Anal. Chem. 2000, 72, 2377-2382
Ion-Selective Electrode for Dodecyldimethylamine Oxide: A “Twice-Nernstian” Slope for the Determination of a Neutral Component V. Peyre,* S. Baillet, and P. Letellier
Laboratoire Energe´ tique et Re´ activite´ aux Interfaces, Universite´ Pierre et Marie Curie, Case 39, 4, place Jussieu, 75252 Paris Ce´ dex 05- France
An electrode originally sensitive to dodecyltrimethylammonium (DTA+) was proven to be sensitive to dodecyldimethylamine oxide (DDAO), a surfactant with acidobasic properties. The response of the electrode was tested from pH 2 to 9.3. Its slope is Nernstian when the surfactant is entirely protonated. At a pH where the molecule is mainly under the neutral form, the electrode responds with a “twice-Nernstian” slope around 120 mV/ decade. The validity of this electrode for measurements was checked by confronting the evolution of the critical micelle concentration of DDAO vs pH with data already published and by determining the complexation constant of DDAO and β-cyclodextrin. A possible explanation of the “twice-Nernstian” slope, using a dimer of DDAO is proposed.
dependent on pH. The extraction of phenolic compounds in their neutral form in the membrane can be responsible for the response of liquid PVC membrane electrodes under certain conditions.6,7 In this case again, the pH of the solution plays an important role, and the electrode enables the detection of neutral compounds with super-Nernstian slopes. This field of non-Nernstian slopes develops very fast and a theoretical effort is made to understand them better.8-10 We are interested in the measurement of dodecyldimethylamine oxide (DDAO). This surfactant can be cationic or neutral according to the following protonation equation:
DDAO + H+ ) DDAOH+ Assimilating activities and concentrations at low concentrations of surfactant, the acidity constant of DDAO below its cmc is Ka ) 10-4.95 ) [DDAO][H+]/[DDAOH+].11,12 The ionic and neutral forms are thus always present in solution, and their ratio is determined by Ka and the proton concentration. The detection of the ionic form thanks to a DDAOH+-specific electrode should thus always be feasible whatever the pH, as long as the [DDAOH+] concentration lies within the range of sensitivity of the sensor. Since ion-specific electrodes are not highly specific toward surfactants of the same nature (chain length and charge),13 we use a dodecyltrimethylammonium (DTA+)-sensitive electrode to detect DDAOH+. The response of the electrode is examined between pH 2 and 9.3, leading to super-Nernstian slopes. After a validation of this response by comparison with literature results, an interpretation of this slope is proposed.
Surfactants can be classified between ionic (cationic or anionic) and neutral molecules (uncharged or zwitterionic). The detection and measurement of the ionic surfactants has been highly improved recently by development of ion-selective electrodes. On the other hand, neutral or zwitterionic are still difficult to detect in situ, due to lack of efficient sensors. In some cases, a Ba2+selective electrode can be used to detect neutral surfactant with an ethylene oxide (EO) chain, via the complex that is formed between the metal ion and the EO chain.1 Observations of “super-Nernstian” slopes have been reported for various electrodes, resulting from different phenomena. In the case of electrodes sensitive to nitric acid, the super-Nernstian slopes were interpreted as the result of the formation of complexes of the primary ion NO3- with nitric acid NO3-‚nHNO3.2-4 More recently, the same phenomenon of super-Nernstian slopes with a salicylate-selective electrode was mentioned.5 The extraction of neutral salicylic acid inside the membrane seams to be responsible for this behavior. The selectivity of such electrodes is then highly
MATERIALS AND METHODS Materials. DDAO was from Fluka and was used as received. β-Cyclodextrin (β-CD) was from Janssen-Chimica. All solutions were made up in distilled water.
* Corresponding author: (e-mail)
[email protected]. (1) Porter, M. R. In Recent Developments in the Analysis of Surfactants; Porter, M. R., Ed.; Elsevier: London 1991; p 22. (2) Materova, E. A.; Alagova, Z. S.; Zhes’ko, V. P. Elektrokhimiya 1974, 10, 1568 (p 1491, English translation). (3) Materova, E. A.; Grekovich, A. L.; Garbuzova, N. V. J. Anal. Chem. 1974, 29, 1900 (p 1638, English translation). (4) Materova, E. A.; Garbuzova, N. V. Elektrokhimiya 1977, 13, 1846 (p 1592, English translation). (5) Egorov, V. V.; Borisenko, N. D.; Rakhmank’ko, E. M. J. Anal. Chem. 1998, 53, 855 (p 750, English translation).
