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AC impedance investigation of the kinetics of ion transport in Nafion® perfluorosulfonic membranes
Journal of Membrane Science, 45 (1989) 37-53 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
AC IMPEDANCE INVESTIGATION OF THE KINETICS TRANSPORT IN NAFION@ PERFLUOROSULFONIC MEMBRANES*
C. GAVACH’, G. PAMBOUTZOGLOU’,
37
OF ION
M. NEDYALKOV’ and G. POURCELLY’
‘CNRS - UA 330, LPCSP, B.P. 5051,34033 Montpellier Ceder (France) 2Department of Physical Chemistry, Faculty of Chemistry, University of Sofia, Anton Zvanov, 1126 Sofia (Bulgaria) Received July 24,198’7; accepted in revised form November 4,1988)
Summary The high-frequency resistance of a Nafion @ perfluorosulfonic membrane is measured by means of the AC impedance technique. Using a mercury cell, it is possible to follow the variation of the resistance as a function of the water content and of the nature of the cation present in the membrane. In all cases, the number of sorbed co-ions is very low. When only one counter-ion is present within the membrane phase, the results show that the percolation theory is valid only for lower degrees of swelling. For higher water content, the rate constant of the elementary ion transfer reaction of alkaline cations varies in the same way as their hydration state in water. When the membrane contains both sodium ion and proton, the variation of individual mobility of sodium ion with the molar fraction is deduced from the value of the self-diffusion coefficient measured using a radiotracer. In this case, conductivity measurements reveal that the mobility of the proton increases by up to 150% when the number of sodium ions increases in the membrane.
Introduction In polymeric ion-exchange materials, the degree of swelling is related to the balance between the internal osmotic pressure and the counteracting elasticity of the polymeric matrix [1,21. With a given ion-exchange membrane at the equilibrium state, and with aqueous electrolyte solutions, the degree of swelling will depend on the hydration state of the counter-ions and, to a much less extent, that of sorbed co-ions, as well as on the external electrolyte concentration, which affect the water activity in the membrane-solution system. Therefore, in a series of conductivity measurements performed with membranes at partition equilibrium with different aqueous solutions, the water content will alter from one solution to the other. Ionomeric perfluorosulfonic membranes show phase separation into an in*Presented at ICOM ‘8’7, Tokyo, Japan, June 8-12,1987.
0376-7388/89/$03.50
0 1989 Elsevier Science Publishers B.V.
38
verted micellar structure connected by short narrow channels [ 31. A theoretical analysis of swelling equilibrium with cluster-forming ionomer membranes has been already attempted [ 41. The conductivity of this membrane material is related to the probability of finding chains of conducting clusters in contact forming conduction pathways. It has been shown that the conductivity variations of ionomer membranes are quite well described by the percolation theory [5, 61. With these ionomer membranes, a change in the degree of swelling affects the conductivity of the material via two distinct effects: a change of the ionic hydration, which determines the rate constant of the elementary ion transfer reaction, and a change of the volume fraction of the aqueous microdomains, which determines the probability of the formation of conduction pathways. In order to get a better insight into the elementary processes underlying the ionic conducting properties of ionomer perfluorosulfonic membranes, it is necessary to determine the variation of the conductivity of the membrane phase as a function of its ionic composition and of its water content. Measurements of conductivity of the polymeric membrane with controlled water swelling have already been performed by Wallace and co-workers [ 7-91. Their experimental method consists in tightly clamping the membrane between two platinum coated electrodes and in applying Ohm’s law to the linear variation of the DC intensity above the decomposition voltage. The use of mercury cells for determining the AC resistance of the polymeric membrane was investigated by Subrahmanyan and Lakshminarayanaiah [lo]. This technique was used later by Meshechkov and coworkers [ 111, who stated that measurements must be performed in the high-frequency range, and by D’Alessandro [ 121, who used only 1 kHz frequency. In the present work, the conductivity of a Nation@* membrane has been measured, again by using a mercury cell, but with recording of the whole impedance diagram between 1 Hz and 1 MHz. The experimental technique used enables determination of the value of the conductivity of the membrane phase at which the swelling by water can be modified at will: from the swelling state of the membrane equilibrated with an aqueous electrolyte solution to the completely dried state [ 13, 141. The study is achieved with a Nafion 117 membrane (equivalent weight 1100) with which swelling degree can be varied over a wide range. The purpose of this work is to determine experimentally the variation of the membrane conductivity as a function of the water content and ionic composition. These two parameters are here fixed independently, whereas in previous works on the percolation conductivity of ionomer perfluorosulfonic membranes [ 5,6] the ionic composition of the membrane as well its water content were changed simultaneously. *Nafion @, registered trademark for perfluorosulfonic acid membranes from Du Pont, Wilmington, DE. U.S.A.
