Electroneutrality breakdown and specific ion effects in nanoconfined aqueous electrolytes observed by NMR

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Ion distribution in aqueous electrolytes near the interface plays a critical role 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 towards 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.

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### ARTICLE

Received 17 Sep 2014 | Accepted 23 Jan 2015 | Published 20 Feb 2015 DOI: 10.1038/ncomms7358
## Electroneutrality breakdown and specific ion effects in nanoconfined aqueous electrolytes observed by NMR

Zhi-Xiang Luo 1, Yun-Zhao Xing 2, Yan-Chun Ling 2, Alfred Kleinhammes 1 & Yue Wu 1,2

Ion distribution in aqueous electrolytes near the interface plays a critical role in electro
chemical, 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 towards 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.

1 Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599-3255, USA. 2 Department of Applied Physical
Sciences, University of North Carolina, Chapel Hill, North Carolina 27599-3216, USA. Correspondence and requests for materials should be addressed to Y.W.
(email: [yuewu@physics.unc.edu).](mailto:yuewu@physics.unc.edu)

lectric double layer near the interface is of fundamental
importance in various applications ranging from electrochemistry 1 and electrophoresis 2, to colloidal particles
# E
assembly 3 and nanofluidics 4 . The neutrality of the total charge
is an important condition in deriving the ion distribution near the
interface in the electric double layer theory. For an uncharged
hydrophobic surface such as the water/air interface, positive and
negative ions can still be separated in the interfacial region
(B10 Å) due to different propensities towards the interface
between the cations and anions 5–8 ; such effect is called specific
ion effect 9–13 since it is driven by non-electrostatic interactions
that vary significantly between different ions even for ions with
the same electrovalency (for example, F � and 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 understanding of some very important processes such as
energy storage in supercapacitor 14, ion transport through
nanochannels 15 and ionic processes in proteins 9 .

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 16–20 .
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 9,12,21 . A
typical ranking is SO4 2 � oF � oCl � oBr � oNO3 � oI �
oBF4 � oClO4 � for some anions with increasing protein
solubility in aqueous electrolytes to the right side (often
referred to as the chaotropic side) 12 . 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 is 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 equation in nanopores, demonstrating that
specific ion interfacial effect can indeed dominate the electrostatic

interactions leading to the breakdown of electroneutrality inside
nanoconfined regions.

Results
Electroneutrality breakdown in nanoconfinement. A highquality nanoporous carbon derived from polymer polyetheretherketone (PEEK) 22,23 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 from wall surface to wall surface assuming a slit-shaped
pore (1.2 nm from carbon centre to carbon centre) according to
the previous study 17 . 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 centres), labelled 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 Fig. 1a where the
1H, 19F and 23Na static NMR spectra of NaBF4 electrolyte
injected into P-40 are shown (see Methods). All spectra consist of
two peaks. The peak centred at 0 p.p.m., chosen as the reference,
comes from electrolyte outside the nanopores while the peak
centred at - 7 p.p.m. is from electrolyte inside nanopores 16 .
All the three nuclei show the same chemical shift at - 7 p.p.m.
because the shift is completely determined by the nucleusindependent chemical shift 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 p.p.m.,
respectively. Similarly, numbers of BF4 � 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 the nanopores can be determined
(see Methods). Fig. 1b shows the normalized ion concentrations,
c/c0, where c is the average ion concentration in nanopores and c0
is the injected electrolyte concentration (1 mol kg � 1 except for
NaF 0.8 mol kg � 1 due to its lower water solubility), for NaF,
NaNO3, NaBF4 electrolytes in P-40 and NaBF4 electrolyte in
P-92. One of the surprising phenomena revealed by measurements shown in Fig. 1b is the drastic concentration difference
between cations and anions, particularly significant in nanoconfined aqueous electrolytes of NaNO3 and NaBF4. The concentration inside nanopores is c/c0 ¼ 1.92 for BF4 � and c/c0 ¼ 0.64 for
Na þ . In the larger pore P-92 sample, the concentration inside
nanopores is c/c0 ¼ 1.34 for BF4 � and c/c0 ¼ 0.70 for Na þ . 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 þ, OH � or 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 þ
and OH � . The PEEK-derived activated carbon is of high quality
and contains very few surface functional groups 23,24 that do not
produce H þ or OH � . So we can conclude that all the H þ and
OH � in this system are from the dissociation of water
(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

2.0

1.6

1.2

0.8

0.4

0.0

1.5

1.0

0.5

19F NMR

1H NMR

23Na NMR

15 10 5 0 –5 –10 –15 –20 –25

Chemical shift (p.p.m.)

