J. Phys. Chem. 1995,99, 12915-12924
12915
Equilibrium Partitioning of Monovalent/Divalent Cation-Salt Mixtures in Nafion Cation-Exchange Membranes P. N. Pintauro* and R. Tandon Department of Chemical Engineering, Tulane University, New Orleans, Lousiana 70118
L. Chao, W. Xu, and R. Evilia Department of Chemistry, University of New Orleans, New Orleans, Lousiana 70148 Received: March 20, 1995; In Final Form: June 13, 1 9 9 P
A molecular-level equilibrium partition coefficient model has been formulated and tested for the uptake of aqueous monovalent/divalent cation-salt mixtures into a Nafion 1 17 perfluorosulfonic acid cation-exchange membrane. The model utilizes a simple cylindrical-pore microstructure for Nafion and considers ion hydration free energy changes which occur during solute partitioning, the orientation of water dipoles within a membrane pore due to the strong electric field generated by the membrane's fixed-charge sites, and the formation of contact ion pairs (coordinate covalent bonds) between divalent cations and membrane ion-exchange sites. Membrane structure parameters in the model (pore-radius and pore-wall fixed-charge concentration) were determined from membrane porosity experiments and X-ray diffraction data in the literature. When the fraction of sulfonate sites which bind to divalent cations was used as an adjustable parameter, the model was able to predict accurately the divalent/monovalent cation selectivity (membrane-phase concentrations) of Pb2+ and Cd2+ with a coabsorbed alkali metal cation (either Li+, Na+, K+, or Cs+) for external salt concentrations of 0.05 and 0.25 M. Independent verification and quantification of the extent of divalent cation binding were made by NMR analyses of salt-equilibrated membranes. The NMR results and model predictions for the fraction of total membrane-phase lead that was bound to sulfonate sites were found to be in excellent agreement with an average error less than 6% for a series of 16 uptake experiments with Pb2+ and either Li+ or K+.
Introduction The overall permselectivity of an ion-exchange membrane is governed by equilibrium solubility (partitioning) of cations and anions at the upstream and downstream membrqelsolution interfaces and ion transport through the interior portions of the membrane. Bontha and Pintauro' recently developed a model that predicted accurately cation partitioning from two- and threecomponent aqueous mixtures of alkali metal chloride salts into a Nafion peffluorosulfonic acid cation-exchange membrane (Nafion is a registered trademark of E. I. DuPont de Nemours and Co.). The observed alkali metal cation selectivity sequence, where the cation with the higher surface charge density was preferentially excluded from the membrane, was shown to be due to the combined effects of (i) iodfixed-charge site electrostatic interactions in the cylindrical pores of the membrane, (ii) solvent dipole alignment by the radial direction electric field generated by the membrane's fixed-charge sites, and (iii) ion hydration free energy changes which occur when ions solubilize in the low-dielectric constant pore fluid. The selectivity criterion established by Bontha and Pintauro (Le,, exclusion of high-surface charge density cations) was not observed in prior studies with cation-exchange membranes and resins that were exposed to solutions containing a mixture of + 1 and +2 metal cation salts. Bonner and Smith,2for example, found preferential absorption of high-surface charge divalent cations (e.g., Mg2+, Zn2+, Ni2+, Ca2+, and Pb2+) as compared to monovalent alkali metal cations in Dowex 50 poly(styrenesulfonic acid) cation-exchange resins. When Boyd et aL3 examined the equilibriumpartitioning of dilute aqueous mixtures of Zn2+ and Na+ in Dowex 50, the selective uptake of Zn2+
* To whom all correspondence should be sent. @
Abstract published in Advance ACS Abstracts, August 1, 1995.
was observed. A number of investigators concluded that multiply-charged cations form contact ion pairs with the fixedcharge sites of cation-exchange membranes and gels. In 1957, Rosenberg et aL4 studied the t r ~ s p o r and t equilibrium uptake properties of a sulfonated, cross-linked, polystyrene-typecationexchange membrane with aqueous solutions of KCl, BaC12, LaC13, and ThCl4. The co-ion concentration within the membrane was found to increase as the cation valency increased. For ThC14 solutions, the membrane actually became anion selective, with the transference number of Th4+ x0.3. These results suggested that multivalent cations were neutralizing fixed charges, thus allowing appreciable co-ion intrusion into the polymer network. The higher the surface charge density of the multiply-charged cation, the more firmly it is attached to the ion-exchange sites, as evidenced by the Th4+results. KOro~y,~ working with a parchment film that was impregnated and cured with a phenolsulfonic acid-formaldehyde resin, found the permselectivity of the cation-exchange membrane toward K+ and C1- could be lowered or reversed by soaking the film in a dilute solution of Th4+. Hittorf transference number experiments with solutions containing either 0.10 N KCl or 0.10 N KCl 0.008 N ThC4 showed an increase in the C1- transference number from near 0 to 0.6 upon exposing the membrane to Th4+. By examining the absorption of singly- and multiply-charged metal ions in cation-exchange gels (Dowex-SOW) of various cross-linking, Boyd6 found large decreases in volume and positive entropy changes when heavily cross-linked gels were exposed to solutions of multivalent cations (e.g., Ba2+, Ca2+, La3+, and Th4+), again suggesting that such cations were releasing a portion of their water of coordination and forming contact ion pairs with the resin's charged sites. In the same study, field binding (solvent-separated ion pairs) of monovalent cations was inferred from enthalpy and entropy measurements
0022-365419512099-12915$09.00/0 0 1995 American Chemical Society
+
12916 J. Phys. Chem., Vol. 99, No. 34, 1995 with lightly cross-linked gels. In a more recent experimental study of divalent cationfhydrogen ion uptake in Nafion membranes for alkaline earth ions, Co2+, and Zn2+,Yeager and cow o r k e r ~found ~ , ~ the order of exchange selectivities to be Ba2+ > Sr2+ > Ca2+ > Mg2+ > Co2+ > Zn2+;Le., the larger cation in the series is selectively absorbed, as was the case for monovalent cations in Bontha and Pintauro's 1994 paper.' Yeager and co-workers, however, argued against the possibility of ion-pair formation in Nafion (a process requiring that the cations lose a portion of their hydrated water) due to the low concentration of membrane fixed-charge sites and the high degree of membrane swelling by water (a consequence of the lack of chemical cross-links in the membrane) which allow fullyhydrated divalent cations to absorb into the polymer phase. The present study was undertaken to clarify and better understand the physicochemical processes which govem the partitioning of monovalent/divalent cation-salt mixtures in Nafion cation-exchange membranes. Experimental and theoretical equilibrium absorption studies were carried out with a Nafion 117 peffluorosulfonic acid cation-exchange membrane and aqueous two component solutions of an alkali metal cation and either Pb2+or Cd2+. Selective absorption of divalent cations in the presence of various alkali metal ions was observed. When the equilibrium uptake model of Bontha and Pintauro' was modified to include the formation of contact ion pairs (coordinate covalent bonds) between divalent ions and the membrane's sulfonate charge sites, quantitative agreement between the theory and experimentalcation selectivity data was achieved. Independent verification of divalent ion binding was made by NMR spectroscopic analyses of salt-equilibrated Nafion films.
