Donnan Membrane Technique (DMT) for Anion Measurement

Mar 11, 2010 - Donnan membrane technique (DMT) is developed and tested for determination of free anion concentrations. Time needed to reach the Donnan...
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Donnan Membrane Technique (DMT) for Anion Measurement Flora Alonso Vega, Liping Weng,* Erwin J. M. Temminghoff, and Willem H. Van Riemsdijk Department of Soil Quality, Wageningen University, P.O. Box 47, 6700 AA, Wageningen, The Netherlands Donnan membrane technique (DMT) is developed and tested for determination of free anion concentrations. Time needed to reach the Donnan membrane equilibrium depends on type of ions and the background. The Donnan membrane equilibrium is reached in 1 day for Cl-, 1-2 days for NO3-, 1-4 days for SO42- and SeO42-, and 1-14 days for H2PO4- in a background of 2-200 mM KCl or K2SO4. The strongest effect of ionic strength on equilibrium time is found for H2PO4-, followed by SO42- and SeO42-, and then by Cl- and NO3-. The negatively charged organic particles of fulvic and humic acids do not pass the membrane. Two approaches for the measurement of different anion species of the same element, such as SeO42- and HSeO3-, using DMT are proposed and tested. These two approaches are based on transport kinetics or response to ionic strength difference. A transport model that was developed previously for cation DMT is applied in this work to analyze the rate-limiting step in the anion DMT. In the absence of mobile/labile complexes, transport tends to be controlled by diffusion in solution at a low ionic strength, whereas at a higher ionic strength, diffusion in the membrane starts to control the transport. Reliable evaluation of bioavailability and toxicity of compounds should be built upon chemical analysis that determines not only the total concentration, but also the distribution over different chemical species. Free ion is chemically very well-defined and under most conditions the species that can be taken up by organisms, and therefore considered as the major determinant of bioavailability and toxicity of the chemicals.1-6 A range of environmental relevant chemicals are present as anions. Examples are phosphate (PO43-), sulfate (SO42-), selenate (SeO42-), selenite (SeO32-), arsenate (AsO43-), and arsenite (AsO33-). Whereas for cations the term “free ion” often refers to only the (hydrated) free cations (Mz+), for anions we prefer to include their protonated forms as well (Az-, HxAx+z-). In fact, * To whom correspondence should be addressed. E-mail: [email protected]. (1) Bell, P. F.; Chaney, R. L.; Angle, J. S. Plant Soil 1991, 130, 51–62. (2) Campbell, P. G. C. In Metal Speciation and Bioavailability in Aquatic Systems; Tessier, A., Turner, D. R., Eds.; John Wiley & Sons: Chichester, UK, 1995; pp 45-102. (3) Parker, D. R.; Pedler, J. F. Plant Soil 1997, 196, 223–228. (4) Sauve, S.; Dumestre, A.; McBride, M.; Hendershot, W. Environ. Toxicol. Chem. 1998, 17, 1481–1489. (5) Ge, Y.; Murray, P.; Hendershot, W. H. Environ. Pollut. 2000, 107, 137– 144. (6) Hough, R. L.; Tye, A. M.; Crout, N. M. J.; McGrath, S. P.; Zhang, H.; Young, S. D. Plant Soil 2005, 270, 1–12.

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once the concentration of one of these forms is known, the concentration of all other (de)protonated forms can be calculated from protonation constants and pH. It is still a challenge to obtain accurate and reliable results of the free ion concentrations in natural systems because of their sometimes very low concentrations and the presence of various other chemical species. Commonly used approaches for measuring free anion concentration include ion selective electrode (e.g., fluoride), ion chromatography (in principle applicable for all anions), spectrophotometery methods (e.g., phosphate), voltametry (e.g., arsenic), etc. Each technique has its advantages and limitations. Conventionally, aquatic samples and soil or sediment extracts are filtered through 0.45 µm filters to obtain the operationally defined “dissolved” fraction. However, besides the simple inorganic ions, a variety of molecules/particles can also pass the filter, including colloidal particles (operational defined size range 1 nm-1 µm7). It is well-known that a large proportion of vital or toxic compounds in environmental systems is associated with colloidal particles.8 The presence of colloidal associated elements complicates interpretation of the analytical results of “dissolved” compounds. Many research has shown that release of colloids-associated phosphorus (P) during spectrophotometery measurement can lead to significant overestimation of the free P concentration in lakes,9 rivers,10 runoff,11 and soil solutions.10-14 The presence of colloidal particles can also influence the measurement using other analytical techniques. Sinaj et al.14 found that colloidal particles may lead to artifacts in ion chromatography analysis. The elution in chromatographic methods can in principle result in changes of solution chemistry and redistribution over various species. Elution also leads to dilution, which can be a problem when the initial concentration is low. The theory and application of the Donnan membrane technique (DMT) have been developed in the past years.15-19 The technique has the advantage that (1) interference from other components (7) Kretzschmar, R.; Borkovec, M.; Grolimund, D.; Elimelech, M. Adv. Agron. 1999, 66, 121–193. (8) Buffle, J.; Leppard, G. G. Environ. Sci. Technol. 1995, 29, 2169–2175. (9) Hudson, J. J.; Taylor, W. D.; Schindler, D. W. Nature 2000, 406, 54–56. (10) Haygarth, P. M.; Warwick, M. S.; House, W. A. Water Res. 1997, 31, 439– 448. (11) Turner, B. L.; Kay, M. A.; Westermann, D. T. J. Environ. Qual. 2004, 33, 1464–1472. (12) Hens, M.; Merckx, R. Water Res. 2002, 36, 1483–1492. (13) Shand, C. A.; Smith, S.; Edwards, A. C.; Fraser, A. R. Water Res. 2000, 34, 1278–1284. (14) Sinaj, S.; Machler, F.; Frossard, E.; Faisse, C.; Oberson, A.; Morel, C. Commun. Soil Sci. Plant Anal. 1998, 29, 1091–1105. (15) Weng, L. P.; Van Riemsdijk, W. H.; Temminghoff, E. J. M. Anal. Chem. 2005, 77, 2852–2861. (16) Fitch, A.; Helmke, P. A. Anal. Chem. 1989, 61, 1295–1298. 10.1021/ac9029339  2010 American Chemical Society Published on Web 03/11/2010

