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Adsorption Behavior of Oxyethylated Alcohols at the Solution/Air Interface V. B. Fainerman,† R. Miller,*,‡ and E. V. Aksenenko§ International Medical Physicochemical Centre and Institute of Technical Ecology, 25 Shevchenko Boulevard, 340017, Donetsk, Ukraine, Max-Planck-Institut fu¨ r Kolloid- und Grenzfla¨ chenforschung, Forschungscampus Golm, Am Mu¨ hlenberg 2, D-14476 Golm, Germany, and Institute of Colloid Chemistry and Chemistry of Water, 42 Vernadsky Avenue, 252680 Kiev, Ukraine Received November 17, 1999. In Final Form: February 11, 2000 Experimental data for oxyethylated alcohols CnEOm (linear as well as crown ethers) are analyzed on the basis of recently developed thermodynamic models taking into consideration a change in the surface molar area from ω2 to ω1, or a possible aggregation of adsorbed surfactant molecules. The data analysis shows that the characteristic parameters of the CnEOm adsorption layers have extremum values at a certain alkyl chain length: a maximum in the ω1 was found at C13 and a flat maximum in ω2 in the alkyl chain length range C11-C13. The parameter R, a measure for the difference in the surface activity of the different adsorption states, exhibits a weak minimum in the same range of the hydrocarbon chain length. The extremum behavior can possibly be explained by the counterbalance of the two effects made by the hydrocarbon and oxyethylene group, respectively. In contrast to the surfactants with a linear oxyethylene group, the crown ether C12H25OCH2-18-crown-6 exhibits the formation of aggregates: dimers and trimers at diluted surface layers, and larger aggregates of more than 50 molecules at higher surface coverage.
Introduction The composition of mixed adsorption layers of surface active molecules is governed not only by the bulk concentration and adsorption activity of the components, or their interaction in the surface layer, but also by the surface pressure.1-4 At low surface pressure, this selfregulation mechanism leads to a preferential accumulation of molecules with large partial molar surface area. On the contrary, at high surface pressure, most of the adsorbed surfactant molecules occupy a minimal molar area. These effects are observed for asymmetric surfactant molecules, which are capable of adsorbing in two or more states characterized by different partial molar areas. In such adsorption layers, the fraction of molecules existing in a state with a certain molar area depends on the surface pressure.3-6 Equations of state and adsorption isotherms for such systems were proposed elsewhere;7,8 however, no attempt was made to account for the self-regulation behavior mentioned above. A thermodynamic theory for the description of this self-regulation mechanism of the surface layer composition was developed only recently.4,9,10 * To whom correspondence may be addressed. † International Medical Physicochemical Centre and Institute of Technical Ecology. ‡ Max-Planck-Institut fu ¨ r Kolloid- und Grenzfla¨chenforschung. § Institute of Colloid Chemistry and Chemistry of Water. (1) Joos, P. Bull. Soc. Chim. Belg. 1967, 76, 591. (2) Lucassen-Reynders, E. H. J. Colloid Interface Sci. 1972, 41, 156. (3) Joos, P.; Serrien, G. J. Colloid Interface Sci. 1991, 145, 291. (4) Fainerman, V. B.; Lucassen-Reynders, E. H.; Miller, R. Colloids Surf., A 1998, 143, 141. (5) Fainerman, V. B.; Makievski, A. V.; Joos, P. Colloids Surf., A 1994, 90, 213. (6) Fainerman, V. B.; Miller, R.; Makievski, A. V. Langmuir 1995, 11, 3054. (7) Damaskin, B. B.; Frumkin, A. N.; Djatkina, S. L. Izv. Akad. Nauk SSSR, Ser. Chim. 1967, 2171. (8) Damaskin, B. B. Izv. Akad. Nauk SSSR, Ser. Chim. 1969, 346. (9) Fainerman, V. B.; Miller, R.; Wu¨stneck, R.; Makievski, A. V. J. Phys. Chem. 1996, 100, 7669. (10) Fainerman, V. B.; Miller, R.; Wu¨stneck, R. J. Phys. Chem. B 1997, 101, 6479
This reorientation theory explains quite well the equilibrium adsorption behavior in the homologous series of betains10 and dimethyl alkyl phosphine oxides.11 The theory provides also a reliable description of the behavior of oxyethylated decyl alcohol C10EO8 at the water/air and water/oil interfaces.12,13 The oxyethylated surfactants differ from other surface-active substances in that the oxyethylene chain, the hydrophilic part of the molecule, exhibits an adsorption activity at low surface layer coverages,5,6 which affects the total surface activity of the molecule in the unfolded state. The experimental surface tension isotherms for various oxyethylated alcohols were reported in a number of publications.12-23 In some of these studies measurements were performed in a wide range of surfactant concentrations and surface pressures, spanning the interval from 1 to about 38 mN/m. In ref 18 even the influence of the hydrocarbon chain length was systematically studied. All these studies provide a pool of data which enable one to compare the predictions of various theoretical models. (11) Makievski, A. V.; Grigoriev, D. O. Colloids Surf., A 1998, 143, 233. (12) Ferrari, M.; Liggieri, L.; Ravera, F. J. Phys. Chem. B 1998, 102, 10521. (13) Miller, R.; Aksenenko, E. V.; Liggieri, L.; Ravera, F.; Ferrari, M.; Fainerman, V. B. Langmuir 1999, 15, 1328. (14) Schick, M. J. Colloid Sci. 1962, 17, 801. (15) Lange, V. H. Kolloid Z. Z. Polym. 