Anal. Chem. 1994,66,2544-2551
Chemically Facilitated Donnan Dialysis and I t s Application in a Fiber Optic Heavy Metal Sensor Zhlhao Lln and Lloyd W. Burgess’ Center for Process Analytical Chemistry, Department of Chemistry, B G 10, University of Washington, Seattle, Washington 98 195
Chemically facilitated Donnan dialysis (CFDD) of heavy metal ions in combination with continuous reagent flow has been studied. A simplified model to describe this process has been established. The model relates the diffusion behavior of metal ions through a Nafion cation-exchange membrane with the stability constant of complexation, the ionic strength of the receiving and sample solutions, the flow rate of the receiving solution, and the area-to-volumeratio of the membrane dialysis cell. A novel fiber optic heavy metal sensor has been fabricated by directly interfacing the dialysis device with a fiber optic colorimetric detection mechanism. The sensor is specific for the measurement of Pb(I1) and Cd(I1) in aqueous solutions, utilizing sodium thiosulfatein the receivingsolutionto selectively enhance the mass transport of these two ions. In a stoppedflow operation mode, the sensor detection limit is 3 X l o 9 M Pb(I1) or Cd(I1) (S/N = 3) at 20 min accumulation. On the basis of the theoretical model, the factors affecting the sensor selectivityand dynamic range have been identified and discussed. Donnan dialysis takes place when a permeable membrane separates a relatively low ionic strength sample from a concentrated receiving electrolyte. The counter ions (the ions bearing the same charge as the sample ions) in the receiving solution diffuse through the membraneunder a relatively large concentration gradient, inducing an electric potential gradient acrossthe membrane. Driven by the electric potential gradient, the sample ions can be concentrated into the receiving solution. Due to the advantages of sample enrichment and matrix normalization (when an ion-exchange membrane is used), this technique has become an interesting research and has found many applications in chemical analysis of metal ions8-’ and charged organic s p e c i e ~ . ~ ~ J ~ For chemical analysis, the selectivity of Donnan dialysis is an important concern. In the case of metal ion dialysis, the selectivity relies mainly on the electrostatic interactions (1) Matsuyama, H.; Fujii, K.; Teramoto, M. J. Chem. Eng. Jpn. 1991, 24 (2),
253-5. (2) Hamil, H. F.; Report. Order No. PB83-148155, P 39. Available from NTIS 1982. (3) Osseo-Asare, K.; Xue, T. J . Membr. Sci. 1989,43,5-17. (4) Bcrggren, D. Inr. J. Enuiron. Anal. Chem. 1990,41 ( 3 4 , 13348. (5) Koropchak, J. A.; Dadek-Zlotorzynska, E. Appl. Spectrosc. 1987,41 (7), 1231- 5 .
(6)Brajter, K.; Slonawska, K.; Cox, J. A. Anal. Lett. 1989,22 (3). 779-90. (7) Cox, J. A.; DiNunzio, J. E. Anal. Chem. 1977.49. 1272-5. (8) Cox, J. A.; Olbrych, E.; Brajter, K. Anal. Chem. 1981,53, 1309-11. (9) DiNunzio, J. E. Report. W79-0034, OWKT-A-87-ILL(2); Order No. PB288182, P 170. Available from NTIS, 1977. (10) Cox, J. A.; Twardowski, Z. Anal. Lett. 1980,13 (A14), 1283-91. (1 1) Cox, J. A.; Slonawska, K.; Gatchell, D. K.; Hiebert, A. G. Anal. Chem. 1984, 56,65C-3. (12) J. A. Cox; Cheng, K. Anal. Chem. 1978,50, 601-2. (13) Cox, J. A.; Poopisut, N. Anal. Chem. 1992,64,423-6.