39
Experimental Before measurements, pre-treatment is carried out in order to remove impurities from the membrane phase. At room temperature, the membrane is successively immersed in aqueous hydrochloric acid ( 1 hr ), distilled water (2 hr ) and aqueous sodium hydroxide (1 hr ) . This cycle is repeated once before boiling the membrane for 1 hr in deionized water and reconverting it to M+ form. After this treatment, the membrane is considered to contain only M+ ions as counter-ions and no sorbed electrolyte. It has also been verified that boiling does not modify the exchange capacity of the membrane. The electrolytes are Merck Suprapur products; 22Na-labelled NaCl solutions were obtained from Amersham Radiochemical Centre (UK). The amount of water in the membrane is deduced from the difference of weights: firstly during the experiment with a membrane in the Mf form and secondly when the sample contains no more water, i.e., when it has been maintained under vacuum for 3 days at 90” C in the tetrabutylammonium form. The conductivity of membrane phases having the same swelling but different ionic compositions have been compared by AC impedance measurements carried out as follows. After having been immersed in the equilibrium solution for 24 hr, the sample is gradually dried by exposure to vacuum. At regular intervals of time, the membrane is weighed and an impedance measurement is carried out. It has been verified that during the measurement period (about 30 set) the amount of water in the membrane does not change significantly. This method enables the study of the dependence of membrane impedance on degree of swelling for a given cationic form. The membrane resistance value is deduced from the intercept of the impedance diagram with the real axis. In order to check the reproducibility, each measurement is performed three times using different membrane samples. Self-diffusion fluxes of Na+ ion have been measured at 25°C using a twocompartment Teflon cell in which the membrane is placed between two identical aqueous solutions of 0.1 A4 NaCl which are continuously renewed by means of two peristaltic pumps. Each half-cell volume (1.4 cm diameter; 2.0 cm length) is completely renewed within 2 sec. The total volume of solution in each halfcircuit is 100 ml. Before the experiment, the membrane sample was equilibrated for 24 hr in the studied solution. Then, a very small amount of 22Na-labelled NaCl solution (40 ~1) is added to one side. At regular intervals of time, small volumes (100 ~1) are removed from each half-circuit, and the radioactivity of these samples is measured using a Packard auto-gamma spectrometer. The values of the ionic unidirectional fluxes crossing the membrane (through a section of 0.95 cm2) are evaluated from the variation of the radioactivity of the second solution by using a previously described method [ 151. Self-diffusion fluxes of Na+ ion in presence of H+ ion have also been mea-
40
sured, using 0.1 M (NaCl, HCl) aqueous solutions, i.e., [H+ ] + [Na+ ] = 0.1 M. In this case, the ratio X= nNa+ ( nNa+ -t nn+ ) can be evaluated, where aNa+ and nn+ are, respectively, the numbers of Na+ and H+ ions in the membrane phase. The sample is immersed up to the equilibrium state in the 22Na-labelled aqueous solution of NaCl+ HCl; c1 and c2 are the respective concentrations of NaCl and HCl in the equilibrating solution; cl + c2 = 0.1 M. The sample is then removed from solution and its surface is dried by blotting with filter paper. Afterwards the membrane is immersed in a solution of unlabelled NaCl+ HCI at the same concentrations c1 and c2, the solution being thoroughly stirred. By measuring the increase of the radioactivity in the solution at regular intervals of time, it is possible to follow the kinetics of exchange between labelled and unlabelled Na+ ions. The amount of Na+ ion in the membrane can be deduced from the measured radioactivity in the solution. In the absence of co-ions, the amount of H+ ion in the membrane is deduced from the equation: fiNa+ +fin+=x
(1)
tiNa+ and tin+ being the respective molalities of Na+ and H+ ions in the membrane and .?? the molality of the fixed sites, which is deduced from the values of the exchange capacity. Results
a. For only one counter-ion present in the membrane phase The membrane does not contain any sorbed electrolyte. The only mobile ion is the counter-ion present in the membrane phase. The following cations have been studied: H+, Li+, Na+, Cs+, tetramethylammonium (TMA+). The results are shown in Fig. 1. The water content is represented by N, which is the number of water molecules per sulfonic site. It can be seen that, for the lower values of N, the membrane resistance increases, reaching very high values as the water content decreases. A transition domain appears, in which the variation of the membrane resistance, R, depends on the nature of the counter-ion. Figure 2 shows the variation of log R within this transition domain. b. For two counter-ions present in the membrane Figures 3 and 4 show the variation of the membrane resistance with the ratio of the number of water molecules to the number of sulfonic groups. The membrane had previously been equilibrated with an aqueous solution containing NaCl+ HCI or LiCl+ HCI. In Fig. 5, the self-diffusion flux of Na+ is plotted as a function of the molar fraction of Na+, x=c&+/(c~~+ + c$+ ), in the external aqueous solution. Figure 6 shows the variation of the molar fraction of Na+ in the membrane
41
Fig. 1. Variation of the high-frequency membrane resistance for different cation species.
Fig. 2. Variation of the membrane resistance in the transition domain. 0: H+, 0: Li+, +: Na+, A: Cs+, 0: (CHB)4N+.
42
IO
I5
0
X=0
+
x=0.1
0
x=0.2
*
~~0.5
.
rr
20
x1.
n&+ nN_+ + nH +
I
30
25
--
Fig. 3. Variation of the membrane resistance with the ratio of the number of water molecules over the number of sulfonic groups. the membrane containing both Na+ and H+ ions.
0
X=0
+
razo.2
x
x=0.4
A
X:.0.6
q
SCiO.8
.
Jc=
xs
nLi+ nLi+ +nH+
I
Fig. 4. Variation of the membrane resistance with the ratio of the number of water molecules over the number of sulfonic groups, the membrane containing both Li+ and H+ ions.
43
0.05
0
w 0.2
0.4
0.8
0.6
x'
Fig. 5. Variation of the self-diffusion flux of Na+ as a function of the molar fraction of Na+ in the aqueous solution; n = cza+ / (cE+ ).
0.75.
oso-
0.8
x
I
-
Fig. 6. Variation of the molar fraction of Na+ in the membrane as a function of the molar fraction of Na+ in the aqueous solution.
I 0
t 0.2
0.4
0.6
0.8
Fig. 7. Variation of the water content of the membrane at equilibrium NaCl+ HCl as a function of the molar fraction of Na+ in the solution.
x
1
with aqueous solution of
phase over the molar fraction in the aqueous solution. A linear variation observed. Figure 7 represents the variation of the water content of the membrane equilibrium with an aqueous solution of NaCl+ HCl.
is at
Discussion
For a water content of 16 molecules per fixed site, values of conductivity are obtained from the values of the membrane resistance, by interpolation of the curve R=f(nn,o). Th is calculation takes into account of variations of membrane thickness with swelling:
(2) where L is the specific conductivity of the membrane, e, the dry sample thickness, A the cross sectional area, R the membrane resistance, N the number of Hz0 molecules per sulfonic site, and a the ratio, Unzo /u,, of the molar volume of water u&o to the volume of dry polymer up per mole of SO,. Consequently, and supposing that the volume of polymer plus water obeys an additive law, the term between brackets represents the volume increase
ratio of a sample containing N water molecules per site. Considering swelling as an isotropic phenomenon, the wet sample thickness is then e, (1 + cxN) !. The variation of conductivity of the membrane with the water content has two different origins. The first is a change in the rate constant of the elementary ion transfer reaction. The interactions between the fixed sites and the mobile cations, and incidentally the height of the activation energy barrier of the ion transfer reaction, will depend on their hydration states. The second origin is connected to the microstructure of the membrane material. Smallangle X-ray and neutron scattering experiments have clearly indicated [ 16, 201 that ionic clustering is present in perfluorosulfonic membranes. The cluster network model suggests that solvent and ion exchange sites undergo phase separation from the fluorocarbon matrix to form inverted micellar structures connected by short narrow channels. Hsu et al. [5] have suggested that, according to this cluster network model, the ionic conduction across the ionomer membranes follows a percolation process. To recall the main features of percolation theory applied to conduction phenomena in ionomer membranes: the membrane phase is considered as a three-dimensional lattice in which the ionic clusters correspond to the lattice nodes. In such a system, the conductivity obeys the following law: A(z) z (3C-X,Y
(4)
where x denotes the concentration of conducting phases and t a universal critical exponent. x, correspond to the “insulator-to-conductor” transition threshold. In a site percolation model, a theoretical estimate oft is 1.5 + 0.2 [ 211, and Scher and Zallen [ 221 proposed the critical volume fraction of the conducting phase as a characteristic constant. On this basis the conductivity law takes the form: n=n,(u-u,)”
(5)
where A,, is the specific conductivity of the conducting phase. In order to compare our results with this model, the values of membrane conductivity has been plotted as a function of the volume fraction of the aqueous phase, r (Fig. 8). The value of z is calculated from VW,the water volume in the membrane phase, and VP,the dry polymer volume:
Using the previously defined parameters N, u, and u,, relationship (6) becomes:
Nuw T=Nu,+u,=30.55+N
N
46
/
0
H'
