Electrochemical Characterization of an Asymmetric Nanofiltration
Membrane with NaCl and KCl Solutions: Influence of Membrane
Asymmetry on Transport Parameters
A. Ca˜nas and J. Benavente1
Grupo de Caracterizaci´on Electrocin´etica y de Transporte en Membranas e Interfases, Departamento de F´ısica Aplicada, Facultad de Ciencias, Universidad de M´alaga, E-29071 M´alaga, Spain
Received July 27, 2001; accepted October 30, 2001; published online January 10, 2002
Electrochemical characterization of a nanofiltration asymmetric membrane was carried out by measuring membrane potential, salt diffusion, and electrical parameters (membrane electrical resistance and capacitance) with the membrane in contact with NaCl and KCl solutions at different concentrations (10−3≤c(M)≤5×10−2).
From these experiments characteristic parameters such as the effec-tive concentration of charge in the membrane, ionic transport num-bers, and salt and ionic permeabilities across the membrane were determined. Membrane electrical resistance and capacitance were obtained from impedance spectroscopy (IS) measurements by us-ing equivalent circuits as models. This technique allows the determi-nation of the electrical contribution associated with each sublayer; then, assuming that the dense sublayer behaves as a plane capacitor, its thickness can be estimated from the capacitance value. The influ-ence of membrane asymmetry on transport parameters have been studied by carrying out measurements for the two opposite external conditions. Results show that membrane asymmetry strongly af-fects membrane potential, which is attributed to the Donnan exclu-sion when the solutions in contact with the dense layer have concen-trations lower than the membrane fixed charge (Xef≈ −0.004 M),
but for the reversal experimental condition (high concentration in contact with the membrane dense sublayer) the membrane poten-tial is practically similar to the solution diffusion potenpoten-tial. The comparison of results obtained for both electrolytes agrees with the higher conductivity of KCl solutions. On the other hand, the influ-ence of diffusion layers at the membrane/solution interfaces in salt permeation was also studied by measuring salt diffusion at a given NaCl concentration gradient but at five different solutions stirring rates. °C2002 Elsevier Science (USA)
Key Words: asymmetric nanofiltration membrane; impedance spectroscopy; membrane potential; salt diffusion.
1. INTRODUCTION
Membrane separation techniques are now commonly used in many industrial processes, and different materials and mem-brane structures are being investigated to obtain the highest retention and flux since these two parameters are normally used
1To whom correspondence should be addressed.
to characterize membrane performance (1–3). Both parameters depend to a large extent on the membrane morphology, but when the transport of electrolytes across membranes are consid-ered, the membrane fixed charge is another important parameter, which can account for the selectivity of membranes (4–9). On the other hand, membranes used in most of the separation pro-cesses under pressure (reverse osmosis, nanofiltration, and ultra-filtration) are nonsymmetrical membranes consisting, basically, of two layers from the same or different materials (asymmetric or composite membranes, respectively). It is possible to con-sider reverse osmosis and nanofiltration membranes as a series association of two homogeneous elements with different struc-tural and, in the case of composite membranes, even different transport properties, which consist of a thin, dense active layer and a thick, porous support (although a nonwoven structure is also commonly used for reinforcement). For this reason, tech-niques able to characterize the different sublayers, and not only the whole membrane, can give basic information for predicting membrane behavior.
Impedance spectroscopy (IS) is a relatively new nondestruc-tive technique for characterizing materials and interfaces, which has emerged with the development of instruments capable of measuring impedance as a function of frequency in a very wide range (from 10−3 to 106 Hz). It is being used as a successful
tool to determine the electrical properties of heterogeneous sys-tems formed by a series array of layers with different electrical/ structural properties such as symmetric membrane/electrolyte or even composite membrane/electrolyte systems since it permits us to evaluate separately the electrical contribution of each sub-layer (10–13). IS measurements enable us to obtain information about systems by using the impedance plots and the equiva-lent circuits as models, where the different circuit elements are related to the structural/transport properties of the systems.
