A Computer Simulation Study - American Chemical Society

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Lateral Dynamics of Surfactants at the Free Water Surface: A Computer Simulation Study Nóra A. Rideg,† Mária Darvas,†,‡ Imre Varga,†,* and Pál Jedlovszky†,§,∥,* †

Laboratory of Interfaces and Nanosize Systems, Institute of Chemistry, Eötvös Loránd University, Pázmány P. Stny 1/A, H-1117 Budapest, Hungary ‡ Institut UTINAM (CNRS UMR 6213), Université de Franche-Comté, 16 route de Gray, F-25030 Besançon Cedex, France § MTA-BME Research Group of Technical Analytical Chemistry, Szt. Gellért tér 4, H-1111 Budapest, Hungary ∥ EKF Department of Chemistry, Leányka U. 6, H-3300 Eger, Hungary ABSTRACT: Molecular dynamics simulations of the adsorption layer of five different surfactant molecules, i.e., pentyl alcohol, octyl alcohol, dodecyl alcohol, sodium dodecyl sulfate, and dodecyl trimethyl ammonium chloride are performed at the free surface of their aqueous solution at two surface densities, namely 1 and 4 μmol/m2 at 298 K. The results are analyzed in terms of the two-dimensional single molecule dynamics, in particlular, lateral diffusion of the surfactants at the liquid surface, in order to distinguish between two possible adsorption scenarios, namely the assumptions of localized and mobile surfactants. The obtained results, in accordance with the dynamical nature of the liquid phase and liquid surface, clearly support the latter scenario, as the time scale of lateral diffusion of the surfactant molecules is found to be comparable with that of the three-dimensional diffusion of water in the bulk liquid phase. The mechanism of this lateral diffusion is also investigated in detail by calculating binding energy distribution of the water molecules in the first hydration shell of the surfactant headgroups and that of the nonfirst shell surface waters, and by calculating the mean residence time of the water molecules in the first hydration shell of the surfactant headgroups. This time is found to be at least an order of magnitude smaller than the characteristic time of the lateral diffusion of the surfactants, revealing that surfactant molecules move without their first shell hydration water neighbors at the surface.

1. INTRODUCTION The interfacial properties of surfactant solutions have a major impact on the efficiency of various industrial formulations. This explains the widespread interest in surfactant adsorption studies and the large number of experimental and theoretical investigations in the field.1−10 The experimental adsorption isotherms are usually interpreted in terms of adsorption models (surface equations of state), which are always based on a priori model assumptions.11 One of the main assumptions used in the interpretation of the experimental surfactant adsorption data is the choice if the adsorption layer is considered localized or mobile.11 In the former case, a lattice model is used to describe the adsorption layer and it is assumed that the surfactant molecules adsorb on N0 fixed adsorption sites. Typical examples of the localized adsorption layer models are the Langmuir and Frumkin adsorption isotherms − both of which were originally developed to describe adsorption at solid surfaces. Contrary to the localized approach, in mobile adsorption layer models the adsorbate is viewed as a twodimensional gas that can move freely in the adsorption layer. A corresponding equation of state has been proposed by Volmer.11−13 As can be expected, mobile adsorption layers have considerably larger entropy than localized adsorption layers at a given surface coverage, which results in steeper adsorption isotherms at low surface coverage but flatter © 2012 American Chemical Society

isotherms and lower adsorbed amounts at high surface coverage.11 Despite the fact that at fluid interfaces (e.g., at the air/ solution interface) localized adsorption sites cannot be identified, the localized adsorption layer models are widely and successfully used to describe surfactant adsorption.14−30 A possible explanation for the surprising success of these models may be related to the restricted horizontal mobility of the surfactant molecules due to the entanglement of the surfactant alkyl chains in the adsorption layer, in particular, at high enough surface coverage values. However, an experimental test of this assumed behavior is extremely difficult due to the lack of surface sensitive methods that can selectively probe the dynamics of single molecules located right at the surface of their phase. Another possible way of studying this problem is the use of computer simulation methods. In a computer simulation, a detailed, three-dimensional insight of atomistic resolution is gained in the structure and dynamics of an appropriately chosen model of the system of interest. Obviously, this model has to be validated by comparing simulated properties to Received: July 25, 2012 Revised: September 26, 2012 Published: September 27, 2012 14944

