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Mass transfer in Nation membrane systems: Effects of ionic size and charge on selectivity
Science, 58 (1991) 175-189 Elsevier Science Publishers B.V.. Amsterdam
175
Journal of Membrane
Mass transfer in Nafion membrane systems: Effects of ionic size and charge on selectivity T. Xue, R.B. Longwell and K. Osseo-Asare Department of Materials Science and Engineering, University Park, PA 16802 (U.S.A.)
The Pennsylvania
State University,
(Received June 24, 1988; accepted in revised form October 19,199O)
Abstract The interdiffusion of metal ion-hydrogen ion couples in Nafion membrane systems has been measured by a rotating diffusion cell (RDC) technique. At low metal concentrations, the transport rate is controlled by boundary layer diffusion and the metal flux follows the order Li+ < Na+ < K+ < Rb+ < Cs+ for alkali metals, and Ca2+ < Sr2+ < Ba2+ for alkaline earth metals. At high metal concentrations, the transport process is controlled by membrane diffusion and the order of the flux is Li+ < Cs+ < Rb+ < Na+
water sorption
Introduction
In membrane transport systems, there are a number of factors which may affect the overall transport process, e.g. solution stirring speed, solution concentration, ionic size and charge of the diffusing species, as well as the microstructure of the membrane. Nafion membranes developed by DuPont have the following structure: -[ (CF,-CF,),-CF,-CF,],
!’1 I
0
CF:!
CFPCFS
(m=5-13.5,
0-CF,CFP;O,H n= ~1000,~=1,2,3...)
Unlike conventional cross-linked membranes, there are no cross-linkers; in0376-7388/91/$03.50
0 1991-
Elsevier Science Publishers B.V.
176
stead, phase separation which is due to the aggregation of ions and water to form hydrophilic ionic clusters in the hydrophobic organic matrix, has been observed [ 1,2]. The unusual chemical and thermal stabilities, as well as the transport properties of Nafion membranes are largely dependent on this peculiar morphology. For conventional cross-linked membranes, it is well known that both ionic size and charge can play dominant roles in the interdiffusion process [ 3-71. For Nafion membranes, however, although a series of investigations dealing with Donnan dialysis or interdiffusion have been reported [ 8-151, there is still a lack of complete understanding of the nature of the metal ion-hydrogen ion interdiffusion process. Controversies still exist; for example, in previous work, Heitner-Wirgin [ 151 measured the interdiffusion rates (J) for a number of metal ions and found that JNa+ > JK+ >Jcs+ at pH l/l (i.e. pH in feed compartment = 1 and pH in strip compartment = 1). However, these results are questionable since it was reported that J Na+ at pH l/l is greater than that at pH 7.2/l. As is well known, for metal ion-hydrogen ion couples, the pH difference between the feed and strip chambers is the main driving force for Donnan dialysis. It is also suggested that there is no ionic charge effect for the Nafion systems because the same magnitude of the flux was observed for Cu2+, Co2+ andA13+ [15]. H owever, more work such as a comparison of single and triple charged ions, is needed to confirm this. In another series of investigations [ 1618]Yeager et al. observed that in Nafion membranes, the self diffusion coefficients for Na+ and Cs+ follow the order DNa+>Dcs+ , which is opposite to that observed in the case of conventional cross-linked membranes (i.e. D Na+ <%+I oes this mean that the transport rate trend for alkali i19l.D metal ions in Nafion membranes would be the total opposite of that found with conventional cross-linked membranes? In order to address this question systematic comparative studies involving several alkali metals must be undertaken. In the present work, the mass transport of ions in Nafion membrane systems is investigated systematically by controlling for ionic charge (Li +, Na+, K+, Rb+, Cs+; Ca’+, Sr2+, Ba2+), and ionic size [Na+ (0.97 A), Ca2+ (0.99 A), Y3+ (0.93 A) ] [ 201. Interdiffusion measurements were carried out in a rotating diffusion cell (RDC ) . In previous work from this laboratory [ 211, it was demonstrated that the RDC offers a reliable means of defining the hydrodynamics of Donnan dialysis transport systems and permits one to readily discriminate between boundary layer and membrane control transport processes. Experimental
Double-distilled water and reagent grade chemicals (e.g. LiCl, NaCl, KCl, etc) were used in this study. The ion-exchange membrane was Nafion 117 with a nominal exchange capacity of 0.91 mequiv/g dry H-form polymer and a nominal thickness of 0.017 cm.
177
The water content in the membrane was measured by the following procedure: a piece of 2 x 4 cm2 membrane was immersed in 0.1 mol/l of the relevant salt solution for 48 hr. After the surface was dried with filter paper, the sample was weighed ( ITI); then the sample was dried in a vacuum oven at 100°C for 24 hr and weighed again (IV,). The fraction of water absorbed was taken as (WI-- W,)lW,. The transport rate of the cations was measured with a rotating diffusion cell (RDC ). A detailed description of the RDC and the related experimental procedures has been given in a previous paper [ 211. A cross-section of the rotating diffusion cell is shown schematically in Fig. 1. A membrane is mounted on a rotating Teflon (PTFE) cylinder. The acid (strip) solution is loaded into the inner cylinder through the hollow shaft and salt (feed) solution is placed into the outer cylinder. Inside the cylinder there is a PTFE stationary baffle so that when the cylinder is rotated the gap ( - 2 mm) between the bottom of the baffle and the membrane and the slots cut on the baffle cause circulation of the inner solution, i.e. the fluid flows out centrifugally through the gap and returns through the slots. As a result, the same fluid flow pattern is obtained on both sides of the membranes. The surface area of the exposed membrane was 2.83 cm’. The membrane was initially soaked in distilled water at room temperature for 24 hr. Following this, it was immersed in HCl solution (1 mol/l) for 4 hr. The thickness of the membrane was measured with a micrometer, as 0.022 cm. The ratio between the feed and the strip solution volume was 250: 50. The concentration of cations was varied from 2 x 10W3to 0.1 mol/l. The rotating speed of the RDC was varied from 200 to 800 min-’ with a variable speed motor.
baffle
II___
Fig. 1. Schematic illustration of rotating diffusion cell (RDC).