(6) Ito, T.; Radecka, H.; Tohda, K.; Odashima, K.; Umezawa, Y. J. Am. Chem. Soc. 1998, 120, 3049. (7) Ito, T.; Radecka, H.; Umezawa, K.; Kimura, T.; Yashiro, A.; Lin X. M.; Kataoka, M.; Kiumura E.; Sessler J. L.; Odashima, K.; Umezawa Y. Anal. Sci. 1998, 14, 89. (8) Amemiya, S.; Bu ¨ hlmann, P.; Umezawa, Y. Anal. Chem. 1998, 70, 445. (9) Amemiya, S. Bunseki Kagaku 1999, 48, 529. (10) Bu ¨ hlmann, P.; Umezawa, Y. Electroanalysis 1999, 11, 687. (11) Rathman, J. F.; Christian, S. D. Langmuir 1990, 6, 391. (12) Tokiwa, F.; Ohki, K. J. Phys. Chem. B 1966, 70, 3437. (13) Jezequel, D. The`se de l’Universite´ Paris VI, 1991.
10.1021/ac9911387 CCC: $19.00 Published on Web 04/26/2000
© 2000 American Chemical Society
Analytical Chemistry, Vol. 72, No. 11, June 1, 2000 2377
Table 1. Experimental Conditions of Buffersa pH
buffer
buffer concn (mM)
ionic strength (M)
2 3 3.5 4 4.5 5.5 7.12 7.4 7.9 9.3
HCl citric acid/NaOH id id id id H3PO4/NaOH Tes/NaOH Tris/HCl H3BO3/NaOH
10 20 id id id 15 12.5 10 20 20
0.11 0.11 0.12 0.13 0.14 0.13 0.13 0.11 0.11 0.11
aTris, tris(hydroxymethyl)aminomethane; Tes, N-tris(hydroxymethyl)methyl-2-aminoethanesulfonic acid. In addition to the buffering salt, all solutions contain NaCl, 0.1 mol/L. The ionic strength is calculated as I ) 0.5Σzi2ci. In the text, the solutions are referred to by their pH value.
The buffers used are listed in Table 1. All solutions contained 0.1 M NaCl; their ionic strength varies between 0.11 and 0.14 mol/ L. They are identified only by their pH value. Potentiometry. The electrode tested here is a classical DTABr-sensitive electrode, described elsewhere.14-16 It is composed of a liquid junction PVC membrane, plasticized by dinonyl phthalate. The ion exchanger is tetraphenylborate. The electrochemical chain is as follows:
To check that DDAO was not interfering with the calomel electrode, a glass electrode was taken sometimes as reference I instead of the calomel. Since the solutions were all buffered, the glass electrode had a constant potential. This change of reference did not affect the results. The reference solution of the ISE was either 0.001 M DTABr or 0.001 M DDAOH+ in 0.01 M HCl, 0.1 M NaCl. Procedure Measurement: Calibration at Various pHs. A 10-mL aliquot of buffer solution were introduced in a thermostated cell at 25 °C. It was determined that the response of the electrode was unaffected by the buffer, as long as its concentration remained constant. Aliquots of 0.001 or 0.1 M DDAO in the same buffer were added to the solution and the emf was recorded. The emf is stable after 1 min for the lowest concentrations or a few seconds for higher concentrations. Between two experiments, the electrode was left in water under stirring for ∼10 min, to rinse it and enhance reproducibility of the measurements. Each experiment was made at least twice, with a reproducibility of (2 mV. Complexation Constant. The complexation constant DDAO/ β-cyclodextrin was determined by the alternated additions method. The thermodynamic background has been described elsewhere.17 (14) Jezequel, D.; Mayaffre, A.; Letellier, P. Can. J. Chem. 1991, 69, 1865. (15) Jezequel, D.; Mayaffre, A.; Letellier, P. J. Chim. Phys. 1991, 88, 391. (16) Martin, J. V.; Turmine, M.; Letellier, P.; Hemery, P. Electrochim. Acta 1995, 40, 2749. (17) Palous, J. L.; Turmine, M.; Letellier, P. J. Phys. Chem. B 1998, 102, 5886.
