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Dielectric properties of cellulose acetate reverse osmosis membranes in aqueous salt solutions
Journal of Membrane Science, 50 (1990) 71-84 Elsevier Science Publishers B.V., Amsterdam - Printed
71 in The Netherlands
DIELECTRIC PROPERTIES OF CELLULOSE ACETATE REVERSE OSMOSIS MEMBRANES IN AQUEOUS SALT SOLUTIONS
KINZI ASAKA Institute
for Chemical Research, Kyoto University, Gokashou, Uji 611 [Japan)
(Received February 21,1989; accepted in revised form September
26,1989)
Summary The dielectric properties were studied of cellulose acetate asymmetric membranes in aqueous electrolyte solutions. The value of the membrane capacitance was 395 nF/cm’, which was attributed to the dense layer in the asymmetric membrane. The thickness of the dense layer was calculated to be 27 nm from the value of the membrane capacitance. The membrane conductance depended on the type of electrolyte, while the membrane capacitance remained almost unchanged irrespective of the kind of electrolyte. The dependence of membrane conductance on the type of electrolyte showed that more highly hydrated ions were only capable of permeating the membrane with more difficulty.
Introduction Since Loeb and Sourirajan made a success of the reverse osmosis method by use of asymmetric cellulose acetate (CA) membranes [ I], asymmetric membranes have played an important role in reverse osmosis, ultrafiltration and other practical applications. A two-layer model, which consists of an ultrathin dense layer and the thick porous layer, was proposed on the basis of electron microscopic observations of the structure of asymmetric CA membranes [241. According to this model, the dense portion controls the relative flux rates of salt and water, whereas the porous part plays a part in supporting the membrane mechanically. Besides electron microscopic observations, dielectric measurements are widely used in the study of the asymmetric structure of membranes [ 5-101. According to theoretical consideration of the dielectric relaxation due to interfacial polarization, the dielectric relaxations are equal to the interfaces in number [ 111. For instance, one dielectric relaxation was observed for measuring cell systems composed of a homogeneous membrane and aqueous salt solutions [ 12,131. Two dielectric relaxations were observed for cell systems composed of a membrane with bilayer structure and ambient aqueous salt solutions [ 5-81.
0376-7388/90/$03.50
0 1990 Elsevier Science Publishers
B.V.
72
Hence this method has the advantage that one can obtain information on the structure of membranes in aqueous solutions. In this study, dielectric measurements were carried out on CA reverse osmosis (RO) membranes in aqueous salt solutions. The capacitance and the conductance of the RO membranes were evaluated from the dielectric relaxation data by use of a theory of dielectric relaxation due to interfacial polarization. The thickness of the dense layer in the RO membranes was estimated from the membrane capacitances. The ion selectivity of the RO membranes is discussed in connection with the data on the membrane conductances. Theoretical Dielectric relaxations due to interfacial polarization were observed in heterogeneous systems composed of various phases. The theories and some experimental results were summarized in a review by Hanai [ 141. The first system considered consists of a homogeneous membrane (having capacitance Cr and conductance G,) separating two electrolyte solutions of the same concentration (with capacitance C, and conductance G,) as illustrated in Fig. 1 (a). The equivalent circuit model, which is shown in Fig. 1 (b) , can be measured in terms of the parallel equivalent capacitance C and the parallel equivalent conductance G at each frequency, as shown in Fig. 1 (c). The complex capacitance C* is represented by a relationship:
$=$+&, f
(1)
w
where C; and Cc are the complex capacitances of the membrane phase and the aqueous phase, respectively. The complex capacitances are defined by relationships of the following form:
c*=c+L j2nf
’
where f is the frequency of the applied AC voltage, and j is the imaginary ber defined by j = J-- 1. After rearrangement of eqn. ( 1)) we have:
num-
G-C,
c=ch+l+ (f/f())" G-G
-
+
1
(6 -G,) (f/fo)” 1+ (f/fJ2
where f, is the relaxation frequency and C,, Ch, G1and Gh are the limiting values of the capacitance C and the conductance G at low (subscript “1”) and high
73
(a)
(b)
Fig. 1. (a) Diagrammatic representation of cell system composed of a homogeneous membrane separating two electrolyte solutions of the same concentration. (b) Circuit model of the cell system shown in Fig. 1 (a). (c) Parallel equivalent circuit model composed of C and G. (d) Frequency dependence of C and G for the cell system shown in Fig. 1 (a). (e) Complex plane plots of C and G for the same cell system.
(subscript “h”) frequencies, respectively. These dielectric parameters are given by the following equations:
Ch$$ f
(6) w
GG,
(7)
G1= G,+G, G _G,C;
+-G&,2
h-
(8)
wf+cw)2
fo=
G+Gw +Cw)
2n(C,
(9)
Figure 1 (d) gives the frequency dependence of the capacitance C and the conductance G derived from eqn. (1)) showing one dielectric relaxation. The
74
complex plane plots of the complex capacitance and the complex conductance are shown in Fig. 1 (e) , and appear as semicircles. The phase parameters Cf, C,, Gf and G, are evaluated from the observed parameters C,, Ch, G, and Gh by use of the following equations [ 13 ] :
($_l)1’2
A=[(l-$-($1)-‘]
(10)
yf+~[l+(~)‘l”2
(11)
Cfz+
(12)
c&d=& - f
(13)
f
ifA>O,
X,= y,+[
ifA
XfZy,_CYf
Yf (I-
Yf) ($-l)]l’z
(I-Y,)
(14)
($l)l”
G,+
(161 f
GW=++ -
(17) f
The second system considered consists of an asymmetric membrane of bilayer structure separating two electrolyte solutions of the same concentration, as illustrated in Fig. 2 (a). Figure 2 (b) shows the equivalent circuit model. In the figure, subscripts “d” and “p” designate the dense layer and the porous layer, respectively. The complex capacitance C* of the parallel equivalent circuit shown in Fig. 2 (c ) is represented by the following relations:
&=$+$+$ d P
Rewriting
(18) w
eqn. (18), we have: C,-Ci
Ci-Ch
c=ch+1+(~/~~)2+1+(~/~~)2 G
=
G
+
1
(Gi -G) V/fpc+ (Gh-Gi) (f/fq)” 1+ Wfp)”
1+ Wq)”
(19) (20)
(a) cd (b)
(d);
Fig. 2. (a) Diagrammatic representation of cell system composed of a membrane of bilayer structure separating two electrolyte solutions of the same concentration. (b) Circuit model of the cell system shown in Fig. 2 (a). (c) Parallel equivalent circuit model composed of C and G. (d) Frequency dependence of C and G for the cell system shown in Fig. 2 (a). (e) Complex plane plots of C and G for the above cell system.