The interdiffusion flux was directly measured with the pH-stat technique [21,22], i.e. the pH of the feed solution was adjusted to a preset value by the addition of a small amount of HCl, then the H+ released by the strip solution during the transfer process was neutralized with standardized hydroxide solution. A Radiometer pH-stat apparatus, including a PHM84 pH meter with a combination electrode, an ABU80 autoburette and a TTT80 titrator, was used. An Apple IIe microcomputer was interfaced with the autoburette to record and process the data. In our previous work [22], it was reported that the flux of HSO; due to anion invasion has a linear relationship with the acid (i.e. H&SO,) concentration. In the present study, it was observed that with the indicated HCl concentration, the anion invasion effect was negligible. Thus the metal ion flux is given directly by the pH-stat technique through the following equation:
where JM and JH are the fluxes of metal ion and hydrogen ion respectively and z is the electric charge on the metal ion. The pH of the feed solution was fixed at 4.50 in the experiments and the H+ released during the interdiffusion was neutralized by a standardized NaOH solution so that the flux of metal ions could be calculated with the aid of the volume and concentration of the consumed NaOH. All experiments were carried out at 25’ C. The flux results were reproducible and the error was usually less than 5 5%. Results and discussion
The boundary layer vs. membrane diffusion control: The Levich equation In Donnan dialysis, the interdiffusion rate can be controlled either by the boundary layer or the membrane. At low metal ion concentrations or low rotating speed, the transport rate is controlled by boundary layer diffusion while at high metal ion concentration or high rotating speed, the process is dominated by membrane diffusion. Also the thinner the membrane, the higher the metal ion concentration required to shift rate-control from boundary layer to membrane diffusion. It was demonstrated in a previous paper [21] that the rotating diffusion cell provides a convenient means of distinguishing between these two transport control mechanisms. In using the RDC, the hydrodynamic flow pattern can be controlled in the laminar region so that the boundary layer thickness 6 (cm) on both sides of the membrane is defined by the Levich equation [23] a_- (). 643 v1/6D1/3o
-
l/2 (2)
where v is the kinematic viscosity (cm2-see-l), D is the diffusion coefficient (cm2-set-‘), an d w is the rotation speed (see-l).
179
If the transport rate is controlled by the boundary layer (usually on the feed side because Cn+ B CM*+), Fick’s first law gives (3) where CM, CL are respectively the metal ion concentrations (mol-cm -3) in the bulk solution and at the interface on the feed side. Combining eqns. (2) and (3) gives J1M=1.555V-1’60~3W1’2(c~-cc;11)
(4)
It follows from eqn. (4) that if the interdiffusion process is controlled by the boundary layer, a plot of J-’ vs. CO-‘/~ will be a straight line passing through the origin. On the other hand, an intercept will be observed if the process is controlled by membrane diffusion. Figure 2 is a typical example of the application of eqn. (4). It can be seen that at low metal ion concentrations (i.e. 2 x 10W3and 10m2mol/l Na+ ), the Levich equation is obeyed and therefore the process is totally controlled by boundary layer diffusion. Increase in metal ion concentration and rotating speed leads to a conversion from boundary layer diffusion control to membrane diffusion control, as indicated by the relatively slight dependence of J on a, and by the y-axis intercept of the 0.1 mol/l Na+ data. Equation (4) enables one to
5c
I 2 4-
X
;
x
3 3-
-2
Fig.2. Effect of stirring rate on sodium flux for different constant NaCl solutions in the feed chamber.
180
determine the aqueous phase diffusion coefficient. At low metal concentrations, since Cl, < CM, the slope of the J-l vs. o-112 plot can be used to calculate DM. Boundary layer diffusion control: Hydration size effect In aqueous solutions, metal ions are generally surrounded by a layer (or multilayer) of water molecules. As a result, the diffusion rate of an ion in aqueous solution depends on the hydration size. The hydration number depends on both ionic radius and charge; usually the smaller the size and the higher the charge, the greater the hydration number. The ionic radii and hydration numbers for the metal ions studied in the present work are listed in Table 1.It is worth mentioning here that the reported hydration numbers must be considered to be qualitative, the assigned values depending on the method used [24]. If the transport rate in Nation membrane systems is controlled by the boundary layer, then the transport behavior of ions should follow that in the aqueous solution and should not be dependent on the structure or morphology of the membrane. This is shown in Figs, 3 and 4 for alkali and alkaline earth metals respectively, i.e. at low metal ion concentrations, the interdiffusion order is Li+
Radius” (A)
Li+ Na+ K+ Rb+ cs+ Ca2+ sr2+ Ba2+ yS+
0.68 0.97 1.33 1.47 1.67 0.99 1.12 1.34 0.93
“From Ref. (20 ) . bFrom Ref. (25 ) “From Ref. (26). dFrom Ref. (27). ‘Approximated with the value for La”+.
Hydration numberb 7.1 3.5 1.9 1.2 0 12.0 10.7 7.7 (7.5)’
DM (cm’-secP1) X 10” 0.71 1.47 1.84 2.04 2.33 0.54 1.02 1.33 0.99
(1.03)’ (1.33)’ (1.96)’ (2.07)’ (2.06)’ (0.79)’ (0.79)’ (0.85)’ (0.55)d
181
I 2.5 -
I
I
I
CM’1 = 2 x 10-3mol C HCI 1 = 0.2 pH
I
dmm3
mol dme3
= 4.50
2.0 -
Li+
: 0 _ 7
1.5-
,i
3 -
l.O-
0.5 -
0 0
0.1
0.2
0.3
0.4
0.5
0.6
Fig. 3. Effect of stirring rate on the flux of alkali metal ions at relatively low salt concentrations (2X10-3mol/l).
