J. Phys. Chem. B 2007, 111, 1769-1774
1769
Counterion and Surface Density Dependence of the Adsorption Layer of Ionic Surfactants at the Vapor-Aqueous Solution Interface: A Computer Simulation Study Gyo1 rgy Hantal and Lı´via B. Pa´ rtay Laboratory of Interfaces and Nanosize Systems, Institute of Chemistry, Eo¨tVo¨s Lora´ nd UniVersity, Pa´ zma´ ny Pe´ ter stny. 1/a, H-1117 Budapest, Hungary
Imre Varga† Department of Chemistry, Royal Institute of Technology, Drottning Kristinas Va¨g 51, SE-10044 Stockholm, Sweden
Pa´ l Jedlovszky* and Tibor Gila´ nyi* Laboratory of Interfaces and Nanosize Systems, Institute of Chemistry, Eo¨tVo¨s Lora´ nd UniVersity, Pa´ zma´ ny Pe´ ter stny. 1/a, H-1117 Budapest, Hungary ReceiVed: October 24, 2006; In Final Form: December 13, 2006
To test the validity of currently used adsorption theories and understand the origin of the lack of their ability of adequately describing existing surface tension measurement data, we have performed a series of molecular dynamics simulations of the adsorption layer of alkali decyl sulfate at the vapor/aqueous solution interface. The simulations have been performed with five different cations (i.e., Li+, Na+, K+, Rb+, and Cs+) at two different surface concentrations (i.e., 2 µmol/m2 and 4 µmol/m2). The obtained results clearly show that the thickness of the outer Helmholtz plate, a key quantity of the various adsorption theories, depends on two parameters, that is, the size of the cations and the surface density of the anionic surfactant. Namely, with increasing surface concentration, the electrostatic attraction between the two, oppositely charged, layers becomes stronger, leading to a considerable shrinking of the outer Helmholtz plate. Furthermore, this layer is found to be thicker in the presence of larger cations. The former effect could be important in understanding the anomalous shape of the adsorption isotherms of alkali alkyl sulfate surfactants, while the second effect seems to be essential in explaining the cation specificity of these isotherms.
1. Introduction The adsorption of ionic surfactants, a phenomenon of both scientific and technological importance, has been the subject of intensive scientific investigations for more than a century. To accurately describe this type of adsorption and understand its physical background, various theories have been developed at different levels of approximation in the literature. The simplest approach is the application of ‘‘pseudo-non-ionic models”. In this case, an adsorption isotherm derived for non-ionic surfactants is used for the fitting of the experimental data. However, these models give limited physical insight due to the neglected electrostatic interactions and cannot interpret any of the specific characteristics of the experimental isotherms.1 More realistic adsorption theories of ionic surfactants at planar interfaces incorporate an electrostatic contribution in the adsorption free energy by means of the Gou¨y-Chapman approximation,2,3 in which (i) the interface is modeled by a plane (i.e., its width is neglected), and the charged surfactants are regarded to lay in this plane (i.e., form an infinitely thin layer), and (ii) the size of the counterions is neglected (i.e., they are regarded as charged, point-like objects), and they follow a Poisson-Boltzmann * To whom correspondence should be addressed. E-mail: pali@ chem.elte.hu;
[email protected]. † On leave from: Laboratory of Interfaces and Nanosize Systems, Institute of Chemistry, Eo¨tvo¨s Lora´nd University, Pa´zma´ny Pe´ter stny. 1/a, H-1117 Budapest, Hungary.
