Issue-07 (10/2004)

Equilibrium isotherms of ionic surfactants on fluid interfaces:
Determination of the adsorption and the covered area fraction; role of the salt and the type of the hydrophobic phase

T. Gurkov, D. Dimitrova, K. Marinova, I. Ivanov
Lab. Chemical Physics & Engineering, Faculty of Chemistry, University of Sofia, 1164 Sofia, Bulgaria (www.lcpe.uni-sofia.bg)

C. Bilke-Krause, C. Gerber
KRÜSS GmbH, Wissenschaftliche Laborgeräte, 22453 Hamburg, Germany

Abstract

We present a simple thermodynamic method for determination of the adsorption (amount per unit area) of ionic surfactant on a fluid interface. The adsorption is obtained from a polynomial fit of the equilibrium interfacial tension, measured in the presence of arbitrary (and fixed) concentration of inorganic electrolyte, vs. the logarithm of the mean ionic activity. We performed measurements with sodium dodecyl sulfate (SDS) on air/ water and oil/ water boundaries, at different salt concentrations. On oil/ water interfaces the adsorption is always lower than that on air/ water surface; addition of inert electrolyte increases the adsorption.

In the case of Langmuir isotherm (with account for the counterion binding), we have derived an asymptotic functional dependence of the adsorption vs. the concentration. This dependence is used for fitting of experimental data, with a very good agreement. We determine the limiting adsorption at maximum coverage (i.e., at saturation), and therefrom, we estimate the degree of coverage of the interface with surfactant. It turns out that at the CMC the coverage is lower than about 90% (i.e., there is no saturation). The dependence of the surface coverage upon the mean ionic activity is rather insensitive toward the type of the fluid interface (air/ water, oil/ water with different hydrocarbons), and the salt concentration.

Article

Introduction

The macroscopic properties of the liquid dispersions (foams and emulsions), such as the stability, rheology, etc., are largely determined by the amount of surfactant on the liquid boundaries. This amount, taken per unit area, is called "the adsorption", Γ. So, it is important to have a simple and reliable method for determination of Γ. The surface (air/ water) and interfacial (oil/ water) tensions, σ, can easily be measured by means of convenient experimental methods. In the literature, the adsorption (Γ) has been obtained by differentiation of the equilibrium surface tension isotherm according to the Gibbs adsorption equation. However, this was done in the simple cases without inorganic salt [1, 2], or in a large excess of salt [3]. Rehfeld [2] proposed that the isotherm of σ vs. the surfactant concentration, c, should be fitted with a polynomial in powers of ln(c) (for systems without added electrolyte). Then, differentiation of the fitting function with respect to ln(c) yields Γ [2].

 

In the present work we combine the approach of Rehfeld with the more general case of Gibbs adsorption equation written in a form suitable for arbitrary concentration of added inorganic salt. Thus, from the isotherm of s measured at a fixed salt content one can obtain the amount of surfactant per unit area (Γ). The proposed procedure is suitable both for air/ water and for oil/ water boundaries. Comparison of data reveals the influences of the type of the fluid interface (air/ water; oil/ water), and the presence of inert electrolyte.

We also explore the asymptotic behavior of Γ at high concentrations. Plots of Γ in an appropriate scale allow determination of the limiting adsorption at maximum coverage (Γ∞). The calculated degree of surface coverage, θ = Γ/Γ∞ , helps us to resolve the controversy existing in the literature about the behavior of Γ around the CMC (the Critical Micellization Concentration). Our results support previous findings [4, 5] that at the CMC the interface is not completely covered by surfactant.

We show that for different systems, containing adsorbed SDS on air/ water and oil/ water interfaces in the presence of various amounts of NaCl, the concentration dependence of q lies on a “master curve”, in other words, the degree of surface coverage does not essentially depend on the type of the system.

 

Experimental

We measured the surface tension of aqueous solutions of the ionic surfactant sodium dodecyl sulfate (SDS, product of Acros, USA). The surfactant was used as received (special measures to avoid the influence of impurities are described below). All solutions were prepared with deionized water from a Milli-Q purification system (Millipore, USA). Additionally, the prepared aqueous solutions contained inorganic electrolyte, NaCl, with concentration 0.010 M or 0.150 M. The used NaCl (product of Merck, Germany) was preliminarily roasted at 500 °C for 3 hours to remove any organic contaminations.

