . This shift provides a clear NMR marker for selectively and quantitatively monitoring the electrolyte inside nanometer-sized regions confined by hydrophobic graphitic-like carbon surfaces. It provides an excellent tool for determining quantitatively the cation and anion concentrations inside nanopores. Ions, especially anions, can be ordered by their influence on a vast variety of specific ion effects, called the Hofmeister series 7,10,19 . A typical ranking is SO 4 2-< F -< Cl -< Br -< NO 3 -< I -< BF 4 -< ClO 4 for some anions with increasing protein solubility in aqueous electrolytes to the right side (often referred to as the chaotropic side) 10 . Evaluating the electroneutrality with systematic change of anions according to the Hofmeister series provides another avenue for revealing the potential electroneutrality breakdown caused by the ion-specific interfacial effect.
Here we report such a quantitative NMR study of the ion concentrations in nanoconfined aqueous electrolytes. Hydrophobic graphitic-like porous carbon is used as a model system to provide the nanoconfinement. Direct experimental evidence is observed for a significant electroneutrality breakdown of the total charge inside nanometer-sized regions even when the carbon material is uncharged. Interfacial specific ion effects and ion-ion correlations are shown to play crucial roles in determining the degree of electroneutrality breakdown inside nanopores.
The importance of the specific-ion interfacial effect is further revealed by the asymmetric and nonlinear responses of cation and anion concentrations to the external charging of the nanoconfining carbon walls. Such information was obtained using a charge-controlling device built into the NMR probe. The experimental results are further validated by a numerical calculation using the generalized Poisson-Boltzmann (PB) equation in nanopores, demonstrating that specific-ion interfacial effect can indeed dominate the electrostatic interactions leading to the breakdown of electroneutrality inside nanoconfined regions.

Electroneutrality breakdown in nanoconfinement
A high quality nanoporous carbon derived from polymer poly(etheretherketone) (PEEK) 20, 21 is used to provide the hydrophobic nanoconfinement in this work (See Methods).
The activated carbon sample is designated as P-40 and the average pore size is 0.9 nm (wall surface to wall surface assuming a slit-shaped pore) and 1.2 nm (carbon to carbon centers) according to the previous study 15 . Unless specified, all results discussed here refer to that obtained using P-40. However, activated carbon with pore size of 1.9 nm (carbon to carbon centers), labeled P-92, was also used in the current study and will be mentioned as well. The capability of NMR approach to selectively and quantitatively study nanoconfined fluids is demonstrated in Figure 1a where the 1 H, 19 F, and 23 Na static NMR spectra of NaBF 4 electrolyte injected into P-40 are shown (See Methods). All spectra consist of two peaks. The peak centered at 0 ppm, chosen as the reference, comes from electrolyte outside the nanopores while the peak centered at -7 ppm is from electrolyte inside nanopores 22 . All three nuclei show the same chemical shift at -7 ppm because the shift is completely determined by the NICS effect.
Since the NMR signal is proportional to the number of spins, numbers of cations outside and inside the nanopores can be determined by the 23 Na peak intensities at 0 and -7 ppm, respectively. Similarly, numbers of BF 4 anions and water molecules outside and inside nanopores can be determined from the corresponding peak intensities of the 19 F and 1 H NMR spectra, respectively. From these numbers the cation and anion average concentrations inside nanopores can be determined (See Methods). Figure 1b shows the normalized ion concentrations, c/c 0 , where c is the average ion concentration in nanopores and c 0 is the injected electrolyte concentration (1 mol/kg except for NaF 0.8 mol/kg due to its lower water solubility), for NaF, NaNO 3 , NaBF 4 electrolytes in P-40 and NaBF 4 electrolyte in P-92. One of the surprising phenomena revealed by measurements shown in Figure 1b is the drastic concentration difference between cations and anions, particularly significant in nanoconfined aqueous electrolytes of NaNO 3 and NaBF 4 . The concentration inside nanopores is c/c 0 =1.92 for BF 4 and c/c 0 =0.64 for Na + . In the larger pore P-92 sample, the concentration inside nanopores is c/c 0 =1.34 for BF 4 and c/c 0 =0.70 for Na + . The anomalous concentration difference is a strong indication of the electroneutrality breakdown of the total charge inside the nanopores. As expected, the electroneutrality breakdown is less in the larger pore P-92 sample but it is nevertheless still very significant.
The possibility that the electrolyte neutrality might be maintained by other ions such as H + , OHor trace impurities can be ruled out in the current experimental approach. Take NaF electrolyte in P-40 as an example to estimate the amount of H + and OH -. The PEEK derived activated carbon is of high quality and contains very few surface functional groups 21, 23 that does not produce H + or OH -. So we can conclude that all the H + and OHin this system are from water dissociation (depending on the point of zero charge and pH, the activated carbon can be positively or negatively charged, but the source of the charge still comes from water dissociation). Since only limited electrolyte is injected into the activated carbon, the electrolyte amount in the intergranular space is only about three times that inside carbon nanopores. The intergranular electrolyte pH is measured to be 10 in the slurry. Therefore the net charge due to H + or OHinside carbon nanopores is at most 4 3 10   mol/kg which is negligible compared to the ion concentration inside nanopores (Na + 0.17 mol/kg, F -0.24 mol/kg). Similar estimate can be applied to other ions and the trace impurities (less than 1%) in the as-purchased chemicals.
This shows that the electroneutrality breakdown of the total charge inside carbon nanopores is an intrinsic property of nanoconfined aqueous electrolytes in this system.