2.4

In P–92

BF4–

BF4

Na +

NO3–

Na + Na +

Na +

F –

NaBF4 NaBF4

NaF

NaNO3

Chaotropic

Kosmo– Chaotropic

tropic anions

tropic

anions

0.0

NaF

NaF NaBr Nal NaClO4

Na2SO4 NaCl NaNO3 NaBF4

NaBr Nal

NaNO3

NaBF4

Figure 1 | Ion concentrations c/c0 in uncharged P-40 carbon nanopores.
(a) 19 F, 1 H and 23 Na static NMR spectra of 30 ml 1 mol kg � 1 NaBF4
electrolyte in 20 mg P-40. The peak on the left is chosen as the reference
(0 p.p.m.) and the right peak is centred at - 7 p.p.m. for all the three nuclei
due to nucleus-independent chemical shift. (b) Cation and anion
concentrations of NaF, NaNO3 and NaBF4 electrolytes inside P-40
nanopores. NaBF4 electrolyte in a larger pore size sample P-92 is also
shown for comparison. (c) Na þ concentration inside the nanopores for
different sodium salt electrolytes plotted in the sequence of the anionic
Hofmeister series.

H þ or OH � inside carbon nanopores is at most
3 � 10 � 4 mol kg � 1, which is negligible compared with the ion
concentration inside nanopores (Na þ 0.17 mol kg � 1, F �
0.24 mol kg � 1 ). Similar estimate can be applied to other ions
and the trace impurities (o1%) in the as purchased chemicals.
Even if the impurities are all segregated into the nanopores, the
maximum concentration is at most four times the impurity
concentration in the bulk electrolyte. This would give rise
to an estimated impurity concentration of 0.04 mol kg � 1,
which is insignificant compared with the charge imbalance on

the order of 0.5 mol kg � 1 . 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 Fig. 1b is the strong influence of anions on Na þ
concentration. Although the experiments are carried out with
similar electrolyte concentrations and electrolyte/carbon ratios,
the Na þ concentrations vary significantly among the different
electrolytes. Na þ concentration for NaF electrolyte in nanopores
is highly suppressed while that for NaNO3 is close to the injected
electrolyte concentration. It is interesting to note that the anion
concentration increases in the order F � oNO3 � oBF4 � with F �
concentration being also highly suppressed in the nanopores
while NO3 � and BF4 � concentrations being greatly enhanced.
The F � oNO3 � oBF4 � 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 9 .

Systematic testing on a series of sodium salt electrolytes whose
anions are chosen from the Hofmeister series SO4 2 � oF � oCl �
oBr � oNO3 � oI � oBF4 � oClO4 � provides more insights into
the anion-dependent Na þ concentrations inside the nanopores.
The normalized average Na þ cation concentration c/c0 for the
sodium salt series is shown in Fig. 1c. Na þ concentration inside
nanopores increases gradually from Na2SO4 to NaClO4 following
the anion Hofmeister series with NaNO3 being a clear exception
(and slightly for NaI). It is of note that Na þ concentration inside
nanopores is highly suppressed to c/c0 o0.2 for Na2SO4 and NaF,
o0.4 for NaCl and NaBr, and o0.7 for NaI and NaBF4. Even
though I � and BF4 � are ranked to the right side (the chaotropic
side) of NO3 � in the Hofmeister series, c/c0 ¼ 0.86 for NaNO3 is
significantly higher than that of NaI and NaBF4. It is also of note
that unlike other electrolytes, Na þ concentration for NaClO4 in
nanopores is substantially enhanced (c/c0 ¼ 1.32) rather than
suppressed. Because limited amount of electrolyte is added to the
sample, Na þ concentration outside the nanopores also differs
from c0. The Na þ concentration in nanopores normalized by
that outside the nanopores shows slightly different values from c/
c0 but maintains the same trend of Na þ concentration increase
including the NaNO3 anomaly.

