Determination of Surfactants Based on Mixed-Micelle Formation

Rubio, and Dolores. Perez-Bendito. Anal. Chem. , 1995, 67 (11), pp 1872–1880. DOI: 10.1021/ac00107a018. Publication Date: June 1995. ACS Legacy Arch...
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Anal. Chem. 1995, 67, 1872-1 880

Determination of Surfactants Based on Mixed-Micelle Formation Dolores Sicilia, Soledad Rubio, and Dolores P&ez-Bendito*

Department of Analytical Chemistty, Faculty of Sciences, University of Cordoba, E- 14004 Cordoba, Spain

A new approach to the determination of surfactants is proposed, based on the formation of mixed micellesfrom binary surfactant solutions, one of the surfactants being the an*. The theory for nonideal mixed micelles, according to which the critical micelle concentration of mixed systems depends on the solution composition,was used to derive an expression that provides linear calibrations for the determination of surfactants. The hypothesis put forward for the analytical applicability of the proposed expression is experimentally verified. The analytical applicability of this methodology is demonstrated by quantitating major nonionic alkoxylated surfactants; the linear surfactant concentration range achieved was from 0.2 to 4 mg L-l. The main advantages of the proposed methodology over most analytical methods using monomeric nonionic surfactants include responses that are not dependent on the molecular weight or on the ethylene oxide units in the alkoxylated surfactant, experimental convenience (no extraction or precipitation of the product formed in the determinative step is required),and rapidity (mixed micelles are formed instantaneously). The methodology can be extended to the determination of all types of surfactants in aqueous and organic media. The need to routinely determine low concentrations of major surfactants in formulated products, environmental samples, and laboratory test liquors has led to the development of a vast analytical methodology.’ The powerful capabilities of modem chromatographic techniques, particularly HPLC, facilitate separation of all major surfactant classes for analysis under appropriate conditions. However, effective use of the full separation capabilities of these techniques is hindered by (A) the need to develop concentration/separation schemes to isolate sufiicient material of acceptable purity for analysis; (€3) the need for suitable detection systems capable of sensitively and specifically determining separated surfactant components; and (C) the need to correctly assign chromatographic peaks to different surfactant types and their oligomers and isomers. All these call for simpler, faster methods amenable to routine laboratory testing for biodegradability and aquatic toxicity of surfactants, as well as to rapid analysis of formulated products.’ Focusing, for example, on nonionic surfactants, quantitation of the most important alkoxylated surfactants [general formula RO(CHzCHzO),H, where R is an alkyl (c12-cl8) or alkylphenyl group (octyl-/nonylphenol) and n an average of 4-20] is routinely performed by using a fairly small number of nonspecific proce(1) Waters, J. In Recent Developments in the Analysis of Su$actants; Porter, M. R, Ed.; Critical Reports on Applied Chemistry 32; Elsevier: New York, 1991; pp 161-218.

1872 Analytical Chemistry, Vol. 67, No. 7 7, June 7, 7995

dures that have gained widespread general acceptance. Some of the most frequently cited procedures for this purpose involve bismuth active substances (BIAS) reaction^,^^^ cobaltothiocyanate active substances (CI’AS) reaction^,^'^ thin-layerchromatography (TLC)? and potassium picrate active substances (PPAS) react i o n ~ The . ~ chemical foundations of the analytical determination steps in all these methods, and many others, are essentially similar and involve complex formation reactions between the polyether chain of the nonionic surfactant and either an inorganic metal or organic salt. The abovementioned methods can provide acceptable accuracy and precision when wellcharacterized media are used (e.g., under laboratory testing conditions) ; however, despite the improvements on the original methods, they still have some serious drawbacks. Thus, the response of a nonionic surfactant is dependent upon both its molecular weight and its poly (oxyalkylene) chain length. Consequently, results for samples in which the nature of the nonionic surfactant is unknown (particularly environmental samples) should be expressed arbitrarily in terms of a suitable reference surfactant [usually a nonylphenol ethoxylate with an average of 8-10 ethylene oxide (EO) units]. The PPAS procedure7f gives a relatively uniform response on a weight basis for alkoxylated nonionic surfactants with an average of 8-15 EO units; however, little or no reaction is obtained for surfactants containing an average of 4 or fewer EO units. Also, the procedures are tedious and time consuming (about 90 min is required for the determination sequence to complete), and the extraction efficiency is quite low up to n = 9.7 One other major drawback is that these methods are not specific for nonionic surfactants, so the detected entities are correctly referred to as “reagent active substances” when no sample cleanup is done. All available methods for the determination of total surfactants are based on reactions or physicochemical properties of their monomers in solution. In this work, however, the determination of surfactants based on measurements of the critical micelle concentration (cmc) of mixed micelles as a function of the analyte surfactant concentration was undertaken for the first time. Previous studies9 have showed micellar catalysis to be experimentally simpler and more selective than methods based on monomer properties for the determination of sodium dodecyl sulfate, the (2) Wickbold, R. Tenside Deterg. 1972,9,173. (3) Waters, J.; Longman, G. F. Anal. Chim. Acta 1977,93,341. (4) Boyer, S. L.; Guin, K F.; Kelley, R M.; Mausner, M. L.; Robinson, H. F.; Schmitt, T. M.; Stahl, C. R.; Setzkom, E. A. Environ. Sci. Technol. 1977, 11, 1167. (5) Petts, K. W.; Sliney, I. Water Res. 1981,15, 129. (6) Patterson, S. J.; Hunt, E. C.; Tucker, K B. E. I. Proc. Inst. Sewage Put$