 

As oil phase we used hexadecane (C16) and soya bean oil (SBO). Hexadecane (Merck, Germany) was purified by applying 2 to 3 consecutive passes through a column filled with adsorbents Silica gel (Merck, Germany) and activated magnesium silicate (Florisil®, Sigma-Aldrich, Germany). The interfacial tension of purified hexadecane against pure water was 54.0 ± 0.5 dyn/cm. SBO (commercial product for food application) was purified by passing through a column filled with adsorbents bentonite (Teokom, Bulgaria) and Florisil®. Up to three consecutive passages were applied in order to obtain oil that was free of substances decreasing its interfacial tension against water with more than 0.2 dyn/cm for 30 minutes. The value of the interfacial tension of the purified SBO was 30.5 ± 0.5 dyn/cm, which is close to that of other pure food-grade oils (~ 31 dyn/cm).

The air-water surface tension was measured by the Wilhelmy plate method, by means of a digital tensiometer Krüss K10ST (Krüss GmbH, Hamburg, Germany), at 23.3 ± 0.3 °C, using a sand-blasted glass plate or a platinum plate. The kinetics of the surface tension relaxation for all solutions was followed during at least 20 minutes. The signal of the tensiometer was recorded and stored on a PC. The equilibrium value of σAW was determined from the intercept of the plot σAW vs. t–1/2 [6].
The interfacial tension (o/w) was measured by applying drop shape analysis to pendant oil drops on a Drop Shape Analysis System DSA 10 (Krüss GmbH, Hamburg, Germany), at 23.3 ± 0.5 °C. The equilibrium value of σOW was determined from the intercept of the plot of σOW vs. t–1/2 [6], for times up to 20 minutes.

 

Results and Discussion

Isotherms of σ

The measured surface and interfacial tension isotherms of SDS in the presence of two different NaCl concentrations are shown in Fig. 1. For comparison, values of σAW obtained by Tajima [7] are given in Fig. 1a. The experimental values of Tajima coincide fairly well with our measurements.

Surface (a) and interfacial (b) tension isotherms of SDS in the presence of NaCl with two different concentrations: 0.01 M and 0.15 M.
Fig. 1. Surface (a) and interfacial (b) tension isotherms of SDS in the presence of NaCl with two different concentrations: 0.01 M and 0.15 M.

Both the surface (Fig. 1a) and the interfacial (Fig. 1b) tensions of the solutions are lower in the presence of higher electrolyte concentration, as has to be expected [8]. The effect is due mainly to the electric double layer (the existence of electrostatic contribution to the surface pressure).•Determination of the adsorption, ΓFor a system containing ionic surfactant and inorganic electrolyte with a common counterion, such as, e.g., sodium dodecyl sulfate (SDS) and NaCl (monovalent ions), the Gibbs adsorption equation reads:

 

------> Bitte Formeln 1, 2, 9 und 3 mit Zwischentexten einfügen

 

Experimental data are fitted with Eq. (3), and differentiation is applied to the fitting polynomial according to Eq. (1). This procedure is applicable to systems with arbitrary concentration of salt.
In such a way, the isotherms in Fig. 1 were processed to give the surfactant adsorption, Γ. Examples of the fits for two isotherms are shown in Fig. 2.



Interfacial tension isotherms of SDS at air/water (empty circles) and C16/ water (full diamonds) boundaries, in the presence of 0.15 M NaCl. The solid lines are best fit curves, according to Eq. (3).
Fig. 2. Interfacial tension isotherms of SDS at air/water (empty circles) and C16/ water (full diamonds) boundaries, in the presence of 0.15 M NaCl. The solid lines are best fit curves, according to Eq. (3).

 

The calculated adsorption, G (see Eq. 1), is presented in Fig. 3. The figure includes all systems investigated by us (Fig. 1), as well as results from processing of isotherms taken from the literature [2, 11, 12].

