Journal of Membrane Science 668 (2023) 121184

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Journal of Membrane Science

journal homepage: www.elsevier.com/locate/memsci

Influence of electrolyte on concentration-induced

conductivity-permselectivity tradeoff of ion-exchange membranes
Yuxuan Huang a, Hanqing Fan a, Ngai Yin Yip a, b, *
a
Department of Earth and Environmental Engineering, Columbia University, NY, 10027-6623, United States
b
Columbia Water Center, Columbia University, NY, 10027-6623, United States

A R T I C L E I N F O A B S T R A C T

Keywords: In ion-exchange membranes (IEMs), the concentration-induced tradeoff between conductivity and permse­
Ion-exchange membranes lectivity constrains process performance. This study investigates the impacts of different electrolytes on the
Conductivity-permselectivity tradeoff conductivity-permselectivity tradeoff of commercial cation and anion exchange membranes. Nine different
Ion valency
electrolyte solutions containing mono-, di-, and trivalent ions, and spanning 1.5 orders of magnitude in con­
Ion mobility
Donnan exclusion
centration were examined. Effective conductivity is found to be determined by valency and mobility of the
counterion and is insensitive to the co-ion identity. Apparent permselectivity declines with higher valency of the
counterion and with lower valency of the co-ion. Overall, the IEMs exhibited different conductivity-
permselectivity tradeoff behaviors across the electrolyte solutions investigated. The disparate tradeoff trends
are shown to be governed by counter- and co-ion valencies, and counterion diffusivity. The study sheds light on
the principal factors underpinning the tradeoff and advances the understanding of attainable conductivity-
permselectivity performance in more complex water chemistries that are pertinent for practical IEM applications.

1. Introduction applications.
Permselectivity and ionic conductivity are not intrinsic properties of
Ion-exchange membranes (IEMs) are polymeric films with a high the membranes but are affected by operating conditions, specifically
density of charged functional groups, which allow the selective trans­ composition and concentration of the external solutions. Recent studies
port of oppositely-charged counterions, while retaining like-charged co- revealed a tradeoff relationship between IEM conductivity and perm­
ions by charge exclusion [1–3]. Membranes with negative fixed charges, selectivity induced by solution concentration: an increase in concen­
e.g., sulfonate, preferentially allow the transport of cations and are tration of the external NaCl solution enhances conductivity but
classified as cation exchange membranes (CEMs), whereas anion ex­ compromises permselectivity between Na+ and Cl− [8–10]. The
change membranes (AEMs) have positive fixed charges, e.g., quaternary conductivity-permselectivity tradeoff constrains the performance of IEM
amines, and selectively permeate anions [1,4]. IEMs have been broadly processes and can also narrow the scope of application [8]. IEMs operate
employed in water, energy, and chemical production applications, such in different electrolytes beyond pure NaCl solutions [3,11,12]. There­
as electrodialysis desalination, redox flow batteries, and the fore, it is of significance to study the tradeoff behaviors of IEMs in
chlorine-alkaline process, respectively [5–7]. The performance of various electrolytes and shed light on the underlying factors governing
IEM-based technologies is largely determined by the two principal pa­ the tradeoffs. Previous work characterized the conductivity, or resis­
rameters of ionic conductivity and permselectivity [1,4]. Ionic conduc­ tance, of IEMs in a range of electrolytes and concentrations [9,13,14],
tivity determines contribution of the IEMs to overall stack resistance and other studies evaluated membrane permselectivity in electrolytes
and, thus, affects energy consumption and process kinetics or, equiva­ besides NaCl [11,15,16]. However, these investigations focused sepa­
lently, membrane area required. Permselectivity quantifies the mem­ rately on either conductivity or permselectivity; comprehensive and
brane selectivity for counterion transport over co-ion and, hence, systematic studies that simultaneously examine IEM conductivity,
influences current efficiency and separation specificity. Both high con­ permselectivity, and the tradeoff relationship in different electrolyte
ductivity and high permselectivity are desired in almost all IEM solutions and concentrations are absent.

* Corresponding author. Department of Earth and Environmental Engineering, Columbia University, NY, 10027-6623, United States.
E-mail address: n.y.yip@columbia.edu (N.Y. Yip).

https://doi.org/10.1016/j.memsci.2022.121184
Received 17 August 2022; Received in revised form 23 October 2022; Accepted 11 November 2022
Available online 17 November 2022
0376-7388/© 2022 Elsevier B.V. All rights reserved.
Y. Huang et al. Journal of Membrane Science 668 (2023) 121184

This study investigates the influence of electrolyte on the (dVblank/di). Subtracting the blank reading from the combined resis­
concentration-induced conductivity-permselectivity tradeoff of cation tance yields the ASR [20]:
and anion exchange membranes. Effective ionic conductivities and
dVm dVblank
apparent permselectivities of commercial IEMs were characterized in ASR = − (1)
di di
nine different electrolyte solutions containing mono-, di-, and trivalent
3+
ions, over four concentrations spanning 1.5 orders of magnitude. Effects Note that for NH4Cl and AlCl3, the cations, NH+
and Al , can
4
of counter- and co-ion identities on the conductivities and permse­ deprotonate and complex with OH− , respectively. Nonetheless, the
3+
lectivities were analyzed to elucidate the principal factors and governing predominant species in the corresponding solutions are NH+ 4 and Al
mechanisms underpinning the observed trends. The analysis then ex­ across the concentration range according to the acid dissociation and
amines the role of electrolyte and solution concentration on the stability constants, and the concentration of H+ was negligible relative
conductivity-permselectivity tradeoff. Lastly, implications for practical to the cations.
applications of IEM in different water chemistries are discussed. Thicknesses of hydrated membrane coupons, l, were measured using
a digital micrometer (Series 293, Mitutoyo Co., Japan). The effective
2. Materials and methods ionic conductivity, κ, is then calculated using [9,20].
l
2.1. Membranes and chemicals κ= (2)
ASR