/
/
P
0
0.2 Fig. 8. Membrane the membranes.
conductivity
/
0.4
0.6
1 as a function
7
of the volume fraction
T of the aqueous phase in
in which the value 30.55 is the ratio of the volume of dry polymer per mole of SO; to the molar volume of water. Extrapolation of the curves to A= 0 gives the value of 7_ the conductivity threshold, which depends on the cationic species, as shown in Fig. 9. According to the percolation theory [21], log A must be a linear function of log (z- 7,) with slope 1.5 t 0.2. The results shown in Fig. 10 are in relatively good agreement with the theoretical equation over only a limited range. The values of the exponent t are 1.53 for H+, 1.51 for K+, 1.57 for Li+, 1.43 for Na+ and 1.28 for Rb+. For higher values of water content, the variation of membrane conductivity does not follow the theoretical law. This fact suggests that, in this case, there are no more isolated micro-domains and the percolation model cannot be applied. The values of the threshold volume fraction 7, range from 0.2 to 0.3. They depend on both the dimensionality and the manner in which the clusters are dispersed. For a three-dimensional continuous random system, tC is 0.15. A larger value applies when ion clusters flocculate into several well isolated regions [ 51. On the other hand, it may be noted that the membrane conductivity with different cations present follows a sequence opposite to the sequence of cation mobilities in water, except for the proton, which is suspected to follow a hopping transport mechanism. Thus, for high water contents, membrane conductivity depends on the interactions between the fixed sites and the mobile ions. When the distance of these interacting charged species increases, i.e., with
41
I 0
0. I
0.2
0.3
,,-TMA+ 0.4
0.5
t 2
Fig. 9. Determination of conductivity different cation species.
threshold
tC by extrapolation
of the curves 1 = f(~) for
more highly hydrated ions, an increase in membrane conductivity may be expected, resulting from a lowering of coulombic interactions. This conclusion is in agreement with the experimental results, which reveal that membrane conductivity follows the same sequence as the hydration state of the cation: ALi+
>ANa
+ >AK+
>lLcs+
(8)
By applying the Stokes-Einstein equation and the rate process to ionic migration [ 231, it will be possible to calculate for two different ions the difference between their activation free energies of the elementary ion-transfer reactions, the proton being chosen as the reference ion: d(dC”t)=dcyj--dGR+#=RTln~ L
(9)
Equation (9) means that, for a given membrane, the rate-determining step
NAFION 117 A
2
T L”s@-z)
Fig. 10. Validity of the percolation theory; slopes of the linear function log(d) as a function of log( r- rc) for different cation species. TABLE 1 Difference between the proton and some monovalent cations, i, of the activation free energy of the ion transfer reaction in Nafion 117 membrane ( n,,,/ns,3 = 16) Cation i
AC?+-&”
H+
(kcal-mol-‘)
+
Li+
Na+
K+
(CH,),N+
0.425
0.540
0.696
2.22
for the counter-ion diffusion-migration process is the elementary ion-transfer reaction between two adjoining sites, all the sites being considered as energetically equivalent. This situation is to be expected for high degrees of swelling. The values of the difference between the activation free energies for the diffusion-migration of the cations corresponding to a swelling degree of 16 water molecules per SO; group are reported in Table 1. The results confirm
49
that, for the alkali cation series, the rate of diffusion-migration in this perfluorosulfonic membrane is determined by the electrostatic interactions between the fixed charged group and the mobile ion, the more hydrated ion having the lower attraction energy for the fixed anionic group. An attempt has been made to analyse the results for membrane conductivity obtained in the presence of two counter-ions in the membrane phase. Consider first the case where the membrane contains Na+ and H+ as the only mobile ions. From the results of self-diffusion flux measurements, values of the selfdiffusion coefficient of Na+ ion are obtained, from which it will be possible, by applying the Nernst-Einstein relationship, to obtain the value of the individual mobility of Na+ ion in the membrane containing both Na+ and H+ counterions. Figure 11 shows the variation of the relative mobility of Na+ ions, ON,+, which is the ratio of the mobility of Na+ in the membrane equilibrated with aqueous solutions of a mixture of NaCl and HCl (molar ratio of Na+ =x) over the mobility of Na+ in the membrane equilibrated with an aqueous solution containing only NaCl (x = 1):
u-r
UNa+ (x)
DONa+ (x)
N”+=ONa+(~=l)=D&a+(~=l)
(10)
0 and Do being the mobility and the self-diffusion coefficient, respectively, in the membrane phase. It may be noted that the points of Fig. 11 correspond to different degrees of swelling of the membrane; the water content of the membrane depends on the value of x (cf. Fig. 7). When the membrane contains only H+ and Na+ cations, its conductivity can be expressed as follows:
with
x;+
nH+
= nNa+
+nH+
nH+ Z-X x
l-f&+
Figure 12 shows the variations of L with x=&a+. The value of K is deduced from the conductivity value of a membrane equilibrated only with NaCl (x = 3tNa+= 1) . For x = 0, &+ = 1 and %Na+= 0. In this case, eqn. (11) gives:
OH+(x=0) =
(12)
Knowing the value of K and combining eqns. (11) and (12) one obtains:
‘Jr,
=
u No+( X) “,a+
1.5
(x I I)
0.54
0
0.2
0.4
0.8
0.6
I
X
-
Fig. 11. Relative mobility of Na+ as a function of the molar fraction of Na+ in the membrane phase;x = nNa+/(nNa+ +nH+).