1966,2,190. (7) Favretto, L.; Stancher, B.; Tunis, F. Analyst 1980,105, 833. (8) Toei, K.; Motomizu, S.; Umano, T. Talunta 1982,29,103. (9)Sicilia, D.; Rubio, S.; Perez-Bendito, D. Anal. Chim. Acta 1994,298,405. 0003-2700/95/0367-1872$9.00/0 0 1995 American Chemical Society

main limitation of which is their high detection limits. The use of mixed micelles considerably decreases the surfactant concentration that can be determined relative to single micelles; if the cmc for the micelle concerned is low enough, the proposed micellebased method can compete with monomer-based methods in terms of sensitivity. It is, therefore, interesting to explore the analytical potential of the properties of mixed micelles for the determination of surfactants in search of more straightforward, rapid, and efficient alternatives to existing procedures. THEORETICAL BACKGROUND

Several theoretical formulations are available for describing the behavior of multicomponent ideal (e.g., homologous series of surfactants with similar head groups) and binary nonideal (e.g., mixtures of ionic and nonionic surfactants or two surfactants having different head groups) mixed micelle system^.'^-'^ The models provide simple tools for analysis and prediction of the main properties of mixed micelles, including mixed cmc values, micellar mole fractions, and monomer concentrations. Thus, the cmc value for a binary nonideal surfactant mixture (C*) can be expressed as a function of the cmc values for the constituent single surfactants as follows:10-12

where C1 and CZ are the cmcs of pure surfactants 1 and 2, a is the mole fraction of surfactant 1in the total mixed solute, and f i andfi are the activity coefficients of surfactants 1 and 2 in the mixed micelle. These coefficients are equivalent to the micellar activity of each surfactant and represent the ratio of an effective over actual mole fraction for a given component of the mixed micelle. For typical surfactants, the coefficients are usually less than unity; also, by definition, they are unity for both ideal mixtures and pure components. Since the c* value for two given surfactants is a function of the mole fraction of the two, this relationship could be used for analytical purposes. Thus, eq 1 can be rearranged as follows:

which permits calculation of the mole fraction for surfactant 1from the parameter 1/c* - l/fiCz. In order to obtain calibrations as a function of the surfactant concentration instead of the mole fractions, the amount of micelles present at the mixed cmc is assumed to be small; accordingly, one can equate the composition of the monomers to that of the total surfactant. As a result, the mole fractions of surfactants in the mixed micelle will be given by (10) Puwada, S.; Blankschtein, D. In Mixed Surfactant Systems; Holland, P. M., Rubingh, D. N., Eds.; ACS Symposium Series 501; American Chemical Society: Washington, DC, 1992; pp 96-113. (11) Rubingh, D. N. In Solution Chemistty of Sulfactants; Mittal, K. L., Ed.; Plenum Press: New York, 1978; Vol. 1, pp 337-354. (12) Holland, P. M. In Mixed Sulfactant Systems; Holland, P. M., Rubingh, D. N., Eds.; ACS Symposium Series 501; American Chemical Society: Washington, DC, 1992 pp 31-44. (13) Clint, J. J. Chem. Soc., Faraday Tram. 1 1975,71, 1327.

a=

=-b1

C,M

+ c," c* C2M

1-a= C,"

+ C,M

- C," --

c*

(3)

(4)

where CIM and C Z denote ~ the concentrations of monomeric surfactants 1and 2, respectively. Substituting eq 3 into eq 2 and rearranging gives

For binary ideal mixtures, eq 5 reduces to

Linear calibrations for ideal mixtures can be obtained by plotting 1 - P / C Zversus ClM. For nonideal mixtures, linearity will be fulfilled only over the CIM range where f i and f i are constant. Analytically, ideal mixtures could be used to determine surfactants with similar hydrophobic tails and head groups (e.g., some manufactured products). Determining total surfactants (e.g. environmental samples), however, entails the existence of some extent of nonideality. To this end, we tested the analytical applicability of eq 5. For this purpose, we assumed the micellar activity of surfactant 2 in the mixed micelle not to be significantly different from that of the single micelle at concentrations of surfactant 1 where c* approximates CZ and hence f i is unity. If the constancy of f i implies that the micellar activity of surfactant 1 in the mixed micelle will remain virtually unchanged over the range of ClMvalues considered, then a plot of 1 - C / C Z versus CIM will be linear and eq 5 will reduce to

(7)

Parameters c* and CZcan be measured from several properties, namely surface tension, equivalent conductivity, osmotic pressure, detergency, spectral changes in some dyestuffs, etc. Experimentally, the use of dyestuff^'^-*^ is a simple, rapid method for determining cmc values; while the presence of the dyestuff may affect the cmc, this is unimportant when the parameter of interest is the variation of the cmc value as a function of the surfactant concentration. The determination of surfactant cmc values using dyestuffs is easily performed titrimetrically.2O However, the determination of c'values in this way requires the use of the surfactant 1-surfactant 2 mixture as titrant; because its composition changes at each surfactant 1 concentration tested, the procedure is rather impractical. For this reason, for titrime(14) Rosenthal, K. S.; Koussale, F. Anal. Chem. 1983,55, 1115. (15) Montal, M.; Gitler, C. Bioenergetics 1973,4, 363. (16) Femandez, M. S.; Fromherz, P. J. Phys. Chem. 1977,81, 1755. (17) Moller, J. V.; Kragh-Hansen, U. Biochemistty 1975,14, 2317. (18) Minch, M. J.; Giaccio, M.; WOW, RJ. Am. Chem. SOC.1975,97, 3766 (19) Bunton, C. A; Minch, M. J. J. Phys. Chem. 1974,78, 1490. (20) Ledbetter, J. W.; Bowen, J. R Anal. Chem. 1971,43, 773.

