Anal. Chem. 2001, 73, 5468-5471
Use of Ultrafiltration on the Analysis of Low Molecular Weight Complexing Molecules. Analysis of Iminodiacetic Acid at Constant Ionic Strength Ignacio Moreno-Villoslada,*,† Eduardo Quiroz,† Carla Mun˜oz,‡ and Bernabe´ L. Rivas‡,§
Chemistry Institute, Faculty of Sciences, Universidad Austral de Chile, Casilla 567, Valdivia, Chile, and Department of Polymers, Faculty of Chemistry, University of Concepcio´ n, Casilla 160-C, Concepcio´ n, Chile
Low molecular weight complexing molecules may be indirectly analyzed by ultrafiltration with the aid of a watersoluble polymer. The theory concerned is developed and the analysis of iminodiacetic acid (IDAA) is performed by ultrafiltration of aqueous solutions containing poly(sodium-4-styrenesulfonate) (PSS), Cu(NO3)2, and IDAA in variable concentrations. The technique allows measuring IDAA in a range of concentrations between 10-4 M and 10-5 M when a 1.6 × 10-4 M Cu2+ solution is ultrafiltered in the presence of PSS and IDAA. Ultrafiltration of aqueous solutions through a known exclusionrate ultrafiltration membrane allows separation of particles whose size is greater than the membrane pores from smaller molecules, with potential applications in processing waste solutions, preconcentration of solutes for analysis or recuperation, and separation science.1-8 This technique has been used to evaluate the interactions of metal ions with water-soluble polymers,3-14 since the former stay retained by the polymer inside the ultrafiltration cell when high interaction rates are found. Polyelectrolytes are an interesting group of water-soluble polymers that undergo electrostatic interactions with metal ions. These interactions are very dependent on the ionic strength.13,14 When the ionic strength is kept constant during filtration, the ratio of metal ions bound to * Fax: 56-63-221597. E-mail:
[email protected]. † Universidad Austral de Chile. ‡ University of Concepcio ´ n. § Fax: 56-41-245974. E-mail:
[email protected]. (1) Kunikane, S.; Magara, Y.; Itoh, M.; Tanaka, O. J. Membrane Sci. 1995, 102, 149-154. (2) Tran-Ha, M. H.; Wiley, D. E. J. Membrane Sci. 1998, 145, 99-110. (3) Uludag, Y.; O ¨ zbelge, H. O ¨ .; Yilmaz, L. J. Membr. Sci. 1997, 129, 93-99. (4) Geckeler, K. E.; Lange, G.; Eberhardt, H.; Bayer, E. Pure Appl. Chem. 1980, 52, 1883-1905. (5) Bayer, E.; Eberhardt, H.; Grathwohl, P. A.; Geckeler, K. E. Isr. J. Chem. 1985, 26, 40-47. (6) Geckeler, K. E.; Bayer, E.; Spivakov, B. Ya.; Shkinev, V. M.; Vorob’eva, G. A. Anal. Chim. Acta 1986, 189, 285-292. (7) Geckeler, K. E.; Bayer, E.; Vorob’eva, G. A.; Spivakov, B. Ya. Anal. Chim. Acta 1990, 230, 171-174. (8) Rivas, B. L.; Moreno-Villoslada, I. J. Appl. Polym. Sci. 1998, 69, 817-824. (9) Rivas, B. L.; Geckeler, K. E. Adv. Polym. Sci. 1992, 102, 171-188. (10) Rivas, B. L.; Pereira, E.; Martı´nez, E.; Moreno-Villoslada, I. Bol. Soc. Chil. Quim. 2000, 45, 199-205. (11) Rivas, B. L.; Moreno-Villoslada, I. Chem. Lett. 2000, 166-167. (12) Rivas, B. L.; Moreno-Villoslada, I. J. Phys. Chem. B 1998, 102, 11024-11028. (13) Rivas, B. L.; Moreno-Villoslada, I. J. Phys. Chem. B 1998, 102, 6994-6999. (14) Rivas, B. L.; Moreno-Villoslada, I. J. Membr. Sci. 2000, 178, 165-170.