where Ci and Gi are the capacitance and the conductance at intermediate frequencies, and f, and f, are the relaxation frequencies. The capacitances Cl, Ci, Ch, the conductances G1,Gi, Gh and the relaxation frequencies fP, fq are represented by use of the parameters C,,, C,, C,, G,,, Gdand G, in a complicated form [141. Figure 2 (d) shows the frequency dependence of the capacitance C and the conductance G. Two dielectric relaxations are found in the figure. The complex plane plots of the complex capacitance and the complex conductance are shown in Fig. 2 (e ) , and appear as a sequence of two semicircles. Experimental Reverse osmosis membranes The reverse osmosis membranes used in this work were DRS 97,92,50 and 10, which were kindly supplied by Daicel Co. Ltd., Japan. These membranes are composed of 40.4% acetylated cellulose acetate. The figures in the names of the membranes represent NaCl rejections (in % ) assessed by the manufac-
76
Fig. 3. Measuring cell system. Area of electrodes is 3.14 cm2 and distance between the two trades is 1.4 cm.
turer. These membranes have the same thickness are 72 ,um and 68 wt.%, respectively. Dielectric
and water content,
which
measurements
Dielectric measurements were carried out with a Yokogawa Hewlett Packard 4192A impedance analyzer operating in a frequency range between 5 Hz and 13 MHz. The measuring cell system is shown in Fig. 3. All measurements were carried out at 25’ C. Results and discussion
Figure 4 shows the frequency dependence of the capacitance C and the conductance G observed for the cell systems composed of the DRS membranes and having the compartments filled with a 20 mM NaCl solution. The capacitance increases and the conductance decreases with decreasing frequency f in the data for the DRS 10 and 50 membranes. The data for the DRS 92 and 97 membranes show a similar tendency below 1 kHz. These phenomena may be attributed to electrode polarization, which is outside the present discussion. Dielectric relaxations are observed between 1 kHz and 1 MHz in the data for DRS 92 and 97, and may be caused by interfacial polarization between the membrane phase and the aqueous phase. Figures 5 (a) and 5 (b) show the complex plane plots of C and G for the same data of the DRS 97 membrane. The observed parameter Ch and Gh are determined graphically from Fig. 5. It is difficult to determine the parameters C, and G, from Fig. 5, since the electrode polarization affects the data on interfacial polarization in the low frequency region (l-3 kHz). In order to eliminate the effect of electrode polarization, a graphical method was adopted, as illustrated in Fig. 6. Graphical representation of G against C as shown in Fig. 6 gives two straight lines: one for interfacial polarization and the other for electrode polarization. By eliminating the term f/f0 from eqns. (3 ) and (4 ) , we have:
17
, ~/HZ
Frequency
Fig. 4. Frequency dependence of the capacitance C and the conductance Gobservedfor cell systems composed of DRS membranes and compartments filled with a 20 mA4 NaCl solution.
+ f0
; 20 2 4
f-30
-:
0
0
IOh
10
t
0
OTch (a)
(i-d
k
10
30 20 Capacitance
Conductance
40
,
ClnF
50
$60
, GlmS
Fig. 5. Complex plane plots of the capacitance C (a) and the conductance G (b) for the same data of the DRS 97 membrane as shown in Fig. 4.
78
36
OCI
0.2
0.4 06 0.8 Capacitance , C/ pF
Fig. 6. Plots of conductance the values at the intersecting
1
12
C against capacitance C. The parameters point of the two straight lines.
C, and G, are obtained
as
108 lo7 IL 2"
106
-
105
E 5 r
10L
0
lo3
ma u
IO2 10'
8 m E
6
3 g-
4 1.5 2
5 z
0.5 E 0.3
$ 0.2 E $0.05
0.04100 IO’
102 103
lo4
Frequency
,
105
106
107
f/Hz
Fig. 7. Frequency dependence of the capacitance C and the conductance G observed for cell systems composed of DRS 97 membrane and compartments filled with NaCl solutions of different concentrations.
G=G,
+$+C, 1
-C>
(21)
h
which gives a straight line. In the region of electrode polarization, it was found by experiment that G is linearly dependent on Cover a limited frequency range. Hence the following empirical relationship holds in the region of the electrode polarization:
79 TABLE
1
Observed dielectric parameters and calculated phase parameters for cell systems composed of DRS 92 and 97 membranes and compartments filled with NaCl solutions of different concentrations a. Observed dielectric parameters RO
membrane
NaCl concn.