2378
Analytical Chemistry, Vol. 72, No. 11, June 1, 2000
Figure 1. Comparison of the calibration of the electrode in 0.01 M HCl, 0.1 M NaCl, by DTA+ or DDAOH+. c is the concentration of the surfactant, in moles per liter.
The method is briefly summarized below: in a solution of given activity of DDAO (i.e., of fixed emf), aliquots δnCD of β-CD (in mole units) were added as a concentrated solution of β-CD in the same solvent. This caused the emf to decrease because of the formation of a complex. The stoichiometry of the complex(es) was unimportant at this experimental level. DDAO was then added to restore the initial emf, as a quantity δnDDAO. This was repeated several times for one experiment. The amount of DDAO necessary to restore the potential was exactly equal to the quantity that disappeared in the formation of the β-CD-DDAO complex at this activity of DDAO, after volume correction for dilution were made. One then plotted ΣδnDDAO vs ΣδnCD. It lead to a straight line of slope r passing through origin. The choice of a model for the complexation reaction then permitted the calculation of the complexation constant. This is addressed in the results section. RESULTS Selectivity of the Electrode. The response of the electrode to DDAOH+ was first studied at pH 2, where 99.9% of the DDAO molecules are protonated. The results are displayed on Figure 1, as well as the response of the electrode to DTA+ ion in the same medium. The cmc was found to be (2.4 ( 0.1) × 10-3 mol/L. The response is Nernstian between a surfactant concentration of 10-5 mol/L and the cmc. The selectivity between DTA+ and DDAOH+ was calculated according to the Eisenman-Nikolsky equation.18
∆Φ ) C + (RT ln/F) log([DTA+] + S[DDAOH+]) (1)
where ∆Φ is the potential recorded by the electrode, C is a constant depending on the medium, and S is the selectivity constant between DTA+ and DDAOH+. From Figure 1, one can calculate S ) 0.71 ( 0.05. This indicates that the electrode is nonselective between these two ions and that it can be used to detect either of them indifferently, as long as no other ion interferes with the potential. (18) Bakker, E.; Bu ¨ hlmann, P.; Pretsch, E. Chem. Rev. 1997, 97, 3083.
Figure 3. Cmc of DDAO vs pH. Buffers (in 0.1 M NaCl) are detailed in Table 1, I ) 0.135 ( 0.025 M, T ) 25 °C. Key: (9) this study; (×) Rathman and Christian,11 in 0.06 M NaBr; (4) Maeda et al.,19 in 0.1 M NaCl; (O) Tuncay and Christian,21 in 0.1 M NaCl.
Figure 2. Calibration by DDAO at various pH. Buffers used are listed in Table 1. Lines are calculated as explained in the text, with R ) 1.8.
