The City College and The Graduate Center of

1. Wetting of hydrophobic substrates by aqueous surfactant solutions: A classical molecular dynamics study A doctoral research proposal by Jonathan D. Halverson1 Under the faculty advisement of J. Koplik2, A. Couzis1, C. Maldarelli1 Department of Chemical Engineering1, Department of Physics2 The Benjamin Levich Institute of Physico-chemical Hydrodynamics The City College and The Graduate Center of The City University of New York Second Examination September 16, 2004

2. Wetting phenomena According to hydrodynamic theory, a drop on a flat surface assumes the shape of a spherical cap: The Young equation relates the contact angle θ of a sessile drop to the various interfacial tensions: where γSVis the solid-vapor tension, γis the liquid-vapor tension, and γSLis the solid-liquid tension.

3. Surfactants A molecule formed by the bonding of a hydrophilic group to a lipophilic group is said to be amphiphilic due to its attraction for both water and oil phases. Amphiphilic molecules are driven towards interfaces making them interface- or surface-active agents or surfactants. CH3(CH2)11OSO3Na Surfactant molecules display a rich phase behavior above a critical concentration.

4. Motivation In the application of paint, ink, a herbicide solution, or a coating to a hydrophobic surface it is important for the fluid to completely wet the surface. Surfactants may be used to enhance the wetting of aqueous solutions on hydrophobic substrates.

5. Objectives Elucidate the mechanism by which surfactants enhance the spreading of aqueous solutions on hydrophobic solid substrates. Offer a molecular explanation as to why some surfactant molecules are more effective than others. Identify alternative surfactants that would be expected to enhance wetting.

6. Outline • Surfactants • Molecular simulation of wetting systems: • Wetting of a Lennard-Jones solid by water • Wetting of graphite by water • Wetting of a semi-infinite, continuous Lennard-Jones solid by a water-alcohol solution • Wetting of a semi-infinite, continuous Lennard-Jones solid by a water-surfactant solution • Simulation challenges • Proposed research

7. (Fatty) Alcohol surfactants Alcohols with long alkyl chains are the simplest nonionic surfactant molecules. Linear alcohols have the chemical formula CH3(CH2)nOH. CH3CH2OH CH3(CH2)17OH Alcohols do not exhibit surfactant phase behavior (i.e., they do not form molecular aggregates or micelles).

8. Polyoxyethylene surfactants Polyoxyethylene (POE) compounds are the most important nonionic surfactants in commercial use. POE surfactants with an alkyl ether link have the chemical formula CiEj, where Ci is CH3(CH2)i-1 and Ej is (OCH2CH2)jOH. C12E2 A methyl-capped polymethylene chain serves as the hydrophobic moiety. A hydroxyl-terminated polyoxyethylene chain serves as the hydrophilic moiety.

9. Superspreaders Trisiloxane alkoxylate surfactants have superior wetting properties. They have been shown to increase the wetted area of a sessile drop by 25 times in comparison to conventional organic surfactants. Trisiloxane ethoxylate surfactants consist of oxyethylene groups (-OCH2CH2-) which act as the hydrophile while the nonpolar trisiloxane groups (-SiOSiOSi-) serves as the hydrophobe. Nikolov, A. D., et al.

10. Introduction to molecular simulation Molecular dynamics simulation is the numerical solution of Newton’s equations of motion for a system of interacting molecules in 3-dimensions: Intermolecular interactions (U2) are computed by summing over all pairs of interactions sites. Intramolecular interactions (U3 and U4) arise from valence and dihedral angle potentials.

11. TIP3P water geometry Mass and electron distributions are modeled as point masses and point charges. Bond lengths and the valence angle are kept fixed using RATTLE. Molecular parameters: rOH = 0.9572 Å, θ = 104.52º, qO = -0.834 e, qH = 0.417 e, and σOO = 3.15061 Å.

12. TIP3P water potential The potential energy of interaction between a pair of TIP3P water molecules is There is one Lennard-Jones interaction and nine Coulomb interactions between each pair of water molecules.

13. TIP3P water versus experiment This simple potential function reproduces many properties of ambient liquid water.

14. Water on Lennard-Jones substrate An equilibrated drop of 1000 TIP3P water molecules at 298 K is placed in the vicinity of a solid substrate. Water interacts with substrate atoms through a L-J potential. The microscopic contact angle is found to be 117º. The contact angle is found by assuming the drop forms a spherical cap of uniform density.

15. Water on graphite (validation) Other workers have studied the interaction of water and graphite. Lennard-Jones parameters have been found for the SPC/E water model that reproduce the equilibrium contact anglea. Good agreement is observed. a The left imagea features 2000 SPC/E water molecules on graphite while the right imageb shows 900 TIP3P water molecules on a graphene sheet. aT. Werder, J. H. Walther, R. L. Jaffe, T. Halicioglu, P. Koumoutsakos, J. Phys. Chem. B, 107, 1345 (2003). bM. Lundgren, N. L. Allen, T. Cosgrove, N. George, Langmuir, 18, 10462 (2002).

16. Simplified substrate interaction Comparison of real versus half space solids: The solid is assigned the Lennard-Jones parameters of a TraPPE CH2 united atom (S = 3.95 Å, S = 0.382 kJ/mole). The number density is taken as S = 3 O-3.

