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Notes Adsorption of Alkali Dodecyl Sulfates on Air/ Water Surface Stoyan Karakashev,† Roumen Tsekov,*,‡ and Emil Manev† Department of Physical Chemistry, University of Sofia, 1126 Sofia, Bulgaria, and Max Planck Group for Colloids and Surfaces, TU Bergakademie, 09599 Freiberg, Germany Received April 20, 2001. In Final Form: June 5, 2001
The properties of colloids are strongly related to the state of the interfaces dividing the dispersion phase from medium. For this reason, considerable efforts are devoted to investigate the behavior of adsorbed surfactant monolayers. The effect of counterions on the adsorption saturation is observed;1 the addition of electrolytes can even change the slope of the surface tension isotherm. The influence of counterions on the zeta2 and surface3 potentials of bubbles in aqueous surfactant solutions is also investigated. The counterion adsorption is measured for a system containing sodium dodecyl sulfate (NaDS) and CaCl2 by a radiochemical method with labeled 45Ca2+, and competitive adsorption of Na+ and Ca2+ ions is detected.4 The Gibbs isotherm is confirmed5 by independent measurements of the surface tension and adsorption at various salt concentrations, and the counterion adsorption is determined via thermodynamic considerations.6 Another useful method for investigation of adsorbed layers is the neutron reflection,7 which provides information about the adsorption and structure of adsorbed layers on air/water interface. It is established8 that the size of the hydration shell of counterions affects the adsorption of the surfactant ions; the adsorption of surfactant ions is larger for less hydrated counterions, a fact confirmed by model calculations9 as well. The theoretical description of charged interfacial layers follows the invention of the electric double-layer model. First, the contribution of the Debye electrostatic tail to the surface tension is considered in the case of weakly populated adsorption layers10 without accounting for the counterion binding to the surface. The surface tension * Corresponding author. † University of Sofia. ‡ Max Planck Group for Colloids and Surfaces. (1) van Voorst Vader, F. Trans. Faraday Soc. 1960, 88, 1067. (2) Usui, S.; Sasaki, H. J. Colloid Interface Sci. 1977, 65, 36. (3) Vakarelski, I.; Dushkin, C. Colloids Surf. A 2000, 163, 177. (4) Cross, A.; Jayson, G. J. Colloid Interface Sci. 1993, 162, 45. (5) Tajima, K.; Muramatsu, M.; Sasaki, T. Bull. Chem. Soc. Jpn. 1970, 43, 1991. Tajima, K. Bull. Chem. Soc. Jpn. 1970, 43, 3063; 1971, 44, 1767. (6) Motomura, K.; Ando, N.; Matsuki, H.; Aratono, M. J. Colloid Interface Sci. 1990, 139, 188. (7) Simister, E.; Thomas, R.; Penfold, J.; Aveyard, R.; Binks, B.; Cooper, B.; Fletcher, P.; Lu, J.; Sokolowski, A. J. Phys. Chem. 1992, 96, 1383. Simister, E.; Lee, E.; Thomas, R.; Penfold, J. J. Phys. Chem. 1992, 96, 1373. (8) Lu, R.; Marroco, A.; Su, T.; Thomas, R.; Penfold, J. J. Colloid Interface Sci. 1993, 158, 303. Lyttle, D.; Lu, R.; Su, T.; Thomas, R. Langmuir 1995, 11, 1001. (9) Karakashev, S.; Manev, E.; Karakashev, G. Bulg. Chem. Commun. 2001, 32, 2. (10) Davies, J.; Rideal, E. Interfacial Phenomena; Academic Press: London, 1963.