in the sample is minimal, (2) the perturbation of the substrate solution equilibrium can be negligible, (3) it can be applied for a wide range of concentrations, (4) simultaneous determination of various ions in one sample is possible, (5) it can be applied in the lab or in situ in the field. Mineral or organic colloids do not pass the membrane and artifacts due to filtration are absent if the technique is used in situ. So far, this technique has been tested and applied to determine mainly free cation concentrations in synthetic solutions,17,19-22 milk,23 soil solutions,16,18,24-31 surface waters,20,32 animal slurries,33 and sludge.34,35 Donnan dialysis using anion exchange membrane to remove unwanted anions in water is an active field of research.36-39 However, application of the DMT for speciation analysis of anions hardly exists in the literature. In this work, anion DMT was developed and tested to measure free anion concentrations. Influence of type and charge of ions and the ionic strength on the speed of ion transport was studied. Tests were carried out to see if colloidal particles can be transported through the membrane. Methodologies that can be used to measure simultaneously different anions of the same element were proposed and tested. A kinetic model concept that has been developed for cation DMT15 was extended and applied in this work to explain and understand the transport of anions. This work lays the basis for further development and application of the anion DMT. PRINCIPLES AND MODELING Donnan Membrane Equilibrium. In the DMT, a charged ion exchange membrane is inserted into the DMT cell that (17) Lampert, J. K. Ph.D Thesis, University of Wisconsin, Madison, 1982. (18) Minnich, M. M.; McBride, M. B. Soil Sci. Soc. Am. J. 1987, 51, 568–572. (19) Temminghoff, E. J. M.; Plette, A. C. C.; Van Eck, R.; Van Riemsdijk, W. H. Anal. Chim. Acta 2000, 417, 149–157. (20) Cox, J. A.; Slonawska, K.; Gatchell, D. K.; Hiebert, A. G. Anal. Chem. 1984, 56, 650–653. (21) Kalis, E. J. J.; Weng, L. P.; Temminghoff, E. J. M.; Van Riemsdijk, W. H. Anal. Chem. 2007, 79, 1555–1563. (22) Marang, L.; Reiller, P.; Pepe, M.; Benedetti, M. F. Environ. Sci. Technol. 2006, 40, 5496–5501. (23) Gao, R.; Temminghoff, E. J. M.; Van Leeuwen, H. P.; Van Valenberg, H. J. F.; Eisner, M. D.; Van Boekel, M. Int. Dairy J. 2009, 19, 431–436. (24) Fest, E.; Temminghoff, E. J. M.; Comans, R. A. J.; Van Riemsdijk, W. H. Geoderma 2008, 146, 66–74. (25) Kalis, E. J. J.; Temminghoff, E. J. M.; Town, R. M.; Unsworth, E. R.; Van Riemsdijk, W. H. J. Environ Qual. 2008, 37, 2221–2231. (26) Koopmans, G. F.; Schenkeveld, W. D. C.; Song, J.; Luo, Y. M.; Japenga, J.; Temminghoff, E. J. M. Environ. Sci. Technol. 2008, 42, 1123–1130. (27) Li, Y. T.; Becquer, T.; Dai, J.; Quantin, C.; Benedetti, M. F. Environ. Pollut. 2009, 157, 1249–1257. (28) Luo, X. S.; Zhou, D. M.; Wang, Y. J. J. Environ Sci. (Beijing, China) 2006, 18, 927–931. (29) Van Laer, L.; Smolders, E.; Degryse, F.; Janssen, C.; De Schamphelaere, K. A. C. Anal. Chim. Acta 2006, 578, 195–202. (30) Weng, L.; Temminghoff, E. J. M.; Van Riemsdijk, W. H. Eur. J. Soil Sci. 2001, 52, 629–637. (31) Weng, L. P.; Temminghoff, E. J. M.; Lofts, S.; Tipping, E.; Van Riemsdijk, W. H. Environ. Sci. Technol. 2002, 36, 4804–4810. (32) Kalis, E. J. J.; Weng, L. P.; Dousma, F.; Temminghoff, E. J. M.; Van Riemsdijk, W. H. Environ. Sci. Technol. 2006, 40, 955–961. (33) Van der Stelt, B.; Temminghoff, E. J. M.; Van Riemsdijk, W. H. Anal. Chim. Acta 2005, 552, 135–140. (34) Bartacek, J.; Fermoso, F. G.; Baldo-Urrutia, A. M.; Van Hullebusch, E. D.; Lens, P. N. L. J. Ind. Microbiol. Biotechol. 2008, 35, 1465–1474. (35) Fermoso, F. G.; Collins, G.; Bartacek, J.; O’Flaherty, V.; Lens, P. Biodegradation 2008, 19, 725–737. (36) Altintas, O.; Tor, A.; Cengeloglu, Y.; Ersoz, M. Desalination 2009, 239, 276–282. (37) Rozanska, A.; Wisniewski, J. Desalination 2009, 240, 326–332. (38) Wisniewski, J. A.; Kliber, S. Environ. Protect. Eng. 2008, 34, 95–104. (39) Wisniewski, J. A.; Kliber, S. Ochr. Srodowiska 2009, 31, 35–39.