In this paper an electrochemical characterization of a com-mercial asymmetric polyethersulfone membrane for nanofiltra-tion, in contact with NaCl and KCl solutions at different salt concentrations, was carried out by means of different kinds of measurements. Membrane potential and salt diffusion val-ues permit us to determine characteristic membrane transport
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°2002 Elsevier Science (USA) All rights reserved.
parameters such as ion transport numbers, effective fixed charge concentration, and salt permeability. Impedance spectroscopy allows both electrical and geometrical characterizations using equivalent circuits as models. From electrical resistance and membrane potential results, ionic permeabilities at different av-erage concentrations were also determined. The influence of so-lution layers on the permeability of NaCl across the membrane was also studied. Ionic permeabilities in the membrane were determined from electrical resistance and membrane potential, and quite good agreement for salt permeability directly obtained from diffusion measurements and that determined from cation and anion permeabilities was found. On the other hand, the effect of membrane asymmetry on transport parameters was checked by comparing measurements carried out for the two symmetri-cal external conditions since the concentration profiles in each sublayer were not the same in both cases.
2. EXPERIMENTAL
2.1. Material
A commercial polyethersulfone asymmetric membrane (PES-10) for nanofiltration processes by Hoechst Celanese was stud-ied. Membrane thickness (including the unwoven support) is 1xm=(100±5) µm, while the hydraulic permeability
given by the supplier ranged between 1.4×10−11 and 2.8×
10−11m/(s Pa) (at 40 bar). Electrochemical measurements were
carried out with the membrane samples in contact with aque-ous NaCl and KCl solutions at different concentrations (10−3≤
c(M)≤5×10−2), at room temperature t=(25.0±0.3)◦C and
standard pH (5.8±0.3). Before use, the membranes were immersed for at least 6 h in a solution of the appropriate concentration.
2.2. Measurements of Membrane Potential, Impedance Spectroscopy, and Salt Diffusion
Membrane potential, impedance spectroscopy, and salt diffu-sion measurements were carried out in a test cell similar to that described elsewhere (14). The membrane was tightly clamped between two glass half-cells by using silicone rubber rings. To minimize concentration–polarization at the membrane surfaces, a magnetic stirrer was placed at the bottom of each half-cell and its speed rate was externally controlled; most of the measure-ments were carried out at a stirring rate of 525 rpm, which was the highest speed easily controlled for at least 5 h.
• The electromotive force (1E) between both sides of the membranes caused by a concentration gradient was measured by two reversible Ag/AgCl electrodes connected to a digital voltmeter (Yokohama 7552, 1 GÄinput resistance). Measure-ments were carried out following two different procedures: (i) keeping the concentration ratio of the solutions at both sides of the membrane constant, c2/c1=g=2, for concentration
c1 ranging between 0.005 and 0.1 M; (ii) keeping the
con-centration c1constant (c1=0.01 M) and changing gradually the
concentration c2from c2=10−3M to c2=0.1 M. Membrane
potential,1øm, was determined from measured1E values by
subtracting the electrode potential contribution.
• For impedance spectroscopy (IS) measurements an imped-ance analyzer (Solartron 1260) controlled by a computer was used. The experimental data were corrected by software, as well as the influence of connecting cables and other parasite capaci-tances. The measurements were carried out using 100 different frequencies in the range 10 to 106Hz at a maximum voltage of 0.01 V, while the salt concentration ranged between 10−3 and 5×10−2M, the solutions at both sides of the membrane having the same concentration.
• In salt diffusion measurements the membrane was initially separating a concentrated solution (c1) from a diluted one
(ini-tially distilled water, c2 =0). Changes in the solution on side 2
were recorded versus time by means of a conductivity cell con-nected to a digital conductivity meter (Radiometer CDM 83). To see the effect of concentration gradients (1c=c1−c2) on
salt permeability, three concentrated solutions (c1=10−2 M,
5×10−2 M, and 10−1 M) were used, although the
influ-ence of concentration gradient orientation on salt permeability was also considered by measuring salt diffusion for the op-posite concentration gradients: 1ca=ca−cp=0.05 M and
1cp=cp−ca=0.05 M. On the other hand, the influence of
concentration–polarization on diffusion measurements was also studied by carrying out experiments at five different speed rates:
ν=0, 180, 525, 850, and 1100 rpm and1ca=5×10−2M.