403. A.
(&cm-‘)
15
f
0
0.2
.
0.4
0.6
0.8
x
*
I
Fig. 12. Variation of the membrane conductivity with the molar fraction of Na + in the membrane chase.
51
1
A
0.2
0.4
0.6
0.8
3c
I
Fig. 13. Relative mobility of H+ as a function of the molar fraction of Na+ in the membrane phase.
OH+(xl u-1.u+=&+(X=O)=
[n(X)-XNa+~~*+(X)~(3C=1)~Na+(X=l)] )A(x=O) (l-f&+
(13)
Figure 13 shows the variation of U -&+ with z. It may be noted that the individual mobility of the proton increases up to 150% as the number of Na+ ions increases in the membrane. The presence of Na+ in the membrane increases the rate of proton migration, despite the fact that the water content is reduced. On the other hand, the relative mobility, ON,+, of Na+ has values higher than unity for fNa+ < 0.5, and values lower than unity for &+ > 0.5. However, the maximum variation of UNa+never exceeds 20%. The steady increase of the individual mobility of the proton with the molar fraction of Na+ ion can be attributed to an increase of the proton hydration, Na+ being less hydrated than H+. Despite the lower swelling, the number of water molecules solvating a reference proton may be higher when the membrane contains less-hydrated sodium ions than when it contains protons only. In order to analyse the variation of the individual mobility of Na+ ion, account should be taken of the higher total number of water molecules (lower values of fNa+ and the hydration competition between proton and sodium ion (higher values of 3cNy,+ ). For the system Li+-H+, as Li+ has no radioactive isotope, the variation of its individual mobility cannot be determined by means of self-diffusion flux
52
measurement. Nevertheless, it may be noted that, despite the conductivity of the membrane containing only Li+ being lower than that of the membrane containing only H+, the conductivity of the membrane as a function of x passes through a maximum. This fact shows that the mobility of at least one of the two ions is increased when at least 20% of the Li+ ions are replaced by protons.
References 1 2 3
4 5 6 I 8 9 10 11 12 13
14 15 16 17 18 19
F. Helfferich, Ion Exchange, McGraw Hill Book Co., New York, NY, 1962, Chap. 5. K.A. Mauritz and A.J. Hopfinger, in: J.O’M. Bockris, B.E. Conway and R.E. White (Eds.), Modern Aspects of Electrochemistry, 14, Plenum Press, New York, NY, 1982, p. 425. T.D. Gierke and W.Y. Hsu, in: A. Eisenberg and H.L. Yeager (Eds.), Perfluorinated Ionomer Membranes, ACS Symp. Ser., No. 180, American Chemical Society, Washington, DC, 1982, p. 283. K.A. Mauritz and C.E. Rogers, A water sorption isotherm model for ionomer membranes with cluster morphologies, Macromolecules, 18 (1985) 483. W.Y. Hsu, J.R. Barkley and J. Meakin, Ion percolation and insulator conductor transition in Nafion perfluorosulfonic acid membranes, Macromolecules, 13 (1980) 198. R. Wodzi, A. Nerebska and W. Kwas, Percolation conductivity in Nafion membranes, J. Appl. Polym. Sci., 30 (1985) 769. C.S. Fadley and R.A. Wallace, Electropolymer studies. II. Electrical conductivity of a polystyrene sulfonic acid membrane, J. Electrochem. Sot., 115 (1968) 1264. R.A. Wallace, Effect of membrane matrix on the transport of potassium ions, J. Appl. Polym. Sci., 18 (1974) 2855. R.A. Wallace and J.P. Ampaya, Transport within ion-exchange membranes, Desalination, 14 (1974) 121. V. Subrahmanyan and N. Lakshminarayanaiah, A rapid method for the determination of electrical conductance of ion-exchange membranes, J. Phys. Chem., 72 (1968) 4314. AI. Meshechkov, O.A. Demina and N.P. Gnusin, Impedance diagram of a mercury contact cell with ion-exchange membrane, Electrokhimiya, 23 (10) (1987) 1452. S. D’Alessandro, Equilibrium and transport properties of ion-exchange membranes, J. Membrane Sci., 17 (1984) 63. M. Nedyalkov, D. Schuhmann and C. Gavach, Impedance of Nation perfluorosulfonic membranes. Influence of cation and water content, Spring Meet. Electrochem. Sot., Boston, MA, 1986, Extended Abstracts, No. 86-1, p. 654. M. Nedyalkov and C. Gavach, Percolation conductivity in a perfluorosulfonic membrane with sorbed NaOH, J. Electroanal. Chem. Interfacial Electrochem., 234 (1987) 941. C. Gavach, A. Lindheimer, D. Cros and B. Brun, Selectivity of ion transfer in carboxylic ion exchange membranes, J. Electroanal. Chem. Interfacial Electrochem., 190 (1985) 33. C. Yeo and A. Eisenberg, Effect of ion placement and structure on properties of plasticized polyelectrolytes, J. Appl. Polym. Sci., 21 (1977) 875. J. Ceynowa, Electron microscopy investigation of ion exchange membranes, Polymer, 19 (1978) 73. E.J. Roche, M. Pineri, R. Duplessix and A.M. Levelut, Small-angle scattering studies of Nafion membranes, J. Polym. Sci., Polym. Phys. Ed., 19 (1981) 1. T.D. Gierke, C.E. Munn and F.C. Wilson, The morphology in Nafion perfluorinated membrane products as determined by wide and small-angle X-ray studies, J. Polym. Sci., Polym. Phys. Ed., 19 (1981) 1687.
53 20
21 22 23
M. Fujimura, T. Hashimoto and H. Kawai, Small-angle X-ray scattering study of perfluorinated ionomer membranes. I. Origin of two scattering maxima, Macromolecules, 14 (5) ( 1981) 1309. S. Kirkpatrick, Percolation and conduction, Rev. Mod. Phys., 45 (4) (1973) 574. H. Scher and R. Zallen, Critical density in percolation processes, J. Chem. Phys., 53 (1970) 3759. J.O’M. Bockris and A.K. Ready, Modern Electrochemistry, Vol. 1, Plenum Press, New York, NY, 1970, p.387.