separates the sample solution (donor) from a blank background solution (acceptor). To determine anionic species it is necessary to use a positively charged anion exchange membrane to allow the transport of anionic species and to retard the transport of cations. After a certain time, the Donnan membrane equilibrium will be reached for anions, at which the activity/concentration of the anionic species in the donor equals that in the acceptor if there is no ionic strength difference between the donor and acceptor. If there is a difference in ionic strength, it is necessary to apply a correction factor:40

( ) ( ) ai,don ai,acc

1/zi

)

aj,don aj,acc

1/zj

(1)

where a represents the activity of an ion under concern (i) and a reference ion (j), and zi and zj are, respectively, their charges. The subscripts “don” and “acc” refer to, respectively, the donor and acceptor solution. Transport Kinetics. Ion concentration in the acceptor (Ci,acc) after a certain time (t) from the start of the DMT analysis can be described with the linear driving force equation:15,19 Ci,acc,t ) Ci,acc,0 + (Ci,acc,∞ - Ci,acc,0)(1 - e-bt)

(2)

where Ci,acc,0, Ci,acc,t, and Ci,acc,∞ are respectively concentration of ion i in the acceptor at time 0, time t and at Donnan membrane equilibrium, and b is a parameter related to ion transport kinetics. Under steady state, the value of b is a constant and can be obtained empirically by fitting the model (eq 2) to experimental data. If the value of b is obtained, the time to obtain the Donnan membrane equilibrium can be conveniently compared for different ions using t95%, that is, time needed to obtain 95% of equilibrium concentration when Ci,acc,0 ) 0 and when there is no sampling and dilution of the acceptor until equilibrium: t95% ) -

ln(0.05) b

(3)

The value of b depends on volume of the acceptor solution (Vacc) and the flux of ion transport from the donor to the acceptor. In a previous article, a model has been proposed to represent the ion diffusion process in a cation DMT system.15 A similar model concept can be applied to the anion DMT. Ion diffusion in the DMT system can be separated into solution diffusion and membrane diffusion. Transport of ions between the bulk solution and membrane and between the membrane and acceptor solution is controlled by solution diffusion. A value of 0.05 mm was chosen for the thickness of the diffusion layer (δsol) at the donor-membrane and acceptor-membrane interface.15 Ion transport through the membrane is controlled by diffusion through the membrane. In case of solution diffusion controlled transport, the value of b can be expressed as15 b)

AeDi Vaccδsol

(4)

(40) Helfferich, F. G. In Mass Transfer and Kinetics of Ion Exchange; Liberti, L., Helfferich, F. G., Eds.; Martinus Nijhoff Publishers: The Hague, 1983; pp 157-180.

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Table 1. Some Characteristics of the Anion Exchange Membrane (BDH 55164 2S) thickness (δm)

dry weight

surface area (Am)

mass charge density

volumetric charge density (σ)

(mm)

(g cm-2)

(cm2 membrane-1)

(mmol g-1)

(mol L-1)

0.15

0.036

7.07

0.18

4.32

where Ae is the effective surface area of the membrane, Di the diffusion coefficient of free ions in water. When diffusion in the membrane is the rate-limiting step, the value of b can be expressed as15

b)

AeDiBzi Vaccλiδm

(5)

where B is the Boltzmann factor, λi is a tortuosity/retardation factor, δm is the thickness of the membrane. When dissociation/desorption takes place in the donor solution, the rate of ions released from complexes/particles may influence the net ion transport flux.41 MATERIALS AND METHODS DMT Sep-Up. For the experiment, the so-called lab DMT cells were used. The design of the ion exchange cell has been described by Temminghoff et al.19 In these experiments, a positively charged anion exchange membrane (BDH 55164 2S) was used to separate the donor and acceptor chambers. The membrane consists of a matrix of polystyrene, cross-linked with divinylbenzene, to which quaternary ammonium (sNR3+) groups are attached. Some basic properties of the membrane are listed in Table 1. The mass charge density was derived by measuring anion exchange capacity of the membrane. The volumetric charge density was derived from the mass charge density and the water volume of the membrane (see the Transport Modeling section). All cells, bottles, and test tubes were washed before use with 0.1 M HNO3 and ultra pure water (UPW) (each step a few hours). Before analysis, the membranes were prepared by shaking several times successively with 0.1 M HCl, UPW, concentrated background solution (0.5 or 1.0 M) and background solution at the concentration that was going to be used in the experiment. Pump tubes were cleaned with 0.1 M HNO3, UPW and background solution. During the DMT analysis, both the donor and the acceptor solution were circulated constantly by pumping at 2.5 mL minute-1 (peristaltic pump, Gilson Miniplus III). All the experiments were done at 20 °C degree in a controlled temperature room. Experiment 1. Equilibrium Time of Various Anions in Difference Background. Six synthetic solutions consisting of, respectively, 2, 20, 200 mM KCl or K2SO4 as background electrolyte were prepared. Each solution was divided into two parts: 1 L was used as donor solution and 15 mL as acceptor solution. Stock solutions of KH2PO4, KNO3, and Na2SeO4 were added to all donor solutions. K2SO4 was added to donor solutions with KCl as the background electrolyte, whereas KCl (41) Weng, L. P.; Van Riemsdijk, W. H.; Temminghoff, E. J. M. Environ. Sci. Technol., accepted.