Theory The equilibrium partition coefficient model described here for the uptake of monovalent/divalent cation-salt mixtures into a cation-exchange membrane is a modified version of the theory developed by Bontha and Pintauro.' The present model considers the neutralization of membrane fixed-charge sites by the formation of divalent catiordfixed-charge site contact ion pairs. The membrane is modeled as an array of parallel cylindrical pores with ion-exchange sites distributed uniformly on the pore-wall surface. At equilibrium, the electrochemical potential of each ionic species inside the membrane is equal to its electrochemical potential in the extemal solution, in which case the radial concentration distribution of anions and cations within a pore is described by a modified Boltzmann equation,
Pintauro et al. solubilize in the low-dielectric constant pore fluid. As shown previously,' AZcGi(r)is a function of the size and charge of the absorbing ion, the solvent type, and the local value of the pore-solvent dielectric constant, € ( I ) . The inclusion of this Gibbs energy term allows the uptake model to distinguish between ions of like charge and different size. In order to use eq 1 to compute the concentration of one or more counterions and co-ions inside a membrane pore, the variation in electrostatic potential and solvent dielectric constant with radial pore position must be determined. This is accomplished by solving Poisson's equation with a nonuniform dielectric constant for n mobile ion species,
where E* is the permittivity of vacuum and c ( r ) is given by eq 1. Booth's equation? which takes into account the permanent dipoles and dipole-dipole interactions of the solvent species, is used to relate the change in the water dielectric constant with electric field strength in a membrane pore,
where
In eqs 3 and 4,K is Boltzmann's constant, and 7, a, and cb are the optical refractive index, dipole moment, and dielectric constant of the bulk solvent, respectively. Symmetry at the pore centerline is used to generate boundary conditions at r = 0, d@/dr=O and
= cb
(5)
The second boundary condition for this problem is a modified form of Gauss's law at the pore wall ( I = a), where the net surface charge on the pore is given by the surface density of ion-exchange sites on the membrane pore wall (a, with units of C/m2) minus the product of the surface concentration and charge of those divalent cations that form contact ion pairs with the membrane's charge sites (in accordance with refs 2 and 6), 0-
d@ dr where @ is the electric potential, z is the charge number of the ionic species ( z is > O for cations and < O for anions), C is concentration, F is Faraday's constant, and R and Tare the gas constant and absolute temperature. The first exponential term on the right side of eq 1 represents the electrostatic interaction energy between absorbing ions and the membrane's fixed-charge sites. For cations absorbing into a cation-exchange membrane, this term (zF@/RT)is A L even ~ though the surface charge density of Pb2+ is less than that of Li+. Once @ ( r )and E(r) have been determined, the concentration profile of each ion in the membrane pore is computed using eq 1 . Often, the equilibrium uptake of co-ions and counterions from a multicomponent extemal solution is described in terms of partition coefficients and membrane selectivities. The partition coefficient of an ion species, Ki (with units of mol/m3 of wet membrane/moUm3 of solution), is defined as the concentration ratio of ions inside and outside the membrane. K; is related to the computed radial concentration profile in a membrane pore by
where 8 is the membrane porosity (which is used to convert
pore concentrations from units of mol/m3 of solution to mol/ m3 of wet membrane). The membrane selectivity of ion species i with respect to species j is determined from the ratio of the partition coefficients,
Experimental Section Equilibrium Salt Uptake Experiments. Monovalent/divalent equilibrium adsorption experiments were performed with an unreinforced Nafion 117 perfluorosulfonic acid cationexchange membrane at 25 OC. The following aqueous solutions were examined: Pb(NO&-LiN03, Pb(N03)2-KN03, Pb(N03)2-NaN03, Pb(N03)2-CsN03, Cd(N03)2-LiN03, and Cd(NO&-KNO3 at a total external salt concentration of 0.05 and 0.25 M. For each binary salt mixture the concentration ratio of monovalent to divalent cation was varied from 1:4 to 4:1. Conventional method^'^.'^ of soaking, leaching, analysis, and drying were used to determine directly the membrane-phase concentration of cations. Rectangular strips of Nafion (5 x 2 cm2) were pretreated by boiling for 90 min in 6.0 M HN03 followed by boiling in distilled water. The membranes were stored wet until used in a partition coefficient experiment. Salt equilibration was established by boiling the membrane samples for 90 min in the desired salt solution followed by a 24 h equilibration at room temperature, during which time the soak solution was changed frequently. After equilibration, the membrane strips were removed from the salt solution and excess electrolyte was wiped off their surface with filter paper. Each Nafion strip was weighed, and its thickness and area were measured to determine the wet membrane volume and wet density for that particular salt mixture. The membrane samples were then soaked repeatedly in 50 mL of deionized and distilled water for 12 h to leach all mobile cations from the membrane. The accumulated leaching solutions for a given membrane sample were collected and analyzed for metal cations by flame atomic absorption spectrophotometry (Perkin-Elmer Model 5000). Next, each membrane strip was soaked twice in 50 mL of 2.0 M HN03 to extract field-bound mono- and divalent cations and those divalent cations which ion pair to the membrane's fixed-charge sites. Again, the leaching solutions were collected and analyzed for metals by atomic absorption spectrophotometry. As will be discussed below in our presentation and explanation of NMR analyses of membrane samples, divalent cations were not irreversibly bound to SO3- sites in Nafion and could be removed from the membrane by a strong acid wash.