Commercial cation exchange membrane and anion exchange mem­ κ is termed effective ionic conductivity since it includes the contri­
brane, Selemion CMV and Selemion AMV, respectively, used in the study butions from the IEM and diffusion boundary layers (further elaborated
were acquired from Asahi Glass Co. (Japan). Ion exchange capacities of in Section 3.1.1). For each electrolyte solution and concentration, at
CMV and AMV are reported as 2.11 ± 0.02 and 1.95 ± 0.07 meq/g dry least three ASR measurements were carried out on the same membrane
polymer, respectively, while swelling degrees in pure water are 0.314 ± coupon.
0.007 g water/g dry polymer for CMV (in Na+ counterion) and 0.183 ±
0.003 g water/g dry polymer for AMV (in Cl− counterion) [17]. The 2.2.2. Apparent permselectivity
electrolytes investigated are NaCl, KCl, NH4Cl, MgCl2, CaCl2, AlCl3, Permselectivity is a measure of the ability of the IEM to selectively
NaBr, Na2SO4, and MgSO4. All the salts are reagent grade and were allow for counterion transport over co-ions. The static method was
purchased from Thermo Fisher Scientific (Waltham, MA). Deionized employed for this study to determine the apparent permselectivities. In
(DI) water was purified with a Milli-Q system (MilliporeSigma, Bur­ the static characterization method, there is no net ionic flux across the
lington, MA). Before conductivity or permselectivity measurements, membrane. Therefore, the measured permselectivity is slightly different
membrane samples were equilibrated in 1.0 eq/L of the test solution for from the true permselectivity in dynamic processes with net ionic fluxes,
at least 24 h, to swap the counter- and co-ions in the membrane to the e.g., electrodialysis, and is, hence, termed the apparent permselectivity
cation and anion being characterized. (discussions on the distinctions can be found in literature [1,12,21]).
Nevertheless, apparent permselectivity has been found to adequately
describe the ability of IEMs to differentiate between counter- and
2.2. Membrane characterization
co-ions; the parameter is, thus, broadly adopted in IEM research [1,22,
23]. Importantly, the analyses in this study focus on the trends in
2.2.1. Resistance and conductivity
permselectivity with varying solution concentration and different
Area specific resistances (ASRs) in the different electrolyte solutions
counter- and co-ion identities; such trends are expected to hold for both
at concentrations, c, of 0.030, 0.10, 0.30, and 1.0 eq/L were charac­
true and apparent permselectivities. Two solutions of different concen­
terized using an electrochemical test setup based on a two-chamber cell
trations contact the membrane on either side and the potential differ­
system with a four-electrode configuration [1]. Membrane coupons
ence across the IEM was used to determine the apparent permselectivity,
were clamped between the two chambers of the cell, with an active
membrane area of 3.14 cm2 (2.0 cm diameter circle). Electrolyte solu­
α [1]. The high concentrations adopted for this characterization are
identical to the concentrations utilized in the ionic conductivity mea­
tion volume in each chamber is ≈16 mL. On each end of the cell, one
surements, i.e., 0.030, 0.10, 0.30, and 1.0 eq/L, and the high:low con­
Pt-coated Ti mesh (4 cm × 4 cm) was used as working or counter elec­
centration ratio is set at 5.0 (commonly used in α characterizations [22,
trodes. Two Ag/AgCl reference electrodes (BASi RE-5B, Bioanalytical
24,25]). For example, for the high concentration of 0.30 eq/L, the low
Systems, Inc., West Lafayette, IN) were positioned 3.5 mm from either
concentration would be 0.060 eq/L. Before characterization at each
side of the membrane to measure the potential difference. Prior to
concentration pair, the membrane samples were immersed in an equil­
resistance measurements, membrane samples were equilibrated in test
ibration bath of the high concentration solution for 24 h, with the bath
solutions for 24 h, with the solution renewed after 12 h.
solution replaced after 12 h.
Direct current method was employed to characterize resistances
The apparent permselectivity can be defined in terms of electro­
since IEM applications are operated with unidirectional ion flow. The
migration transport numbers, t, by [1].
differences between direct and alternating current techniques can be
found in literature [1,18,19]. An electrochemical workstation (Interface tctm − tcts
α= (3)
1010E, Gamry Instruments, Warminster, PA) was used to measure the s
tco
membrane resistance. Test solutions were circulated through both
chambers of the test cell at 4 mL/min using a peristaltic pump (BT101S, where subscripts ct and co refer to counterion and co-ion, respectively,
Golander Pump, Norcross, GA). Direct current was applied to the system and superscripts m and s represent membrane phase and solution phase,
in galvanostatic mode from 1.0 to 10 mA (i.e., current density, i, of respectively. For solutions containing a single electrolyte and assuming
0.32–3.2 mA/cm2), in increments of 1.0 mA, and the potential differ­ the electromigration transport numbers to be constant across the
ence between the two reference electrodes was recorded. At the lowest membrane thickness [23], the membrane potential, Vm, is related to t by
concentration of 0.030 eq/L, a smaller current range was used (0.10–1.0 [2].
mA, in increments of 0.10 mA). Each current step was maintained for 10
tctm RT aLC tm RT aLC
s and the voltage drop, Vm, was recorded every second. The slope of Vm = − ct
ln HC − co ln co (4)
zct F act zco F aHC
voltage drop as a function of current density, i.e., dVm/di, gives the co

combined area resistance of the IEM and solution. Solution resistances

where R is the gas constant, F is the Faraday constant, T is absolute
were measured using the same protocol but without the IEM in the cell

2
Y. Huang et al. Journal of Membrane Science 668 (2023) 121184

temperature, z is ion valence, a is ion activity, and superscripts LC and Subtracting the offset potential and junction potential difference from
HC denote low and high concentrations, respectively. Since tct m
+ tco
m
=1 the steady state measurement yields the membrane potential, Vm [26].
and further assuming aLCct /aHC
ct =a LC
co /aHC
co =a LC
/aHC
[2], Eq. (4) can be Solution phase transport numbers were determined using [29].
simplified to ui
(m ) tis = (9)
t 1 − tctm RT aHC uct + uco
Vm = ct + ln (5)
zct zco F aLC
where u is ion electrical mobility obtained from Ref. [12]. Using tct
s
and
tco
s
calculated with Eq. (9), the experimentally characterized Vm, and the
where the activity, a, could be expressed as the product of molar con­
Nernst potential computed with mean activity coefficients estimated by
centration, c, and mean activity coefficient, γ ± , i.e., a = γ ± c. If the IEM
the Pitzer model [30,31], α can be determined through Eq. (8). Perm­
is perfectly permselective, only counterions can permeate across the
selectivity values of at least duplicate measurements are reported for
membrane, i.e., tct
m
= 1; then the theoretical potential in the ideal case,
each condition tested on the same membrane coupon.
Vtheo (or, equivalently, the Nernst potential), is [1,2,26]