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was added to the donor solutions with K2SO4 as the background. The final concentration of added anion in the donor is 0.1 mM. All the donor and acceptor solutions were adjusted to pH 5 with NaOH and HCl or H2SO4 before the DMT analysis. Based on speciation calculations,42 >99% of the total Cl, N, P and Se are present as, respectively, Cl-, NO3-, H2PO4-, and SeO42-. For SO4, >97% of the total S is in the form of SO42- in all treatments except in 200 mM KCl and K2SO4. In 200 mM KCl and K2SO4, respectively, 88 and 80% of S are present as SO42-, and the rest as KSO4-. 3.5 mL samples of both donor and acceptor were taken before the start of the experiment (t0) and after 4, 8, 24, 48, 72, 144, 192, 240, and 336 h. pH, Cl, N, P, S, and Se were measured in all samples. Experiment 2. Transport of Humic Particles. Purified humic acids (HA) and fulvic acids (FA) were used to represent natural organic colloidal particles. HA (carbon content 54%, molar mass 13.2 kDa) was prepared from the B-horizon of a forest soil from The Netherlands (Tongbersven).43 FA (carbon content 43%, molar mass 0.683 kDa) was prepared from the Bs-horizon of a peat soil from Scotland (Strichen).44 Four synthetic solutions were prepared, in which two use 20 mM KCl as the background and two use 10 mM CaCl2. Each solution was divided into two parts: 200 mL as the donor solution and 15 mL as the acceptor solution. Stock solution of HA or FA was added to the donor solutions to a final concentration of 100 mg L-1. pH of both the donor and acceptor solutions was adjusted to 5 with NaOH and HCl. Samples of both donor and acceptor were taken at start (t0) and after 8, 24, 48, 72, and 144 h. pH, TOC (total organic C) concentration and UV light absorbance at 254 nm were measured in all samples after filtration over 0.45 µm membrane filter (Whatman AQUA 30/0.45 CA). Experiment 3. Measure Free Phosphate in Suspensions Containing Mineral Particles. Eight synthetic solutions consisting of 2 mM KCl as the background electrolyte were prepared. Each one was divided into two parts: 1 L as donor solution and 15 mL as acceptor solution. To all donor solutions, 0.1 mM AlCl3 and 0.1 mM KNO3 were added. To each donor solution 1, 2, 3, 5, 10, 20, 30, or 100 µM KH2PO4 was added (P:Al ratio e1). The pH of both the donor and acceptor solution was adjusted to 5.2 with NaOH and HCl. At this pH, more than 98% of free P is H2PO4-. DMT analysis started one day after the donor solutions were prepared. Samples of both donor and acceptor were taken at start (t0) and after 48 and 96 h. pH was measured in all samples. Certain pH shift was observed during the experiment and pH was readjusted to the nominal level (5.2) after the sampling at 48 h. Aliquots of the donor samples were filtered over 0.45 µm membrane filter. Concentrations of Cl, N, P, and Al were measured in all samples. Experiment 4-1. Measuring Anions of the Same Element, Kinetic Approach. Three synthetic solutions all consisting of 20 mM K2SO4 as the background electrolyte were prepared. Each solution was divided into two parts: 1 L as donor solution and 15 mL as acceptor solution. To all donor solutions, 0.1 mM (42) Keizer, M. G.; Van Riemsdijk, W. H. ECOSAT: Equilibrium Calculation of Speciation and Transport; Agricultural University of Wageningen: Wageningen, 1994. (43) Temminghoff, E. J. M.; Van der Zee, S.; De Haan, F. A. M. Environ. Sci. Technol. 1997, 31, 1109–1115. (44) Weng, L. P.; Van Riemsdijk, W. H.; Koopal, L. K.; Hiemstra, T. Environ. Sci. Technol. 2006, 40, 7494–7500.

KNO3 was added. To the donor solution, 0.10 mM selenate, 0.10 mM selenate + 0.084 mM selenite, 0.084 mM selenite were added, respectively. Selenate and selenite were added in the form of, respectively, Na2SeO4 and Na2SeO3. pH of both the donor and acceptor solution was adjusted to 5 with NaOH and H2SO4. At this pH, more than 99% of selenate is present as SeO42- and more than 99% of selenite as HSeO3-. Samples of both donor and acceptor were taken at start (t0) and after 8, 24, 48, 72, and 144 h. pH, concentrations of N, S, and Se were measured in all samples. Experiment 4-2. Measuring Anions of the Same Element, Ionic Strength Approach. Five donor solutions all consisting of 20 mM K2SO4 as the background electrolyte were prepared. To all donor solutions 0.1 mM KCl was added. A mixture of selenate (Na2SeO4) and selenite (Na2SeO3) was added to a final total Se concentration of 0.1 mM. The ratio of selenate to selenite in the five donor solutions is, respectively, 100:0. 75:25, 50:50, 25:75, and 0:100. Each donor solution was connected via two DMT cells to two different acceptor solutions (15 mL of 10 mM or 2 mM K2SO4). pH in both the donor and acceptor solution was adjusted to 5 with NaOH and H2SO4. Samples of both donor and acceptor were taken at start (t0) and after 72, 144, and 192 h. pH and concentrations of Cl, S and Se were measured in all samples. Measurement. pH was measured using a pH meter (Radiometer Analytical PHM210) with a combined glass-calomel electrode (Beckman 511084). Chloride (Cl) concentration was measured using a Foss-Tecator Fiastar 5000 (continuous flow system). Concentrations of N-NO3- and C-TOC were measured using a segmented flow analyzer (SFA) (Skalar). Concentrations of P, S, Se, and Al were measured with a high resolution ICP-MS (Thermo Scientific, Element2) or with ICP-AES (Thermo Scientific, Iris advantage). RESULTS AND DISCUSSION Equilibrium Time. For the results of Experiment 1, using NO3- as the reference ion, the expected equilibrium concentration (Ci,acc,∞) of the other anions in the acceptor is calculated using eq 1. The ratio of anion concentration measured at a certain time (Ci,acc,t) to their expected equilibrium concentration (Ci,acc,∞) was then calculated (Figure 1a-e). By fitting eq 2 to the data, the values of b were derived and the t95% was calculated using eq 3. These results can be found in Table 2. Lines in Figure 1 are fitted curves using eq 2 and b values in Table 2. The irregularity in the lines is caused by dilution after each sampling and refilling. Please note that the t95% is calculated for situations when the acceptor was not sampled and refilled before the equilibrium was reached. In Experiment 1, sampling led to longer equilibrium time compared to the calculated t95%. The results for each anion are discussed below. Chloride. In the K2SO4 treatments, Cl- is present as an added anion to the donor and concentration of Cl- in the donor remained unchanged during the experiment (data not shown). The results show that the initial Cl- concentration in the acceptor is not zero and it increases with background K2SO4 concentration (Figure 1a). The initial Cl- in the acceptor may come from K2SO4 solution as impurities. The results of Cl- in 2 mM K2SO4 treatment were neglected due to low reliability as a result of low concentration. Using the b values derived