Pintauro et al.
12918 J. Phys. Chem., Vol. 99, No. 34, 1995 60 I
I
P, /b-K
+ +
I
0'
0
1
2
3
4
5
External C,/C,,
I
Pb-K
Pb-NI
0
TABLE 2: Experimentally Determined Nafion Porosities and Calculated Pore Radii and Pore-Wall Charge Densities for Divalent/Monovalent Nitrate-Salt Mixtures at 25 "C pore-wall extemal cation membrane pore radius charge density (m) (a,C/m2) concn x 1 0 - ~(mol/m3) porosity (e) x 0.260 24.4 0.556 0.04 Pbz+ 0.01 K+ 0.03 PbZf + 0.02 K+ 0.256 24.1 0.560 0.02 PbZf 0.03 K+ 0.252 24.0 0.568 0.01 Pb2++ 0.04 Kf 0.248 23.7 0.576 0.20 Pb2+ 0.05 Li+ 0.244 23.9 0.591 0.15 Pb2+ 0.10 Lif 0.272 25.0 0.531 0.10 Pb2++ 0.15 Li+ 0.281 25.2 0.513 0.05 Pb2++ 0.20 Li+ 0.255 24.7 0.579 0.04 CdZ+ 0.01 K+ 0.276 25.1 0.528 0.03 Cdz+ 0.02 K+ 0.257 24.4 0.566 0.02 Cd2++ 0.03 K+ 0.264 24.4 0.544 0.01 Cd2+ 0.04 K+ 0.238 23.1 0.59 1 0.20 CdZ++ 0.05 Li+ 0.336 28.0 0.442 0.15 CdZ+ 0.10 Li+ 0.341 28.2 0.437 0.10Cd2++ 0.15 Li+ 0.331 28.1 0.455 0.05 Cd2++ 0.20 Li+ 0.327 27.6 0.455
1 2 3 4 External C,/C,,
5
Figure 1. Experimentally determined cation partition coefficients in Nafion 117 at 25 "C as a function of the monovalent/divalentcation concentration ratio in the extemal solution. Total external salt concentration is 0.05 M. (a) Lead partition coefficients in the presence of different alkali metal cations. (b) Alkali metal cation partition coefficients in the presence of Pb2+. Each uptake experiment was performed in triplicate to ensure reproducibility. Representative experimental results for Pb2+ uptake by Nafion in the presence of alkali metal cations are shown in Figure l a as the lead partition coefficient (Kpb, as defined by eq 10) vs the external solution monovalent/divalent cation mole ratio for a total external salt concentration of 0.05 M. The data show (i) Nafion is behaving as a cation-exchange membrane toward lead because Kpb =- 1, (ii) as would be expected, Kpb for the various mixed-salt systems converge to a single-valued partition coefficient as the concentration of the alkali metal cations in the external solution approach zero, and (iii) at a given external monovalent/Pb2+cation molar ratio, KPb decreases with increasing size (decreasing surface charge density) of the coabsorbed alkali metal cation. In Figure lb, experimentally measured alkali metal cation partition coef' ficients in the presence of Pb2+ are plotted as a function of the external solution composition for a total external salt concentration of 0.05 M. The results show that the alkali metal ion partition coefficient ordering for the Pb2+/monovalent cation solutions is in the reverse sequence of the monovalent ion's surface charge density; i.e., the ordering is the same as that reported by Bontha and Pintauro' for a divalent-ion-freeexternal electrolyte. Determination of Pore Size and Pore-Wall Charge Density. The two membrane structure parameters which must be known to solve the uptake model equations are the pore radius ( a ) and pore-wall fixed-charge density (a). The radius of an average cylindrical pore in a rectangular Nafion strip that has been equilibrated in a given salt solution (with a salt-equilibrated wet membrane area S and membrane porosity 0) was related to the pore radius, rectangular area, and porosity of a pure waterequilibrated membrane (aw, SW,and &, respectively) by the following relationship'
+ +
+ + + +
a = aw[& where aw = 2.75 nm, as determined from low angle X-ray diffraction m e a s ~ e m e n t s . ' ~The membrane porosity terms in eq 12 were determined experimentally from dry and wet volumes of a membrane sample,
The wall charge density of SO3- sites on the walls of Nafion pores was computed from the following equation'