1965, 201, 131. (16) Rosen, M. J.; Anna, A. W.; Dahanayake, M.; Hua, X. J. Phys. Chem. 1982, 86, 541. (17) Meguro, K.; Takasawa, Y.; Kawahashi, N.; Tabata, Y.; Ueno, M. J. Colloid Interface Sci. 1981, 83, 50. (18) Ueno, M.; Takasawa, Y.; Miyashige, H.; Tabata, Y.; Meguro, K. Colloid Polym. Sci. 1981, 259, 761. (19) Sokolowski, A.; Burczyk, B. J. Colloid Interface Sci. 1983, 94, 396. (20) Ozeki, S.; Ikegava, T.; Takahashi, H.; Kuwamura, T. Langmuir 1988, 4, 1070. (21) Ozeki, S.; Ikegava, T.; Inokuma, S.; Kuwamura, T. Langmuir 1989, 5, 222. (22) Lin, S.-Y.; Tsay, R.-Y.; Lin, L.-W.; Chen, S.-I. Langmuir 1996, 12, 6530. (23) Chang, H. C.; Hsu, C. T.; Lin, S.-Y. Langmuir 1998, 14, 24761.
10.1021/la991502x CCC: $19.00 © 2000 American Chemical Society Published on Web 04/03/2000
Adsorption Behavior of Surfactants
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The aim of the present paper is to analyze experimental results in the framework of the reorientation adsorption model, to discuss the regularities in the dependence of the adsorption isotherm parameters on the hydrocarbon or oxyethylene chain length, and to compare the adsorption behavior of linear and crown ethers at the water/air interface. The inflection point which exists in the surface tension isotherm of crown ethers was attributed in refs 20 and 21 to the aggregation of these molecules in the solution bulk. To describe these results, a theoretical model is applied which considers aggregation of molecules in the adsorption layer.4 Theory and model calculations Let us consider the case when adsorbed molecules in the surface layer can exist in two states, 1 and 2, with the different partial molar areas ω1 > ω2. The corresponding values of equilibrium adsorption in these states are Γ1 and Γ2, respectively, with the total adsorption defined by Γ ) Γ1 + Γ2. According to the theory developed in refs 4, 9, and 10 for the surface layer in this system, the generalized Szyszkowski-Langmuir equation of state is valid
RT ln(1 - Γω) ω
Π)-
Figure 1. Schematic of the surface layer coverage comprised of molecules adsorbed in two states with two different orientations to the interface
(1)
while the adsorption isotherm equation is
bc )
Γ2ω
(2)
(1 - Γω)ω2/ω
The ratio of the adsorption in these two states (the generalized Joos equation) and the average molar area of the two states ω are given by the following expressions
[
]
Γ1 Π(ω2 - ω1) ) β exp Γ2 RT ω)
ω2 + ω1 β exp[Π(ω2 - ω1)/RT] 1 + β exp[Π(ω2 - ω1)/RT]
(3)
(4)
where
β ) exp
(
)
ω1 - ω2 (ω1/ω2)R ω
(5)
Here R is the gas constant, T is the absolute temperature, Π ) γ0 - γ is the surface pressure, γ0 and γ are the surface tensions of the solvent and the solution, respectively, b is the adsorption equilibrium constant, c is the concentration of the surfactant in the solution bulk, and R is a constant. The pre-exponential factor β (see eq 5) expresses the relative activity of the states of the surfactant molecule with different areas and involves two cofactors. The first of these factors results from the theory which takes into account the nonideality of the surface layer entropy caused by the difference between the molar areas, while the second cofactor (which involves the constant R) is empirical and reflects the effect of the additional surface activity of the state 1 as compared with the state 2. A schematic of the changing composition of an adsorption layer comprised of molecules changing the orientation to the surface normal due to increased packing is given in Figure 1. While the number of molecules in state 2 with the larger molar area passes a maximum, the number of molecules adsorbed in the state with the minimum molar area increases continuously until saturation is reached
Figure 2. Dependence of surface pressure on bulk concentration for the parameters R ) 0, ω2 ) 2.5 × 105 m2/mol, and ω1 ) 5 × 105 m2/mol (0), 1.5 × 106 m2/mol (]), 2.0 × 106 m2/mol (4) and 4.0 × 106 m2/mol (O). The dotted line is calculated from the Langmuir model with ω ) 2.5 × 105 m2/mol.
