Anal. Chem. 1982, 5 4 , 1153-1157
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Optimization of Ion Exchange Membrane Structures for Donnan Dialysis J. A. Cox,* R. Gajek,’ G. R. Lltwlnskl, and J. Carnahan Department of Chemistry and Biochemistry, Southern Illinois University, Carbondaie, Illinois 6290 7
W. Trochimczuk Institute of Polymer and Organic Chemistty, Wroclaw Technical University, Wroclaw, Poland
Most Donnan dlalysls experlments have the objective of p r e concentratlng Ions of a glven charge sign from aqueous samples wlthout perturblng their relative concentratlons. Ideal Ion exchange membranes for these studles are those whlch permlt site-to-site dlffuslon as the mass transport llmltlng step. Thls mechanlsm was found to be favored by membranes wlth high Ion exchange capacities, cross-llnking below 15 %, and a backbone structure that ylelded contlnuous polyelectrolyte networks throughout the bulk of the membrane. Anion exchange membranes prepared from 4-vlnylpyrldlne and low density polyethylene yielded such a structure. Actlvation energy measurements as a functlon of cross-llnklng and transport rate determinations as a functlon of membrane thlckness were used to verlfy the mechanlsm. Catlon exchange membranes wlth Teflon and wlth poly(styrenesulfonate) backbones falled to yleld the Ideal mechanlsm. I n these cases, the role of the receiver electrolyte In optimizing the Donnan dlalysls of cations across membranes wlth dlscontinuous polyelectrolyte networks was establlshed.
Donnan dialysis (1-3) is being applied to such diverse problems as enrichment of trace levels of ions, metal separations, water softening, and recovery of metals from waste streams (ref 4-6 and citations therein). The primary problem limiting the applications is the transport rate of counterions across the ion exchange membranes. T o devise improved systems, it is necessary to consider all of the factors that contribute to the transport rate. The following describes an ideal Donnan dialysis system: (a) the transport across the membrane would be diffusion-limited; (b) the membrane structure and a large ion exchange capacity would favor site-to-site rather than1 volume diffusion (7, 8); (c) the acid/base strength of the fixed exchange sites on the membrane would not cause strong association with the test ions (4,6);(d) the receiver electrolyte would be selected to minimize the association between the fixed sites and the test ions (4, 9); (e) the sample and recleiver electrolyte (or stripper solution) would be efficiently stirred to minimize concentration polarization. Of these factors, those related to membrane structure have received the least attention. In the above model, site-to-site diffuriion is transport along a fixed, continuous polyelectrolyte network that is anchored by the ion exchange sites; volume diffusion is a mechanism that involves residence of the analyte ion within the solvent-filled channels in the membrane. A frequent assumption, based on self-diffusion coefficient measurements, is that transport in ion exchange membranes is diffusion-controlled. The diffusion coefficients are typically only 10-30% of the values in water because of the volume occupied by the polymer, tortuosity, restricted channel size, On leave from Wroclaw Technical University.