RT aHC 3. Results and discussion

Vtheo = ln (6)
zct F aLC
3.1. Influence of counterion on conductivity
The number of cations and anions each electrolyte dissociates into
are denoted by ν+ and ν− , respectively. For a ν+:ν− electrolyte, the
3.1.1. Diffusion boundary layer resistance is dominant at low electrolyte
expression of tctm can be obtained by substituting Eq. (6) into Eq. (5)
concentrations
together with zct νct + zco νco = 0:
A high ionic conductivity or, equivalently, low ionic resistance is
vct Vm
+ vco crucial for the performance of IEM-based processes [4]. Fig. 1 shows the
(7)
Vtheo
tctm = effective ionic conductivity, κ, of the CEM (Fig. 1A and B) and AEM
vct + vco
(Fig. 1C and D) as a function of electrolyte concentration, c, for different
Eq. (7) is further substituted into Eq. (3) to yield the final expression counterions with co-ions fixed (Cl− and SO2− 2+
4 for CEM; Na and Mg for
+
of α for a ν+:ν− electrolyte: AEM). Note that both axes of the plots are on logarithmic scales. The
1
[
νct Vm
] results show that κ is dependent on the concentration of the external
α= + νco − (νct + νco )tcts (8) electrolyte solution. With increasing c, the conductivities first increase
(νct + νco )tco Vtheo
s
relatively sharply and then gradually level off (correspondingly, ASRs
The equations of apparent permselectivity for various types of elec­ steeply decline and subsequently plateau). This trend is observed across
trolytes in contact with CEM and AEM can be obtained by substituting all electrolyte solutions for both CEM and AEM, and, is consistent with
the values of ν+ and ν− into Eq. (8). The resultant equations are sum­ results reported in previous studies [9,13,18,32].
marized in Table 1 and are consistent with permselectivity expressions The diminished κ at low concentrations is mainly due to the mass
in literature [1,23,26]. transfer resistance contribution from the diffusion boundary layer (DBL)
The potential difference across the membrane, Vm, was measured [11,32,33]. Because of the difference in transport numbers between the
using the technique described in previous studies [20,23,26] and briefly aqueous solution and IEM, concentration polarization is established at
described here. Membrane coupons with an active area of 3.14 cm2 were the solution-membrane interfaces during ion transport, which produces
installed in a two-chamber cell (60 mL for each chamber), which con­ a depletion of ions on one side of the IEM and ion enrichment on the
tained high and low concentration solutions. The open-circuit potentials other side [33–35]. Particularly for the depleted side, the lowered ion
were measured by two Ag/AgCl reference electrodes (Single-Junction concentration leads to an elevated ionic resistance in the DBL [29,34].
Standard Model, Fisher Scientific, Pittsburgh, PA) connected to the The resistance characterization measures the overall resistance of the
electrochemical workstation (Interface 1010E, Gamry Instruments, IEM and the DBLs. Therefore, the measured ASRs are the total re­
Warminster, PA). The solutions were well-mixed by stirring during the sistances in series [1,11], and the resulting effective conductivity, κ,
potential measurements. After the reading between the two reference contains contributions of the IEM and DBLs. At low c, the resistance of
electrodes had stabilized (fluctuations were within 0.1 mV over 5 min) the ion-depleted DBL is typically much higher than IEM resistance and,
[26–28], the potential was averaged over 15 min to give the steady state hence, dominates the effective ASR [11,18]. With increasing c, resis­
measurement. Offset potentials between the reference electrodes were tance of the ion-depleted DBL rapidly declines [11,18], while the IEM
recorded in the high concentration solution with the same stabilization resistance remains almost constant [9]. Note that the practically con­
criterion. Junction potential differences between the two reference stant IEM resistance is valid for the solution concentration range
electrodes across high and low concentration solutions were estimated investigated in this study, which are lower than the membrane fixed
using the activity-corrected form of the Henderson equation [26]. charge concentrations [9]. Therefore, the DBL contribution to net
resistance is lessened and the membrane resistance eventually becomes
Table 1 dominant with rising c. As a result, the overall ionic conductivities
Summary of apparent permselectivity equations for different types of initially increase with higher electrolyte concentrations (κ limited by
electrolytes. DBL) and then progressively level off at higher c (measured κ is
approximately ionic conductivity of solely the IEM). This influence of
ν+:ν− CEM AEM
DBL has been reported for NaCl solutions [18,32,34] and was quantified
1:1 (e.g., NaCl) Vm Vm
+1− 2tct
s
+1− 2tct
s using electrochemical impedance spectroscopy and other techniques
Vtheo Vtheo
α =
2tco
s
α =
2tco
s [11,18,35]. This study further elucidates the role of DBL resistance by
1:2 (e.g., CaCl2) Vm 2Vm extending to a broader range of various electrolytes.
+2− 3tct
s
+1− 3tct
s
V
α = theo s
V
α = theo s The effective conductivities, i.e., the overall contributions from DBL
3tco 3tco
and IEM, of both cation and anion exchange membranes in different
1:3 (e.g., AlCl3) Vm 3Vm
+3− 4tct +1− 4tct electrolyte solutions tend to converge at the lower concentrations
s s
V V
α = theo s α = theo s
4tco 4tco investigated. More specifically, κ approaches ≈0.05–0.1 S/m for both
2:1 (e.g., Na2SO4) 2Vm
+1− 3tct
s Vm
+2− 3tct
s CEM and AEM at the lowest c of 0.030 eq/L in almost all electrolyte
V V
α = theo s α = theo s solutions, as shown in Fig. 1 and Tables 2 and 3. Similar observations
3tco 3tco

3
Y. Huang et al. Journal of Membrane Science 668 (2023) 121184

Fig. 1. Effective ionic conductivity, κ, as a function of electrolyte concentration, c, for CEM in solutions with different counterions and co-ion as A) Cl− and B) SO2−
4 ,
and AEM in solutions with different counterions and co-ion as C) Na+ and D) Mg2+. Data points and error bars are means and standard deviations, respectively, from
at least triplicate experiments on the same membrane coupon.

Table 2 Table 3
Effective conductivity, κ, of CEM in various electrolyte solutions and concen­ Effective conductivity, κ, of AEM in various electrolyte solutions and concen­
trations. Values denote means and standard deviations of at least triplicate trations. Values denote means and standard deviations of at least triplicate
measurements on the same membrane coupon. measurements on the same membrane coupon.
Concentration CEM effective conductivity, κ (S/m) Concentration AEM effective conductivity, κ (S/m)
(eq/L) (eq/L)
NaCl KCl NH4Cl MgCl2 CaCl2 NaCl KCl NH4Cl MgCl2 CaCl2

0.030 0.081 ± 0.102 ± 0.105 ± 0.052 ± 0.058 ± 0.030 0.097 ± 0.096 ± 0.104 ± 0.099 ± 0.103 ±
0.001 0.012 0.013 0.003 0.005 0.002 0.012 0.006 0.004 0.000
0.10 0.165 ± 0.271 ± 0.277 ± 0.074 ± 0.088 ± 0.10 0.228 ± 0.234 ± 0.234 ± 0.246 ± 0.248 ±
0.010 0.009 0.005 0.005 0.003 0.029 0.025 0.004 0.015 0.022
0.30 0.335 ± 0.583 ± 0.602 ± 0.086 ± 0.119 ± 0.30 0.350 ± 0.354 ± 0.342 ± 0.345 ± 0.379 ±
0.028 0.001 0.004 0.002 0.002 0.025 0.004 0.008 0.000 0.011
1.0 0.461 ± 0.958 ± 1.005 ± 0.111 ± 0.164 ± 1.0 0.362 ± 0.362 ± 0.400 ± 0.383 ± 0.398 ±
0.086 0.128 0.115 0.009 0.004 0.027 0.055 0.015 0.037 0.037

AlCl3 NaBr Na2SO4 MgSO4 AlCl3 NaBr Na2SO4 MgSO4

0.030 0.00035 ± 0.00000 0.087 ± 0.015 0.086 ± 0.014 0.052 ± 0.001 0.030 0.096 ± 0.005 0.084 ± 0.002 0.085 ± 0.009 0.090 ± 0.005
0.10 0.0010 ± 0.0001 0.172 ± 0.001 0.158 ± 0.004 0.079 ± 0.004 0.10 0.237 ± 0.011 0.156 ± 0.011 0.161 ± 0.007 0.164 ± 0.031
0.30 0.0044 ± 0.0002 0.344 ± 0.022 0.361 ± 0.006 0.091 ± 0.002 0.30 0.346 ± 0.030 0.191 ± 0.000 0.203 ± 0.001 0.213 ± 0.009
1.0 0.0074 ± 0.0008 0.430 ± 0.052 0.508 ± 0.027 0.112 ± 0.003 1.0 0.405 ± 0.052 0.206 ± 0.022 0.216 ± 0.017 0.216 ± 0.008

