Cooperative Effects in Surfactant Adsorption Layers at Water/Alkane Interfaces

In the present work, the properties of dodecyl dimethyl phosphine oxide (C12DMPO) at the water/decane interface are studied and compared with those obtained earlier at the interface to hexane. To simulate the interfacial behavior, a two-component thermodynamic model is proposed, which combines the equation of state and Frumkin isotherm for decane with the reorientation model involving the intrinsic compressibility for the surfactant. In this approach, the surface activity of decane is governed by its interaction with C12DMPO. The theory predicts the influence of decane on the decrease of the surface tension at a very low surfactant concentration for realistic values of the ratio of the adsorbed amounts of decane and surfactant. The surfactant’s distribution coefficient between the aqueous and decane phases is determined. Two types of adsorption systems were used: a decane drop immersed into the C12DMPO aqueous solution, and a water drop immersed into the C12DMPO solution in decane. To determine the distribution coefficient, a method based on the analysis of the transfer of C12DMPO between water and decane is also employed.


Introduction
Studies on the adsorption of various types of surfactants at fluid interfaces have been frequently performed. The most important facts are summarized in several books, such as by Möbius et al. [1], Kronberg et al. [2], Rosen [3], or most recently by Rosen and Kunjappu [4], being the fourth edition of [3]. The knowledge presented in these and other textbooks still remains correct and represents the fundamentals of surfactants at interfaces. However, recent papers report on new features of adsorbed surfactant molecules [5][6][7][8][9][10][11] and new experimental methods, such as [12,13] in particular, where studies were performed at water/oil interfaces. As a general fact, it is very clear that the adsorption behavior of surfactants at the surface of an aqueous solution is rather different from that at the interfaces between these solutions and an oil phase. In particular, the distribution coefficient of non-ionic surfactants

Materials and Methods
The interfacial tension measurements were performed with the bubble/drop profile analysis tensiometers PAT-1 and PAT-2P (SINTERFACE Technologies, Germany) as described in detail elsewhere [22]. The dynamic interfacial tension values were measured in the time range from seconds up to the equilibrium state of adsorption at 5 h for the higher and 25 h for the lower surfactant concentrations. Dodecyl dimethyl phosphine oxide (C 12 DMPO) was synthesized and purified as described in [23] and had a purity of better than 99%. The measurement temperature was kept constant at 25 • C. The decane for the oil phase was of spectroscopic grade (Labscan, Thailand) with a purity of better than 99% and used as received. All aqueous surfactant solutions were prepared using Milli-Q water. The experiments were performed with the buoyant (sessile) drop mode of PAT. The aqueous C 12 DMPO solutions were filled into the measuring cell having a volume of 20 mL. The decane drops were then formed at the bottom tip of a vertical steel capillary. The internal profile of the capillary was conical with an inner tip diameter of 2.0 mm. The drops formed in the experiments had a surface area between 31 and 34 mm 2 . The PAT software produced drops with an initial size of 21 to 23 mm 3 and kept the size constant over the entire experiment.
Two methods were employed to determine the surfactant's distribution coefficient. Similarly to what was reported in [15], the interfacial tensions were measured of decane drops formed in the aqueous surfactant solution and of water drops formed in surfactant solutions in decane. From the two adsorption isotherms of a surfactant thus obtained, it was possible to determine the distribution coefficient via the ratio of concentrations in oil and water, respectively, at which the interfacial tension was the same. Another method proposed in [14] was applied to determine the distribution coefficient. To the cell containing 18 mL of aqueous C 12 DMPO solution, 5 mL of decane was added at the top of the solution. The diffusion of surfactant occurred in the decane. After equilibration (which required more than one day), the surfactant concentration in the aqueous solution decreased, which resulted in an increase of the interfacial tension as compared to that measured before the addition of the decane. Then, from the interfacial tension isotherm of the aqueous solution, the C 12 DMPO concentration in the solution was determined, which finally gave the distribution coefficient.

Theory
The effect of alkanes on the interfacial tension can be described either by their co-adsorption with surfactants in a mixed adsorption layer or only by a modification of the surface layer properties of the surfactant molecules. In contrast to the model described in [21], where the adsorption of both components was assumed to obey the Frumkin model, here we consider a combined model. This model assumes the co-adsorption of alkane adsorbed from the oil drop governed by the Frumkin model, and surfactant adsorbed from the aqueous solution in the cuvette obeying the reorientation model. In what follows, the subscripts F and R refer to the quantities relative to the Frumkin and reorientation model, respectively. This combined model, first proposed in [24], is formulated as follows.