3. RESULTS AND DISCUSSION
3.1. Membrane Potential
The electrical potential difference at both sides of a membrane when it is separating two solutions of the same electrolyte but different concentrations (c1and c2) is called “membrane
poten-tial” (1øm). According to the Teorell–Meyer–Sievers or TMS
theory (15, 16), the membrane potential can be considered as the sum of two Donnan potentials (one at each membrane/solution interface) plus a diffusion potential in the membrane; this means
1øm=1øDon(I)+1ødif+1øDon(II). The expressions for these
potentials, when 1 : 1 electrolytes and diluted solutions are con-sidered (concentrations are used instead of activities), are (17)
1øDon=(RT/F )ln[(wXf/2c)+[(wXf/2c)2+1)1/2] [1]
1ødif=(RT/F )[(t−−t+)ln(c1/c2)], [2]
where Xfis the membrane fixed charge concentration,w= −1
or+1 for negatively or positively charged membranes, respec-tively, ti is the transport number of the ion i in the membrane (i= +for cation,−for anion), R and F are the gas and Faraday constants, and T is the temperature of the system. Transport number, ti, represents the amount of current transported for one ion with respect to the total current crossing the membrane, ti =Ii/IT; this means t++t−=1.
FIG. 1. Membrane potential versus salt concentration for g=c1/c2. (a) NaCl solutions: cd=c2(d); cp=c2(s), (b) Comparison of both electrolytes and cp=c2: NaCl (s); KCl (d).
However, for slightly charged membranes, or when the exter-nal salt concentration is higher than the membrane fixed charge (cÀXf), Aizawa et al. (18) obtained the following
approxi-mation,
1øm=(RT/F )[(1−2t+)+(2g−1)(t+t−/g)(Xf/c2)], [3]
where g is the concentration ratio (g=c2/c1). If the parameter
g is constant, Eq. [3] represents a linear relationship between
1ømand 1/c2.
Figure 1a shows membrane potential versus salt concentra-tion (1ømvs 1/c2) for the nanofiltration membrane with NaCl
solutions keeping the concentration ratio (c2/c1 =2) constant
for both opposite external conditions: cd=c2 and cp=c2; a
comparison of the values obtained with NaCl and KCl solu-tions when cp=c2 is shown in Fig. 1b. The fitting of the
lin-ear relationships obtained allows the determination of the fixed charge concentration and the average ion transport numbers in the membrane by means of Eq. [3]. Xf andht+ivalues
deter-mined for the PES-10 membrane with both electrolytes are indi-cated in Table 1. As can be seen, average transport numbers in the membrane do not differ from their values in solution (tNao+ =
0.38 and tKo+=0.48), in agreement with the very low value
ob-TABLE 1
Average Cation Transport Numbers, htNa+i and htK+i, Fixed
Charge Concentration, Xef, and Salt Permeability, Ps, for NaCl
and KCl Solutions
Electrolyte ht+i Xef(M) Ps(m/s)
NaCl (0.40±0.03) −(3.0±0.4)×10−3 (6.9±0.5)×10−8
KCl (0.48±0.12) −(4.0±0.6)×10−3 (8.8±0.3)×10−8
tained for the concentration of fixed charge in the membrane. It seems that for this measurement procedure and interval of con-centrations the main effect corresponds to the porous sublayer.