interactions with fixed sites, potential gradients from coion penetration, and nonoverlapping centers (10). Both poly(styrenesulfonate) and Nafion perfluorosulfonate polymer exchangers have been hypothesized to have an inverse micelle structure with spherical regions on the order of 1000 nm diameter connected by narrow channels (11, 12). This structure has been considered as the cause of a much higher activation energy for Cs+ transport than for Na+ in Nafion (13). If ion-pairing (electrostatic interactions) between the test ion and the fixed sites limits the transport rate, the system may not be strictly diffusion-controlled. For example, if the activation energy for the dissociation reaction is high, there will be a chemical kinetic limitation. If it is low but the rate is limited by the concentration of a chemical component such as proton in the membrane phase, the system will behave as one limited by volume diffusion. Such interactions have been reported (14,15),but the results cannot be directly applied to Donnan dialysis systems as the presence of the receiver electrolyte causes competing reactions at the fixed sites. We have demonstrated that by using a receiver electrolyte containing cations, such as Mg2+,with a high affinity for the fixed sulfonate sites on cation exchange membranes, Donnan dialysis is facilitated ( 4 ) . The resulting hypothesis that ion pairing between sulfonate and the test cations is decreased, so volume diffusion rather than chemical kinetics limits the transport, was supported by experiments on the effects of an ac field on the rate of Donnan dialysis (9). In the present study, activation energy measurements were made which verify the advantages of such a receiver electrolyte for Donnan dialysis across ion exchange membranes which do not have a structure that permits site-to-sitediffusion. With site-to-site diffusion the analyte ion would not have to be displaced into the open channels in order to cross the membranes; and, therefore, the composition of the receiver electrolyte would not be important. Further, the tortuosity would be decreased. Blaedel et al. (16) employed a model for Donnan dialysis that included the heterogeneous exchange reactions a t the membrane/solution interphases, reaction kinetics within the membrane, and diffusion in the membrane phase as possible rate-determining steps. Indirect evidence for chemical kinetic limitation was obtained for Ag+ transport in poly(styrenesulfonate) membranes. Wendt et al. (17) used a model that assumed local equilibrium a t the interphases and Fick’s diffusion behavior within the membrane. The model successfdly predicted Na+ and Ca2+transport in Nafion. A significant contribution of concentration polarization (boundary layer resistance to flux that occurs when the receiver solution convection is not sufficient to immediately transport ions from the interphase to the bulk solution) was observed. Wen and Hamil demonstrated that concentration polarization becomes negligible if rapid, turbulent flow is employed (6). The chemical composition and general structure of ion exchange membranes are well-known to influence ion transport. The ion cluster model of Ndion and the resulting effects
0003-2700/82/0354-1153$01.25/0 0 1982 American Chemical Societv
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ANALYTICAL CHEMISTRY, VOL. 54, NO. 7, JUNE 1982
on diffusion coefficients are now well established. The effect of water content on transport has been discussed in terms of discontinuities in the charge fields within the membrane (7, 8) and in terms of the tortuosity factor (15,18). Acrylic acid grafted polyethylene membranes were found to give slower cation transport than sulfonated styrene-grafted polyethylene membranes because of strong ion pairing with carboxyl groups (6). In that study metal transport was found to be favored by higher ion exchange capacities. In the present study the importance of the exchange capacity and other factors in Donnan dialysis is demonstrated and discussed in terms of promotion of the site-to-site diffusion mechanism. EXPERIMENTAL SECTION Two general types of anion and cation exchange membranes were used. The first were membranes made on a perfluorinated (Teflon) backbone obtained from RAI Research Corp., Hauppauge, NY. The cation exchangers (RAIP-1010) were sulfonated, and the anion exchangers (RAI P-1025) contained pyridinium methyl iodide. The thicknesses of the membranes were about 0.035-0.050 mm. The second type of membranes were prepared in-house based on a recently reported procedure (19). The primary component of the membranes is low density polyethylene. A powdered form, polyethylene LDS, was obtained from Plastic Coatings Ltd., England. The anion exchange membranes contained 4-vinylpyridine (Matheson, Coleman and Bell) that was vacuum distilled (2-4 torr) just prior to use. Styrene (Aldrich Chemical Co.) was used in the cation exchange membranes; it was likewise distilled. Other chemicals used were the following: (CH30)2S02,the quaternization agent for the anion exchangers (Aldrich Chemical Co.); a,a'-azoisobutylnitrile, the initiator for the 4-vinylpyridine polymerization (Fluka AG, Busch SG., Switzerland); benzoyl peroxide, the styrene polymerization initiator (Matheson, Coleman and Bell); Cyanox 425 (American Cyanamid Co.), an inhibitor to prevent surface polymerization (20);divinylbenzene (DVB), the cross-linking agent (BHD Chemicals Ltd., England). In the preparation of the anion exchangers, 5 g of a mixture of monomers was first made. For anion exchangers of normal capacity (1.2 mequiv/g) with 1% cross-linking the mixture contained 99.0% 4-vinylpyridine and 1.0% divinylbenzene. Low capacity membranes were prepared by substituting a fraction of the 4-vinylpyridine with styrene. To the mixtures, 0.05 g of Cyanox 425 and 0.1 g of the initiator were added. Ordinarily a,#'-azoisobutyronitrile was used as the initiator for the