Anal. Chem. 2001, 73, 4592-4598
Optical Sensors and the Salt Effect: A Dual-Transducer Approach to Acidity Determination in a Salt-Containing Concentrated Strong Acid Leonardo R. Allain, T. Andrew Canada, and Ziling Xue*
Department of Chemistry, The University of Tennessee, Knoxville, Tennessee 37996-1600
A dual-transducer approach has been developed to decompose the optical signals of acid sensors in saltcontaining concentrated acid solutions and to give acid and salt concentrations in concentrated LiCl-HCl, CaCl2HCl, and AlCl3-HCl solutions, respectively. The optical acid sensors in this approach are films of porous sol-gel SiO2 or SiO2-Nafion composite doped with low-pKa indicators. A novel linear relationship (DA/DCsalt)Cacid ) β‚ (dA0/dCacid)Csalt)0 (A ) absorbance of the sensor in a saltcontaining HCl solution; A0 ) absorbance of the sensor in a salt-free acid solution) was found, and the current approach is based on a set of nonlinear equations derived from this relationship. Optical chemical sensors are of intense current interest. In particular, their uses in multicomponent systems have been actively studied.1-5 In such systems, it is desirable to measure each component accurately and minimize or compensate matrix interferences. In general, the response of optical sensors that are based on indicator equilibria as the transducing mechanism is significantly affected by changes in ionic strength, I. Variations in ionic strength shift the indicator equilibrium in an optical sensor, and, thus, change the optical parameters, such as indicator absorbance. As Rilbe aptly put, “it varies with the milieu in which the protolyte dwells.”6 Furthermore, these changes in the optical parameters caused by ionic strength are often indistinguishable from signal changes caused by the analyte. Edmonds and co-workers have shown that an increase in ionic strength from 0.01 to 3.00 M can shift the pKa′ value by as much as 1.23 units.1 If no correction for ionic strength is made, the ionic (1) Edmonds, T. E.; Flatters, N. J.; Jones, C. F.; Miller, J. N. Talanta 1988, 35, 103. (2) Opitz, N.; Lu ¨ bbers, D. W. Sens. Actuators 1983, 4, 473. (3) (a) Wolfbeis, O. S. Fiber Optic Chemical Sensors and Biosensors; CRC Press: Boca Raton, FL, 1991; Vol. 1; p 363. (b) Wolfbeis, O. S.; Offenbacher, H. Sens. Actuators 1986, 9, 85. (4) Lavigne, J. J.; Savoy, S.; Clevenger, M. B.; Ritchie, J. E.; McDoniel, B.; Yoo, S.-J.; Anslyn, E. V.; McDevitt, J. T.; Shear, J. B.; Neikirk, D. J. Am. Chem. Soc. 1998, 120, 6429. (5) (a) Aussenegg, F. R.; Brunner, H.; Leitner, A.; Lobmaier, C.; Schalkhammer, T.; Pittner, F. Sens. Actuators, B 1995, B29, 204. (b) Zhang, L.; Langmuir, M. E.; Bai, M.; Seitz, W. R. Talanta 1997, 44, 1691. (c) McCurley, M. F.; Seitz, W. R. Anal. Chim. Acta 1991, 249, 373. (6) Rilbe, H. pH and Buffer Theory: A New Approach; Wiley: New York, 1996.