It is assumed that the surfactant molecules can be adsorbed in two orientations, corresponding to the molar areas ω R1 and ω R2 , respectively. For definiteness, we assume ω R1 < ω R2 . The partial adsorptions of the reorientation species in the two states, Γ R1 and Γ R2 , respectively, are described by the equations: where ω R is the average molar area of the reorientation component and θ R is the partial coverage of surface by the molecules of reorientation species.
Assuming the non-ideal enthalpy and entropy of the interfacial layer, the equation of state for the mixed layer is: where R and T are the gas law constant and absolute temperature, respectively, Π = γ 0 − γ is the surface pressure, and γ 0 and γ are the surface tension of solvent and solution, respectively. The parameter ω R10 is the molar area of the reorientable component in its state 1 when the surface coverage is infinitely small, and the parameters a R , a F , and a RF account for the interactions between the molecules of corresponding species in the adsorbed layer. The total surface coverage θ is related to the partial coverages as θ = θ R + θ F . The average molar area for the mixture is approximated by the relation: The adsorption isotherm for the reorientation component in state 1 is: Here, b R1 and c R are the adsorption equilibrium coefficient for the state 1 and the bulk concentration of the reorientation component. Assuming that the interrelation between the adsorption equilibrium Colloids Interfaces 2019, 3, 67 4 of 11 coefficients for states 1 and 2 of the reorientation component follows the power law: b 2 = (ω 2 /ω 1 ) α b 1 , the distribution between the two states is expressed by the equation: For the Frumkin component, the adsorption isotherm reads: The model assumes that the adsorption equilibrium parameter for the Frumkin component b F depends on the surface coverage by the reorientation component θ R : The model involves intrinsic compressibility in the adsorption layer. More specifically, it is assumed that the molar areas ω R1 and ω F decrease with the increase of total surface coverage and surface pressure: where ε R and ε F are the intrinsic compressibility coefficients and ω F0 is the molar area of the Frumkin component when the surface coverage is infinitely small.

Results and Discussion
Let us consider first the adsorption kinetics. In Figure 1, the dynamic interfacial tension at the interface between a decane drop and the surrounding aqueous solution of C 12 DMPO at several low concentrations is shown. Included is also the time dependence for the pure water at the interface with decane. It is seen that during 55,000 s the interfacial tension at the water/decane interface decreased only by 0.8 mN/m, which is obviously caused by the presence of small admixtures in the decane sample. For the solutions with surfactant concentrations of 10 −9 , 10 −8 , and 10 −7 mol/L the interfacial tension is lower than that for the pure water/decane interface by 5 to 8 mN/m. Figure 2 illustrates the results obtained for higher C 12 DMPO concentrations (black curves); also shown are the results obtained for a water drop surrounded by the C 12 DMPO solution in decane for three concentrations (10, 30, and 100 µmol/L, red curves). The equilibrium interfacial tension for a water drop in the C 12 DMPO solution in decane is by 6-7 mN/m higher than that for the same C 12 DMPO concentration in the aqueous solution. These results were used to determine the distribution coefficient of C 12 DMPO between the water and decane phases. It should be noted that the dynamics of adsorption from the surfactant solution in decane is different from that from the aqueous solution. The equilibration in the solution in decane is attained faster than in the aqueous solution; this is attributable to a higher C 12 DMPO diffusion coefficient in decane than in water. The dependencies for the C 12 DMPO solutions at the interface with hexane studied in [21] are rather similar to those shown in Figure 2, i.e., the tension at the alkane drop/aqueous solution interface is approximately equal for the two alkanes.
The results of interfacial tension measurements performed to determine the distribution coefficient via the method proposed in [14] are shown in Figure 3. The lower curves were obtained for a 10 µmol/L aqueous C 12 DMPO concentration with solution volumes of 20 mL and 18 mL (as shown in the Figure). The upper curves were obtained for the experiment in which 5 mL of decane were added on top of the solution. To estimate the effect caused by the partial penetration of the surfactant from its aqueous solution into the decane phase, two sets of measurements were performed, with different time lags between the addition of decane (24 and 48 h, as indicated in the Figure). It is seen that Colloids Interfaces 2019, 3, 67 5 of 11 the curves are virtually the same for times longer than 9000 s, which shows that the equilibrium is attained. The penetration results in the decrease of the surfactant concentration in its aqueous solution, which leads to an increase in the interfacial tension. Thus, it becomes possible to use the interfacial tension values and the C 12 DMPO adsorption to determine the surfactant concentrations in water and decane, and hence to calculate the distribution coefficient.
where εR and εF are the intrinsic compressibility coefficients and ωF0 is the molar area of the Frumkin component when the surface coverage is infinitely small.

