Article Cite This: Macromolecules XXXX, XXX, XXX−XXX
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Effect of Water Content on Sodium Chloride Sorption in CrossLinked Cation Exchange Membranes Eui-Soung Jang,† Jovan Kamcev,† Kentaro Kobayashi,† Ni Yan,† Rahul Sujanani,† Samantha J. Talley,‡ Robert B. Moore,‡ Donald R. Paul,† and Benny D. Freeman*,† †
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McKetta Department of Chemical Engineering, Texas Materials Institute, Center for Energy and Environmental Resources, and Center for Research in Water Resources, The University of Texas at Austin, 10100 Burnet Road, Bldg. 133 − CEER Austin, Texas 78758, United States ‡ Department of Chemistry, Macromolecules Innovation Institute, Virginia Tech, Blacksburg, Virginia 24061, United States S Supporting Information *
ABSTRACT: Ion exchange membranes used for energy generation and water purification selectively transport ions, and this characteristic is strongly influenced by ion sorption in such membranes. Although water content and fixed charge group concentration are key factors affecting ion sorption in ion exchange membranes, their individual effects on ion sorption are not often studied. Here, a series of cross-linked cation exchange membranes (CEMs) were synthesized with different water uptake values and similar fixed charge group concentrations to study the effect of water content on ion sorption in such materials. Equilibrium co-ion concentrations in all membranes were very similar at a given external salt concentration, suggesting that co-ion sorption in these materials was mainly influenced by fixed charge group concentration rather than water content per se. Equilibrium co-ion sorption data were interpreted using a thermodynamic model based on Donnan theory and Manning’s counterion condensation theory. The inhomogeneous morphology of the membranes was characterized by small-angle X-ray scattering (SAXS). The Manning parameter was used as an adjustable constant to account for morphological heterogeneity. The Manning parameter was less than the critical value for these CEMs, suggesting no counterion condensation occurred. Good agreement was observed between the model and experimental co-ion sorption data.
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INTRODUCTION In membrane-based technologies, a key property is the ability of a membrane to control the permeation of a target species through the membrane.1−4 Ion exchange membranes (IEMs) play a crucial role in applications such as electrodialysis, reverse electrodialysis, fuel cells, batteries, and so forth because of their ability to selectively permeate specific charged species (e.g., ions).5−8 Polymers used for IEMs contain ionizable functional groups covalently bonded to their backbone.9,10 These groups are either negatively charged for cation exchange membranes (CEMs) or positively charged for anion exchange membranes (AEMs). These charged groups bestow hydrophilicity, as well as electrostatic interactions with ions, to polymers that are often otherwise hydrophobic or weakly hydrophilic.9−12 The fixed charge group concentration is a crucial factor governing the ability of IEMs to selectively permeate some ions (e.g., cations) but not others (e.g., anions). Ion transport in IEMs can be interpreted within the framework of the solution-diffusion model, where sorption of ions in the membrane from an external aqueous salt solution (i.e., ion partitioning) is the initial step in transport.13,14 Equilibrium ion sorption in charged polymers is strongly © XXXX American Chemical Society
affected by water content and electrostatic interactions between fixed charge groups and mobile ions.9,15−17 In the absence of fixed charge groups (i.e., uncharged polymers), ion partition coefficients are sometimes proportional to polymer water content.15,18 Ion sorption in polymers, however, is also influenced by the presence of fixed charge groups, which induce strong electrostatic interactions.15,16 To isolate the effect of water content on ion sorption in charged polymers, a series of polymers are required where water content is independently varied while keeping fixed charge group concentration constant. Recently, we reported the effect of fixed charge group concentration on ion sorption, isolated from the effect of water content, in charged polymers as a counterpart to this study.16 A better understanding of the influence of these two important factors (i.e., water content and fixed charge group concentration) on ion sorption should contribute to improved understanding of structure/property relations to design improved IEMs. Received: November 30, 2018 Revised: February 28, 2019
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DOI: 10.1021/acs.macromol.8b02550 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