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strength of the sample has to be kept constant during calibration and pH measurements. Opitz and Lu ¨ bbers have developed an approach employing a dual pH fluorescence indicator system that is based on indicators having different relationships between pKa and ionic strength.2 These relationships yielded two independent equations to measure both the ionic strength and pH;3a however, such relationships are highly nonlinear, thus limiting the use of regression analysis. In addition, this approach using pH fluorescence indicators was suitable for low-to-medium ionic strength (0.1-1 M) and near neutral pH (6.5-7.5). In an approach developed by Wolfbeis and Offenbacher, a combination of sensors was used to measure both pH and ionic strength through two independent pH measurements.3b This method was based on covalent immobilization of a dye onto porous glass supports having distinct surface chemistries. In one sensor, the environment around the indicator was noncharged, whereas in the other sensor, a highly charged environment surrounded the indicator. The charged environment made the indicator chemical equilibrium less susceptible to further changes in ionic strength. In other words, the sensor was desensitized to changes in salt concentration. A sensor array was recently reported using a multicoated sensor surface integrated with a CCD (charge-coupled device) detector to simultaneously determine the concentrations of various analytes (pH, Ca2+, Ce3+, and fructose).4 In this approach, there is a nonspecific transducer for each analyte, and a set of independent equations containing an equal number of variables is solved to yield the concentrations of the analytes. Although not stated, the effects of, for example, temperature and ionic strength could also, a priori, be treated by increasing the number of independent equations, that is, transducers. Another approach to ionic strength measurement was based on optical interference by a swelling polymer in which the degree of swelling is a function of ionic strength at a constant pH.5 These reported approaches to correct ionic strength in optical sensing were designed for the pH region and solutions of lowto-medium ionic strength.2-5 The approaches by Opitz and Wolfbeis and co-workers, for example, are based on equations derived from the Debye-Hu¨ckel theory and, thus, valid for relatively low ionic strength.2,3 Concentrated strong acids, such as HCl, are among the largest volume chemicals manufactured in the world and are widely used 10.1021/ac010166y CCC: $20.00
© 2001 American Chemical Society Published on Web 08/25/2001
in many chemical processes.7 However, rapid and reliable methods for their on-line determination and quality control are limited, mainly because of the high concentration and corrosive nature of the analyte matrix. Concentrated strong acids such as HCl are often used in the presence of salts, and the ionic strength changes by these salts further complicate the acidity measurement. In the use of a fast and reversible acid sensor that we recently developed for highly acidic solutions ([H+] ) 1-11 M),8-10 we found that the ionic strength change by the salts was a considerable source of analytical error and had to be addressed to give the accurate acidity. The salt concentrations used in these systems far surpass the limits of the previous approaches.2-5 This prompted us to develop a new approach to accurately measure acid and salt concentrations in salt-containing, highly acidic solutions. In the current work, we observed a novel linear relationship between (∂A/∂Csalt)Cacid and (dA0/dCacid)Csalt)0 for indicators doped in sol-gel sensors, and we developed a dual-transducer approach based on this relationship to obtain the acid and salt concentrations in salt-containing concentrated strong acids. The dual transducer approach here requires a decomposition algorithm that utilizes the combination of two different sensors. These two sensors have distinct ionic strength dependencies, and the signal array can be decomposed to give the acid and salt concentrations. This new approach has been used to accurately predict acid and salt concentrations in concentrated strong acid solutions with a salt contribution of up to 5.5 M to ionic strength. EXPERIMENTAL SECTION Visible spectra were recorded using a single-array, dual beam spectrometer (Rainbow Meter, American Holographic Inc., Fitchburg, MA) with a xenon flashlamp as the light source. Solutions of HCl, LiCl-HCl, CaCl2-HCl, and AlCl3-HCl were prepared by gravimetric dilution and titrated with NaOH standards (Fisher) to the phenolphthalein end point. Bromocresol Purple (BCP, 90% dye content, Aldrich), Bromocresol Green (BCG, 95% dye content, Eastman), Neutral Red (NR, 60% dye content, Eastman), Acid Blue 147 (∼75% dye content, Aldrich), Si(OMe)4 (99+%, Aldrich), MeOH (certified ACS, Fisher), cetyltrimethylammonium bromide (CTAB, Aldrich), Nafion (5% Nafion in an alcoholic mixture containing 5% w/w water, Aldrich), HCl (37.5%, certified ACS, Fisher), and AlCl3‚6H2O (99%, Acros) were used as received. CaCl2‚2H2O (certified ACS, Fisher) and LiCl (99% anhydrous, Acros) were kept at 45 °C for one and two weeks, respectively, (7) (a) Hisham, M. W. M.; Bommaraju, T. V. In Encyclopedia of Chemical Technology, 4th ed.; Wiley: New York, 1995; Vol. 13, p 894. (b) Greenwood, N. N.; Earnshaw, A. Chemistry of the Elements, 2nd ed.; ButterworthHeinemann: Oxford, U.K., 1997; p 811. (8) (a) Allain, L. R.; Sorasaenee, K.; Xue, Z.