C, W)
fo
Ch
G
G
(PF)
(mS)
(mS)
&Hz)
(mw DRS 97
0.1 1 5 20 30
0.860 13.9 67.5 56.7 55.0
16.1 16.1 16.1 16.1 16.1
0.0447 0.230 0.895 4.16 5.51
0.0462 0.264 1.22 5.29 7.05
0.29 0.40 0.72 3.0 4.3
DRS 92
20
18.5
16.1
4.38
5.00
4.6
fo
G
G
G
G.2
&Hz)
W’)
(PF
(mS)
(mS)
0.283 0.388 0.765
0.799 0.839 0.953
16.1 16.1 16.1
1.38 1.78 3.36
0.0462 0.264 1.22
3.18 4.44 5.24
1.24 1.16 1.20
16.1 16.1 16.1
b. Calculated phase parameters RO
membrane
NaCl concn.
1
Cd) DRS 97
DRS 92
0.1 1 5 20 30 20
NaCl concentration I m
5.29 7.05 5.00
mol4’
Fig. 8. The NaCl concentration dependence ductance Gf of the DRS 97 membrane.
G=G, +const- (C-C,)
19.5 25.3 35.3
of the membrane capacitance
C, and membrane con-
(22)
Consequently the parameters C, and G, can be obtained as the values at the intersecting point of the two straight lines in Fig. 6. The obtained C1and G, can be checked by the complex plane plots as illustrated in Fig. 5. Figure 7 shows the frequency dependence of C and G observed for cell sys-
80 TABLE
2
Calculated phase parameters for cell systems composed filled with different types of salt solution Electrolyte
of DRS 97 membrane and compartments
G
Cf (QF)
GE (mS)
GW (mS)
LiCl KC1 RbCl CsCl NH&l
1.05 1.20 1.19 1.33 1.33
8.07 21.7 22.3 22.1 27.6
2.30 6.51 6.43 6.46 6.50
3.51 3.34 3.47 3.42 4.24
CaCI, M&I, CUCI, MnCl, ZnCl,
1.09 1.08 1.14 1.09 1.16
12.0 14.1 15.1 14.1 12.7
4.49 6.12 5.48 5.33 3.74
2.68 2.31 2.75 2.65 3.40
AlCI, LaCI, CeCl,
1.00 1.00 0.92
21.6 10.4 8.18
5.34 6.16 5.07
4.04 1.69 1.61
NaF NaCl NaBr NaI NaNO, NaNO,, NaHCO, NaHSO, NaH2P0,
1.18 1.24 1.21 1.56 1.40 1.16 1.45 1.10 1.07
8.64 19.5 25.2 31.5 33.0 73.2 19.6 16.7 6.15
3.76 5.29 5.01 5.29 5.29 5.24 4.01 4.74 3.50
2.30 3.68 5.04 5.96 6.25 14.0 4.90 3.52 1.76
Na,SO, Na,S,Oa Na,HPO,
1.06 1.09 1.16
5.79 6.52 10.2
4.85 5.19 4.78
1.19 1.26 2.12
G,
terns composed of the DRS 97 membrane and NaCl aqueous solutions of different concentrations. The relaxation frequencies f0 shift to higher values with increasing NaCl concentration. By means of graphical analyses as in Figs. 5 and 6, the dielectric parameters C,, Ch, G, and Gh can be determined for DRS 92 and 97 membranes. The membrane capacitance and conductance Cf and Gf and those of the aqueous phase C, and G, are then evaluated from these observed parameters by use of eqns. (IO)-(17). The observed values, C,, Ch, G,, Gh and f. and the values Cf, C,, G,, G, and f. calculated by eqns. (lo)- (17) are summarized in Table 1. Since the values of the calculated relaxation frequencies f, are in conformity with the observed values, the analysis used above may be reasonable. The membrane capacitance Cf of DRS 97 slightly increases with increase in
81
\/ cation
anion
Fig. 9. Dependence of the conductance ratio GJG, of the DRS 97 membrane on the type of electrolyte in the ambient aqueous solution.
the concentration of the surrounding NaCl aqueous solutions, while the membrane conductance Gf depends on the concentrations quite markedly, as illustrated in Fig. 8. It is inferred that the dependence of Gf on the concentration is attributable to the fixed charge of the membranes. This problem will be addressed in a later paper, but is outside the present discussion. The slight decrease in the membrane capacitance Cf as the NaCl concentration decreases is considered to be due to an error, as follows. The relaxation frequency f0 shifts to a lower value with decrease in concentration of the surrounding NaCl solution, and the dielectric relaxations are masked by the electrode polarization. Hence it is difficult to determine clearly the value of C, from the data for surrounding NaCl solution of low concentration. The data of the capacitance Cf of the membrane are therefore considered for an aqueous solution of high concentration. The values of the membrane capacitance Cf of DRS 92 and 97 are too large to be considered as being the values for the whole membrane, the thickness of which is ca. 70 pm. These extraordinarily large values, therefore, must apply to the dense layer in the asymmetric membrane. In the following discussion, the thickness of the dense layer of DRS 97 is estimated. Provided that the value of the relative permittivity ed of the dense layer is known, the thickness t of the dense layer of the DRS 97 membrane can be evaluated by use of the following equation: (23) where E, is the permittivity of vacuum and S is the area of the membrane. In a previous paper [151,the dielectric behaviour was studied of dense CA membranes with different degrees of acetyl substitution in aqueous salt solutions. The relative permittivities ef of the dense membranes were directly propor-
82
tional to the water contents of the membranes, which increased with the decrease in the degree of acetyl substitution. The values of ef were ca. 8 and 12 for 43.8% and 39.2% acetylated CA membranes, respectively. In consideration of the high solute rejection of the DRS 97 membrane, the water content of the dense layer of this membrane may be almost the same as that of the dense membrane. The value of 12 for the relative permittivity of the 39.2% acetylated dense CA membrane has therefore been adopted as the value of the relative permittivity td of the dense layer. By substituting the values into eqn. (23)) the thickness of the dense layer of the DRS 97 membrane is calculated to be 27 nm. In Ref. [ 161 it was reported that the thicknesses of the dense layer of reverse osmosis membranes in practical use were estimated to be of the order of 10 nm by electron microscopic observations. The result of the present dielectric observation can be compared with these literature data. The conductivity & of the dense layer is evaluated by use of the following equation:
By substituting the values of 27 nm for the thickness of the dense layer and 19.5 mS for the conductance into eqn. (24)) xd is calculated to be 16.8 r&-cm- ‘. This value is in agreement with the reported values of l-8 nS-cm-’ for the conductivity of the 39.2% acetylated dense CA membrane [ 151. It was not possible to observe dielectric relaxations attributable to the porous layer in the data for the DRS 92 and 97 membranes, for the following reason. The porous layer contains much water (70 wt.% ). The relative permittivity E, and the conductivity “p of the porous layer are therefore nearly equal to the relative permittivity E, and the conductivity IC, of the aqueous phase. Hence the following relationship holds:
(25) Since the thickness of the porous layer, tP, is much smaller than that of the aqueous phase, t,, the following inequality may hold:
As already mentioned, the complex capacitance C* of the cell system is represented by the following equation: (27)
83
In consideration of relationships (25) and (26)) the following relationships are derived:
(28)
As is clear from the inequality (28), the term Cz is negligible in eqn. (27). Hence we can merely observe the dielectric relaxation attributable to the combination of the dense layer and the aqueous phase in the data for the DRS 92 and 97 membranes. For the same reason, dielectric relaxations are not observed in the data for the DRS 10 and 50 membranes. The dense layers in the DRS 10 and 50 membranes may contain more water than those in the DRS 92 and 97 membranes. By use of the DRS 97 membrane, the dielectric observations were extended further to cases with different types of electrolyte solutions of concentration 0.02 eq/l. The results for the phase parameters are summarized in Table 2. The value of the membrane capacitance C, remains almost unchanged irrespective of the type of electrolyte solution, and is 1.1-1.2 pF. Such values are attributed to the dense layer, as already discussed. Since the membrane capacitance Cf and the conductance G,are considered to be values for the same phase, the values of Gf are also attributed to the dense layer. The values of Gf depend markedly on the type of electrolyte solution. Figure 9 shows the conductance ratio GJG, for the data of Table 2. Features of the results are as follows: (1) In the case of different cations and a common anion, Cl-, the values of G,/ G, decrease with the increase in valence of the cation. There is little difference among the values of G,/G, for different cations of the same valence. (2 ) In the case of the same cation, Na+, and different anions, the values of G,/ G, decrease in the order of the lyotropic ion series. These results mean that the more hydrated ions can permeate the membrane with greater difficulty. Matsuura et al. studied the reverse osmosis separation of different electrolytes in aqueous solution by use of asymmetric CA membranes [ 171. They reported that the solute separations were in the orders NaH,P04 > NaF > NaCl > NaBr > NaI > NaNO, > NaNO, and MgCl, > CaCl, > CsCl >, RbCl 2 KC1 2 NaCl >, LiCl. This sequence is the same as that for the value of G,/G, observed in the present study. From these findings, it is suggested that the ion selectivity of asymmetric membranes may be studied by use of the dielectric method. Acknowledgements The author wishes to express his gratitude to Professor T. Hanai for valuable discussion and suggestions. He is also grateful to the staff of the Research
84
Centre of Daicel Chemical Industries Co. Ltd. for kindly supplying the reverse osmosis membranes. References 1
S. Loeb and S. Sourirajan, High-flow semipermeable membranes saline solutions, Adv. Chem. Ser., 38 (1963) 117-132.
2
R. Riley, J.O. Gardner and U. Merten, Cellulose acetate membranes: electron microscopy of structure, Science, 143 (1964) 801-803. R.L. Riley, U. Merten and J.O. Gardner, Replication electron microscopy of cellulose acetate osmotic membranes, Desalination, 1 (1966) 30-34. G.J. Gittens, P.A. Hitchcock, D.C. Sammon and G.E. Wakley, The structure of cellulose
3 4
acetate membranes dope, Desalination, 5
6
7
8
9
for reverse osmosis. 8 (1970) 369-391.
Part
1. Membranes
for separation
prepared
of water from
from a dioxan based
H.G.L. Coster and J.R. Smith, The molecular organisation of bimolecular lipid membranes: a study of the low frequency Maxwell-Wagner impedance dispersion, Biochim. Biophys. Acta, 373 (1974)151-164. R.G. Ashcroft, H.G.L. Coster and J.R. Smith, The molecular organisation of bimolecular lipid membranes: the effect of benzyl alcohol on the structure, Biochim. Biophys. Acta, 469 (1977) 13-22. R.G. Ashcroft, K.R. Thulborn, J.R. Smith, H.G.L. Coster and W.H. Sawyer, Perturbations to lipid bilayers by spectroscopic probes as determined by dielectric measurements, Biochim. Biophys. Acta, 602 (1980) 299-308. R.G. Ashcroft, H.G.L. Coster and J.R. Smith, The molecular organisation of bimolecular lipid membranes: the dielectric structure of the hydrophilic/hydrophobic interface, Biochim. Biophys. Acta, 643 (1981) 191-204. J.B. Hasted, preparations
H.M. Millany and D. Rosen, Low-frequency electrical properties of multilayer of haemoglobin, J. Chem. Sot., Faraday Trans. 2,77 (1981) 2289-2302.