were reported in previous studies for other commercial and lab- concentrations in the electrolyte solutions are low during ASR charac­
fabricated IEMs [13,15]. As DBL resistance dominates at the low con­ terization (application of constant current sweeps), and posits that the
centration range, the convergence in κ indicates that the limiting factor high resistance can possibly be explained by deposition of Al(OH)3
on overall transport is the diffusion current, which is proportional to the precipitates on the anodic surface of the CEM and electrolysis of water
product of the valency, |z|, and bulk solution diffusivity, Ds, of the ions [36]. However, we note that the difference in κ between AlCl3 and other
[1,29]. |z|Ds of the cations and anions examined here are within a factor chloride electrolytes is sizeable (>≈150×) and further investigations
of 2 (1.33×10− 9− 2.14×10− 9 m2/s) [12], in general agreement with the will likely be necessary to verify if the above-mentioned phenomena can
κ range at low c. indeed quantitatively account for the considerable disparity.
The only exception is CEM in AlCl3 solution, where κ ≈ 0.00035 S/m
at 0.030 eq/L is around two orders of magnitude lower than other 3.1.2. Higher valency counterions exhibit lower ionic conductivity
electrolytes (Fig. 1A and Table 2). This atypical behavior of Al3+ has The influence of counterion identity on the effective conductivities
been reported in a past study and was attributed to the applied current can be examined by comparing κ for electrolytes with the same co-ion
density exceeding the limiting current density [36]. Specifically, the but different counterions (i.e., analyzing the data points within each
study suggests that the process is in the over-limiting region when AlCl3 panel of Fig. 1). In general, i) κ for counterions with the same valency

4
Y. Huang et al. Journal of Membrane Science 668 (2023) 121184

tend to group together, and ii) higher valency counterions exhibit lower may be factors in addition to ion electrical mobility playing a significant
conductivities, with the disparity in κ greater at higher c. For example, role in the conductivity of AEM with Br− . Transport across IEMs can be
for CEM with Cl− as co-ion (Fig. 1A), the sequence of conductivities described by the obstruction theory [46,47], where ions migrate
2+
follows monovalent (K+, NH+ 4 , and Na ) > divalent (Ca
+
and Mg2+) > through a tortuous path formed by the water phase of the membrane
trivalent (Al3+). Similarly, when the co-ion of AEM is Mg2+ (Fig. 1D), κ matrix, i.e., space occupied by the polymer is inaccessible. The
with monovalent counterion (Cl− ) is greater than divalent counterion Mackie-Meares model relates ion electrical mobilities in hydrated IEM to
(SO2−
4 ). The same trends are also observed in Fig. 1B and C. These ob­ bulk solution phase by um = us [fw /(2 − fw )]2 , where fw is volume frac­
servations are consistent with experimental conductivity or resistance tion of water in the membrane, to account for the spatial effects [46].
measurements reported in literature [13,14,37,38]. Swelling degree, SD, is defined as the mass ratio of sorbed water to dry
For the range of solution concentrations investigated here, coun­ polymer and is related to fw by fw = SD /(SD + ρw /ρp ), where ρw and ρp
terion is the main charge carrier in the IEMs, i.e., ionic current due to co- are the densities of water and polymer, respectively [20,48,49]. SD of
ions is negligibly small [8]. Under an applied external current, ionic the AEM in Br− and Cl− counterions were characterized as 0.129 ±
conductivity of just the IEM, κm, is effectively proportional to the 0.010 and 0.171 ± 0.005, respectively, in NaBr and NaCl electrolyte
product of valency, concentration, and mobility of the counterion in the solutions using the gravimetric method [2,20]. The 24.6% lower SD with
membrane phase, κm ∝ ≈ |zct |cm ct uct (according to the Nernst-Planck
m
Br− corresponds to a 21.2% reduction in membrane water volume
equation, the Einstein relation, and Ohm’s law) [1,7,9,29,39], where fraction, fw. Therefore, according to the Mackie-Meares model, the
superscript m denotes membrane phase. Because |zct |cm ct is practically spatial effects lower the ionic conductivity of Br− by 39.0%, relative to
equivalent to the membrane fixed charge density in order to preserve Cl− , explaining the experimentally observed difference of 43.1% in
electroneutrality [8], the product of valency and concentration can be Fig. 1C.
considered to be the same for counterions with different valencies.
Therefore, membrane conductivity is primarily determined by coun­ 3.2. Conductivity is insensitive to co-ion identity
terion mobility within the IEM, um ct . While counterions with higher
valencies generally have larger hydrated radii and correspondingly The influence of co-ion on the effective ionic conductivities can be
lower mobilities (the Stokes-Einstein relation) [11,12,40], electrostatic investigated by examining κ of the membranes in electrolyte solutions
interactions between the mobile counterions and fixed charges in the with different co-ions but the same counterion. κ as a function of solu­
membrane matrix were found to be the primary cause for the greater tion concentration, c, for counterions of Na+ and Mg2+ for CEM and Cl−
reduction in um ct for higher valency counterions [41], with uct ∝
m
and SO2−4 for AEM are shown in Fig. 2A and B, respectively. Note that
2
uct exp(− zct ) (superscript s denotes solution phase) [17]. The marked
s
both axes of the plots are on logarithmic scales. For the same counterion,
decrease in um ct of counterions of higher charge has also been reported in
other studies [42–44]. Because IEM resistance dominates over the
contribution from DBL at greater solution concentrations, the difference
in κ is more pronounced at higher c.
However, Br− in AEM is an exception to the above-discussed trend
(Fig. 1C). According to the trend, the effective conductivities of mono­
valent counterions are supposed to be higher than divalent counterions,
but the AEM actually exhibits slightly lower conductivity in Br− than
SO2−
4 . This behavior was also observed in another study [13]. Possible
reasons for this deviation will be discussed in Section 3.1.3.

3.1.3. Aqueous diffusivity differentiates conductivity of counterions with

same valency
For counterions with the same valency, ions with greater diffusiv­
ities, Ds, or, equivalently, electrical mobility, us, in the bulk phase
aqueous solution show higher κ. Note that D = uRT/|z|F [12,29]. Again,
the difference is more pronounced at higher c, where the membrane
resistance is dominant. For instance, the sequence of aqueous ion elec­
trical mobilities for three monovalent counterions in Fig. 1A is K+ ≈
NH+ 4 > Na
+
(7.62×10− 8, 7.63×10− 8, and 5.19×10− 8 m2V− 1s− 1,
respectively) [12], which is consistent with the conductivity ranking
among these counterions. The same trend is also observed for the two
divalent counterions, Ca2+ and Mg2+, where Ca2+ has higher us than
Mg2+ (6.17×10− 8 and 5.49×10− 8 m2V− 1s− 1, respectively) [12] and,
correspondingly, κ with Ca2+ counterion is greater. These findings are in
agreement with conductivity and resistance measurements reported in
previous studies as well [13,45]. As discussed earlier, κm is primarily
determined by counterion mobility in the membrane, um ct . Since uct ∝ uct
m s

for counterions with the same valency [17], κ trends at the higher c
investigated can, therefore, be explained by the electrical mobilities of
the ions in bulk phase aqueous solution.
Among the counterions investigated, Br− is observed to not conform
to the above-mentioned κ trend. us of Br− is very similar to Cl−
(8.09×10− 8 and 7.91×10− 8 m2V− 1s− 1, respectively) [12]. But contrary Fig. 2. Effective ionic conductivity, κ, as a function of electrolyte concentra­
to expectation, AEM conductivity in Br− is much lower than Cl− and is tion, c, for A) CEM in solutions with different co-ions and counterion as Na+ and
even slightly below SO2−4 (Fig. 1C), as pointed out in Section 3.1.2 and Mg2+, and B) AEM in solutions with different co-ions and counterion as Cl− and
also reported in another study [13]. This discrepancy implies that there SO2−
4 . Data points and error bars are means and standard deviations, respec­
tively, from at least triplicate experiments on the same membrane coupon.

