The City College and The Graduate Center of

1. Wetting of hydrophobic substrates by aqueous surfactant solutions: A classical molecular dynamics study An ongoing doctoral research project 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 American Institute of Chemical Engineers Austin Convention Center, Austin, TX November 11, 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. • Use the new information to suggest forms of new surfactants or mixtures.

6. Outline • Surfactants • Molecular simulation of wetting systems: • Wetting of graphite by water • Wetting of graphite by water-alcohol solutions • Wetting of graphite by water-poly(oxyethylene) surfactant solutions • Simulation challenges

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. Molecular dynamics simulation Intermolecular or nonbonded interactions (U2) are computed by summing over all pairs of interaction sites. Intramolecular interactions (U3 and U4) arise from valence and dihedral angle potentials. A finite system is simulated. A soft repulsive potential is used to prevent the drop from evaporating.

10. SPC/E water model Mass and electron distributions are modeled as point masses and point charges. Bond lengths and the valence angle are kept fixed using RATTLE. Parameters: rOH = 1.0 Å, θ = 109.47º, qO = -0.8476 e, qH = 0.4238 e, σOO = 3.166 Å, and eOO = 650.2 J/mole.

11. SPC/E water potential The potential energy of interaction between a pair of SPC/Ec water molecules is There is one Lennard-Jones interaction and nine Coulomb interactions between each pair of water molecules. The cutoff distance is taken as rc = 13 Å. cH. J. C. Berendsen, J. R. Grigera, T. P. Straatsma, J. Phys. Chem., 91, 6269 (1987).

12. SPC/E water versus experiment This simple interaction potential reproduces many properties of ambient liquid water.

13. Water-graphite interaction Water interacts with atoms in the lattice through a Lennard-Jones interaction with eCO = 392.0 J/mole and sCO = 3.19 Å. Workersa have determined the parameters to reproduce the equilibrium contact angle of 86. Lattice atoms are kept fixed in position. The experimental interlayer distance of 3.41 Å is used. aT. Werder, J. H. Walther, R. L. Jaffe, T. Halicioglu, P. Koumoutsakos, J. Phys. Chem. B, 107, 1345 (2003).

14. Wetting of graphite by water A cluster of water molecules spontaneously takes on the shape of a sphere in vacuum. The equilibrated drop of 2197 SPC/E water molecules at 298 K is placed in the vicinity of two graphene sheets: The contact angle of the sessile drop is seen to fluctuate. A soft potential maintains a vapor pressure.

15. Vertical distribution of water The solid substrate induces structure on the fluid in the vicinity of the substrate. Water is first found 2.5 Å away from the graphite lattice.

16. Contact angle measurement The liquid-vapor interface occurs where the density falls to half the bulk value of the liquid. The contact angle is found to be 82.6.

17. Water on graphite Several contact angle measurements have been made for water on graphite. 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).

18. polyoxyethylene/alcohol model Head groups are modeled using the OPLS force field. Partial electrical charges are assigned to the atoms of the surfactant/alcohol head group. The united atom approximation is applied to each CH2 and CH3 group. The TraPPE force field is used. Valence angle potential: Combining rules: Dihedral angle potential:

19. Water-C3E0 simulation Nwater = 4096, Nsurfactant = 240 (top view) (bottom view)

20. C3E0 = 240, H2O = 4096 (top view)

21. C3E0 = 240, H2O = 4096 (bottom view)

22. C3E0 = 240, H2O = 4096 (side view)

23. Water-C3E0 simulation At 20 Å away from the surface, water is found to exist in bulk. Few propanol molecules are found in bulk.

24. Water-C3E0 simulation Nwater = 4096, Nsurfactant = 480 (top view) (bottom view)

25. Previous: CH3(CH2)2OH Current: CH3(CH2)3OH Water-C4E0 simulation Nwater = 4096, Nsurfactant = 240 (top view) (bottom view)

26. Previous: CH3(CH2)3OH Current: CH3(CH2)4OH Water-C5E0 simulation Nwater = 4096, Nsurfactant = 240 (top view) (bottom view)

27. Previous: CH3CH2CH2(CH2)2OH Current: CH3CH2O(CH2)2OH Water-C2E1 simulation Nwater = 4096, Nsurfactant = 240 (top view) (bottom view)

28. Water-C6E0 simulation Nwater = 4096, Nsurfactant = 121 (top view) (bottom view) 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.

29. Water-C6E0 simulation At 20 Å away from the surface, water is found to exist in bulk. Few hexanol molecules are found in bulk.

30. C6E0 = 240, H2O = 4096 (top view)

31. C6E0 = 240, H2O = 4096 (bottom view)

32. C6E0 = 240, H2O = 4096 (side view)

33. Water-C3E1 simulation The radial density profile was determined for a system of water and C3E1 in vacuum by averaging for 200 ps.

34. Previous: CH3(CH2)2CH2(CH2)2OH Current: CH3(CH2)2O(CH2)2OH Water-C3E1 simulation Nwater = 4096, Nsurfactant = 121 (top view) (bottom view)

35. C3E1 = 121, H2O = 4096 (top view)

36. C3E1 = 121, H2O = 4096 (bottom view)

37. C3E1 = 121, H2O = 4096 (side view)

38. Water-C3E1 At 20 Å away from the surface, water is found to exist in bulk. Few surfactant molecules are found in bulk.

39. Surfactant distributions Two distinct peaks are seen in the vertical distribution of surfactant molecules. Alcohols have a higher first peak.

40. Water distributions Surfactant changes the vertical distribution of water molecules.

41. Combined wetting results A plot of the center-of-mass vertical coordinate versus time reveals that negligible to no increased wetting is observed.

42. Simulation challenges The radius of curvature of the sessile drop must be much greater than the thickness of the liquid-vapor and solid-liquid interfaces. Cases (d), (c), and maybe (b) are sufficiently large for the surfactants considered in this work.

43. Simulation challenges The number of water molecules consisting of a sessile drop may be related to the contact angle q and radius of curvature R: The number of surfactant molecules consisting of a sessile drop may be related to the various concentrations and radius of curvature R:

44. Conclusions Simulations of aqueous surfactant droplets on graphite gave the physically correct molecular behavior. Low-molecular weight alcohols and polyethoxylate surfactants are found at the contact line and vapor-liquid interface. As the length of the hydrocarbon chain increases these molecules become directed radially from the center of the drop. The solid-liquid surface concentration is low in all cases. Surfactant molecules are not seen to diffuse from the contact line or bulk to this interface. A significant increase in wetting is not observed in any of the cases considered.

45. Future work The perils of a truncated Coulomb potential have been well-documented. Electrostatic interactions will be computed using the 3-d fast multipole algorithm. An implementation of the 2-d version has been completed. To allow for larger systems the computer code will be parallelized using either the spatial or domain decomposition techniques. A parallel code for water using a truncated potential has been completed.

46. Acknowledgements Funding provided by NSF IGERT Graduate Research Fellowship

47. 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.

48. Surfactant model parameters

49. Surfactant model parameters