The strongly anion-dependent Na þ concentration inside
carbon nanopores revealed by the quantitative NMR analysis
demonstrates the intriguing interplay between cations and anions.
Na þ is a strongly hydrated cation with hydration free energy of

- 87 kcal mol � 1, hydration number of 5–6 in the first hydration
shell 25,26, and no propensity for the interface 10 . In fact, strong
hydration leads to a free-energy barrier of several kBT (T ¼ 300 K)
or higher for Na þ ions to enter the hydrophobic nanopore with
diameter o2 nm (ref. 27). This is clearly reflected by the low
value of c/c0 o0.2 for Na þ in NaF. Theory predicts
F � oCl � oI � to be the ranking based on their propensity for
the interface 10 . This trend is expected to hold for most anions in
the Hofmeister series where the hydration enthalpy becomes less
negative towards the chaotropic side of the series 28 . In nanopore
confinement, the different ion–water and ion-surface interactions
among those anions lead to the differences in Na þ cation
concentrations.

Specific ion effects are ubiquitous in electrochemical and
biological systems 9,10,12,29 . It is very fascinating that very different
effects such as the bulk effect of viscosity 30,31 and interfacial effect
such as surface tension 21,32 all follow the same trend as described
by the Hofmeister series. The common thread linking all these

effects is hydration and the unique properties of water. It was
suggested that when ion–water interaction is stronger than
water–water interaction the Jones–Dole coefficient B is positive
(for example, F � ), whereas it is negative when water–water
interaction is stronger than ion–water interaction (for example,
BF4 � and NO3 � ). In fact, the sign change in B (positive to
negative) is correlated with our observation where anion
concentration changes from being suppressed to being
enhanced. This indicates that the relative strength of ion–water
versus water–water interaction also plays a dominant role
in the specific ion effects in nanoconfinement by hydrophobic
surfaces.

Numerical calculation. More insight into the anion’s influence
on Na þ concentration can be gained by looking at the various
factors determining the ion distribution near the interface. The
ion distribution for ion i with valency zi is given by 32,33

- �

exp - ziecðxÞ þ V i extðxÞ þ corriðxÞ ð1Þ
kBT

we could not assume the surface charge is 0 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 simultaneously to
find the ion distribution inside nanopores (see Methods).

Ion distribution in a 1 nm 1D planar pore is illustrated in
Fig. 2b. In this calculation we use Bi value - 58 � 10 � 50 J m 3
and 46 � 10 � 50 J m 3 (about 5 kBT at 0.3 nm from the surface) for
anions and cations, respectively. Anions are preferentially
adsorbed on the surface because an attractive potential Vi extðxÞ

is chosen, whereas cations are repelled from the surface. The
average anion concentration in the nanopore is much higher than
that of cation, indicating an electroneutrality breakdown of the
total nanoconfined charge. Clearly, the ion-surface interaction is
responsible for such electroneutrality breakdown. If only
Columbic interaction is considered as in the Gouy–Chapman
theory, that is, Vi extðxÞ ¼ 0, bulk concentration will be obtained in

nanopores and the total charge is neutral.

The ion concentrations depend on the pore size and the
strength of the anion–surface interactions. The average ion
concentration versus pore size is shown in Fig. 2c. The Bi values
are the same as in Fig. 2b. The electroneutrality breakdown is
prominent only when the pore size is o2 nm. As the pore size
increases, the concentration difference between the cations and
anions disappears and both the 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 þ is fixed
at 46 � 10 � 50 J m 3 while B � varies from 40 � 10 � 50 to

- 70 � 10 � 50 J m 3 to represent the increased ion propensity for
the interface. The average anion concentration increases as
expected when B � becomes more negative. Although B þ is kept
unchanged, cation concentration also increases because of the
increased electrostatic attraction to the anions. The electroneutrality breakdown is more prominent as the propensity difference
between cations and anions grows. It is of note that the numerical
calculation here shows a monotonic increase of the cation
concentration, which could not explain the anomaly of high
Na þ concentration in nanoconfined NaNO3 electrolyte. This is
mainly because ion–ion correlations are not included in this
calculation.