5
Y. Huang et al. Journal of Membrane Science 668 (2023) 121184

κ of different co-ions are effectively equal across the concentration range Table 4
analyzed. Importantly, the effective ionic conductivities are practically Apparent permselectivity, α, of CEM in various electrolyte solutions and con­
identical i) at both low and high concentrations, where DBL and mem­ centrations. Values denote means and standard deviations of at least duplicate
brane resistances, respectively, are dominant (discussed earlier in Sec­ measurements on the same membrane coupon.
tion 3.1.1); ii) for different co-ion valences (i.e., κ of mono-, di-, and Concentration CEM apparent permselectivity, α (− )
trivalent co-ions are alike); and iii) for different co-ions with dissimilar (eq/L)
NaCl KCl NH4Cl MgCl2 CaCl2
s − 8
electrical mobilities (e.g., NH+ 4 and Na have u of 7.63×10
+
and
0.030 0.988 ± 0.982 ± 0.987 ± 0.943 ± 0.945 ±
5.19×10− 8 m2V− 1s− 1, respectively, but undistinguishable κ). This in­ 0.012 0.010 0.010 0.008 0.003
dicates that κ is insensitive to the co-ion identity, in agreement with 0.10 0.989 ± 0.977 ± 0.978 ± 0.933 ± 0.930 ±
membrane resistances and conductivities observed in previous studies 0.002 0.008 0.006 0.003 0.010
[13,38]. The insignificance of co-ions in membrane phase charge 0.30 0.975 ± 0.969 ± 0.962 ± 0.919 ± 0.920 ±
0.008 0.005 0.003 0.011 0.029
transfer is consistent with the charge exclusion effect of IEMs, which
1.0 0.930 ± 0.910 ± 0.917 ± 0.865 ± 0.860 ±
results in orders of magnitude lower concentration of co-ions than 0.027 0.008 0.004 0.001 0.008
counterions within the IEMs [1,8,9]. The result here further confirms
AlCl3 NaBr Na2SO4 MgSO4
that the co-ion also plays a minor role in the resistance of DBL layer [39,
50,51]. Therefore, charge transfer in both IEM and DBL is governed by 0.030 0.873 ± 0.016 0.983 ± 0.017 1.03 ± 0.01 0.986 ± 0.037
0.10 0.850 ± 0.010 0.982 ± 0.018 1.03 ± 0.02 0.984 ± 0.003
counterions and the role of co-ions is insignificant.
0.30 0.762 ± 0.006 0.971 ± 0.003 0.988 ± 0.009 0.968 ± 0.004
1.0 0.615 ± 0.017 0.934 ± 0.001 0.969 ± 0.004 0.941 ± 0.004
3.3. Influence of counterion on permselectivity

3.3.1. Permselectivity is lowered at higher concentrations due to weakened depends on the external solution concentration, with apparent permse­
charge exclusion lectivities declining at an increasing rate with greater c. This deterio­
Permselectivity is a measure of the ability of the membrane to rating trend of apparent permselectivity is consistently observed for
selectively allow for counterion transport over co-ions and is also an both CEM and AEM in the different electrolytes investigated and is in
important parameter, along with ionic conductivity, for IEM perfor­ good agreement with findings of past studies [8,11,16].
mance; a high permselectivity is always desired in IEM-based separa­ The lower α reflects increased transport of co-ions across the IEM,
tions [1]. Fig. 3 displays the apparent permselectivity, α, of CEM (Fig. 3A which is caused by the weakened charge exclusion at higher solution
and B) and AEM (Fig. 3C and D) as a function of solution concentration, concentrations [1,7,12]. Exclusion of co-ions from the IEM is governed
c, for various counterions but same co-ion of Cl− or SO2− 4 for CEM and
by the Donnan potential, the electrical potential difference at the
Na+ or Mg2+ for AEM. Note that the horizontal axes are on logarithmic membrane-solution interface: the sign convention of the Donnan po­
scales and vertical axes are on linear scales for all plots. The same data is tential is such that co-ions are repelled from the IEM (and counterions
summarized in Tables 4 and 5. Some experimentally determined are attracted into the membrane) and the magnitude determines the
apparent permselectivities values are larger than unity. This is due to extent of repulsion [1,12,52,53]. The Donnan potential is inversely
experimental artifacts inherent to the α characterization method and proportional to the external solution concentration [1,7,54]. Thus, as c
will be further discussed in Section 3.3.2. The results indicate that α increases, the Donnan potential is diminished and the ability of IEM to

Fig. 3. Apparent permselectivity, α, as a function of electrolyte concentration, c, for CEM in solutions with different counterions and co-ion as A) Cl− and B) SO2−
4 ,
and AEM in solutions with different counterions and co-ion as C) Na+ and D) Mg2+. Data points and error bars are means and standard deviations, respectively, from
at least duplicate experiments on the same membrane coupon.