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Analytical Chemlstty, Vol. 66, No. 15, August 1, 1994
between the functional groups of the membrane and the metal ions.14 Highly selective dialysis can only be achieved in some cases where metal ions have different valences. Chemically facilitated Donnan dialysis ( O D ) can improvethe selectivity of conventional Donnan dialysis by using the receiving solution that contains a chemical reagent to selectively react with the targeted ions and alter them into the species that are not retained by the membrane. This technique has been studied by researchers such as C O X , ’ ~ Kasthurikrishnan,” J~ and HuangI8 and applied to chemical analysis. In their work, the receiving solutions in the dialysis cell were transferred into flasks after dialysis and analyzed with separate instruments. To extend the application of CFDD into an increasingly important area, in situ chemical analysis, the dialysis cell should be integrated into an analytical device. For this purpose, the flow-probe format19is suitable. In a flow probe, the dialysis cell serves as the sampling head and is directly interfaced with a detection mechanism. A wide range of chemical reactions as well as the hydrodynamics of the reagent flow can be used to facilitate the measurement. This will not only offer a new variety of chemical sensors for in situ, low concentration level analysis but will also open up an area of chemical sensor research where two-dimensional (second-order) in situ analyzers can be developed, utilizing the dynamics of dialysis as the means to discriminate the species in the temporal domain. For this reason, it is desirable to have a theoretical model that relates thermodynamic parameters of the chemical reactions (e.g., the stability constant of complexation)and hydrodynamic parameters of the flowing stream with concentrationvariations of ions collected into the receiving solution, so the process can be well understood and optimized to satisfy various analytical interests. In this paper, a simplified model to describe the mass transport of the CFDD process is developed. Also demonstrated here is a fiber optic heavy metal sensor in which the CFDD cell is directly interfaced with a fiber optic colorimetric detection system. The sensor is specific for the measurement of Pb(I1) and Cd(I1) in aqueous solutions, which is an important aspect in environmental protection and industrial waste discharge monitoring. In response to the increasing demand for the devices that are able to make in situ measurement of Pb(I1) and Cd(II), research has been focused (14) Yeager, H. L. Perfluorinured Ionomer Membranes; ACS Symposium Series 180; American Chemical Society, Washigton, DC, 1982; pp 25-39. (15) Cox, J. A.; Al-Shakshir, S . A w l . Lett. 1988,21(9), 175769. (16) Cox, J. A.; Olbrych, E.; Brajter, K. Anal. Chem. 1981,53, 1308-9. (17) Kasthurikrishnan, N.; Koropchak, J. A. A w l . Chem. 1993,65,857-62. (18) Huang, T. C.; Lin, Y. K. J . Chem. Eng. Jpn. 1987, 20 ( 5 ) . 511-7. (19) Berman, R. J.; Christian, G.D.; Burgess, L. W .Anal. Chem. 1990,62,206671.
0003-270Of 94fO366-2544$04.50/0
0 1994 Amerlcan Chemical Society
on the ion-selective electrode (ISE) technique,2G24because ISEs are inexpensive and easy to operate. However, heavy metal ISEs still suffer from two major disadvantages: insufficient long-term stability and selectivity. It is difficult to solve the problems by only using conventional approaches based on membrane modification. In addition, the monovariate nature of ISE detection offers no opportunity to take advantage of higher order calibration. In the proposed sensor, a semiselectivebut stable Nafion cation-exchangingmembrane and a reagent-renewing technique are used. Therefore, the sensor has very good long-term stability. Furthermore, replacing the single wavelength detector with a spectrophotometer can extend this sensor into a second-order device that has greater analytical capability than a conventional zeroorder sensor. THEORY The major difference between CFDD and conventional Donnan dialysis is that, in CFDD, the mass transport of a targeted ion is selectively enhanced and its dialysis process is driven beyond the conventional Donnan equilibrium by two factors: (1) diffusivity of the targeted ion in the membrane phase is increased and (2) concentration gradient of the targeted ion across the membrane is enhanced. Both effects are achieved simultaneously in CFDD by the chemical reaction between the targeted ions and the facilitation reagent in the receiving solution that alters the targeted ions into membrane incompatible species. In order to react with the targeted ions in the membrane phase so that the products can travel faster than the bare metal ions, reagents must penetrate into the membrane phase. Reagent penetration into the membrane phase can occur even if the reagent bears the same charge as the functional groups of the ion-exchange membrane.25 If the concentration of the receiving solution is not too high, the intermembrane concentration of reagent gradually decreases to zero in the region close to the sample. As metal ions permeate through the membrane, they meet with the reagent, which is thiosulfate in this study. Thiosulfate selectively complexes with the targeted Pb(I1) and Cd(I1) ions, forming 1:1 (metal ion-to-ligand) complexes in the low thiosulfate concentration region that isat thesamplesideofthemembrane. The diffusivities of Pb(I1) and Cd(I1) are increased because the neutralized complexes are not retained by functional groups of the membrane. The complexed species will diffuse in both directions, toward the receiving solution and the sample solution as well. However, diffusion toward the receiving solution predominates because as the complexed species moves toward the receiving solution, they can further react with thiosulfate to form complexes in a 1:2 or 1:3 ratio.26 Thus, the decreasing chemical potential from the sample side of the membrane toward the receiving solution side guarantees that the complexed ions diffuse predominantly in the direction ~~~
~
(20) Pungor, E. Ion-selectiue electrodes; Elsevier: Amsterdam, 1985; Vol. 22. (21) Borracino, A.; Campanella, L.; Sammatino, M. P.;Tomassetti, M.; Battilotti, M. Sensors Actuafors B 1992, 87 (1-3). 535-9. (22) Stevens, A. C.; Fresier, H.A d . Chim. Acta 1993, 248 (2), 315-21. (23) Anuar, K.; Hamdan, S. Talonto 1992, 39, (12), 1653-6. (24) Hampton, M. D.; Peters, C. A.; Wellington, L. A. Anal. Chim. Acta 1987, 194, 171.