-L. Anal. Chem. 1997, 69, 3076. (b) Allain, L. R.; Xue, Z.-L.; Roberts, M. J. J. Process Anal. Chem. 1998, 3, 98. (9) Allain, L. R.; Xue, Z.-L. Anal. Chim. Acta 2001, 433, 97. (10) For our recent studies of organofunctional sol-gels, see also (a) Allain, L. R.; Xue, Z.-L. Anal. Chem. 2000, 72, 1078. (b) Im, H.-J.; Yang, Y.; Allain, L. R.; Barnes, C. E.; Dai, S.; Xue, Z.-L. Environ. Sci. Technol. 2000, 34, 2209. (c) Yost, T. L., Jr.; Fagan, B. C.; Allain, L. R.; Barnes, C. E.; Dai, S.; Sepaniak, M. J.; Xue, Z.-L. Anal. Chem. 2000, 72, 5516. (d) Dai, S.; Burleigh, M. C.; Ju, Y. H.; Gao, H. J.; Lin, J. S.; Pennycook, S. J.; Barnes, C. E.; Xue, Z.-L. J. Am. Chem. Soc. 2000, 122, 992. (e) Dai, S.; Shin, Y. S.; Ju, Y. H.; Burleigh, M. C.; Lin, J. S.; Barnes, C. E.; Xue, Z.-L. Adv. Mater. 1999, 11, 1226. (f) Dai, S.; Burleigh, M. C.; Shin, Y. S.; Morrow, C. C.; Barnes, C. E.; Xue, Z.-L. Angew. Chem., Int. Ed. Engl. 1999, 38, 1235. (g) Fagan, B. C.; Tipple, C. A.; Xue, Z.-L.; Sepaniak, M. J. Talanta 2000, 53, 599.
prior to use. Literature procedures were used to process substrates and prepare three Bromocresol Purple sensors (BCP1-3).8 Data analysis was conducted with Sigma Plot (SPSS Inc., 233 S. Wacker Drive, 11th Floor, Chicago, IL 60606-6307; http://www.spss.com), Matlab (The MathWorks, Inc., 3 Apple Hill Drive, Natick, MA 01760-2098; http://www.mathworks.com), and Maple (Waterloo Maple Inc., 57 Erb Street, W. Waterloo, Ontario, Canada N2L 6C2; http://www.maplesoft.com) programs. Preparation of Three Neutral Red Sensors (NR1-3). A typical procedure for NR2 is given here. Neutral Red (12 mg) was dissolved in a mixture of HCl (100 µL, 0.01 N), MeOH (40 µL), and 158 mg of Nafion with stirring. Si(OMe)4 (300 µL) was then added, and the mixture was stirred for 46 h. At this point, the solution was coated onto a glass surface through a spin coating process (1650 rpm). The sensor films were left to cure in air at room temperature. After 1 day at ambient conditions, the films were heated to 45 °C for 5 days. Preparation of Bromocresol Green Sensors (BCG1 and 3). A typical procedure for BCG1 is given here. H2O (60 µL), HCl solution (0.01 M, 17 µL), MeOH (130 µL), CTAB (4.0 mg), and Bromocresol Green (55.3 mg) were allowed to stir for 5 min in a glass vial at 23 °C to ensure complete solubility of all of the components. Si(OMe)4 (200 µL) was then added, and the solution was stirred for 50 min at room temperature. The solution was then spin-coated onto individual glass substrates. The spin coating process lasted about 30 s at a spinning rate of 1800 rpm for each thin film produced. The sensors were cured for 5 days in air at room temperature and then in an oven at 45 °C for 15 days. Preparation of an Acid Blue 147 Sensor (AB). Si(OMe)4 (200 µL), Acid Blue 147 (12 mg), HCl solution (0.01 M, 36 µL), MeOH (180 µL), and CTAB (4.0 mg) were mixed and stirred together in a glass vial for 30 min to form a clear solution. The solution was then coated onto a glass surface via a spin coating process (1650 rpm). No more than 10 s of spinning was needed for the sol-gel to produce a thin and viscous film. The sol-gel film was first dried in air for 3 days and then it was heated at 41 °C for 14 days in an oven. The Acid Blue 147 sensor AB was used in the measurement of CaCl2-HCl solutions. Measurement Procedure. The sensor element, an indicatordoped film coated onto a glass slide, was first conditioned as reported earlier8 and then mounted in a Teflon cell, leaving a 0.7 mm space along the optical path for contact with the flowing liquid sample. A regular glass slide without any coating was used as a blank. The apparatus used for the measurement was reported earlier.8b RESULTS AND DISCUSSION Nonlinear Transducing Mechanism of Optical Sensors. There are two important issues to be considered in acidity measurement in salt-containing concentrated strong acids: (1) how proton activity varies in concentrated acid, an issue already addressed by the Hammett indicator acidity functions; and (2) how proton activity is affected by ionic strength. The latter has been considered, to a smaller extent, in the study of the acidity functions of some indicators.11,12 In the case of HCl, [H+] in the (11) Hammett, L. P.; Deyrup, A. J. J. Am. Chem. Soc. 1932, 54, 2721. (12) (a) Paul, M. A.; Long, F. A. Chem. Rev. 1957, 57, 1. (b) Cox, R. A.; Yates, K. Can. J. Chem. 1981, 59, 2116. (c) Rochester, C. H. Acidity Functions; Academic Press: London, 1970.