Specific ion effects on ion concentrations
Another intriguing phenomenon beyond the electroneutrality breakdown revealed by the data in Figure 1b is the strong influence of anions on the Na + concentration. Although the experiments are carried out with similar electrolyte concentrations and electrolyte/carbon ratios, the Na + concentrations vary significantly among different electrolytes. Na + concentration for NaF electrolyte in nanopores is highly suppressed while that for NaNO 3 is very close to the injected electrolyte concentration. It is interesting to note that the anion concentration increases in the order F -< NO 3 -< BF 4 with Fconcentration being also highly suppressed in the nanopores while NO 3 and BF 4 concentrations being greatly enhanced. The F -< NO 3 -< BF 4 ranking based on their concentrations is fully consistent with the ranking of the Hofmeister series where the anions are known to have different propensities for a hydrophobic surface 7 .
Systematic testing on a series of sodium salt electrolytes whose anions are chosen from the Hofmeister series SO 4 2-< F -< Cl -< Br -< NO 3 -< I -< BF 4 -< ClO 4 provides more insights into the anion-dependent Na + concentrations inside nanopores. The normalized average Na + cation concentration c/c 0 for the sodium salt series is shown in Figure 1c. Na + concentration inside nanopores increases gradually from Na 2 SO 4 to NaClO 4 following the anion Hofmeister series with NaNO 3 being a clear exception (and slightly for NaI). It is of note that Na + concentration inside nanopores is highly suppressed to c/c 0 <0.2 for Na 2 SO 4 and NaF, <0.4 for NaCl and NaBr, and <0.7 for NaI and NaBF 4 . Even though Iand BF 4 ranked to the right side (the chaotropic side) of NO 3 in the Hofmeister series, c/c 0 =0.86 for NaNO 3 is significantly higher than that of NaI and NaBF 4 . It is also of note that unlike other electrolytes, Na + concentration for NaClO 4 in nanopores is substantially enhanced (c/c 0 =1.32) rather than suppressed compared to that of the bulk concentration. Because limited amount of electrolyte is added to the sample, Na + concentration outside the nanopores also differs from c 0 . The Na + concentration in nanopores normalized by that outside nanopores shows slightly different values from c/c 0 but maintains the same trend of Na + concentration increase including the NaNO 3 anomaly.
The strongly anion-dependent Na + concentration inside carbon nanopores revealed by the quantitative NMR analysis demonstrates the intriguing interplay between cations and anions. Na + is a strongly hydrated cation with hydration free energy of -87 kcal/mol, hydration number of 5 to 6 in the first hydration shell 24,25 , and no propensity for the interface 8 . In fact, strong hydration leads to a free energy barrier of several k B T (T=300 K) or higher for Na + ions to enter the hydrophobic nanopore with diameter less than 2 nm 26 . This is clearly reflected by the low value of c/c 0 <0.2 for Na + in NaF. Theory predicts F -< Cl -< Ito be the ranking based on their propensity for the interface 8 . This trend is expected to hold for most anions in the Hofmeister series where the hydration enthalpy becomes less negative toward the chaotropic side of the series 27 . The differences among those anions give rise to the different Na + cation concentrations.