(Θ is the relative surface coverage by molecules in a certain state). The maximum in the relative adsorption in state 2 is located at the concentration where molecules are forced to change orientation and adsorb in state 1. The composition of the interfacial layer is controlled by the generalized Joos eq 3 given above. The influence of the parameters of the reorientation model on the shape of surface pressure isotherms was discussed in detail elsewhere;9 however, only the second cofactor was taken into account, while the first factor was introduced into the model only recently.10 The dependence of the surface pressure isotherms on the maximum area ω1 is illustrated by Figure 2. Here eqs 1-5 were employed with ω2 ) constant and R ) 0. All calculated curves are normalized such that for the concentration 10-4 mol/L, the surface pressure is 30 mN/m. One can see that with increasing of ω1 an inflection point in the isotherm becomes more pronounced. For a ratio of ω1/ω2 ) 4 the calculated curve almost coincides with the one calculated from the Szyszkowski-Langmuir equation (1) which assumes that the molecules in the monolayer can exist in one state only with ω ) constant, while for lower values of this ratio the shape of the isotherms is less convex than that for the Langmuir isotherm. As compared with our earlier estimates,9 the consideration of the first cofactor in eq 5 leads to a more pronounced difference between the reorientation and the Langmuir isotherm. For nonzero R values, which are especially characteristic for oxyethylated alcohols,12,13 this difference becomes even more significant. For example, the isotherms calculated for R values in the range from 0 to 5 and ω1/ω2 ) 4 are presented in Figure 3. It is
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Figure 3. Dependence of surface pressure on bulk concentration for the parameters ω2 ) 2.5 × 105 m2/mol, ω1 ) 106 m2/mol, and R ) 0 (0), 1 (]), 2 (4), 3 (O), 4 (*), 5 (+).
Figure 4. Dependence of adsorption layer coverage (Γiωi) in states 1 (solid line) and 2 (dotted line) on the bulk concentration for ω2 ) 2.5 × 105 m2/mol, ω1 ) 106 m2/mol, and R ) 3.
seen that the increase of R corresponds to a sharp increase of the surface activity of the surfactant at very low concentrations. Here the surface pressure isotherm appears as if it consists of two curves with quite different shapes. This behavior can be attributed to the fact that in the low and medium Π range the surfactant molecules adsorb preferentially with a molar surface area ω1, while for high Π values the molecules can occupy a small molar area ω2. This is illustrated in Figure 4, where the surface layer coverage is plotted vs the bulk concentration. The “partial coverage” Γiωi for the two states of adsorbed molecules (i ) 1, 2) was calculated with the isotherm parameters ω1 ) 106 m2/mol, ω2 ) 2.5 × 105 m2/mol, and R ) 3, which are typical for oxyethylated alcohols (see below). It is seen that the maximum coverage by molecules in state 1 is obtained for a concentration of 2 × 10-6 mol/L, while for c ) 5 × 10-5 mol/L (when the curve for the parameter set of Figure 2 exhibits a sharp increase) the coverages for the two states of adsorbed molecules become approximately equal (cf. Figure 4). Note that at concentrations above 2 × 10-6 mol/L the adsorption layer consists almost exclusively of surfactant molecules adsorbed with a large molar area ω2, and further increase in adsorption takes place only by molecules adsorbed in the state with minimal partial molar area ω1 at the expense of the molecules adsorbed before.
Fainerman et al.
Figure 5. Experimental (ref 18) and theoretical surface pressure isotherms for C9EO8 (4), C10EO8 (0), and C11EO8 (]). Theoretical curves were calculated from the reorientation (solid line) and Langmuir (dotted line) models using the parameters of Table 1.
Figure 6. Experimental (ref 18) and theoretical surface pressure isotherms for C12EO8 (4), C13EO8 ([), C14EO8 (0), and C15EO8 (2). Theoretical curves were calculated from the reorientation (solid line) and Langmuir (dotted line) models using the parameters of Table 1.