The ion–ion correlations based on electrostatic and ion-specific
interactions are predicted to be of crucial importance in
nanoconfined electrolytes 33,36,38,42,43 . Although the preferentially adsorbed anions in the nanopores could attract Na þ
cations via electrostatic interactions as demonstrated by both the
experiments and the simulation, the higher Na þ concentration
associated with NaNO3 electrolyte is not due to the anomalous
interfacial affinity of NO3 � since its concentration is consistent
with the ranking of the Hofmeister series, that is, lower than
the BF4 � concentration (Fig. 1b). Clearly, specific ion–ion
correlations must be invoked to explain the abnormal Na þ
concentration in NaNO3. Correlations of Na þ with NO3 � appear
to be stronger than that with I � and BF4 �, suggesting
a more negative R dmean correlation corr þ, defined by
expð � bcorr þ Þ ¼ d 1 0 exp ð � bcorr þ ðxÞ Þdx, for Na þ inside the

riðxÞ ¼

- �
exp mi
kBT

L 3 i

where e is the elementary charge, Li is the de Broglie thermal
wavelength of ion i, mi is the chemical potential of ion i, c(x) is
the local electrostatic potential at the location x inside nanopores,
Vi extðxÞ is the ion-surface potential that depends on the ion-

specific propensity for the interface 33,34 and corri (x) is the freeenergy contribution from ion–ion correlations. For 1 mol L � 1
monovalent ions, the electrostatic correlation 35 is of minor
importance and corri (x) is dominated by the non-electrostatic
excluded-volume interactions, which require molecular scale
structural information to obtain, such as via theory and molecular
dynamics simulations 33 . corri (x) depends on both the ionspecific short-ranged pair potential and the ion concentrations,
which are implicitly affected by the electrostatic potential
c(x). The ion concentration measured by RNMR d is the averaged
value over the pore width d : r�i ¼ d 1 0 riðxÞdx. Although

R d

value over the pore width d : r�i ¼ d 1 0 riðxÞdx. Although

ion-surface potential Vi extðxÞ is generally position dependent

and has an oscillatory character 34,36, it is expected that
the1 R d mean� potential �V � i ext for anions, defined by expð � bV � i extÞ ¼

d 0 exp � bV i extðxÞ dx, ranks according to the Hofmeister series

the1 R d mean� potential �V � i ext for anions, defined by expð � bV � i extÞ ¼

d 0 exp � bV i extðxÞ dx, ranks according to the Hofmeister series

in P-40 nanopores. As such, a larger - V � i ext value for the more

chaotropic anion would lead to a higher anion concentration and
that would attract more Na þ counterions into nanopores
electrostatically. Of course, this argument does not take into
considerations of the ion–ion correlations (that is, corri(x) ¼ 0).

Numerical calculation using the generalized Poisson–
Boltzmann equation in a 1D planar pore is carried out to reveal
the mechanism of the electroneutrality breakdown in nanoconfined aqueous electrolytes (see Methods). Since the ion-surface
potential 34,37 and ion–ion correlation functions 36,38,39 from
molecular dynamics simulation are not available for our system,
we ignore the ion–ion correlations at this moment and use a
simplified ion-surface interactions potential 40 Vi extðxÞ ¼ x B3i. Here

x is the distance from the ion centre to the confining surface
(x 4xmin, xmin is the cutoff distance from ion centre to the
surface, which defined the Helmholtz plane); Bi characterizes the
strength of the ion-specific interfacial interaction whose value is
about few kBT near the surface 41 . To focus on the effects of ionspecific interactions, the electrostatic interaction with its image
charge is not accounted here since it is not ion-specific. Similar to
the Jones–Dole coefficient B, positive Bi will be used for strongly
hydrated ions (for example, F � and Na þ ), which are repelled
from the surface, whereas weakly hydrated ions (for example,
BF4 � and NO3 � ) will have negative Bi indicating their affinity to
the surface. Because the boundary condition on the metal plate is
unknown (even though the net charge on the metal plate is 0,

R d

expð � bcorr þ Þ ¼ d 1 0 exp ð � bcorr þ ðxÞ Þdx, for Na þ inside the

nanopores. It is interesting to note that the formation of
solvent-separated Na þ and NO3 � ion pairs in bulk electrolyte
has been recognized by both computational and experimental
studies 44,45 . The formation of solvent-separated Na þ and ClO4 �
ion pairs was also found in bulk electrolyte 46 . Such molecular
scale ion–ion correlations could become more significant at the
interface and in nanoconfined environment giving rise to the
observed anomaly in the Na þ concentration of NaNO3 and
the substantially enhanced Na þ concentration in NaClO4
aqueous electrolyte.