Numerical calculation
More insight can be gained by looking at the various factors determining the ion distribution near the interface. The ion distribution for ion i with valency z i is given by 28 where e is the elementary charge, Λ is the de Broglie thermal wavelength of ion i, μ i is the chemical potential of ion i, ψ(x) is the local electrostatic potential at the location x inside nanopores, V i ext (x) is the ion-surface potential that depends on the ion-specific propensity for the interface 28,29 , and corr i (x) is the free energy contribution from ion-ion correlations, a quantity that requires molecular scale structural information to obtain such as via theory and molecular dynamics simulations 28 . corr i (x) depends on both the ion-specific short-ranged pair potential and the counterion concentration, which is implicitly affected by the electrostatic potential ψ(x). The ion concentration measured by NMR is the averaged value over the pore width d: . Although ion-surface potential V i ext (x) is generally position dependent and has an oscillatory character 29,30 , it is expected that the effective potential ̅ for anions, defined by , ranks according to the Hofmeister series in P-40 nanopores. As such, a larger − ̅ value for the more chaotropic anion would lead to a higher anion concentration and that would attract more Na + counterions into nanopores electrostatically.
Of course, this argument does not take into considerations of the ion-ion correlations (i.e.

( ) = 0).
Numerical calculation of the generalized PB equation 7 in a slit-shaped nanopore is carried out to reveal the mechanism of the electroneutrality breakdown in nanoconfined aqueous electrolytes (See Methods). Since the ion-surface potential 29,31 and ion-ion correlation functions 30, 32, 33 from MD simulation are not available for our system, we ignore the ion-ion correlations at this moment and use a simplified ion-surface interactions potential 34 ( ) = 3 .
Here r is the distance from the ion to the confining surface; i B characterizes the ion-surface interaction strength whose value is about few B kT near the surface 35 . Because the boundary condition on the metal plate is unknown (even though the net charge on the metal plate is zero, we could not assume the surface charge is zero because the inner surface and outer surface may carry induced charges of an equal amount but opposite signs), electrostatic potentials both inside and outside the nanopore need to be solved jointly in order to find the ion distribution inside nanopores (See Methods).
Ion distribution in a 1 nm pore is illustrated in Figure 2b.  Figure 2b. The electroneutrality breakdown is prominent only when the pore size is less than 2 nm. As the pore size increases, the concentration difference between cations and anions disappears and both ion concentrations approach that of the bulk value. Figure 2d shows the average ion concentration versus B -, demonstrating the specific ion effects on the extent of the electroneutrality breakdown in 1 nm pores. Here, B + is fixed at The ion-ion correlations based on electrostatic and ion-specific interactions are predicted to be of crucial importance in nanoconfined electrolytes 28,30,32,36,37 . Although the preferentially adsorbed anions in the nanopores could attract Na + cations via electrostatic interactions as demonstrated by both the experiments and the simulation, the higher Na + concentration associated with NaNO 3 electrolyte is not due to the anomalous interfacial affinity of NO 3 since its concentration is consistent with the ranking of the Hofmeister series, i.e. lower than the BF 4 concentration ( Figure 1b). Clearly, specific ion-ion correlations must be invoked to explain the abnormal Na + concentration in NaNO 3 . Correlations of Na + with NO 3 appear to be stronger than that with Iand BF 4 -, suggesting a more negative effective correlation ̅̅̅̅̅̅ + , defined by exp(− ̅̅̅̅̅̅ + ) = 1 ∫ exp(− + ( )) 0 , for Na + inside the nanopores. It is interesting to note that the formation of solvent-separated Na + and NO 3 ion pairs in bulk electrolyte has been recognized by both computational and experimental studies 38,39 . The formation of solventseparated Na + and ClO 4 ion pairs was also found in bulk electrolyte 40 . Such molecular scale ionion correlations could become more significant at the interface and in nanoconfined environment giving rise to the observed anomaly in the Na + concentration of NaNO 3 and the substantially enhanced Na + concentration in NaClO 4 aqueous electrolyte.