Analytical Chemistry, Vol. 67, No. 11, June 1, 1995

1873

~

~~

~

Table I.Analytical Figures of Merit of the Proposed Method for the Determination of Nonionic Suctactants of the Type RO(CH&HZO)~H

R

n 4 6 9 10 23 4 5 6 9 12 10 10 10

product name Brij 30

&laurylether %lauryl ether 10-lauryl ether Brij 35 Triton N-42 Triton N-57 Triton N-60 Nemol K-39 Nemol K-1032 10-tridecylether Brij 56 Brij 76

C1 (x

(M)

4.0 4.5 5.0 5.1 6.0 5.0 5.1 6.0 7.5 8.0 2.4" 0.21 0.18"

slo e f SD (mg-' L)

(x lo-!)

8.6 f 0.2 9.2 f 0.1 8.8 f 0.1 9.4 f 0.1 9.2 f 0.3 9.2 f 0.2 9.3 f 0.2 9.8 f 0.1 8.5 f 0.2 9.6 f 0.3 8.5 f 0.2 9.4 f 0.1 9.06 f 0.04

intercept f SD (x 10-2)

1.1 f 0.4 -0.4 f 0.4 0.3 f 0.4 0.1 i 0.2 -0.007 f 0.4 0.3 f 0.4 0.7 i 0.4 0.6 f 0.3 -111 -0.4 f 0.7 -0.07 f 0.3 -0.003 f 0.3 1.53 f 0.07

SEEb (x

6.7 4.1 5.9 3.7 4.8 7.1 5.6 4.1 9.3 9.8 2.2 5.2 0.7

r 0.997 0.9993 0.9990 0.9990 0.9996 0.998 0.998 0.9996 0.998 0.9990 0.9998 0.9997 0.9990

f2

fi

1.00 f 0.01 1.00 f 0.01 1.00 f 0.01 1.00 0.01 0.99 f 0.01 1.00 f 0.01 1.00 10.01 1.00 f 0.01 1.00 f 0.02 1.00 f 0.01 1.00 f 0.01 1.00 f 0.01 1.01 f 0.02

0.803 0.536 0.390 0.333 0.151 0.548 0.479 0.351 0.255 0.174 0.784 7.595 8.636

*

Photometrically determined using the dye CBBG. Stardard error of the estimate. Correlation coefficient, n = 8.

tries, eq 1 should be rearranged for practicality (e.g., by using surfactant 2 as the titrant). For this purpose, eqs 1,3, and 4 can be combined to give

based on which linear relationships will be obtained by using surfactant 2 as the titrant and plotting the parameter 1 - CzM/C2 as a function of the concentration of surfactant 1 (CI'), provided the above hypotheses are fulfilled. Parameters CZand C Z can ~ be easily obtained from titrations performed in the absence and presence of surfactant 1in the titration vessel, respectively. The sensitivity for the determination of surfactant 1 will depend on both its cmc value (CJ and its micellar activity in the mixed micelle fi). Therefore, the titration should, in principle, be performed in a medium that lowers the cmc of surfactants (e.g., one with a high ionic strength) and using titrants that are structurally very different from the analytes in order to obtain surfactant mixtures that deviate markedly from ideality. The usefulness of eq 8 for the determination of surfactants is tested below for alkoxylated nonionic surfactants. Alcohol ethoxylates (R between 12 and 18 carbons and n between 4 and 23) and alkylphenol ethoxylates (nonylphenols with n between 4 and 12) were chosen for this purpose. The selected titrant was an anionic surfactant (sodium dodecyl sulfate) since surfactants of this type interact more strongly with alkyl ethoxylate nonionics than do cationic surfactants of equivalent chain lengths." EXPERIMENTAL SECTION

Apparatus. The equipment used consisted of a Mettler DL 40 Memotitrator furnished with a 10-mLautoburet, a fan stirrer, a titration vessel, and a Mettler GA 14 recorder. The detection unit was a Metrohm 662 spectrophotometer equipped with an inmersion probe. Reagents. The highest grade commercially available reagents were used throughout without further purification. A 6.6 x M aqueous solution of Coomassie Brilliant Blue G (CBBG, Sigma) was made by dissolving 0.0626 g of the reagent in 1L of distilled water with sonication for 15 min. Aqueous solutions of sodium chloride (5 M) and sodium dodecyl sulfate (SDS) (11 g L-l, 1874 Analytical Chemistry, Vol. 67,