Results and Discussion
Let us consider first the adsorption kinetics. In Figure 1, the dynamic interfacial tension at the interface between a decane drop and the surrounding aqueous solution of C12DMPO at several low concentrations is shown. Included is also the time dependence for the pure water at the interface with decane. It is seen that during 55,000 s the interfacial tension at the water/decane interface decreased only by 0.8 mN/m, which is obviously caused by the presence of small admixtures in the decane sample. For the solutions with surfactant concentrations of 10 −9 , 10 −8 , and 10 −7 mol/L the interfacial tension is lower than that for the pure water/decane interface by 5 to 8 mN/m.   Figure 2 illustrates the results obtained for higher С12DMPO concentrations (black curves); also shown are the results obtained for a water drop surrounded by the С12DMPO solution in decane for three concentrations (10, 30, and 100 µmol/L, red curves). The equilibrium interfacial tension for a water drop in the С12DMPO solution in decane is by 6-7 mN/m higher than that for the same С12DMPO concentration in the aqueous solution. These results were used to determine the distribution coefficient of C12DMPO between the water and decane phases. It should be noted that the dynamics of adsorption from the surfactant solution in decane is different from that from the aqueous solution. The equilibration in the solution in decane is attained faster than in the aqueous solution; this is attributable to a higher C12DMPO diffusion coefficient in decane than in water. The dependencies for the C12DMPO solutions at the interface with hexane studied in [21] are rather similar to those shown in Figure 2, i.e., the tension at the alkane drop/aqueous solution interface is approximately equal for the two alkanes. The results of interfacial tension measurements performed to determine the distribution coefficient via the method proposed in [14] are shown in Figure 3. The lower curves were obtained for a 10 μmol/L aqueous C12DMPO concentration with solution volumes of 20 mL and 18 mL (as shown in the Figure). The upper curves were obtained for the experiment in which 5 mL of decane   Figures 1 and 2. The experimental values of surface tension for single hexane and decane drops in C12DMPO solutions are shown by solid symbols. It is seen that above 1 μmol/L C12DMPO concentrations, the isotherms for hexane and decane drops in C12DMPO aqueous solutions almost coincide, while at concentrations below 1 μmol/L the interfacial tension at the interface with decane is lower than that with hexane. It was shown previously in [21] that the decrease of tension at very low surfactant concentrations is caused by the adsorption of alkane rather than by the adsorption of surfactant molecules. The present results show that the adsorption of decane is stronger than the adsorption of hexane.   The experimental values of surface tension for single hexane and decane drops in C 12 DMPO solutions are shown by solid symbols. It is seen that above 1 µmol/L C 12 DMPO concentrations, the isotherms for hexane and decane drops in C 12 DMPO aqueous solutions almost coincide, while at concentrations below 1 µmol/L the interfacial tension at the interface with decane is lower than that with hexane. It was shown previously in [21] that the decrease of tension at very low surfactant concentrations is caused by the adsorption of alkane rather than by the adsorption of surfactant molecules. The present results show that the adsorption of decane is stronger than the adsorption of hexane.   Figures 1 and 2. The experimental values of surface tension for single hexane and decane drops in C12DMPO solutions are shown by solid symbols. It is seen that above 1 μmol/L C12DMPO concentrations, the isotherms for hexane and decane drops in C12DMPO aqueous solutions almost coincide, while at concentrations below 1 μmol/L the interfacial tension at the interface with decane is lower than that with hexane. It was shown previously in [21] that the decrease of tension at very low surfactant concentrations is caused by the adsorption of alkane rather than by the adsorption of surfactant molecules. The present results show that the adsorption of decane is stronger than the adsorption of hexane.   The theoretical values calculated using Equations (1)- (7) with the parameters listed in Table 1 are shown in Figure 4 by solid curves. The theoretical results are in good agreement with the experimental data. It is seen that, while the model parameters relative to the C 12 DMPO for both interfaces (decane and hexane) are almost the same, the b Fmax parameter for decane is twice as large as that for hexane. The values calculated with the parameters for C 12 DMPO listed in Table 1 for the case of negligible alkane adsorption (dash-dotted curve in Figure 4) are also in good agreement with the experiments at concentrations above 1 µmol/L. Figure 4 also shows the experimental isotherms for water drops in C 12 DMPO solutions in hexane and decane (open symbols). The interfacial tension values for the solutions in hexane are higher than those in decane, which is caused by the higher solubility of C 12 DMPO in hexane than in decane, i.e., by the different distribution coefficients. Note, the concentrations for these data are those in the alkane phase, while for the other experimental points the abscissa refers to concentrations in the aqueous phase.