Figure 1. Relative change of Cl (a), NO3- (b), H2PO4- (c), SO42(d) and SeO42- (e) concentration in the acceptor of Experiment 1. Lines are fitted curves based on eq 2 and the values of b are given in Table 2. The irregularity in the lines is caused by dilution after each sampling and refilling.

(Table 2), the calculated t95% for Cl-, if the initial acceptor concentration was zero (CCl,acc,0 ) 0), are respectively, 0.4 and 0.9 days for 20 mM and 200 mM K2SO4 treatments. Nitrate. Concentration of NO3- in the donor decreased by 7-26% (data not shown). Up to 5% decrease can be accounted for by transport to the acceptor. Extra loss can be caused by accumulation in the membrane. It shows that the anion exchange membrane has a relatively higher specific affinity for NO3- than for Cl- and H2PO4-. Donnan membrane equilibrium is reached for NO3- between 0.5-2.2 days (Table 2). In general, NO3- transport gets faster with the increase of background concentrations (Figure 1b, Table 2). Equilibrium for NO3- is fastest in 200 mM KCl (0.5 days) and slowest (2.2 days) in 2 mM KCl. Phosphate. Concentration of H2PO4- in the donor decreased by 2-14% (data not shown). Speed of H2PO4- transport in both KCl and K2SO4 solutions decreases with the increase of background concentration (Figure 1c, Table 2). Equilibrium for H2PO4- is fastest in 2 mM KCl (1.0 day) and slowest in 200 mM KCl (14 days) (Table 2). The dilution after each sampling and refilling has a more obvious effect when the transport is slow, like the one of phosphate at high background concentrations (Figure 1c). This effect is very well reproduced by the model using the same b value over the whole experimental time. Sulfate. The total sulfate concentration in the donor decreased by 31, 10, and 4%, respectively, in 2, 20, and 200 mM KCl (data not shown). The strong decrease at low KCl concentration can be attributed to adsorption to the membrane. Because most of sulfate occurs as bivalent SO42-, it is preferred electrostatically by the positively charged membrane over the monovalent anions. At equilibrium, in the 2 mM KCl treatment the positive Analytical Chemistry, Vol. 82, No. 7, April 1, 2010

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Table 2. Theoretical (Assuming Solution Diffusion Controlled, Ignore Accumulation in the Membrane) t95% (Days) and Empirical b (× 10-6) and t95% (Days). Both t95% Are Calculated for When There Is No Dilution Due to Sampling and Refilling

theoretical Empirical KCl

2 mM 20 mM 200 mM

K2SO4

2 mM 20 mM 200 mM

Cl-

NO3-

H2PO4-

SO42-

SeO42-

t95% 0.4

t95% 0.4

t95% 0.8

t95% 0.7

t95% 0.7

b

t95%

100 40

0.4 0.9

b 16 33 65

t95% 2.2 1.1 0.5

b 34 8.5 2.4

t95% 1.0 4.1 14

19 33 25

1.8 1.1 1.4

13 7.7 2.8

2.7 4.5 13

charge of the membrane will be neutralized largely by the bivalent SO42- and SeO42- and initially present Cl- ions will be released by anion exchange. The transport of SO42- is fastest at a medium KCl or K2SO4 concentration (Figure 1d). Equilibrium is reached most quickly (1.4 days) in 20 mM KCl, followed by 2 mM KCl (3.1 days) and 200 mM KCl (4.3 days) (Table 2). Selenate. Behavior of SeO42- is rather similar to SO42-. There is a 3-38% decrease of SeO42- concentration in the donor and the maximum decrease happened in the 2 mM KCl treatment (data not shown). The transport is fastest at a medium KCl or K2SO4 concentration (Figure 1e). The fastest equilibrium (1.0 day) is reached in 20 mM K2SO4, whereas the slowest happens in 2 mM KCl (3.8 days) (Table 2). For both sulfate and selenate at low background concentrations, the model temporarily overestimated the transport at a later stage of the experiment (Figure 1d, 1e). It shows that the kinetic parameter b may change in these cases with time during the experiment. In these treatments, large amounts of anions under concern accumulate in the membrane and this amount is several times larger than that transported to the acceptor. This phenomena leads to prolongation of equilibrium time. Because equilibrium between donor and membrane is reached slowly, the system is not in steady state when most of the transport takes place. Therefore the value of b is not a constant. In addition, with a very low background concentration (2 mM KCl), the electrostatic potential of the membrane depends on the bivalent anions added. Due to the decrease of SO42- and SeO42- in the donor, the electrostatic potential varies during the experiment, which explains further the change of the kinetic parameter b during the analysis. In other treatments with a higher background concentration, the electrostatic potential in the membrane depends mainly on the background anions (Cl- or SO42-) and the membrane electrostatic potential of these treatments remains practically constant during the experiment. The DMT technique can be applied based on equilibrium or kinetics.15 The equilibrium mode DMT is preferred if possible because data interpretation is then straightforward in most cases. The above results show that for all the anions studied equilibrium can be reached in 1-2 days under optimal background compositions. The ionic strength has the strongest effect on equilibrium time of H2PO4-. The equilibrium time derived in this experiment corresponds to the setup used. Equilibrium time can be shortened by reducing the volume of acceptor and/or increasing the surface area of the membrane. Significant decrease of 2936