dx.doi.org/10.1021/la302998k | Langmuir 2012, 28, 14944−14953

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Figure 1. Schematic structure of the five surfactant molecules considered in this study. simulation box has contained 1598 water and 12 (at 1 μmol/m2) or 48 (at 4 μmol/m2) surfactant molecules; equal number of surfactants being placed at the two liquid surfaces present in the basic box. In the case of ionic surfactants, the corresponding number of Na+ or Cl− ions have also been added to the liquid phase. The lengths of the X, Y, and Z edges of the basic box have been 250.0, 31.41, and 31.41 Å, respectively, X being the axis perpendicular to the macroscopic plane of the liquid surface. Standard periodic boundary conditions have been used in all three dimensions. The total energy of the system has been calculated as the sum of intra- and intermolecular contributions. The intramolecular energy term included contributions from bond angle bending and torsional rotations of the surfactants, while all bond lengths have been kept fixed in the simulations. The energy corresponding to dihedral rotations has been calculated using the Ryckaert−Bellmans potential function.31 The intermolecular energy term has been calculated as the sum of the Coulomb and Lennard−Jones contributions of all atom pairs, apart from those being in 1−2 or 1−3 position, or being beyond the interaction cutoff distance. CH2 and CH3 groups have been treated as united atoms. All intermolecular interactions have been truncated to zero beyond the group-based cutoff distance of 15.0 Å; the long-range part of the electrostatic interaction has been accounted for using the Particle Mesh Ewald method.32 Intra- and intermolecular interactions of the surfactants and counterions have been described by the GROMOS force field,33,34 using the charge distribution proposed by Schweighofer and Benjamin35 for the headgroup of the dodecyl trimethyl ammonium (DTA) ion. Water molecules have been modeled by the rigid three-site SPC potential.36 The interaction parameters used to calculate the intermolecular energy contribution are summarized in Table 1. The simulations have been performed by the GROMACS 3.3.2 program package.37 The equations of motion have been integrated in time steps of 1 fs. The temperature of the systems has been controlled using the weak coupling algorithm of Berendsen et al.38 The geometry of the water molecules and bond lengths of the surfactants have been kept unchanged by means of the SETTLE39 and LINCS40 algorithms, respectively. Starting configurations of the 4 μmol/m2 systems have been generated in the following way. First, the adsorption layer has been created separately from a crystal-like layer consisting of 24 molecules placed equidistantly. After energy minimization this layer

experimental data. Therefore, molecular dynamics simulation seems to be a very powerful tool in studying the problem of lateral dynamics of surfactant molecules. In the present paper, we report molecular dynamics simulations of the adsorption layer of five different surfactants at the free water surface. To eliminate the arbitrariness of the chosen surfactant molecule, and to systematically study the effect of both the headgroup and the alkyl chain length on the dynamics of the adsorption layer, we have chosen three dodecyl derivative surfactants, namely the anionic sodium dodecyl sulfate (SDS), the cationic dodecyl trimethyl ammonium chloride (DTAC), and the nonionic dodecyl alcohol (DA) molecules, and three alcohols of different chain lengths, i.e., besides DA, octyl alcohol (OA), and pentyl alcohol (PA). The schematic structure of these surfactants is shown in Figure 1. To clearly distinguish between the scenarios consistent with the Langmuir and Volmer description, we calculate the lateral diffusion coefficient of these surfactants at two different surface densities, i.e., at low surface coverage and close to the saturation of the monolayer. To shed light to the energetic background of the lateral dynamics of the adsorbed surfactant molecules, we also analyze their binding energy at the surface in detail. The paper is organized as follows. In sec. 2 details of the simulations performed are given. The obtained results are presented and discussed in detail in sec. 3. Finally, the main conclusions of this study are summarized in sec. 4.