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range of 1-11 M changes by more than 1 order of magnitude; however, the proton activity in fact varies by about 3.5 orders of magnitude.12a This is a unique behavior of concentrated acid solutions explored by Hammett six decades ago.11 The transducing mechanism of the sensor depends on the acid-base equilibrium (eq 1) of an indicator that is positively charged in a concentrated acid.
HInd+ ) Ind + H+ (Ka) Ka ) γ
[H + ][Ind] [HInd + ]
) γ Ka′′
(1) (2) Figure 1. Calibration plot of A vs Cacid for a Bromocresol Purple sensor.
(γ ) activity coefficient ratio; Ka ) thermodynamic equilibrium constant; Ka′′ ) stoichiometric equilibrium constant) For dilute electrolyte solutions (I < 0.5 M), the changes in pKa′′ due to ionic strength can be addressed by the DebyeHu¨ckel equation.2 Solutions with higher ionic strength (I > 0.5 M) cannot be adequately treated with the Debye-Hu¨ckel approximation, and empirical relationships are often used instead. In eq 2, ionic strength changes γ and, thus, shifts the indicator equilibrium and indicator absorbance A. This change cannot be isolated from that caused by the analyte H+. In other words, ionic strength is potentially a considerable source of error. The total concentration of the indicator IndT for a given system is a constant. Figure 2. Response of Bromocresol Purple sensor BCP3 to Csalt in AlCl3-HCl solutions.
+
IndT ) [HInd ] + [Ind] [HInd+] )
IndT[H+] Ka′′ + [H+]
(3)
The plot of A0 (A0 ) absorbance of the sensor in a salt-free acid solution) is proportional to, for example, [HInd+] and is, theoretically, a nonlinear function (eq 4).
IndT[H+] A0 ) κ‚ Ka′′ + [H+]
(4)
Thus, an optical sensor that bases its transducing mechanism on an indicator chemical equilibrium may show a nonlinear relationship between its analytical signal and analyte concentration. Nonlinear relationships between A0 and [H+] () Cacid) were observed in the current studies. An experimental plot of A0 vs Cacid for the Bromocresol Purple sensor 2 (BCP2) is given in Figure 1.13 The fitting of these experimental plots is discussed below. The nonlinear relationship between analytical signal and analyte concentration in optical sensors contrasts with the more common linear (or logarithmic) relationship found in other transducing mechanisms. Electrochemical sensors, for example, have a logarithmic relationship between electrode potential and hydrogen ion activity. In these sensors, ionic strength has a much smaller effect on electrochemical pH measurements than they do (13) See Supporting Information for details and additional information.