3.0
2.5
CM’+3
= 2 x 10w3mol
CHCII
= 0.2
dms3
moldme
2.0 ID
I cl x
I.5
T 3 1.0
0 0
0.1
0.2
0.3 w
0.4
0.5
0.6
-I/2
Fig. 4. Effect of stirring rate on the flux of the alkaline earth metal ions at relatively low salt concentrations (2 X low3 mol/l).
182
Membrane diffusion control: Size and charge effects At high metal ion concentrations, the interdiffusion is almost completely controlled by membrane diffusion as shown in Fig. 2 for 0.1 mol/l Na+, where the flux shows very little dependence on rotation. Plots of J-l vs. m-1/2 at 0.1 mol/l are shown in Fig. 5 for alkaline metals and in Fig. 6 for alkaline earth metals and Y3+. It can be seen that for each of the metal ions there is very little change in J-’ as w-“~ is varied. This trend confirms that the transport behavior at this relatively high metal ion concentration is controlled by the membrane diffusion. Thus in this case the transport rate of ions will be closely related to the microstructure of the membrane. Figure 7 illustrates the effects of ionic size on the interdiffusion under conditions where membrane diffusion is rate controlling (i.e. [M” + ] = 0.1 mol/l). It can be seen that for alkali metals the transport rate increases from Li+ to K+, then decreases from K+ to Cs+ while for the alkaline earth metals, the rate increases from Ca2+ to Sr2+ and then decreases to Ba2+, although the difference is much smaller than that for alkali metals. The trend reported here for alkali metals (i.e. JK+ > JNa+> JRb+> Jc,+ > JLi+ ) differs from that obtained by Heitner-Wirguin (i.e. JNa+> JK+ > JC,+ ) [ 151. Figure 8 presents flux data for the case where the bare ionic size was controlled (i.e. r=0.93-0.99 A). From curve A it can be seen that at low metal concentrations (i.e. 2 x 1O-3 mol/l), when the transport process is controlled by boundary layer diffusion, the flux shows the trend JNa+> J,,+ > JCa2+.As can be seen from the hydration numbers listed in Table 1, this trend follows
WC
CHCII = 0.2 moldrf3 CM+1
0
0. I
= 0.1 mol dme3
0.2
0.3
0.4
0.5
0.6
w-l/2
Fig. 5. Effect of stirring rate on the flux of alkaline metal ions at relatively high salt concentrations (0.1 mol/l).
183 71
c
I
I
I
I
7
I
CHCII = 0.2moldme
6
CM’+1
= 0.1
moldme J
5 c
I 0 -
4
x ;
-J
3
2
0
0.1
0.2
0.3
0.4
0.5
0.6
(&-l/Z
Fig. 6. Effect of stirring rate on the flux of alkaline earth metal and yttrium ions at relatively high salt concentrations (0.1 mol/l).
0
0.5 IONIC
1.0
1.5
RADIUS
(%I
2.0
Fig. 7. Effect of ionic size on metal flux at relatively high salt concentrations (0.1 mol/l).
that of the hydrated radii. On the other hand, under membrane diffusion control (i.e. high metal concentration, 0.1 mol/l), the flux follows a different trend, i.e. JNa+> Jca2+> Jy3+; the decrease from Na+ to Ca2+ is much greater than that from Ca2+ to Y3+ . It appears that in the case of membrane diffusion con-
184
CMZ+l
= 2 x ld3”ol
bA I-LA tl
t2
t3
Na
Ca
Y
dm-3
-
t4
Fig. 8. Effect of ionic charge on metal flux for Na+ (r=0.97 A), Cazt (r-=0.99 A) and y3+ (rz0.93 A); A: relatively low salt concentrations (2x 10m3 mol/l), B: relatively high salt concentrations (0.1 mol/l).
trol, the flux follows a trend based on the ionic charge, i.e. the higher the ionic charge, the lower the flux. Effect of the water content
The results of the water content measurements are listed in Table 2. These results are very similar to those obtained previously by Steck and Yeager [ 281. From Table 2, it is clear that for both the alkali and alkaline earth metals, the water content decreases with increase in the size of the naked ion, this effect being especially pronounced for the alkali metals. In contrast, the water content varies very little for Na+, Ca2+ and Y 3+ . This means that the presence of different ionic charges on these three metal ions does not have a significant effect on the amount of absorbed water. In Nafion membrane systems, the transport behavior is closely dependent on the amount of water absorbed. Water molecules may be inserted between metal ions and the anionic sulfonate groups leading to a complete dissociation of all ion pairs. In this case, the metal ion-sulfonate group interactions would be relatively weak. On the other hand, a decreased water content would be expected to cause stronger interaction between metal cations and the anionic groups in the membrane. In a previous IR study [ 291, it was observed that the -SO, symmetric stretch band ( - 1060 cm-l), which can be used to measure the strength of the interaction between cations and the SO; group, is practically the same for Li+(1058 cm-‘), Na+(1058 cm-‘), K+(1058 cm-‘), and
185 TABLE 2 Membrane water content, metal ion fluxes and interdiffusion coefficients Ion
H,O Content
mol H,O/mol
J”
[(W;-Wo)l
SO,
(mol-cm-*-set-‘)
14.0 11.4 7.46 5.97 5.24 11.5 10.9 9.22 10.7
13.0 17.8 19.4 16.8 15.1 3.46 4.45 3.91 2.19
X 10’
rr,MI
(cm’-set-‘)
X lo7
W,] x 100 Li+ Na+ K+ Rb+ cs+ Ca*+ Sr’+ Ba2+ Y3+
23.0 18.7 12.2 9.92 8.58 18.8 17.8 15.1 17.6
9.62
12.6 13.7 11.2 9.62 7.09 9.43 7.58 8.37
“Flux obtained at rpm= 800 min-‘.