AC IMPEDANCE INVESTIGATION OF THE KINETICS TRANSPORT IN NAFION@ PERFLUOROSULFONIC MEMBRANES*
C. GAVACH’, G. PAMBOUTZOGLOU’,
37
OF ION
M. NEDYALKOV’ and G. POURCELLY’
‘CNRS - UA 330, LPCSP, B.P. 5051,34033 Montpellier Ceder (France) 2Department of Physical Chemistry, Faculty of Chemistry, University of Sofia, Anton Zvanov, 1126 Sofia (Bulgaria) Received July 24,198’7; accepted in revised form November 4,1988)
Summary The high-frequency resistance of a Nafion @ perfluorosulfonic membrane is measured by means of the AC impedance technique. Using a mercury cell, it is possible to follow the variation of the resistance as a function of the water content and of the nature of the cation present in the membrane. In all cases, the number of sorbed co-ions is very low. When only one counter-ion is present within the membrane phase, the results show that the percolation theory is valid only for lower degrees of swelling. For higher water content, the rate constant of the elementary ion transfer reaction of alkaline cations varies in the same way as their hydration state in water. When the membrane contains both sodium ion and proton, the variation of individual mobility of sodium ion with the molar fraction is deduced from the value of the self-diffusion coefficient measured using a radiotracer. In this case, conductivity measurements reveal that the mobility of the proton increases by up to 150% when the number of sodium ions increases in the membrane.
Introduction In polymeric ion-exchange materials, the degree of swelling is related to the balance between the internal osmotic pressure and the counteracting elasticity of the polymeric matrix [1,21. With a given ion-exchange membrane at the equilibrium state, and with aqueous electrolyte solutions, the degree of swelling will depend on the hydration state of the counter-ions and, to a much less extent, that of sorbed co-ions, as well as on the external electrolyte concentration, which affect the water activity in the membrane-solution system. Therefore, in a series of conductivity measurements performed with membranes at partition equilibrium with different aqueous solutions, the water content will alter from one solution to the other. Ionomeric perfluorosulfonic membranes show phase separation into an in*Presented at ICOM ‘8’7, Tokyo, Japan, June 8-12,1987.
0376-7388/89/$03.50
0 1989 Elsevier Science Publishers B.V.
38
verted micellar structure connected by short narrow channels [ 31. A theoretical analysis of swelling equilibrium with cluster-forming ionomer membranes has been already attempted [ 41. The conductivity of this membrane material is related to the probability of finding chains of conducting clusters in contact forming conduction pathways. It has been shown that the conductivity variations of ionomer membranes are quite well described by the percolation theory [5, 61. With these ionomer membranes, a change in the degree of swelling affects the conductivity of the material via two distinct effects: a change of the ionic hydration, which determines the rate constant of the elementary ion transfer reaction, and a change of the volume fraction of the aqueous microdomains, which determines the probability of the formation of conduction pathways. In order to get a better insight into the elementary processes underlying the ionic conducting properties of ionomer perfluorosulfonic membranes, it is necessary to determine the variation of the conductivity of the membrane phase as a function of its ionic composition and of its water content. Measurements of conductivity of the polymeric membrane with controlled water swelling have already been performed by Wallace and co-workers [ 7-91. Their experimental method consists in tightly clamping the membrane between two platinum coated electrodes and in applying Ohm’s law to the linear variation of the DC intensity above the decomposition voltage. The use of mercury cells for determining the AC resistance of the polymeric membrane was investigated by Subrahmanyan and Lakshminarayanaiah [lo]. This technique was used later by Meshechkov and coworkers [ 111, who stated that measurements must be performed in the high-frequency range, and by D’Alessandro [ 121, who used only 1 kHz frequency. In the present work, the conductivity of a Nation@* membrane has been measured, again by using a mercury cell, but with recording of the whole impedance diagram between 1 Hz and 1 MHz. The experimental technique used enables determination of the value of the conductivity of the membrane phase at which the swelling by water can be modified at will: from the swelling state of the membrane equilibrated with an aqueous electrolyte solution to the completely dried state [ 13, 141. The study is achieved with a Nafion 117 membrane (equivalent weight 1100) with which swelling degree can be varied over a wide range. The purpose of this work is to determine experimentally the variation of the membrane conductivity as a function of the water content and ionic composition. These two parameters are here fixed independently, whereas in previous works on the percolation conductivity of ionomer perfluorosulfonic membranes [ 5,6] the ionic composition of the membrane as well its water content were changed simultaneously. *Nafion @, registered trademark for perfluorosulfonic acid membranes from Du Pont, Wilmington, DE. U.S.A.