(25) Walton, H.; Rocklin, R. D. Ion Exchange in Analytical Chemistry; CRC Press Inc.: Boca Raton, FL, 1990; Chapter 3. (26) Lange’s Handbook of Chemistry, 13th ed.; McGraw-Hill Book Co.: New York, 1985; pp 5-76.
from sample to receiving solution. Once entering the receiving solution, the complexed ions can not go back into the receiving solution, because they are rejected by the membrane phase. Since reagent concentration in the receiving solution is high, the amount of “free”, unreacted targeted ions that are capable of back-diffusion through the membrane is small. Therefore, the initially high analyte concentration gradient can be maintained for a much longer time than in a conventional Donnan dialysis process. The theoretical model of CFDD is developed for the application where the chemical sensors are exposed to the samples for a certain period of time and then placed back into the blank solution in the measurement. The dialysis cell consists of a piece very thin cation-exchange membrane that separates the sample and the receiving solution. The ions partitioned into the membrane phase can be considered to have a linear distribution over the very small thickness of the membrane. Thus, the model can be based on Fick’s first law of diffusion. The detailed derivations are given in the Appendix. When the sensor is exposed to the samples, the ions are dialyzed into the receiving solution. The concentration of ions in the receiving solution, C increases according to eq 1:
:
After a certain period of exposure time (re), the sensor is placed back into the blank solution. Ci then gradually decrease, described by eq 2, as the ions loaded in the membrane are released into the receiving solution:
c:
=
DaA(1+
+
DaAFrj3 &US - D, (1 {exp[-2Da(1
+ H - 0 V) X~
+ H - P)’]ti2
- exp[-(2DaAF1j3
+
eao
where C: is sample concentration. and C:(tE) are respectively the analyte concentrations loaded in the membrane phase and that in the receiving solution at the time (a)when the sample is replaced by the blank solution. The measurement time is denoted by t . D, is the diffusivity of the ion in the membrane phase. A and V represent the surface area and internal volume of the dialysis cell, respectively. u is the volumetric flow rate of the receiving solution, and a is the mass transport efficiency of the flowing stream in the sensor. 6 denotes the thickness of the membrane. The fraction number of the free ions in the receiving solution is represented by 8, which is inversely related to the equilibrium constant of the chemical reaction between the facilitation reagent and the targeted ions. Obviously, one always has 0 C j3 I 1. For this particular sensor, j3 is a function of the stability constants of thiosulfate-Pb(I1) or thiosulfateCd(I1) complexes. Fr and Fsdenote the conditional partition coefficients of ions in the membrane phase at the receiving solution side and the sample solution side, respectively. In this particular case, Fsand F r Ana&ticalChemistty, Vol. 66,No. 15, August I , 1994
2545
can be described by empirical adsorption models based on the following assumptions: (1) Adsorption can be considered as a monolayer phenomenon. The first layer of the functional groups around the pores of the membrane surface is activesites for adsorption. Monovalent activesites are neutralized once they are associated with ions. Therefore, no multilayer adsorption will occur; (2) The analyte concentration is very low, making interactions among the ions negligible. This ensures that diffusion of an ion in the membrane matrix is independent of others. Fsand Fr are given by
S
& .,,,.:.:;::::
............
OF
Ir
ifa
c; = Frc;f=
(4)
where Ka is the partition coefficientof the ion in a sodium form cation-exchangemembrane; Kci is the partition coefficient of the ith counter ion; C :i and C ii are concentrations of counter ions in thesample and receiving solutions, respectively; and are membrane-phase concentrations of ions at the samplesolution and receiving solution interfaces, respectively; C ifdenotes the concentration of free, unreacted ions, which is determined by the complexation equilibriumin the receiving solution; Za and Zi represent thevalance number of the analyte ion (the ion that is under consideration) and the ith counter ion, respectively. Finally, the factor Hin eqs 1 and 2 describes the Donnan effect, which is a function of the ionic strength difference between the sample and the receiving solutions:
c
c:
.,
:
where C and C denote the total concentration of counter ions in the receiving solution and the sample, respectively. is the concentration of functional groups of the ion-exchange membrane. In normal cases, one has 0 5 H 5 1. Equations 1 and 2 in combination describe the elution behavior of a particular ion. The key parameters are diffusivity, Da, and fraction number, 8, of the ions. The reciprocal of the fraction number of free ions, l/& can be viewed as the concentration gradient enhancement factor due to the chemical reaction. For a targeted ion, its Da and 1/p are selectively increased. It passes through the membrane easily, resulting in a high and symmetric elution peak. The nontargeted ions, on the other hand, are retained by the membrane functional groups (small Da) and do not have enhanced concentrationgradient (small 1 Therefore, they are slowly released from the membrane phase, resulting in low and tailed elution peaks. Selectivity of CFDD not only relies on different elution peak heights but also, more importantly, on different characteristic peak shapes of various ions. Indeed, it is the information-rich CFDD dynamics (characteristic elution peak shapes) that make it possible to use the technique as the temporal species discrimination mechanism in second-order devices. Other parameters in eqs
c~
/a).