Rb+ (1057 cm-’ ) in hydrated membranes. This implies that for Li+, Na+ and K+, the presence of well developed hydration shells results in the formation of completely dissociated ion pairs, i.e. there is no strong cation-anion interaction. Therefore, even though the water content decreases from Li+ and K+, the transport rate still increases with decrease in the effective (i.e. hydrated) ionic size, as observed in Figure 7. On the other hand, because there is no extensive hydration shell on Rb+ and Cs+, these cations can approach the -SO; groups more closely, leading to stronger cation-anion interaction, and a corresponding interference with the transport process. A similar explanation applies to the alkaline earth metals, i.e. the decrease in flux on going from Sr2+ to Ba2+ is attributed to the lesser hydration and therefore the greater metalsulfonate interaction of Ba2+. It can be seen from Figure 7 that interdiffusion rates for the alkaline earth metals are much lower than those for the alkaline metals in the Nation membranes. An interesting IR study of the OH stretching ( - 3520 cm-‘) and HO-H bending ( - 1630 cm-l ) bands by Quezado et al. [ 301 shows that at low water content, the attachment of water molecules to cations and anions in Nafion membranes may have the following three modes:
H’
(a)
(b)
-H (cl
In mode (a), the water molecules are inserted between the cation and anion, while in modes (b) and (c), the water molecules are attached to the cation-
186
anion pair without disrupting the cation-anion bond. It would be expected that the interaction between cation and anion in mode (a) would be weaker than that in modes (b) and (c). Quezado et al. [30] found that alkali metals followed mode (a) primarily, while for alkaline earth metals, modes (b) and (c) were dominant. This means that the interaction between the alkaline earth metal ions and the -SO; groups is generally stronger than that for the alkali metal ions; this greater interaction further accounts for the lower interdiffusion rates of the alkaline earth metals. Metal ion-sulfonate interactions also account for the trend JNa+> Jca2+> J,,+ observed in Fig. 8 under membrane diffusion control conditions (i.e. high metal ion concentration, 0.1 mol/l) . In this case the water content of the membrane is nearly the same for all three metal ions (see Table 2); therefore the differences in the flux must be attributed primarily to differences in ionic charge. That is, the more highly charged the metal ion, the greater the electrostatic cation-sulfonate interaction and therefore the greater the subsequent slowdown in the flux. Finally, it can be seen further from Fig. 8 (curve B) that the difference between Ca’+ and Y’+ is much smaller than that between Na+ and Ca2+. The water screening effect noted above is probably the main reason for the marked difference between the behavior of the monovalent and divalent ions. Calculation of membrane diffusion coefficients To calculate the interdiffusion coefficient in the membrane the following equations may be used [ 12,13,21]:
(5) (6) Zero current and electroneutrality in the membrane require that: CZJ~=O
(7)
and CZ~i =~
(8)
where &, Dn=diffusion coefficients for metal ions and hydrogen ion, &_n = interdiffusion coefficient in the membrane, CM,Cu = bulk Mz+ and H+ concentrations in the feed solution, CL, Cn = interfacial M”+ and H+ concentrations in the aqueous phase on the feed side, e;, , Pg = interfacial Mz+ and H+ concentrations in the membrane phase on the feed, side C&, C& =interfacial Mz+ and H+ concentrations in the membrane phase on the strip side, C;cI, C& = interfacial Mz+ and H+ concentrations in the aqueous phase on the strip side, C”, = bulk H + concentration in the strip solution, 6= boundary
187
W-’
Fig. 9. Plots of 0~'~ vs.w -'for the LiCl/HCl system.
layer thickness, L=membrane thickness, z=electric charge on metal ion, X= negative ion concentration in the membrane. At each interface, Donnan equilibrium is assumed to prevail, i.e. on the feed side,
(9) and on the strip side,
(10) If the negative ion concentration is taken as 4 mol/l according to Yeo’s model [ 311, the interdiffusion coefficient can be calculated with the aid of eqns. (5)-
(10). In previous work [21], it was observed that if D&r is plotted against -’ (i.e. if &_u is extrapolated to relatively high rotating speed), then CL) D$u will converge to a constant value with increase in metal ion concentration as shown in Fig. 9. Values of &_n calculated from this procedure are listed in Table 2. It can be seen that the calculated &_u values generally follow the same trend as the transport rate measurements (see Fig. 7 and the flux (J) values in Table 2 ).
188
Conclusions This study of interdiffusion in Nation membrane systems shows that at low metal concentrations, the transport rates are independent of the membrane structure and only depend on the transport behavior of the ions in the aqueous solution. Therefore, under these conditions, the transport rates for alkali and alkaline earth metals are determined primarily by their hydration size. At high metal concentrations, the transport rate depends on a balance between ionic size and charge. Usually, the amount of water absorbed by the membrane decreases as the naked ionic size increases, resulting in increased metal ionsulfonate interaction. However it does not follow from this that the transport rate always increases with increase in the membrane water content. The interdiffusion rate in Nafion membranes continues to increase with decrease in the metal ion hydration size until a large relatively bare ionic size leads to a strong interaction between the moving cation and the fixed anionic groups. When the charge on the metal ion increases, the transport rate decreases; however, the difference between divalent and trivalent ions is smaller than that between univalent and divalent ions. Acknowledgments This research
was supported
by NSF Grant No. RII-8311763.