2. COMPUTATIONAL DETAILS Molecular dynamics simulations of the adsorption layer of five different surfactants, i.e., SDS, DTAC, DA, OA, and PA at the free water surface have been performed on the canonical (N, V, T) ensemble at the temperature of 298 K. To study also the effect of the surfactant surface density on the calculated properties two surface densities, namely Γ = 1 μmol/m2 and Γ = 4 μmol/m2 have been considered for all surfactants. The first of these surface densities corresponds to a rather loosely packed, while the second one to an almost fully saturated adsorption layer of the surfactants. The basic 14945


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Table 1. Interaction Parameters of the Models Used interaction site

σ (Å)

ε (kJ mol−1)

q (e)

CH3(−CH2) CH3(−N) CH2 O (alcohols) −O− (SDS) =O (SDS) O (water) S N H (alcohols) H (water) Na+ Cl−

3.90 3.96 3.90 2.96 3.00 3.17 3.17 2.42 3.80

0.733 0.607 0.495 0.847 0.717 0.785 0.650 1.045 0.209

2.58 4.45

0.062 0.446

0.000 0.250 0.000a −0.690 −0.459 −0.654 −0.820 1.284 0.000 0.400 0.410 1.000 −1.000

a

The CH2 groups chemically bound to the alcoholic O, sulfate O, and N atoms carry the fractional charges of 0.290, 0.137, and 0.250, respectively. has been placed to the close vicinity of both liquid−vapor interfaces of the pre-equilibrated water system in the basic box, consisting of 1598 water molecules. For ionic surfactants, to retain electroneutrality, an equal number of counterions (Na+ for dodecyl sulfate, and Cl− for DTA) have been inserted randomly into the bulk liquid phase. After energy minimization, these systems have been pre-equilibrated for a period of up to 1 ns with progressively increasing integration time steps, in order to avoid numerical overflow in the simulation. Finally, starting configurations of the 1 μmol/m2 systems have been created by randomly removing 18−18 surfactants from the two adsorption layers of the corresponding 4 μmol/m2 systems. All systems have been equilibrated for 5 ns. Then, in the 5 ns long production stage of the simulations, 1000 sample configurations per system, separated by 5 ps long trajectories each have been dumped for further evaluation. Equilibrium snapshots of the systems containing SDS or PA are shown in Figure 2 as taken out from the simulations with both surface densities considered.

Figure 2. Instantaneous equilibrium snapshots (side view) of the surface region of the aqueous phase, containing PA (top panels) and SDS (bottom panels) molecules adsorbed at the surface at the surface densities of 1 μmol/m2 (left panels) and 4 μmol/m2. Water molecules are shown by blue sticks; the O, C, and S atoms of the surfactants are indicated by red, black and yellow color, respectively. H atoms are omitted from the snapshots for clarity.

3. RESULTS AND DISCUSSION 3.1. Density Profiles. The mass density profiles of the systems, calculated along the surface normal axis X are shown in Figure 3, whereas the number density profiles of the water O atoms, chain terminal CH3 groups and all of the C atoms of the surfactants as well as that of the central atom of their headgroup (i.e., O for the alcohols, N for DTAC and S for SDS) are plotted in Figure 4 as obtained in the 10 systems simulated. As is seen, the surfactant molecules are indeed located at the boundary of the two phases, no surfactant molecule entered into the bulk aqueous phase in any case, with the exception of PA, which dissolved in the aqueous phase in a detectable but still negligible concentration. The polar headgroups are always inwardly oriented; the increasing separation of the density peaks of the headgroup central atom and chain terminal CH3 group with increasing surface density (i.e., from 3 to 3.8 Å for PA, from 4 to 6.9 Å for OA, from 5 to 10.1 Å for DA, from 7.3 to 11.9 Å for DTAC and from 6.2 to 11.1 Å for SDS when increasing the surface density from 1 to 4 μmol/m2) indicates that upon saturation of the surface the preferential alignment of the surfactant molecules turns out to be considerably more tilted relative to the surface plane. This change of the orientational preference of the surfactants from slightly to strongly tilted alignment with increasing saturation is also seen from the change of the mass density profiles of the alcohol containing systems (lower panel of Figure 3). Namely, at the surface density of 4 μmol/m2, the low density hydrocarbon