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AnatyticalChemistry, Vol. 66, No. 15, August 1, 1994
Figure 1. Configurationof the sensor system: C, computer:CP, coupler: DC, dialysis cell; F, optical filters; IS,indicator syringe; RS, reagent syringe; LA, lock-in amplifier: LS, light source: M, mixer and mixing coil; MC, mechanical chopper; OC, optical cell; OF, optical fiber; PMT, photomultiplier tubes; S, sample.
1 and 2 are nonselective parameters, because they are not affected by the chemical reaction. These parameters do not determine the characteristic shape of the elution peaks. For example, the Donnan effect, H , nonselectively affects the mass transport of all ions according to the ionic strength difference between the sample and the receiving solutions. The surface area-to-volumeratio of the dialysiscell, A/V, affects the speed of the dialysis process to reach equilibrium state. EXPERIMENTAL SECTION Materials and Reagents. The sensor configuration is illustrated in Figure 1. A Nafion tubular membrane (1 100 EW, 610 pm o.d., 410 pm i.d., 90 mm long) with one end plugged is used as the dialysis cell (sensor head). Fused silica capillary column (250 pm i.d., 345 pm 0.d.; Polymicro Tech. Inc.), inserted into the bottom of the membrane cell, is used to deliver the receiving solution and to reduce the internal volume of the dialysis cell. The receiving solution flows out of the dialysis cell through Teflon tubing (430 pm i.d.; Alltech Associates, Inc., Deerfield, IL). It is mixed with a metal indicator, 4-(2-pyridylazo)resorcinol (PAR) solution in a Y-type mixer, which is connected with a mixing coil made of 100-mm Teflon tubing (430 pm i.d.) to ensure adequate mixing. During mixing, PAR chelates with transition metal ions, forming various orange-red complexes. The mixed solution then moves into an optical cell for detection. The optical cell is a glass capillary (800 pm o.d., 400 pm i.d., Drummond Scientific Co., Broomall, PA) with inlet and outlet capillaries attached at both ends. The illumination and signal fibers (Model HCN-HO125T- 14, Ensign-BickfordOptics Co., Avon, CT) are placed at the ends of the cell to perform transmissionmeasurement. The optical path length is 10mm. The signal fiber is connected with two beam-splitting fibers through a GRIN lens, which expands the beam diameter of the signal fiber for easier optical coupling. Each of the beamsplitting fibers are connected to photomultiplier tubes (Model IP28), through band pass filters (Microcoatings, Inc., Westford, MA, Models ML2-540 and ML2-660), 560 nm for Pb(I1) detection or 500 nm for Cd(I1) detection and the 660
nm for reference. A pair of photometers (Model 126; Pacific Instruments) amplify signals from PMTs and send the output to a lock-in amplifier (Model SR575; Stanford Research Systems, Inc.). The lock-in amplifier amplifies the differential signal, converts it into digital form, and sends it to a Leading Edge PC. The computer is used to acquire, store, and display data with software provided by Stanford Research. The indicator and receiving solutions are delivered by a microinjection syringe pump (Model CMA/ 100;Carnegie-Medicin, Solna, Sweden) with two syringes (10 and 2.5 mL; Hamilton Co., Reno, NV), whose diameters set the volumetric flow rate ratio of receiving solution to indicator solution at 3:l. The light source is a focused lens-end tungsten lamp (Model L1024; Gilway Technical Lamp, Woburn, MA). A mechanical chopper (Model SR540, Stanford Research Systems, Inc., Palo Alto, CA) modulates the light at 32 Hz. Nafion tubular membrane was obtained from Perma Pure Products. Inc. The metal indicator 4-(2-pyridylazo)resorcinol (PAR) was purchased from Aldrich Chemical Co. (Milwaukee, WI). Sodium borate, sodium thiosulfate, sodium acetate, and acetic acid (aldehyde free) are analytical degree and were obtained from Baker Inc. Sodium hydroxide solution was purchased from VWR company. All nitrates of Pb(II), Cd(II), Cu(II), Ni(II), Mn(II), Fe(III), and Zn(I1) are analytical grade and were obtained from Aldrich Chemical Co. Deionized water used in this experiment was produced by a Nanopure D3700 deionization system. Procedures. Receiving solution is prepared by dissolving 12.4 g of