1. INTRODUCTION:

Structure and dynamics of organized surfactant assemblies at different interfaces and in bulk solutions is of great importance in various industrial processes, such as detergency, oil recovery, purification, food processing, paints, lubrication and so forth¹. A number of workshas been reported to understand the properties of surfactant aggregates in solutions ^2-4, but at interfaces, proper systematic studies of adsorbed films are still lacking. This is mainly due to the general lack of suitable experimental techniques.

A large number of experimental studies have been reported on the properties of different surfactant layers adsorbed at vapour/liquid, liquid/liquid, and liquid/solid interfaces^5-8. Only recently the relatively new technique of neutron reflection has been successfully employed by Thomas and co-workers^9-12 to study the properties of various surfactant layers, including C_mE_n type of surfactants adsorbed at air/liquid, liquid/liquid, and liquid/solid interfaces.

The time scales associated with the adsorption of surfactants leading to the formation of a monolayer at the air/water interface or the exchange of monomers between the monolayer and those in the bulk solution are in the range of micro to milliseconds and therefore are beyond the scope of current generation atomistic molecular dynamics (MD) simulations. However, it is possible to study the microscopic properties of surfactant monolayer already adsorbed at an interface within a reasonable time. This approach has been employed in several simulation studies^13-17.

In this work, the dynamics of surfactant monolayers of monododecyl diethylene glycol, C₁₂E₂ , adsorbed at the air/water interface at a surface coverage corresponding to its cmc (34 Å²/molecule) have been studied using MD simulation techniques. The setup of the simulation system and a brief description of the methodologies employed, discussed in the next section. The results obtained from the investigations are presented and discussed in the following section.

System setup and Simulation Details:

There are several choices that need to be made when setting up the system and specifying the boundary conditions in simulations of monolayers of surfactant/water systems. One possibility is to simulate a single monolayer in contact with the aqueous solution and confine the solution by placing a hard wall below the interface^18. But this requires large bath of water molecules for a given number of surfactants to avoid artifacts due to the long-ranged structuring of water by the wall¹⁹. Another possibility is to simulate two monolayers on opposite sides of a slab of an aqueous solution with the thickness of the slab chosen sufficiently large that the monolayers are effectively isolated (i.e., there is a region of bulk solution between the monolayers). Given these considerations, we have opted to use the two monolayers on a slab arrangement and use three-dimensional periodic boundary conditions and an Ewald summation with a large value for the dimension of the simulation cell in the direction normal to the interface (z). The initial configuration of the constant temperature and volume (NVT) simulation system was set up by arranging a uniform monolayer of 64 surfactants with the hydroxyl group on an appropriate 8×8 square lattice in the xy plane with the hydrocarbon chains extending perpendicular to the lattice plane in all trans configuration. The lattice constants were chosen to give the surface area per molecule of 34 Å², corresponding to the experimentally observed value for adsorption at the air/water interface at the cmc. Then two such Langmuir type monolayers were placed, with their headgroups solvated, in the xy plane of a roughly 30 Å thick slab of water molecules. A 30 Å thick layer of water should be large enough to give a distinct region of bulk solution in the middle of the simulation cell. The overall system contained 128 surfactants and 2127 water molecules. The dimension of the simulation box in the x and y direction was 46 Å, while the z dimension was kept large at 100 Å. This is done to minimize the interactions between the periodic replicas in the z direction.

The simulations utilized the Nosé-Hoover chain thermostat extended system method ²⁰as implemented in the PINY-MD computational package²¹. A recently developed reversible multiple time step algorithm²⁰ allowed us to employ a 4-fs MD time step. This was achieved using a three-stage force decomposition into intramolecular forces (torsion/bend-bond), short-range intermolecular forces (a 7.0 Å RESPA cutoff distance), and longe-range intermolecular forces. Electrostatic interactions were calculated by using the particle mesh Ewald method ²². The minimum image convention²³ was employed to calculate the Lennard-Jones interactions and the real-space part of the Ewald sum using a spherical truncation of 7 and 10 Å respectively. The intermolecular potential model was based on pair wise additive site-site electrostatic and Lennard-Jones contributions. The rigid three-site SPC/E model²⁴ was employed for water. The CH₃ and CH₂ groups of the surfactants were treated as united atoms. The potential parameters for the alkane chain groups were taken from the work of Martin and Siepmann²⁵ while the oxy ethylene groups were modeled using the OPLS parameters^26-27. The surfactant chains were made flexible by including bond stretching, bending, and torsion interactions.

RESULTS AND DISCUSSION:

The dynamics of surfactant near the interface play a crucial role in determining the behavior of surfactant aggregates. In this work the detail of surfactant orientations and dynamics is studied.