17. Simplified substrate interaction The potential energy of interaction between a Lennard-Jones atom and a semi-infinite, continuous Lennard-Jones solid (or half space) of densitySis According to the Lorentz-Berthelot combining rules:

18. Water-ethanol simulation While ethanol is fully soluble in water it preferentially adsorbs at the liquid-vapor and solid-liquid interfaces (NH2O = 1000, NCH3CH2OH = 168). The alcohol is found to decrease the contact angle by lowering γLVand γSL.

19. Surfactant model The polyoxyethylene surfactant C12E2 or CH3(CH2)11(OCH2CH2)2OH is sparingly soluble in water. The united atom approximation is applied to each CH2 and CH3 group. Partial charges are assigned to the nine atoms of the surfactant head group. Valence angle potential: Dihedral angle potential:

20. Water-C12E2 simulation The animations below feature 2000 TIP3P water molecules and 36 C12E2 molecules interacting on a continuous Lennard-Jones solid at 298 K. (side view) (bottom view)

21. Water-C12E2 simulation Surfactant molecules are distributed around the contact line with their backbones orientated in the radial direction. Only head groups are found inside of the drop. (bird’s eye view) (solvent removed)

22. Simulation challenges The figures on the preceding slide reveal two challenges that must be overcome: • The size of the drop is too small. Surfactant molecules consist of 10% of the drop. • The use of a truncated Coulomb potential may introduce artifacts.

23. Overview of proposed research These shortcomings can be overcome by the following: • Simulate large systems where the contact angle is independent of drop size • Compute long-range interactions using the fast multipole algorithm • Use a proper model for the solid substrate • Study various types of surfactants • Compute properties • What can be learned from these simulations?

24. Large-scale simulation The following inequality may be used to guide decisions concerning the drop size: The radius of curvature of the sessile drop must be much greater than the thickness of the liquid-vapor and solid-liquid interfaces. If the above inequality is satisfied then a bulk region will exist in the center of the drop. Also, the contact angle should be independent of molecule numbers in this regime.

25. Large-scale simulation Simulations must be conducted in the regime where the contact angle is independent of drop size. The area per surfactant molecule should be a constant. Cases (d), (c), and maybe (b) are sufficiently large for the surfactants considered in this work.

26. Parallel simulation Large molecular systems must be simulated. A single-processor computer code will take too long to run. By parallelizing the computer code simulations can be completed in reasonable times. Parallel simulations using the spatial and particle decomposition approaches have been completed for water in free space using a shifted-force potential.

27. Long-range interactions It is necessary to compute long-range or Coulomb interactions accurately. The use of a truncated Coulomb potential may give rise to artificial behavior. The amount of computation associated with the direct calculation (i.e., every particle interacts with every other particle) is O(N2). This approach is not feasible for large systems. The fast multipole algorithm (FMA) by Greengard and Rokhlin (1987) may be used to compute long-range interactions towithin round-off error. The computational complexity of the method is O(N).

28. Fast multipole algorithm The basic idea of the method is that a particle interacts with the multipole expansion of a distant group instead of with each individual member of the group. Once the multipole coefficients for each box have been computed, interactions are computed using three translation operators: shifting the center of a multipole expansion, converting a multipole expansion into a local expansion, and shifting the center of a local expansion. A hierarchical decomposition of space is used to determine distant groups. Rigorous error bounds have been analytically derived for the FMA. Board, J. et al.

29. Fast multipole algorithm (3-d) Suppose N charges are located with a sphere of radius a centered about the origin. For any point outside of this sphere, the electrostatic potential is Suppose N charges are located outside of a sphere of radius a centered about the origin. For any point inside this sphere, the electrostatic potential is

30. Substrate models The solid-liquid interaction is as important as the liquid-liquid interaction. An acceptable solid model must be used. Graphite may be a thoughtful choice. Workers have found Lennard-Jones parameters for the water-graphite interaction that reproduce the macroscopic contact angle. This was done for SPC/E water. Lattice atoms have been kept fixed in position. Is lattice atom motion important for the wetting systems considered in this work? Can a model of a hydrophobic solid of industrial importance be found?

31. Surfactant models The computational machinery will soon be in place to simulate a series of homologs (C8E2,C9E2, …, CnE2), ethoxylogs (C12E2, C12E3, …, C12En), and linear alcohol solutions. Work will continue on these surfactant classes. Ionic surfactants such as sodium dodecyl sulphate may also be studied. Numerous models of ionic surfactants have been published. Potential functions for the superspreaders are not currently available.

32. Property calculations Before useful generalizations regarding the role of surfactants on wetting processes can be made, well-defined properties of each system must be examined. Candidate properties include the microscopic contact angle, base radius or wetted area, surfactant concentration field, interfacial thickness, radius of curvature, orientational distribution of surfactant backbones, and many structural properties. Based on the molecular trajectories and property calculations, commentary of the role played by surfactant molecules on wetting processes will be given.

33. Summary Preliminary work on a droplet of water containing surfactant molecules was found to give qualitatively correct behavior. Large-scale molecular dynamics simulations may be used to elucidate the mechanism by which surfactants enhance the wetting of aqueous solutions on hydrophobic solid substrates. The properties of the surfactant molecules responsible for the enhanced wetting may also be gotten from this technique. Long-range interactions must be properly treated. An appropriate model of the solid substrate must be used.

34. Acknowledgements Funding provided by NSF IGERT Graduate Research Fellowship