R d

i ext for anions, defined by expð � bV � i ext

i extðxÞ ¼ x B3i

R d

a b

_�_ ( _x_ )

_x_ min _x_ min _x_ min

Pore size

_x_

Anion

Cation

_x_ min

_x_ 1 _x_ 2

Bulk Nanopore Bulk

c d

0.35 0.45 0.55 0.65

Distance to left surface (nm)

2.5

1.5

Anion

Cation

1 2 3 5 10

Pore size (nm)

Anion

Cation

40 20 0 –20 –40 –60

_B–_ (10 –50 J m 3 )

Figure 2 | Numerical calculation using generalized Poisson–Boltzmann equation. (a) Two conducting metal plates are immersed in 1 M 1:1
electrolyte to simulate the 1D planar carbon nanopore with pore size d. The pore centre is set as x ¼ 0. xmin is defined as the closest distance that
the ions can approach the surface. (b) Ion distribution in 1-nm pores for B þ ¼ 46 � 10 � 50 J m 3, B � ¼ - 58 � 10 � 50 J m 3 . (c) Average ion concentration in
nanopores versus pore size. (d) Average ion concentration in nanopores versus the parameter B � . The parameter B þ ¼ 46 � 10 � 50 J m 3 is fixed.

Ion concentrations in charged nanopores. To further demonstrate how the non-electrostatic specific ion effects including
ion–ion correlations dominate the electrostatic interactions inside
the nanopores and lead to the intriguing electroneutrality
breakdown, ion concentrations versus confining wall surface
charging is measured with the in situ NMR 47–49 . As a model
system to investigate electrolyte properties under hydrophobic
nanoconfinement, the electric conducting property of activated
carbon is an additional benefit that allows fine control of
the surface charge to tune the electrostatic interactions.
This is achieved by incorporating a device similar to a
supercapacitor 14,50,51 into an NMR probe (see Methods). As
illustrated in Fig. 3a, two electrodes made of P-40 are separated by
a glass fibre and immersed in an aqueous electrolyte. Voltage can
be applied between the two electrodes to change the surface
charge while NMR spectrum is acquired in situ. 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.

Figure 3b shows the ion concentrations inside P-40 nanopores
versus charging voltage for NaBF4 electrolyte measured by 19 F
and 23 Na NMR. On positive charging ( þ V), both Na þ and BF4 �
concentrations respond linearly with the charging voltage. The
influence of the non-electrostatic interactions is reflected on the
huge initial concentration difference at 0 V. Because the surface is
already crowded with anions at 0 V, further positive charging is
unlikely to bring in more anions to the surface where nonelectrostatic interactions are dominant. Therefore, such a linear
behaviour 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 33 . In contrast, both Na þ and

BF4 � exhibit nonlinear behaviour on negative charging ( � V).
Na þ 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 BF4 � concentration
levels off beyond 0.6 V. The nonlinear behaviour, particularly the
unexpected Na þ 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 þ and the
negatively charged surface tends to bring Na þ into the
nanopores, whereas the decreased BF4 � concentration favours
the dragging of Na þ out of the nanopores. When the latter effect
dominates, the Na þ concentration can actually decrease with
further negative charging as observed in Fig. 3b. It is also
interesting to note that even at 1.0 V charging, the BF4 �
concentration in nanopores is still higher than that of Na þ,
demonstrating the strong ion-surface attractions that overcomes
the enormous Coulombic forces due to the net charge in the
nanopores and the repulsion between the anions and the negative
charged surface.

