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Use of visible spectral displacement method to determine the concentration of surfactants in aqueous solution
Use of a Visible Spectral Displacement Method to Determine the Concentration of Surfactants in Aqueous Solution K. JAMES SASAKI, S H E R R I L D. CHRISTIAN, 1 AND E D W I N E. T U C K E R Department of Chemistry and Biochemistry and Institute for Applied Surfactant Research,
University of Oklahoma, Norman, Oklahoma 73019 Received January 16, 1989;accepted May 9, 1989 A substitution method in which phenolphthalein is displaced from the/3-cyclodextrin cavityby the hydrocarbon moiety of a surfactant is used to determine the concentration of the surfactant. The 1:1 complex of phenolphthalein with/3-cyclodextrinhas an absorbancepracticallyequal to zero in the region of the 550-nm band of the basic form of phenolphthalein. When solute molecules containing an alkyl moiety displace some of the phenolphthalein at a pH of approximately 10.5, the absorbance at 550 nm is significantlyincreased and serves as a direct measure of the concentration of the solute. The method is useful in determining concentrationsof surfactants suchas sodium dodecylsulfate and N,N-dimethylN-dodecylamineoxide, which do not contain chromophores. © 1990AcademicPress,Inc. INTRODUCTION
Determining the concentration of aliphatic solutes in aqueous solution can be quite difficult in the case of compounds that do not have a chromophore in the accessible ultraviolet or visible regions of the spectrum. However, a simple spectral method based on the displacement of phenolphthalein at a pH > 10 from the cavity of/3-cyclodextrin may be used to determine concentrations of surfactants like sodium dodecyl sulfate (SDS) and N , N dimethyl-N-dodecylamine oxide ( D D A O ) , which possess the dodecyl moiety. Previous studies have shown that the 1:1 complex between phenolphthalein a n d / 3 - c y clodextrin, at pH 10.5, has a formation constant of approximately 2.1 × 104 liters mole-I at 25°C ( 1 - 3 ) . Careful studies of the dependence of the absorption band of phenolphthalein at 550 n m on the concentration of/3-cyclodextrin have shown that at pH 10.5 the complexed phenolphthalein has an absorptivity practically equal to zero (3). By measuring the increase in absorbance of the 550 nm band as a function of added concentrations of ni To whom correspondence should be addressed.
alkyl alcohols and other solutes containing an aliphatic moiety, we were able to determine 1:1 formation constants for these solutes with fl-cyclodextrin (3). It occurred to us that this method might be a useful analytical technique for determining the concentrations of surfactants and other compounds containing n-alkyl or other aliphatic groups, The present note describes our use of the displacement method to determine concentrations of sodium dodecyl sulfate and N,N-dimethyl-N-dodecylamine oxide in water, at concentrations greater than 0.01 m M . Results are correlated by the competitive equilibrium model described previously (3), using a nonlinear least-squares program to relate the total concentration of the surfactant to the increase in spectral absorbance at 550 nm that occurs when the surfactant is added to a solution offl-cyclodextrin, phenolphthalein, and sodium carbonate buffer at 25°C. EXPERIMENTAL
A stock solution of phenolphthalein was prepared by dissolving 0.0477 g of Aldrich reagent grade c o m p o u n d in 96% ethanol to a
412
0021-9797/90 $3.00 Copyright © 1990 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journalof ColloidandInterfaceScience,Vol. 134, No. 2, February 1990
SURFACTANT CONCENTRATION