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R.S. Yeo and H.L. Yeager, Structure and transport properties of perfluorinated ion-exchange membranes, in: B.E. Conway, R.E. White and J.O’M. Bockris (Eds.), Modern Aspects of Electrochemistry, No. 16, Plenum, New York, NY, 1985,437-504. R.J. Stewart and W.F. Graydon, Ion-exchange membranes. II. Ion transfer rates, J. Phys. Chem., 60 (1956) 750-754. A.S. Tombalakian, C.Y. Yeh and W.F. Graydon, Mass transfer coefficients across ion-ex-
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F. Helfferich, Ion Exchange, McGraw-Hill, New York, NY, 1962. M.A. Lake and S.S. Melsheimer, Mass transfer characterization of Donnan dialysis, AIChE J., 24 (1978) 130-137.
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175
Journal of Membrane
Mass transfer in Nafion membrane systems: Effects of ionic size and charge on selectivity T. Xue, R.B. Longwell and K. Osseo-Asare Department of Materials Science and Engineering, University Park, PA 16802 (U.S.A.)
The Pennsylvania
State University,
(Received June 24, 1988; accepted in revised form October 19,199O)
Abstract The interdiffusion of metal ion-hydrogen ion couples in Nafion membrane systems has been measured by a rotating diffusion cell (RDC) technique. At low metal concentrations, the transport rate is controlled by boundary layer diffusion and the metal flux follows the order Li+ < Na+ < K+ < Rb+ < Cs+ for alkali metals, and Ca2+ < Sr2+ < Ba2+ for alkaline earth metals. At high metal concentrations, the transport process is controlled by membrane diffusion and the order of the flux is Li+ < Cs+ < Rb+ < Na+
water sorption
Introduction
In membrane transport systems, there are a number of factors which may affect the overall transport process, e.g. solution stirring speed, solution concentration, ionic size and charge of the diffusing species, as well as the microstructure of the membrane. Nafion membranes developed by DuPont have the following structure: -[ (CF,-CF,),-CF,-CF,],
!’1 I
0
CF:!
CFPCFS
(m=5-13.5,
0-CF,CFP;O,H n= ~1000,~=1,2,3...)
Unlike conventional cross-linked membranes, there are no cross-linkers; in0376-7388/91/$03.50
0 1991-
Elsevier Science Publishers B.V.
176
stead, phase separation which is due to the aggregation of ions and water to form hydrophilic ionic clusters in the hydrophobic organic matrix, has been observed [ 1,2]. The unusual chemical and thermal stabilities, as well as the transport properties of Nafion membranes are largely dependent on this peculiar morphology. For conventional cross-linked membranes, it is well known that both ionic size and charge can play dominant roles in the interdiffusion process [ 3-71. For Nafion membranes, however, although a series of investigations dealing with Donnan dialysis or interdiffusion have been reported [ 8-151, there is still a lack of complete understanding of the nature of the metal ion-hydrogen ion interdiffusion process. Controversies still exist; for example, in previous work, Heitner-Wirgin [ 151 measured the interdiffusion rates (J) for a number of metal ions and found that JNa+ > JK+ >Jcs+ at pH l/l (i.e. pH in feed compartment = 1 and pH in strip compartment = 1). However, these results are questionable since it was reported that J Na+ at pH l/l is greater than that at pH 7.2/l. As is well known, for metal ion-hydrogen ion couples, the pH difference between the feed and strip chambers is the main driving force for Donnan dialysis. It is also suggested that there is no ionic charge effect for the Nafion systems because the same magnitude of the flux was observed for Cu2+, Co2+ andA13+ [15]. H owever, more work such as a comparison of single and triple charged ions, is needed to confirm this. In another series of investigations [ 1618]Yeager et al. observed that in Nafion membranes, the self diffusion coefficients for Na+ and Cs+ follow the order DNa+>Dcs+ , which is opposite to that observed in the case of conventional cross-linked membranes (i.e. D Na+ <%+I oes this mean that the transport rate trend for alkali i19l.D metal ions in Nafion membranes would be the total opposite of that found with conventional cross-linked membranes? In order to address this question systematic comparative studies involving several alkali metals must be undertaken. In the present work, the mass transport of ions in Nafion membrane systems is investigated systematically by controlling for ionic charge (Li +, Na+, K+, Rb+, Cs+; Ca’+, Sr2+, Ba2+), and ionic size [Na+ (0.97 A), Ca2+ (0.99 A), Y3+ (0.93 A) ] [ 201. Interdiffusion measurements were carried out in a rotating diffusion cell (RDC ) . In previous work from this laboratory [ 211, it was demonstrated that the RDC offers a reliable means of defining the hydrodynamics of Donnan dialysis transport systems and permits one to readily discriminate between boundary layer and membrane control transport processes. Experimental
Double-distilled water and reagent grade chemicals (e.g. LiCl, NaCl, KCl, etc) were used in this study. The ion-exchange membrane was Nafion 117 with a nominal exchange capacity of 0.91 mequiv/g dry H-form polymer and a nominal thickness of 0.017 cm.
177
The water content in the membrane was measured by the following procedure: a piece of 2 x 4 cm2 membrane was immersed in 0.1 mol/l of the relevant salt solution for 48 hr. After the surface was dried with filter paper, the sample was weighed ( ITI); then the sample was dried in a vacuum oven at 100°C for 24 hr and weighed again (IV,). The fraction of water absorbed was taken as (WI-- W,)lW,. The transport rate of the cations was measured with a rotating diffusion cell (RDC ). A detailed description of the RDC and the related experimental procedures has been given in a previous paper [ 211. A cross-section of the rotating diffusion cell is shown schematically in Fig. 1. A membrane is mounted on a rotating Teflon (PTFE) cylinder. The acid (strip) solution is loaded into the inner cylinder through the hollow shaft and salt (feed) solution is placed into the outer cylinder. Inside the cylinder there is a PTFE stationary baffle so that when the cylinder is rotated the gap ( - 2 mm) between the bottom of the baffle and the membrane and the slots cut on the baffle cause circulation of the inner solution, i.e. the fluid flows out centrifugally through the gap and returns through the slots. As a result, the same fluid flow pattern is obtained on both sides of the membranes. The surface area of the exposed membrane was 2.83 cm’. The membrane was initially soaked in distilled water at room temperature for 24 hr. Following this, it was immersed in HCl solution (1 mol/l) for 4 hr. The thickness of the membrane was measured with a micrometer, as 0.022 cm. The ratio between the feed and the strip solution volume was 250: 50. The concentration of cations was varied from 2 x 10W3to 0.1 mol/l. The rotating speed of the RDC was varied from 200 to 800 min-’ with a variable speed motor.
baffle
II___
Fig. 1. Schematic illustration of rotating diffusion cell (RDC).