No. 1 1 , June 1, 1995

Aldrich) were also made. The chemical formulas of the poly(oxyethylene) alkyl (aryl) ether nonionic surfactants used are given in Table 1; the sources of these materials and their concentrations (in distilled water) are listed below Brij 30, &lauryl ether, Slauryl ether, and lblauryl ether (Sigma, 1g L-9; Brij 35 (Merck, 1g L-l); Triton N-42, Triton N-57, and Triton N-60 (Sigma, 0.2 g L-9; Nemol K-39 and Nemol K-1032 (Mass6 and Carol, Barcelona, Spain, 0.2 g L-*); lbtridecyl ether (Sigma, 0.2 g L-l); Brij 56 and Brij 76 (Sigma, 0.1 g L-l). The stock solutions were stable for at least 1 month. Procedure. Volumes of 12 mL of 6.6 x M CBBG solution, 10 mL of 5 M sodium chloride, and an aliquot of standard solution of nonionic surfactant were placed in a 5bmL standard flask, and distilled water was added to the mark. Aliquots were chosen to contain 0.2-4.0 mg L-' nonionic surfactant in the final 5bmL volume. This solution, at pH 5-10, was placed in a lob mL titration vessel and titrated with 11g L-' SDS from the buret at a rate of 10 mL min-'. The stirring speed was set at 250 rpm, the added autocontrol system at position 1, and the initial absorbance at 0.200. The endpoint of the titration curve recorded (absorbance at 620 nm as function of titrant volume) was graphically determined from the intercept of the straight line extrapolations before and after the equivalence point. The amount of SDS consumed in the titration, expressed as a molar concentration, corresponded to the concentration of monomeric anionic surfactant (Cz') needed to obtain the cmc of the mixed micelle (P).Likewise, the cmc of SDS single micelles (Cz)was determined by a similar titration procedure in the absence of nonionic surfactant in the titration vessel. Calibration graphs were constructed by plotting the parameter 1 - CZM/Cz as a function of the concentration of nonionic surfactant (CIM). RESULTS AND DISCUSSION

CBBG was used for the spectrophotometricmeasurement of the cmcs of both SDS single micelles (CZ) and SDS alkoxylated nonionic mixed micelles (P). The spectral features of this dye are modfied by the presence of both nonionic and ionic micelles (the dye has been used for rapid cmc determination^).'^ In an aqueous medium, CBBG exhibits an absorption peak at 580 nm (Figure 1, curve 1) that is not altered by the presence of either nonionic or ionic monomers of detergent. Formation of anionic

L 00

700

6 00

5 00

800 h(nm)

Figure 1. Spectra for Coomassie Brilliant Blue G (1.58 x M) in an aqueous medium (curve 1) and in micellar media of sodium M) (curve dodecyl sulfate (1.0 x lo-' M) (curve 2), Brij 35 (2.0 x 3), and SDS-Brij 35 (1.0 x and 2.0 x M, respectively)

(curve 4). 0.4

w V

0.3 4

m

One very important step in optimization via the relationship of the parameter 1 - CzM/C2 to each variable studied was to ensure the absence of dilution effects in obtaining CZand CzM.As shown in Figure 3 4 such dilution effects result in apparently increased Cz and CZMvalues, and, as can be inferred from the greater volume of titrant required to obtain CZ relative to CzM, they affect CZto a greater extent. As a result, the measurement parameter 1 - Cz'/Cz is apparently increased (Figure 3B). No dilution effects on the system under study were observed at SDS concentrations above 10 g L-I (Figure 3A); therefore, the maximum titrant volume that could be added to the titration medium was 4% of the total volume. Figure 3C shows the influence of dilution effects on calibration. The intercept of the calibration graph run in the presence of dilution effects (line 2, [SDSI = 6 g L-') was roughly equal to the apparent enhanced sensitivity at the titrant concentration tested (see Figure 3B). The effect of electrolytes on micellization of both single SDS and mixed SDS-Brij 35 micelles and on the measurement parameter 1 - CzM/C2was examined using sodium chloride and sodium sulfate, both of which exhibited a similar influence at a given ionic strength between 0 and 2.5 M. Micellization of both anionic and anionic-nonionic micelles was markedly favored by increasing ionic strength up to about 0.5 M (Figure 4&. The effect of electrolyte concentration at an ionic strength between 0 and -1 M fitted the general equation

a 0

m

1

1.0

2 .o

1

30

Volume of I I ~ L - ' SDS (mL) Flgure 2. Variation of the absorbance of Coomassie Brilliant Blue G (1.58 x M) at 620 nm as a function of the volume of titrant (1 1 g L-l) sodium dodecyl sulfate added to a titration vessel containing no nonionic surfactant (curve 1) or Brij 35 concentrations of 1 (curve 2), 2.5 (curve 3), and 4 mg L-I (curve 4).

and nonionic single or mixed micelles (Figure 1, curves 2-4, respectively) causes an increase in the absorbance at 620 nm that is linearly dependent on the detergent concentrationto the point where the dye concentrationbecomes a limiting factor. Figure 2 shows typical titration curves experimentally obtained at 620 nm by using CBBG in the absence (curve 1)and presence of different alkoxylated nonionic surfactant concentrations (curves 2-4). The parameter Cz and the different CzMvalues can be easily calculated from the volume of titrant consumed at the endpoint of the curves. Optimization. Brij 35 was selected for optimization purposes, and two objectives were considered in selecting the best experimental conditions: (a) the highest possible sensitivity in the determination of the nonionic surfactant and (b) the highest possible precision in the determination of the titration endpoint. In order to ensure the maximum possible sensitivity, those variables allegedly affecting the C1 value (ionic strength, pH and temperature) were investigated; an approximation of the influence of the titrant on f i is made below. The best possible precision was determined by studying the effect of the CBBG concentration.