The influence of anions on the cation’s behaviour via ion–ion
correlations is evidenced by comparing Na þ behaviours between
NaBF4 and NaNO3 electrolytes shown in Fig. 3c. For the
convenience of comparison, the concentration has been normalized by their respective value at 0 V. On positive charging, Na þ
concentrations in both NaBF4 and NaNO3 decrease linearly
because they are mainly affected by the change in electrostatic
interactions. However, drastically different behaviours are
observed on negative charging: while response of Na þ in NaBF4
electrolyte first increases then decreases, the Na þ concentration
for NaNO3 almost does not change with charging voltage,

1.5

1.0

0.5

0.0 0.2 0.4 0.6 0.8 1.0

Charging voltage (V)

–V NaBF4

Current collector

Copper shield

Glass fiber separator

Sample holder

NMR RF coil

_In situ_
charging

Carbon electrodes

BF4

Na +

––V

BF4

Na +

–V

NaBF4

–V NaNO3

NaNO3

0.0 0.2 0.4 0.6 0.8 1.0

Charging voltage (V)

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 fibre (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. (b) Nanoconfined ion concentrations for 1 mol kg � 1 NaBF4
electrolyte in P-40 versus charging voltage. (c) Comparison of Na þ

concentrations c(V)/c(0) between NaBF4 and NaNO3 electrolytes versus
charging voltage.

indicating that the correlation between Na þ and NO3 � is
stronger than that in NaBF4. The Coulombic attraction on the
cations by the negatively charged surface is completely

compensated by the ion–ion correlations that drags Na þ out of
the nanopores when the anions are repelled from the nanopores.

Discussion
Charge separation is a critical step in many biological processes
and important device applications. For instance, when the
confining walls of a nanochannel carry certain preset surface
charge, complete screening inside the nanochannel cannot be
accomplished by the counter ions when the nanopore size
becomes comparable to the Debye length. A potential difference,
the Donnan potential 52–54, between the inside and outside of the
nanochannel is established and this can have a strong influence
on ionic transport and the properties of nanofluidics devices.
Even without the preset surface charge on the confining walls, as
shown in this work, a potential difference between inside and
outside nanopores can be established based on hydration and
interfacial effects with non-electrostatic interactions. Substantial
charge neutrality breakdown occurs inside nanopores and charge
balance is only maintained when ionic charges inside and outside
nanopores are included. This is also reflected by the nanopore
model used in this work that is distinct from the conventional
way of describing charge distribution inside nanopores in two key
aspects, one is the inclusion of non-electrostatic interactions and
the other is solving the charge distributions inside and outside the
nanopore simultaneously with no preset boundary conditions (a
given surface potential or a preset surface charge density).

To summarize, we employed quantitative NMR measurements
and numerical calculations on a new nanopore model to
investigate the electroneutrality condition in nanoconfined
aqueous electrolytes. Substantial electroneutrality breakdown of
the total charge is observed inside uncharged activated carbon
nanopores. The ion-specific interfacial interactions and ion–ion
correlations are found to play critical roles in determining the
extent of the electroneutrality breakdown. These effects are
further investigated in charged carbon nanopores, which lead to
strong asymmetric responses of cations and anions to the
confining wall surface charging. Moreover, anions impose great
influence on the cation’s behaviour via the ion–ion correlations.

Our study demonstrates that graphitic-like porous carbon
provides an ideal model system, and that 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 ionspecific properties beyond their electrovalencies (for example, ion
solvation, interaction with the surface, ion–ion correlations) are
also of relevance. The NMR approach is also of great value for
validating theories 36,55,56 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.

Methods
Carbon material P-40 preparation. Porous carbon used in this work is derived
from high-temperature PEEK using a procedure modified from previous
reports 17,22 . PEEK pellets are carbonized at 900 �C for 30 min in Argon
atmosphere. The carbonized chunk is then cooled down to room temperature and
subsequently ground into small particles of B0.5 mm in diameter. The pulverized
sample is activated at 900 �C under water vapour 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 from wall surface to wall surface assuming a slitshaped pore (1.2 nm from carbon centre to carbon centre) according to the
previous study 17 . The sample that has undergone a mass reduction of 92% during
the activation process is labelled as P-92, whose pore size is 1.9 nm (carbon to
carbon centres).