39
Experimental Before measurements, pre-treatment is carried out in order to remove impurities from the membrane phase. At room temperature, the membrane is successively immersed in aqueous hydrochloric acid ( 1 hr ), distilled water (2 hr ) and aqueous sodium hydroxide (1 hr ) . This cycle is repeated once before boiling the membrane for 1 hr in deionized water and reconverting it to M+ form. After this treatment, the membrane is considered to contain only M+ ions as counter-ions and no sorbed electrolyte. It has also been verified that boiling does not modify the exchange capacity of the membrane. The electrolytes are Merck Suprapur products; 22Na-labelled NaCl solutions were obtained from Amersham Radiochemical Centre (UK). The amount of water in the membrane is deduced from the difference of weights: firstly during the experiment with a membrane in the Mf form and secondly when the sample contains no more water, i.e., when it has been maintained under vacuum for 3 days at 90” C in the tetrabutylammonium form. The conductivity of membrane phases having the same swelling but different ionic compositions have been compared by AC impedance measurements carried out as follows. After having been immersed in the equilibrium solution for 24 hr, the sample is gradually dried by exposure to vacuum. At regular intervals of time, the membrane is weighed and an impedance measurement is carried out. It has been verified that during the measurement period (about 30 set) the amount of water in the membrane does not change significantly. This method enables the study of the dependence of membrane impedance on degree of swelling for a given cationic form. The membrane resistance value is deduced from the intercept of the impedance diagram with the real axis. In order to check the reproducibility, each measurement is performed three times using different membrane samples. Self-diffusion fluxes of Na+ ion have been measured at 25°C using a twocompartment Teflon cell in which the membrane is placed between two identical aqueous solutions of 0.1 A4 NaCl which are continuously renewed by means of two peristaltic pumps. Each half-cell volume (1.4 cm diameter; 2.0 cm length) is completely renewed within 2 sec. The total volume of solution in each halfcircuit is 100 ml. Before the experiment, the membrane sample was equilibrated for 24 hr in the studied solution. Then, a very small amount of 22Na-labelled NaCl solution (40 ~1) is added to one side. At regular intervals of time, small volumes (100 ~1) are removed from each half-circuit, and the radioactivity of these samples is measured using a Packard auto-gamma spectrometer. The values of the ionic unidirectional fluxes crossing the membrane (through a section of 0.95 cm2) are evaluated from the variation of the radioactivity of the second solution by using a previously described method [ 151. Self-diffusion fluxes of Na+ ion in presence of H+ ion have also been mea-
40
sured, using 0.1 M (NaCl, HCl) aqueous solutions, i.e., [H+ ] + [Na+ ] = 0.1 M. In this case, the ratio X= nNa+ ( nNa+ -t nn+ ) can be evaluated, where aNa+ and nn+ are, respectively, the numbers of Na+ and H+ ions in the membrane phase. The sample is immersed up to the equilibrium state in the 22Na-labelled aqueous solution of NaCl+ HCl; c1 and c2 are the respective concentrations of NaCl and HCl in the equilibrating solution; cl + c2 = 0.1 M. The sample is then removed from solution and its surface is dried by blotting with filter paper. Afterwards the membrane is immersed in a solution of unlabelled NaCl+ HCI at the same concentrations c1 and c2, the solution being thoroughly stirred. By measuring the increase of the radioactivity in the solution at regular intervals of time, it is possible to follow the kinetics of exchange between labelled and unlabelled Na+ ions. The amount of Na+ ion in the membrane can be deduced from the measured radioactivity in the solution. In the absence of co-ions, the amount of H+ ion in the membrane is deduced from the equation: fiNa+ +fin+=x
(1)
tiNa+ and tin+ being the respective molalities of Na+ and H+ ions in the membrane and .?? the molality of the fixed sites, which is deduced from the values of the exchange capacity. Results
a. For only one counter-ion present in the membrane phase The membrane does not contain any sorbed electrolyte. The only mobile ion is the counter-ion present in the membrane phase. The following cations have been studied: H+, Li+, Na+, Cs+, tetramethylammonium (TMA+). The results are shown in Fig. 1. The water content is represented by N, which is the number of water molecules per sulfonic site. It can be seen that, for the lower values of N, the membrane resistance increases, reaching very high values as the water content decreases. A transition domain appears, in which the variation of the membrane resistance, R, depends on the nature of the counter-ion. Figure 2 shows the variation of log R within this transition domain. b. For two counter-ions present in the membrane Figures 3 and 4 show the variation of the membrane resistance with the ratio of the number of water molecules to the number of sulfonic groups. The membrane had previously been equilibrated with an aqueous solution containing NaCl+ HCI or LiCl+ HCI. In Fig. 5, the self-diffusion flux of Na+ is plotted as a function of the molar fraction of Na+, x=c&+/(c~~+ + c$+ ), in the external aqueous solution. Figure 6 shows the variation of the molar fraction of Na+ in the membrane
41
Fig. 1. Variation of the high-frequency membrane resistance for different cation species.
Fig. 2. Variation of the membrane resistance in the transition domain. 0: H+, 0: Li+, +: Na+, A: Cs+, 0: (CHB)4N+.
42
IO
I5
0
X=0
+
x=0.1
0
x=0.2
*
~~0.5
.
rr
20
x1.
n&+ nN_+ + nH +
I
30
25
--
Fig. 3. Variation of the membrane resistance with the ratio of the number of water molecules over the number of sulfonic groups. the membrane containing both Na+ and H+ ions.
0
X=0
+
razo.2
x
x=0.4
A
X:.0.6
q
SCiO.8
.
Jc=
xs
nLi+ nLi+ +nH+
I
Fig. 4. Variation of the membrane resistance with the ratio of the number of water molecules over the number of sulfonic groups, the membrane containing both Li+ and H+ ions.
43
0.05
0
w 0.2
0.4
0.8
0.6
x'
Fig. 5. Variation of the self-diffusion flux of Na+ as a function of the molar fraction of Na+ in the aqueous solution; n = cza+ / (cE+ ).
0.75.
oso-
0.8
x
I
-
Fig. 6. Variation of the molar fraction of Na+ in the membrane as a function of the molar fraction of Na+ in the aqueous solution.
I 0
t 0.2
0.4
0.6
0.8
Fig. 7. Variation of the water content of the membrane at equilibrium NaCl+ HCl as a function of the molar fraction of Na+ in the solution.
x
1
with aqueous solution of
phase over the molar fraction in the aqueous solution. A linear variation observed. Figure 7 represents the variation of the water content of the membrane equilibrium with an aqueous solution of NaCl+ HCl.
is at
Discussion
For a water content of 16 molecules per fixed site, values of conductivity are obtained from the values of the membrane resistance, by interpolation of the curve R=f(nn,o). Th is calculation takes into account of variations of membrane thickness with swelling:
(2) where L is the specific conductivity of the membrane, e, the dry sample thickness, A the cross sectional area, R the membrane resistance, N the number of Hz0 molecules per sulfonic site, and a the ratio, Unzo /u,, of the molar volume of water u&o to the volume of dry polymer up per mole of SO,. Consequently, and supposing that the volume of polymer plus water obeys an additive law, the term between brackets represents the volume increase
ratio of a sample containing N water molecules per site. Considering swelling as an isotropic phenomenon, the wet sample thickness is then e, (1 + cxN) !. The variation of conductivity of the membrane with the water content has two different origins. The first is a change in the rate constant of the elementary ion transfer reaction. The interactions between the fixed sites and the mobile cations, and incidentally the height of the activation energy barrier of the ion transfer reaction, will depend on their hydration states. The second origin is connected to the microstructure of the membrane material. Smallangle X-ray and neutron scattering experiments have clearly indicated [ 16, 201 that ionic clustering is present in perfluorosulfonic membranes. The cluster network model suggests that solvent and ion exchange sites undergo phase separation from the fluorocarbon matrix to form inverted micellar structures connected by short narrow channels. Hsu et al. [5] have suggested that, according to this cluster network model, the ionic conduction across the ionomer membranes follows a percolation process. To recall the main features of percolation theory applied to conduction phenomena in ionomer membranes: the membrane phase is considered as a three-dimensional lattice in which the ionic clusters correspond to the lattice nodes. In such a system, the conductivity obeys the following law: A(z) z (3C-X,Y
(4)
where x denotes the concentration of conducting phases and t a universal critical exponent. x, correspond to the “insulator-to-conductor” transition threshold. In a site percolation model, a theoretical estimate oft is 1.5 + 0.2 [ 211, and Scher and Zallen [ 221 proposed the critical volume fraction of the conducting phase as a characteristic constant. On this basis the conductivity law takes the form: n=n,(u-u,)”
(5)
where A,, is the specific conductivity of the conducting phase. In order to compare our results with this model, the values of membrane conductivity has been plotted as a function of the volume fraction of the aqueous phase, r (Fig. 8). The value of z is calculated from VW,the water volume in the membrane phase, and VP,the dry polymer volume:
Using the previously defined parameters N, u, and u,, relationship (6) becomes:
Nuw T=Nu,+u,=30.55+N
N
46
/
0
H'