total volume of 100 ml ( 1.51 × 10 -3 M); this solution was quite stable during a period of several weeks. A 0.0010 M solution of 3-cyclodextrin (0.2838 g of the monohydrate (Aldrich) dissolved in water to a total volume of 250 ml) was also prepared. Solutions of the surfactant at concentrations between 0.010 and 2.00 m M w e r e prepared. Sodium carbonate (0.2120 g) was placed in a preweighed 100ml volumetric flask and 10 g of the phenolphthalein solution was added and weighted and the resulting solution was diluted to 100 ml with water. Five grams of the cyclodextrin solution and 10 g of the surfactant solution were mixed in a preweighed 25-ml volumetric flask; the flask was thermostatted in a water bath at 25°C for at least 10 min. Next, 5 ml of the thermostatted phenolphthalein solution ( 1.5 X 10 -4 M ) was added to the flask with a volumetric pipet. Water was added to a total volume of 25 ml and the absorbance was meaTABLE I
413 TABLE II
Observed and Calculated Absorbances of Solutions Containing Varying Concentrations of Surfactant and Fixed Concentrations of Phenolphthaleina and 3-Cyclodextrin b [DDAOy ( mll~ )
Ao~rved d
A , ~
e
0.800 0.428 0.377 0.321 0.303
0.7006 0.5478 0.5222 0.4973 0.4681
0.6973 0.5464 0.5234 0.4969 0.4684
0.263 0.217 0.177 0.132 0.089
0.4354 0.4002 0.3744 0.3308 0.2940
0.4373 0.4039 0.3775 0.3350 0.2971
0.045 0.004 0
0.2622 0.2346 0.2310
0.2629 0.2354 (0.2310)
Total phenolphthalein concentration, 3.00 X 10-5 M. b Total cyclodextrin concentration, 2.00 × 10-4 M. c Total concentration of N,N-dimethyl-N-dodecylamine oxide.
Observed and Calculated Absorbances of Solutions Containing Varying Concentrations of Surfactant and Fixed Concentrations of Phenolphthaleina and 3-Cyclo-
d Observed absorbance at 550 nm, l-cm cell. e Absorbance at 550 nm, calculated using the model described in the text.
dextrin b [SDS]~ (m M )
Ao~,,e a
A~e,a~ e
0.800 0.428 0.377 0.321 0.303
0.7359 0.6079 0.5652 0.5363 0.5273
0.7404 0.6076 0.5765 0.5363 0.5219
0.263 0.217 0.177 0.132 0.089
0.4908 0.4459 0.4083 0.3578 0.2940
0.4871 0.4425 0.4003 0.3510 0.3047
0.045 0.004 0
0.2598 0.2325 0.2232
0.2613 0.2263 (0.2232)
a Total phenolphthalein concentration, 3.00 × 10-3 M. b Total cyclodextrin concentration, 2.00 X 10-4 M. c Total concentration of sodium dodecyl sulfate. d Observed absorbance at 5 5 0 nm, 1-cm cell e Absorbance at 550 nm, calculated using the model
described in the text.
sured immediately. All spectral measurements were made within 2 h after the phenolphthalein stock solution was diluted. Tables I and II list concentrations of the two surfactants, SDS and DDAO, and the absorbances of the final solutions containing phenolphthalein, 3-cyclodextrin, and sodium carbonate. Each solution contained 3.00 × 10 -5 M phenolphthalein and 2.00 × 10 -4
M cyclodextrin. In determining the concentrations of surfactants in solutions of interest, standard surfactant solutions were made up and analyzed concurrently with the unknowns. With care, the absorbances of replicate samples were reproducible to approximately 0.005. TREATMENT OF DATA
As in our previous study of the formation of 1:1 complexes between 3-cyclodextrin and Journal of Colloid and Interface Science, Vol. 134,No. 2, February1990
414
SASAKI, CHRISTIAN, AND TUCKER
aliphatic alcohols (or other solutes containing alkyl moieties) (3), we assume that the total concentrations of cyclodextrin, phenolphthalein, and added surfactant ( [ C D ] , [P], and [ A ], respectively) are given by [CD]
=
CCD -~
[P]
=
C p -~-
KCCDCp -1- K'CcDCA
[1]
K¢cDCp
[2]
[A] = cA+K'CcDCA,
[3]
and
where CCD,Cp, and CArepresent the molar concentrations o f u n c o m p l e x e d ( m o n o m e r i c ) cyclodextrin, phenolphthalein, and surfactant, respectively, and K and K' are the equilibrium constants for formation of the 1:1 complexes of cyclodextrin with phenolphthalein and surfactant. Previously (3) we had determined that the absorptivity of phenolphthalein in the 1:1 complex with ¢/-cyclodextrin was practically zero, so that the absorbance of the solutions could be equated to A = eCp/,
[4]