10
G. Alberti, C. Bastioli, M. Casciola, F. Marmottini, G. Capannelli and S. Munari, Properties of polyvinylidene fluoride membranes at low degrees of sulphonation and their characterization by concentration potential coupled with AC. impedance measurements, J. Membrane Sci., 16 (1983) 121-135.
11
T. Hanai, associated
12
H. Zhang, K. Sekine, T. Hanai and N. Koizumi, Dielectric properties of underwater styrene films related to microcapsules, Maku (Membrane), 8 (1983) 249-254.
13
H. Zhang, T. Hanai and N. Koizumi, Dielectric analysis of interfacial polarization in bilamellar structure as applied to underwater polystyrene films, Bull. Inst. Chem. Res. Kyoto Univ., 61 (1983) 265-281.
14
T. Hanai, Electrical properties of emulsions, demic Press, London, 1968, Chap. 5.
in: P. Sherman
15
K. Asaka, Dielectric Maku (Membrane),
acetate
16
Y. Kurihara, Asymmetric and composite membranes (in Japanese), in: Kagaku Sousetu, Gakkai Syuppan Center, Tokyo, Japan, 45 (1984) 30-38. T. Matsuura, L. Pageau and S. Sourirajan, Reverse osmosis separation of inorganic solutes in aqueous solutions using porous cellulose acetate membranes, J. Appl. Polym. Sci., 19 (1975) 179-198.
11
H. Zhang, K. Sekine, K. Asaka and K. Asami, The number of interfaces and the dielectric relaxations in heterogeneous systems, Ferroelectrics, 86 (1988) 191-204.
properties of cellulose 14 (1989) 54-63.
(Ed.),
membranes
Emulsion
in aqueous
Science,
poly-
Aca-
salt solutions,
71 in The Netherlands
DIELECTRIC PROPERTIES OF CELLULOSE ACETATE REVERSE OSMOSIS MEMBRANES IN AQUEOUS SALT SOLUTIONS
KINZI ASAKA Institute
for Chemical Research, Kyoto University, Gokashou, Uji 611 [Japan)
(Received February 21,1989; accepted in revised form September
26,1989)
Summary The dielectric properties were studied of cellulose acetate asymmetric membranes in aqueous electrolyte solutions. The value of the membrane capacitance was 395 nF/cm’, which was attributed to the dense layer in the asymmetric membrane. The thickness of the dense layer was calculated to be 27 nm from the value of the membrane capacitance. The membrane conductance depended on the type of electrolyte, while the membrane capacitance remained almost unchanged irrespective of the kind of electrolyte. The dependence of membrane conductance on the type of electrolyte showed that more highly hydrated ions were only capable of permeating the membrane with more difficulty.
Introduction Since Loeb and Sourirajan made a success of the reverse osmosis method by use of asymmetric cellulose acetate (CA) membranes [ I], asymmetric membranes have played an important role in reverse osmosis, ultrafiltration and other practical applications. A two-layer model, which consists of an ultrathin dense layer and the thick porous layer, was proposed on the basis of electron microscopic observations of the structure of asymmetric CA membranes [241. According to this model, the dense portion controls the relative flux rates of salt and water, whereas the porous part plays a part in supporting the membrane mechanically. Besides electron microscopic observations, dielectric measurements are widely used in the study of the asymmetric structure of membranes [ 5-101. According to theoretical consideration of the dielectric relaxation due to interfacial polarization, the dielectric relaxations are equal to the interfaces in number [ 111. For instance, one dielectric relaxation was observed for measuring cell systems composed of a homogeneous membrane and aqueous salt solutions [ 12,131. Two dielectric relaxations were observed for cell systems composed of a membrane with bilayer structure and ambient aqueous salt solutions [ 5-81.
0376-7388/90/$03.50
0 1990 Elsevier Science Publishers
B.V.
72
Hence this method has the advantage that one can obtain information on the structure of membranes in aqueous solutions. In this study, dielectric measurements were carried out on CA reverse osmosis (RO) membranes in aqueous salt solutions. The capacitance and the conductance of the RO membranes were evaluated from the dielectric relaxation data by use of a theory of dielectric relaxation due to interfacial polarization. The thickness of the dense layer in the RO membranes was estimated from the membrane capacitances. The ion selectivity of the RO membranes is discussed in connection with the data on the membrane conductances. Theoretical Dielectric relaxations due to interfacial polarization were observed in heterogeneous systems composed of various phases. The theories and some experimental results were summarized in a review by Hanai [ 141. The first system considered consists of a homogeneous membrane (having capacitance Cr and conductance G,) separating two electrolyte solutions of the same concentration (with capacitance C, and conductance G,) as illustrated in Fig. 1 (a). The equivalent circuit model, which is shown in Fig. 1 (b) , can be measured in terms of the parallel equivalent capacitance C and the parallel equivalent conductance G at each frequency, as shown in Fig. 1 (c). The complex capacitance C* is represented by a relationship:
$=$+&, f
(1)
w
where C; and Cc are the complex capacitances of the membrane phase and the aqueous phase, respectively. The complex capacitances are defined by relationships of the following form:
c*=c+L j2nf
’
where f is the frequency of the applied AC voltage, and j is the imaginary ber defined by j = J-- 1. After rearrangement of eqn. ( 1)) we have:
num-
G-C,
c=ch+l+ (f/f())" G-G
-
+
1
(6 -G,) (f/fo)” 1+ (f/fJ2
where f, is the relaxation frequency and C,, Ch, G1and Gh are the limiting values of the capacitance C and the conductance G at low (subscript “1”) and high
73
(a)
(b)
Fig. 1. (a) Diagrammatic representation of cell system composed of a homogeneous membrane separating two electrolyte solutions of the same concentration. (b) Circuit model of the cell system shown in Fig. 1 (a). (c) Parallel equivalent circuit model composed of C and G. (d) Frequency dependence of C and G for the cell system shown in Fig. 1 (a). (e) Complex plane plots of C and G for the same cell system.