where @dry is the density of the dry membrane (1.84 x lo3 kg/ m3 for Nafion) and IEC is the ion-exchange capacity of the membrane (0.909 equivkg for Nafion 117). Representative examples of measured membrane porosities, computed pore radii, and wall charge densities for selected aqueous monovalent/ divalent salt solutions are listed in Table 2. N M R Studies. These experiments were carried out to obtain independentquantitativeverification of Pb2+binding to Nation's fixed-charge sites. Membrane samples for NMR examination were prepared by equilibration with cation mixtures using the identical procedure described above for the ion uptake experiments. NMR samples consisted of 4 x 5 cm pieces of membrane rolled into a cylinder and inserted into 10 mm 0.d. glass NMR sample tubes (Wilmad 513-5pp). A concentric 5 mm 0.d. NMR sample tube containing 0.5 M lead(I1) nitrate in 1:1 2H20/'H20 solvent served as both the deuterium lock signal and lead(I1) reference. All membrane equilibrations were conducted in pure 'H20.All 207PbNMR spectra were acquired at 83.4 MHz on a Varian Unity 400 NMR spectrometer equipped with a 9.4 T magnet. All spectra were obtained at a probe ambient temperature of 20 f 1 "C. Typical acquisition parameters consisted of a 45" transmitter pulse (-22 ps), 20 kHz spectral width, 64K data points, and a 5 Hz line broadening apodization. In most cases averaging 128 spectral acquisitions yielded a sufficient signal-to-noise ratio.
Results and Discussion Equilibrium Uptake Studies. In order to obtain values of the monovalent and divalent cation concentrations in Nafion
MonovalentDivalent Cation-Salt Mixtures in Nafion
J. Phys. Chem., Vol. 99, No. 34, 1995 12919
TABLE 3: Comparison of Experimental and Computed Membrane-Phase Monovalent and Divalent Cation Concentrations in Nafion (0.25 M Total External Salt Concentration at 25 "C) predicted membrane concn x (mol/m3) exptl membrane external &/CPb concn x ( m ~ V m - ~ ) rPb 10-18 with optimized r p b without r p b (M = monovalent cation) Pb M (atom/m2) Pb (mobile) Pb (bound) Pb (total) M Pb M Li+/Pb2+ 0.25 0.041 1.47 0.149 0.487 0.636 0.640 0.041 0.126 1.15 0.633 0.67 0.085 1.24 0.136 0.447 0.583 0.085 0.099 1.27 1S O 0.575 0.162 1.15 0.1 10 0.426 0.536 0.162 0.097 1.09 4.00 0.492 0.257 1.28 0.067 0.441 0.508 0.252 0.062 1.25 K+IPb2+ 0.25 0.215 1.21 0.132 0.392 0.524 0.215 0.127 1.17 0.555 0.67 0.394 1.01 0.109 0.3 16 0.424 0.393 0.107 1.21 0.435 1.50 0.257 0.607 0.080 1.34 0.606 0.881 0.080 0.337 0.333 0.5 13 4.00 0.824 0.056 0.140 0.196 0.913 0.056 1.41 0.193 0.502 0.716 0.135 0.256 0.392 0.495 0.134 1.11 Cs+/Pbz+ 0.25 0.452 0.780 0.756 0.101 0.253 0.354 0.726 0.101 1.27 0.67 0.364 0.935 0.747 0.071 0.225 0.296 1.038 0.07 1 1.88 1.50 0.255 1.51 0.108 0.159 1.107 0.051 0.051 1.133 0.363 4.00 0.157 pores from the equilibrium uptake model, the number of bound divalent cations (r in eq 6) must be specified. Our approach was to combine a computer optimization program using the direct search technique of Hooke-Jeeve~'~with the finitedifference algorithm for the solution of eqs 1-3 to find systematically the value of r which allowed the partition coefficient model prediction of both monovalent and divalent cation concentrations to match experimental data for a given external salt concentration. Once @(r) and € ( I ) were computed for the correct value of r, the radial-direction concentration profiles of all mobile cations were determined using eq 1. The r) profiles were then integrated numerically across our average membrane pore and multiplied by the membrane porosity to obtain the Nafion-phase concentration of each mobile ion, with units of mol/m3 of wet membrane. The total divalent cation concentration was found by adding the integrated mobile cation concentration to the wet membrane volume concentration of bound cations, which was obtained by combining the optimized r with the surface areaholume of a cylindrical Nafion pore, Avagadro's number, and the membrane porosity,
-0.20
z -
--
-
-0.40
6
at
L
-0.60 -0.60
-Pb-Cs case
1
c(
-1.00' 0.0
"
0.2
"
0.4
"
"
0.6
0.8
'
1.0
Radial Position (r/a)
Figure 2. Computed radial direction electric potential profile in a Nafion pore during Pb2+/Cs+and Pb2+/Li+uptake. Total external salt concentration = 0.25 M, external concentration ratio of monovalent cationlPb2+= 1.5, and temperature = 25 "C.