m u m in the sum of squares of residuals -- Aexperimental). The o p t i m u m values of the complex formation constants for the two surfactant cyclodextrin complexes were: for SDS, K -- 18,500 + 300 liters mole -1, and for DDAO, K = 12,800 + 100 liters mole -1. The root-mean-square deviation in absorbance was equal to 0.0062 for the SDS results and 0.0030 for the D D A O data. The final colu m n in Table I lists values of the absorbance calculated by the nonlinear least-squares method. Figure 1 shows the absorbance of the 550-nm phenolphthalein band plotted as a function of total concentration of added SDS and DDAO, and the calculated curve derived from the nonlinear least-squares analysis of data for each system. (Acalculated
0.S" 0.7 0.6 0,5 0.4"
where e is the absorptivity of the phenolphthalein (3.3 × 10 4 liters m o l e - ' cm -1) and l is the cell pathlength. Thus, the only species having an absorbance in the visible region is assumed to be the colored form of phenolphthalein uncomplexed by cyclodextrin. In order to fit absorbance data like those given in Table I to Eqs. [ 1 ] - [ 4 ] , a nonlinear leastsquares method was used to determine an opt i m u m value of the parameter K'. In this procedure, an initial provisional value of K' was used, together with the known value of K and the concentrations of all three solutes for each data set to solve Eqs. [ 1] - [ 3 ] simultaneously for the three unknown values of the m o n o m e r concentrations (COD, Ce, and CA). The absorbance of the visible band for each set was then predicted by Eq. [ 4], using the derived value of Cp and the previously determined value of e. A nonlinear least-squares program ( N L L S Q ) (4) was utilized to obtain the opt i m u m value of K', corresponding to a miniJournal of Colloid and Interface Science, Vol.
134, No. 2, February 1990
0.3 0.2 0.0
i
!
i
0.2
0.4
0.6
0.8
[SDS]/mM
0.8" 0.7
0.6 0.5 0.4 0.3 0.2
• 0.0
•
i 0.2
-
•
i 0.4
-
•
i 0.6
-
0.8
[DDAO~mM
FIG. 1. Dependence of absorbance at 550 nm on concentration of surfactant. Solutions contain 3.0 × 10-5 M phenolphthalein and 2.0 × 1 0 - 4 M/3-cyclodextrin, at indicated concentrations of sodium dodecyl sulfate [SDS] and N,N-dimethyl-N-dodecylamine oxide [DDAO]. Points are experimental and curves are calculated by the model described in the text.
SURFACTANT CONCENTRATION
415
DISCUSSION
lines drawn in Fig. 1 are theoretical, correAn excellent correlation of spectral data for sponding to values of K equal to 18,500 liters each system is achieved by the nonlinear least- mole -1 for SDS and 12,800 liters mole -1 for squares model described above, involving only DDAO, and forcing the curves to start at the the single adjustable parameter, K', and em- measured absorbance of the blank solution, ploying previously determined values of the which contains only phenolphthalein and cyabsorptivity ofuncomplexed phenolphthalein clodextrin in the aqueous buffer. There have and the formation constant for the 1:1 com- been two previous determinations of equilibplex between phenolphthalein and /3-cyclo- rium constants for formation of 1:1 complexes dextrin. The absorbance does not depend lin- between SDS and/~-cyclodextrin, both based early on the surfactant concentration in the on conductivity measurements (5, 6). The region 0 to 0.10 m M , although the variation values of K inferred from the conductivity results are considerably smaller than the value is nearly linear in the range 0.10 to 0.30 m M . The absorbance of the "blank" solution con- obtained here, although the conductivity extaining no added surfactant reflects the con- periments were carried out with much larger centration of uncomplexed phenolphthalein concentrations of SDS, and in a range where K appears to decrease rapidly as the concenin the buffered solution (see Eq. [4]). In many analytical applications, it may be tration increases (6). However, the new specsatisfactory to construct a calibration curve tral displacement results and data from our resembling either curve in Fig. 1, for solutions previous study (3) are well correlated by the containing known concentrations of the sur- present model, indicating that a single