(subscript “h”) frequencies, respectively. These dielectric parameters are given by the following equations:
Ch$$ f
(6) w
GG,
(7)
G1= G,+G, G _G,C;
+-G&,2
h-
(8)
wf+cw)2
fo=
G+Gw +Cw)
2n(C,
(9)
Figure 1 (d) gives the frequency dependence of the capacitance C and the conductance G derived from eqn. (1)) showing one dielectric relaxation. The
74
complex plane plots of the complex capacitance and the complex conductance are shown in Fig. 1 (e) , and appear as semicircles. The phase parameters Cf, C,, Gf and G, are evaluated from the observed parameters C,, Ch, G, and Gh by use of the following equations [ 13 ] :
($_l)1’2
A=[(l-$-($1)-‘]
(10)
yf+~[l+(~)‘l”2
(11)
Cfz+
(12)
c&d=& - f
(13)
f
ifA>O,
X,= y,+[
ifA
XfZy,_CYf
Yf (I-
Yf) ($-l)]l’z
(I-Y,)
(14)
($l)l”
G,+
(161 f
GW=++ -
(17) f
The second system considered consists of an asymmetric membrane of bilayer structure separating two electrolyte solutions of the same concentration, as illustrated in Fig. 2 (a). Figure 2 (b) shows the equivalent circuit model. In the figure, subscripts “d” and “p” designate the dense layer and the porous layer, respectively. The complex capacitance C* of the parallel equivalent circuit shown in Fig. 2 (c ) is represented by the following relations:
&=$+$+$ d P
Rewriting
(18) w
eqn. (18), we have: C,-Ci
Ci-Ch
c=ch+1+(~/~~)2+1+(~/~~)2 G
=
G
+
1
(Gi -G) V/fpc+ (Gh-Gi) (f/fq)” 1+ Wfp)”
1+ Wq)”
(19) (20)
(a) cd (b)
(d);
Fig. 2. (a) Diagrammatic representation of cell system composed of a membrane of bilayer structure separating two electrolyte solutions of the same concentration. (b) Circuit model of the cell system shown in Fig. 2 (a). (c) Parallel equivalent circuit model composed of C and G. (d) Frequency dependence of C and G for the cell system shown in Fig. 2 (a). (e) Complex plane plots of C and G for the above cell system.
where Ci and Gi are the capacitance and the conductance at intermediate frequencies, and f, and f, are the relaxation frequencies. The capacitances Cl, Ci, Ch, the conductances G1,Gi, Gh and the relaxation frequencies fP, fq are represented by use of the parameters C,,, C,, C,, G,,, Gdand G, in a complicated form [141. Figure 2 (d) shows the frequency dependence of the capacitance C and the conductance G. Two dielectric relaxations are found in the figure. The complex plane plots of the complex capacitance and the complex conductance are shown in Fig. 2 (e ) , and appear as a sequence of two semicircles. Experimental Reverse osmosis membranes The reverse osmosis membranes used in this work were DRS 97,92,50 and 10, which were kindly supplied by Daicel Co. Ltd., Japan. These membranes are composed of 40.4% acetylated cellulose acetate. The figures in the names of the membranes represent NaCl rejections (in % ) assessed by the manufac-
76
Fig. 3. Measuring cell system. Area of electrodes is 3.14 cm2 and distance between the two trades is 1.4 cm.
turer. These membranes have the same thickness are 72 ,um and 68 wt.%, respectively. Dielectric
and water content,
which
measurements
Dielectric measurements were carried out with a Yokogawa Hewlett Packard 4192A impedance analyzer operating in a frequency range between 5 Hz and 13 MHz. The measuring cell system is shown in Fig. 3. All measurements were carried out at 25’ C. Results and discussion
Figure 4 shows the frequency dependence of the capacitance C and the conductance G observed for the cell systems composed of the DRS membranes and having the compartments filled with a 20 mM NaCl solution. The capacitance increases and the conductance decreases with decreasing frequency f in the data for the DRS 10 and 50 membranes. The data for the DRS 92 and 97 membranes show a similar tendency below 1 kHz. These phenomena may be attributed to electrode polarization, which is outside the present discussion. Dielectric relaxations are observed between 1 kHz and 1 MHz in the data for DRS 92 and 97, and may be caused by interfacial polarization between the membrane phase and the aqueous phase. Figures 5 (a) and 5 (b) show the complex plane plots of C and G for the same data of the DRS 97 membrane. The observed parameter Ch and Gh are determined graphically from Fig. 5. It is difficult to determine the parameters C, and G, from Fig. 5, since the electrode polarization affects the data on interfacial polarization in the low frequency region (l-3 kHz). In order to eliminate the effect of electrode polarization, a graphical method was adopted, as illustrated in Fig. 6. Graphical representation of G against C as shown in Fig. 6 gives two straight lines: one for interfacial polarization and the other for electrode polarization. By eliminating the term f/f0 from eqns. (3 ) and (4 ) , we have:
17
, ~/HZ
Frequency
Fig. 4. Frequency dependence of the capacitance C and the conductance Gobservedfor cell systems composed of DRS membranes and compartments filled with a 20 mA4 NaCl solution.
+ f0
; 20 2 4
f-30
-:
0
0
IOh
10
t
0
OTch (a)
(i-d
k
10
30 20 Capacitance
Conductance
40
,
ClnF
50
$60
, GlmS
Fig. 5. Complex plane plots of the capacitance C (a) and the conductance G (b) for the same data of the DRS 97 membrane as shown in Fig. 4.