Figure 3. Mass density profiles of the ten systems simulated along the surface normal axis X. Top panel: profiles in systems containing ionic surfactant; bottom panel: profiles in systems containing nonionic surfactant. All of the profiles shown are symmetrized over the two liquid surfaces present in the basic simulation box.

region of the surfactant tails gets progressively broader with increasing tail length, while no such marked effect is seen at 1 μmol/m2, when the surfactant molecules are preferentially lying nearly parallel with the surface. To confirm that surfactant molecules prefer increasingly tilted orientations relative to the surface plane with increasing saturation, we have calculated the mean angle formed by the surface plane and the vector 14946


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Figure 4. Number density profiles of the water O atoms (black solid lines), headgroup central atoms (blue dash-dot-dotted lines), chain terminal CH3 groups (red dash-dotted lines) and all C atoms of the hydrocarbon chains (green dashed lines) along the surface normal axis X, as calculated in the systems containing PA (top panels), OA (second panels), DA (third panels), DTAC (fourth panels) and SDS (bottom panels) at the surface concentrations of (a) 1 μmol/m2 and (b) 4 μmol/m2. The scales at the left refer to the water O atom and hydrocarbon chain C atom, whereas those at the right to the headgroup central atom and chain terminal CH3 group profiles. All of the profiles shown are symmetrized over the two liquid surfaces present in the basic simulation box.

connecting the two terminal C atoms of the hydrocarbon chain of the surfactants. The results reveal that while this mean angle is always around 30° at the surface density of 1 μmol/m2, it becomes 45−50° when the surface density is increased to 4 μmol/m2 in every case. 3.2. Lateral Diffusion of the Surfactant Molecules. In order to have a quick insight into the time scale of the lateral diffusion of the surfactant molecules we have followed the trajectory of arbitrarily chosen surfactant molecules in the surface plane YZ of the systems during the course of the 5 ns long production runs. Examples for such trajectories are shown in Figure 5 both for an ionic (SDS) and for a nonionic surfactant (DA) at both surface densities considered. Trajectories corresponding to the four consecutive 1.25 ns long blocks of the production run are marked by different colors. Similar pictures were obtained in the other systems simulated, as well. As is clearly seen, the surfactant molecules can easily diffuse throughout the entire surface portion of the basic simulation box in the order of nanoseconds in every case. In other words, the surfactant molecules can freely move along the surface of the aqueous phase on the time and length scales of the simulation. To quantify the lateral diffusion of the surfactant molecules, we have calculated their lateral diffusion coefficient Dlat in the YZ plane of the basic box using the Einstein relation:41 2tD lat =

1 MSD 2

(1)

Figure 5. Trajectory of an appropriately chosen DA (left panels) and SDS (right panels) molecule in the surface plane YZ of the aqueous phase as obtained in the 5 ns long production stage of the simulation of systems of 1 μmol/m2 (top panels) and 4 μmol/m2 (bottom panels) surface densities. The trajectories are based on the position of the headgroup O (for DA) and S (for SDS) atom. The trajectories corresponding to the four consecutive 1.25 ns long blocks of the production phase are marked by black, red, green, and blue colors, respectively.