5 and 6. The theoretical curves calculated from the twostate model of eqs 1-5 and from the SzyszkowskiLangmuir equation (single-state model) are also presented. To determine the values of the parameters of eqs 1-5 fitting the experimental data best, the following fitting procedure was employed. For each particular set of parameters ω1, ω2, and R, the values of bi for each of the m experimental points Πi ) Πi(ci), i ) 1, 2, ..., m, were calculated and b was calculated as the average weighted over all n pressure values m
b)
bi ∑ Π i)1
∆Πi
m
- Πl
(6)
where ∆Πi ) (Πi+1 - Πi-1)/2 is the pressure range corresponding to the ith point. The values of the parameters ω1, ω2, and R were varied stepwise in intervals between physically reasonable minimum and maximum values of the parameters. That set of parameters ω1, ω2, and R was considered optimal where the “target function” was minimum24
Discussion of the Experimental Data The experimental results reported in ref 18 for oxyethylated alcohols CnEO8 (n ) 9-15) are shown in Figures
(24) Fainerman, V. B.; Aksenenko, E. V.; Miller, R. J. Phys. Chem., in press.
Adsorption Behavior of Surfactants m
)
∆ci
∑ i)1 c
ex,i
∆Πi Πm - Πl
Langmuir, Vol. 16, No. 9, 2000 4199
) min
(7)
where ∆ci ) |cex,i - ccal,i|; the subscripts “ex” and “cal” refer to the experimental and calculated surfactant concentrations (for the same Πi), respectively, is the weighted average of the relative deviations between the experimental and calculated ci values. For the Langmuir model, only the ω parameter was optimized. Comparing the experimental data with the calculated surface pressure isotherms for adsorption layers of oxyethylated alcohols (cf. Figures 5 and 6), one can see that perfect agreement exists between the model of eqs 1-5 and the experimental results, while the Langmuir model does not describe the actual data properly. In Table 1 the optimized values of the parameters and target function are presented for the two theoretical models compared. The Langmuir model parameters ω, b, and , denoted by subscript L, are listed in parentheses. The values of the model parameters for C10EO8 and C12EO8 ethers were calculated also from data reported in refs 22 and 23. The corresponding theoretical curves for C12EO8 are presented in Figure 7, while the data for C10EO8 have been reported in ref 13. Analyzing the data of Table 1, one first notes a significant difference in the fitting error calculated for the two models. For the Langmuir model these values are 5 to 10 times higher than those for the reorientation model. The parameters of the reorientation model listed in Table 1 correspond to the deepest minimum of the target function ) (ω1,ω2,R). For example, for C10EO8 this minimum is ) 0.02%, and the parameters have the following values: ω1 ) 7.6 × 105 m2/mol, ω2 ) 3.3 × 105 m2/mol, and R ) 3.5. There exists also other local minima corresponding to higher values; for example, several parameter sets were found in the range ω1 ) (7.2-8.0) × 105 m2/mol, ω2 ) (3.0-3.6) × 105 m2/mol, and R ) 3.2-3.9, for which e 2.5%, each of these giving rather good correspondence with the experimental isotherm. The effect of the experimental error of surface tension measurements on the calculated isotherm parameters has also been analyzed. For surface tension deviations of the order of (0.2 mN/m, the variations of the optimized parameters were found to be within the intervals given above. Therefore, the error limits of the optimized isotherm parameters shown in Table 1 do not exceed 5-10%. There exists a certain dependence of the reorientation isotherm parameters on the hydrocarbon chain length of the ether molecule, which cannot be attributed to any experimental or calculation errors; a maximum in ω1 was found at C13 and a smooth maximum of ω2 in the range C11-C13, while R exhibits a weak minimum in the same hydrocarbon chain length range. This extremal behavior could possibly be explained by the interaction between the hydrocarbon and oxyethylene groups.25,26 It should be noted that a similar extremal dependence of the molar surface area per molecule on the alkyl chain length was found also for the homologous series of sodium alkyl sulfates.27 Here the minimum of the area was observed at C10-C11, followed by an increase at higher chain lengths which was attributed to the enhanced electrostatic repulsion between the “head” groups of the surfactant mol(25) Lu, J. R.; Li, Z. X.; Su, T. J.; Thomas, R. T.; Penfold, J. Langmuir 1993, 9, 2408. (26) Lu, J. R.; Li, Z. X.; Thomas, R. T.; Staples, E. J.; Tucker, I.; Penfold, J. J. Phys. Chem. 1993, 97, 8012. (27) Lunkenheimer, K.; Czichocki, G.; Hirte, R.; Barzyk, W. Colloids Surf., A 1995, 101, 187.