sodium thiosulfate into 500 mL sodium acetateacetic acid buffer. The buffer contains 0.05 M sodium acetate and required an amount of aldehyde-free acetic acid to adjust the pH to 5.1. At this pH, the complexation of acetate with metal ions is weak so that its interference to thiosulfate's complexation is negligible. The detection solution is prepared by adding 0.059 g of PAR to 250 mL of pH 10.8 sodium borate buffer. The buffer is prepared by mixing 125 mL of 0.1 M sodium borate solution and 60.6 mL of 0.4 M NaOH and diluting it to 250 mL with distilled deionized (DI) water. The sample solutions are prepared by diluting the stock solutions, which are prepared from metal nitrates. The pH of the sample solutions is in the range of 5.6-5.9, depending on the pH of the DI water. Nafion membrane is converted from protonated form into sodium form by immersing it into 0.1 N HCl for 2 h and then in a 0.8 M NaNO3-.2 M NaOH mixture for 10 h. After that time, the membrane is rinsed with DI water. Before measurement, the sensor head is filled with the receiving solution and immersed in DI 'water for more than 12 h to stabilize the membrane microstructure in the measuring environment. The sample volume for all measurements is 250 mL. Sample solutions are stirred with a magnetic stirring bar during measurement. RESULTS AND DISCUSSION The elution peaks of different ions are shown in Figure 2. Using the theoretical model, computer simulation of the CFDD process was performed. The simulated elution peaks are also displayed in Figure 2 for comparison. Selective parameters, Da and 0 were optimized to best fit the simulated profiles with the experimental results while nonselective parameters such as F,, F,, and a were predetermined and fixed during the
Zn(ll) Da=l.18x10-"mZ/sec.
E
h
8
9
-0.1
I0
I
5
I
I
1
10
15
20
Time:
0.3
I 25
minutes
Co(II) D a = 7 . 1 0 ~ 1 0 - ~ ~ m ~ / s e c .
0.25
gm
0.2
n
a
0.15 0.1
0.05 0
-0.051 0
I
I
I
I
5
10
15
20
Time:
I
25
minutes
Flgure 2. Elution profiles. of different Ions: dotted lines, measured profiles: solM lines, simulated profiles based on the model; Pb(I1) and W I I ) concentration, 2.0 X 104 M: Zn(I1) and W I I ) concentratlon, 4.0 X 1o-B M: flow rate of the recehdng solution, 15 pL/min.
Table 1. Parameten h o d In Stmulath
parameters ions
Pb(I1) Cd(I1) Co(I1) Zn(I1)
D,(mZ/s) 3.9 X 10-" 4.8 X 7.1 X 1.18 X
fi
Fs
F,
a
c(AU/cm.mol)
0.028 0.043 0.61 0.5
1.60 1.30 1.50 1.55
1.38 1.12 1.30 1.34
0.62 0.62 0.62 0.62
1.34X 105 8.06 X 104 1.81 X lo5 1.24 X lo5
curve-fitting process. Predetermination of a, F,, and Fs introduces an ambiguity within the constraints of 0 < a < 1 and the relative affinity of the ions to the membrane phase.27 Due to the ambiguity, the simulation does not yield accurate Da and 8. However, it demonstrates how these key factors effectively determine the elution behavior of ions and, hence, the sensor specificity. Da and j3 obtained from the simulation are in a reasonable range for the different sets of F,,F,,and a values used, and the sequence of selective parameters for different ions is consistent with predictions of the theory. Absorptivitiesused in the simulation werecalculated by adding metal ions directly to the receiving solution and measuring the signal intensity. The parameters are shown in Table 1. The sensor responses to a series of concentrations of Pb(N03)2 and Cd(NO& at different flow rates of receiving solution are shown in Figure 3. Each response is calculated at a steady state of dialysis processes. A slower flow rate (27) Korkisch.Handbook of Ion Exchange Resin?: Their Application to Inorgawk Analytical Chemistry; CRC Pres,Inc.: Boca Raton, FL, 1989; Vol. 1.
AnalyticaiChemistty, Voi. 66, No. 15, August 1, 1994
2547
16
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Pb(II) concentration: pM
Flow rates:
Q
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Q
e
9
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e
A A X
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Cd(II) concentration: pM Figuro 3. Sensor response at different flow rate of the recehring solution: (A) Pb(1 I) measurement; (B)Cd(I I) measurement. Responses at dlfferent flow rate of recelvlng solutlon: (El)10; (0)15; (A)20; (X): 25 pL/mln.