(2)

Here, ri(t0) and ri(t0+t) are the position vectors of the particle i in the YZ plane at the times t0 and t0 + t, respectively, and the brackets ⟨...⟩ denote ensemble averaging. Dlat can thus be

where MSD = ⟨|ri(t0 + t ) − ri(t0)|2 ⟩

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determined from the slope of the straight line fitted to the MSD(t) data as Dlat = MSD/4t. The MSD(t) data obtained from the simulations together with the straight lines fitted to them are shown in Figure 6, while the Dlat values obtained are

on the diffusion coefficient values in respect the question to be addressed in the present paper. As is seen, the diffusion of the ionic surfactants is slower by about a factor of 2 than that of the alcoholic ones, and the saturation of the surface (i.e., the increase of the surface density from 1 to 4 μmol/m2) slows down this diffusion by 25−45%. As a general trend, it is also seen that the lateral diffusion of the surfactants is somewhat slowed down by the increase of the hydrocarbon tail length, and this effect is clearly more pronounced at high surface density, i.e., when the preferred alignment of the surfactant molecules is strongly tilted relative to the surface plane. It should also be pointed out that the obtained Dlat values are comparable, being even somewhat larger than the (three-dimensional) diffusion coefficient of the water molecules, calculated to be 0.29 Å2/ps, in accordance with the experimental value of 0.23 Å2/ps.42 Finally, to characterize the time scale of the lateral diffusion of the surfactant, we have calculated the characteristic time τdiff within which the surfactant molecules can fully explore the area equivalent with the surface portion they occupy, i.e., the average surface area per headgroup, Ahg. More precisely, assuming that lateral diffusion can be described as a random walk, τdiff is the time after which the positions visited by a surfactant molecule follow a Gaussian distribution with the width √Ahg. The value of τdiff can be calculated as follows:

Figure 6. Mean square lateral displacement of the PA (squares), OA (circles), DA (triangles), DTAC (stars), and SDS (pentagons) molecules in the surface plane of the aqueous phase, YZ, as obtained in the systems of 1 μmol/m2 (top panel) and 4 μmol/m2 (bottom panel) surface densities. The straight lines fitted to the simulated data are shown by dashed lines.

τdiff =

PA OA DA DTAC SDS

surface density (μmol/ m2)

Dlat (Å2ps−1)

τdiff (ps)

τ0 (ps)

1 4 1 4 1 4 1 4 1 4

0.837 0.653 0.741 0.566 0.704 0.492 0.313 0.174 0.429 0.253

49.11 15.74 55.48 18.16 58.39 20.89 131.3 59.06 95.82 40.62

0.85 1.20 0.88 1.21 0.89 1.24 1.29 (8.20)a 1.47 (7.79)a 1.15 (12.13)a 1.50 (8.80)a

4D lat

(3)

2YZ Nsurf

(4)

where

Ahg =

Nsurf being the total number of surfactant molecules in the system. (The factor of 2 in eq 4 accounts for the presence of two liquid surfaces in the basic box.) The τdiff values obtained are also included in Table 2. As is seen, this characteristic time is in the order of a few tens of picoseconds, being somewhat larger for ionic surfactants (as they diffuse slower), and at smaller surface density (i.e., when the area per headgroup is larger). Further, these values are comparable, being only one order of magnitude larger than the characteristic time of the (three-dimensional) diffusion of the water molecules, i.e., within which they can explore the volume equivalent with their molecular volume Vmol of 29.94 Å3, estimated to be 5.5 ps using the relation Vmol = ((6Dτdiff)3)1/2. 3.3. Mechanism of the Lateral Diffusion. The finding that the lateral diffusion of the surfactants is comparable with the three-dimensional diffusion of the water molecules raises the question of what is the mechanism of this diffusion, i.e., whether the surfactants diffuse together with the first hydration shell of their headgroup, or their diffusion is independent of even these first shell hydrating water molecules. In the former case, the first shell water molecules should stay next to the headgroup on time scales longer than the characteristic time of the lateral diffusion of the surfactant, and the energy of their interaction with the rest of the aqueous phase (practically, that with their water neighbors) should be considerably weaker than that of the surface water molecules that do not belong to the hydration shell of the headgroup of any surfactant. However, if the diffusion of the surfactant molecules is not coupled to that of their first hydration shell no marked difference in the interaction energy of the first shell and nonfirst shell surface