Response with pH. The response was tested in different buffered solutions. The emf are shown on Figure 2 for pH 2 to 9.3. They all exhibit the same behavior: a linear part centered around log [DDAO] ) -4, preceded by a zone of lower slope, and followed by a plateau. Two groups of curves can be distinguished. First, for pH between 2 and 4.5, the curves have a common point at log [DDAO] ) -4.8. The slope of their linear part increases with pH from 60 mV/decade at pH 2 to 113 mV/ decade at pH 4.5. In the meantime, the plateau starts earlier. In the second group, from pH 4.5 to 9.3, the curves all have the same linear part of slope around 106 mV/decade. The variation of the slope (between 101 and 113 mV/decade) depends on the history of the electrode. The difference lays in the position of the curves: the higher the pH, the lower the emf. The nature of the salt and the ionic strength do not affect the slope, as was seen by changing the concentration of the buffer. Reproducibility and Stability. The electrode has to be rinsed between two experiments to give reproducible results. If this step is omitted, (1) the lower detection limit of the electrode increases and (2) the electrode becomes sensitive to [OH-]: the emf vs pH plot exhibits a negative (anionic) slope for pH >5. Since this
phenomenon is not the point of this article, it was not investigated further. If the electrode has been properly rinsed, the emf is stable over 30 min. This enables the alternated addition method to be used. Validity of the Electrode. Since the response of the electrode is not classical, it had to be checked and compared with already published data. The first point deals with the sharp end of the linear region. For “classical” electrodes, this breaking point corresponds to the cmc. Above the cmc, the activity of the surfactant remains almost constant when the total concentration is increased, and so does the emf. The concentration corresponding to the breaking point in the calibration with DDAO is reported vs pH in Figure 3. One obtains a characteristic curve with a minimum at pH ∼5. The results compare very well with the plot cmc ) f (pH) obtained from Rathman and Christian11 and Maeda et al.,19 though they were obtained under slightly different conditions (0.06 M NaBr or 0.1 M NaCl, pH adjusted with HCl). Second, the complexation constant of β-CD and DDAO was determined at pH 5.5. β-CD is a commonly used complexant for surfactant. It is a crown molecule made of sugar entities, forming a hydrophobic cavity. The aliphatic chain of the surfactant enters the hydrophobic cavity. A 1:1 complex model is usually sufficient to interpret the results, though a 2:1 complex can be used in some cases.14 A 1:1 model was used here and a mass law action constant derived:
DDAO + β-CD ) DDAO-β-CD Kc ) [DDAO-β-CD]/[DDAO][β-CD]
(2)
The alternated additions method enables the calculation of the association constant Kc in the following manner: [DDAO] is chosen at the beginning of each series of alternated additions. (19) Maeda, H.; Muroi, S.; Ishii, M.; Kakehashi, R.; Kaimoto, H.; Nakahara, T.; Motomura, K. J. Colloid Interface Sci. 1995, 175, 497.
Analytical Chemistry, Vol. 72, No. 11, June 1, 2000
2379
Figure 4. Slope r from the alternated additions of β-CD and DDAO at pH 5.5. Calculated curve with Kc ) 12 300.
Mass conservation is written for DDAO and β-CD.
[DDAO]tot ) [DDAO] + [DDAO-β-CD]
(3)
[β-CD]tot ) [β-CD] + [DDAO-β-CD]
(4)
In the process of alternated additions, the amount of DDAO added is exactly that needed to compensate for the formation of the complex. The slope r ) ΣδnDDAO/ΣδnCD thus stands for the ratio [DDAO-β-CD]/[β-CD]tot. Using eq 4 and the definition of Kc, r can be expressed as
r ) [DDAO]Kc/(1 + [DDAO]Kc)
(5)
the behavior of the calibration curve and its capacity to be used as a reliable captor at all pHs. To understand the reason for the super-Nernstian slope, one can suppose the formation of a dimer of DDAO-DDAOH+ inside the membrane of the electrode. This would be supported by the following arguments: (1) The formation of H-bonds between the polar heads of DDAO and DDAOH+ in the micelles has already been suggested to explain the dependence of the cmc on pH.22,23 Though a proper dimer in aqueous solution has never been evidenced, it may exist in a different medium such as the liquid membrane of the electrode. (2) The electrode has to be rinsed between two titrations to give reproducible results, otherwise it becomes sensitive to OH-. This suggests that some adsorption of DDAOH+ occurs at the interface solution/membrane or that DDAOH+ exchanges with DTA+, the original ion present in the membrane. DDAO, as a neutral species, can freely penetrate into the PVC phase. Both species DDAO and DDAOH+ can be easily present inside the membrane. The response of the electrode in the case of the formation of a dimer will be calculated in the following section and will be compared to experimental results. Equilibrium in Solution. For the sake of simplicity, DDAO and DDAOH+ are called L and LH+. The dimer DDAO-DDAOH+ is consequently L2H+. All equilibriums are written in the aqueous phase. If the dimer exists in the membrane, it can be expressed in aqueous solution too, via an activity transfer coefficient. Concentrations are supposed small enough to replace activities in equilibrium constants. The acidity properties of DDAO are
L + H+ ) LH+
Ka ) [L][H+]/[LH+]
(6)
KD ) [LH+][L]/[L2H+]
(7)
The dimerization is written as The alternated additions are performed so that the final concentration of β-CD in solution is 6 × 10-4 M. Once experimental values for r are determined as a function of [DDAO], a least-squares fitting program is used to determine the best value for Kc. It leads to Kc ) 12 300 ( 500, if all concentrations are expressed in moles per liter. Experimental values of slope r are shown in Figure 4 as well as the fit obtained with this value of Kc. This value is similar to that of 12 800 ( 100 obtained by a spectrometric method by Sasaki et al.20 at pH 10.5. Tunc¸ ay and Christian21 studied this association constant by surface tension measurement. Their values at pH 5 (7000 ( 400 in water and 8700 ( 550 in 0.1 M NaCl) are lower than by potentiometry and spectrometry. Surface tension may not be an adequate method to determine bulk behavior in these conditions. Indeed, the cmc of DDAO vs pH given in 0.1 M NaCl in the same reference is not similar to that obtained by other techniques (Figure 3).