Membrane potential values obtained with NaCl solutions when the concentration in contact with one sublayer is kept constant (ccte=0.01 M) and the concentration of the solution in
contact with the other sublayer changes (0.001≤cv(M)≤0.1)
are shown in Fig. 2, (1ømvs ln ci) for both reverse external con-ditions (cd=ccteand cp=ccte). As can be observed in this
pic-ture, clear differences exist for both opposite external situations at low concentrations (c<0.01 M), but for salt concentrations higher than the constant concentration no difference in the mem-brane potential values due to memmem-brane orientation exists. These
FIG. 2. Membrane potential versus c2for NaCl solutions and c1=0.01 M
at two reverse external conditions. (d) c2=cd; (s) c2=cp. Calculated
results can be explained taking into account the TMS theory and the results given in Table 1:
(i) If ccte =0.01 M is in contact with the porous sublayer,
some values of the concentration cv=cd are lower than the
membrane fixed charge and a contribution of the Donnan poten-tial must exist; however, when cv=cdincreases, the Donnal
po-tential contribution to the membrane popo-tential can be neglected and a linear dependence between 1øm and ln cv is obtained,
which corresponds to a diffusion potential;
(ii) If ccte=0.01 M is in contact with the dense layer, all
measurements are carried out at cdÀXfbecause of which no
Donnan contribution for the whole range of cv values exists
and only the diffusion potential contribution is obtained (dashed straight line).
To verify these assumptions, the total membrane potential values were calculated by using Xf andht+iresults shown in
Table 1 and taking into account both Donnan and diffusion con-tributions (Eqs. [1] and [2]); calculated values are also drawn in Fig. 2 as a dotted line and, as can be observed, very good agree-ment between experiagree-mental and calculated values was obtained.
3.2. Impedance Spectroscopy
The analysis of impedance data was carried out by the com-plex plane Z∗ method, which involves plotting the impedance imaginary part (−Zimg) versus the real part (Zreal). A single
par-allel (RC) circuit gives rise to a semicircle in the Z∗plane, which has intercepts on the Zrealaxis at R∝(ω→∝) and Ro(ω→0),
(Ro−R∝) being the resistance of the system. The maximum
of the semicircle equals 0.5(Ro−R∝) and occurs at a frequency
such thatωRC=1, RC being the relaxation time (19). However, complex systems usually present a distribution of relaxation
FIG. 3. Impedance plots with NaCl (s) and KCl (n) solutions (c=10−3M) and equivalent circuits for the PES-10 membrane/electrolyte systems. (a) Nyquist plot; (b) Bode plot.
times and the resulting plot is a depressed semicircle; in such cases a nonideal capacitor, which is called a constant phase element (CPE), is considered (19). The impedance for the CPE is expressed by Q(ω)=Yo(ω)−n, where the admittance
Yo(Äs−n) and n are two empirical parameters (0≤n ≤1).
A particular case is obtained when n=0.5; then the circuit element corresponds to a “Warburg Impedance”, which is asso-ciated with a diffusion process according to Fick’s first law.
Experimental data (−Zimg vs Zreal) for the asymmetric
PES-10 membrane at c=10−3 M NaCl are shown in Fig. 3a, and a comparison of the Bode plot (−Zimgvs f ) for the
mem-brane in contact with NaCl and KCl solutions (c=10−3 M) is shown in Fig. 3b. Similar types of curves were obtained for the other concentrations studied. From both kinds of represen-tations, different relaxation processes can be seen: at the high-est frequencies ( f >6×104 Hz), the electrolyte contribution
was obtained; while the membrane contribution appears for fre-quency ranging between 50 and 5×104Hz. For both electrolyte
and membrane some differences were found depending on the electrolyte. The circuit associated with the whole system (asym-metric membrane/solution) is also shown in Fig. 3a and it con-sists in a series association of
(i) a resistance parallel to a capacitor (ReCe) for the
elec-trolyte part.
(ii) a parallel association of a resistance and a capacitor (RdCd) for the dense sublayer of the asymmetric membrane.
(iii) a parallel association of a resistance and a Warburg impedance for the porous sublayer of the asymmetric membrane.
This kind of circuit was found for different composite mem-branes (20, 21).
The fitting of the experimental points by means of a nonlin-ear program (22) allows the determination of the different circuit
FIG. 4. Concentration dependence for the electrical resistance of each sub-layer with both electrolytes. Dense sub-layer: (m) KCl; (d) NaCl. Porous layer: (n) KCl; (s) NaCl.
parameters (relative errors lower that 10%), although only the membrane contribution (dense and porous sublayers) is consid-ered in the following discussion.