where a and b are constants for a given surfactant ionic head at a particular temperature and Ci is the total (univalent) counterion concentration (in mol/L) . The cmc depression in ionic surfactants is reportedly due mainly to the decrease in the thickness of the ionic atmosphere around ionic head groups in the presence of the additional electrolyte and the consequently decreased electrical repulsion between them in the micelles.21 No significant differences between the cmc values for single SDS and mixed SDSBrij 35 micelles were observed at an ionic strength above 2.5 M. The measurement parameter was maximum at ionic strength values between 0.5 and 1.7 M and decreased outside this range (Figure 4B). This behavior may be exhibited by nonionic surfactant analytes. Thus, the change in the cmcs of nonionics on addition of an electrolyte is ascribed to salting out or salting in of the hydrophobic groups in the aqueous solvent by the electrolyte rather than the effect of the latter on the hydrophilic groups of the surfactant?' When the monomeric form of a surfactant is salted out by the presence of an electrolyte, micellization is favored, and the cmc of the surfactant is decreased [in this case, C1 decreases, and hence 1 - CzM/Cz increases over the ionic strength range from 0 to 0.5 M, Figure 4B]; when the monomeric form is salted in, the cmc is increased, and so should be 1 - CzM/C2(e.g., for Brij 35, this is the case at ionic strength values greater than 1.7 M, Figure 4B). The salting out and salting in effects may cancel each other over a given ionic strength interval; as a result, the cmc of the surfactant will remain constant, as will 1 - CzM/Cz. As can be inferred from Figure 4B,the ionic strength enhances the signal only about 2-fold, which implies that the Cl value is reduced only (21) Rosen,M. J. Surfactants and Interfacial Phenomena; Wiley: New York, 1978 pp 83-122.

Analytical Chemistry, Vol. 67,No. 11, June 1, 1995

1875

I

I

A

6

4

I

a

10

12

[SDS], (gL-')

Figure 3. (A) Influence of the sodium dodecyl sulfate concentration on C, and GM.(B) Variation of the measurement parameter 1 - GM/C, as a function of the titrant concentration; [Brij 351 = 1 mg L-l. (C)Calibration curves for Brij 35 at SDS concentrations of 11 (curve 1) and 6 g L-' (curve 2). (For details, see text).

-

-

N

0.2

-

u

I N

t:

0.1-

I c

1

2 [Ionic strength] (M)

Figure 4. (A) Influence of the ionic strength, adjusted with sodium chloride, on C, and GM. (B) Variation of the measurement parameter as a function of the ionic strength; [Brij 351 = 1 mg L-l.

by a factor of 2. Therefore, this variable will enhance the sensitivity for the determination of ionic surfactants to a greater extent than for the determination of nonionic surfactants since the effect of electrolytes on their cmc is more pronounced (e.g., see the dependence of CZon ionic strength in Figure 4A). Analytically, an ionic strength of 1 M is recommended for determining nonionic surfactants in real samples on the basis of the increased sensitivity and precision achieved, as well as the unlikely dependence of the signal on the electrolyte content in the analyzed sample. The optimum working pH was determined by using hydrochloric acid and sodium hydroxide for adjustment. In principle, the effect of acids or bases on micellization, and hence on the 1876 Analytical Chemistry, Vol. 67, No. 1 1 , June 1, 1995

measurement parameter, should be essentially an electrolytic effect. Therefore, in order to establish the effectiveness of H+ and OH- in decreasing the cmc of the systems considered, the experiment was carried out with no salts added. Figure 5A depicts the effect of pH values from 3 to 11.5 on CZand CzM. The results show that micebtion of SDS and SDS-Brij 35 micelles is hardly affected by pH over the range from about 5 to 8.5; more acidic or basic media decrease the cmcs of the micelles studied. On the other hand, the decrease is similar to that produced by neutral electrolytes [CZwas also reduced by about 1 order of magnitude in the presence of hydrochloric acid (Figure 5C, [HCll = 0.1 M)]. The influence of hydrochloric acid concentrations greater than 0.1 M on Cz and CzM (Figure 5C) cannot be ascribed to an electrolytic effect since identical concentrations of sodium chloride or sodium sulfate are known to favor micelliiation (Figure 4A). The measurement parameter was increased about 2-fold in the presence of HCl and NaOH (Figure 5B). This maximum value (-0.19) was found to remain constant at hydrochloric acid concentrations between and 0.1 M, and it was roughly equal to that obtained in the presence of neutral salts (see Figure 4B). Therefore, the effective reduction of CI by electrolytes was similar and independent on the ions involved, even though it occurred at a lower ionic strength when protons were used for adjustment. Concentrations of hydrochloric acid greater than 0.1 M sharply decreased 1 - CzM/C2 (Figure 5D). In analytical terms (sensitivity and precision), using an ionic strength between 0.5 and 1.7 M adjusted with sodium chloride and 0.1 M adjusted with hydrochloric acid proved or between indifferent. However, for samples with unknown electrolyte content, it is advisable to use a pH between 5 and 10 and an ionic strength of 1M adjusted with sodium chloride. The temperature, the effect of which was studied between 20 and 50 "C, affected micellization of single SDS and mixed SDSBrij 35 micelles similarly. The parameters CZ and CzM hardly changed between 20 and 30 "C; however, they exhibited a nearly exponential dependence on the temperature above 30 "C. The parameter 1 - CzM/Cz remained essentially constant over the temperature range studied, which is logical taking into account that this variable affects nonionic surfactants to a lesser extent relative to ionic surfactants. The range from 20 to 30 "C is optimal

0

u .

0.2

0.2

. - 0 .a

N

N

V

0.1

N"'

IN U

v

-

O''

v

I

I

00 2.0

A

2.8

0

2

-I

2.2

2.2

X

a.