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on the indicator equilibrium in optical sensors.14 This is the underlying reason pH optical sensors are less accurate than their electrochemical counterparts in the normal pH range, a subject already explored by Janata.14 However, in concentrated acid or base solutions at the extreme pH, electrochemical measurements usually show severe deviations, and currently there is no reliable approach to acidity measurements in salt-containing concentrated strong acids. The Salt-Effect and Dual Optical Transducer Approach.13,15 LiCl, CaCl2 and AlCl3, M+, M2+, and M3+ salts, respectively, were chosen for the current studies to give solutions of different ionic strength. We observed that when a large amount of each of these three salts was added to an acid solution of a fixed concentration, the absorbances of the Bromocresol Purple (BCP1-3), Neutral Red (NR1-3), Bromocresol Green (BCG1 and 3), and AB sensors varied proportionally to the amount of the added salt. Such linear plots for BCP3 sensor in AlCl3-HCl solutions are shown in Figure 2, and a three-dimensional experimental plot of A (A ) absorbance of the sensor in a salt-containing HCl solution) vs Cacid and Csalt (AlCl3) is given in Figure 3.13 In high-ionic-strength solutions, as expected, the magnitude of change in sensor response varies with different salts in the solutions. The experimentally observed saltfree (Csalt ) 0 M) A0 vs Cacid plots are different from each other for these nine sensors (BCP1-3, NR1-3, BCG1 and 3, and AB (14) Janata, J. Anal. Chem. 1987, 59, 1351. (15) The conductance of salt-containing solutions was also evaluated as a secondary transducer; however, for the range of acidity studied here, it was not a suitable method.
Figure 3. 3-Dimensional plot of response of BCP3 in AlCl3-HCl solutions.
Figure 5. Plots of (dA0/dCacid)Csalt)0 vs (∂A/∂Csalt)Cacid in CaCl2-HCl solutions: (a) BCP2; (2) NR2; and (c) AB (unit: mol-1 L).
between the slopes of A vs Csalt plots (in, e.g., Figure 2) and the first derivatives of A0 vs Cacid curves (in, e.g., Figure 1) for each of these nine sensors in LiCl-HCl, CaCl2-HCl, and AlCl3-HCl solutions. Such linear plots for the BCP1, NR1, and BCG1 sensors in LiCl-HCl solutions, BCP2, NR2, and AB sensors in CaCl2HCl solutions, and BCP3, NR3, and BCG3 sensors in AlCl3-HCl solutions are shown in Figures 4-6, respectively. In other words, there exists a new relationship in eq 5.
(∂A/∂Csalt)Cacid ) β‚(dA0/dCacid)Csalt)0
Figure 4. Plots of (dA0/dCacid)Csalt)0 vs (∂A/∂Csalt)Cacid in LiCl-HCl solutions: (a) BCG1; (b) BCP1; and (c) NR1 (unit: mol-1 L).
sensors). We found, however, that the slope of A vs Csalt at a given acid concentration, (∂A/∂Csalt)Cacid, is proportional to the respective tangent of the A0 vs Cacid plot for a salt-free acid solution, (dA0/ dCacid)Csalt)0 for these sensors. A linear relationship was observed
(5)
The ranges of error in Figures 4-6 as percentages of the dynamic ranges are 0.122-6.89% in (dA0/dCacid)Csalt)0 and 0.1658.83% in (∂A/∂Csalt)Cacid. The origin of this, to our knowledge, previously unknown relationship for these nine sensors is not clear. It forms the basis in the current work to estimate acid (Cacid) and salt concentration (Csalt) in salt-containing concentrated strong acid. In salt-free (Csalt ) 0) acid solutions, the plot of A vs Cacid (e.g., Figure 3) for each of these nine sensors13 is best fitted by an Analytical Chemistry, Vol. 73, No. 19, October 1, 2001
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(∂A/∂Csalt)Cacid is the slope of the change in A vs added salt (Csalt) and is a constant at a given Cacid in our systems; however, this slope is an unknown function of Cacid. Using the relationship in eq 5 observed in the current studies, (∂A/∂Csalt)Cacid can be replaced by β(dA0/dCacid)Csalt)0. Furthermore, (dA0/dCacid)Csalt)0 could be replaced by df(Cacid)/dCacid using eq 6 to give eq 9.