6
Y. Huang et al. Journal of Membrane Science 668 (2023) 121184

Table 5 reduce the Donnan potential, giving rise to greater co-ion concentrations
Apparent permselectivity, α, of AEM in various electrolyte solutions and con­ in the membrane matrix and eventually lowering the permselectivity
centrations. Values denote means and standard deviations of at least duplicate [57,60,61]. Additionally, affinity between counterions and fixed charge
measurements on the same membrane coupon. groups can produce a screening effect that reduces the effective fixed
Concentration AEM apparent permselectivity, α (− ) charge density in the membrane, thus weakening the ability of IEMs to
(eq/L)
NaCl KCl NH4Cl MgCl2 CaCl2 exclude co-ions [11,23]. This affinity and, hence, screening effect are
generally stronger for higher valency counterions [40,62] and may also
0.030 0.995 ± 1.00 ± 0.997 ± 1.06 ± 1.05 ±
0.021 0.02 0.021 0.01 0.00
contribute to the lessened α with greater zct. The diminished co-ion
0.10 0.982 ± 0.995 ± 0.993 ± 1.04 ± 1.04 ± exclusion by IEMs with increasing counterion valency has been found
0.002 0.003 0.009 0.00 0.01 in several ion sorption studies [55,57,63].
0.30 0.967 ± 0.984 ± 0.989 ± 0.993 ± 0.996 ± At low concentrations, a few αs in Fig. 3 are slightly larger than unity.
0.012 0.003 0.011 0.021 0.009
For example, at c of 0.030 eq/L, apparent permselectivities of CEM in
1.0 0.864 ± 0.870 ± 0.869 ± 0.878 ± 0.884 ±
0.002 0.008 0.012 0.008 0.006 Na2SO4 (Fig. 3B and Table 4) and AEM in MgCl2 (Fig. 3D and Table 5)
are experimentally determined to be 1.03 and 1.06, respectively. In
AlCl3 NaBr Na2SO4 MgSO4
principle, however, IEM permselectivity should not exceed 1, as perm­
0.030 1.11 ± 0.01 1.00 ± 0.03 0.947 ± 0.043 0.996 ± 0.022 selectivity of 1 already signifies perfect selectivity for counterions over
0.10 1.08 ± 0.02 0.990 ± 0.020 0.868 ± 0.015 0.951 ± 0.029
co-ions [1,26]. Thus, permselectivities >1 are physically not meaning­
0.30 1.04 ± 0.01 0.968 ± 0.002 0.756 ± 0.003 0.865 ± 0.027
1.0 0.897 ± 0.018 0.891 ± 0.002 0.567 ± 0.021 0.633 ± 0.059 ful. The abnormal values can be explained by the method employed to
determine apparent permselectivity α. As presented in Eq. (8) and
Table 1, the apparent permselectivity is calculated using the ratio of the
exclude co-ions is suppressed [55–57], resulting in the progressive experimentally measured membrane potential to the theoretical poten­
compromise of permselectivity. The effect of external solution concen­ tial, i.e., Vm/Vtheo. However, Vm and Vtheo can be very close at low c,
tration on α has been characterized in NaCl [11,14,16]. The present such that even a small variation in the measured Vm (e.g., <1 mV) yields
study widens the range of electrolytes and quantifies the influence of c Vm > Vtheo and, subsequently, an apparent permselectivity surpassing
on apparent permselectivity trends across different counter- and co-ion unity. One primary contributor to this variation in the measured Vm is
pairs. the different junction potential at the tips of reference electrodes from
For the well-studied NaCl, the decline in α accelerates as c increases. different compositions and concentrations between the electrode filling
For instance, the CEM apparent permselectivity remains at around 0.99 solution and the external test solution [26,29]. Although correcting for
when the NaCl concentration increases from 0.030 to 0.10 eq/L, but the activity in the Henderson equation can minimize this inaccuracy, the
drops from 0.975 to 0.930 as c further rises from 0.30 to 1.0 eq/L equation itself is based on simplifying assumptions and, hence, un­
(Fig. 3A and Table 4). A similar α trend is observed for AEM in NaCl. In certainties cannot be completely eliminated [26]. In the present study, a
the lower concentration range, i.e., c < 0.10 eq/L in Fig. 3A and C, discrepancy of ≈1 mV between experimental measurements and Hen­
membrane concentration of the co-ion is orders of magnitude lower than derson equation calculations for the junction potential difference be­
the counterion [8,54,58] and, hence, α is only slightly lowered even tween two reference electrodes is large enough to have some Vm slightly
though the relative increase in membrane co-ion concentration is sub­ exceed Vtheo, thus causing a few αs to be greater than unity; such margins
stantial due to the elevated c [8]. As the external solution concentration in Vm have been reported in a past study [26]. Another possible factor is
approaches the membrane fixed charge density (2.01 and 1.87 eq/L for small but unavoidable experimental variations arising from disassem­
the CEM and AEM in this study, respectively), the membrane concen­ bling and reassembling of the test cell between replicate measurements.
tration of co-ion gradually becomes comparable and nonnegligible While such variations can be minimized with careful techniques, they
relative to counterion. The charge exclusion ability of the IEMs is cannot be entirely eradicated and are often on the order of 1 mV [28].
eventually overwhelmed when NaCl solution concentrations reach Both these factors could be responsible for some α apparent permse­
around the level of membrane fixed charge density [8,59,60]. However, lectivities being larger than unity. Regardless of the effects of inherent
α trends significantly dissimilar from NaCl are observed for some of the limitations in the experimental characterization protocol on the absolute
other electrolytes, e.g., apparent permselectivities of CEM in AlCl3 and value of α, the qualitative trends still hold, namely, permselectivities for
AEM in Na2SO4 are appreciably compromised even at solution concen­ counterions with same valency group together and higher valency
trations well below the membrane fixed charge density. Possible factors counterions lower the IEM permselectivities.
contributing to such divergences are discussed next.
3.3.3. Specific interactions between counterions and fixed charge groups
3.3.2. Higher valency counterions experience lower permselectivity can affect IEM permselectivity
The impact of counterion identity on the apparent permselectivity is As discussed in the preceding section, the apparent permselectivities
investigated by comparing α for electrolytes with different counterions with different counterions of the same valency are very similar, as the
but the same co-ion (i.e., examining the data points within each panel of Donnan potential is affected by the same zct. However, small but sig­
Fig. 3). Trends similar to the analysis of conductivity in Section 3.1.2 nificant disparities between α are still observed, e.g., α for CEM in Na+ is
were observed: i) α for counterions with same valency tend to gather slightly higher than K+ and NH+ 4 (Fig. 3A). The specific binding affinity
into groups and ii) higher valency counterions show lower apparent between counterions and fixed charge groups could possibly explain
permselectivity, with the difference generally more prominent in the some of these discrepancies: counterions that have greater affinity with
high c range. For instance, when the co-ion is maintained as Cl− the fixed moieties will better screen the electric field of the charged
(Fig. 3A), the order of α for CEM follows monovalent (K+, NH+ 4 , and functional groups. This lowers the effective fixed charge concentration
Na+) > divalent (Ca2+ and Mg2+) > trivalent (Al3+). Likewise, AEM in the membrane and weakens the exclusion of like-charged co-ions,
exhibits greater α for monovalent counterions (Cl− and Br− ) than the eventually leading to compromised permselectivity [23,27]. Relative to
divalent counterion of SO2− 4 , when the co-ion is Na (Fig. 3C). These
+
K+ and NH+ 4 , Na is reported to have marginally weaker affinity with
+

features are consistent with experimental results reported in previous sulfonate functional group [62], which is the fixed charge moiety of the
studies [11,14,15]. CEM used in this study. On the other hand, K+ and NH+ 4 share very
As discussed earlier, the exclusion of co-ions is governed by the similar affinities with sulfonate [12,62]. Therefore, K+ and NH+ 4 expe­
Donnan potential. The Donnan potential is inversely proportional to the rience practically identical α trends, and both are slightly lower than
counterion valency [1,55,57]. Thus, higher counterion valencies will Na+, as is presented in Fig. 3A. However, the specific interactions

7
Y. Huang et al. Journal of Membrane Science 668 (2023) 121184

between counterions and fixed charge groups do not explain some of the in Fig. 4B and D, and are in qualitative agreement with previous studies
other differences in α of the same valencies. In the case of the two on IEM transport numbers [38,61]. The greater α for electrolytes with
divalent counterions in Fig. 3A, although Ca2+ exhibits slightly greater higher co-ion valencies is readily explained by the charge exclusion
affinity with sulfonate groups than Mg2+ [62], there is no noticeable principle at Donnan equilibrium: higher valency co-ions experience
difference in α between them [37]. Additionally, Br− is supposed to have greater repulsion, resulting in lower co-ion concentrations in the
slightly stronger affinity with the quaternary amine groups in AEM than membrane matrix [1,53].
Cl− (according to the Hofmeister series and the Collins rule [12]), but
the AEM displays somewhat higher permselectivity in Br− than Cl− 3.4.2. Specific co-ion effects can affect IEM permselectivity
(Fig. 3C) [64]. The inadequacy of the specific interactions between Although the IEMs have very similar α values for different co-ions
counterions and fixed charge groups to fully explain all observations with the same valency, there are still small variations. E.g., CEM has
implies that other factors, such as counterion size, polarizability, and slightly greater α in Cl− than Br− (for counterion of Na+, Fig. 4A) and
interactions with co-ions, may play a role as well [27]. But overall, these AEM has marginally lower apparent permselectivity for Na+ than K+
effects are relatively minor compared to the influence of counterion and NH+ 4 (with the counterion of Cl , Fig. 4C). These deviations in α for
−