The interdiffusion flux was directly measured with the pH-stat technique [21,22], i.e. the pH of the feed solution was adjusted to a preset value by the addition of a small amount of HCl, then the H+ released by the strip solution during the transfer process was neutralized with standardized hydroxide solution. A Radiometer pH-stat apparatus, including a PHM84 pH meter with a combination electrode, an ABU80 autoburette and a TTT80 titrator, was used. An Apple IIe microcomputer was interfaced with the autoburette to record and process the data. In our previous work [22], it was reported that the flux of HSO; due to anion invasion has a linear relationship with the acid (i.e. H&SO,) concentration. In the present study, it was observed that with the indicated HCl concentration, the anion invasion effect was negligible. Thus the metal ion flux is given directly by the pH-stat technique through the following equation:
where JM and JH are the fluxes of metal ion and hydrogen ion respectively and z is the electric charge on the metal ion. The pH of the feed solution was fixed at 4.50 in the experiments and the H+ released during the interdiffusion was neutralized by a standardized NaOH solution so that the flux of metal ions could be calculated with the aid of the volume and concentration of the consumed NaOH. All experiments were carried out at 25’ C. The flux results were reproducible and the error was usually less than 5 5%. Results and discussion
The boundary layer vs. membrane diffusion control: The Levich equation In Donnan dialysis, the interdiffusion rate can be controlled either by the boundary layer or the membrane. At low metal ion concentrations or low rotating speed, the transport rate is controlled by boundary layer diffusion while at high metal ion concentration or high rotating speed, the process is dominated by membrane diffusion. Also the thinner the membrane, the higher the metal ion concentration required to shift rate-control from boundary layer to membrane diffusion. It was demonstrated in a previous paper [21] that the rotating diffusion cell provides a convenient means of distinguishing between these two transport control mechanisms. In using the RDC, the hydrodynamic flow pattern can be controlled in the laminar region so that the boundary layer thickness 6 (cm) on both sides of the membrane is defined by the Levich equation [23] a_- (). 643 v1/6D1/3o
-
l/2 (2)
where v is the kinematic viscosity (cm2-see-l), D is the diffusion coefficient (cm2-set-‘), an d w is the rotation speed (see-l).
179
If the transport rate is controlled by the boundary layer (usually on the feed side because Cn+ B CM*+), Fick’s first law gives (3) where CM, CL are respectively the metal ion concentrations (mol-cm -3) in the bulk solution and at the interface on the feed side. Combining eqns. (2) and (3) gives J1M=1.555V-1’60~3W1’2(c~-cc;11)
(4)
It follows from eqn. (4) that if the interdiffusion process is controlled by the boundary layer, a plot of J-’ vs. CO-‘/~ will be a straight line passing through the origin. On the other hand, an intercept will be observed if the process is controlled by membrane diffusion. Figure 2 is a typical example of the application of eqn. (4). It can be seen that at low metal ion concentrations (i.e. 2 x 10W3and 10m2mol/l Na+ ), the Levich equation is obeyed and therefore the process is totally controlled by boundary layer diffusion. Increase in metal ion concentration and rotating speed leads to a conversion from boundary layer diffusion control to membrane diffusion control, as indicated by the relatively slight dependence of J on a, and by the y-axis intercept of the 0.1 mol/l Na+ data. Equation (4) enables one to
5c
I 2 4-
X
;
x
3 3-
-2
Fig.2. Effect of stirring rate on sodium flux for different constant NaCl solutions in the feed chamber.
180
determine the aqueous phase diffusion coefficient. At low metal concentrations, since Cl, < CM, the slope of the J-l vs. o-112 plot can be used to calculate DM. Boundary layer diffusion control: Hydration size effect In aqueous solutions, metal ions are generally surrounded by a layer (or multilayer) of water molecules. As a result, the diffusion rate of an ion in aqueous solution depends on the hydration size. The hydration number depends on both ionic radius and charge; usually the smaller the size and the higher the charge, the greater the hydration number. The ionic radii and hydration numbers for the metal ions studied in the present work are listed in Table 1.It is worth mentioning here that the reported hydration numbers must be considered to be qualitative, the assigned values depending on the method used [24]. If the transport rate in Nation membrane systems is controlled by the boundary layer, then the transport behavior of ions should follow that in the aqueous solution and should not be dependent on the structure or morphology of the membrane. This is shown in Figs, 3 and 4 for alkali and alkaline earth metals respectively, i.e. at low metal ion concentrations, the interdiffusion order is Li+
Radius” (A)
Li+ Na+ K+ Rb+ cs+ Ca2+ sr2+ Ba2+ yS+
0.68 0.97 1.33 1.47 1.67 0.99 1.12 1.34 0.93
“From Ref. (20 ) . bFrom Ref. (25 ) “From Ref. (26). dFrom Ref. (27). ‘Approximated with the value for La”+.