C, = 2rtWNa A comparison of experimental and computed Li+/Pb2+, K+/ Pb2+,and CsfPb2+ membrane-phase concentrations (with and without the inclusion of divalent ion binding) for a 0.25 M extemal salt solution is presented in Table 3. When ion binding is not considered, the predicted Pb2+ concentration in the membrane is always too low (due to the large value of Apb, hydration forces exclude preferentially Pb2+ from the lowdielectric constant pore fluid) and the computed Li+, Na+, and Cs+ ion concentrations are too high (because monovalent cations, as opposed to Pb2+, are maintaining electroneutrality in the pore with the membrane's negative fixed-charge sites and mobile anions). With the optimized values of r p b , the model predicts accurately the Li+, Kf, Cs+, and total Pb2+ concentrations, with an average error of 6.5% for lead and 3.6% for the monovalent species. The results in Table 3 also show (i) the concentration of bound lead is always greater than the mobile (solution-phase) Pb2' concentration and (ii) the pore solution monovalent/divalent concentration ratio is dependent on the surface charge density of the monovalent species and on the extemal salt solution's monovalent/divalent concentration ratio (e.g., although the pore concentration of Cs+ always exceeds that of mobile lead, the membrane-phase Pb2+ concentration is higher than that for Li+ when c L i / c p b in the extemal salt solution is small). The computed electric potential, dielectric constant, and cation concentration profiles in a Nafion pore for the Csf/Pb2+ and
0 '
0.0
0.2
0.4
0.6
0.8
1.0
Radial Posltlon (rla)
Figure 3. Computed radial direction water dielectric constant profile in a Nafion pore during Pb2+/Cs+and PbZ+/Li+uptake. Total extemal salt concentration = 0.25 M, external concentration ratio of monovalent cationPb" = 1.5, and temperature = 25 "C. Li+/Pb2+ cases in Table 3 further demonstrate the molecularlevel events which control monovalent/divalent cation partitioning. A small electric field (the radial direction gradient in the electric potential) and a moderate degree of water dipole alignment are predicted during Li+/Pb2+partitioning, as shown in Figures 2 and 3, because of the large number of ion-exchange sites neutralized by lead ion pairing. The repulsive hydration forces acting on Lif are smaller than those repelling mobile
Pintauro et al.
12920 J. Phys. Chem., Vol. 99, No. 34, 1995
t 4.0
i
4
1 -Pb*+
10 Pb-K
n S v)
. ,
0.1 I 0
1
2
3
4
5
External C,/C,,
.- I 0.0 0.2
0.4 0.8 0.8
1.0
Radial Position (rla) Figure 4. Computed radial direction Pb2+and LPconcentration profiles in Nafion. Total extemal salt concentration = 0.25 M, extemal Lit/ Pbz+concentrationratio = 1.5, and temperature = 25 "C.
9
0
1
Ih
-
p
b
- Pb-Cr K
1
I I
1
0.1
10.0
8.0
r
2
3
4
5
External C,/C,,
-Pbl'
Figure 6. Comparison of measured and predicted leadmonovalent cation Nafion selectivities as a function of the extemal solution composition. Symbols are experimental data points, and lines are model predictions. (a) Total extemal salt concentration = 0.05 M. (b) Total extemal salt concentration = 0.25 M.
Cs+ '?
2 4.0 -
L2.0
I-
0.0
0.2
0.4
0.8
0.8
1.0
Radial Posltlon (r/a)
Figure 5. Computed radial direction Pb2+ and Cs+concentration profiles in Nafion. Total extemal salt concentration = 0.25 M, extemal Cs+/Pb?+concentrationratio = 1.5, and temperature = 25 "C. lead cations from the pore-wall region ( i . e . , ALi < Apb in eq 7 ) , and thus, the concentration profile of lithium ions in Figure 4 monotonically increases as the pore wall is approached. The shape of the mobile lead concentration profile for Li+/Pb2+ absorption in Figure 4 is a result of the combined effects of electrostatic attraction forces, which dominate in that part of the pore where the dielectric constant is near 78, and repulsive hydration forces in the low-dielectric constant pore-wall region, which lowers the Pb2+ concentration to essentially zero at the pore wall. The expulsion of Pb2+ from the pore-wall region is more pronounced in the leadcesium system, as shown in Figure 5. When Pb2+ and Cs+ absorb into Nafion, the computed radialdirection electric field is larger (Figure 2 ) and the alignment of pore water more extensive (Figure 3) than the PbLi case because there is less Pb2+binding to the wall charges (cf.the optimized r p b values in Table 3). The large electrostatic attraction forces near the pore wall cannot overcome the repulsive hydration forces acting on Pb2+ because of the unusually large value of the hydration parameter Apb. The local maximum in the Pb2+ concentration seen in Figures 4 and 5 was observed for all monovalent/divalent cation-salt systems examined. Although a generalized adsorption model for membrane-bound lead or cadmium has not been developed yet, we did find that the optimized values of r for both lead and cadmium correlated qualitatively with the proximity of the concentration maximum to the pore wall.