isotherm derived is tested experimentally, but only qualitative agreement is observed.11 Later, on the basis of the Frumkin adsorption isotherm coupled with the Poisson equation, a surface tension isotherm is derived12 for the case of more populated adsorption layers, where the interaction between the surfactant ions in the adsorption layer is important. It is further developed13 by employment of the Stern adsorption isotherm for the counterion layer. This model is experimentally tested, and a good agreement to experimental data for the surface tension is observed.9 It demonstrates, however, some disadvantages. In the application to NaDS the model predicts an equilibrium constant of Na+ adsorption 7 orders of magnitude smaller than the constant of DSadsorption, which contradicts the coverage of the Stern layer commensurable with the adsorption layer. This is due to the approximations employed in the derivation of the model; it describes the lateral interaction between the surfactant ions but does not take into account the lateral interaction of the counterions. Moreover, the model is a four-parametric one, which generates degenerate solutions during a numerical fit, corresponding to different states of the adsorbed layer. For this reason, it is important to diminish the number of fitting parameters. In the present paper a more accurate model is developed, which accounts for the specific interactions of all adsorbed species and has only one free parameter. The adsorption of ionic surfactants generates an adsorption layer of surfactant ions, a Stern layer of counterions bounded to the surfactant layer, and a diffuse tail of counterions distributed by the electric field of the charged surface. Every layer has its own contribution to the surface tension. The DS- adsorption is well described by the Frumkin isotherm
K1a )
(
)
Γ1 - Γ2 2β1Γ1 + Fφ exp Γ∞ - Γ1 RT
(1)
where the effect of counterions to restrict the ability of surfactant to desorb is accounted for. Here K1 is the equilibrium constant of DS- adsorption, a ) c exp(-0.037xc) is the activity of the surfactant with bulk concentration c, Γ∞ is the surfactant adsorption at closed packing, Γ1 and Γ2 are the adsorptions of the surfactant and counterions, respectively, β1 is a parameter of interaction between DS- ions, φ is the surface potential, and F is the Faraday constant. The adsorption of counterions is also described by the Frumkin isotherm
K2a )
(
)
Γ2 2β2Γ2 - Fφ exp Γ1 - Γ2 RT
(2)
Here K2 is the equilibrium constant of counterion adsorption, and β2 is a parameter of the lateral interaction between the counterions in the Stern layer. One can easily (11) Lukassen-Reynders, E. J. Phys. Chem. 1966, 70, 1777. (12) Borwankar, R.; Wasan, D. Chem. Eng. Sci. 1988, 43, 1323. (13) Kralchewsky, P.; Danov, K.; Broze, G.; Mehreteab, A. Langmuir 1999, 15, 2351.
10.1021/la010584y CCC: $20.00 © 2001 American Chemical Society Published on Web 07/24/2001
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Langmuir, Vol. 17, No. 17, 2001
Notes
Table 1. Specific Constants of the Surfactants surfactant
K1 [m3/mol]
Γ∞ [µmol/m2]
v2 [Å3]
d12 [Å]
12
∆µ2 [kJ/mol]
LiDS NaDS KDS RbDS CsDS
137.2 137.2 137.2 137.2 137.2
3.2 3.3 3.9 4.5 4.3
165.2 88.3 52.5 49.8 49.8
5.8 5.2 4.8 4.7 4.7
5.7 5.6 5.3 5.2 5.1
41.6 47.5 55.5 56.4 58.0
recognize in the β parameters the second virial coefficients from the state equations of the layers, which in the case of sufficiently weak interaction acquire the form14
∫d∞Uir dr
βi ) -NA2π
i
(3)
Here Ui is the interaction energy between two neighboring ions and di is the ion diameter. From electrostatics the following relation between the charge density and the surface potential holds
Γ2 - Γ1 ) 4(a/κ) sinh(Fφ/2RT)
(4)
where κ ) F(2a/0RT)1/2 is the reciprocal value the Debye length. Applying now the rigorous Gibbs isotherm13 coupled with the equations above, one yields the following relation for the surface tension σ on air/water surface of the surfactant solution
σ ) σ0 + Γ∞RT ln(1 - Γ1/Γ∞) + β1Γ12 + β2Γ22 8RT(a/κ)[cosh(Fφ/2RT) - 1] (5) where σ0 is the surface tension of pure water and the last term accounts for the contribution of the electric double layer. A possibility to determine the five unknown parameters K1, K2, β1, β2, and Γ∞ in the above four-equation system is to fit experimental data for the surface tension dependence on the surfactant concentration. Such an approach is already proposed13 for description of NaDS adsorption without accounting for the lateral interaction of counterions (β2 ) 0). We tried to fit the experimental data8 for the surface tension isotherms of the alkali dodecyl sulfates. An optimization procedure on five parameters based on the least-squares method, however, provides many commensurable minima, corresponding to different states of the adsorption layer and undistinguishable by the optimization procedure. For this reason, it is important to reduce the number of variables by physical modeling. There is only repulsion between the counterions, while the surfactant ions undergo attraction between the hydrophobic tails and repulsion between the heads. The interaction between two counterions in the Stern layer is described well by the Debye-Hu¨ckel expression
U2 ) (e2/4π0r) exp(-κr)
(6)
Substituting this relation in eq 3 and using the inequality κd2 , 1, one yields
β2 ) -F2/40κ
(7)
The attraction energy between two parallel hydrophobic chains is given by15 -3πCL/8δ2r,5 where C ) 5 × 10 - 78 J/m6 is the London constant, δ ) 1.27 Å is the diameter of a methylene groups, and L ) 12δ is the length of the (14) Hill, T. An Introduction in Statistical Thermodynamics; AddisonWesley: Reading, MA, 1962. (15) Israelachvili, J. Intermolecular and Surface Forces; Academic Press: London, 1991.
