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A Dynamical Model of Molecular Monolayers: Why Tethers Don’t Snap?

A Dynamical Model of Molecular Monolayers: Why Tethers Don’t Snap?. Lu Zou, * Violeta Beleva, * Andrew J. Bernoff, # James C. Alexander, + J. Adin Mann Jr. ! Elizabeth K. Mann * *Dept. of Physics, Kent State University # Dept. of Mathematics, Harvey Mudd College

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A Dynamical Model of Molecular Monolayers: Why Tethers Don’t Snap?

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  1. A Dynamical Model of Molecular Monolayers:Why Tethers Don’t Snap? Lu Zou,* Violeta Beleva,* Andrew J. Bernoff,# James C. Alexander,+ J. Adin Mann Jr.! Elizabeth K. Mann* *Dept. of Physics, Kent State University # Dept. of Mathematics, Harvey Mudd College + Dept of Mathematics, Case Western Reserve University ! Dept of Chemical Engineering, Case Western Reserve University

  2. Relaxation of 8CB on Water/Air Interface Why Don’t Tethers Snap?

  3. OVERVIEW • Introduction on Rayleigh instability (3D) and Hele-Shaw flow (2D) • A dynamic model of molecular monolayers (2D) • Simulation and experimental results • Conclusion and prospects

  4. Rayleigh Instability [1878] • Pure, cylindrical 3D fluid • Varicose mode fluctuations • Decrease area/surface energy • Break into droplets

  5. Hele-Shaw Cell constrains Height of gap

  6. Evolution of a long, narrow bubble Ref: Glasner, Karl A diffuse interface approach to Hele-Shaw flow NONLINEARITY 16 (1): 49-66 JAN 2003

  7. A dynamic model of molecular monolayers Z Ω Z = 0 Subphase fluid Fundamental Hydrodynamic Equations • Stokes Equation • Continuity Equation

  8. Assumptions on the subphase fluid • Horizontal flow • Boundary condition • Bulk viscosity ηbulk[Ref] Ref: Elizabeth K. Mann Hydrodynamics of Domain Relaxation in a Polymer Monolayer PRE 51 (6): 5708-5720 JUN 1995

  9. Assumptions on the surface gas Ω • 2D Fluid (η and KG) • One component [Ref1]: • Elasticity KG[Ref1]: • Surface pressure Π • Surface Viscosities [Ref2]: • Electrostatic forces liquid Ref1: H. A. Stone; H. M. McConnell; Proc. R. Soc. Lond. A448: 97-111 1995 Ref2: Elizabeth K. Mann; PRE 51 (6): 5708-5720 JUN 1995

  10. Result on Small Distortion Limit For 2D (n=2) L w Ref: H. A. Stone; H. M. McConnell Hydrodynamics of quantized shape transitions of lipid domainsProc. R. Soc. Lond. A448: 97-111 1995

  11. Lubrication Theory H(x, t) X Ref: L. Zhornitskaya; A. L. Bertozzi Positivity-preserving numerical schemes for lubrication-type equationsSIAM J. NUMER. ANAL.37(2): 523-555 2000

  12. Simulation result Initial state:

  13. Discussion on the Simulation • Periodic Boundary condition • No ends What constrains should be applied at the ends of the tether?

  14. Hole Closing Poly(dimethyl)siloxane (PDMS) monolayer on water/air interface

  15. Conclusion • A simplified model with assumptions close to the real experimental conditions Prospect • Line tension determination • Entire range of the relaxation behavior

  16. Acknowledgement • Dr. Elizabeth K. Mann (Kent State University) • Dr. Andrew J. Bernoff (Harvey Mudd College) • Dr. James C. Alexander (Case Western Reserve University) • Dr. J. Adin Mann Jr. (Case Western Reserve University) • Ms. Violeta Beleva (Kent State University) • Ms. Ji Wang (Kent State University) • Supported by National Science Foundation under Grant No. 9984304

  17. Frequent Questions • Brewster Angle Microscope (set-up) • Green Function  Hele Shaw • F(n=2)=5PI/16 (Stone); F(n=2)=5PI/12 • Hole closing, linearly

  18. CCD L1 L2 Ei P A B Water Surface Brewster Angle Microscope (set-up)

  19. Hole Closing Linearly

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