Using the method explained in [21], based on the comparison of two types of isotherms, the distribution coefficients K for C 12 DMPO between water and hexane (K = 6.4-6.8) and between water and decane (K = 3.8-4.1) were estimated. From the values of equilibrium interfacial tension ( Figure 3) and the isotherm for decane drops in water, the distribution coefficient of the C 12 DMPO between decane and water was determined. The interfacial tension increase caused by the transfer of C 12 DMPO from water into decane (Figure 3) results in a decrease of the C 12 DMPO concentration in water from 10 µmol/L to 5.5-5.8 µmol/L. Then, from the volume (18 mL) and the difference in concentrations, it is possible to calculate the amount of C 12 DMPO and its concentration in 5 mL of decane. This yields a distribution coefficient of 4.1-4.7. Therefore, both methods used lead to close results, and for the distribution coefficient of C 12 DMPO between water and decane, a value of K = 4 was obtained. Figure 5 illustrates the adsorptions of alkanes and C 12 DMPO. For the water-decane system, the decane adsorption is somewhat higher, and the C 12 DMPO adsorption is somewhat lower than the corresponding values for the water-hexane system. At surfactant concentrations below 2 × 10 −8 mol/L the alkanes, adsorption dominates, while at higher surfactant concentrations the adsorption of surfactant molecules prevails. The reorientation model for the surfactant yields real values for the alkane:surfactant adsorption ratio for the lowest surfactant concentrations. For the two alkanes considered here, the maximum value of this ratio is 6, which agrees quite well with the results of quantum chemical calculations [25] where it was predicted that this ratio cannot exceed a value of 8.
The results obtained in the dilation rheology studies at the water/hexane interface (data from [21]) and at the water/decane interface using alkane drops in C 12 DMPO aqueous solutions after equilibration are illustrated by Figures 6 and 7. It is seen that the visco-elasticity modulus increases with the increase of the oscillation frequency. For the water/decane interface, the modulus values are somewhat higher than for the water/hexane interface, and the concentration dependencies of the visco-elasticity modulus exhibit a maximum at the concentration of 0.01 µmol/L for hexane, and 0.3 µmol/L for decane. This indicates that the alkanes contribute significantly to the rheological properties. Note, the experiments for water drops in C 12 DMPO solutions in alkane show modulus values approximately twice as higher as for the same surfactant concentrations in water. This can be explained by the controlled (lower) concentration of the surfactant in alkane for water drops formed in surfactant in alkane solutions.
Of interest are the dependencies of the phase angle as shown in Figure 7. At low concentrations, the phase angle values do not exceed 10 • and become higher at concentrations above 1 µmol/L. This suggests that the presence of alkanes in the surface layer hampers the phase shift. The phase angle increases with the increase of oscillation frequency; for decane, the angle is approximately two times higher than for hexane at the same concentrations.     Of interest are the dependencies of the phase angle as shown in Figure 7. At low concentrations, the phase angle values do not exceed 10° and become higher at concentrations above 1 μmol/L. This suggests that the presence of alkanes in the surface layer hampers the phase shift. The phase angle increases with the increase of oscillation frequency; for decane, the angle is approximately two times higher than for hexane at the same concentrations.