A ) f(Cacid) + β(dA0/dCacid)Csalt)0‚Csalt ) f(Cacid) + β(df(Cacid)/dCacid)‚Csalt ) f(Cacid) + βf ′(Cacid)‚Csalt
(9)
where f ′(Cacid) ) df(Cacid)/dC(acid). In other words, the relationship in eq 5 converts an unknown function in eq 8 to a function (eq 9) of absorbance A with Cacid and Csalt. This nonlinear equation (eq 9) is based on the empirical sigmoid curve f(Cacid) in eq 6 that best fits the experimental A0 vs salt-free Cacid plot (e.g., Figure 2) for each sensor. By using two different (and thus, independent) transducers 1 and 2, the following two equations and two variables (Cacid and Csalt) are obtained.
A1 ) f1(Cacid) + β1‚f1′(Cacid)Csalt
(10)
A2 ) f2(Cacid) + β2‚f2′(Cacid)Csalt
(11)
In the current case, the first derivative of the empirical sigmoid curve f(Cacid) (eq 6) is
f ′(Cacid) ) df(Cacid)/dCacid )
Figure 6. Plots of (dA0/dCacid)Csalt)0 vs (∂A/∂Csalt)Cacid in AlCl3-HCl solutions: (a) BCG3; (b) BCP3; and (c) NR3 (unit: mol-1 L).
a 1+e
(b-Cacid)/c
)B+
a 1+x
(6)
where x ) e(b - Cacid)/c, and B, a, b, and c are constants for each indicator from the curve fit. The addition of a salt to an acid solution will lead to an increase ∆A (salt) in absorbance, which, in our systems, is proportional to the salt concentration Csalt (Figure 2 and Supporting Information).
∆A ) (∂A/∂Csalt)Cacid‚(Csalt - 0) ) (∂A/∂Csalt)Cacid‚Csalt (7) The total absorbance A in a salt-containing acid is thus
Atot ) A0 + ∆A ) f(Cacid) + (∂A/∂Csalt)Cacid‚Csalt 4596
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(8)
(12)
where x ) e(b-Cacid)/c, and a, b, and c are constants for each indicator from the curve fit. Thus, eqs 10-11 turn into eqs 10a-11a.
A1 ) B1 +
a1 a1‚x1 + β1‚ ‚Csalt 1 + x1 c1(1 + x1)2
(10a)
A2 ) B2 +
a2 a2‚x2 + β2‚ ‚Csalt 1 + x2 c2‚(1 + x2)2
(11a)
empirical sigmoid curve in eq 6.
A0 ) f(Cacid) ) B +
a‚x c(1 + x)2
The solutions to this set of equations could be obtained through a series of iterations. A program was written in Matlab to calculate Cacid and Csalt for given A1 and A2. An initial Cacid(predicted) was obtained from the A vs Cacid curve for the salt-free HCl. For a given Ai of sensor i, the iteration program yields a curve of Cacid(predicted) vs Csalt(predicted). The interception of the two independent curves for the two sensors gives Cacid and Csalt. The use of BCP2 and NR2 sensors for Cacid and Csalt determination in a CaCl2-containing HCl solution is given in Figure 7 as an example. Additional plots are provided in Supporting Information. Figure 8 shows the errors in acidity determination for 5-6 M HCl solutions containing LiCl, CaCl2, and AlCl3 using BCP1 and BCG1, BCP2 and NR2, and BCP3 and NR3, respectively.13 The
Figure 7. Plots of computed (Csalt, Cacid) pairs for given A readings from BCP2 and NR2 sensors in a CaCl2-HCl solution.
Figure 9. Validation plots of predicted vs actual salt concentrations in salt-HCl solutions (unit: g L-1): (a) BCG1 and BCP1 sensors in LiCl-HCl, (b) BCP2 and NR2 sensors in CaCl2-HCl, and (c) BCP3 and NR3 sensors in AlCl3-HCl. Predicted values were computed by a signal deconvolution algorithm.
Figure 8. Comparison of errors in Cacid measurements before and after the corrections for (a) LiCl-HCl, (b) CaCl2-HCl, and (c) AlCl3HCl solutions.
acid concentration of 5-6 M was chosen, because it is approximately in the middle of the range of concentrated HCl (112 M). Our studies showed that without correction for the ionic
strength, these acid sensors gave significant errors in the presence of salts. These errors in Cacid can be as large as 24.3% for LiClHCl, 60% for CaCl2-HCl, and 43.0% for AlCl3-HCl solutions, respectively (Figure 8). The use of the current dual-transducer approach led to a significant drop in the error in Cacid to