5468 Analytical Chemistry, Vol. 73, No. 22, November 15, 2001
the polymer versus metal ions free in the solution is practically constant when the polymer is in excess over the metal species. Under such conditions, the retention profiles have been mathematically described under a model previously discussed.13 The study of multicomponent systems, including low molecular weight molecules by ultrafiltration is under development nowadays. We recently observed that when iminodiacetic acid (IDAA) is added to a solution containing poly(sodium-4-styrenesulfonate) (PSS) and Cu2+, its ability to form coordination complexes with the metal ion yields in a displacement of the metal species bound to the polymer to favor the complex formation.15 The complex is eluted out of the ultrafiltration cell during the ultrafiltration experiment. Current analytical methods for IDAA are UV-vis spectrophotometry and other techniques that use the same method as detector. When using Cu2+ as chromophore, a detection limit is found to be around 10-4 M of complex concentration. In the present work, the theory involved in the indirect analysis of a low molecular weight complexing molecule (LMWCM) by ultrafiltration is developed. The problem of analyzing a LMWCM concentration is changed to analyzing a metal species concentration, resulting in a potential increase in the sensibility. Some results concerning the analysis of IDAA concentrations by the use of the ultrafiltration technique of several aqueous solutions containing constant amounts of PSS, Cu(NO3)2, NaNO3, and variable amounts of IDAA in the range of 10-4 to 10-6 M, ultrafiltered with a NaNO3 aqueous solution, will be shown. The Cu2+ concentrations in the filtrates will be analyzed by atomic absorption spectrometry, a technique that allows determining concentrations lower than 10-6 M. The results will be compared with the IDAA concentration of the solutions. THEORY Retention (R) of a certain metal ion (M) in ultrafiltration experiments is defined as the fraction of metal ion remaining in the cell per unit of metal ion at every instant, that is, R ) Mc/ Minit, where Mc is the absolute amount of metal ions in the cell, and Minit is the initial absolute metal ion amount. The filtration factor (F) is defined as the volume ratio of the filtrate, Vf, versus the volume of the solution in the cell, Vc. The species present in the system under study are shown and related in Scheme 1. The (15) Moreno-Villoslada, I.; Rivas, B. L. Macromol. Rapid Commun. 2001, 22, 1191-1193. 10.1021/ac010476g CCC: $20.00
© 2001 American Chemical Society Published on Web 10/05/2001
Scheme 1
species bound to the polymer are not able to pass through the membrane, but small ions, molecules, and complexes are allowed to exit the cell during filtration. If the volume inside the cell is kept constant during the experiment, R, which is function of F, can be expressed in terms of concentrations as follows,
decay on cfree and cLMWCM, respectively, and cfree-init and cLMWCM-init are the respective initial values (F ) 0). When F ) 0, R ) 1, and consequently,
cfree-init )
R(F) )
(1 + K2f) LMWCM-init cinit c (1 + K1f) (1 + K1f)
(4)
cfree(F) + cpolymer(F) + cLMWCM(F) + cpolymer-LMWCM(F) and
cinit (1) cfree
cpolymer
where is the concentration of M free in the solution, is the concentration of M bound to the polymer, cLMWCM is the concentration of M bound to the complexing molecule, cpolymer-LMWCM is the concentration of M both bound to the polymer and to LMWCM, and cinit is the initial metal concentration. When the polymer is in excess over LMWCM and M, its concentration, or the concentration of binding sites, may be assumed to be constant, and then cpolymer ) K1fcfree, where K1f is an apparent formation constant for the interaction of the polymer with free M at these experimental conditions, and cpolymer-LMWCM ) K2fcLMWCM, where K2f is an apparent formation constant for the interaction of the polymer with the complex M/LMWCM at these experimental conditions. Then
R(F) )
(1 + K1f)cfree(F) + (1 + K2f)cLMWCM(F) cinit
(2)
R(F) ) exp(-k1F) + (1 + K2f)[ exp(-k2F) - exp(-k1F)] LMWCM-init c (5) cinit The total concentration of LMWCM at the beginning of the experiment ([LMWCM]), that is, the concentration of LMWCM in the samples to be analyzed, is given by
[LMWCM] ) [LMWCM]free-init + cLMWCM-init + cpolymer-LMWCM-init (6) where [LMWCM]free-init is the concentration of free complexing molecule, and -init is applied for initial conditions. If the ability of LMWCM for forming coordinating bonds with M is high enough, the concentration of free LMWCM may be negligible, and then, it can be assumed that
cLMWCM-init ) On the basis of previous work,13 an exponential decay on cfree and cLMWCM during filtration may be assumed so that
1 [LMWCM] 1 + K2f
(7)
Substituting,
R(F) ) (1 + K1f)cfree-initexp(-k1F) + (1 + K2f)cLMWCM-initexp(-k2F)
R(F) ) exp(-k1F) +
(3)
[exp(-k2F) - exp(-k1F)] [LMWCM] (8) cinit
where k1 and k2 are experimental parameters related with the
Consequently, for every single experiment, the retention profile
cinit
Analytical Chemistry, Vol. 73, No. 22, November 15, 2001
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Table 1. Values for the Variables of the Corresponding Experiments concn (M) experiment
PSS
PSS-IDAA-Cu-01 PSS-IDAA-Cu-02 PSS-IDAA-Cu-03 PSS-IDAA-Cu-04 PSS-IDAA-Cu-05
0.02 0.02 0.02 0.02 0.02
a
init
Cu2+
1.6 × 10-4 1.6 × 10-4 1.6 × 10-4 1.6 × 10-4 1.6 × 10-4
NaNO3a
init IDAA
pHa
0.04 0.04 0.04 0.04 0.04
0 5 × 10-6 2 × 10-5 5 × 10-5 1 × 10-4
4 4 4 4 4
Values for both the cell solution and the reservoir solution.