Hydration numberb 7.1 3.5 1.9 1.2 0 12.0 10.7 7.7 (7.5)’
DM (cm’-secP1) X 10” 0.71 1.47 1.84 2.04 2.33 0.54 1.02 1.33 0.99
(1.03)’ (1.33)’ (1.96)’ (2.07)’ (2.06)’ (0.79)’ (0.79)’ (0.85)’ (0.55)d
181
I 2.5 -
I
I
I
CM’1 = 2 x 10-3mol C HCI 1 = 0.2 pH
I
dmm3
mol dme3
= 4.50
2.0 -
Li+
: 0 _ 7
1.5-
,i
3 -
l.O-
0.5 -
0 0
0.1
0.2
0.3
0.4
0.5
0.6
Fig. 3. Effect of stirring rate on the flux of alkali metal ions at relatively low salt concentrations (2X10-3mol/l).
3.0
2.5
CM’+3
= 2 x 10w3mol
CHCII
= 0.2
dms3
moldme
2.0 ID
I cl x
I.5
T 3 1.0
0 0
0.1
0.2
0.3 w
0.4
0.5
0.6
-I/2
Fig. 4. Effect of stirring rate on the flux of the alkaline earth metal ions at relatively low salt concentrations (2 X low3 mol/l).
182
Membrane diffusion control: Size and charge effects At high metal ion concentrations, the interdiffusion is almost completely controlled by membrane diffusion as shown in Fig. 2 for 0.1 mol/l Na+, where the flux shows very little dependence on rotation. Plots of J-l vs. m-1/2 at 0.1 mol/l are shown in Fig. 5 for alkaline metals and in Fig. 6 for alkaline earth metals and Y3+. It can be seen that for each of the metal ions there is very little change in J-’ as w-“~ is varied. This trend confirms that the transport behavior at this relatively high metal ion concentration is controlled by the membrane diffusion. Thus in this case the transport rate of ions will be closely related to the microstructure of the membrane. Figure 7 illustrates the effects of ionic size on the interdiffusion under conditions where membrane diffusion is rate controlling (i.e. [M” + ] = 0.1 mol/l). It can be seen that for alkali metals the transport rate increases from Li+ to K+, then decreases from K+ to Cs+ while for the alkaline earth metals, the rate increases from Ca2+ to Sr2+ and then decreases to Ba2+, although the difference is much smaller than that for alkali metals. The trend reported here for alkali metals (i.e. JK+ > JNa+> JRb+> Jc,+ > JLi+ ) differs from that obtained by Heitner-Wirguin (i.e. JNa+> JK+ > JC,+ ) [ 151. Figure 8 presents flux data for the case where the bare ionic size was controlled (i.e. r=0.93-0.99 A). From curve A it can be seen that at low metal concentrations (i.e. 2 x 1O-3 mol/l), when the transport process is controlled by boundary layer diffusion, the flux shows the trend JNa+> J,,+ > JCa2+.As can be seen from the hydration numbers listed in Table 1, this trend follows
WC
CHCII = 0.2 moldrf3 CM+1
0
0. I
= 0.1 mol dme3
0.2
0.3
0.4
0.5
0.6
w-l/2
Fig. 5. Effect of stirring rate on the flux of alkaline metal ions at relatively high salt concentrations (0.1 mol/l).
183 71
c
I
I
I
I
7
I
CHCII = 0.2moldme
6
CM’+1
= 0.1
moldme J
5 c
I 0 -
4
x ;
-J
3
2
0
0.1
0.2
0.3
0.4
0.5
0.6
(&-l/Z
Fig. 6. Effect of stirring rate on the flux of alkaline earth metal and yttrium ions at relatively high salt concentrations (0.1 mol/l).
0
0.5 IONIC
1.0
1.5
RADIUS
(%I
2.0
Fig. 7. Effect of ionic size on metal flux at relatively high salt concentrations (0.1 mol/l).
that of the hydrated radii. On the other hand, under membrane diffusion control (i.e. high metal concentration, 0.1 mol/l), the flux follows a different trend, i.e. JNa+> Jca2+> Jy3+; the decrease from Na+ to Ca2+ is much greater than that from Ca2+ to Y3+ . It appears that in the case of membrane diffusion con-
184
CMZ+l
= 2 x ld3”ol
bA I-LA tl
t2
t3
Na
Ca
Y
dm-3
-
t4
Fig. 8. Effect of ionic charge on metal flux for Na+ (r=0.97 A), Cazt (r-=0.99 A) and y3+ (rz0.93 A); A: relatively low salt concentrations (2x 10m3 mol/l), B: relatively high salt concentrations (0.1 mol/l).
trol, the flux follows a trend based on the ionic charge, i.e. the higher the ionic charge, the lower the flux. Effect of the water content
The results of the water content measurements are listed in Table 2. These results are very similar to those obtained previously by Steck and Yeager [ 281. From Table 2, it is clear that for both the alkali and alkaline earth metals, the water content decreases with increase in the size of the naked ion, this effect being especially pronounced for the alkali metals. In contrast, the water content varies very little for Na+, Ca2+ and Y 3+ . This means that the presence of different ionic charges on these three metal ions does not have a significant effect on the amount of absorbed water. In Nafion membrane systems, the transport behavior is closely dependent on the amount of water absorbed. Water molecules may be inserted between metal ions and the anionic sulfonate groups leading to a complete dissociation of all ion pairs. In this case, the metal ion-sulfonate group interactions would be relatively weak. On the other hand, a decreased water content would be expected to cause stronger interaction between metal cations and the anionic groups in the membrane. In a previous IR study [ 291, it was observed that the -SO, symmetric stretch band ( - 1060 cm-l), which can be used to measure the strength of the interaction between cations and the SO; group, is practically the same for Li+(1058 cm-‘), Na+(1058 cm-‘), K+(1058 cm-‘), and
185 TABLE 2 Membrane water content, metal ion fluxes and interdiffusion coefficients Ion
H,O Content
mol H,O/mol
J”
[(W;-Wo)l
SO,
(mol-cm-*-set-‘)
14.0 11.4 7.46 5.97 5.24 11.5 10.9 9.22 10.7
13.0 17.8 19.4 16.8 15.1 3.46 4.45 3.91 2.19
X 10’
rr,MI
(cm’-set-‘)
X lo7
W,] x 100 Li+ Na+ K+ Rb+ cs+ Ca*+ Sr’+ Ba2+ Y3+
23.0 18.7 12.2 9.92 8.58 18.8 17.8 15.1 17.6
9.62
12.6 13.7 11.2 9.62 7.09 9.43 7.58 8.37
“Flux obtained at rpm= 800 min-‘.