valency. In other words, counterion valency is the primary factor gov­ co-ions of the same valency has been reported in previous studies [23,
erning IEM permselectivity. 64,65] and can generally be ascribed to co-ion properties of polariz­
ability, charge density, and hydration enthalpy. Specifically, co-ions
with lower polarizabilities, higher charge densities, and lower hydra­
3.4. Influence of co-ion on permselectivity
tion enthalpies produce higher IEM permselectivities.
Co-ions with greater polarizabilities are more stable in the high
3.4.1. Membranes have greater permselectivity for higher valency co-ions
dielectric environment of IEM matrices and, hence, favorably sorb into
The influence of co-ion on apparent permselectivities is analyzed
the membrane, leading to lower permselectivities [23,65]. Br− is re­
through the comparison between electrolyte solutions of different co-
ported to be more polarizable compared with Cl− [65], which can
ions but identical counterion. Fig. 4 depicts α as a function of solution
explain the lower α of CEM with Br− in Fig. 4A. However, for other
concentration, c, with various co-ions and the same counterion of Na+ or
co-ions of same valency, another mechanism might be more dominant.
Mg2+ for CEM (Fig. 4A and B, respectively) and Cl− or SO2− 4 for AEM
Relative to Na+, AEM with NH+ 4 co-ion has slightly higher apparent
(Fig. 4C and D, respectively). Note that in all plots the horizontal axes
permselectivity (Fig. 4C), even though NH+ 4 is more polarizable [13,23].
are on a logarithmic scale and the vertical axes are on a linear scale. The
NH+ 4 has, however, higher charge density than Na because of its
+
experimental artefact of α > 1 has been discussed earlier in Section
smaller hydrated radius [13,23] and is, thus, more excluded from the
3.3.2.
membrane matrix [23]. This eventually results in a higher α of AEM
Overall, i) α for co-ions with the same valency tend to group together
characterized in NH4Cl than NaCl (Fig. 4C). The effects of different
and ii) higher valency co-ions exhibit greater apparent permselectivities.
co-ion properties can potentially negate each other, e.g., for the two
As an example, CEM shows greater α for the divalent co-ion of SO2− 4 than
divalent co-ions in Fig. 4C, Ca2+ has greater charge density than Mg2+
monovalent co-ions of Cl− and Br− , when counterion is Na+ (Fig. 4A).
but also greater polarizability [13], which can explain the almost
Similarly, for AEM with Cl− as counterion (Fig. 4C), the order of
identical α trends. A previous study postulated that co-ions with lower
apparent permselectivity follows trivalent (Al3+) > divalent (Ca2+ and
hydration enthalpies are excluded by the membrane to a greater extent
Mg2+) > monovalent (K+, NH+ 4 , and Na ). The same trends are observed
+

Fig. 4. Apparent permselectivity, α, as a function of electrolyte concentration, c, for CEM in solutions with different co-ions and counterion as A) Na+ and B) Mg2+,
and AEM in solutions with different co-ions and counterion as C) Cl− and D) SO2−4 . Data points and error bars are means and standard deviations, respectively, from at
least duplicate experiments on the same membrane coupon.

8
Y. Huang et al. Journal of Membrane Science 668 (2023) 121184

[64], thus providing a rationale for the slightly higher α in NH+4 than counterions (κ and α of Al3+ are significantly lower). As c rises, apparent
Na+ (Fig. 4C), since NH+4 has comparatively lower hydration enthalpy. permselectivity deteriorates and effective conductivity increases for all
The study, however, did not further elaborate on the underlying prin­ electrolytes, i.e., the external solution concentration produces a tradeoff
ciples for hydration enthalpy to influence co-ion exclusion. The above­ between α and κ, as indicated by negative slopes in Fig. 5. Such tradeoff
mentioned factors can contribute to the different α observed for co-ions relationship has been reported in recent studies on Na+ and Cl− [8–10]
with same valency, but deeper understanding of the fundamental phe­ and are extended to a wider range of ionic species here to investigate the
nomena will be required to more precisely elucidate the relative role of counter- and co-ions on the κ-α trends.
importance of each effect. Crucially, these factors play a minor role in The external solution concentration concomitantly affects the
comparison to co-ion valency, i.e., valency is the principal co-ion effective conductivities and apparent permselectivities (as explained in
property affecting IEM permselectivity. Sections 3.1.1 and 3.3.1, respectively). Specifically, raising c lowers the
DBL resistance, thus enhancing the effective conductivity, particularly
3.5. Influence of counterion on the concentration-induced conductivity- in the low concentration range of <0.1 eq/L. At the same time, as c
permselectivity tradeoff increases, the Donnan potential declines and charge exclusion is weak­
ened, resulting in the progressive diminishing of α, especially as c ap­
3.5.1. External solutions concentrations cause tradeoff between proaches the membrane fixed charge density. Further analysis reveals
conductivity and permselectivity that the κ-α tradeoff relationships in Fig. 5 are influenced by the counter-
As discussed in previous sections, both the effective ionic conduc­ and co-ion identities, and are discussed next.
tivity and the apparent permselectivity are influenced by the electrolyte
and concentration of the external solution, c. Fig. 5 depicts α and κ with 3.5.2. Higher valency counterions exhibit lower conductivities and
increasing c, indicated by the black arrows, for CEM (Fig. 5A, B, and C) permselectivities
and AEM (Fig. 5D and E). Each panel shows the κ-α trends with different The effect of counterions on the tradeoff relationship can be evalu­
counterions but the same co-ion (Cl− or SO2− 4 for CEM and Na or Mg
+ 2+ ated through the comparison of κ-α profiles for different counterions but
for AEM). Note that horizontal axes in Fig. 5A, B, and C are on loga­ the same co-ion, i.e., each panel in Fig. 5. Generally, i) counterions with
rithmic scales, whereas horizontal axes in Fig. 5D and E are on linear identical valency have tradeoff trends that tend to group together and ii)
scales; vertical axes in all five plots are on linear scales. Fig. 5B displays counterions with higher valency exhibit relatively more inferior effec­
the data of Fig. 5A but without Al3+ for better visualization of the other tive conductivities and apparent permselectivities, particularly at higher

Fig. 5. Apparent permselectivity, α, and effective

ionic conductivity, κ, (vertical and horizontal axes,
respectively) for different electrolyte concentrations,
c, of 0.030, 0.10, 0.30, and 1.0 eq/L. CEM is in solu­
tions with different counterions and the same co-ions
of A) Cl− , B) Cl− , but with Al3+ counterion data not
presented, and C) SO2− 4 . AEM is in solutions with
different counterions and the same co-ions of D) Na+
and E) Mg2+. Direction of black arrows indicates
increasing c. Data points and error bars are means and
standard deviations, respectively, from at least tripli­
cate experiments for κ and duplicate experiments for α
on the same membrane coupon.