value factant, and fixed concentrations of both phe- of K suffices to fit data for each solute-cyclonolphthalein and cyclodextrin. Then, the dextrin complex throughout the range of conconcentration of the unknown solution can centrations employed. be inferred directly from the calibration curve, Obviously the presence of any solute in adby interpolation. However, for the most ac- dition to the surfactant that can form an incurate determination of surfactant concentra- clusion complex with/3-cyclodextrin will intions, it is probably desirable to infer the con- terfere with the analysis described here. Howcentration of monomeric phenolphthalein (Cl,) ever, in many studies of physical properties of from each measured absorbance, by using Eq. aqueous surfactant systems, the interferences [4] with the known value of e (determined in will be minor or can be accounted for without a separate series of experiments). Next, Eq. great difficulty. We have used the displacement [ 2 ] can be solved for the concentration o f m o - method to determine the concentration of nomeric cyclodextrin (CcD) using the known DDAO in the presence of known concentravalue of K. Equation [1] can then be solved tions ofphenethyl alcohol in semiequilibrium for the concentration of uncomplexed surfac- dialysis experiments (7). The effect of the tant, CA, and finally, [A] is calculated from phenethyl alcohol on the measured absorbance Eq. [3]. An uncertainty in the measured simply adds to the spectral effect of DDAO, change in absorbance (between that of the so- so that calibration curves can be constructed lution containing the surfactant and that of corresponding to known concentrations of the the blank) of 0.005 corresponds to an error in alcohol, determined by UV spectroscopy. We surfactant concentration of approximately plan to use the spectral displacement method 0.005 m M , under the conditions described in to determine concentrations of numerous the Experimental section. other ionic and nonionic surfactants passing The nonlinearity of plots of absorbance vs through the membrane in dialysis or ultrafilconcentration of the surfactant is predictable tration experiments. Such results are needed with the competitive equilibrium model used in studies of the binding of molecular and ionic to correlate data (vide supra). Thus, the solid solutes to micelles. Experience with /3-cycloJournal of Colloid and Interface Science, Vol. 134, No. 2, February 1990
416
SASAKI, CHRISTIAN, AND TUCKER
dextrins indicates t h a t surfactants c o n t a i n i n g at least C8-alkyl chains o r n o n b r a n c h e d a l k y l aryl groups can be d e t e r m i n e d with the m e t h o d . H o w e v e r , the m o s t i m p o r t a n t use o f the spectral d i s p l a c e m e n t m e t h o d will p r o b ably be the analysis o f ionic o r n o n i o n i c c o m p o u n d s c o n t a i n i n g no c h r o m o p h o r i c groups, such as the straight-chain C12 to C16 alkyl- a n d a l k y l p o l y o x y e t h y l e n e surfactants. ACKNOWLEDGMENTS Financial support for this research was provided by the National Science Foundation under Grant CHE 8701887 and the Office of Basic Energy Sciences of the Department of Energy under Grant DE-FG01-87FE61146.
Journal of Colloid and Interface Science, Vol. 134, No. 2, February 1990
REFERENCES 1. Buvari, A., and Barcza, L., Inorg. Chim. Acta 33, L179 (1979). 2. Vikmon, M., in "Proceedings, First International Symposium on Cyclodextrins" (J. Szetli, Ed.), pp. 69-74. Reidel, Boston/London, 1982. 3. Sasaki, K. J., Christian, S. D., and Tucker, E. E., "Fluid Phase Equilibria," 49, 281 (1989). 4. Christian, S. D., and Tucker, E. E., Amer. Lab. 14(8), 36; 14(9), 31 (1982). 5. Satake, I., Yoshida, S., Hayakawa, K., Maeda, T., and Kusumoto, Y., Bull. Chem. Soc. Japan 59, 3991 (1986). 6. Palepu, R., and Reinsborough, V. C., Canad. J. Chem. 66, 325 (1988). 7. Uchiyama, H., Christian, S. D., Scamehorn, J. F., and Tucker, E. E., in preparation.