Ion concentrations in charged nanopores
To further demonstrate how the non-electrostatic specific ion effects including ion-ion The ion concentration inside the nanopores versus charging voltage is measured for a single electrode while the other one is covered with a copper foil to shield the radio frequency pulse and signal.  linear behavior is expected when the ion concentration change is mainly due to ions away from the interface and is affected by the change of electrostatic interactions 28 . In contrast, both Na + and BF 4 exhibit nonlinear behavior on negative charging (-V). Na + concentration increases with voltage from 0 to 0.6 V but then starts to decrease with further negative charging. Concomitantly, the initial linear decrease of BF 4 concentration levels off beyond 0.6 V. The nonlinear behavior, particularly the unexpected Na + concentration decrease with negative charging beyond 0.6 V, demonstrates the competing effect between the ion-ion correlations and the ion-surface electrostatic interactions. The attractive Coulomb interaction between Na + and the negatively charged surface tends to bring Na + into the nanopores whereas the decreased BF 4 concentration favors dragging Na + out of the nanopores. When the latter effect dominates, the Na + concentration can actually decrease with further negative charging as observed in Figure 3b. It is also interesting to note that even at 1.0 V charging, the BF 4 concentration in nanopores is still higher than that of Na + , demonstrating the strong ion-surface attractions that overcomes the enormous Coulombic forces due to the net charge in the nanopores and the repulsion between anions and the negative charged surface.
The influence of anions on the cation's behavior via ion-ion correlations is evidenced by comparing Na + behaviors between NaBF 4 and NaNO 3 electrolytes shown in Figure 3c. For the convenience of comparison, the concentration has been normalized by their respective value at 0 V. On positive charging, Na + concentrations in both NaBF 4 and NaNO 3 decrease linearly because they are mainly affected by the change in electrostatic interactions. However, drastically different behaviors are observed on negative charging: while response of Na + in NaBF 4 electrolyte first increases then decreases, the Na + concentration for NaNO 3 almost does not change with charging voltage, indicating that the correlation between Na + and NO 3 is stronger than that in NaBF 4 . The Coulombic attraction on the cations by the negatively charged surface is completely compensated by the ion-ion correlations which drags Na + out of the nanopores when the anions are repelled from the nanopores.

Discussion
In this study, quantitative NMR measurements and numerical simulations are employed to investigate the electroneutrality condition in nanoconfined aqueous electrolytes. Substantial Our study demonstrates that graphitic-like porous carbon provides an ideal model system and the novel in-situ NMR approach opens a new avenue for quantitative experimental evaluations of various ion-specific interactions near the interface and under nanoconfinement.
Although our work is based on aqueous electrolytes, it can be generally applied to other systems such as organic electrolyte and ionic liquids where the strong ion-specific properties beyond their electrovalencies (e.g. ion solvation, interaction with the surface, ion-ion correlations) are also of relevance. The NMR approach is also of great value for validating theories 30,45,46 where the possibility of nanoconfinement-induced electrolyte non-neutrality in aqueous electrolytes is often ignored in computational studies which commonly assume a priori a neutrality of the total charge in nanoconfined regions. The findings revealed by the NMR study have broad implications because the electroneutrality breakdown in aqueous electrolytes can be very substantial in nanoconfined regions, which exist in many systems including proteins, desalination devices, colloidal suspensions and supercapacitors.

Carbon material P-40 preparation
Porous carbon used in this work is derived from high-temperature polymer poly(etheretherketone) (PEEK) using a procedure modified from previous reports 15,47 . PEEK pellets are carbonized at 900 º C for 30 minutes in Argon atmosphere. The carbonized chunk is then cooled down to room temperature and subsequently ground into small particles of approximately 0.5 mm in diameter. The pulverized sample is activated at 900 º C under water vapor for a designated time to achieve certain burn-off percentage. The pulverization ensures uniform activation which leads to a narrow pore size distribution. The mass reduction achieved by the activation process is 40% and the corresponding sample is designated as P-40. The average pore size of P-40 is 0.9 nm (wall surface to wall surface assuming a slit-shaped pore) and 1.2 nm (carbon to carbon centers) according to the previous study 15 . The sample which has mass reduction 92% during the activation process is labeled as P-92, whose pore size is 1.9 nm (carbon to carbon centers).