appears as a sum of two exponential functions, since
(
R(F) ) 1 -
)
[LMWCM] init
c
exp(-k1F) + [LMWCM] cinit
exp(-k2F) (9)
Figure 1. Experimental retention values (R) as a function of F: (*) PSS-IDAA-Cu-01, (×) PSS-IDAA-Cu-02, (2) PSS-IDAA-Cu-03, (9) PSS-IDAA-Cu-04, and ([) PSS-IDAA-Cu-05, and adjustment following eq 9.
Considering a set of experiments in which the total initial concentration of LMWCM is changing and the ionic strength is kept constant,14 it is possible to think that the values of k1 and k2 should not differ much from one experiment to the next. Under this approximation, for a given F value, there is a linear dependency of R on the concentration of LMWCM in the samples, since
R ) a + b[LMWCM]
(10)
where a ) exp(-k1F) and b ) [exp(-k2F) - exp(-k1F)]/cinit, as can be deduced from eq 8. EXPERIMENTAL SECTION Reagents. Commercially available poly(sodium 4-styrenesulfonate) (PSS, monomeric unit molecular mass ) 206.2) (Aldrich, synthesized from the para-substituted monomer), iminodiacetic acid (IDAA, MW ) 133.10) (Aldrich), Cu(NO3)2, and NaNO3 (Merck) were used to prepare initial solutions. NaNO3 was used to maintain a constant ionic strength. The pH was adjusted with NaOH and HNO3. Equipment. The unit used for retention studies consisted of a filtration cell equipped with a magnetic stirrer, a membrane with an exclusion rating of 3000, 10 000, or 100 000 Da (Filtron, Pall Gelman), a reservoir, a selector, and a pressure source. Metal ion concentrations were measured by atomic absorption on a Unicam Solaar M5 spectrometer. The pH was controlled on a H. Ju¨rgens & Co. pH meter. Procedure. Prior to use, the PSS was ultrafiltered over a 100 000 Da ultrafiltration membrane with water in the presence of 0.1 M NaNO3, pH 4, and then with pure water. The polymeric fraction obtained was freeze-dried. PSS, IDAA, and metal salts were dissolved in 20 mL of twice-distilled water, adjusting the pH to 4. The exact amounts used are listed in Table 1. A 0.04 M NaNO3 solution at pH 4 was placed in the reservoir. The filtration runs were carried out over a membrane with an exclusion rating of 5000 Da under a total pressure of 3 bar, keeping the solution volume in the cell constant by creating a continuous flux of liquid 5470
Analytical Chemistry, Vol. 73, No. 22, November 15, 2001
Figure 2. Retention as a function of [IDAA] at constant F values: ([) F ) 0, (9) F ) 1, (2) F ) 2, (×) F ) 3, (*) F ) 4, (b) F ) 5, (+) F ) 6, (-) F ) 7, and adjustment following eq 10 (see Table 2 for values of a and b). Table 2. Values of the Parameters a and ba and the Square Regression Factors (R2) F
a
b
R2
0 1 2 3 4 5 6 7
1 0.9086 0.8177 0.7251 0.6378 0.5587 0.4849 0.4179
0 -2635.5 -3346.2 -3270.5 -2964.4 -2640 -2314.5 -1992.7
1.0000 0.9838 0.9793 0.979 0.9806 0.9833 0.9746 0.9584
a Corresponding to the expressions of the linear adjustment of the values of R as a function of [IDAA] at constant F.