University of Oklahoma, Norman, Oklahoma 73019 Received January 16, 1989;accepted May 9, 1989 A substitution method in which phenolphthalein is displaced from the/3-cyclodextrin cavityby the hydrocarbon moiety of a surfactant is used to determine the concentration of the surfactant. The 1:1 complex of phenolphthalein with/3-cyclodextrinhas an absorbancepracticallyequal to zero in the region of the 550-nm band of the basic form of phenolphthalein. When solute molecules containing an alkyl moiety displace some of the phenolphthalein at a pH of approximately 10.5, the absorbance at 550 nm is significantlyincreased and serves as a direct measure of the concentration of the solute. The method is useful in determining concentrationsof surfactants suchas sodium dodecylsulfate and N,N-dimethylN-dodecylamineoxide, which do not contain chromophores. © 1990AcademicPress,Inc. INTRODUCTION
Determining the concentration of aliphatic solutes in aqueous solution can be quite difficult in the case of compounds that do not have a chromophore in the accessible ultraviolet or visible regions of the spectrum. However, a simple spectral method based on the displacement of phenolphthalein at a pH > 10 from the cavity of/3-cyclodextrin may be used to determine concentrations of surfactants like sodium dodecyl sulfate (SDS) and N , N dimethyl-N-dodecylamine oxide ( D D A O ) , which possess the dodecyl moiety. Previous studies have shown that the 1:1 complex between phenolphthalein a n d / 3 - c y clodextrin, at pH 10.5, has a formation constant of approximately 2.1 × 104 liters mole-I at 25°C ( 1 - 3 ) . Careful studies of the dependence of the absorption band of phenolphthalein at 550 n m on the concentration of/3-cyclodextrin have shown that at pH 10.5 the complexed phenolphthalein has an absorptivity practically equal to zero (3). By measuring the increase in absorbance of the 550 nm band as a function of added concentrations of ni To whom correspondence should be addressed.
alkyl alcohols and other solutes containing an aliphatic moiety, we were able to determine 1:1 formation constants for these solutes with fl-cyclodextrin (3). It occurred to us that this method might be a useful analytical technique for determining the concentrations of surfactants and other compounds containing n-alkyl or other aliphatic groups, The present note describes our use of the displacement method to determine concentrations of sodium dodecyl sulfate and N,N-dimethyl-N-dodecylamine oxide in water, at concentrations greater than 0.01 m M . Results are correlated by the competitive equilibrium model described previously (3), using a nonlinear least-squares program to relate the total concentration of the surfactant to the increase in spectral absorbance at 550 nm that occurs when the surfactant is added to a solution offl-cyclodextrin, phenolphthalein, and sodium carbonate buffer at 25°C. EXPERIMENTAL
A stock solution of phenolphthalein was prepared by dissolving 0.0477 g of Aldrich reagent grade c o m p o u n d in 96% ethanol to a
412
0021-9797/90 $3.00 Copyright © 1990 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journalof ColloidandInterfaceScience,Vol. 134, No. 2, February 1990
SURFACTANT CONCENTRATION
total volume of 100 ml ( 1.51 × 10 -3 M); this solution was quite stable during a period of several weeks. A 0.0010 M solution of 3-cyclodextrin (0.2838 g of the monohydrate (Aldrich) dissolved in water to a total volume of 250 ml) was also prepared. Solutions of the surfactant at concentrations between 0.010 and 2.00 m M w e r e prepared. Sodium carbonate (0.2120 g) was placed in a preweighed 100ml volumetric flask and 10 g of the phenolphthalein solution was added and weighted and the resulting solution was diluted to 100 ml with water. Five grams of the cyclodextrin solution and 10 g of the surfactant solution were mixed in a preweighed 25-ml volumetric flask; the flask was thermostatted in a water bath at 25°C for at least 10 min. Next, 5 ml of the thermostatted phenolphthalein solution ( 1.5 X 10 -4 M ) was added to the flask with a volumetric pipet. Water was added to a total volume of 25 ml and the absorbance was meaTABLE I