0.1
u 0
1
2
3
4
5
External C,/C,,
Figure 7. Comparison of measured and predicted cadmiurdlithium and cadmiudpotassium Nafion selectivities as a function of the extemal solution composition: (A) and (e)s'," at 0.05 M total external salt concentration; (A) and (0) s"," at 0.25 M total external salt concentration. Solid lines are model predictions. An overall comparison of theoretical and experimental membranes selectivities for Pb2+ with respect to an alkali metal cation (SE, as defined by eq 11 where M denotes either Li+, Na+, K+,or Cs+) is shown in Figure 6, a and b, for total extemal salt concentrations of 0.05 and 0.25 M, respectively. Experimental and theoretical Cd2+/Li+ and Cd2'/Kt selectivities for the same extemal concentrations are shown in Figure 7 . With the proper choice of r p b or r C d , the theoretically predicted ion selectivities were in excellent agreement with those obtained experimentally, with an average error of 5.5% for all of the data. The optimized values of rpb and r C d are plotted in Figures 8a,b and 9 as the fraction of surface sites neutralized by contact ion pair formation vs CM/CPb or CM/CCd in the extemal bulk solution. The selectivity results show that the magnitude of Sc and s'," in Nafion at a given extemal monovalent/divalent cation concentration ratio decreases with decreasing surface charge density of the coabsorbed alkali metal cation. As was the case for the data in Table 3, the extent of divalent ion binding (i) increases with increasing surface charge density of the coabsorbed monovalent cation and (ii) increases with increasing external divalentlmonovalent cation concentration ratio. The model results indicate that a large fraction of Nafion's so3-
MonovalentDivalent Cation-Salt Mixtures in Nafion 1.00
computed from the theoretical uptake model and experimentally measured ion concentrationsin Nafion. Lead@) is a good probe ion for these verification studies because of its common formation of covalent-type bonds in metal complexes and the great sensitivity of the lead NMR chemical shift to these bonding details. Under conditions of rapid chemical exchange, the observed 207Pbchemical shift is the weighted average of its shifts in the various chemical environments in which it exists. For the purposes of this study, the lead signal was analyzed on the basis of rapid exchange between two chemically different sites. Exchange between these two sites involves replacement of a water from the lead(I1) coordination sphere by an oxygen of a Nafion sulfonate group, and vice versa. Under these conditions the chemical shift is given by
I
I
Pb-LI
0.80 0
%
L 0
0.80
1
0.40 o.20
,
(a)
,
0.00 0
1
2
3
4
J. Phys. Chem., Vol. 99, No. 34, 1995 12921
1
5
External C,/C,,
D
I L
m
cu
0.00
'
0
Pb-CI '
'
'
'
1
2
3
4
'
5
External C,/C,,
Figure 8. Fraction of sulfonate fixed-charge sites in Nafion that are ion-paired with lead as a function of the external monovalent cation/ Pb2+ concentration ratio. (a) Total external salt concentration = 0.05 M. (b) Total external salt concentration = 0.25 M. 1.00 1
-
0.80 0 L Q
I
cu
0.80
0.40 0.20
0.00
'
0
1
2
3
4
5
External C,/C,,
Figure 9. Fraction of sulfonate fixed-charge sites in Nafion that are ion-paired with cadmium as a function of the extemal monovalent/ Cd2+ concentration ratio: (A)Li/Cd and (e) WCd at 0.05 M total external salt concentration; (A) LUCd and ( 0 ) WCd at 0.25 M total external salt concentration. ion-exchange sites are contact ion-paired with lead or cadmium, thus lowering the effectiveness of the membrane to act as a cation exchanger. In the present study we did not see unusually high membrane-phase concentrations of co-ions (NO3-), even for the Li+/Pb2+ system where between 81% and 88% of the fixed-charge sites were neutralized, because the ion-exchange capacity of the membrane was so high that a sufficient number of active SO3- sites remain intact to exclude low external concentrations of co-ions. This may not be the case when the extemal concentration of mixed salts is high, but such systems were not investigated in the present study. The results in Figures 8 and 9 also show that the extent of divalent cation binding does not diminish in the same ratio as the extemal dilution factor for lead and cadmium. The implications here are that the presence of even small amounts of divalent cations in the solution adjacent to a Nafion membrane may alter significantly the membrane's effective ion-exchange capacity and its ability to function as a cation exchanger. NMR Analysis of Pb2+in Nafion. 207Pbnuclear magnetic resonance (NMR) spectroscopy of lead-containing Nafion membranes was performed in an attempt to directly verify the formation of Pb(I1)-sulfonate coordinate-covalent bonds and to quantitatively compare any such bonding observed to that
where dabs is the experimentally observed chemical shift, f~ is the fraction of lead ions in the membrane that is bonded to sulfonate fixed-charge sites, 68 is the chemical shift of the sulfonate-bound lead, and 6, is the shift of the unbound (i.e., aqueous) lead. To calculate f~ from eq 16, it was necessary that the assumption of rapid chemical exchange be valid and the values of 6~ and 6, be known. That this system involved rapid chemical exchange was demonstrated by the fact that only a single lead resonance signal was observed for all the ion competition experiments performed in this work. A lowtemperature spectrum (0 "C) showed broadening of the resonance and the development of a shoulder characteristic of slowed chemical exchange. Unfortunately, because of freezing of the water and the resultant extreme line broadening, it was not possible to obtain a spectrum at a sufficiently low temperature to directly observe the two sites free of exchange. Nevertheless, these results demonstrated that the observed resonance position results from rapid chemical exchange. A more difficult problem was the determination of the correct values of 68 and 6,. The selection of these values required considerable care since the reliability of the calculated ~B'S is determined by the accuracy of these values. The sensitivity of lead chemical shifts to complexing anion concentrations complicated the process.I6 The approach taken to estimate 6g involved forcing lead binding by repeated equilibration of the membrane with excess Pb2+ until all of the exchange capacity of the membrane was occupied by lead(I1) ions. The chemical shift of lead in a membrane treated as described above was found to be 151 ppm versus 0.5 M Pb(N03)2. In another experiment, the solution-phase lead(I1) chemical shift was measured as a function of triflic acid (CF3SO3H) concentration. Solutions were prepared by dissolving PbO in excess triflic acid. Examination of the Pb2+ chemical shift as a function of triflic acid concentration showed that the shift approached approximately 156 ppm at very high triflate concentrations. Thus, the average lead environment in a hydrated Nafion membrane appeared to be quite similar to that in a highly concentrated triflic acid solution. Previous workers have noted the similarity of the 23Na membrane shift to that of Na(CF3S03) at a comparable H20/ Na+ ratio.I7 Unfortunately, neither the 1eadNafion nor the lead triflate value of 6~ was necessarily correct because some, unknown, fraction of the lead was uncoordinated in both instances. To obtain a better estimate of d ~the , effect of drying an equilibrated membrane on the chemical shift of its internal Pb2+ was measured. The effect of drying on the chemical shift of the retained lead(I1) was a relatively small chemical shift change and an increase in signal line width. When completely
Pintauro et al.