Table 2. Lateral Diffusion Constant and Characteristic Diffusion Time of the Surfactant Molecules, and Mean Residence Time of the Water Molecules in the First Hydration Shell of their Headgroup as Obtained in the Ten Systems Simulated surfactant

Ahg

a The values before the parentheses are the τ(1) 0 , whereas the values in parentherses are the τ(2) 0 values when the process can be described by the sum of two exponentially decaying functions (see the text).

collected in Table 2. To estimate the error of these values due to the finite size effect, we have repeated the 1 mmol/m2 SDS simulation in a basic box of four time larger cross section. The obtained value of 0.36 Ǻ 2/ps agrees reasonably well with the value of 0.429 Ǻ 2/ps resulting from the original simulation, indicating that finite size effect has a negligibly small influence 14948


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The L(t) survival probabilities are shown in Figure 8 as obtained in the ten systems simulated. In the case of the

water molecules with the rest of the waters is expected, and the mean residence time of a water molecule in the first hydration shell of a surfactant headgroup should be smaller than the characteristic time of the lateral diffusion of the surfactants. To distinguish between these two possible scenarios we have calculated the survival probability L(t) and mean residence time τ0 of the water molecules in the first hydration shell of the surfactant headgroups, and also the interaction energy distribution of the first shell water molecules as well as that of the surface water molecules that do not belong to the first shell of any surfactant both with the other water molecules surf (Uwat b ) and with the surfactants (Ub ). The survival probability L(t) is defined as the probability that a molecule that belongs to the first hydration shell of a surfactant headgroup at the time t0 remains uninterruptedly in this shell up to t + t0, and in the case of exponentially decaying L(t) curve τ0 is simply the mean value of this distribution. In some cases, considerably better fit of the L(t) data can be obtained using the sum of n exponential terms, i.e., Σin = 1Aiexp(−t/τ0(1)). This indicates that there are n differently bound types of hydrating waters and they leave the hydration shell on different time scales. Here τ(i) 0 is the characteristic time corresponding to the ith possible process. In the present analyses, a water molecule is regarded to belong to the first hydration shell of a PA, OA, or DA molecule if the distance of its oxygen from the alcoholic O atom is smaller than 3.4 Å, to that of a DTAC molecule if its oxygen is closer to the N atom than 5.4 Å, and to that of a SDS if its oxygen is closer to the S atom than 4.9 Å. These cutoff values correspond to the first minimum position of the pair correlation function of the respective atom pairs (see Figure 7). Finally, nonfirst shell water molecules that are located at the surface of the aqueous phase are identified by means of the Identification of the Truly Interfacial Molecules (ITIM) method.43

Figure 8. Survival probability of the water molecules in the first hydration shell of the polar or ionic headgroup of the PA (squares), OA (circles), DA (triangles), DTAC (stars), and SDS (pentagons) surfactant molecules, as obtained in the systems of 1 μmol/m2 (top panel) and 4 μmol/m2 (bottom panel) surface densities. For the definition of the first shell water molecules, see the text. The exponentially decaying functions fitted to the simulated data are shown by dashed lines.