413 TABLE II
Observed and Calculated Absorbances of Solutions Containing Varying Concentrations of Surfactant and Fixed Concentrations of Phenolphthaleina and 3-Cyclodextrin b [DDAOy ( mll~ )
Ao~rved d
A , ~
e
0.800 0.428 0.377 0.321 0.303
0.7006 0.5478 0.5222 0.4973 0.4681
0.6973 0.5464 0.5234 0.4969 0.4684
0.263 0.217 0.177 0.132 0.089
0.4354 0.4002 0.3744 0.3308 0.2940
0.4373 0.4039 0.3775 0.3350 0.2971
0.045 0.004 0
0.2622 0.2346 0.2310
0.2629 0.2354 (0.2310)
Total phenolphthalein concentration, 3.00 X 10-5 M. b Total cyclodextrin concentration, 2.00 × 10-4 M. c Total concentration of N,N-dimethyl-N-dodecylamine oxide.
Observed and Calculated Absorbances of Solutions Containing Varying Concentrations of Surfactant and Fixed Concentrations of Phenolphthaleina and 3-Cyclo-
d Observed absorbance at 550 nm, l-cm cell. e Absorbance at 550 nm, calculated using the model described in the text.
dextrin b [SDS]~ (m M )
Ao~,,e a
A~e,a~ e
0.800 0.428 0.377 0.321 0.303
0.7359 0.6079 0.5652 0.5363 0.5273
0.7404 0.6076 0.5765 0.5363 0.5219
0.263 0.217 0.177 0.132 0.089
0.4908 0.4459 0.4083 0.3578 0.2940
0.4871 0.4425 0.4003 0.3510 0.3047
0.045 0.004 0
0.2598 0.2325 0.2232
0.2613 0.2263 (0.2232)
a Total phenolphthalein concentration, 3.00 × 10-3 M. b Total cyclodextrin concentration, 2.00 X 10-4 M. c Total concentration of sodium dodecyl sulfate. d Observed absorbance at 5 5 0 nm, 1-cm cell e Absorbance at 550 nm, calculated using the model
described in the text.
sured immediately. All spectral measurements were made within 2 h after the phenolphthalein stock solution was diluted. Tables I and II list concentrations of the two surfactants, SDS and DDAO, and the absorbances of the final solutions containing phenolphthalein, 3-cyclodextrin, and sodium carbonate. Each solution contained 3.00 × 10 -5 M phenolphthalein and 2.00 × 10 -4
M cyclodextrin. In determining the concentrations of surfactants in solutions of interest, standard surfactant solutions were made up and analyzed concurrently with the unknowns. With care, the absorbances of replicate samples were reproducible to approximately 0.005. TREATMENT OF DATA
As in our previous study of the formation of 1:1 complexes between 3-cyclodextrin and Journal of Colloid and Interface Science, Vol. 134,No. 2, February1990
414
SASAKI, CHRISTIAN, AND TUCKER
aliphatic alcohols (or other solutes containing alkyl moieties) (3), we assume that the total concentrations of cyclodextrin, phenolphthalein, and added surfactant ( [ C D ] , [P], and [ A ], respectively) are given by [CD]
=
CCD -~
[P]
=
C p -~-
KCCDCp -1- K'CcDCA
[1]
K¢cDCp
[2]
[A] = cA+K'CcDCA,
[3]
and
where CCD,Cp, and CArepresent the molar concentrations o f u n c o m p l e x e d ( m o n o m e r i c ) cyclodextrin, phenolphthalein, and surfactant, respectively, and K and K' are the equilibrium constants for formation of the 1:1 complexes of cyclodextrin with phenolphthalein and surfactant. Previously (3) we had determined that the absorptivity of phenolphthalein in the 1:1 complex with ¢/-cyclodextrin was practically zero, so that the absorbance of the solutions could be equated to A = eCp/,
[4]
m u m in the sum of squares of residuals -- Aexperimental). The o p t i m u m values of the complex formation constants for the two surfactant cyclodextrin complexes were: for SDS, K -- 18,500 + 300 liters mole -1, and for DDAO, K = 12,800 + 100 liters mole -1. The root-mean-square deviation in absorbance was equal to 0.0062 for the SDS results and 0.0030 for the D D A O data. The final colu m n in Table I lists values of the absorbance calculated by the nonlinear least-squares method. Figure 1 shows the absorbance of the 550-nm phenolphthalein band plotted as a function of total concentration of added SDS and DDAO, and the calculated curve derived from the nonlinear least-squares analysis of data for each system. (Acalculated