-

0

v

X

-

v1

-I

0

fi

1.E

I n

l.E

D

?s

1.c

4

,

I

8

12

1.o

PH

Figure 5. (A) Influence of pH on G and GM.(B) Variation of the measurement parameter as a function of pH; [Brij 351 = 1 mg L-', [SDS] = 11 g L-I, (C) Influence of the hydrochloric acid concentration on C2 and GM. (D) Dependence of 1 - GM/G on the hydrochloric acid concentration; [Brij 351 = 1 mg L-l, [SDS] = 1 g L-l.

in terms of precision, and measurements can be performed at room temperature without thermostating. In order to ensure the highest possible precision in measuring the endpoints of the titration curves, we determined the optimum CBBG concentration. The dye was found not to affect micellization of single SDS or mixed SDS-Brij 35 micelles, thus conkring its usefulness for the determination of the cmcs of both types of micelles. CBBG concentrationsbelow about 1.3 x M proved inadvisable since the absorbance increase at 620 nm as a function of the concentration of micelles was very low, causing lack of precision in the determination of the titration endpoint. Maximum absorbance increase at 620 nm as a function of the concentration of micelles was obtained at CBBG concentrations above about 1.5 x M (1.58 x M was selected as optimal). Dye concentrations above 1.7 x M did not improve the second portion of the titration curve but resulted in a gradually increased initial absorbance as a function of the CBBG concentration owing to the absorption of this compound at 620 nm (Figure 1, curve 1). Calibration. After all experimental parameters were optimized, calibration graphs for nonionic surfactants of the type RO(CH2CH20),H were run by plotting 1 - GM/C2 versus the nonionic surfactant concentration (ClM). Table 1shows the alkyl group (R) and degree of polymerization (n) of the surfactants examined. Their cmc values were either taken from the literature15 or, when unavailable, photometrically determined using CBBG; they varied between about 1 x and 1 x M (most commercially available nonionic surfactants have cmc values in this range). As shown in Table 1,linear calibrations were obtained in all cases [standard errors of the estimate and correlation coefficients varied over the ranges (0.7-9.8) x and 0.997 and 0.9998, respectively]; also, intercept values were not sign%-

cantly different from zero. The linear concentrationrange for all nonionic surfactants was 0.2-4 mg L-I, so the concentrations determined were of the same order of magnitude as those measured by methods based on monomer^.^ As can be inferred from the slopes of the calibration curves obtained (Table l), a nearly uniform response on a weight basis was exhibited by the alkoxylated nonionic surfactants examined. Such a relatively uniform response was obtained from surfactants having as fews as 4 EO units and n-alkyl groups between 12 and 18 carbons, thus surpassing monomer-based methods, the response of which is dependent on both the molecular weight and number of EO units of the alkoxylated nonionic surfactant concerned. In order to determine whether the analytical signal obtained for the different nonionic surfactants, 1 - CzM/C2,was additive, a solution containing a 10 mg L-'concentration of each of the surfactants listed in Table 1was prepared, and a calibration graph was run from them. The graph was linear over the range from 0.2 to 4.0 mg L-' nonionic surfactant. The standard error of the estimate was 7.2 x M, and the correlation coefficient was 0,9991 (n = 7). The slope and intercept of the graph were (9.4 f mg-' L and (0.03 f 0.3) x respectively, which 0.3) x indicates the absence of synergistic effects. The precision of the proposed method, expressed as the relative standard deviation, was 2.5%(n = 11) for a total concentration of surfactants of 1 mg

L-1. Validation of the Proposed Mixed-MicellesMethodology. From the results shown in Table 1, it follows that fi and f i are constant over the linear nonionic surfactant concentrationrange. Also, the near-zero intercepts obtained imply that fi (the activity coefficient for SDS in the mixed micelles) is approximately unity. Analytical Chemistry, Vol. 67, No. 11, June 1, 1995

1877

Table 2. Analytical Figures of Merit of the Determinationof 4.Octyl Ether by Titration with Different Surfactants by Formatlon of Mixed Micelles

surfactant titrant

slope f SD (M-I)

fi

a range for linearity

sodium dodecyl sulfate sodium bis (Zethylhexyl)sulfosuccinate (aerosol OT)

375 f 11 304 f 5

0.356 0.04-0.308 0.439 0.06-0.679

sodium pdodecylbenzenesulfonate sodium hexadecyl sulfate sodium heptadecyl sulfate Triton X-100 Brij 35