nonionic surfactants the L(t) data can always be well fitted by a single exponentially decaying function, while in the case of the two ionic surfactants a considerably better fit is obtained using the sum of two exponential terms. The τ0 (for nonionic surfactants) and τ(1) and τ(2) (for ionic surfactants) mean 0 0 residence time values are included in Table 2. The P(Uwat b ) and P(Usurf b ) distributions of the water and surfactant contributions to the binding energy of the first shell and of the nonfirst shell surface water molecules are plotted in Figures 9 and 10, respectively, whereas the mean values of these distributions are collected in Table 3. All of these results clearly support the second scenario, namely that the diffusion of the surfactant molecules at the liquid surface is not coupled to that of their hydration waters. The mean residence time of the water molecules in the headgroup first hydration shell of the alcohols is below 2 ps in every case, being at least 1 order of magnitude smaller than the characteristic time of the surfactant diffusion. In the case of the two ionic surfactants, the characteristic time of the faster process also falls in this range, whereas that of the slower process is still around 10 ps. This finding clearly indicates that during the time a surfactant molecule explores the surface area equal to the average area per headgroup Ahg, water molecules exchange several times between its first hydration shell and the rest of the system, maintaining thus thermodynamic equilibrium between hydration and nonfirst shell waters even on the time scale characteristic of the surfactant diffusion. The analysis surf of the Uwat b and Ub binding energy distributions (Figures 9 and 10) leads to similar conclusions. As is seen, the mean binding energy of a first shell water to the surfactants is not particularly

Figure 7. Pair correlation function of the water O atoms with alcoholic O atoms (top panel; PA: solid black line, OA: dotted red line, DA: dashed blue line), DTAC N atoms (middle panel) and SDS S atoms (bottom panel) as calculated from the 4 μmol/m2 surface density simulations. The dashed vertical lines mark the position of the first minima, used as cutoff values in defining first hydration shell water molecules (see the text). 14949


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Figure 9. Distribution of the interaction energy of the water molecules belonging to the first hydartion shell of a surfactant headgroup with the wat surfactant molecules (Usurf b , top panels) and with the other water molecules in the system (Ub , bottom panels) in the systems containing PA (open circles), OA (full circles), DA (solid lines), DTAC (dash-dot-dotted lines), and SDS (dashed lines) at surface densities of 1 μmol/m2 (left) and 4 μmol/m2 (right).

Figure 10. Distribution of the interaction energy of the surface water molecules that do not belong to the first hydartion shell of a surfactant wat headgroup with the surfactant molecules (Usurf b , top panels) and with the other water molecules in the system (Ub , bottom panels) in the systems containing PA (open circles), OA (full circles), DA (solid lines), DTAC (dash-dot-dotted lines), and SDS (dashed lines) at surface densities of 1 μmol/m2 (left) and 4 μmol/m2 (right).

the water contribution to the binding energy of a first hydration shell water is not much smaller (in several cases it is even

strong, remaining always below or close to the energy of a single hydrogen bond of about −25 kJ/mol. More importantly, 14950


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Table 3. Mean Interaction Energies of the Water Molecules in the First Shell of a Surfactant Headgroup and of Non-First Shell Surface Water Molecules with the Other Water Molecules and with the Surfactants in the Ten Systems Simulated first hydration shell waters surfactant PA OA DA DTAC SDS

nonfirst shell surface waters

surface density (μmol/m2)