distribution. Considering also the finite size of the counterions, a neutral layer, called the outer Helmholtz plate, was introduced in the theory, to account for the fact that the counterions cannot approach the layer of the adsorbed charged surfactants infinitely close.2,3 It should also be noted that the Gou¨y-Chapman theory was originally developed for idealized metal/solution interfaces, at which the first of the above two assumptions is not at all far from reality. However, the application of this theory for fluid/ fluid (e.g., liquid/vapor) interfaces without appropriate modifications might lead to dubious results. To avoid this problem, the original Gou¨y-Chapman theory has been further elaborated in various ways, for example, by applying different geometrical models of the adsorbed layer4-8 or by taking the “chemical” binding of the counterions to the adsorbed monolayer also into account.5-8 While all these theories can explain, at least qualitatively, the effect of the ionic strength on the adsorption isotherm, the ion specificity (i.e., the role of the counterions) can only be addressed by the ones also containing ion-specific parameters.5-9 Another problem related to such adsorption theories is that one has to face serious difficulties when trying to check their validity on the basis of existing experimental data. These difficulties partly originated in the fact that all of the adsorption theories of ionic surfactants contain an electrostatic and a nonelectrostatic (i.e., hydrophobic interaction) term, which cannot be experimentally separated. Furthermore, due to the
10.1021/jp066969c CCC: $37.00 © 2007 American Chemical Society Published on Web 01/31/2007
1770 J. Phys. Chem. B, Vol. 111, No. 7, 2007 several fitting parameters used in the theories, the same experimental adsorption isotherm can often be well described by conceptually different theories. Some of these difficulties could be overcome by computer simulation methods, which can complement well the real experiments in testing the reliability of various theories. In particular, computer simulations can provide exact results for the studied model systems, which are unaffected by the approximations inherent in the various theories.10 Further, computer simulations can provide a detailed, atomistic level insight into the three-dimensional structure of the studied model system. However, in spite of the growing number of simulation studies on adsorption layers formed by cationic,11-13 anionic,13-16 zwitterionic,17-20 or non-ionic surfactants,21-24 their mixtures25,26 or small molecules27-35 at various interfaces, the potential of this methodology in addressing theoretical problems concerning surface adsorption is far from being fully explored. In this paper, we present a set of molecular dynamics simulations of the adsorption layer of alkali decyl sulfate surfactants at the interface between their aqueous solution and its vapor. In these simulations, the alkali cation is systematically varied from Li+ to Cs+. To exclude the possibility of the arbitrariness of the results due to the particular choice of the potential model chosen, the full set of the simulations is repeated with a different set of potential parameters describing the cations. The effect of the surface concentration of the surfactant on the structure of the adsorption double layer, formed by oppositely charged ions, is investigated by studying systems of two different surface concentrations. The penetration of the cations into the adsorption layer of the anionic surfactant as well as the dependence of the distance of the two ionic layers on the cation size are discussed in detail on the basis of these simulations. 2. Molecular Dynamics Simulations Molecular dynamics simulations of the adsorption layer of alkali decyl sulfate surfactants at the aqueous solution/vapor interface have been performed in the canonical (N,V,T) ensemble at a temperature of 298 K. To investigate the effect of the cation size on the structure of the adsorption double layer, the simulations have been done with five different alkali cations, that is, Li+, Na+, K+, Rb+, and Cs+. The X, Y, and Z edges of the rectangular basic simulation box have been 208.18 Å, 28.815 Å, and 28.815 Å long, respectively, with the X axis being perpendicular to the interface. The basic box contained 3000 water molecules, described by the SPC36 potential model. The systems have been simulated at two different surface concentrations of the surfactant, that is, 2 and 4 µmol/m2. These systems, roughly corresponding to an unsaturated and a saturated adsorption layer of the decyl sulfate (DeS-) ions,8 have consisted of 20 and 40 ion pairs, respectively. The DeS- ions have been modeled by the potential developed by Schweighofer et al.14 In the simulations, the bond lengths of the DeS- ion have been kept fixed at their equilibrium values. This model uses the united atom approach for the CH2 and CH3 groups. In describing the torsional rotations of the DeS- ions, the parameters of Domı´nguez and Berkowitz16 have been used. The alkali cations have been described by the potential model of Åqvist.37 To stress that the obtained results are independent of the potential model used, the simulations of the 4 µmol/m2 surface concentration systems have also been repeated using the OPLS potential model38 for the cations. All the above potential models describe the electrostatic and nonelectrostatic parts of the interaction between the particles
Hantal et al. TABLE 1: Interaction Parameters of the Potential Models Used particle
σ/Å
atom
water (SPC)a
H O CH3 CH2 CH2 c O Od S Li+ Na+ K+ Rb+ Cs+ Li+ Na+ K+ Rb+ Cs+
DeS- ionb
cations (OPLS potential) e
cations (Åqvist potential) f
3.166 3.909 3.905 3.905 3.150 3.000 3.550 2.126 3.330 4.935 5.622 6.716 1.458 1.825 2.221 2.371 2.592
/kJ·mol-1
q/e
0.650 0.733 0.494 0.494 0.837 0.712 1.047 0.0765 0.0116 0.00137 0.000715 0.000339 0.283 0.110 0.0379 0.0273 0.0188
0.41 -0.82 0.000 0.000 0.137 -0.654 -0.459 1.284 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
a Reference 36. b Reference 14. c Last CH2 group of the decyl chain, attached to the sulfate group. d O atom attached to the decyl chain. e Reference 38. f Reference 37.