78
36
OCI
0.2
0.4 06 0.8 Capacitance , C/ pF
Fig. 6. Plots of conductance the values at the intersecting
1
12
C against capacitance C. The parameters point of the two straight lines.
C, and G, are obtained
as
108 lo7 IL 2"
106
-
105
E 5 r
10L
0
lo3
ma u
IO2 10'
8 m E
6
3 g-
4 1.5 2
5 z
0.5 E 0.3
$ 0.2 E $0.05
0.04100 IO’
102 103
lo4
Frequency
,
105
106
107
f/Hz
Fig. 7. Frequency dependence of the capacitance C and the conductance G observed for cell systems composed of DRS 97 membrane and compartments filled with NaCl solutions of different concentrations.
G=G,
+$+C, 1
-C>
(21)
h
which gives a straight line. In the region of electrode polarization, it was found by experiment that G is linearly dependent on Cover a limited frequency range. Hence the following empirical relationship holds in the region of the electrode polarization:
79 TABLE
1
Observed dielectric parameters and calculated phase parameters for cell systems composed of DRS 92 and 97 membranes and compartments filled with NaCl solutions of different concentrations a. Observed dielectric parameters RO
membrane
NaCl concn.
C, W)
fo
Ch
G
G
(PF)
(mS)
(mS)
&Hz)
(mw DRS 97
0.1 1 5 20 30
0.860 13.9 67.5 56.7 55.0
16.1 16.1 16.1 16.1 16.1
0.0447 0.230 0.895 4.16 5.51
0.0462 0.264 1.22 5.29 7.05
0.29 0.40 0.72 3.0 4.3
DRS 92
20
18.5
16.1
4.38
5.00
4.6
fo
G
G
G
G.2
&Hz)
W’)
(PF
(mS)
(mS)
0.283 0.388 0.765
0.799 0.839 0.953
16.1 16.1 16.1
1.38 1.78 3.36
0.0462 0.264 1.22
3.18 4.44 5.24
1.24 1.16 1.20
16.1 16.1 16.1
b. Calculated phase parameters RO
membrane
NaCl concn.
1
Cd) DRS 97
DRS 92
0.1 1 5 20 30 20
NaCl concentration I m
5.29 7.05 5.00
mol4’
Fig. 8. The NaCl concentration dependence ductance Gf of the DRS 97 membrane.
G=G, +const- (C-C,)
19.5 25.3 35.3
of the membrane capacitance
C, and membrane con-
(22)
Consequently the parameters C, and G, can be obtained as the values at the intersecting point of the two straight lines in Fig. 6. The obtained C1and G, can be checked by the complex plane plots as illustrated in Fig. 5. Figure 7 shows the frequency dependence of C and G observed for cell sys-
80 TABLE
2
Calculated phase parameters for cell systems composed filled with different types of salt solution Electrolyte
of DRS 97 membrane and compartments
G
Cf (QF)
GE (mS)
GW (mS)
LiCl KC1 RbCl CsCl NH&l
1.05 1.20 1.19 1.33 1.33
8.07 21.7 22.3 22.1 27.6
2.30 6.51 6.43 6.46 6.50
3.51 3.34 3.47 3.42 4.24
CaCI, M&I, CUCI, MnCl, ZnCl,
1.09 1.08 1.14 1.09 1.16
12.0 14.1 15.1 14.1 12.7
4.49 6.12 5.48 5.33 3.74
2.68 2.31 2.75 2.65 3.40
AlCI, LaCI, CeCl,
1.00 1.00 0.92
21.6 10.4 8.18
5.34 6.16 5.07
4.04 1.69 1.61
NaF NaCl NaBr NaI NaNO, NaNO,, NaHCO, NaHSO, NaH2P0,
1.18 1.24 1.21 1.56 1.40 1.16 1.45 1.10 1.07
8.64 19.5 25.2 31.5 33.0 73.2 19.6 16.7 6.15
3.76 5.29 5.01 5.29 5.29 5.24 4.01 4.74 3.50
2.30 3.68 5.04 5.96 6.25 14.0 4.90 3.52 1.76
Na,SO, Na,S,Oa Na,HPO,
1.06 1.09 1.16
5.79 6.52 10.2
4.85 5.19 4.78
1.19 1.26 2.12
G,
terns composed of the DRS 97 membrane and NaCl aqueous solutions of different concentrations. The relaxation frequencies f0 shift to higher values with increasing NaCl concentration. By means of graphical analyses as in Figs. 5 and 6, the dielectric parameters C,, Ch, G, and Gh can be determined for DRS 92 and 97 membranes. The membrane capacitance and conductance Cf and Gf and those of the aqueous phase C, and G, are then evaluated from these observed parameters by use of eqns. (IO)-(17). The observed values, C,, Ch, G,, Gh and f. and the values Cf, C,, G,, G, and f. calculated by eqns. (lo)- (17) are summarized in Table 1. Since the values of the calculated relaxation frequencies f, are in conformity with the observed values, the analysis used above may be reasonable. The membrane capacitance Cf of DRS 97 slightly increases with increase in
81
\/ cation
anion
Fig. 9. Dependence of the conductance ratio GJG, of the DRS 97 membrane on the type of electrolyte in the ambient aqueous solution.