367 f 6 505 f 10 179 f 7 185 f 5 213 f 1

0.363 0.264 0.745 0.718

The real value of fi for the different SDS-nonionic surfactant mixed micelles studied was obtained from eq 2 by plotting 1/C* versus a (the mole fraction of nonionic surfactant as d e h e d by eq 3). Calibration data were used for the plot, andfi was readily calculated from the intercept of the straight lines obtained with the gaxis since Cz had a constant value of 2.67 x M, as experimentally found using the abovedescribed procedure. The results obtained (Table 1) demonstrate that the activity coefficient for SDS in the mixed micelle is approximately unity despite the fact that nonideal mixing of SDS-nonionic surfactants occurs, as reflected in experimental slopes different from l/C1 V; * 1). Therefore, the micellar activity of SDS in single and mixed micelles is the same over the linear nonionic surfactant concentration, and our hypothesis is confirmed. The parameterfi was readily estimated from the slopes of the experimental calibration curves (see eq 8), which were equal to l/(ClfiPml) x 103. The C1 values used are given in Table 1;the results obtained (also shown in the Table) demonstrate thatfi is a function of the surfactant. Thus, for a given alkyl or alkylphenyl group,fi decreases proportionally to the degree of polymerization of the ethoxy group, which indicates that mixed micelles gradually deviate from ideal mixing conditions in proportion to steric interactions between the head groups of SDS and nonionic surfactants. A comparison of surfactants bearing the same ethoxy group (e.g., Brij 30 and Triton N-42 or &lauryl ether and Triton N-60) revealed nonideality to be more marked for the alkylphenyl surfactants, which differ from SDS in both hydrophobic taillengths and the sizes of their polar head groups, while alkyl surfactants differ only in their head groups. The behavior of the n-alkyl poly(oxyethy1ene) surfactants with CI6 and C18warrants special attention. As shown in Table 1,the slopes of the calibration curves for these surfactants were similar to those for n-dodecyl and nonylphenyl poly(oxyethylene), even though their cmc values were signi6cantlylower (by about 1order of magnitude); this behavior was a result of their increased fi values. Because nonideal surfactant mixtures generally feature fi values lower than 1,we believed it to be of interest to investigate whether the high fi values found were a general consequence of mixing the given surfactants under the experimental conditions where linear calibration was obtained. Parameters Affecting f ~ Various . experiments showed the CZ/C1 ratio and C1, in addition to the structures of the analyte and titrant, to influencefi (the effect of C1 was somewhat more marked). Thus, the fi value obtained when Brij 76 was titrated with Brij 35 (C,/C, = 33 and C1= 1.8 x M), 3.823, was lower than found in the titration of Brij 76 with SDS (Cz/C, = 1500, C1 = 1.8 x M,fi = 8.819; see Table 1). On the other hand, the fi value obtained in the titration of Nemol K-1032 with SDS, a 1878 Analytical Chemisity, Vol. 67,No. 11, June 1, 1995

0.153-0.612 0.342-0.971 0.410-0.995 0.634-0.992 0.626 0.932-0.997

system featuring a CZ/CIratio of about 33 and C1 = 8 x M, was 0.174 (Table 1). In parallel experiments, anionic alkyl sulfate surfactants (with 8-lkarbon alkyl group) were titrated with Triton X-100. The Clvalues thus obtained for the systems studied ranged from 5.5 x to 8.0 x 10-7 M. fi values greater than unity were obtained for Cl&O4--Triton X-100 and C1&04-Triton X-100 systems (4.918 and 11.950,respectively),the C1 values for which are 6 x and 8 x 10-7 M, respectively. Therefore, fi values greater than unity can be expected for surfactants with very low cmc values; although a near-unity value could be obtained by using titrants with similar cmc values, this could be analytically impractical since titrations with surfactants having a CZvalue of about M produce curves whose endpoints cannot be determined precisely. On the other hand, this behavior can be turned to advantage for the total determination of surfactants featuring different cmcs, as shown by the resuts in Table 1 for nonionic surfactants. In any case, further research is required in order to elucidate the actual effect of various parameters on fi. Scope of the Proposed Approach. We believed it to be important to determine whether the behavior exhibited by nonionic alkoxylated surfactants-SDS systems was general or limited to some analyte-titrant mixtures. As can be inferred from the cmc data listed in Table 1, all the systems studied featured CZ/CI ratios greater than unity (between about 30 and 1500). Mixed micelles are known to be more markedly enriched with the lower cmc component (only at high surfactant concentrations relative to the cmc does the micelle composition approach the bulk compositionlo). Therefore, the mixed micelles of all the systems studied were preferentially enriched with nonionic surfactant; as a result, the mole fraction of nonionic surfactant in the mixed total solute at which linearity was fultilled was very low We thus over the a range from about 1 x to 1 x believed it important to determine whether analyte-titrant systems with C2/Cl < 1, and hence mole fractions of the analyte in the mixture above 0.1, would also fit eq 8. For this purpose, the nonionic surfactant Coctyl ether (R = CaHlj-, n = 4, C1= 7.5 x M) was used as the analyte and titrated with various nonionic and anionic surfactants with cmc values greater than C1. Table 2 shows the names and structures of the surfactants tested. The CZ/C1 ratios for these analyte-titrant mixtures ranged from about 0.5 to 0.005. The calibration graphs obtained for all the systems studied were found to be linear, so fi and fi were constant throughout the CIM range considered; also, fi = 1. Therefore, it seems reasonable to predict that most binary mixtures of surfactants will fit eq 8 over a given range of analytesurfactant concentrations. No clear relationship between the cmc or the nature of the titrant and the fi value was found, however. Therefore, further experiments are required in order to ascertain

where V is the initial titrant volume. In order to avoid dilution effects, 6should have a maximum value equal to 0.04 V; therefore, KZand 0.05Vz are negligible relative to the product KV, so eq 11 reduces to x,,

0.2

0.4

0.6

1.o

0.8

d Figure 6. Dependence of the mole fraction of 4-octyl ether in the for mixed mixed micelle (4on its mole fraction in total mixed solute (a) micelles consisting of 4-octyl ether and (curve 1) SDS, (curve 2) Aerosol OT, (curve 3) sodium pdodecylbenzenesulfonate, (curve 4) sodium hexadecyl sulfate, (curve 5) Triton X-100 or Tergitol 7, and (curve 6) Brij 35.