by the Coulombic potential acting between fractional point charges and the Lennard-Jones potential, respectively. Thus, the total energy of the interaction between two particles is calculated as N1
U)
N2
∑ ∑ i)1 j)1
qiqj rij
[( ) ( ) ]
+ 4ij
σij rij
12
-
σij rij
6
(1)
where N1 and N2 are the number of interacting sites on the two molecules, q is the fractional charge located at the corresponding site, ij and σij are the parameters of the Lennard-Jones interaction between the ith site of the first and jth site of the second molecule (related to the Lennard-Jones parameters characteristic of the individual sites through the LorentzBerthelot combination rule10), and rij is the distance between these two sites. The interaction parameters (i.e., q, σ and ) of the potential models used are summarized in Table 1. The total potential energy of the system has been calculated as the sum of the intramolecular energy terms and the potential energy of all particle pairs. In preparing the starting configuration of the simulations, 3000 water molecules have been placed in a basic simulation box with a size of 108.18 Å × 28.815 Å × 28.815 Å, corresponding to the density of bulk liquid water. This system has been equilibrated for 400 ps. Then, the required number of cations has been randomly inserted into the system, two interfaces have been created by increasing the length of the X edge of the basic box by 100 Å, and finally the anions have randomly been placed, in equal number, to these two interfaces. The simulations have been performed using the GROMACS molecular dynamics program package.39,40 The temperature of the system has been kept constant at 298 K by the Berendsen algorithm.41 The coupling parameter of the thermostat has been set to 0.1 ps. Bond lengths have been kept fixed in the simulations using the SETTLE42 and LINCS43 algorithms for the water molecules and DeS- ions, respectively. Periodic boundary conditions have been applied in all directions. All interactions have been truncated to zero beyond the cutoff distance of 9.0 Å. The long-range part of the electrostatic interactions has been accounted for using the particle mesh Ewald method.44 The equilibration and production phases of the simulations have been 1 and 2 ns long, respectively, using
Adsorption Layer of Ionic Surfactants
J. Phys. Chem. B, Vol. 111, No. 7, 2007 1771
Figure 1. Instantaneous equilibrium snapshot of the 2 µmol/m2 surface concentration NaDeS system simulated. Water O atoms, DeS- O, S, and C atoms and Na+ ions are shown in gray, red, yellow, green, and purple colors, respectively. For better visualization, the Na+ ions are shown enlarged, whereas the H atoms are omitted from the picture.
an integration time step of 2 fs. To confirm that this run length is sufficient to equilibrate the systems well, we have evaluated the density profiles of the water O and DeS- S atoms as well as the cations along the interface normal axis in the first and second 1 ns part of the production phase of the different runs. No systematic change of the data has been observed in any case. In the production stage, 1000 sample configurations, separated by 2 ps long runs each, have been saved for analysis of each of the systems simulated. Finally, all saved configurations have been translated along the X axis of the basic box in such a way that the center-of-mass of the 3000 water molecules has been placed to the middle of the box (i.e., X ) 0 Å), to avoid artificial broadening of the interface due to its translation along the X axis in the simulations. An equilibrium snapshot of the 2 µmol/m2 surface concentration NaDeS system is shown in Figure 1. Results and Discussion The number density profiles of the water molecules (represented by the position of their O atoms), the negatively charged sulfate group of the DeS- ions (represented by the position of their S atom), and cations are shown in Figure 2 as obtained in the five 4 mol/m2 surface concentration systems using the Åqvist cation potentials. All the profiles shown are symmetrical over the two interfaces present in the basic simulation box. The effect of the cation potential and anion surface concentration on these profiles is demonstrated in Figure 3, showing the water, sulfate, and cation density profiles as obtained in the three systems containing Na+ cations. It is evident that the results obtained with the two different cation potentials agree very well with each other, whereas the surface density of the surfactant has a considerable effect on the arrangement of the particles along the interface normal axis. As is seen from Figure 2, the obtained water density profiles are independent of the type of cations present in the system; the observed differences are in the order of the statistical noise of the calculated functions (see the inset of the figure). On the other hand, the drop of the water density from the bulk-phase value to zero becomes sharper with decreasing surface concentration of the surfactant (see Figure 3). To emphasize this effect, the water density profile obtained at the liquid/vapor interface of pure water45 is also indicated in the figure. This finding can be explained by the fact that, due to the excluded volume of the cations and negatively charged ionic groups at the interfacial region, the volume accessible by the water molecules that are hydrating these ions is considerably smaller than that in the bulk liquid phase.