through the cell solution from the reservoir. The filtrates were collected in fractions, and the copper concentrations were analyzed. RESULTS AND DISCUSSION The presence of IDAA in the bulk of the solutions produces differences on the retention profiles of Cu2+, which are shown in
Table 3. Calculated [IDAA] as a Function of F from the Experimental Retention Values and the Corresponding Mean Values Using Equation 8a F
PSS-IDAA-Cu-01
PSS-IDAA-Cu-02
PSS-IDAA-Cu-03
PSS-IDAA-Cu-04
PSS-IDAA-Cu-05
1 2 3 4 5 6 7 mean values
-1.5525 × 10-5 -1.0404 × 10-5 -7.9896 × 10-6 -5.2977 × 10-6 -2.8222 × 10-6 2.1115 × 10-7 3.4256 × 10-6 -5.486 × 10-6
-1.3293 × 10-5 -1.6015 × 10-5 -1.1647 × 10-5 -6.3437 × 10-6 5.2583 × 10-8 6.8315 × 10-6 1.4528 × 10-5 -3.6982 × 10-6
3.1302 × 10-5 2.2687 × 10-5 1.875 × 10-5 1.6364 × 10-5 1.4354 × 10-5 1.4965 × 10-5 1.7022 × 10-5 1.9349 × 10-5
7.0387 × 10-5 6.1251 × 10-5 5.5983 × 10-5 5.3272 × 10-5 5.2134 × 10-5 5.4297 × 10-5 5.7268 × 10-5 5.7799 × 10-5
1.40301 × 10-4 1.16136 × 10-4 9.98445 × 10-5 9.00748 × 10-5 8.55012 × 10-5 8.33689 × 10-5 8.24587 × 10-5 9.96692 × 10-5
a
k1 ) 0.1187; k2 ) 0.48
Figure 4. Plot of ln(bcinit + a) versus F. Figure 3. Plot of ln a ([) and ln R when [IDAA] ) 0 (9) versus F and plot of the functions ln a ) -0.1187F and ln a ) -0.1171F as the respective linear adjustments (square regression factors, 0.9915 and 0.9939, respectively).
Figure 1, where R is plotted versus F. For a given F value, the value of R may be plotted as a function of the IDAA concentration. It is found that these values follow a straight linear adjustment (eq 10), as can be seen in Figure 2. As errors in the calculation of R accumulate as F increases, only values up to F ) 7 are considered, thus obtaining square regression factors higher than 0.95 (see Table 2). The values of the logarithm of the parameter a are plotted versus F in Figure 3, and k1 is obtained. Note that the values of k1 do not differ much one from the other, and it can be assumed that k1 ) 0.1187 for all of the experiments, a value that is very close to the one obtained by direct ultrafiltration of Cu2+ in the absence of IDAA, which is 0.1171. The plot of ln(bcinit + a) versus F shows deviations from linearity, as is shown in Figure 4, that are attributed to a dependency of k2 on F as a result of the chemical conditions of the solution, which may include amounts of the reactants and polymer conformation, at every instant during filtration. Therefore, an approximated value of k2 for every experiment must be calculated in order to obtain a better adjustment in the correlation with [LMWCM] from the experimental values of the retention by means of eq 8: for k2 ) 0.48 and k1 ) 0.1187, the IDAA concentration of the samples may be deduced using eq 10, which yields for every experiment a set of [IDAA] values from the values of R as a function of F (see Table 3). Although good results are found for values of [IDAA] up to
10-5 M, when lower IDAA concentrations are used, analysis and real values lack agreement, since the experimental retention profiles are very close to the retention profile obtained in the absence of IDAA. All of the single retention profiles may be mathematically described by means of eq 9, as is shown by the lines in Figure 1. CONCLUSIONS The ultrafiltration technique can be used to analyze concentrations of low molecular weight complexing molecules by evaluating the retention of a metal ion in the presence of a polyelectrolyte. The sensitivity of the analysis is determined by the sensitivity of the equipment used to analyze the metal ion. Atomic absorption spectrometry is a developed technique that allows quantifying metal ions in the range of micrograms per milliliter or per liter. Some analyses of IDAA in the presence of Cu2+ and PSS have been performed, and the optimal analyses are obtained for concentrations of IDAA 1 order of magnitude lower than the initial Cu2+ concentration. ACKNOWLEDGMENT The authors thank the Fondecyt (Grant No. 8990011), the Direccio´n de Investigacio´n of the Universidad Austral de Chile (Grants Nos. S-199906 and S-200126) for financial support. Received for review April 27, 2001. Accepted August 29, 2001. AC010476G
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