Nanoconfined electrolytes preparation. The sodium salts are purchased from
Sigma-Aldrich and used as purchased without further purification. The purity is
499.0% expect for NaBF4 (498%). The aqueous electrolytes are prepared to
contain Na þ cations 1 mol kg � 1 except for NaF (0.8 mol kg � 1 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 � 1 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 fibre and immersed in the aqueous electrolyte (1 mol kg � 1 NaBF4 or NaNO3).
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 process is
similar to a supercapacitor. In brief, cations are driven away from the surface and
anions are attracted to the surface of positive charging such that the net charge on
the electrolyte side balances the electric charge on the carbon surface.

Static NMR on uncharged P-40. 1 H, 23 Na, 19 F (for NaF and NaBF4) and 15 N (for
NaNO3, 15 N enriched) static spectra on the electrolyte/P-40 mixture are measured
with a 400 MHz pulsed NMR system at 293 K. A single-pulse sequence is used for
measurement and the last delay is set long enough to make sure the signal is fully
recovered after each scan. Free induction decay data acquisition starts at 5 ms (ringdown time) after the 90� pulse. The spectral linewidth of full-width at half-maximum is B5 p.p.m. for all the nuclei determined by susceptibility anisotropy
broadening. Since the peak widths associated with nuclei inside and outside pores
are very similar, the T2 � effect will not cause biased estimate of the ratio between the

peak intensity for ions inside nanopores versus that outside nanopores. It is this
ratio that was used to calculate the ion concentrations. T2 � is about 160 ms for 19F

and about 640 ms for 23 Na. These are much longer than 5 ms and the intensity decay
over 5 ms is insignificant. It was found that extrapolating the free induction decay
intensity back to t ¼ 0 exponentially does not change the determination of the ion
concentrations. The 90� pulse of Na þ inside P-40 nanopores is shown to be the
same as Na þ in the intergranular space as well as in pure aqueous electrolyte
solution. 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 Ain (inside nanopores) and
Aout (outside nanopores). Since the total number of Na þ cations ntot 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
nin ¼ ntot Ain þAin Aout . Using the same procedure the amounts of water inside and
outside nanopores can be determined. From these numbers we can calculate the
Na þ concentration c inside the P-40 nanopores. The concentrations of BF4 � and
NO3 � 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 that is equipped with a charging system controlled by
Labview. The device to control P-40 surface charging is charged from 0 to 1.0 V
with a step of 0.1 V. Static NMR spectrum is acquired when the charging reaches
equilibrium, typically after 2 h. For 19 F NMR, the last delay is 5 s and the spinlattice relaxation time (T1) is 0.7 s. For 23 Na, the last delay is 0.5 s and T1 is 20 ms.
Charging has little effect on the T1 relaxation times, T2 �, and the 90� pulses for both

19F and 23Na. Quadrupole interaction effect for 23Na 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 symmetric monovalent
electrolyte to simulate the 1D planar carbon nanopore with pore size d. Water is
assumed to be a continuum with a dielectric constant e ¼ 78.5. x1 and x2 are the ion
locations closest to the inner surface and the outer surface respectively, that is, the
Helmholtz plane. The cutoff distance xmin that an ion can approach the surface is
limited by the finite ion size. Here we use the typical hydrated ion radii 57 0.35 nm
as xmin for both cations and anions. Using different cutoff distances for cations and
anions will only affect the numerical values of the ion concentrations but does not
change the electroneutrality breakdown and its dependence on B � . The effect of a
smaller cutoff distance for anions on the ion concentration in nanopores is

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Acknowledgements
This work was partially supported by the U.S. Army Research Office, W911NF-14-10321 and by the U.S. National Science Foundation, DMR 0906547.

Author contributions
Y.-Z.X. prepared the activated carbon material; Z.-X.L. and Y.-C.L. conducted the NMR
experiments and analysed the data; Z.-X.L. carried out the numerical calculation; Y.W.
and A.K. supervised the project; Z.-X.L. and Y.W. wrote the manuscript.

Additional information
Competing financial interests: The authors declare no competing financial interests.

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How to cite this article: Luo, Z.-X. et al. Electroneutrality breakdown and specific ion
effects in nanoconfined aqueous electrolytes observed by NMR. Nat. Commun. 6:6358
doi: 10.1038/ncomms7358 (2015).

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