- If the system contains inorganic salt, the adsorption of surfactant depends only on the mean ionic activity

 

------> Bitte Formel einfügen

 

and the salt concentration per se is unimportant. Note that the curves Γ(c*) for 0.01 and 0.15 M NaCl coincide in the cases of air/ water and SBO/ water interfaces, and lie very close in the case of C16/ water interface (Fig. 3). On the other hand, the complete absence of inert electrolyte in the solution of SDS leads to lower values of Γ, compared to the systems with salt at the same c* (the curves without salt lie below those for the respective systems containing NaCl- Fig. 3). So, the mere presence of inorganic salt (at levels above 10 mM) is likely to promote the adsorption of SDS. Perhaps, the reason for this effect is connected with enhanced electrostatic screening in the double layer and decreased repulsion between the surfactant ions.

- Remarkable is the fact that the adsorption, Γ, is lower on oil/water interfaces (for C6, C16, C17, and even lower for SBO), than on water/air boundary (Fig. 3). This result is contrary to what one would expect solely from the adsorption free energy of the hydrocarbon tail of the surfactant molecule. This free energy is higher on oil/ water interfaces [13]. Explanation of the observed peculiarity may be sought in lateral interactions between the heads, influenced by out-of-plane fluctuations. On oil/ water interface, since the hydrocarbon tails of the surfactant ions are pulled more strongly into the oil, the fluctuations of protrusion will be suppressed and consequently, the lateral electrostatic repulsion between the charged heads will be stronger. Thus, the surfactant chemical potential will rise and the adsorption will eventually be lower.

 

Fig. 3. Determined adsorption, Γ, at different interfacial boundaries: air/water, hexadecane/ water, heptadecane/water (data from Ref. [2]), hexane/ water (data from Ref. [12]), and soybean oil/ water, in the presence of different amounts of NaCl. The data of Rehfeld [2], Hines [11], and Motomura et al. [12] were obtained in absence of additional inorganic electrolyte.

 

Asymptotic behavior of the adsorption at large surfactant concentrations

The Langmuir adsorption model assumes existence of a limiting maximum adsorption, Γ∞ , which corresponds to the closest possible packing in the surface layer. (It should be mentioned that Γ∞ is a model parameter.) The isotherm of Γ is usually represented in terms of θ=Γ/Γ∞ (called “degree of surface coverage”). In the asymptotic case of θ close to unity, one can derive the concentration dependence of Γ in the form:

 

-----> Bitte Formel einfügen

 

where χ and Ρ are constant numerical coefficients. The interval of concentrations where Eq. (4) is expected to hold is around (and below, but near) the CMC. Fits of data for Γ for particular systems demonstrate that Eq. (4) is very well satisfied. An example is presented in Fig. 4. The limiting adsorption at full coverage of the interface, Γ∞ , is obtained by extrapolation of the theoretical dependence of Γ, Eq. (4), toward 1/c*2 = 1/(a.at) → 0.

 

Fig. 4. Determination of the limiting adsorption of fully saturated layer, Γ∞ , from the data of Hines [11] for SDS on air/water interface, applying the asymptotic relation at high concentrations, Eq. (4).

 

In the same way we processed the data for Γ from Fig. 3. The results for Γ∞ are listed in Table 1. The comparison of different systems reveals that (I) addition of salt (from 0 to 0.01 M) increases Γ∞ ; (II) on oil/ water interfaces Γ∞ is lower than on air/ water surface (moreover, there is no difference between hexane and heptadecane); (III) the lowest limiting adsorption belongs to SBO.

The surface coverage

Table 1 displays the values of θ=Γ/Γ∞ at the CMC of the studied systems. Impressive is the fact that no value is higher than 0.91; for hydrocarbon/ water interface without salt θcmc <0.85. These findings indicate absence of saturation of the surface layer up to the CMC, in full agreement with the results reported by Thomas and co-workers [4, 5].

 

Table 1. Determined adsorption at maximum saturation of the interface, Γ∞ , the corresponding area per molecule, Α∞ = (Γ∞) –1, and the surface coverage at the CMC, θcmc = Γ(CMC)/Γ∞ .