(smaller u ) yields higher sensitivity, as predicted by the model. At 25 pL/min flow rate, the slopes of Pb(I1) and Cd(I1) response curves (linear portion) are 0.24 and 0.13 AU/pM, respectively. They increase to 0.53 and 0.29 AU/pM, respectively, when the flow rate decrease to 10 pL/min. A slow flow rate also narrows the dynamic range of the sensor, as shown by the flattened responsecurve at high concentrations. Since this nonlinearity is flow-rate dependent, it can be attributed in part to incomplete chelation between the metal ions and indicator (PAR) when the metal ion concentration in the receiving solution is high. The effect of metal ion hydrolysis is avoided in this study where the analyte concentrations are low ( < l o 5 M) and the sample pH is in the range from 5.6 to 5.9, in which almost all Pb(I1) and Cd(I1) exist in free ion form.28 It is also found that the flow rate of receiving solution affects the sensor responses to the targeted ions and other ions differently. Figure 4 shows that Cd(II)/ Cu(1I) and Cd(II)/Ni(II) response ratios increaseas the flow rate is increased, indicating that the Cd(I1) response does not decrease as fast as the Cu(I1) and Ni(II1) responses do. This can be attributed to the improvement of ligand supply at the (28) Base, C. F.,Jr. The Hydro/ysis ofCarlom; John Wiley & Sons: New York, 1972.
2548
yllmin.
Figures. EffectofthereceMngsdutionflowratetothesensorrespcnse of different lons. (0)Cd/Cu response ratio; (m) Cd/NI response ratlo; Concentration of metal lons, 2 X 104 M; recehring solution, 0.1 M Na2S203,unbuffered.
Amlyt/ca/Cbemisby, Vol. 66, No. 15, August 1, 1994
membrane interface as the reagent flow rate increases. Since Cd(I1) forms complex with the reagent, dilution of the metal ions in the receiving solution caused by increased flow rate is compensated by the improvement of ligand supply, which results in an increased concentration enhancement factor, 1/& to increase the mass transport. For ions forming a labile complex with thiosulfate, such as Cu(I1) and Ni(II), the compensation effect is small. Since their mass transport is mainly driven by the Donnan effect that is not affected by the flow rate of the receiving solution, a fast flow rate only dilutes them and reduces the signals. Therefore, for a given flow rate increment, the signals of Cu(I1) and Ni(I1) will decrease faster than that of Cd(II), resulting in improved selectivity of Cd(I1) over Ni(I1) and Cu(I1). This phenomenon may be used to optimize selectivity to a given analyte in a specific application by simply adjusting the flow rate of the receiving solution. The high sensitivity of the sensor is demonstrated by measuring samples containing 5 X l o 9 M Pb(I1) or 5 X l o 9 M Cd(I1) in stopped-flow preconcentration mode. For each measurement, the receiving solution flow was stopped for a fixed period of time to preconcentrate the ions. Then, the flow was resumed to move the ions into the optical cell for detection. As shown in Figure 5A, Cd(1I) preconcentration reached equilibrium in about 50 min, whereas Pb(I1) required more than 70 min. The result is consistent with the fact that, compared to Cd(II), Pb(I1) has a smaller diffusivity in a sulfonated ion-exchange polymer matrix2’ and a smaller free ion fraction number, 8, calculated with eq A5 using published stability constants.26 The limit of the ion enrichment factor is imposed by the osmotic flow of water from the relatively low ionic strength sample solution into the receiving solution. The actual enrichment factor is not larger than 2 orders of magnitude, estimated by comparing the stopped-flowresponses to the results of direct injection of sample indicator solutions of known concentration into the optical cell. The low limit of detection for Cd(I1) or Pb(I1) is 3 X l o 9 M with 20-min preconcentration and a signal to noise ratio of 3.0. The preconcentration speed can be increased by increasing the
0’05
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/ 0
,
, 10
,
, 20
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,
,
30
K(I) concentration:
,
,
40
I 50
mM
Flgure 6. Effect of the counter (co-existing) Ion concentration In the sample matrix to the sensor response: (El)experlmental;(0)calculated based on the model; flow rate of the recehrlng solution, 15 pUmln; analyte, 1.0 X 10“ M Pb(I1).