It follows from the data shown in Figure 5 that at C12DMPO concentrations above 1 μmol/L, the influence of decane adsorption is negligible. Therefore, in this concentration range, we can calculate the dilational visco-elasticity using equations valid for individual C12DMPO solutions. Moreover, only the diffusion from the alkane drop could be taken into account, while the diffusion from the aqueous solution can also be neglected because the equilibrium concentration of surfactant in the alkane drop is essentially higher than that in the water phase. Moreover, the surfactant diffusion in the alkane is several times higher than in water. In Figure 8, the experimental data are compared with the theoretical values calculated using a software elaborated in [25], which assumed a four-fold concentration increase (K = 4) and a C12DMPO diffusion coefficient of 10 −9 m 2 /s. A rather moderate agreement between the calculated results and the experimental data is observed. Presently, an improved software is under development, which is capable of accounting for both the diffusion from the aqueous solution and the adsorption of alkane molecules.  It follows from the data shown in Figure 5 that at C 12 DMPO concentrations above 1 µmol/L, the influence of decane adsorption is negligible. Therefore, in this concentration range, we can calculate the dilational visco-elasticity using equations valid for individual C 12 DMPO solutions. Moreover, only the diffusion from the alkane drop could be taken into account, while the diffusion from the aqueous solution can also be neglected because the equilibrium concentration of surfactant in the alkane drop is essentially higher than that in the water phase. Moreover, the surfactant diffusion in the alkane is several times higher than in water. In Figure 8, the experimental data are compared with the theoretical values calculated using a software elaborated in [25], which assumed a four-fold concentration increase (K = 4) and a C 12 DMPO diffusion coefficient of 10 −9 m 2 /s. A rather moderate agreement between the calculated results and the experimental data is observed. Presently, an improved software is under development, which is capable of accounting for both the diffusion from the aqueous solution and the adsorption of alkane molecules. Of interest are the dependencies of the phase angle as shown in Figure 7. At low concentrations, the phase angle values do not exceed 10° and become higher at concentrations above 1 μmol/L. This suggests that the presence of alkanes in the surface layer hampers the phase shift. The phase angle increases with the increase of oscillation frequency; for decane, the angle is approximately two times higher than for hexane at the same concentrations.
It follows from the data shown in Figure 5 that at C12DMPO concentrations above 1 μmol/L, the influence of decane adsorption is negligible. Therefore, in this concentration range, we can calculate the dilational visco-elasticity using equations valid for individual C12DMPO solutions. Moreover, only the diffusion from the alkane drop could be taken into account, while the diffusion from the aqueous solution can also be neglected because the equilibrium concentration of surfactant in the alkane drop is essentially higher than that in the water phase. Moreover, the surfactant diffusion in the alkane is several times higher than in water. In Figure 8, the experimental data are compared with the theoretical values calculated using a software elaborated in [25], which assumed a four-fold concentration increase (K = 4) and a C12DMPO diffusion coefficient of 10 −9 m 2 /s. A rather moderate agreement between the calculated results and the experimental data is observed. Presently, an improved software is under development, which is capable of accounting for both the diffusion from the aqueous solution and the adsorption of alkane molecules.

Conclusions
In many studies on surfactant's adsorption at their aqueous solution interface with oil, the decrease of interfacial tension at very low surfactant concentrations was reported. In the present work, the experimental data obtained for the water/decane interface are compared with the results obtained in [21] for C 12 DMPO solutions at the water/hexane interface. For the theoretical analysis of the tensiometric and rheological properties, the model of a two-component interfacial layer is used, which assumes the presence of alkane molecules in this layer interacting with the adsorbed surfactants. The model is based on the combination of the Frumkin isotherm for the alkane, and the reorientation model for the surfactant, i.e., the model involves the combined equations of state and the assumption that the layer of adsorbed molecules exhibits intrinsic compressibility at larger coverages. The model also assumes that the surface activity of the alkane molecules depends on its interaction with the surfactant, i.e. it depends on the alkane chain length. The theory predicts that the influence of this interaction with decane results in a decrease of the interfacial tension from 51-52 mN/m (pure water at the interface with decane) to 49-45 mN/m at very low surfactant concentrations, and also yields real values for the ratio of the adsorbed amount of alkane to surfactant.
In the study, the surfactant's distribution coefficient between the water and decane phases is also determined. Similar to [15], two series of measurements were performed to determine the adsorption isotherms for two types of the system: alkane drops in the surfactant aqueous solution, and water drops in the surfactant's solution in the alkane. Also, an alternative method was used similar to that employed in [14], where the transfer of surfactant between the aqueous phase and the oil phase was analyzed to determine the distribution coefficient from the resulting mass balance.