Figure 2. Number density profiles of the water O atoms (top panel), DeS- S atoms (middle panel), and counterions (bottom panel) as obtained in the 4 µmol/m2 surface concentration systems using the Åqvist cation potential. The profiles obtained in the systems containing Li+, Na+, K+, Rb+, and Cs+ ions are shown by full, dashed, dotted, dash-dotted, and dash-dot-dotted lines, respectively. All the profiles shown are symmetrized over the two interfaces present in the basic simulation box. The insets show the highest density part of the profiles on an enlarged scale.
When the ion density profiles obtained in the 4 µmol/m2 surface concentration systems are analyzed, it is seen that the adsorption peak of the sulfate ionic group is located at about an X value of 55 Å, where the water density is about 65% of its bulk liquid-phase value. This result clearly indicates that, contrary to the saturated adsorption layer of non-ionic ethyleneoxide surfactants,24 the hydrophilic head group of the DeS- ions is indeed fully hydrated (i.e., surrounded by water molecules) rather than just being attached to the water surface. The peak of the cation density profiles is located at the X value at which the water density is about 70% of its bulk liquid-phase value. It is also clear from Figures 2 and 3 that the density peaks of the two ions considerably overlap each other: the cation density peak is located at the position where the anion density is about
1772 J. Phys. Chem. B, Vol. 111, No. 7, 2007
Hantal et al.
Figure 4. Illustration of the procedure of calculating the outer Helmholtz plate thickness δ in the simulation, on the example of the 2 µmol/m2 surface concentration CsDeS system.
Figure 3. Number density profiles of the water O atoms (top panel), DeS- S atoms (middle panel), and Na+ ions (bottom panel) as obtained in the 4 µmol/m2 surface concentration NaDeS system using the OPLS (dashed lines) and Åqvist (full circles) cation potentials and in the 2 µmol/m2 surface concentration NaDeS system (solid lines). For comparison, the water density profile obtained at the liquid/vapor interface of pure water45 is also shown (open circles). All the profiles shown are symmetrized over the two interfaces present in the basic simulation box. The inset shows the pair correlation function of the sulfate S and water O atoms in the 2 µmol/m2 and 4 µmol/m2 surface concentration NaDeS systems, simulated with the Åqvist cation potential.
95% of its maximum value, whereas at the position of the anion density peak, the cation density is still 85-90% of the density at its maximum. This finding clearly contradicts the naive picture that is behind the simplifying assumptions on which the Gou¨yChapman and related theories are based when applied to a vapor/ solution interface. The main effect of the decrease of the surface concentration on the distribution of the ions along the interface normal axis is that the density peaks of the unlike ions move farther apart from each other: the density peak of the sulfate ionic groups moves closer to the water surface whereas that of the counterions becomes closer to the bulk liquid phase of water. Thus, in the 2 µmol/m2 surface concentration systems simulated, the sulfate ion density peak appears at about X ) 59 Å, whereas the water density is just about 15% of the bulk-phase value. To demonstrate that this water density is still enough to fully hydrate the sulfate ionic groups, we have calculated the pair correlation function of the sulfate S and water O atoms both in the 2 µmol/m2 and in the 4 µmol/m2 surface concentration NaDeS systems simulated with the Åqvist cation potential (see the inset of Figure 3). The integration of these functions up to the first minimum at 4.8 Å reveals that the first coordination shell of the S atoms contains about 10 water molecules in both of these systems. Nevertheless, it is clear that in the higher surface concentration systems the amphiphilic anions penetrate considerably deeper into the aqueous phase than those in the case of the 2 µmol/m2 surface concentration systems. This observed surface concentration dependence of the preferred location of the cations and anions along the surface normal axis, a feature that is not predicted by any of the adsorption theories, can be