ecules.27 Clearly, in the oxyethylated alcohols series studied here, another reason of the extremal behavior should be anticipated. It is essential to note that the parameter R, which characterizes the extra adsorption activity of molecule existing in the unfolded state, that is, solely the effect of the oxyethylene chain EO8, is almost independent of the hydrocarbon chain length; for the solution/water interface this parameter is of the order of 3.0. It was shown earlier13 that for C10EO8 at the solution/oil interface this parameter is approximately two times larger. Moreover, the adsorption behavior in the homologous series of betains10 and dimethyl alkyl phosphine oxides11 is well described by the two-state model with R ) 0. Thus, a nonzero value of R is caused only by the oxyethylene chain. To estimate the influence of the oxyethylene chain length on the R value, an analysis of the data reported in ref 21 for C12EO6 was performed. These results, along with the data obtained in ref 22 for C12EO8, are shown in Figure 7, while the calculated parameters of the two models for C12EO6 are summarized at the end of Table 1. One can see that, while the values of ω1 and ω2 for the two compared ethers are approximately the same, the value of R for C12EO6 is significantly lower than that for C12EO8. Figure 8 shows the surface tension isotherms for the aqueous solutions of a linear ether C12EO6, and the crown ether C12H25OCH2-18-crown-6 (C12-OM-crown) solutions in water and in 0.01 M KCl.21 In contrast to the C12EO6 molecule containing a linear oxyethylene chain, the crown ether molecule possesses a closed crown ring. Figure 8 shows that this difference in the structure of the ether group results in a significant difference in the adsorption behavior. Note that the adsorption activity of the C12OM-crown ether at low concentration is significantly lower than that of C12EO6. It was mentioned above that the increased activity of C12EO6 at low concentrations can be explained by the reorientation and adsorption of the oxyethylene group at the solution/fluid interface. For the crown ether molecule, the reorientation of the oxyethylene group in the surface layer quite impossible. As the oxyethylene ring plane of the adsorbed crown ether molecule is located approximately perpendicular to the interface (which follows from the estimated molar area21), strong interaction between the ether rings can arise due to the formation of hydrogen bonds. This can result in an aggregation of the C12-OM-crown molecules both in the solution bulk and within the surface layer. The slight decrease of the surface tension in the concentration range 50 3 >50
0.01
Figure 9. Experimental (ref 21) and theoretical surface pressure isotherms for the C12H25OCH2-18-crown-6 solution without any addition of KCl. Model parameters are listed in Table 2.
Figure 10. Experimental (ref 21) and theoretical surface pressure isotherms for the C12H25OCH2-18-crown-6 solution with 0.01 M KCl. Model parameters are listed in Table 2.
21. The aggregation number for these complexes in the precritical region is approximately 2. In region 2, similar to solutions without added KCl, also systems containing salt can form large clusters at the surface. Conclusions The effect of the reorientation model parameters on the shape of the surface tension isotherms of surfactant solutions is discussed. The experimental isotherms for
oxyethylated alcohols CnEO8 with n ) 9-15 are in good agreement with the model, which assumes two states of adsorbed molecule. It is shown that at low concentrations the area occupied by these molecules is 3 to 4 times larger than that characteristic for higher concentrated solutions. The adsorption activity of the oxyethylated alcohol molecules in the unfolded state (ω1/ω2)R is 20-50 times higher that than in the state of minimum surface area. These features of oxyethylated alcohols result in an extremely high surface activity at low concentrations and an unusual shape of the surface tension isotherms completely incompatible with the Langmuir model. It is shown that the unusual adsorption behavior of the crown ether C12H25OCH2-18-crown-6 can be explained by the formation of dimers in diluted adsorption layers and of small two-dimensional clusters in concentrated surface layers. The theoretical model, which accounts for these aggregation phenomena, yields quite reasonable values for the model parameters. To summarize, with proper account for the reorientation of adsorbed molecules or their aggregation in the surface layer, respectively, and assuming ideal behavior in the bulk and at the interface (with respect to the enthalpy), the surface tension isotherms of oxyethylated alcohols can be interpreted with respect to the effects of the hydrocarbon and oxyethylene chain lengths and even of the different (linear or crown ring) oxyethylene chain structures. Unfortunately, there are no methods sensitive enough. Acknowledgment. The work was financially supported by the Fonds der Chemischen Industrie (RM 400429) and projects of the Max Planck Society and the European Union. LA991502X