Dependence of Rdand Rp values with salt concentration is
shown in Fig. 4; higher values for the electrical resistance of the porous sublayer were obtained, which is due to its higher thickness. In both cases, a decrease of membrane electrical re-sistance when the salt concentration increases was found, which is attributed to the concentration dependence of the electrolyte filling the membrane matrix (13, 21); in fact, the lower values obtained for KCl solutions in comparison with NaCl ones agree with this assumption. On the other hand, dense layer capaci-tance values are practically independent of salt concentration and electrolyte, and the following average values for the whole range of concentrations,hCdli, were determined.
NaCl solutions: hCdli =(2.7±0.3)×10−8F
KCl solutions: hCdli =(3.2±0.6)×10−8F.
The thickness of the dense layer (1xd) can be estimated from hCdlivalues, assuming this layer behaves as a plate capacitor (11,
23):hCdli =εoεdSm/1xd, where Smis the membrane area, while
εo andεd are the permittivity of vacuum and the dense layer
dielectric constant, respectively. A thickness 1xd=(0.20±
0.03)µm for the active layer was obtained, which agrees with the thickness estimated for other composite membranes and with that expected from polymer diffusion (1).
3.3. Salt Permeability
Salt permeability through the membrane can be determined from salt diffusion measurements. According to Fick’s first law, the salt flux through a membrane (for a quasi-steady state) can
be written as
Js=Ps(c1−c2), [5]
where Jsis the diffusive salt flux and Psis the salt permeability
in the membrane and c1and c2are the external concentrations.
On the other hand, the molar salt flux through the membrane at any time instance is give by
Js=(1/Sm)(dn/dt )=(Vo/Sm)(dc2/dt ), [6]
where Vois the volume of the solution at the side of concentration
c2. From Eqs. [5] and [6] the following expression is obtained
(assuming c1is constant):
(dc2/dt)=(Sm/Vo)Ps(c1−c2)=(Sm/Vo)Ps1c. [7]
If the conductivity of solution 2 (σ2) is measured as a function
of time, Eq. [7] can be written as
(dσ2/dt )=(S/Vo)(dσ/dc)ePs1c, [8]
where (dσ/dc)e is characteristic of each electrolyte. Changes
in the conductivity of the solution c2as a function of time, for
the three different NaCl concentration gradients studied (10−2,
5×10−2, and 10−1M) and a stirring rate of 525 rpm are shown
in Fig. 5a, while Fig. 5b shows a comparison of NaCl and KCl experimental values (1cd=5×10−2M). According to Eq. [8],
salt permeability through the membrane can be determined from the slopes of the straight lines shown in Fig. 5, and its average values for the different concentration gradients and electrolytes are indicated in Table 1. The slightly higher values obtained for KCl solutions agree with the higher mobility of this salt. On the other hand, the effect of membrane asymmetry on salt diffusion is shown in Fig. 6 (1c=5×10−2M NaCl); as can be seen, small differences were obtained in salt diffusion measure-ments and, consequently, in salt permeability due to membrane orientation:
1c=cd−cp=0.05 M NaCl, Ps=(6.90±0.12) ×10−8m/s,
1c=cp−cd=0.05 M NaCl, Ps=(5.82±0.08) ×10−7m/s.
However, due to the diffusion layers at the membrane solution/ interface, salt permeability in the membrane ( Psm) can differ from the Ps values obtained for the “membrane system” since
the higher or lower influence of the solution layers (Po s) are
also included in this last case. The influence of concentration– polarization layers on salt transport across the PES-10 mem-brane was studied by measuring NaCl diffusion at different solutions stirring rates (ν) and1c=5×10−2 M. Salt
FIG. 5. Conductivity of solution in half-cell 2 versus time at different NaCl concentration gradients (1cd=cd−cp). (a)1cd=0.01 M: (x),1cd=0.05 M:
(1),1cd=0.1 M: (s). (b) Comparison of NaCl and KCl values (1cd=0.05 M): (1) KCl; (s) NaCl.