water was replaced several times to remove solvent and any components not attached to the polymer network. The as-synthesized CEMs were initially in the H+ counterion form, and they were converted to the Na+ counterion form before any characterization by soaking the membranes in 1 M NaCl solution for at least 24 h. The NaCl solution was changed three times during that period to ensure complete conversion. The concentration of mobile ions (i.e., co-ions and their counterions) in the membranes after soaking in 1 M NaCl solution is significant, so membranes from the counterion conversion procedure were placed in DI water, which was changed periodically until the ionic conductivity of the extraction solution was close to that of DI water equilibrated with ambient CO2 (i.e., 0.3 M), co-ion concentration contributes noticeably to increase counterion concentration. Nevertheless, counterion concentration values in all three samples are similar to one another at any given external salt solution concentration. m Membrane ion activity coefficients, γm + γ− , were calculated using eq 10. Measured counter- and co-ion concentrations in the membrane were used in this calculation, along with mean activity coefficients in the external NaCl solution calculated using the Pitzer model.32,33 Figure 6 presents membrane ion
ξ=
λB e2 = b 4πε0εkTb
(12)
where λB is the Bjerrum length, b is the average distance between fixed charges on a polymer chain, e is the protonic charge, ε0 is the vacuum permittivity, ε is the solvent dielectric constant, k is Boltzmann’s constant, and T is absolute temperature. Counterion condensation occurs when ξ is greater than a critical value, ξcrit, which is defined as19,34 ξcrit =
1 |z iz p|
(13)
where zi is the counterion valence (e.g., +1 for Na+) and zp is the valence of the fixed charges (e.g., −1 for SO3−). If ξ is greater than ξcrit, a fraction of the counterions in the membrane “condense” on the fixed charges, until ξ is effectively reduced to the critical value. This phenomenon is called “counterion condensation”.34 When ξ is smaller than ξcrit, counterion condensation does not occur. The average distance between fixed charge groups (i.e., b) was estimated based on the polymer chemistry and IEC (milliequivalents of charge per gram of dry polymer) using the following equation:19 ij n yz b = jjj nc + 1zzz × 0.25 nm j nc z k {
(14)
where nnc and nc are the numbers of noncharged and charged monomers in one repeating unit, respectively, assuming all monomer units are uniformly distributed. (nnc/nc + 1) indicates the number of monomer units between fixed charge groups, and 0.25 nm is the projected length of one monomer unit in a planar zigzag conformation. The water/polymer mixture dielectric constant (i.e., ε value) was estimated as the sum of the dielectric constants of water at ambient conditions (∼78) and dry polymer (∼6) weighted by their volume fractions.19,34,35 The dry polymer dielectric constant was assumed to be ∼6 based on the median value of typically reported dielectric constants of polymers ranging from 2 to 10.36−39 Possible ξ value variations induced by choosing different values of the dry polymer dielectric constant were demonstrated in section S5 of the Supporting Information. Calculated values for b, ε, λB, and ξ are presented in Table 3.
Figure 6. Membrane activity coefficients as a function of external salt concentration. The activity coefficient is calculated based on the volume of water in the swollen polymer. The dashed lines were drawn to guide the eye.
activity coefficients as a function of external NaCl concentration. For all cases, membrane ion activity coefficients were well below 1 and increased as external NaCl concentration increased. Membrane ion activity coefficients for CEM1 and CEM2 were very similar. Membrane ion activity coefficients for CEM3 were somewhat higher than those for CEM1 and CEM2. In all cases, the ion activity coefficients are far from unity, indicating highly nonideal behavior of ions in these membrane, which is consistent with results obtained in other IEMs.19 As shown in Figure 6, strong electrostatic interactions between fixed charge groups and ions in the membrane induce highly nonideal behavior of ions in the CEMs. A recently proposed thermodynamic modeling approach (i.e., Manning/ Donnan model) can be used to interpret such nonideal behavior of ions in ion exchange membranes.19,20 A key feature of the Manning/Donnan model is accounting for thermody-
Table 3. Values for b, ε, λB, and ξ polymer morphology homogeneous
inhomogeneous
F
membrane
b (Å)
ε
λB (Å)
ξ
CEM1 CEM2 CEM3 CEM1 CEM2 CEM3
7.5 9.0 12.0 17.6 20.9 35.4
50 41 35 50 41 35
12.5 13.6 15.9 12.5 13.6 15.9
1.67 1.52 1.36 0.71 0.65 0.45
DOI: 10.1021/acs.macromol.8b02550 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
Figure 7. (a) Scattering intensity as a function of scattering vector q for the CEMs. (b) Model fit eq 16 to scattering intensity for CEM1.
Figure 8. Schematic representation of heterogeneities in the CEM networks showing the characteristic dimensions of the radius of gyration, Rg, attributed to domains with a locally high density of cross-links, and the correlation length, Xc, attributed to a dimension characteristic of the average mesh size within a continuous network.