anion exchangers, but for the low capacity formulations, benzoyl peroxide was used. The resulting mixture was added to 20 g of polyethylene in a rotating Erlenmeyer flask suspended in a water bath. The system was agitated and heated a t 90 "C for 6 h under an argon atmosphere. The powdery product was rinsed with methanol and dried a t 60 "C overnight. The membranes were formed by pressing the powder in a hydraulic press equipped with heated platens (Carver Laboratory Press, Model B, Menominee Falls, WI). The platens were lined with polyester foil prior to pressing. A pressure of (0.6-1) X lo7 N/m2 and a temperature of 130 "C were applied for 2-5 min to obtain visually homogeneous membranes. The thicknesses were controlled by the pressing time and the quantity of powder used. Membranes with 10% or greater cross-linking were clear; the others were translucent. The membranes were quaternized by placing them in a 1:l volume mixture of (CH30)2S02-methanolfor 24 h. The strongly basic membranes that result were rinsed and stored in 1 M KC1 until use. The cation exchange membrane preparation procedure was generally the same. The monomer mixture was styrene-divinylbenzene (6 g total) in proportion to the desired degree of cross-linking. The initiator and inhibitor weights were both 0.15 g. After pressing, the membranes were swollen with 2,2'-dichloroethane for 0.5 h and subsequently chlorosulfonated with a 10% volume solution of chlorosulfonicacid in 2,2'-dichloroethane for 2 h at room temperature. The cation exchange membranes were then hydrolyzed in 10% by weight NaOH solution for 24 h at room temperature. After being rinsed, the membranes were stored in a receiver electrolyte solution until use.
The membrane thicknesses were determined with a micrometer. The measurement was made at five locations on a given section prior to mounting in a dialysis cell. If the relative standard deviation exceeded 5% the section was discarded. The general homogeneity among various batches and freedom from physical imperfections can be substantiated by measuring the permeability of the membranes to a pressurized head of water. The membrane (about 20 cm2) is mounted in a Plexiglas cell so that it rests against a coarse glass frit. A piece of filter paper between the frit and the membrane prevents cutting. Air is removed from the frit by suction, and the cell is filled with water. The inlet side is pressurized by regulated nitrogen (2 kg/cm2). The outlet is connected to a 0.2-mL Mohr pipet graduated in 0.01 mL increments. The flow during the first hour is disregarded. Subsequently the flow is read a t 5-min intervals until the flow rate becomes constant (usually less than 30 additional minutes). If the flow rate varies by more than 10% from the nominal value for a given-membrane formulation, that membrane is discarded. The ion exchange capacities were determined by an approach routinely employed on ion exchange resins. The anion exchange membranes were put into the C1- form with 1 M KC1. The C1was displaced with 1 M KNOB,and the released C1- was determined by biamperometric titration with coulometrically generated Ag+. For the cation exchange capacity measurements, the membranes were soaked in 2 M NaC1, rinsed, and exchanged with 1 M KCI. The displaced Na+ was determined by flame emission spectrometry. The relative standard deviations were less than 5%. The activation energy measurements were made by placing Donnan dialysis cells in jacketed beakers through which fluid was circulated by a Forma Jr. heated or refrigerated bath and circulator. The temperature of the sample solution (200 mL) in the beaker was monitored. The receiver electrolyte (5 mL) was brought to the required temperature and placed in the Donnan dialysis cell. These cells consisted of glass or Plexiglas cylinders that have one end covered by the ion exchange membrane (2). The membranes were held in place by Teflon tape and O-rings and the samples were agitated by a magnetic stirrer. The enrichment factor, EF, was determined (see below) at the prescribed temperature after 0.5 h. The activation energies were calculated from the slopes of plots of log (EF) vs. 1/T over the range 10-50 " C. For the other Donnan dialysis experiments, a thermostated cell was constructed from Plexiglas so the membranes could be held in place between parallel plates that were tapped to accommodate screws. Both the receiver and sample were magnetically stirred. The receiver stirring paddle was supported on a lip to prevent contact with the membranes (21). After the dialyses, the 5 mL receiver electrolytes were diluted to 10 mL to prevent error by osmotic dilution, and the analyte therein was determined. An enrichment factor was calculated as the ratio of the concentration in the 5 mL receiver after dialysis to the initial sample concentration. For experiments on the effect of membrane thickness, the nearness of the system to Donnan equilibrium after a certain time was determined. In these cases the sample and receiver volumes were the same and dilution of the receiver prior to quantification was not necessary as osmosis was insignificant. The analytical methods employed were the following: phosphate, spectrophotometry based on the absorbance of phosphomolybdic acid; nitrate, linear scan voltammetry; sulfate, barium chloranilate spectrophotometric method; and copper, atomic absorption spectrometry. RESULTS AND DISCUSSION 1. Anion Exchange Membrane Studies. Two types of membranes were used in these experiments: The commercially available pyridinium methyl iodide/Teflon-based membranes and polyethylene-based membranes with pyridinium exchange sites that were prepared in-house as described above. Phosphate, nitrate, and sulfate were selected as the test ions for this work. We had earlier demonstrated that the former two ions could readily be Donnan-dialyzed across the Teflon-based membranes whereas sulfate transport was inhibited (2, 22).