0.S" 0.7 0.6 0,5 0.4"
where e is the absorptivity of the phenolphthalein (3.3 × 10 4 liters m o l e - ' cm -1) and l is the cell pathlength. Thus, the only species having an absorbance in the visible region is assumed to be the colored form of phenolphthalein uncomplexed by cyclodextrin. In order to fit absorbance data like those given in Table I to Eqs. [ 1 ] - [ 4 ] , a nonlinear leastsquares method was used to determine an opt i m u m value of the parameter K'. In this procedure, an initial provisional value of K' was used, together with the known value of K and the concentrations of all three solutes for each data set to solve Eqs. [ 1] - [ 3 ] simultaneously for the three unknown values of the m o n o m e r concentrations (COD, Ce, and CA). The absorbance of the visible band for each set was then predicted by Eq. [ 4], using the derived value of Cp and the previously determined value of e. A nonlinear least-squares program ( N L L S Q ) (4) was utilized to obtain the opt i m u m value of K', corresponding to a miniJournal of Colloid and Interface Science, Vol.
134, No. 2, February 1990
0.3 0.2 0.0
i
!
i
0.2
0.4
0.6
0.8
[SDS]/mM
0.8" 0.7
0.6 0.5 0.4 0.3 0.2
• 0.0
•
i 0.2
-
•
i 0.4
-
•
i 0.6
-
0.8
[DDAO~mM
FIG. 1. Dependence of absorbance at 550 nm on concentration of surfactant. Solutions contain 3.0 × 10-5 M phenolphthalein and 2.0 × 1 0 - 4 M/3-cyclodextrin, at indicated concentrations of sodium dodecyl sulfate [SDS] and N,N-dimethyl-N-dodecylamine oxide [DDAO]. Points are experimental and curves are calculated by the model described in the text.
SURFACTANT CONCENTRATION
415
DISCUSSION
lines drawn in Fig. 1 are theoretical, correAn excellent correlation of spectral data for sponding to values of K equal to 18,500 liters each system is achieved by the nonlinear least- mole -1 for SDS and 12,800 liters mole -1 for squares model described above, involving only DDAO, and forcing the curves to start at the the single adjustable parameter, K', and em- measured absorbance of the blank solution, ploying previously determined values of the which contains only phenolphthalein and cyabsorptivity ofuncomplexed phenolphthalein clodextrin in the aqueous buffer. There have and the formation constant for the 1:1 com- been two previous determinations of equilibplex between phenolphthalein and /3-cyclo- rium constants for formation of 1:1 complexes dextrin. The absorbance does not depend lin- between SDS and/~-cyclodextrin, both based early on the surfactant concentration in the on conductivity measurements (5, 6). The region 0 to 0.10 m M , although the variation values of K inferred from the conductivity results are considerably smaller than the value is nearly linear in the range 0.10 to 0.30 m M . The absorbance of the "blank" solution con- obtained here, although the conductivity extaining no added surfactant reflects the con- periments were carried out with much larger centration of uncomplexed phenolphthalein concentrations of SDS, and in a range where K appears to decrease rapidly as the concenin the buffered solution (see Eq. [4]). In many analytical applications, it may be tration increases (6). However, the new specsatisfactory to construct a calibration curve tral displacement results and data from our resembling either curve in Fig. 1, for solutions previous study (3) are well correlated by the containing known concentrations of the sur- present model, indicating that a single value factant, and fixed concentrations of both phe- of K suffices to fit data for each solute-cyclonolphthalein