 

System

Γ∞ x 1014, cm–2

Α∞, Α2

θcmc

Air/ water, 0.15 M NaCl, 23°C

3.142

31.92

0.89

Air/ water, 0.01 M NaCl, 23°C

3.142

31.82

0.87

Air/ water, no salt, 25oC, Ref. [11]

2.871

34.84

0.86

C16/ water, 0.15 M NaCl, 23°C

2.656

37.65

0.91

C16/ water, 0.01 M NaCl, 23°C

2.647

37.78

0.91

C17/ water, no salt, 25oC, Ref. [2]

2.437

41.04

0.84

C6/ water, no salt, 30°C, Ref. [12]

2.424

41.26

0.80

SBO/water, 0.01 and 0.15 M NaCl, 23°C

2.298

43.51

0.72 (0.01 M NaCl)
0.75 (0.15 M NaCl)

 

In Fig. 5 we plot the surface coverage, θ, evaluated at concentrations below the CMC, in the scale vs. the mean ionic activity, c*= (a.at)1/2. All data lie close to a "master curve" for the particular ionic surfactant, SDS, with the exception of the case with soybean oil. Therefore, (I) the dependence θ(c*) is rather insensitive to the type of the hydrophobic phase (air/ water, hydrocarbon/ water); only major changes in the composition of the oil can affect θ – such is the case of SBO (a commercial product which is basically a mixture of fatty acid glycerides); (II) θ (c*) is not significantly influenced by addition of inorganic electrolyte.

 

Fig. 5. Surface coverage of SDS as a function of c* = (a.at)1/2, for different interfaces.

 

 

Summary

- We formulate a simple thermodynamic procedure for determination of the adsorption of ionic surfactant from the interfacial tension isotherm, measured in the presence of arbitrary (and fixed) concentration of inorganic electrolyte. Polynomial fit σ[ln(a.at)] is used.

- On oil/ water boundaries the adsorption is always lower than that on air/ water surface. This effect probably originates from repulsion between the charged surfactant heads. Fluctuations of protrusion are suppressed on o/w interface, so the repulsion is stronger.

- Above a concentration of about 0.01 M, addition of more salt does not affect Γ if the mean ionic activity c* is the same. Thus, one can foresee results for s and Γ in a certain range of salt concentrations without carrying out measurements.

- We obtained the asymptotic functional dependence of the adsorption vs. (a.at) at large concentrations, and used it for fitting of data. By extrapolation of the fits, we determine the limiting adsorption at maximum coverage, Γ∞ . Therefrom, the degree of coverage of the interface with surfactant is estimated, θ=Γ/Γ∞ . It turns out that q at the CMC is lower than about 90% in all studied cases (ionic surfactants do not reach saturation at the CMC).

- The dependence of the surface coverage upon the mean ionic activity, θ c*), is rather insensitive toward the type of the fluid interface (air/ water, oil/ water with different hydrocarbons), and the salt concentration.

 

References

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[2] S.J. Rehfeld, J. Phys. Chem., 71 (1967) 738.
[3] K. Tajima, Bull. Chem. Soc. Japan, 43 (1970) 3063.
[4] J.R. Lu, A. Marrocco, T.J. Su, R.K. Thomas, J. Penfold, J. Colloid Interface Sci., 158 (1993) 303.
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[6] V.B. Fainerman, A.V. Makievski, R. Miller, Colloids Surfaces A, 87 (1994) 61.
[7] K. Tajima, Bull. Chem. Soc. Japan, 44 (1971) 1767.
[8] P.A. Kralchevsky, K.D. Danov, N.D. Denkov, in: K.S. Birdi (Ed.), Handbook of Surface and Colloid Chemistry, CRC Press, New York, 1997, p. 333.
[9] E.A. Moelwyn-Hughes, Physical Chemistry, Pergamon Press, London, 1961.
[10] V.B. Fainerman, E.H. Lucassen-Reynders, Adv. Colloid Interface Sci., 96 (2002) 295.
[11] J.D. Hines, J. Colloid Interface Sci., 180 (1996) 488.
[12] K. Motomura, M. Aratono, N. Matubayasi, R. Matuura, J. Colloid Interface Sci., 67 (1978) 247.
[13] J.T. Davies, E.K. Rideal, Interfacial Phenomena, Academic Press, New York, 1963.