ANALYTICAL CHEMISTRY, VOL. 54, NO. 7, JUNE 1982
Table I. Effect of Cross-Linking on the Behavior of Anion Exchange Membranesa in the Donnan Dialysis of Nitrate exchange capacity, meqiuiv/g
% DVB
2 5 10
15
Table 11. Phosphate Transport Across Anion Exchange Membranes
activation enrichment energy, factor at kJ/mol 25°C
1.44 1.27 1.24 1.39
20 22 22
7.0 7.1 6.8 5.7
21
Pyridinium/polyethylene membranes prepared inhouse. Experimental conditions: sample, 200 mL of 0.10 mM KNO,;receivler, 5 mL of 0.10 M KCl; dialysis time, 0.50 h. a
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receiver pH
membrane PT PT PPb PP
2 4
2 4
activation enrichment energy, factor (25 "C) kJ mol-' 19 15 19 19
6.9 4.9 6.0 6.0
Pyridinium/Teflon-based membranes, RAI-P1025. Pyridinium/polyethylene membranes prepared inhouse. Conditions: sample, 0.10 mM KH,PO,, 200 mL; receiver, 5 mL of 0.lO M KNO, with 0.1 M chloroacetic acid a t pH 2 or 0 . 1 M citric acid at pH 4; dialysis time, 0.50 h; all membranes thicknesses, 0.035 mm. a
lot
06
1
0.81
de
0.2
t L
i.lm
120
240
Flgure 1. Effect of the membrane thickness on the Donnan dialysis of nitrate. ,,f ratio of thie quantity of nitrate transported into the receiver electrolyte to the quantity that would be transported if the system reached Donnan equilibrium. Conditions: dialysis time, 0.5 h; sample, 36 mL of 0.10 mM KNOB; receiver, 36 mL of 0.10 M KCI; membrane, 1% cross-linked polyethylene-based anion exchange membrane; a, 1400 rpm stirring of sample and receiver; b, 700 rpm stirring.
Table I contains a mmmary of activation energy measurements for nitrate transport across polyethylene-based membranes of varying percent cross-linking. The average value, 20 kJ/mol, is in the range that is typical for diffusion-controlled processes. Neither the activation energy nor the enrichment factor at a given temperature was dependent upon the cross-linking except that a t 15% cross-linking the Donnan dialysis rate was slower. The nitrate transport was also investigated across polyethylene-based membranes of varying thickness. The results shown in Figure 1 demonstrate two important points. The linearity of the plots precludes the heterogeneous exchange reaction at the solution/membrane interphases being the rate-limiting step. Because such a reaction could be expected to have a low activation energy the Table I results did not eliminate this possibilitg. Secondly, the fact that the plot at 700 rpm stirring rate did not extrapolate to the Donnan equilibrium value at zero membrane thickness indicates an attenuation of the transport rate by concentration polarization with that convection syatem. At 1400 rpm with membranes thicker than 50 pm and the 0.5 h dialysis time concentration polarization was negligible. With thinner membrane and/or shorter dialysis times, concentration polarization would probably be a factor even a t 1400 rpm. As commercially avaiAable membranes cannot be obtained with a wide range of systematically varied parameters, the experiments with the Teflon-based membranes were limited to activation energy measurements. The obtained value, 19 kJ/mol, agrees well with the Table I results. Further, the Donnan dialysis rate (enrichment factor) under a given set of conditions was in agreement with the results obtained with the polyethylene-based membranes. It can therefore be concluded that Donnan dialysis across the anion exchange membranes prepared in-house occurs by
Flgure 2. Effect of the membrane thickness on the Donnan dialysis of phosphate. Sample 0.20 mM KH,P04; sample and receiver stirrlng rate, 1400 rpm; a, pH 2 receiver; b, pH 4 receiver; dialysis time, 15 min. f , was calculated on the basis of equilibrium concentrations of anions in the sample. Other conditions are the same as Figure 1.
