1. Wetting simulations of water with surfactant on solid substrates J. D. Halverson 1, J. Koplik 2, A. Couzis 1, C. Maldarelli 1 The City College and The Graduate Center of The City University of New York New York, NY Department of Chemical Engineering 1, Department of Physics 2 The Benjamin Levich Institute of Physico-chemical Hydrodynamics

2. Motivation Many industrial processes rely on surfactants to enhance the spreading of aqueous solutions on hydrophobic surfaces. A greater understanding of the effects of molecular structure and chemical composition of the surfactant on these wetting processes is needed. The mechanism by which wetting occurs in these systems is also of interest. Molecular dynamics simulation is ideally suited for the study of surfactant systems at the molecular scale.

3. Outline Wetting simulation of water on an atomic surface Comparison of results for water on graphite Water-ethanol wetting simulation Water-poly(oxyethylene) glycol wetting simulation Conclusions

4. TIP3P water model The TIP3P model is empirical, pairwise, and rigid. In a shifted-force representation: Each atom is assigned a partial charge: q O = -0.834 e, q H = 0.417 e. The bond angle of  HOH = 104.52  and the O-H bond length of 0.9572 Å are kept fixed using RATTLE. Group-based interactions are computed.

5. Water on Lennard-Jones substrate An equilibrated drop of 1000 TIP3P water molecules at 298 K is placed in the vicinity of an atomic solid. The interaction potential between a TIP3P oxygen atom and a Lennard-Jones atom in the solid is The wettability of the solvent is determined by C OS.

6. Water on Lennard-Jones substrate The microscopic contact angle may be measured once equilibrium has been achieved. Contact angle is found to be 117  for C OS = 1.0. For a value of C OS = 1.1,  = 100 . The contact angle is found by assuming the drop forms an ideal spherical cap.

7. 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 angle a. Good agreement is observed. The left image a features 2000 SPC/E water molecules on graphite while the right image b shows 900 TIP3P water molecules on a graphene sheet. a T. Werder, J. H. Walther, R. L. Jaffe, T. Halicioglu, P. Koumoutsakos, J. Phys. Chem. B, 107, 1345 (2003). b M. Lundgren, N. L. Allen, T. Cosgrove, N. George, Langmuir, 18, 10462 (2002). a

8. Simplified substrate interaction Comparison of real versus half space solids: The solid is assigned the Lennard-Jones parameters of a TraPPE CH 2 united atom (  S = 3.95 Å,  S = 0.382 kJ/mole). The number density is taken as  S = 3  O -3.

9. Simplified substrate interaction The interaction potential between a Lennard-Jones atom and a semi-infinite continuous Lennard-Jones solid (or half space) of density  S is where according to the Lorentz-Berthelot combining rules,

10. Water-ethanol simulation While ethanol is fully soluble in water the alcohol preferentially adsorbs at the liquid-vapor and liquid- solid interfaces (N H 2 0 = 1000, N CH 3 CH 2 OH = 168). The amphiphilic species is found to decease the contact angle by lowering  LV and  SL.

11. Surfactant model Valence angle potential: Dihedral angle potential: The united atom approximation is applied to each CH 2 and CH 3 group. Partial charges are assigned to the nine atoms of the surfactant head group. The polyethoxylate, CH 3 (CH 2 ) 11 (OCH 2 CH 2 ) 2 OH, or C 12 E 2 is sparingly soluble in water.

12. Water-C 12 E 2 simulation The animations below feature 2000 TIP3P water molecules and 36 C 12 E 2 molecules interacting on a continuous Lennard-Jones solid at 298 K. (side view)(bottom view)

13. Water-C 12 E 2 simulation Surfactant molecules are radially distributed around the drop at the contact line. The head group of each surfactant molecule is directed into the drop.

14. Summary Molecular dynamics simulations have been used to investigate the wetting of water containing surfactant on various solid substrates. The water-C 12 E 2 simulation gave physically correct behavior for small molecule numbers. Larger systems must be studied before insight into macroscopic systems can be gained.

15. Acknowledgements NSF IGERT Graduate Research Fellowship Graphics by PyMOL (http://pymol.sourceforge.net/)