Surfactant orientation:

To characterize the overall orientation of the surfactants at the interface, we have calculated separately the orientation of the head and the hydrocarbon tail vectors with respect to the normal (z) to the plane of the interface. The vector connecting the OH group oxygen atom (O1) and the second oxy ethylene group oxygen atom (O3) is defined as the head vector, while the vector connecting the first methylene group (CH₂) and the terminal methyl group (CH₃) is defined as the tail vector. Figure 1 displays the probability distribution, ƞ(θ), of the angle θ (tilt angle) between the head or the tail vector with respect to the normal to the plane of the interface or the z axis. These distributions are averaged over both the monolayers. The figure shows that both the head and the tail parts of the surfactant chains are significantly tilted away from the normal to the interfacial plane (z). It is clear that the headgroups are more tilted toward the plane of the interface compare to the tails. The average tilt angles for the head and the tail vectors have been found to be 48.4^o and 38.5^o respectively. The average value for the hydrocarbon tail is comparable to the experimental value of 44^o ¹⁰. There is a large population of the head vector orientation in the range 60^o< θ<90^o, that is, flat with respect to the interface. Howerver, the most striking feature of this distribution is the significant probability of the head vectors with θ>90^o. This means, that some of the head vectors are reoriented toward the interior of the aqueous layer. This arises because of strong interaction between the headgroup atoms and water and the preference of the head groups to form hydrogen-bonded bridged structures with the water molecules. This is an important observation which may influence the overall physical properties of C₁₂E₂ surfactant aggregates.

Figure 1: The distribution of the tilt angle, θ (in degree) of the oxy ethylene headgroup (solid line) and the hydrocarbon tail (dashed line) with respect to the normal to the interface, z.

Surfactant Dynamics:

We have investigated the dynamics of the surfactants by measuring the mean square displacements (MSD), (∆r²), of the center of mass of the surfactant chains from the MD trajectory. The MSD is defined as

(1)

Where,

r_i(t) and r_i(0) are the center of mass coordinates of the i-th surfactant chain at time t and at time t = 0 respectively, and averaging is over both time origins and the surfactant molecules. To examine any anisotropic dynamical behavior in their translational mobility, we have separately measured the center of mass MSDs in the plane of the interface (i.e., in xy plane) and in the direction normal to it (i.e., along z direction), which are displayed in Figure 2. It is clear from the figure that the surfactant chains are more mobile in the plane of the interface than in the direction perpendicular to it. Higher in-plane mobility arises from the lateral rattling motion of the surfactant molecules, which dominates the time scale over which the calculation is carried out. The out-of-plane protrusion of the surfactants is more restricted. Such restricted dynamics of the surfactant molecules is a signature of anomalous sub linear diffusion in a heterogeneous anisotropic or confined system. To investigate the extent of such anomalous diffusion, the curves in Figure 2 are fitted to a law

(2)

Where the exponent α is expected to be smaller than one. The estimated values of α have been found to be 0.64 and 0.41 for the in-plane and out-of-plane motions, respectively. Such small α values clearly show the presence of significant anomaly in the diffusion behavior of surfactant molecules within the time scale of our simulation.

Figure 2: Time evolution of the in-plane (i.e., in xy plane) and the out-of-plane (i.e., along z) mean square displacements of the center of mass of the surfactant molecules.

To investigate the rotational motion of the surfactant molecules, we have measured the reorientational dynamics of the head and the tail vectors of the individual monomers. The reorientational motion has been studied by measuring the time correlation function (TCF), C_b(t), defined as

(3)

Where b_i (t) represents the unit vector corresponding to the head or the tail of the i-th surfactant molecule at time t, and the angular brackets denote averaging over the surfactant molecules and over initial times t. The variation of C_b (t) against time has been displayed in Figure 3. It is clearly evident from the figure that the headgroups of the surfactant molecules reorient faster

than the hydrocarbon tails. The faster reorientational dynamics of the oxy ethylene head vectors may arise due to their relatively shorter lengths as compared to the dodecyl tail vectors. As a result, despite their strong interaction with the interfacial water molecules, the oxy ethylene head groups exhibit relatively faster reorientational motions.

Figure 3: Reorientational time correlation function, C_b (t), for the oxyethylene head vectors and the hydrocarbon tail vectors of the surfactant molecules.

CONCLUSION:

In this article, we have presented results obtained from an atomistic MD simulation of the monolayers of nonionic surfactant C₁₂E₂adsorbed at the air/water interface. The simulation has been performed at a surface coverage of 34 Å²/molecule, which corresponds to the surface coverage at the cmc. It is found that there is a significant fraction of the surfactants with their headgroups reoriented within the aqueous layer close to the interface. This occurs due to strong interaction between polar oxyethylene head groups of the surfactants and the interfacial water molecules. It is also observed from our study that the surfactant chains are more mobile in the plane of the interface than in the direction perpendicular to it along with a faster reorientational dynamics of the oxy ethylene headgroups. This may arise due to their relatively shorter lengths as compared to the dodecyl tail vectors.

ACKNOWLEDGEMENT:

The author wish to thank Prof. Sanjoy Bandyopadhyay, Department of Chemistry, IIT- Kharagpur, for valuable support and advice for preparation of the manuscript. The author also thanks Dr Sudip Chakraborty, Assistant Prof, and Centre for Computational Science, Central University of Punjab, for valuable discussion.

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Received on 30.06.2017 Modified on 09.07.2017

Asian J. Research Chem. 2017; 10(5): 635-638.

DOI: 10.5958/0974-4150.2017.00107.9