a site-to-site diffusion mechanism. Unless the sample and receiver are efficiently stirred, concentration polarization will influence the transport rate. Other possible modes of limiting the Donnan dialysis transport are the heterogeneous exchange reaction and volume diffusion. They were eliminated by the membrane thickness study and the cross-linking study, respectively. Regarding the latter point, volume diffusion control would be manifested by a dependence of enrichment factor on percent cross-linking. At 15% cross-linking there is evidence that the site-to-site transport mechanism occurs to a lesser extent and volume diffusion becomes significant. The Donnan dialysis of phosphate is complicated by the polyprotic nature of that acid. On the basis of our previous study (22),experiments were performed with pH 2 and pH 4 receivers. Activation energies and enrichment factors for dialysis across the two classes of membranes are summarized in Table 11. Figure 2 shows the effect of thickness of the membranes on the rate of Donnan dialysis. Interpretation of the results requires recognition that there will be a proton activity in the membrane phase that depends upon the pH of the receiver electrolyte. The proton will enter the anion exchange membrane from the receiver by "Donnan invasion" (23). Donnan exclusion will dictate that the effective pH within the membrane is much higher than that of the receiver electrolyte. The result is that the primary phosphate species within the membrane are probably H2P04- and HPO>-. The dependence of the transport rate on membrane thickness, shown in Figure 2, indicates that the effect of pH on the Donnan dialysis of phosphate is related to proton activity within the membrane rather than an effect of the heterogeneous exchange reaction. Even though the Figure 2 data are for the polyethylene-based membranes and the pH effect is with Teflon-based membranes, this conclusion is justified because the membrane surfaces are pyridiniumcontaining polymers for both cases.
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ANALYTICAL CHEMISTRY, VOL. 54, NO. 7, JUNE 1982
Table IV. Cation Exchange Membranea Parameter Effects on Donnan Dialysis
Table 111. Donnan Dialysis of Sulfate ion exchange capacity, membrane type mequiv/g
PTa PT PP,b 1%DVB PP, 1%DVB PP, 1%DVB PP, 1%DVB PP, 17% DVB PP, 17% DVB
C C
0.58
0.58 1.2 1.2 0.88 0.88
enrichment receiver factor 0.2MKC1 0.2 M HCl 0.2 MKCl 0.2 M HC1 0.2MKC1 0.2 M HCl 0.2 MKCl 0.2 M HC1
0.0
6.3 3.8 7.0 7.8 7.2 0.9 4.0
See Table 11. Conditions: sample, 0.10 mM Because the backbone is Na,SO,; dialysis time 0.5 h. inert but constitutes a large part of the membrane weight, correlation of Donnan dialysis rates to capacity cannot be made for PT vs. PP membranes. a,b
The important point of the Table I1 data is that the pH dependence on transport did not occur with our polyethylene-based membranes. With the other membranes the Donnan dialysis rate into the pH 4 receiver is slower than into the pH 2 receiver even though the activation energy is lower at pH 4. The results suggest that with the polyethylene-based membranes at both pHs and with the pyridinium/Teflonbased membranes into the pH 2 receiver, Donnan dialysis is limited by diffusion. The activation energy for the process is 19 k J mol-'. With the latter membranes and the pH 4 receiver, the rate-limiting step has nearly the same activation energy, 15 kJ mol-l, but there is a decrease in the transport rate. At pH 4 with the PT membranes the transport process is apparently limited by the activity of a component of a low activation energy reaction; further, the results suggest that this limiting component is proton. The receiver counterion, NOB-,may be too weak a base to displace a dianion such as H P 0 2 - from the pyridinium sites. The rate-limiting reaction may therefore be the protonation of HPOd2-. The above explanation implies that the mode of diffusion in the polyethylene-based membranes is site-to-site. In this case