Nanoconfined electrolytes preparation
The sodium salts are purchased from Sigma-Aldrich and used as purchased without further purification. The purity is >99.0% expect for NaBF 4 (>98%). The aqueous electrolytes are prepared to contain Na + cations 1 mol/kg except for NaF (0.8 mol/kg because of its lower solubility in water). A simple procedure is followed for preparing the nanoconfined aqueous electrolyte. In general, 30 mL electrolyte is injected into 20 mg P-40 sample. The mixture is then tightly sealed in an NMR sample tube. P-40 has a pore volume of 0.5 cm 3 /g therefore 30 mL electrolyte is sufficient to fill the nanopore and about two thirds of the electrolyte is left in the intergranular space.

Device to control carbon surface charging
The device used to control carbon surface charging is comprised of two electrodes made of pure P-40 separated by a glass fiber and immersed in the aqueous electrolyte (1 mol/kg NaBF 4 or NaNO 3 ). Each electrode is 3 mm long and 2.5 mm in diameter. One electrode is shielded with a copper foil so that the detected NMR signal comes only from a single electrode. Potential is applied between the two electrodes. The charging principal is similar to a supercapacitor. In brief, cations are driven away from the surface and anions are attracted to the surface on positive charging such that the electric charge on the surface is maintained to balance the net charge in the liquid side.

Static NMR on non-charged P-40
Furthermore, there are no sidebands under 7 kHz magic angle spinning. All these indicate that the quadrupole interaction effect is negligible for 23 Na NMR.

Ion concentration calculation
The two peaks in the 23 Na NMR spectrum (representing ions in the nanopores and ions in the intergranular space) are well separated and are deconvoluted to obtain the intensities A in (inside nanopores) and A out (outside nanopores). Since the total number of Na + cations n tot associated with the entire NMR spectrum is known based on the amount of the injected electrolyte, the portion inside P-40 nanopores could be calculated by = + . Using the same procedure the amounts of water inside and outside nanopores can be determined. From these numbers we can calculate the Na + concentration c inside P-40 nanopores. The concentrations of BF 4 and NO 3 inside and outside nanopores can be determined similarly.

In-situ NMR on charged P-40
In-situ 19 F, 23 Na NMR experiment is carried out on a homemade probe which is equipped with a charging system controlled by Labview. The device to control P-40 surface charging is charged from 0 V to 1.0 V with a step of 0.1 V. Static NMR spectrum is acquired when the charging reaches equilibrium, typically after 2 hours. For 19 F NMR, the last delay is 5 s and the spin-lattice relaxation time (T 1 ) is 0.7 s. For 23 Na, the last delay is 0.5 s and T 1 is 20 ms.
Charging has little effect on the T 1 relaxation times and the 90 degree pulses for both 19 F and 23 Na. Quadrupole interaction effect for 23 Na is confirmed to be negligible.

Numerical calculation
The nanopore confinement model is illustrated in Fig. 3a. Two conducting metal plates are immersed in 1 mol/L 1:1 electrolyte to simulate slit-shaped carbon nanopore with pore size d.
Water is assumed to be a continuum with a dielectric constant 78.5   . The closest distance min x that ion can approach the surface is limited by the finite ion size. Here we use the typical hydrated ion radii 48 0.35 nm as min x for both cation and anion.
The electrostatic potential near the solid liquid interface is described by Since the system is symmetric from the center of the pore, designated as x=0, we only need to consider the region x>0. In the bulk electrolyte side, the ions only experience surface interactions from one side thus , ( )    23 Na NMR spectra of 30 μL 1 mol/kg NaBF 4 electrolyte in 20 mg P-40. The peak on the left is chosen as the reference (0 ppm) and the right peak is centered at -7 ppm for all three nuclei due to NICS. (b) Cation and anion concentrations of NaF, NaNO 3 , and NaBF 4 electrolytes inside P-40 nanopores. NaBF 4 electrolyte in a larger pore size sample P-92 is also shown for comparison. (c) Na + concentration inside nanopores for different sodium salt electrolytes plotted in the sequence of the anionic Hofmeister series.

Figure 3 | Ion concentrations in charged P-40 nanopores versus charging voltage. (a)
Illustration of the device built into an NMR probe for controlling P-40 surface charging. The device is comprised of two P-40 electrodes immersed in electrolyte and separated by a glass fiber (similar to a supercapacitor). Voltage is applied between the two electrodes such that one electrode is positively charged and the other one is negatively charged. One electrode is covered by copper foil to enable single-electrode NMR measurements.