and cyclodextrin. Then, the dextrin complex throughout the range of conconcentration of the unknown solution can centrations employed. be inferred directly from the calibration curve, Obviously the presence of any solute in adby interpolation. However, for the most ac- dition to the surfactant that can form an incurate determination of surfactant concentra- clusion complex with/3-cyclodextrin will intions, it is probably desirable to infer the con- terfere with the analysis described here. Howcentration of monomeric phenolphthalein (Cl,) ever, in many studies of physical properties of from each measured absorbance, by using Eq. aqueous surfactant systems, the interferences [4] with the known value of e (determined in will be minor or can be accounted for without a separate series of experiments). Next, Eq. great difficulty. We have used the displacement [ 2 ] can be solved for the concentration o f m o - method to determine the concentration of nomeric cyclodextrin (CcD) using the known DDAO in the presence of known concentravalue of K. Equation [1] can then be solved tions ofphenethyl alcohol in semiequilibrium for the concentration of uncomplexed surfac- dialysis experiments (7). The effect of the tant, CA, and finally, [A] is calculated from phenethyl alcohol on the measured absorbance Eq. [3]. An uncertainty in the measured simply adds to the spectral effect of DDAO, change in absorbance (between that of the so- so that calibration curves can be constructed lution containing the surfactant and that of corresponding to known concentrations of the the blank) of 0.005 corresponds to an error in alcohol, determined by UV spectroscopy. We surfactant concentration of approximately plan to use the spectral displacement method 0.005 m M , under the conditions described in to determine concentrations of numerous the Experimental section. other ionic and nonionic surfactants passing The nonlinearity of plots of absorbance vs through the membrane in dialysis or ultrafilconcentration of the surfactant is predictable tration experiments. Such results are needed with the competitive equilibrium model used in studies of the binding of molecular and ionic to correlate data (vide supra). Thus, the solid solutes to micelles. Experience with /3-cycloJournal of Colloid and Interface Science, Vol. 134, No. 2, February 1990
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dextrins indicates t h a t surfactants c o n t a i n i n g at least C8-alkyl chains o r n o n b r a n c h e d a l k y l aryl groups can be d e t e r m i n e d with the m e t h o d . H o w e v e r , the m o s t i m p o r t a n t use o f the spectral d i s p l a c e m e n t m e t h o d will p r o b ably be the analysis o f ionic o r n o n i o n i c c o m p o u n d s c o n t a i n i n g no c h r o m o p h o r i c groups, such as the straight-chain C12 to C16 alkyl- a n d a l k y l p o l y o x y e t h y l e n e surfactants. ACKNOWLEDGMENTS Financial support for this research was provided by the National Science Foundation under Grant CHE 8701887 and the Office of Basic Energy Sciences of the Department of Energy under Grant DE-FG01-87FE61146.
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REFERENCES 1. Buvari, A., and Barcza, L., Inorg. Chim. Acta 33, L179 (1979). 2. Vikmon, M., in "Proceedings, First International Symposium on Cyclodextrins" (J. Szetli, Ed.), pp. 69-74. Reidel, Boston/London, 1982. 3. Sasaki, K. J., Christian, S. D., and Tucker, E. E., "Fluid Phase Equilibria," 49, 281 (1989). 4. Christian, S. D., and Tucker, E. E., Amer. Lab. 14(8), 36; 14(9), 31 (1982). 5. Satake, I., Yoshida, S., Hayakawa, K., Maeda, T., and Kusumoto, Y., Bull. Chem. Soc. Japan 59, 3991 (1986). 6. Palepu, R., and Reinsborough, V. C., Canad. J. Chem. 66, 325 (1988). 7. Uchiyama, H., Christian, S. D., Scamehorn, J. F., and Tucker, E. E., in preparation.