0
10
I
I
20
30
40
Accumulation time: minutes
Fburr 1. Measurementof low concentrationsamples uslng stoppedflow preconcentratlonmode. (A) Responses of measuring(El) Pb(I1) and (0)CCyII) with different preconcentratlon times. Sample concentration, 5 X 10-8 M. (6) Improvement of ion accumulation speed by reducing the internal volume (from 14 to 1.6 pL) of the dialysis cell: (El) Improved; (0)original.
surface area to internal volume ratio of dialysis cell, as predicted by the model. Figure 5B compares the preconcentration speed of the old sensor with an improved sensor with the same cell surface area but with an internal volume of 1.6 pL, A 5-min preconcentration with the improved sensor is equivalent to 20-min preconcentration with the old one, which has an internal volume of 14 pL. Several factors relevant to the chemical conditions of the sample and receiving the solutions have significant influence on the dialysis process. The first one is the counter ions (or called co-existing ions) in the sample. The counter ions compete with targeted ions for the ion-exchangingsites on the membrane surface, causing a decreased amount of targeted ions partitioned in the membrane in a given period of time. This is confirmed by measuring the samples added with different amounts of K(1) that do not form colored species with PAR. Figure 6 shows that the Pb(I1) response starts to decrease as K(1) concentration exceeds about 5 mM, from which the competition effect becomes significant. The “transition point” depends on the relative membrane affinity of the counter ion compared to the targeted ion. If the counter ions have high affinity to the membrane, they have a strong
-
-
competition effect so the response decrease may occur at low concentrations. However, as pointed out by Cox,’ these ions, such as Ca(II), Mg(I1) or Al(III), can block the electrostatic attraction of the functional groups and, hence, increase the diffusivity of other ions. Therefore, the overall result may look complicated if these ions are involved. The simulated K(1) competition effect using the model is also displayed in Figure 6 for comparison. It should be noted that the overall response decrease is also caused in part by a decrease of the Donnan effect as the result of addition of K(1) to the sample solution. The second factor is the pH of the receiving solution. Stability constants of metal ion-thiosulfate complexes and, hence, dialysis selectivity, vary with pH. Metal ion speciation at the interface of the membrane-sample solution and, hence, the recovery rate of Pb(I1) and Cd(I1) also depend on pH of the receiving solution. Stabilizing the pH value by buffering the receiving solution is critical to obtain stable, consistent responses. It can be expected that decreasing pH will further suppress interferences and improve the recovery rate of the targeted ions. However, lowering pH will be limited by instability of thiosulfate ions in an acidic environment. The third factor that affects the dialysis process is reagent concentration in the receiving solution. If the reagent concentration is too high, the partition behavior of metal ions at the sample-membrane interface is affected. Figure 7 compares the elution profiles of Cd(I1) and Co(I1) at different reagent concentrations. At a high concentration, the reagent (thiosulfate ions) penetrates through the cation-exchange membrane and appears at the membrane-sample interface. The reagent then complexeswith the targeted ions, Cd(I1) in this case, forming neutral or negatively charged complexes that are not favorable for partitioning into the membrane. For this reason, the transport rate of Cd(I1) with a 300 mM sodium thiosulfate receiving solution shows a significant decrease (see Figure 7A), as compared by the responses that use 100 and 25 mM thiosulfate receiving solutions. In contrast, Co(I1) transport is primarily a function of the Donnan effect rather than chemical facilitation. The transport rate can be Analyjical Chemistry, Vol. 66,No. 15, August 1, 1994
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1
0.4 I
-0.05
0
I
I
I
I
5
10
15
20
25
Time: minutes I
0.5 I
8
E 8
n
ACKNOWLEDGMENT This work was supported by the Center for Analytical Chemistry (CPAC), a National Science Foundation Industry/ University Cooperative Research Center at the University of Washington. Z. Lin would like to thank Dr. Leslie Moore and Dianna Blair for the valuable discussions.
0.2
a
0.1
0
-0.1
0
5
15
10
20
25
Time: minutes
Flgwe 7. Effect of the ionic strength and thiosulfate concentration of the receivingsolution to the elution profiles of different ions. (A) Cd(I1); (e) Co(I1). NazS203concentration, as labeled. Cd(I1) concentration, 2.0 X lod M. Co(I1)concentration, 4.0 X 10" M. Flow rate of the receiving solution, 15 pL/min. Table 2. Sensor Pb(I1) Selectlvttya
Pb(II)/Zn(II) Pb(II)/Ni(II) Pb(II)/Mn(II)
Response Ratios &/Ri 23.3 Pb(II)/Co(II) 29.2 31.1
Pb(II)/Fe(III) Pb(II)/Cu(II)
