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Hole Dynamics in Polymer Langmuir Films

Hole Dynamics in Polymer Langmuir Films. Lu Zou + , James C. Alexander * , Andrew J. Bernoff & , J. Adin Mann, Jr. # , Elizabeth K. Mann +. + Department of Physics, Kent State University * Department of Mathematics, Case Western Reserve University

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Hole Dynamics in Polymer Langmuir Films

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  1. Hole Dynamics in Polymer Langmuir Films Lu Zou+, James C. Alexander*, Andrew J. Bernoff&, J. Adin Mann, Jr.#, Elizabeth K. Mann+ + Department of Physics, Kent State University * Department of Mathematics, Case Western Reserve University & Department of Mathematics, Harvey Mudd College # Department of Chemical Engineering, Case Western Reserve University Partially under NSF Grant No. 9984304

  2. Why hole-closing is interesting? • Phase coexistence • Biological system, e.g. cell membrane

  3. A gas-phase hole in a 2D polymer liquid

  4. Fundamental Dynamics Equations • Stokes Equation • Continuity Equation

  5. Assumptions on the surface • 2D liquid phase + very dilute 2D gas • surface viscosity  0 • Liquid phase: • High elasticity (incompressible) • Gas phase: • Null compressibility  Elasticity = 0 • Circular hole I I ? I

  6. Assumptions on the subfluid • Incompressible • Bulk viscosity η’ • Velocity

  7. Derivation Result –closing rate ? [Ref]: J. C. Alexander, A. J. Bernoff, E. K. Mann, J. A. Mann Jr., L. Zou, “Hole Dynamics in Polymer Langmuir Films”, Physics Of Fluid, to be published.

  8. Derivation Result –Vertical Motion Vertical Cross section of flow lines in the subfluid

  9. Experimental setup Brewster Angle Microscope PDMS = Poly(dimethylsiloxane) Mw=31600 N=427

  10. Hole-closing images • Monolayer thickness ~ 0.7 nm • Surface vibration • Hole Moving around • Surface concentration 0.35 mg/m2 • Monolayer coverage ~ 70% • Monolayer  dark • gaseous hole  bright 0.27mm X 0.44mm

  11. Experimental result (linear) [Ref] [Ref]: E. K. Mann, et al., Phys. Rev. E 51, 5708 (1995)

  12. Conclusion • Develop a model for the closing of a gaseous hole in a liquid domain within a 2D fluid layer, coupled to a fluid bulk substrate • Experimental result supports the prediction on the hole-closing rate • Suggest an independent means of determining the line tension • Predict the vertical motion of the underlying incompressible fluid

  13. Complete Experiment Result

  14. Future work • Improvement on the current experiment • How to make a better hole? • How to obtain better images? • Observation on the vertical motion of the subfluid

  15. Tether Relaxation

  16. Thank you!

  17. outline • Why interesting (BG and other’s work) • Theory part – model, assumptions, equations and prediction • Experiment part – setup, difficulties, data, result and explanation • Conclusion and future work • Acknowledgement

  18. Acknowledgement • Dr. Elizabeth K. Mann • Dr. James C. Alexander • Dr. Andrew J. Bernoff • Dr. J. Adin Mann, Jr.

  19. hole monolayer ẑ 2 r substrate ρ n θ

  20. hole monolayer ẑ r substrate

  21. 4) 5) 8) 44) 45)

  22. 9)

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