L + LH+ ) L2H+
Mass conservation on DDAO leads to (Lο is the total concentration of DDAO)
Lο ) [L] + [LH+] + 2[L2H+]
(8)
Using eqs 6 and 7, all concentrations can be expressed as functions of Ka, KD, and LH+:
[L2H+] ) Ka[LH+]2/KD[H+]
(9)
[L] ) Ka[LH+]/[H+]
(10)
DISCUSSION Experimental results indeed indicate that the electrode responds to DDAO in a very unusual way, with a super-Nernstian slope. Two points will be discussed here: the possible origin of
If the dimer is present in low proportion in solution (i.e., KD is large), it can be neglected in the mass conservation. [LH+] and [H+] are then linked by
(20) Sasaki, K. J.; Christian, S. D.; Tucker, E. E. J. Colloid Interface Sci. 1990, 134, 412. (21) Tunc¸ ay, M.; Christian, S. D. J. Colloid Interface Sci. 1994, 167, 181.
(22) Kaimoto, H.; Shoho, K.; Sasaki, S.; Maeda, H. J. Phys. Chem. 1994, 98, 10243. (23) Terada, Y.; Maeda, H.; Odagaki, T. J. Phys. Chem. B 1997, 101, 5784.
2380
Analytical Chemistry, Vol. 72, No. 11, June 1, 2000
Figure 5. Schematic representation of the electrode for the calculation of the cross-membrane potential. Cations M+ (i.e., LH+ and L2H+) can cross the membrane; anions Y- and A- cannot. Other notations are the same as in the text.
[LH+] )
Lο 1 + Ka/[H+]
(11)
Potential across the Membrane. To determine the potential across the membrane, we consider the species that are present in the membrane. The membrane is considered as strictly impermeable to anions Y-; that is, no anion can enter or exit the membrane. In our case, the tetraphenylborate ions can be mobile inside the membrane, but they cannot exit into the aqueous phase: the flux of anions through the membrane is zero. The only two species that could diffuse through it are the charged forms of DDAO: LH+ and L2H+. Figure 5 represents a schematic view of this electrode. If the ion pairs LH+, A- and L2H+, A- are completely dissociated inside the membrane, the cross-membrane potential can be expressed as24
(
)
wLH+[LH+]r + wL2H+K[L2H+]r RT Φl - Φr ) ln F wLH+[LH+]l + wL2H+K[L2H+]l
(12)
where wi is the electric mobility of species i in the membrane and K the ion-exchange constant at the interface between membrane and solution:
K)
[LH+]l [L2H+]0 [LH+]0 [L2H+]l
)
[LH+]r [L2H+]e [LH+]e [L2H+]r
(13)
Subscript 1 refers to the “unknown” aqueous solution, r refers to the reference solution, and 0 and e refer to the membrane side of the interface membrane/solution (see Figure 5). Introducing the parameter R as
R)
wL2H+ Ka K wLH+ KD
is eventually given by eq 15. The first term of the right-hand side
( )
[LH+]l RT ln Φ l - Φr ) F [LH+]r
()
(
)
Lοl 1 + Ka/[H+]r RT RT ln ο ln F F Lr 1 + Ka/[H+]l
(
)
1 + RLοl/([H+]l + Ka) RT ln (16) F 1 + RLοr/([H+]r + Ka)
and converting [L2H+] through eq 9, the cross-membrane potential (24) Eisenman, G. In Ion Selective Electrodes; Durst, R. A., Ed.; National Bureau of Standards Special Publication 314, Washington, DC, 1969; Chapter 1.