Figure 1. Fit of the experimental concentration dependence of the surface tension.
dodecyl chain. These parameters correspond the vertical orientation of the surfactant chains, since the lateral interaction becomes important at relatively large Γ1. Since the surfactant ions are also charged, the full potential energy of lateral interaction acquires the form
U1 ) (e2/4π0r) exp(-κr) - 9πC/2δr5
(8)
Substituting eq 8 in eq 3, one yields the surfactant virial coefficient
β1 ) 3NA2π2C/2δd13 - F2/40κ
(9)
Using the virial relation 1/Γ∞ ) NAπd12, β1 acquires finally the form
β1 ) 3NA2π2C(πNAΓ∞)3/2/2δ - F2/40κ
(10)
The driving force for the adsorption of counterions on the adsorbed surfactant ions is the electrostatic interaction promoted by a lower value of the dielectric permittivity at the surface. The free energy of adsorption of counterions on the surfactant ions can be calculated from the following expression
∆µ2 ) eF/4π012d12
(11)
Here 12 and d12 are the dielectric permittivity and the distance between the adsorption and Stern layers, respectively. The distance d12 is equal to the average of the hydration diameters of a sulfate ion and of a counterion (see Table 1). Using eq 11, one is able to calculate the equilibrium constant of counterions adsorption
K2 ) NAv2 exp(∆µ2/RT)
(12)
where v2 is the volume of a hydrated counterion. Further one can employ for Γ∞ the experimental data for the surfactant adsorption at the cmc, measured by neutron reflectivity, and the determined equilibrium constants K1 of surfactant adsorption, which are given8 in Table 1. Thus, we have experimental values for K1 and Γ∞, and analytical expressions for β1, β2, and K2, where all the specific constants are identified. For 12 is known16 that the dielectric permittivity of the first water layer is about 6. However, since this is not an exact value, we are going to fit the surface tension isotherms of all alkali dodecyl sulfates to get 12. (16) Adamson, A. Physical Chemistry of the Surface; Wiley: New York, 1990.
Notes
Figure 2. Concentration dependence of the surfactant adsorption.
Figure 3. Concentration dependence of the counterion adsorption.
The model provides simultaneously the dependence of the surface tension, adsorptions, and surface potential on the surfactant concentration. By this knowledge, it is also possible to calculate the contribution of the interaction between surfactant and counterions to the surface tension. The obtained theoretical dependencies for all five systems are given on the figures below. Figure 1 shows that the model fits reasonably the concentration dependence of
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Figure 4. Concentration dependence of the surface potential.
the surface tension. The adsorption curves of DS- ions in Figure 2 and counterions in Figure 3 are linear, because the layers are still far from Γ∞. In any case, the lateral electrostatic repulsion between the charged surfactant heads prevails over the hydrophobic attraction. A detailed analysis shows that the occupation of the Stern layer Γ2 is about 85% of Γ1 for considered surfactant concentrations. The surface potential curves in Figure 4 are in the reasonable range from -60 to -30 mV. They decrease when changing from Li+ to Cs+, but the dependence of the surface potential on the surfactant concentration becomes stronger. The explicit effect of the double layer on the surface tension is negligible. Note that φ is the contribution of the adsorption only, while the experimentally measured surface potential includes also the surface potential of pure water. In the present paper the latter is included in the adsorption constants K1 and K2. The fitted dielectric permittivity of water between the surfactant and Stern layers depends on the thickness as presented in Table 1. Since the hydration radii of counterions decrease, 12 decreases in the row from Li+ to Cs+. In all cases, the value of 12 corresponds well to the value of the first water layer. Table 1 shows that the free energy of adsorption of counterions increases from Li+ to Cs+, and its value corresponds to the energy of an ionic bond. Acknowledgment. R.T. is thankful to the Alexander von Humboldt Foundation for a granted fellowship. LA010584Y