H P 0 2 - and H2P04- could be transported across the membrane at equal rates. With the Teflon-based membranes, rate-limiting transport by the site-to-site mechanism must be precluded by discontinuities in the polyelectrolyte chains. Instead, displacement of the phosphate from the fixed exchange sites is necessary so that these ions can diffuse through channels between regions of ion exchange groups. Such a model of regions of ion exchange groups separated by open channels has been suggested for some cation exchange membranes (12, 13). The reported procedure for preparing the polyethylene-basedmembranes (19) was based on the objective of attaining continuous polyelectrolyte networks so that the site-to-site mechanism would be facilitated. In order to test the above hypothesis, the Donnan dialysis of sulfate was investigated. In a previous study with Teflon-based membranes, the Donnan dialysis of that anion was found to be significantly slower than for selected monovalent ions (22). Table 111 summarizes the results of the present study. The results are consistent with the interpretation of the phosphate data. The transport across the pyridinium/Teflon-based membranes is slow unless the proton activity in the membrane is increased. With the polyethylene-based membranes a high proton activity is not necessary for facile Donnan dialysis unless low ion exchange capacity or highly cross-linked membranes are employed. In fact, with high capacity, low cross-linked membranes the use of a highly acidic receiver lowers the Donnan dialysis enrichment factor because the Donnan invasion of proton lowers the anion transport number;
receiver
Ib
0.1 M LiCl 0.3 M LiCl 0.6 M LiCl 0.05 M MgCl, 0.1 M MgCl, 0.2 M MgCl,
0.1 0.3 0.6 0.15 0.3 0.6
enrichactivation ment energy, factor kJ/mol (25 "C) 48 31 24 23 23 23
0.4
2.5 3.5 3.1 4.2 4.4
Sulfonate/Teflon-based membranes, RAI P-1010. Ionic strength. Sample, 0.10 mM CuCl,; dialysis time, 0.5 h. a
proton is the most mobile coion in an anion exchange membrane. 2. Cation Exchange Membrane Studies. Previously we established that receiver electrolytes that contain counterions with a high affinity for the sulfonate exchange sites are superior stripping solutions (4). We hypothesized that such ions as Mg(I1) were effective because they decreased the residence time of test ions on the exchange sites. That work was performed with sulfonate/Teflon-based membranes, RAI type P-1010. In the previous section we demonstrated that anionic forms of such membranes did not yield site-to-site diffusion-limited transport. Thus, for the present study membranes were synthesized comparable to the polyethylene-based series of anion exchangers except that sulfonated polystyrene instead of 4-vinylpyridine was used. The intent was to develop membranes that would give the site-to-site mechanism and thus not require cations in the receiver with a higher affinity for sulfonate than the sample ions in order to be effective. Table IV summarizes activation energy and Donnan dialysis transport rate data for sulfonate/Teflon-based membranes with various receiver electrolytes. With LiCl receivers, the activation energy is dependent on ionic strength which indicates that a change in transport mechanism occurs. Considering the anion exchange results, the LiCl data suggest that at low concentrations the rate-determining step may be
+
(RS03-)2Cu2+ 2Li+ + 2RSO,-Li+
+ Cu2+