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b 11 25 8.0

t95% 3.1 1.4 4.3

b 9.2 17 18

t95% 3.8 2.0 1.9

23 34 10

1.5 1.0 3.5

concentration in the donor can be avoided by increasing the buffer capacity of the donor solution (larger donor volume or higher amount of complexed/adsorbed compounds). Transport of Colloidal Particles. Transport of purified fulvic acids (FA) and humic acids (HA) over the DMT membrane was tested in Experiment 2. The experiment was done in a 20 mM KCl and 10 mM CaCl2 background (data not shown). Concentration of TOC in the donor remained constant, except for HA in CaCl2 background. In this case TOC decreases due to flocculation. In all the treatments there is a small increase of TOC (up to 5 mg L-1) in the acceptor side over 6 days (results not shown). However, this TOC increase is also found in blanks and can be attributed to carbon release from the pump tubes. There is no light absorbance measured at 254 nm in the acceptor, which proves also that the small amount of TOC in the acceptor is not FA or HA. Particles of FA have an estimated radius of about 1 nm. Radius of HA particles can be a few nanometers.45 Although FA and HA particles are negatively charged, they cannot pass the anion exchange membrane due to probably size limit. What we observe is that there is a slight change of color of the membrane (from white to yellow) after the experiment with FA and HA. It indicates that some FA and HA particles are attached to the surface or in the membrane. Future research is needed to find out if this attachment influences the measurement of other anions in the DMT. Elements such as phosphorus, sulfur, and selenium can occur as inorganic anions, incorporated in organic particles, or adsorbed to mineral particles. The transport of organic particles or mineral particles that contain these elements in the DMT can interfere with the measurement of free anions. This experiment shows that particles of colloidal size will not be transported over the anion exchange membrane in the DMT analysis, even when the particles are negatively charged. Therefore colloidal particles will not interfere with the measurement of the free ion concentration, which is a big advantage of the method. However, further testing is needed to find out molecules of which size can pass the membrane. Measuring Free Phosphate in the Presence of Inorganic Particles. In Experiment 3, free phosphate concentration was measured when aluminum ion was added to the donor. Aluminum ion (Al3+) can form particles of aluminum hydroxide (Al(OH)3) and/or a precipitate like aluminum phosphate (AlPO4). Phos(45) Weng, L. P.; Van Riemsdijk, W. H.; Hiemstra, T. J. Colloid Interface Sci. 2007, 314, 107–118.

Figure 2. Results of Experiment 3, showing total P (nonfiltered) measured with ICP-MS and free P measured with DMT. The donor contains a mixture of aluminum and phosphate with P:Al ratio e1, pH 5.2. Line is speciation calculation taking into account the formation of amorphous Al(OH)3 (logKs ) -33.34) and AlPO4 (logKs ) -22.05).

phate can be associated with these particles via adsorption to Al(OH)3 or via precipitation. Most samples did not show presence of particles on visual inspection. The DMT measured free H2PO4- concentration is 0.3-55% of the total P in unfiltered solution (Figure 2). In all treatments except the highest P treatment, the ratio of free/total P decreases with the increase of total P. In fact, in these treatments, the free H2PO4- concentration fluctuates between a relatively narrow range of 0.06-0.27 µM (Figure 2). Only in the last treatment with the highest P loading, free H2PO4- concentration jumps to 30 µM. The results can be reasonably explained by formation of AlPO4 precipitates. In Figure 2, a line is given that is the prediction of speciation calculation using the program ECOSAT,42 taking into account the formation of amorphous Al(OH)3 (logKs ) -33.34) and AlPO4 (logKs ) -22.05). The fluctuation of the data around the line can be caused by changes of the minerals formed and variations of solubility product, which is beyond the scope of this study. It seems that the size of particles formed grows relatively fast and filtration over 0.45 µm filter in this case removes most particles after 1 day of aging (data not shown). Analysis of Different Anions of the Same Element in a Mixture. Often there are different anions that contain the same element. Examples are H2PO4- and HPO42-, SeO42- and HSeO3-, AsO43- and H2AsO3-. All forms of these ions can be transported over the anion exchange membrane and the total P, Se, or As concentration measured in the acceptor is the sum of all anions of the same element. For ions that are in fast chemical equilibrium (e.g., H2PO4- and HPO42-), and when parameters for thermodynamic calculations are reliable and easy to obtain (e.g., protonation constants and pH), it is simple to calculate the individual concentrations based on the analysis of one species or the total concentration. For ions of the same element that are not in fast chemical equilibrium or when thermodynamic calculation is impractical, individual species have to be determined. Here we propose and test two approaches that can be used for such a case. Kinetic Approach. Two anions of the same element can be analyzed individually in a mixture when they differ in transport rate over the membrane. For this objective, a precalibration experiment has to be carried out to derive the kinetic parameter,