/
/
P
0
0.2 Fig. 8. Membrane the membranes.
conductivity
/
0.4
0.6
1 as a function
7
of the volume fraction
T of the aqueous phase in
in which the value 30.55 is the ratio of the volume of dry polymer per mole of SO; to the molar volume of water. Extrapolation of the curves to A= 0 gives the value of 7_ the conductivity threshold, which depends on the cationic species, as shown in Fig. 9. According to the percolation theory [21], log A must be a linear function of log (z- 7,) with slope 1.5 t 0.2. The results shown in Fig. 10 are in relatively good agreement with the theoretical equation over only a limited range. The values of the exponent t are 1.53 for H+, 1.51 for K+, 1.57 for Li+, 1.43 for Na+ and 1.28 for Rb+. For higher values of water content, the variation of membrane conductivity does not follow the theoretical law. This fact suggests that, in this case, there are no more isolated micro-domains and the percolation model cannot be applied. The values of the threshold volume fraction 7, range from 0.2 to 0.3. They depend on both the dimensionality and the manner in which the clusters are dispersed. For a three-dimensional continuous random system, tC is 0.15. A larger value applies when ion clusters flocculate into several well isolated regions [ 51. On the other hand, it may be noted that the membrane conductivity with different cations present follows a sequence opposite to the sequence of cation mobilities in water, except for the proton, which is suspected to follow a hopping transport mechanism. Thus, for high water contents, membrane conductivity depends on the interactions between the fixed sites and the mobile ions. When the distance of these interacting charged species increases, i.e., with
41
I 0
0. I
0.2
0.3
,,-TMA+ 0.4
0.5
t 2
Fig. 9. Determination of conductivity different cation species.
threshold
tC by extrapolation
of the curves 1 = f(~) for
more highly hydrated ions, an increase in membrane conductivity may be expected, resulting from a lowering of coulombic interactions. This conclusion is in agreement with the experimental results, which reveal that membrane conductivity follows the same sequence as the hydration state of the cation: ALi+
>ANa
+ >AK+
>lLcs+
(8)
By applying the Stokes-Einstein equation and the rate process to ionic migration [ 231, it will be possible to calculate for two different ions the difference between their activation free energies of the elementary ion-transfer reactions, the proton being chosen as the reference ion: d(dC”t)=dcyj--dGR+#=RTln~ L
(9)
Equation (9) means that, for a given membrane, the rate-determining step
NAFION 117 A
2
T L”s@-z)
Fig. 10. Validity of the percolation theory; slopes of the linear function log(d) as a function of log( r- rc) for different cation species. TABLE 1 Difference between the proton and some monovalent cations, i, of the activation free energy of the ion transfer reaction in Nafion 117 membrane ( n,,,/ns,3 = 16) Cation i
AC?+-&”
H+
(kcal-mol-‘)
+
Li+
Na+
K+
(CH,),N+
0.425
0.540
0.696
2.22
for the counter-ion diffusion-migration process is the elementary ion-transfer reaction between two adjoining sites, all the sites being considered as energetically equivalent. This situation is to be expected for high degrees of swelling. The values of the difference between the activation free energies for the diffusion-migration of the cations corresponding to a swelling degree of 16 water molecules per SO; group are reported in Table 1. The results confirm
49
that, for the alkali cation series, the rate of diffusion-migration in this perfluorosulfonic membrane is determined by the electrostatic interactions between the fixed charged group and the mobile ion, the more hydrated ion having the lower attraction energy for the fixed anionic group. An attempt has been made to analyse the results for membrane conductivity obtained in the presence of two counter-ions in the membrane phase. Consider first the case where the membrane contains Na+ and H+ as the only mobile ions. From the results of self-diffusion flux measurements, values of the selfdiffusion coefficient of Na+ ion are obtained, from which it will be possible, by applying the Nernst-Einstein relationship, to obtain the value of the individual mobility of Na+ ion in the membrane containing both Na+ and H+ counterions. Figure 11 shows the variation of the relative mobility of Na+ ions, ON,+, which is the ratio of the mobility of Na+ in the membrane equilibrated with aqueous solutions of a mixture of NaCl and HCl (molar ratio of Na+ =x) over the mobility of Na+ in the membrane equilibrated with an aqueous solution containing only NaCl (x = 1):
u-r
UNa+ (x)
DONa+ (x)
N”+=ONa+(~=l)=D&a+(~=l)
(10)
0 and Do being the mobility and the self-diffusion coefficient, respectively, in the membrane phase. It may be noted that the points of Fig. 11 correspond to different degrees of swelling of the membrane; the water content of the membrane depends on the value of x (cf. Fig. 7). When the membrane contains only H+ and Na+ cations, its conductivity can be expressed as follows:
with
x;+
nH+
= nNa+
+nH+
nH+ Z-X x
l-f&+
Figure 12 shows the variations of L with x=&a+. The value of K is deduced from the conductivity value of a membrane equilibrated only with NaCl (x = 3tNa+= 1) . For x = 0, &+ = 1 and %Na+= 0. In this case, eqn. (11) gives:
OH+(x=0) =
(12)
Knowing the value of K and combining eqns. (11) and (12) one obtains:
‘Jr,
=
u No+( X) “,a+
1.5
(x I I)
0.54
0
0.2
0.4
0.8
0.6
I
X
-
Fig. 11. Relative mobility of Na+ as a function of the molar fraction of Na+ in the membrane phase;x = nNa+/(nNa+ +nH+).