The higher affinity of the dication for the sulfonate would account for the high activation energy and low enrichment factor. Site-to-site diffusion is apparently not the rate-determining step otherwise MgC12 and LiC1, especially a t the same ionic strength, should have been identically effective as receivers. With MgC1, receivers, the above ion exchange reaction is facilitated by the greater affinity of Mg2+than Cu2+ for sulfonate. The inhomogeneity of the membrane still prevents site-to-site diffusion control, but volume diffusion across the discontinuities occurs readily with Mg2+ as the receiver counterion. With 0.05 M MgClz receivers, the availability of Mg2+in the membrane phase may have limited the transport rate. The above experiments were repeated with polyethylenebased membranes to determine whether they would yield site-to-site transport as in the anion exchange study. The results are summarized in Table V. With Li+ counterions in the receiver, the activation energies are higher and the enrichment factors lower than in the case of a Mg2+-containing receiver. As in the case of the sulfonate/Teflon-based membranes an important contribution of the displacement of bound Cu(I1) by the counterion is apparent. Further, the percent cross-linking influences the activation energy. The more highly cross-linked membranes have greater tortuosity and narrower channels and thus slow the rate of channel diffusion and increase the activation energy
ANALYTICAL CHEMISTRY, VOL. 54, NO. 7, JUNE 1982
Table V. Donnan Dialysis of Cu(11) into Various Receivers Across Polyethylene-Based Membranes
% DVB
receiver
1 10 1 10 1 10
0.8MMgS0, 0.08MMgS0, 0.10 M LiCl 0.10 M LiCl 0.08 M MgCl, 0.08 M MgCI,
a
activation enrichment energy, factor (25 la kJ/mol “C) 0.32 0.32 0.10 0.10
0.24 0.24
19 26 38 54 21 23
5.0
4.7 0.9 0.4 4.6
4.1
Ionic strength; conditions the same as Table IV.
of the process. The effect is especially apparent with the LiCl receivers. Transport control by the site-to-site mechanism apparently is not achieved. Table V also demonstrates that there is a coion effect on Donnan dialysis. Sulfate Donnan-penetrates less than chloride, As a result with the MgS04receiver, the cation transport number is higher than with MgC12, so the enrichment factor is greater. The value of the activation energy is not significantly changed, however, by varying the identity of the coion.
CONCLUSION The above results suggest a model for the optimum ion exchange membranes for Donnan dialysis. The most important factor is the presence of a continuous network of ion exchange sites through the width of the membrane. Site-tosite diffusion can then occur continuously from the sample to the receiver. The membranes do not have to be homogeneous overall as long as the chain of exchange sites is not broken. The “chain” does not have to be a single channel of polyelectrolyte. Tortuosity is in fact diminished if the analyte can cross from channel to channel; however, for the site-to-site mechanism to hold, such crossings must not require the analyte ion to move by vo1,ume diffusion (i.e., it remains under the electrostatic influence of fixed sites a t all times). If the chain model is broken, then the receiver electrolyte system must be selected1 to facilitate volume diffusion across the essentially neutral regions of the membrane. For experiments with the objective of performing separations of ionic species with the mme charge sign, such “imperfections” may be desired as they permit the design of selective receiver systems (5). If the objective is to enrich all ions of the same charge sign without changing their relative concentrations, membranes that permit the site-to-site mechanism are preferable. In the present study the anion exchange membranes that were prepared from 4-viinylpyridine and polyethylene yielded site-to-site diffusion colntrol whereas the cation exchange membranes that contained poly(styrenesu1fonate) and polyethylene did not. The success of the former was probably due to the low miscibility of the molten polymers. The result would be continuous networks of polyelectrolytes. The cross-linking provides the physical stability of the heterogeneous system. In the cation exchange case, the polymers are better blended. ‘The result is dilution of the sulfonate sites by the polyethylene. Volume diffusion then becomes the rate-limiting step. For electrodialysis and for Donnan dialysis in the presence of an applied electrical field (9),site continuity is not necessary as the applied signal can facilitate transport by distortion of the polyelectrolyte chains. Most commercial membranes are prepared for electrodial:ysis, so it is not surprising that they