Figure 3. Relative change of Se concentration in the acceptor of Experiment 4-1. The donor solution contains only selenate (SeO42-), only selenite (HSeO3-), or a mixture (SeO42-+ HSeO3-). The lines are calculations using eq 6 and b values derived (34 × 10-6 for SeO42-, 8 × 10-6 for HSeO3-).

that is, the b value, for both anions (bA and bB). Once the values of b are derived, concentrations of both anions in the donor solution can be determined with DMT by sampling the acceptor solution at least at two different times: one before equilibrium is reached and one when equilibrium is reached. Suppose the total element concentration in the acceptor at the first sampling is Ctot,acc,t and that at the equilibrium is Ctot,acc,∞, under steady state conditions, the equilibrium concentration of individual anions in the acceptor (CA,acc,∞, and CB,acc,∞) can be derived by solving the following equation pair:

(

Ctot,acc,t ) CA,acc,∞(1 - e-bAt) + CB,acc,∞(1 - e-bBt) Ctot,acc,∞ ) CA,acc,∞ + CB,acc,∞

)

(6)

A preliminary test (Experiment 4-1) was carried out to see if this approach is feasible, using selenate (SeO42-) and selenite (HSeO3-) as an example. The change of total Se concentration with time is shown in Figure 3. From treatments of pure SeO42or HSeO3-, the bA and bB values can be derived (34 × 10-6 for SeO42-, 8 × 10-6 for HSeO3-). In the mixture treatment with 54% SeO42- and 46% HSeO3-, the calculated change of total Se concentration in the acceptor using the derived b values is in good agreement with the data (line in Figure 3). Solving eq 6 using total Se measured at 1 or 2 days (Ctot,acc,t) and at equilibrium (Ctot,acc,∞) leads to, respectively, 55 or 58% SeO42-, which is very close to the nominal value (54%). This preliminary test shows that it is possible to analyze different anions of the same element in a mixture based on their transport kinetics. The accuracy of the method needs further study, which is beyond the scope of the present work. Ionic Strength Approach. If the anions have different charge, for instance SeO42- and HSeO3-, the response of their equilibrium concentrations in the acceptor to changes in the background ionic strength differs (eq 1). By measuring the total equilibrium concentration at two ionic strength levels in the acceptor (Ctot,acc,∞ and C′tot,acc,∞), while keeping the ionic strength in the donor constant, two anions of the same element in a mixture can be analyzed. If B stands for the bivalent SeO42-, and M for the monovalent HSeO3-, their concentration in the donor (CB,don and CM,don) can be derived by solving the equation pair below when SO42- is used as the reference ion: Analytical Chemistry, Vol. 82, No. 7, April 1, 2010

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(

Ctot,acc,∞ ) Ctot,acc,∞ ) ′

( ) ( ) CSO4,acc

CSO4,don CSO ′ 4,acc CSO4,don

CB,don + CB,don +

( (

CSO4,acc f2,acc CSO4,don f2.don CSO ′ 4,acc f 2,acc ′ CSO4,don f2.don

) )

1/2

f1,don C f1,acc M,don

1/2

f1,don CM,don f 1,acc ′

)

(7)

where f1 and f2 are activity coefficient for respectively monovalent and bivalent ions. If it is known that both B and M in the donor are present solely as free ions, measurement for only one ionic strength in the acceptor that should differ from that in the donor is necessary. The second equation in the equation pair 7 can be derived from the fact that at equal ionic strength in the donor and acceptor, the total equilibrium acceptor concentration equals to the total concentration in the donor: C′tot,acc,∞ ) CB,don + CM,don. If colloids are present that bind the species of interest one has to do two experiments with different ionic strength in the acceptor. A preliminary test (Experiment 4-2) of this approach was carried out. Although the total Se concentration in the donor is the same for all five treatments, the equilibrium Se concentrations in the acceptor differ (results not shown), and the acceptor Se concentration decreases with the increase of SeO42-/HSeO3- ratio in the donor as expected. This is because the ionic strength difference between the donor and acceptor has a stronger effect on the bivalent SeO42- than on the monovalent HSeO3- (See eq 1). Using total Se measured in the acceptor at 6 and 8 days (used as replicates), the ratio of SeO42-/total Se in the donor was estimated using eq 7. This calculation was done for respectively 2 mM K2SO4 acceptor and 10 mM K2SO4 acceptor. In Figure 4, results of 2 mM K2SO4 treatment are compared to the nominal values. In the figure, the average of the estimation based on data of 6 and 8 days was given as the data points and the standard errors as the error bars. The results show that the agreement between the measured and nominal ratio is reasonable. The agreement between the measured results and the nominal values are less good for the 10 mM K2SO4 treatment (data not shown), due to a too small difference of ionic strength between the donor and acceptor.

Figure 4. Comparison between fraction of SeO4/(SeO4 + HSeO3) measured using DMT and added in Experiment 4-2. The background of the donor solution is 20 mM K2SO4, whereas that in the acceptor is 2 mM K2SO4. The measured ratios are the average of calculated results from data of 6 and 8 days using eq 7 and the error bars are the standard errors of these two measurements. The line is 1:1 line.