12922 J. Phys. Chem., Vol. 99, No. 34, 1995
TABLE 4: Comparison of NMR Experiments and Model Predictions for the Fraction of Total Pore-Fluid Pb,Bound to SOJ- Sites cation total external fraction of total Pb bound mixture salt concn (M) C~lCpb NMR model Li+/Pb2+
0.05
0.25
K+/Pb2+
0.05
0.25
200
160
120
80
40
JL O
0.25 0.67 1S O 4.00 0.25 0.67 1S O 4.00 0.25 0.67 1S O 4.00 0.25 0.67 1S O 4.00
0.78 0.79 0.80 0.79 0.79 0.82 0.89 0.90 0.79 0.76 0.72
0.72 0.77 0.74
0.75 0.76
0.8 1 0.84 0.87
0.88 0.77 0.77 0.80 0.87 0.77 0.78 0.78 0.77 0.75 0.74 0.76 0.7 1
ppm
Figure 10. Effect of K+/Pbz+bulk concentration ratio on the lead NMR spectrum of Nafion 117. Total external concentration= 0.05 M; 0 ppm signal at 0.5 M Pb(N03)2 in 5050 D20:HzO. CK/CP~ ratios: A, 0; B, 0.25;C, 0.67; D, 1.5; E, 4.0.
believe that the source of this concentration-dependentdeviation was a cation concentration dependence on 6, coupled with the high monovalent cation concentrations near the membrane wall (see Figure 4). It is well-known that the presence of high concentrations of salts alters the chemical shift of water hydrogens.'* The sources of these shifts were believed to be polarization and hydrogen bond disruption effects. Depending upon both the cation and anion of the salt, 'H,shifts to either shielding or deshielding directions have been observed and assigned to both cation and anion species. The alkali metal ions, for example, have been reported to produce large shielding effects on the 'H shift of water.I9 To test the possibility that K+ or Li+ ions might affect the chemical shift of free Pb2+ ion and, hence, the observed average chemical shift, the chemical shift of aqueous bulk solution Pb2+ ion was measured as a function of K+ and Li+ concentration. In these experiments the total nitrate concentration was maintained at a constant value by decreasing the Pb(NO& concentration to compensate for the nitrate anions introduced with the potassium or lithium ions. The measured shifts were corrected for the slight alteration in the lead nitrate complexation equilibrium caused by the lowered lead concentrations.16 The result of these measurements was the surprising conclusion that K+ ions produced a shielding shift of 20.5 ppmA4 and Li+ a 15.8 ppm/M shielding shift on Pb2+. Similar effects were seen also for Na+ but not for Zn2+ or any divalent ion. The fundamental reason for this phenomenon is not clearly understood at this time.20 To account for the monovalent cation effect on the lead chemical shift, eq 16 was modified to yield eq 17
+
200
180
120
80
40
--O
ppm
Figure 11. Effect of Li+/Pb2+ bulk concentration ratio on the lead NMR spectrum of Nafion 117. Total external concentration = 0.05 M; 0 ppm signal at 0.5 M Pb(N03)~in 5050 D2O:HzO. CL,/CP~ ratios: A, 0; B, 0.25;C, 0.67; D, 1.5; E, 4.0. dehydrated, the broadness of the lead signal prevented its observation. However, it was possible to extrapolate the chemical shifts of the partially dried membrane samples to arrive at a value of 173 ppm for 88. This value of 6~ represented a much smaller drying effect on the lead chemical shift than that observed for 23Na,indicating that a substantial fraction of the lead was bound even when aquated. For the shift of unbound lead, 6, the shift of aqueous Pb(N03)~extrapolated to infinite dilution, 76 ppm, was used initially.l6 However, as explained below, it was found that 6, was a function of the coabsorbed monovalent cation concentration and, therefore, was not a constant for all experiments. Figures 10 and 11 show the 207Pbspectra resulting from a series of competition experiments between Pb2+ and either K+ or Li+. If one uses the values of dg and 6, above, the computed bonding fractions were found to agree quite well with the uptake experiments at low K+ concentrations and for all Li+ values but deviate systematically at higher K+ concentrations. We
where K; is the molar shift induced by ion i and C; is the molar concentration of ion i. For K+, K; is 20.5 ppm/M, and for Li+ K ; is 15.8 ppm/M. Values off^ were calculated from eq 17, where C; was determined from the theoretically computed concentration of K+ and Li+ at one Pb2+ diameter from the membrane wall. A comparison of the NMR-determined sulfonate-bonded lead fractions with those calculated from the membrane uptake model is presented in Table 4, where the theoretical values OffB (the ratio of the bound lead concentration to the sum of the bound and mobile lead ion concentrations in a Nafion pore) were found using eq 15 and the integrated mobile Pb2+ concentration profiles (such as those shown in Figures 4 and 5 ) . Very good agreement was found for the NMR and
MonovalenVDivalent Cation-Salt Mixtures in Nafion model values OffB with an average error of -5%, thus providing verification of both the existence of divalent ion binding and the accuracy of the uptake model. NMR results were also used to verify the assumption that the acid equilibration technique removed all of the membranebound lead. Because ion uptake is measured by chemical analysis of metal ions displaced from the membrane by acid media, it is important that the completeness of ion removal be verified. An overnight NMR acquisition performed on an acidtreated lead membrane showed no observable lead signal consistent with removal of at least 90% of the previously retained lead from the membrane. A similar investigation was attempted using cadmium(I1) as the probe ion. Although a downfield shift in the membranephase Cd2+ was observed (indicative of cadmium binding to Nafion's fixed charges), the chemical shift difference between membrane-bound and free cadmium ions was too small to allow for meaningful calculations.