the c2–time straight lines as was just indicated. Salt permeability
versus stirring celerity curve is shown in Fig. 7. The thickness of the solution layers, d, can be estimated from these results by fitting the experimental points to the following expression (24),
Ps= £
Psm(1+aν)¤±£1+aν+2¡Psm±Pso¢¤, [9]
where Po
s =Dos/dois the salt permeability in the concentration–
polarization layer; do is the thickness of the polarization layer
when there is not solution stirring, a is an empirical parameter, and Dos is the salt diffusion coefficient in solution. Results give a thickness d =60µm for the concentration–polarization layer
FIG. 6. Conductivity of solution in half-cell 2 versus time: orientation de-pendence. (d)1c=cd−cp=0.05 M NaCl; (s)1c=cp−cd=0.05 M
NaCl.
atν=525 rpm, the value used for solution stirring in all the other measurements, and Pm
s =(10.2±0.4)×10−8m/s.
From membrane potential (1øm) and electrical resistance
(Rm) values, the cationic and anionic permeabilities across the
membrane, P+and P−, were determined by
P+/P−=(exp[F1øm/RT ]−g)/(1−g exp[(F/RT )1øm])
[10]
P++P−= RT/(RmF2)6i ¡
z2icavg ¢
, [11]
where g=c2/c1=2 and the membrane electrical resistance
(Rm=Rd+Rp) at the average concentration cavg=(c1+
c2)/2 was obtained by interpolation of values shown in Fig. 3.
FIG. 8. Ionic permeabilities versus average salt concentration (NaCl solu-tions). P+, (s); P−, (d).
Concentration dependence for ionic permeabilities is shown in Fig. 8 for NaCl solutions. It can be observed that the cationic permeability strongly decreases when the concen-tration increases for c<0.06 M, but a practically constant value is reached at high concentrations, and the following aver-age value can be obtainedhP+i =(3.9±0.5)×10−8m/s, while anionic permeability values are rather constant in the whole range of concentrations and hP−i =(6.2±0.4)×10−8 m/s. For KCl solutions the following average values were obtained:
hP+i =(10.9±1.2)×10−8 m/s and hP
−i =(12.2±1.7)×
10−8m/s.
Assuming for salt and ionic permeabilities a relationship similar to that for salt and ionic diffusion coefficients: Ps∗= 2P+P−/(P++P−), the following values for the salt perme-ability through the membrane were obtained: for NaCl so-lutions, hPs∗i =(4.7±0.9)×10−8 m/s; for KCl solutions, hPs∗i =(12±3)×10−8 m/s. As can be seen, these results do
not differ very much from the Ps values previously obtained
from diffusion measurements (see Table 1).
4. CONCLUSIONS
The different experiments carried out with an asymmetric nanofiltration polyethersulfone membrane in contact with NaCl and KCl solutions allow the determination of characteristic and electrochemical parameters:
• From membrane potential values, the fixed charge con-centration in the bulk membrane Xf= −(4±1)×10−3M and
the ion transport numbers were determined, which indicate a very weak cation exchange character for this ultrafiltration mem-brane. However, the effect of the Donnan exclusion of co-ions
in the membrane was obtained when concentration in contact with the dense sublayer has the lowest values.
• Electrical parameters for dense and porous sublayers (re-sistance and capacitance) were obtained from impedance spec-troscopy measurements. Capacitance values allow the determi-nation of the dense layer thickness, assuming this layer behaves as a plane capacitor.
• Salt permeability in the membrane (Ps) was obtained from
diffusion measurements and the results show that its value is practically independent of the external concentration gradient, although the diffusion layers at the membrane/solution interface affect the real membrane permeability.
• Ionic permeabilities in the membrane were determined from membrane potential and resistance results, which permit us to calculate the salt permeability in the membrane (Ps∗). Good agreement was obtained comparing both Psand Ps∗values.
ACKNOWLEDGMENTS
We thank the European Commission (Project IC15 CT 96-0826) and the Comisi´on Interministerial de Ciencia y Tecnolog´ıa, Espa˜na (Project MAT2000-1140) for financial support.
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