surfactant contribution

water contribution

surfactant contribution

water contribution

1 4 1 4 1 4 1 4 1 4

−25.24 −29.77 −24.56 −28.87 −24.64 −28.95 −16.60 −17.54 −32.75 −36.74

−27.14 −20.96 −24.37 −21.03 −24.21 −21.11 −20.70 −13.69 −23.47 −13.54

−0.96 −2.83 −0.70 −2.95 −0.70 −3.00 −1.72 −5.50 −4.21 −13.69

−23.34 −26.08 −23.36 −25.80 −23.36 −25.84 −17.93 −15.90 −17.29 −9.10

adsorbate assumption, such as the Langmuir or the Frumkin formalism were originally developed for describing adsorption at solid surfaces, where this assumption is far more natural than at the surface of a liquid phase. However, the dynamic nature of the liquid phase and liquid surface on the molecular scale is consistent with the assumption of mobile adsorbates, which is now confirmed by our computer simulation results. Our present results have also clearly shown that the lateral diffusion of the surfactant molecules is not coupled to that of the water molecules in the first hydration shell of their headgroupsin other words, surfactants diffuse without their hydration waters. Thus, the distribution of the interaction energy of the first hydration shell and nonfirst shell surface water molecules with the other water molecules in the system turned out to be rather similar to each other. More importantly, the mean residence time of the water molecules in the first hydration shell of the headgroups resulted in more than 1 order of magnitude smaller than the characteristic time of the lateral diffusion of the surfactants in every case. Thus, the results of the present study led us to the conclusion that surfactants are not only easily diffusing at the surface of their aqueous solution, but this diffusion is not coupled to any kind of particularly strongly bound shell of hydrating waters either. Finally, it should be noted that our present result concerning the residence time of water molecules in the hydration shell of the surfactant headgroup is seemingly in contradiction with the earlier results of Bagchi et al.,46,47 who detected a very slow component, having a characteristic time of several hundreds of picoseconds, of the water exchange dynamics between the surfactant headgroup hydration shell and the bulk phase. No such slow component has been seen in this study in any case. In explaining this marked difference, the different chemical structure of the surfactant molecules considered cannot be excluded (Bagchi et al. used cesium pentadecafluorooctanoate46,47). Hovewer, it seems to be a far more important factor that Bagchi et al. studied micellar aggregates of the surfactants inside the bulk liquid phase, while here we considered the adsorption layer of surfactants at the free water surface. This difference is evidently expected to result in a markedly different mobility of the surfactants themselves (as being bound in a micelle they are not supposed to move as fast as we found at the water surface). Interestingly, this difference seems to also be reflected in the dynamics of the hydrating water, as some of these water molecules might find very strongly bound positions among more than one surfactants. However, to go beyond simple speculation, this point needs to be investigated in further studies.

larger) than that of the nonfirst shell surface water molecules; this difference never exceeds 5 kJ/mol. Thus, there is no particularly strong attraction between the surfactant headgroups and their first shell water molecules, and the vicinity of a polar or ionic headgroup does not considerably weaken the interaction of the nearby waters with the rest of the aqueous phase, indicating that there is no thermodynamic driving force for the hydration water being stuck to the surfactant headgroups. All of these results confirm that the observed rather fast lateral diffusion of the surfactant molecules at the surface of the aqueous phase is not coupled to the diffusion of their hydration water molecules; instead, they diffuse at the water surface as independent entities.

4. CONCLUSIONS In this study, we investigated the lateral dynamics of surfactant molecules at the free surface of their aqueous solution in order to distinguish between two possible scenarios of their adsorption, i.e., the assumptions of localized and mobile adsorption layers. These assumptions are consistent with, among others, the Langmuir and the Volmer descriptions of the adsorption, respectively, and correspond to somewhat different adsorption isotherms, among which, however, it is rather difficult to distinguish by experimental methods. The simulations reported here, however, made a clear distinction between these two possible assumptions, supporting unequivocally the mobile adsorbate scenario. Thus, although the alkyl chain length, the type of the headgroup and the surface density of the surfactants all turned out to influence the lateral dynamics of the surfactant molecules in certain ways, the most important features of the lateral dynamics were found to be, at least qualitatively, independent from these factors. Thus, the time scale of the lateral diffusion of the surfactant molecules at the liquid surface proved to be comparable with that of the three-dimensional diffusion of the water molecules in the bulk liquid phase. Clearly, the surfactant molecules are found to explore the surface portion equivalent with the average surface area per headgroup within 0.1 ns in every case, which clearly invalidates the assumption that they are localized at certain positions at the liquid surface. It should also be emphasized that although the united atom model used in this study results in a somewhat larger mobility of the adsorbed surfactants than allatom models, this difference is far too small to influence this conclusion.44,45 In interpreting this result, it should be emphasized that, in spite of their success in describing surfactant adsorption at fluid interfaces, the adsorption models based on the localized 14951


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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (I.V.); [email protected] (P.J.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This project is supported by the Hungarian OTKA Foundation under Project No. 75328. The authors are gratefully acknowledge fruitful discussions with Dr. Marcello Sega (University of Rome “Tor Vergata”) concerning the characteristic time of diffusion.

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REFERENCES

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