Conclusions A partition coefficient model for the equilibrium uptake of aqueous monovalent/divalent cation-salt mixtures into the cylindrical pores of a Nafion 117 cation-exchange membrane has been formulated and tested. Water dipole alignment by the radial direction electric field generated by the membrane's fixedcharge sites was taken into account, along with ion hydration Gibbs energy changes which occur when the ions solubilize into the low-dielectric constant pore fluid. The model also considers the formation of contact ion pairs (coordinate covalent bonds) between divalent cations and sulfonate charge sites, which neutralizes partially the ion-exchange capacity of Nafion. The inclusion of both dielectric saturation and ion hydration effects allowed the model to distinguish between ions of like charge and different size. Two membrane structure parameters in the model, the radius of membrane pores and the density of fixed charges on the pore wall, were determined from membrane porosity experiments and X-ray diffraction data in the literature. The number density of divalent cations that bind to the porewall charge sites during divalent cation uptake was an adjustable parameter in the model. When this parameter was chosen properly, the theory predicted to within 5.5% the divalent/ monovalent membrane selectivity of Pb2+ or Cd2+ with respect to a coabsorbed alkali metal cation (either Li+, Na+, K+, or Cs+) at a total extemal salt mixture concentration of 0.05 and 0.25 M. Between 10% and 85% of the sulfonate ion-exchange sites in Nafion were found to be neutralized by bound Pb2+ or Cd2+, with the extent of binding increasing with the surface charge density of the coabsorbed monovalent cation and decreasing with increasing total extemal salt concentration.207Pb NMR spectroscopy of salt-equilibrated Nafion membranes was performed to verify directly the formation of Pb(I1)-sulfonate coordinate-covalent bonds and to quantitatively compare any
J. Phys. Chem., Vol. 99, No. 34, 1995 12923
Acknowledgment. This work was funded by the National Science Foundation (Grant EHR-9108765). The authors thank E. I. DuPont de Nemours and Co. for providing the Nafion membranes used in this study.
List of Symbols a Ai
C, e fB
F G
IEC
K, N r R, R
S SJ T V ZI
membrane pore radius, m straight-line slope of (AYacGi- A!acG,) vs (I/€ - lkb) plot, J/mol concentration of species i, moum3 charge on the electron, 1.602 x C fraction of total membrane-phase divalent cations bound to membrane fixed-charge sites Faraday's constant, 96 487 C/equiv ion solvation Gibbs energy, J/mol membrane ion-exchange capacity, equivkg partition coefficient of species i, Avogadro's number, 6.02 x mol-' radial position within the membrane pore, m hard-sphere ion radius, m gas constant, 8.314 J/(mol K) membrane area, m2 membrane selectivity of species i with respect to species j absolute temperature, K volume, m3 charge number of ion species i
Greek Letters dipole moment, C m number density of bound cations, atoms/m2 NMR chemical shift, ppm solvent dielectric constant vacuum permittivity, 8.8542 x F/m refractive index (1.33 for water) membrane porosity Boltzmann constant, 1.381 x J/K dry membrane density, kg/m3 membrane pore-wall charge density, C/m2 electric potential, V
Subscripts and Superscripts b B m
M U
vac W
bulk solution bound species membrane monovalent cation species unbound species vacuum water
such bonding to that computed from the theoretical uptake
References and Notes
model. A significant and reproducible downfield chemical shift for *07Pbin Nafion was observed. The extent of this shift was a function of the type and concentration of the coabsorbed monovalent cation. When a correction factor for monovalent cation shielding shifts was included in the analysis of the lead spectra, the NMR-computed fraction of bound lead in Nafion was in excellent agreement with the model results with an average error less than 6% for a series of 16 uptake experiments with Pb2' and either Li+ or K+.
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No. 180; American Chemical Society: Washington, DC, 1982; pp 195217. (15) Hooke, R.; Jeeves, T. A. J. Assoc. Comput. Mach. 1961, 8, 212. (16) Hanison, P. G.; Healy, M. A.; Steel, A. T. J . Chem. SOC., Dalton Trans. 1983, 1845. (17) Komoroski, R. A.; Mauritz, K. A. J. Am. Chem. SOC. 1978, 100, 7487. (18) Deverell, C. Prog. NMR Spectrosc. 1969, 4 , 235. (19) Holz, M Prog. NMR Spectrosc. 1986, 18, 327. (20) Xu, W.; Evilia, R. F. Presented at the 36th Experimental NMR Conference, Boston, MA, March 26-30, 1995.
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