explained by the increasing electrostatic attraction between the two, oppositely charged, ionic layers. Thus, the increasing surface density leads to an increase in the net positive charge that the negatively charged anionic layer experiences from the liquid side of the interface, which brings them more into the aqueous phase. On the other hand, the increasing electrostatic attraction of the adsorbed layer of anions pulls the more mobile cations closer to the interface. This increasing electrostatic attraction between the two ionic layers leads to the observed considerable decrease in the distance of the two layers of oppositely charged ions, an effect that is neglected in the existing adsorption theories, although could be essential in understanding the anomalous shape of the adsorption isotherms of the anionic surfactants.8 The absolute position of the cation and anion density peaks along the X axis shows slight dependence on the cation type, as demonstrated in the insets of Figure 2. However, besides real physical reasons, such a variation may also reflect several other, sometimes rather arbitrary, differences between the different systems (e.g., excluded volume of the cations, molecular scale roughness of the interface, etc.). Therefore, the dependence of the relatiVe position of the cationic and anionic density peaks on the cation type is of much more physical relevance. Furthermore, the thickness of the outer Helmholtz plate, a key quantity in various adsorption theories, can also be characterized in the simulations by the distance δ of the cation and anion density peaks along the interface normal axis X. To calculate the value of δ in the various systems simulated, we have fitted a Gaussian function to the top part of these density peaks (i.e., to the points corresponding to densities higher than half of the peak density) and defined the thickness of the outer Helmholtz plate δ as the distance of the center of the Gaussians fitted to the cation and anion density peaks. This procedure is illustrated in Figure 4 with the example of the 2 mol/m2 surface concentration CsDeS system using the Åqvist cation potential. The obtained δ values are shown as a function of the LennardJones parameter of the cations (i.e., the parameter that characterizes their size) in Figure 5. The error bar of the values is estimated to be about 0.05 Å. The clear tendency of the outer Helmholtz plate thickness to increase with increasing cation size is evident in every case, at least for small ionic diameters. For the larger ions (i.e., K+, Rb+ and Cs+), the difference of the obtained δ values falls in the range of the error bars, and hence, no definite conclusions can be drawn about the σ dependence
Adsorption Layer of Ionic Surfactants
J. Phys. Chem. B, Vol. 111, No. 7, 2007 1773 clearly reflects the effect of the simplifications inherent in the potential models used in the simulations. We assume that the major factor in this respect is that due to the lack of the explicit treatment of the polarizability of the cations and water molecules the hydrating water molecules are not bound strongly enough to the hydrated cations, and hence the cations can, at least partly, loose their hydration shell at the vicinity of the interface. This problem could be overcome by using polarizable potential models for water and the cations, which would, however, make the simulations computationally far more demanding. Work in this direction is currently in progress. Acknowledgment. This work has been supported by the Hungarian OTKA Foundation under Project Nos. T049673 and T.0443621, by the European Comission under the sixth Framework Program under Contract No. MRTN-CT-2004-512331Project SOCON, and by COST under Project No. D36/0007/ 06. P.J. is a Be´ke´sy Gyo¨rgy fellow of the Hungarian Ministry of Education, which is gratefully acknowledged. References and Notes
Figure 5. Dependence of the outer Helmholtz plate thickness δ on the cation size, represented by its Lennard-Jones size parameter σ in the 4 µmol/m2 surface concentration systems using the OPLS (top panel) and Åqvist (middle panel) cation potentials and in the 2 µmol/m2 surface concentration systems (bottom panel).
of δ for these large cations. It should be noted, however, that this result can still be in full accordance with the experimental findings, showing that the adsorption isotherms of KDeS, RbDeS, and CsDeS agree with each other within the error bars of the experiments, but they are considerably different from that of both LiDeS and NaDeS.8 It is also evident that in the case of lower surface concentration the outer Helmholtz plate becomes considerably thicker than in the higher surface concentration systems, as discussed above. However, this dependence of δ on the surface concentration does not affect its dependence on the cation size. This finding clearly stresses the importance of also accounting for cation size in the adsorption theories, as suggested in an earlier paper.8 Such an improvement in the adsorption theory is not only physically sensible and important, but also mandatory to create a theory that can describe the cation specificity of the measured surface tension data well.8 Finally, it should be noted that our results, although they clearly demonstrate the increasing trend of the outer Helmholtz plate thickness with increasing cation size, are in contrast with the experimental data in the respect that here the relevant parameter characterizing the cation size is the diameter of the bare ion without its hydration shell, whereas in the experimental situation the size of the hydrated cation matters.8 This deviation
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