City College of CUNY, New York, NY 10031

1. A molecular dynamics study of superspreading An ongoing doctoral research project by Jonathan D. Halverson1 With the faculty advisement of J. Koplik2,3, A. Couzis1, C. Maldarelli1,3 Department of Chemical Engineering1, Department of Physics2 The Benjamin Levich Institute for Physico-chemical Hydrodynamics3 City College of CUNY, New York, NY 10031 AIChE Annual Fall Meeting San Francisco Hilton Hotel, San Francisco, CA 14 November 2006

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  of a sessile drop to the interfacial tensions: where SVis the solid-vapor tension, is the liquid-vapor tension, and SLis the solid-liquid tension.

3. Trisiloxane surfactants Trisiloxane surfactants are known as superspreaders. They have been shown to increase the wetted area of a sessile drop by a factor of 25 in comparison to conventional organic surfactants. The trisiloxanes are the only class of surfactant to give the complete wetting of water on highly hydrophobic hydrocarbon substrates. TSE4

4. 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. C12E4 C12E4 is capable of reducing the water contact angle to 40º on highly hydrophobic surfaces.

5. Surfactants in action Superwetting solution: >60 wt.% methyl (propylhydroxide, ethoylated) bis(trimethylsiloxy) silane, 15 - 40 wt.% polyethylene oxide monoallyl ether, <= 9 wt.% polyethylene glycol with 20:1 water Alkyl polyethoxylate/alcohol solution: C12E8 at 7 times the CMC and C12E0 at 21 times the solubility limit

6. Superspreading A consistent theory of superspreading has been emerging since it was first studied during the 1960’s. • Lowering of LV and SL • Molecular structure of the trisiloxane tailgroup • Rapid adsorption kinetics • Marangoni effect • Phase behavior and bilayer aggregates • Humidity

7. SPC/E water potential The interaction potential 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. cH. J. C. Berendsen, J. R. Grigera, T. P. Straatsma, J. Phys. Chem., 91, 6269 (1987).

8. Wetting of graphite by water A cluster of water molecules spontaneously takes on the shape of a sphere in free space (Step 1). The equilibrated drop of 2197 SPC/E water molecules at 298 K is placed in the vicinity of two graphene sheets (Step 2): The contact angle of the sessile drop is seen to fluctuate. A soft potential maintains a vapor pressure.

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

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

11. Water-TSE4 simulation The united atom approximation reduces the number of interaction sites: United atom approximation Bond lengths are kept rigid while valence and dihedral angles vary according to potential functions.

12. Nanodrop of water-TSE4 Cross-sectional view of the drop at initialization. The complete drop consists of 9997 water molecules and 475 surfactant molecules.

13. Nanodrop of water-TSE4 Consider adding TSE4 surfactant molecules to a spherical drop of liquid water with a radius of 4.0 nm: molecules on surface = surface area / maximum packing molecules on surface = 4R2 / (53.4 Å2 / molecule) molecules on surface = 377 molecules TSE4 molecules in bulk = CMC  volume molecules in bulk = (0.11 mole / m3)  4/3R3 molecules in bulk = 0.02 molecules TSE4 At 10  CMC there is less than 1 molecule in the bulk.

14. Water-TSE4 simulation (Nwater = 9997, NS = 475, R = 4.0 nm, t = 0.8 ns, icfg = 200 MD steps / frame, frame rate = 30 fps)

15. Water-C12E4 simulation (Nwater = 9997, NS = 475, R = 4.0 nm, t = 0.8 ns, icfg = 200 MD steps / frame, frame rate = 30 fps)

16. The drop is assumed to maintain the shape of a spherical cap throughout the simulation. The horizontal line indicates the initial radius of the droplet.

18. The area per molecule at the solid-liquid interface is seen to increase with time.

22. Why didn’t the drop spread? NS = 475 The high surface concentration of the TSE4 molecules prevented spreading from occurring.

23. Surfactant molecules are removed NS = 300 The surface is made less crowded by removing 175 of the 475 surfactant molecules.

26. TSE4 in the bulk of the drop NS = 350 Surfactant in the bulk of the drop can adsorb at the interfaces to maintain low tensions during spreading.

27. TSE4 in the bulk of the drop (Nwater = 9997, NS = 350, R = 4.0 nm, t = 2.0 ns, icfg = 250 MD steps / frame, frame rate = 30 fps)

29. Conclusions Overloading the surface with TSE4 molecules prevented spreading. The final wetted area of the C12E4 drops were found to be proportional to the surfactant concentration. Future work will focus of bulk systems and the wetting of larger droplets on surfaces with less hydrophobicity.

30. Acknowledgements San Diego Supercomputer Center and the National Energy Research Scientific Computing Center Funding • NOAA-CREST (2006) • National Science Foundation IGERT Graduate Research Fellowship in Multiscale Phenomena of Soft Materials (2003-2005) • National Science Foundation IGERT Graduate Research Fellowship in Nanostructured Materials and Devices (2002)

31. J. Board et al. Long-range interactions The fast multipole algorithm (FMA) of 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). The basic idea is a particle interacts with the local multipole expansion of its box instead of the individual particles in distant boxes. Interactions are computed directly between particles in neighboring boxes. The mutual electrostatic forces between 200,000 particles can be calculated to within 1% relative error using the FMA in 330.0 s versus 6722.8 s for the direct method (over four time integration steps).

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

34. Water/TSE4 simulation The united atom approximation reduces the number of interaction sites: United atom approximation Intramolecular interactions:

35. Motivation In the application of paint, ink, a herbicide solution, or a generic 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.

37. Humidity at the molecular scale For saturated water at room temperature the number of molecules in the simulation cell should be: molecules in vapor = volume of box / specific volume H20 molecules in vapor = (100 Å)3 / (43400.0 m3 / gm) molecules in vapor = 0.77 molecules H20 According to the Kelvin equation: P / Psat = exp(2M / RsRT) P / Psat = 2.94