tration in the membrane, Cm,w c , using Mathematica. An initial estimation of b and ε, assuming that the membrane was homogeneous (i.e., that the fixed charge groups were distributed uniformly throughout the membrane), resulted in poor agreement and the predicted membrane co-ion concentration being ∼95% on average greater than the experimental data. The results of these calculations are presented in Figure S1 and prompted a more detailed study of membrane morphology, which is described below. The polymers in this study were synthesized via free-radical polymerization of a charged monomer containing acrylamide functionality (i.e., AMPS) with a divinyl monomer (i.e., crosslinker) containing methacrylate functionality (i.e., DEGDMA). In copolymerization between AMPS and a different methacrylate, 2-hydropropyl methacrylate (HPMA), reactivity ratios were reported to be 0.04 for AMPS and 6.30 for HPMA.41 In contrast to ideal copolymers with reactivity ratios equal to 1, such copolymers, with substantial differences in reactivity ratios, generally exhibit inhomogeneous monomer distributions in polymer networks.42 Presumably, AMPS and DEGDMA also exhibit large difference in reactivity ratios. If
Assuming homogeneous morphology of the polymers, the calculated ξ values for this series of CEMs are all greater than 1 as shown in Table 3. Because ξcrit is 1 for a monovalent electrolyte solution (i.e., NaCl) and the membranes considered in this study, these results indicate that counterion condensation occurs in these membranes. In this case, the equilibrium of a 1:1 electrolyte in the membrane and in the contiguous external solution can be expressed as follows:20 ij C m,w /ξ + Ccm,w yz zz (CAm,w + Ccm,w )(Ccm,w )jjj A m,w j CA + Ccm,w zz k { ÅÄÅ ÑÉÑ m,w C Å ÑÑÑ = (γ s)2 (C s)2 × expÅÅÅÅ− m,w A Ñ s ± ÅÅÇ CA + 2ξCcm,w ÑÑÑÖ
(15)
Equation 15 is a key result from our previous modeling approach, which is the combined form of Manning/Donnan theories.20,40 Cm A was calculated as the difference between experimentally determined counterion and co-ion concentrations in the membrane.19 γs± was calculated using the Pitzer model,32,33 and Css is the external salt solution concentration. Equation 15 was numerically solved for the co-ion concenG
DOI: 10.1021/acs.macromol.8b02550 Macromolecules XXXX, XXX, XXX−XXX
Article
Macromolecules
microstructure (cf. Table 3). Thus, based on these X-ray scattering results, the CEMs are inhomogeneous networks. Although SAXS confirmed the inhomogeneous morphology of the CEMs, a direct measure of b value (i.e., the average distance between fixed charged groups) is not currently feasible using SAXS data. Thus, b values were obtained by the best fit values for ξ to experimentally determined ion activity coefficients in the membrane and the estimated dielectric constant of water/polymer mixture and λB (i.e., b = λB/ξ). The detailed description of finding the best fit values for ξ is reported in section S7 of the Supporting Information.16 Interestingly, the length scale of the correlation length (i.e., Xc = 21.8−30.1 Å) was more comparable to the b values (i.e., 17.6−35.4 Å) estimated for an inhomogeneous morphology than to the b values (i.e., 7.5−12.0 Å) estimated for a homogeneous morphology. The fitted ξ values were 0.71 for CEM1, 0.65 for CEM2, and 0.49 for CEM3. The critical Manning parameter, ξcrit, is 1 for 1:1 electrolytes, so these results indicate that counterion condensation does not occur in these materials.34 In this case, the modified expression for electrochemical potential equilibrium of a charged membrane equilibrated with a 1:1 electrolyte incorporating Manning’s model for membrane ion activity coefficients is19,34
so, in the early stages of copolymerization, reactions between DEGDMA molecules are predominant, forming hydrophobic, continuous gel phases. Therefore, the actual distance between fixed charge groups may be different from values calculated based on the assumption of a homogeneous membrane, which, in turn, would change the value of the Manning parameter, ξ. The CEMs are transparent to the naked eye and also when tested by UV−vis (cf. section S6 in the Supporting Information). Optical transparency, however, does not necessarily guarantee homogeneous morphology in copolymers if the size scale of the structural heterogeneities is smaller than the wavelength of visible light.43,44 The inhomogeneous morphology of a polymer gel is related to the spatial concentration fluctuations of monomer units and local heterogeneities in cross-link density, which can be probed by small-angle X-ray scattering.45−47 SAXS scattering profiles for the CEMs are presented in Figure 7a as log I(q) versus the scattering vector q. Following the approach employed by Cohen et al.,46 the SAXS scattering profiles were fit to a model representing microstructural heterogeneity over length scales capturing contributions from semidilute polymer−polymer correlations within a homogeneous gel matrix (i.e., the average “mesh” size of the network) and static density fluctuations characteristic of inhomogeneities arising from locally high polymer concentrations (i.e., clustered domains of relatively high cross-link densities). The inhomogeneous microstructure scattering model used to fit the SAXS profiles for the three CEMs is as follows: i 1 y I(q) = IL(0) + IG(0) expjjj− R g 2q2zzz 2 2 1 + Xc q k 3 {
(CAm,w
Membrane co-ion concentration modeling results, with ξ treated as an adjustable parameter, are presented in Figure 9. The model described the experimental data reasonably well (i.e., the difference between the model and experimental data was