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are not optimal for Donnan dialysis. Nevertheless, by appropriate selection of receiver solutions they can be successfully employed for Donnan dialysis. It is noteworthy that Donnan dialysis membranes are now commercially available (for example, from RAI Research Corp); unfortunately, they were not available for inclusion in the present study. A second important property of a Donnan dialysis ion exchange membrane to be used for quantitative, general enrichment is a high exchange capacity. This fact was also noted by others (6). With low capacity membranes, the continuous network of polyelectrolyte chains needed for the site-to-site mechanism is not possible. The percent cross-linking (and thus the water content, pore size, and tortuosity) is not critical when the site-to-site mechanism applies. With cross-linking above 15% DVB, the electrolyte chains are interrupted. The more rigid membranes also make crossings between chains by the site-to-site mechanism more difficult. When volume diffusion is the limiting step, the Donnan dialysis rate is decreased by increasing the cross-linkingover the entire range studied. This fact is a result of lower water content and increased tortuosity in highly cross-linked membranes. Finally, thinner membranes give more rapid transport as Donnan dialysis is limited by processes in the bulk of the membrane. To take advantage of thin membranes, one should use vigorous stirring of both the sample and receiver solutions. The latter is conveniently accomplished by flowing the receiver solution (6, 24). LITERATURE CITED Wallace, R. M. Ind. Eng. Chem. Process Deslgn Dev. 1967, 6 , 424-43 1. Lundqulst, G. L.; Washinger, G.; Cox, J. A. Anal. Chem. 1975, 4 7 , 3 19-322. Blaedel, W. J.; Haupert, T. J. Anal. Chem. 1988, 3 8 , 1305-1308. Cox, J. A.; DlNunzlo, J. E. Anal. Chem. 1977, 4 9 , 1272-1275. Cox, J. A.; Olbrych, E.; Brajter, K. Anal. Chem. 1981, 5 3 , 1308-1309. Wen, C. P.; Hamll, H. F. J . Membr. Sci. 1981, 8 , 51-68. Jakubovic, A. 0.; Hllls, G. J.; Kltchener, J. A. J . Chim. fhys. 1958, 263-268. Jakubovlc, A. 0.; tlllls, G. J.; Kitchener, J. A. Trans. Faraday SOC. 1959, 55, 1570-1579. Cox, J. A.; Twardowski, Z. Anal. Lett. 1980, 13 (A14), 1283-1291. Helfferlch, F. I n “Ion Exchange”; Marinsky, J. A,, Ed.; Marcel Dekker: New York, 1966; Vol. 1, pp 69-71. Goldrlng, L. S. I n “Ion Exchange”; Marlnsky, J. A,, Ed.; Marcel Dekker: New York, 1966; Vol. 1, Chapter 6. Gierke, T. D. “Ion Clusterlng in Nafion Perfluorosulfonlc Acid Membranes and Its Relationshlp to Hydroxyl Rejection and Chlor-Alkali Efflclency“; 152nd Natlonal Meeting of the Electrochemical Soclety, Atlanta, GA, Qct 1977. Yeager, H. L.; Kipllng, B. J. J . fhys. Chem. 1979, 83, 1836-1839. Soldano, B. A.; Boyd, B. E. J . Am. Chem. SOC. 1954, 7 5 , 6 107-6 110. Fernandez-Prini, R.; Phillp, M. J . Phys. Chem. 1978, 80, 2041-2046. Blaedel, W. J.; Haupert, T. J.; Evenson, M. A. Anal. Chem. 1989, 4 1 , 583-590. Wendt, R. P.; Kleln, E.; Lynch, S . J . Membr. Scl. 1978, 1, 165-175. McCallum, C.; Patterson, R. J . Chem. SOC.,Faraday Trans. 1 1974, 70, 2113-2131. Gajek, R.; Trochlmczuk, W. J . Polym. Sci., Poly. Phys. Ed., in press. Gajek, R.; Trochlmczuk, W., patent pending, Poland 1980. Inenaga, K.; Yoshida, N. J . Membr. Sci. 1980, 6 , 271-282. Cox, J. A.; Cheng, K. H. Anal. Chem. 1978, 5 0 , 601-602. Rleman, W.; Walton, H. F. “Ion Exchange in Analytical Chemistry”; Permagon Press: New York, 1970; Vol. 8, p 29. Cox, J. A.; Twardowski, 2. Anal. Chem. 1980, 52, 1503-1505.
RECEIVED for review November 9,1981. Accepted March 8, 1982. This work was supported by the National Science Foundation under Grant CHE-7908660. Partial support for R.G. was provided by the Eastern European Universities Exchange Program Grant from the U.S. State Department to Southern Illinois University-Carbondale.