whether the most suitable titrant for quantitation of a given analyte or group of analytes can be accurately predicted. The range of mole fractions of 4octyl ether in the total mixed solute, a, over which linearity was fulfilled logically depended on the Cz/C1 ratio (Table 2 shows the ranges for the different titrants tested). However, the minimum mole fraction of analytesurfactant in the mixed micelle, x, that could be determined was found not to be dependent on the nature or the cmc of the titrant and to be between about 0.02 and 0.03. Figure 6 shows the variation of x with a over the 4octyl ether concentration range where linearity was fuElled. As can be seen from the plot, the dependence of x on a is a function of the cmc of the titrant; however, the minimum x value quantified (x,,,iA was similar for all the titrants tested. Since xdn was also between 0.02 and 0.03 for the nonionic surfactant-SDS mixed micelles listed in Table 1,this parameter is also independent of C1. Therefore, if Xmin was independent of the surfactant mixture concerned, it seems reasonable to assume that this parameter is characteristic for the analytical technique used. Minimum Quantifiable Amount of Analyte-Surfactant. The monomer concentration of analyte, ClM,at the mixed cmc can be calculated from"

GM= xf,c,

(10)

Because the amount of micelles at the cmc is small and one can equate'the composition of monomers to that of the total surfactant, the minimum ClMone can determine will be equal to the x& value the analytical technique used can quantify. In titrimetries, %,,in will be obtained for VzM = VZ- 0.05, VzM and 6 being the titrant volumes (expressed in mL) required to obtain C* and Cz,respectively. Combining eqs 8 and 10, one has

0.05 =0.04V

Taking into account that the initial volume for the titrations given in Tables 1 and 2 was 50 mL, eq 12 provides xdn = 0.025, which is consistent with the experimental X& values and confirms the assumptions made in deriving the above expression. The ability to predict the behavior of various analyte-titrant systems as regards such analytical features as sensitivity and the minimum amount of analyte-surfactant that can be determined from available knowledge on these systems under the experimental conditions required for fi = 1 and f i = constant is moderately low. It is therefore necessary to perform a thorough systematic study in order to accurately establish the extent to which C1 depends on different variables for surfactants of diverse nature, as well as to determine the parameters on whichfi depends and the relative significance of the working conditions where the optimum fi and CI values will be obtained. Research in this direction is currently in progress in our laboratory. FINAL REMARKS

The proposed methodology for the determination of surfactants by use of mixed micelles opens up interesting prospects for the simple, rapid estimation of total surfactant concentrations. Some of its features make it a good candidate for application in various areas. Thus, the following points are noted. (a) Because this methodology is based on a general property of surfactants (viz.,their ability to form mixed micelles), it can be applied to all types of surfactants (cationic, anionic, nonionic, and zwitterionic). (b) As with single micelles, the formation equilibrium for mixed micelles is reached very rapidly, which expedites the determination. (c) The general procedure only requires using a mixture of the two surfactants to obtain binary micelles, thus avoiding the need for extraction or precipitation, which are required in most monomer-based surfactant determination methods. The proposed methodology therefore features a high experimental simplicity. (d) The sensitivityachieved with mixed micellebased methods is similar to that obtained with monomer-based methods, at least when titrimetric techniques are used, provided the cmc of the analyte is equal to or less than -1 x M, as is the case with nonionic surfactants. Similar sensitivities can, in principle, be obtained for ionic surfactants which generally have cmc values of about 10-2-10-4 M since such values can be decreased by about 2 or 3 orders of magnitude in the presence of added salts. (e) As regards selectivity, because all surfactants can form mixed micelles, those to be determined should be isolated from other surfactants, as in monomer-based methods. However, the selectivity of the proposed methodology toward inorganic ions can be enhanced by using a preset ionic strength since such ions exert only an electrolytic effect on mixed micelles. This assertion is pending coniirmation in subsequent experiments by our research group. (f) The response is essentially dependent on C1;however, a nearly uniform response is obtained for surfactants with a cmc Analytical Chemistry, Vol. 67,No. 11, June 1, 1995

1879

below -1 x W4M, at least nonionic surfactants. The f i value increases inversely proportionally to CI.Since f i values greater than unity have been also been found for anionic surfactants with a cmc above about 10-6-10-7 M, one may reasonably assume that a uniform response can also be obtained from ionic surfactants, provided appropriate experimental conditions are used. (g) The cmc of the mixed micelle (C*, eq 7) or a C*-related parameter (CZM,eq 8) can be measured with various analytical techniques (photometry, fluorometry, conductimetry,polarography, calorimetry) or derived from physical parameters such as surface tension, osmotic pressure, etc.; therefore, the proposed methodology is highly versatile. 0The approach can be extended to organic media, where mixed micelles are also been known to be formed. This is relevant to water-insoluble surfactants (e.g., biosurfactants) and can be used to develop interesting applications, such as the determination of phospholipids in clinical samples.

1880 Analytical Chemistry, Vol. 67, No. 11, June 1, 1995

In order to determine the analytical potential of this methodology, further research should be aimed at elucidating the behavior

of ionic and zwitterionic surfactants and determining what factors influence f i . It is also important to investigate the applicability of ideal binary surfactant mixtures, which, in principle, should provide broader linear ranges for the determination of surfactants than do nonideal mixtures. ACKNOWLEDGMENT The authors gratefully acknowledge finalcial support from the CICyT (Project No. PB91-0840). Received for review January 9, 1995. Accepted March 14,

1995.a AC9500287 @

Abstract published in Advance ACS Abstracts, April 15, 1995.