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Analytical Chemistry, Vol. 82, No. 7, April 1, 2010

Table 3. Diffusion Coefficients of Different Anions in Water (Di) NO3- H2PO4- SO42- SeO42- HSeO3-

Cl-9

Di (× 10 a

2

-1

a

1.90a

m s ) 2.032

0.88a

1.065a

1.008a

0.86b

Marcus.46 b Vlaev and Genieva.47

Table 4. Boltzmann Term (B) and Retardation Factor (λ) λ -1

B KCl

-2

B

-

Cl

NO3

-

H2PO4- SO42- SeO42-

2 mM 20 mM 200 mM

142 107 21

20063 11414 451

348 245

K2SO4 2 mM 20 mM 200 mM

46 15 6

2104 236 31

98 55 55

9

89

37

17

TRANSPORT MODELING Effective Surface Area (Ae). Not all membrane surface is accessible for diffusion of water and ions. The matrix of the membrane leads to a reduction of the surface area available for diffusion. The fastest transport in DMT can be achieved when transport is controlled by solution diffusion and when the amount of ions accumulated in the membrane is relatively small. In this case, the b value can be expressed by eq 4. Using the fitted b value for the fastest transport observed for Cl- at 20 mM K2SO4 (Table 2) and diffusion coefficient (Di) given in Table 3, the effective surface area (Ae) can be calculated using eq 4. The sum of the thickness of the diffusion layer (δsol) on both the donor and acceptor side is 0.1 mm. The calculated Ae is then compared to the physical surface area of the membrane (Am ) 7.07 cm2). The Ae/Am ratio obtained equals 10%. This value is lower than that found for the cation exchange membrane (20%).15 It is assumed that the porosity of the membrane equals the ratio of Ae/Am (10%). This is in agreement with the normal range of water content (10-20%) of ion exchange membranes.48 The volumetric charge density (σ) of the membrane can then be calculated from the mass charge density of the membrane (Table 1) and the water volume in the membrane. The calculated σ equals 4.3 mol L-1 (Table 1). This volumetric charge density is somewhat higher than that found for the cation exchange membrane (3.5 mol L-1). Using this charge density, the Boltzmann factor (B) can be calculated for each treatment of Experiment 1 (Table 4). Rate-Limiting Step. Assuming a solution diffusion controlled transport and neglecting ion accumulation in the membrane, theoretical t95% can be calculated for each anion in Experiment 1 using eq 3 and 4. Thus calculated theoretical t95% is compared to the empirical t95% in Table 2. For Cl- in 20 mM K2SO4, NO3in 200 mM KCl, H2PO4- in 2 mM KCl, SO42- in 20 mM KCl, SeO42- in 20 mM K2SO4, their empirical t95% is equal or close to (e2 times difference) the respective theoretical t95% and the transport is controlled by diffusion in solution. For NO3- in all (46) Marcus, Y. Ion Properties; Marcel Dekker Inc: New York, 1997. (47) Vlaev, L. T.; Genieva, S. D. J. Struct. Chem. 2004, 45, 825–831. (48) Le, X. T. J. Colloid Interface Sci. 2008, 325, 215–222.

treatments except 200 mM KCl, SO42- in 2 mM KCl and SeO42in 2 mM KCl and K2SO4, their empirical t95% is much larger (g2 times) than the theoretical values (Table 2) and there is also a strong decrease of their concentration in the donor. Transport of these ions in corresponding treatments is not membrane diffusion controlled because the direction of the salt effect is opposite to what it should be in that case. Diffusion in the solution is therefore rate-limiting but equilibrium takes longer than theoretically calculated because in these cases strong accumulation takes place in the membrane, which is ignored in the estimation of t95%. Transportation of ions that accumulate in the membrane delays the Donnan membrane equilibrium. For all other cases (Cl- in 200 mM K2SO4, H2PO4- in all treatments except 2 mM KCl, SO42- in 200 mM KCl, SeO42- in 20 mM and 200 mM KCl and 200 mM K2SO4), the slower than expected transport cannot be explained by accumulation in the membrane and transport also slows down with an increase of background concentration (Table 2). Diffusion in the membrane is in these cases the rate-limiting step. For membrane diffusion controlled transport, the b value can be calculated from eq 5. The tortuosity or retardation factor (λ), which may include more effects than just pore tortuosity, can be derived from the empirical b values (Table 2) for treatments where membrane diffusion is controlling the transport. The fitted values can be found in Table 4. The value of λ depends on type of ion and on the background. The λ increases in the order Cl- < SeO42< SO42- < H2PO4-. The transport of phosphate ion (H2PO4-) is relatively strongly retarded compared to the other ions. For all ions, λ is in the range of 9-98 in a K2SO4 background, which

is in the same order of magnitude as the λ values found for cations with Ca2+ as the background.15 CONCLUSIONS Anion DMT is a promising technique for measuring free anion concentrations. Time needed to reach equilibrium depends on type of ion, valence and background composition. Transport can be controlled by diffusion in the solution phase or in the membrane. With the setup used in this study, equilibrium can be achieved in 1-2 days if the background is optimal. Equilibrium time can be shortened by choosing optimal background composition, increase of the surface area of the membrane or decrease of the volume of the acceptor solution. Anions of the same element can be analyzed under certain conditions using DMT based on their transport kinetics or response to ionic strength difference. Colloidal particles do not pass the anion exchange membrane, thus interference from these particles on the DMT measurement is absent. Anion DMT as a speciation technique has potential for many practical applications. It can be applied both in the lab and in situ. In situ measurement can avoid artifacts associated with sampling, filtration, and other pretreatment. ACKNOWLEDGMENT We thank Bert Van de Stelt for some preliminary test of the technique. Flora Alonso Vega received a fellowship from Direccio´n Xeral de I+D+I (Xunta de Galicia). Received for review December 22, 2009. Accepted February 25, 2010. AC9029339

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