24.1 152.8 12.2
0 Thiosulfate concentration, 25 m M . Buffer concentration, 25 m M . Receiving solution flow rate, 15 pL/min.
dramatically increased by increasing the sodium thiosulfate concentration in the receiving solution, as shown by the response (300 mM) in Figure 7B, and reduced to be almost undetectable by reducing the ionic strength of the receiving solution (25 mM thiosulfate; dashed line of Figure 7B). Experiments with Pb(I1) produce similar results. This phenomenon can be used to increase the sensor selectivity of the targeted ions, Pb(I1) and Cd(II), over other transition metals by using a dilute receiving solution. Table 2 lists the Pb(I1) selectivity coefficient of the sensor using 25 mM sodium thiosulfate as the receiving solution. The price for higher selectivity is that the low ionic concentration of the receiving solution makes the measurement more sensitive to the fluctuation of sample ionic strength. CONCLUSION Chemically facilitated Donnan dialysis can be used as the sampling stage of metal ion sensors that utilize enhanced mass transport of targeted ions by facilitation reagents. The sensor 2550
selectivity is affected by reagent concentration, ionic strength, flow rate, and pH of the receiving solution. The sensor sensitivity and dynamic range are a function of the flow rate of the receiving solution. To improve selectivity, the nonselective Donnan effect should be decreased while the selective chemical facilitation factor is maintained. A major disadvantage of the sensor is the long analysis time. Analysis time can be significantly reduced if the membrane thickness and the internal (void) volume of the sensor are reduced. Substrate-supported thin membrane and micromachining are two key techniques in fabricating truly usable sensors that have short analysis time and consistent sensor-to-sensor performance. Continued research also needs to focus on the improvement of sensor selectivity, which can be achieved using the approach of second-order instrumentation. A secondorder sensor that combines the CFDD device with a photodiode array s p e ~ t r o m e t ecan r ~ ~take full advantage of the selectivity of both domains by using second order tensorial calibration methods.
Analytical Chemlstry, Vol. 66, No. 15, August 1, 1994
APPENDIX If the diffusivity and concentration of the counter ion in the receiving solution are much greater than those of the analyte ion, then based upon the Nernst-Planck equation3O and the charge neutrality restriction, the analyte ion flux (Ja) across a piece of thin, flat ion-exchange membrane can be expressed as dea Ja=Da (dx
- :+-
ZaCadCC ZcCcdr
)
(All
where c i s the ion concentration in the membrane phase; the subscripts a and c refer to the analyte ions and counter ions, respectively. The derivative terms in eq A1 can be approximated by the concentration differences across the membrane divided by the membrane thickness, 6, assuming the ion concentrations have a linear distribution over the small thickness of membrane. Using the empirical adsorption model (eqs 5 and 6 ) to relate the membrane-phase concentration with the solution-phase concentration and approximating the derivative terms of eq A1 with the concentration differences across the membrane, one obtains
where the fraction number of free ions in the receiving solution (29) Lin, Z.; Booksh, K. S.; Burgess, L. W.; Kowalski, B. R. AMI. Chem.,following
paper in this issue. (30) Hwang, S.-T.;Kammermayer, K. Techniques of Chemisrry; John Wiley 8r Sons: New York, 1975; Vol. 11, pp 134-47.
is proportional to the sum of the fraction numbers ( P i ) for each corresponding complexation step before the ion is neutralized?
is given by d e a - - 20,(1 + H - @)C, --
a2
dt
Pa
+ k,[L*] + k , k * [ P - ] 2+ ... + k , ... k,[l*lf 1 + k,[L"] + ... k, ... k/[L"lf+ ... + k, ... k,... kn[Lm-]" 1
Using the concentration of analyte ion loaded into the membrane (&) as the initial condition, integration of eq 16 results in
e, = caoexp[ -2D,( 1 + H - &] a2
(A31 where ki is the stability constants for each step of complexation; m is the valence of the ligand; n is the maximum number of ligand associated with the metal ion; andfis the number of ligands needed to form the least positively charged species. Given a constant volumetric flow rate, u, of receiving solution, the internal volume V, and the surface area of the dialysis cell, the concentration change rate of a particular analyte ion in the receiving solution can be expressed by the following mass balance equation:
Integration of the equation yields the eq 1 that describes the ion concentration increase in the receiving solution:
c:
D,AF,(l + H ) C i = D,AF$( 1 - H) + a d 11 - exp[-(D,AFrj3(1 - H) +
When the sample is replaced by the blank solution, the analyte ion concentration in the membrane decreases. The decreasing rate of analyte ion concentration in the membrane (31) Christian, G. D. Analytical Chemistry, 4th ed.; John Wiley & Sons: New York, 1986; pp 235-6.
(A61
(A7)
Using eq 17 as a sample concentration, analyte concentration change rate in the dialysis cell can be expressed as
where C:(tE) is the initial analyte concentration in the receiving solution, which is calculated from eq 12 at the end of sensor exposing time (tE). Equation 18 then can be integrated to yield
c;
D,A(1+ H ) c a o
= D,AF$
+ US - D,( 1 + H - 8)-V6 X
(exp[ -2D,( 1
+ H - &-] - exp[ -(2D,AFrB + a2
Received for revlew October 19, 1993. Accepted M a y 4, 1994. Abstract published in Aduance ACS Abstracts, June 15, 1994.
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