9
Y. Huang et al. Journal of Membrane Science 668 (2023) 121184

solution concentrations. For example, CEM κ-α tradeoff curves with Cl− hence, lower counterion mobility in the membrane matrix [46]. Some of
as the co-ion shift towards the bottom-left going from monovalent (K+, the marginal discrepancies in α can be caused by the different binding
2+
NH+ 4 , and Na ) to divalent (Ca
+
and Mg2+) to trivalent (Al3+), as affinity between specific counterions and fixed charge groups (as dis­
depicted in Fig. 5A and B. Likewise, when Mg2+ is the co-ion (Fig. 5E), cussed in Section 3.3.3). However, the mechanism alone is not able to
AEM shows lower conductivities and permselectivities for the divalent fully explain all observed behaviors, suggesting there might be other
counterion of SO2− 4 than monovalent Cl at each concentration level.
−
underlying causes. Nonetheless, the influence of counterion valency is
These trends underscore the principal importance of counterion valency still dominant in governing the conductivity-permselectivity tradeoff.
on κ and α. Specifically, zct determines the electrostatic interactions
between mobile counterions and membrane fixed charges, with coun­
terions of higher valency counterions experiencing greater retardation 3.6. Higher valency co-ions exhibit higher permselectivity but similar
(i.e., reduced um
ct ) and, hence, lower IEM conductivity (Section 3.1.2). On
conductivity
the other hand, counterions of higher valencies have a larger effect on
depressing the Donnan potential and screening the effective fixed charge The influence of co-ions on the concentration-induced tradeoff be­
density, thus causing lower permselectivities by diminishing the exclu­ tween effective conductivity and apparent permselectivity is evaluated
sion of co-ions from the membrane matrix (Section 3.3.2). by comparing κ-α trends with different co-ions but the same counterion.
α and κ across a range of solution concentrations, c, for CEM (Fig. 6A and
3.5.3. Counterions with same valency show similar permselectivities but B, with counterion of Na+ and Mg2+, respectively) and AEM (Fig. 6C and
different conductivities D, with counterion of Cl− and SO2− 4 , respectively) are shown in Fig. 6.
Counterions of the same valency generally have small disparities in Note that both axes of all plots are on linear scales. Overall, i) κ-α profiles
α, but significant variance in κ, i.e., the tradeoff curves are stretched/ tend to group together for co-ions having the same valency and ii) co-
compressed along the horizontal axis about the lowest c in the ions of higher valency show similar conductivities but higher permse­
permselectivity-conductivity plots of Fig. 5. The differences in κ are lectivities, i.e., tradeoff curves are shifted vertically upwards. E.g., the
mainly due to the dissimilar ion electrical mobilities in aqueous solution, CEM conductivity-permselectivity tradeoff curve of divalent co-ion
with counterions of greater usct (∝um ct ) showing higher effective conduc­
SO2−
4 is higher than monovalent Cl and Br with Na as the coun­
− − +

tivities (Section 3.1.3). For instance, CEM conductivities in the three terion (Fig. 6A) and the AEM κ-α curve of divalent co-ion Mg2+ is above
monovalent counterions in Fig. 5B are K+ ≈ NH+ 4 > Na , matching the
+ monovalent Na+ with counterion of SO2− 4 (Fig. 6D). Similar observations
order of uct , whereas apparent permselectivities are close among these
s can be found in Fig. 6B and C. As discussed in Section 3.2, effective
counterions. Therefore, compressing the tradeoff curves of K+ and NH+ 4
conductivity is not sensitive to the co-ion identity since co-ions only play
roughly yields the trend for Na+. Similarly for the two divalent coun­ a minor role in the charge transfer of both IEM and DBL. Therefore, the
terions in Fig. 5A, κ with Ca2+ is greater than Mg2+ (usct of Ca2+ > Mg2+) effect of co-ions on κ-α tradeoffs is mainly reflected in the apparent
but α is almost indistinguishable. Thus, stretching the tradeoff curve of permselectivity, i.e., along the vertical axes in Fig. 6. Higher valency co-
Mg2+ gives the trend of Ca2+. Counterion of Br− in AEM is an exception ions experience greater charge exclusion from the membrane matrix,
(Fig. 5D): although Br− and Cl− have very similar usct , AEM shows much thus resulting in larger α (Section 3.4.1) and, consequently, the tradeoff
smaller conductivities in Br− than Cl− , but α are generally alike (yielding curves are shifted upwards. For co-ions of the same valency, the small
a compression from the tradeoff curve of Cl− to Br− ). This atypical disparities in apparent permselectivities can be explained by specific ion
behavior can be primarily attributed to the lower water uptake of AEM properties as detailed in Section 3.4.2. However, these effects are
in NaBr solution, which leads to more tortuous transport pathways and, comparatively insignificant in relation to co-ion valency. Hence, similar
behaviors in the κ-α tradeoff are observed for co-ions of the same

Fig. 6. Apparent permselectivity, α, and effective

ionic conductivity, κ, (vertical and horizontal axes,
respectively) for different electrolyte concentrations,
c, of 0.030, 0.10, 0.30, and 1.0 eq/L. CEM is in solu­
tions with different co-ions and the same counterion
of A) Na+ and B) Mg2+, and AEM is in solutions with
different co-ions and the same counterion of C) Cl−
and D) SO2− 4 . Direction of black arrows indicates
increasing c. Data points and error bars are means and
standard deviations, respectively, from at least tripli­
cate experiments for κ and duplicate experiments for α
on the same membrane coupon.

10
Y. Huang et al. Journal of Membrane Science 668 (2023) 121184

valency, such as CEM with Cl− and Br− (Fig. 6A), as well as AEM with Data availability
Na+, K+, and NH+ 4 (Fig. 6C).
Data will be made available on request.
4. Implications
Acknowledgements
This study investigates the impacts of electrolytes on the
concentration-induced tradeoff relationship between effective conduc­ Acknowledgments are made to the anonymous reviewers for their
tivity and apparent permselectivity of a cation exchange membrane and critical reading of the manuscript and suggestions to improve the
an anion exchange membrane. For the concentration range examined, analysis and discussions.
the dependence of IEM effective conductivity on external solution con­
centration is due to the contribution of mass transfer resistance from the References
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[1] H. Strathmann, Ion-Exchange Membrane Separation Processes, Elsevier, 2004.
declines with higher external concentrations due to suppression of the [2] T. Sata, Ion Exchange Membranes: Preparation, Characterization, Modification and
Donnan potential to exclude co-ions. These concomitant effects result in Application, The Royal Society of Chemistry, Cambridge, 2004.
a tradeoff: raising the external solution concentration enhances κ but [3] J. Ran, L. Wu, Y. He, Z. Yang, Y. Wang, C. Jiang, L. Ge, E. Bakangura, T. Xu, Ion
exchange membranes: new developments and applications, J. Membr. Sci. 522
compromises α. Such tradeoff has been reported for NaCl in past studies
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Yuxuan Huang: Conceptualization, Methodology, Investigation, the resistances of membrane, diffusion boundary layer and double layer in ion
Formal analysis, Visualization, Writing - Original Draft; Hanqing Fan: exchange membrane transport, J. Membr. Sci. 349 (2010) 369–379, https://doi.
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Conceptualization, Methodology, Formal analysis, Writing- Reviewing [19] B. Auclair, V. Nikonenko, C. Larchet, M. Métayer, L. Dammak, Correlation between
and Editing; Ngai Yin Yip: Conceptualization, Supervision, Funding transport parameters of ion-exchange membranes, J. Membr. Sci. 195 (2002)
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Declaration of competing interest memsci.2020.118259.
[21] C. Larchet, L. Dammak, B. Auclair, S. Parchikov, V. Nikonenko, A simplified
The authors declare that they have no known competing financial procedure for ion-exchange membrane characterisation, New J. Chem. 28 (2004)
1260–1267, https://doi.org/10.1039/B316725A.
interests or personal relationships that could have appeared to influence
the work reported in this paper.

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