403. A.
(&cm-‘)
15
f
0
0.2
.
0.4
0.6
0.8
x
*
I
Fig. 12. Variation of the membrane conductivity with the molar fraction of Na + in the membrane chase.
51
1
A
0.2
0.4
0.6
0.8
3c
I
Fig. 13. Relative mobility of H+ as a function of the molar fraction of Na+ in the membrane phase.
OH+(xl u-1.u+=&+(X=O)=
[n(X)-XNa+~~*+(X)~(3C=1)~Na+(X=l)] )A(x=O) (l-f&+
(13)
Figure 13 shows the variation of U -&+ with z. It may be noted that the individual mobility of the proton increases up to 150% as the number of Na+ ions increases in the membrane. The presence of Na+ in the membrane increases the rate of proton migration, despite the fact that the water content is reduced. On the other hand, the relative mobility, ON,+, of Na+ has values higher than unity for fNa+ < 0.5, and values lower than unity for &+ > 0.5. However, the maximum variation of UNa+never exceeds 20%. The steady increase of the individual mobility of the proton with the molar fraction of Na+ ion can be attributed to an increase of the proton hydration, Na+ being less hydrated than H+. Despite the lower swelling, the number of water molecules solvating a reference proton may be higher when the membrane contains less-hydrated sodium ions than when it contains protons only. In order to analyse the variation of the individual mobility of Na+ ion, account should be taken of the higher total number of water molecules (lower values of fNa+ and the hydration competition between proton and sodium ion (higher values of 3cNy,+ ). For the system Li+-H+, as Li+ has no radioactive isotope, the variation of its individual mobility cannot be determined by means of self-diffusion flux
52
measurement. Nevertheless, it may be noted that, despite the conductivity of the membrane containing only Li+ being lower than that of the membrane containing only H+, the conductivity of the membrane as a function of x passes through a maximum. This fact shows that the mobility of at least one of the two ions is increased when at least 20% of the Li+ ions are replaced by protons.
References 1 2 3
4 5 6 I 8 9 10 11 12 13
14 15 16 17 18 19
F. Helfferich, Ion Exchange, McGraw Hill Book Co., New York, NY, 1962, Chap. 5. K.A. Mauritz and A.J. Hopfinger, in: J.O’M. Bockris, B.E. Conway and R.E. White (Eds.), Modern Aspects of Electrochemistry, 14, Plenum Press, New York, NY, 1982, p. 425. T.D. Gierke and W.Y. Hsu, in: A. Eisenberg and H.L. Yeager (Eds.), Perfluorinated Ionomer Membranes, ACS Symp. Ser., No. 180, American Chemical Society, Washington, DC, 1982, p. 283. K.A. Mauritz and C.E. Rogers, A water sorption isotherm model for ionomer membranes with cluster morphologies, Macromolecules, 18 (1985) 483. W.Y. Hsu, J.R. Barkley and J. Meakin, Ion percolation and insulator conductor transition in Nafion perfluorosulfonic acid membranes, Macromolecules, 13 (1980) 198. R. Wodzi, A. Nerebska and W. Kwas, Percolation conductivity in Nafion membranes, J. Appl. Polym. Sci., 30 (1985) 769. C.S. Fadley and R.A. Wallace, Electropolymer studies. II. Electrical conductivity of a polystyrene sulfonic acid membrane, J. Electrochem. Sot., 115 (1968) 1264. R.A. Wallace, Effect of membrane matrix on the transport of potassium ions, J. Appl. Polym. Sci., 18 (1974) 2855. R.A. Wallace and J.P. Ampaya, Transport within ion-exchange membranes, Desalination, 14 (1974) 121. V. Subrahmanyan and N. Lakshminarayanaiah, A rapid method for the determination of electrical conductance of ion-exchange membranes, J. Phys. Chem., 72 (1968) 4314. AI. Meshechkov, O.A. Demina and N.P. Gnusin, Impedance diagram of a mercury contact cell with ion-exchange membrane, Electrokhimiya, 23 (10) (1987) 1452. S. D’Alessandro, Equilibrium and transport properties of ion-exchange membranes, J. Membrane Sci., 17 (1984) 63. M. Nedyalkov, D. Schuhmann and C. Gavach, Impedance of Nation perfluorosulfonic membranes. Influence of cation and water content, Spring Meet. Electrochem. Sot., Boston, MA, 1986, Extended Abstracts, No. 86-1, p. 654. M. Nedyalkov and C. Gavach, Percolation conductivity in a perfluorosulfonic membrane with sorbed NaOH, J. Electroanal. Chem. Interfacial Electrochem., 234 (1987) 941. C. Gavach, A. Lindheimer, D. Cros and B. Brun, Selectivity of ion transfer in carboxylic ion exchange membranes, J. Electroanal. Chem. Interfacial Electrochem., 190 (1985) 33. C. Yeo and A. Eisenberg, Effect of ion placement and structure on properties of plasticized polyelectrolytes, J. Appl. Polym. Sci., 21 (1977) 875. J. Ceynowa, Electron microscopy investigation of ion exchange membranes, Polymer, 19 (1978) 73. E.J. Roche, M. Pineri, R. Duplessix and A.M. Levelut, Small-angle scattering studies of Nafion membranes, J. Polym. Sci., Polym. Phys. Ed., 19 (1981) 1. T.D. Gierke, C.E. Munn and F.C. Wilson, The morphology in Nafion perfluorinated membrane products as determined by wide and small-angle X-ray studies, J. Polym. Sci., Polym. Phys. Ed., 19 (1981) 1687.
53 20
21 22 23
M. Fujimura, T. Hashimoto and H. Kawai, Small-angle X-ray scattering study of perfluorinated ionomer membranes. I. Origin of two scattering maxima, Macromolecules, 14 (5) ( 1981) 1309. S. Kirkpatrick, Percolation and conduction, Rev. Mod. Phys., 45 (4) (1973) 574. H. Scher and R. Zallen, Critical density in percolation processes, J. Chem. Phys., 53 (1970) 3759. J.O’M. Bockris and A.K. Ready, Modern Electrochemistry, Vol. 1, Plenum Press, New York, NY, 1970, p.387.