the concentration of the surrounding NaCl aqueous solutions, while the membrane conductance Gf depends on the concentrations quite markedly, as illustrated in Fig. 8. It is inferred that the dependence of Gf on the concentration is attributable to the fixed charge of the membranes. This problem will be addressed in a later paper, but is outside the present discussion. The slight decrease in the membrane capacitance Cf as the NaCl concentration decreases is considered to be due to an error, as follows. The relaxation frequency f0 shifts to a lower value with decrease in concentration of the surrounding NaCl solution, and the dielectric relaxations are masked by the electrode polarization. Hence it is difficult to determine clearly the value of C, from the data for surrounding NaCl solution of low concentration. The data of the capacitance Cf of the membrane are therefore considered for an aqueous solution of high concentration. The values of the membrane capacitance Cf of DRS 92 and 97 are too large to be considered as being the values for the whole membrane, the thickness of which is ca. 70 pm. These extraordinarily large values, therefore, must apply to the dense layer in the asymmetric membrane. In the following discussion, the thickness of the dense layer of DRS 97 is estimated. Provided that the value of the relative permittivity ed of the dense layer is known, the thickness t of the dense layer of the DRS 97 membrane can be evaluated by use of the following equation: (23) where E, is the permittivity of vacuum and S is the area of the membrane. In a previous paper [151,the dielectric behaviour was studied of dense CA membranes with different degrees of acetyl substitution in aqueous salt solutions. The relative permittivities ef of the dense membranes were directly propor-
82
tional to the water contents of the membranes, which increased with the decrease in the degree of acetyl substitution. The values of ef were ca. 8 and 12 for 43.8% and 39.2% acetylated CA membranes, respectively. In consideration of the high solute rejection of the DRS 97 membrane, the water content of the dense layer of this membrane may be almost the same as that of the dense membrane. The value of 12 for the relative permittivity of the 39.2% acetylated dense CA membrane has therefore been adopted as the value of the relative permittivity td of the dense layer. By substituting the values into eqn. (23)) the thickness of the dense layer of the DRS 97 membrane is calculated to be 27 nm. In Ref. [ 161 it was reported that the thicknesses of the dense layer of reverse osmosis membranes in practical use were estimated to be of the order of 10 nm by electron microscopic observations. The result of the present dielectric observation can be compared with these literature data. The conductivity & of the dense layer is evaluated by use of the following equation:
By substituting the values of 27 nm for the thickness of the dense layer and 19.5 mS for the conductance into eqn. (24)) xd is calculated to be 16.8 r&-cm- ‘. This value is in agreement with the reported values of l-8 nS-cm-’ for the conductivity of the 39.2% acetylated dense CA membrane [ 151. It was not possible to observe dielectric relaxations attributable to the porous layer in the data for the DRS 92 and 97 membranes, for the following reason. The porous layer contains much water (70 wt.% ). The relative permittivity E, and the conductivity “p of the porous layer are therefore nearly equal to the relative permittivity E, and the conductivity IC, of the aqueous phase. Hence the following relationship holds:
(25) Since the thickness of the porous layer, tP, is much smaller than that of the aqueous phase, t,, the following inequality may hold:
As already mentioned, the complex capacitance C* of the cell system is represented by the following equation: (27)
83
In consideration of relationships (25) and (26)) the following relationships are derived:
(28)
As is clear from the inequality (28), the term Cz is negligible in eqn. (27). Hence we can merely observe the dielectric relaxation attributable to the combination of the dense layer and the aqueous phase in the data for the DRS 92 and 97 membranes. For the same reason, dielectric relaxations are not observed in the data for the DRS 10 and 50 membranes. The dense layers in the DRS 10 and 50 membranes may contain more water than those in the DRS 92 and 97 membranes. By use of the DRS 97 membrane, the dielectric observations were extended further to cases with different types of electrolyte solutions of concentration 0.02 eq/l. The results for the phase parameters are summarized in Table 2. The value of the membrane capacitance C, remains almost unchanged irrespective of the type of electrolyte solution, and is 1.1-1.2 pF. Such values are attributed to the dense layer, as already discussed. Since the membrane capacitance Cf and the conductance G,are considered to be values for the same phase, the values of Gf are also attributed to the dense layer. The values of Gf depend markedly on the type of electrolyte solution. Figure 9 shows the conductance ratio GJG, for the data of Table 2. Features of the results are as follows: (1) In the case of different cations and a common anion, Cl-, the values of G,/ G, decrease with the increase in valence of the cation. There is little difference among the values of G,/G, for different cations of the same valence. (2 ) In the case of the same cation, Na+, and different anions, the values of G,/ G, decrease in the order of the lyotropic ion series. These results mean that the more hydrated ions can permeate the membrane with greater difficulty. Matsuura et al. studied the reverse osmosis separation of different electrolytes in aqueous solution by use of asymmetric CA membranes [ 171. They reported that the solute separations were in the orders NaH,P04 > NaF > NaCl > NaBr > NaI > NaNO, > NaNO, and MgCl, > CaCl, > CsCl >, RbCl 2 KC1 2 NaCl >, LiCl. This sequence is the same as that for the value of G,/G, observed in the present study. From these findings, it is suggested that the ion selectivity of asymmetric membranes may be studied by use of the dielectric method. Acknowledgements The author wishes to express his gratitude to Professor T. Hanai for valuable discussion and suggestions. He is also grateful to the staff of the Research
84
Centre of Daicel Chemical Industries Co. Ltd. for kindly supplying the reverse osmosis membranes. References 1
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2
R. Riley, J.O. Gardner and U. Merten, Cellulose acetate membranes: electron microscopy of structure, Science, 143 (1964) 801-803. R.L. Riley, U. Merten and J.O. Gardner, Replication electron microscopy of cellulose acetate osmotic membranes, Desalination, 1 (1966) 30-34. G.J. Gittens, P.A. Hitchcock, D.C. Sammon and G.E. Wakley, The structure of cellulose
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T. Hanai, Electrical properties of emulsions, demic Press, London, 1968, Chap. 5.
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(Ed.),
membranes
Emulsion
in aqueous
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poly-
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salt solutions,