Rb+ (1057 cm-’ ) in hydrated membranes. This implies that for Li+, Na+ and K+, the presence of well developed hydration shells results in the formation of completely dissociated ion pairs, i.e. there is no strong cation-anion interaction. Therefore, even though the water content decreases from Li+ and K+, the transport rate still increases with decrease in the effective (i.e. hydrated) ionic size, as observed in Figure 7. On the other hand, because there is no extensive hydration shell on Rb+ and Cs+, these cations can approach the -SO; groups more closely, leading to stronger cation-anion interaction, and a corresponding interference with the transport process. A similar explanation applies to the alkaline earth metals, i.e. the decrease in flux on going from Sr2+ to Ba2+ is attributed to the lesser hydration and therefore the greater metalsulfonate interaction of Ba2+. It can be seen from Figure 7 that interdiffusion rates for the alkaline earth metals are much lower than those for the alkaline metals in the Nation membranes. An interesting IR study of the OH stretching ( - 3520 cm-‘) and HO-H bending ( - 1630 cm-l ) bands by Quezado et al. [ 301 shows that at low water content, the attachment of water molecules to cations and anions in Nafion membranes may have the following three modes:
H’
(a)
(b)
-H (cl
In mode (a), the water molecules are inserted between the cation and anion, while in modes (b) and (c), the water molecules are attached to the cation-
186
anion pair without disrupting the cation-anion bond. It would be expected that the interaction between cation and anion in mode (a) would be weaker than that in modes (b) and (c). Quezado et al. [30] found that alkali metals followed mode (a) primarily, while for alkaline earth metals, modes (b) and (c) were dominant. This means that the interaction between the alkaline earth metal ions and the -SO; groups is generally stronger than that for the alkali metal ions; this greater interaction further accounts for the lower interdiffusion rates of the alkaline earth metals. Metal ion-sulfonate interactions also account for the trend JNa+> Jca2+> J,,+ observed in Fig. 8 under membrane diffusion control conditions (i.e. high metal ion concentration, 0.1 mol/l) . In this case the water content of the membrane is nearly the same for all three metal ions (see Table 2); therefore the differences in the flux must be attributed primarily to differences in ionic charge. That is, the more highly charged the metal ion, the greater the electrostatic cation-sulfonate interaction and therefore the greater the subsequent slowdown in the flux. Finally, it can be seen further from Fig. 8 (curve B) that the difference between Ca’+ and Y’+ is much smaller than that between Na+ and Ca2+. The water screening effect noted above is probably the main reason for the marked difference between the behavior of the monovalent and divalent ions. Calculation of membrane diffusion coefficients To calculate the interdiffusion coefficient in the membrane the following equations may be used [ 12,13,21]:
(5) (6) Zero current and electroneutrality in the membrane require that: CZJ~=O
(7)
and CZ~i =~
(8)
where &, Dn=diffusion coefficients for metal ions and hydrogen ion, &_n = interdiffusion coefficient in the membrane, CM,Cu = bulk Mz+ and H+ concentrations in the feed solution, CL, Cn = interfacial M”+ and H+ concentrations in the aqueous phase on the feed side, e;, , Pg = interfacial Mz+ and H+ concentrations in the membrane phase on the feed, side C&, C& =interfacial Mz+ and H+ concentrations in the membrane phase on the strip side, C;cI, C& = interfacial Mz+ and H+ concentrations in the aqueous phase on the strip side, C”, = bulk H + concentration in the strip solution, 6= boundary
187
W-’
Fig. 9. Plots of 0~'~ vs.w -'for the LiCl/HCl system.
layer thickness, L=membrane thickness, z=electric charge on metal ion, X= negative ion concentration in the membrane. At each interface, Donnan equilibrium is assumed to prevail, i.e. on the feed side,
(9) and on the strip side,
(10) If the negative ion concentration is taken as 4 mol/l according to Yeo’s model [ 311, the interdiffusion coefficient can be calculated with the aid of eqns. (5)-
(10). In previous work [21], it was observed that if D&r is plotted against -’ (i.e. if &_u is extrapolated to relatively high rotating speed), then CL) D$u will converge to a constant value with increase in metal ion concentration as shown in Fig. 9. Values of &_n calculated from this procedure are listed in Table 2. It can be seen that the calculated &_u values generally follow the same trend as the transport rate measurements (see Fig. 7 and the flux (J) values in Table 2 ).
188
Conclusions This study of interdiffusion in Nation membrane systems shows that at low metal concentrations, the transport rates are independent of the membrane structure and only depend on the transport behavior of the ions in the aqueous solution. Therefore, under these conditions, the transport rates for alkali and alkaline earth metals are determined primarily by their hydration size. At high metal concentrations, the transport rate depends on a balance between ionic size and charge. Usually, the amount of water absorbed by the membrane decreases as the naked ionic size increases, resulting in increased metal ionsulfonate interaction. However it does not follow from this that the transport rate always increases with increase in the membrane water content. The interdiffusion rate in Nafion membranes continues to increase with decrease in the metal ion hydration size until a large relatively bare ionic size leads to a strong interaction between the moving cation and the fixed anionic groups. When the charge on the metal ion increases, the transport rate decreases; however, the difference between divalent and trivalent ions is smaller than that between univalent and divalent ions. Acknowledgments This research
was supported
by NSF Grant No. RII-8311763.
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