)
is the classical contribution of LH+ to the potential, if it is the only diffusion species. The second term is the correction of the potential due to a second diffusing species, when it is linked to the first one by a chemical equilibrium. One notices that only one parameter, R, is needed to describe the system in this case. R is a ratio of chemical constants (Ka and KD), ion exchange constant (K) and diffusion properties (wL2H+ and wLH+), that are experimentally difficult to determine individually. One can, however, notice that the dimer can be efficient in establishing the potential, even though its concentration in solution is very low (KD high): it can be extracted in the membrane (K large) or have a large mobility wL2H+. Fit of Experimental Calibrations. We used eq 15 to reproduce experimental calibrations at various pHs. During the experimental recording of the potential, all solutions were buffered: [H+]1 and [H+]r are fixed in eq 15 for each calibration curve. However, the variable that is experimentally known is the total concentration of DDAO, Lο, and not the concentration of species [LH+]. These two quantities are related by eq 11, if the dimerization constant KD is taken low enough so that eq 11 can be used. At a given pH, Φ1 - Φr is related to Lο via
Φl - Φr ) (14)
(
1 + R[LH+]l/[H+]l RT (15) ln F 1 + R[LH+]r/[H+]r
which is rewritten as Analytical Chemistry, Vol. 72, No. 11, June 1, 2000
2381
Φl - Φr ) -
(
)
Lοl RT RT ln(Lοl) ln 1 + R + F F ([H+]l + Ka) f ([H+]r, [H+]l, Lοr) (17)
f ([H+]r, [H+]1, Lοr) is a constant depending on the reference solution and the pH of the buffered solution. The first two terms in eq 17 are responsible for the slope of the titration curves. The function f ([H+]r, [H+]1, Lοr) gives the position of the curve. Theoretical results are displayed on Figure 2. A single value R ) 1.8 ( 0.2 in eq 16 gives a correct fit of all experiments. At low enough pH (pH 2), 1 . RLο1/([H+]1 + Ka): eq 17 leads to a Nernstian slope RT/F in the plot Φ1 - Φr vs ln(Lο1). At high enough pH (pH >4.5), 1 , RLο1/([H+]1 + Ka): the slope becomes 2RT/F. Between these two extremes, the curve can be fitted by a straight line of intermediate slope. Some authors10 have calculated the response slope of a liquid junction electrode, in the case of the formation of a charged dimer between a primary and a secondary ion inside the membrane. Their calculation leads to a “twice-Nernstian” slope, which corroborates our results. However, they do not formalize the influence of the reference solution, which is of importance for the fitting of our experimental curves.
2382
Analytical Chemistry, Vol. 72, No. 11, June 1, 2000
CONCLUSION The electrode can be used as a powerful captor for DDAO, whatever the pH. It was proven to respond to DDAO in a reproducible way in various media: (1) The shape of Figure 3, with a minimum around pH 5, is sufficiently specific to conclude that the breaking point of the calibration curve indeed corresponds to the cmc and that the electrode responds to DDAO and not to some other species. (2) The reproducibility of the emf in various media, and the slope of calibration beyond pH 4.5, much higher than the Nernstian response 60 mV/decade renders this electrode extremely sensitive for the determination of concentrations, in batch experiments for instance. (3) The stability of the electrode over at least 30 min enables its use for continuous titration, for kinetics of adsorption, etc. Another electrode specific to DDAO was recently mentioned,25 but little information on its calibration is given. In our case, the interpretation for the twice-Nernstian slope, based on the formation of a dimer of DDAO and requesting only one parameter to adjust for all pH, seems coherent with the experimental observations. Received for review October 4, 1999. Accepted February 29, 2000. AC9911387 (25) Katsuura, H.; Takisawa, N.; Manabe, M.; Maeda, H. Colloid Polym. Sci. 1999, 277, 261.
