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

'06 CSSS2 Why hole-closing is interesting? Phase coexistence Phase coexistence Biological system, e.g. cell membrane Biological system, e.g. cell membrane

'06 CSSS3 A gas-phase hole in a 2D polymer liquid

'06 CSSS4 Fundamental Dynamics Equations Stokes Equation Stokes Equation Continuity Equation Continuity Equation

'06 CSSS5 Assumptions on the surface 2D liquid phase + very dilute 2D gas 2D liquid phase + very dilute 2D gas –surface viscosity  0 Liquid phase: Liquid phase: –High elasticity (incompressible) Gas phase: Gas phase: –Null compressibility  Elasticity = 0 –Circular hole I I I

'06 CSSS6 Assumptions on the subfluid IncompressibleIncompressible Bulk viscosity η’Bulk viscosity η’ Velocity Velocity

'06 CSSS7 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.

'06 CSSS8 Vertical Cross section of flow lines in the subfluid Derivation Result – Vertical Motion

'06 CSSS9 Experimental setup Brewster Angle Microscope PDMS = Poly(dimethylsiloxane) M w =31600N=427

'06 CSSS mm X 0.44mm Hole-closing images Monolayer thickness ~ 0.7 nm Monolayer thickness ~ 0.7 nm Surface vibration Surface vibration Hole Moving around Hole Moving around Surface concentration 0.35 mg/m 2 Surface concentration 0.35 mg/m 2 Monolayer coverage ~ 70% Monolayer coverage ~ 70% Monolayer  dark Monolayer  dark gaseous hole  bright gaseous hole  bright

'06 CSSS11 Experimental result (linear) [Ref] [Ref]: E. K. Mann, et al., Phys. Rev. E 51, 5708 (1995)

'06 CSSS12 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 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 Experimental result supports the prediction on the hole-closing rate Suggest an independent means of determining the line tension Suggest an independent means of determining the line tension Predict the vertical motion of the underlying incompressible fluid Predict the vertical motion of the underlying incompressible fluid

'06 CSSS13 Complete Experiment Result

'06 CSSS14 Future work Improvement on the current experiment Improvement on the current experiment –How to make a better hole? –How to obtain better images? Observation on the vertical motion of the subfluid Observation on the vertical motion of the subfluid

'06 CSSS15 Tether Relaxation

'06 CSSS16

'06 CSSS17 outline Why interesting (BG and other ’ s work) Why interesting (BG and other ’ s work) Theory part – model, assumptions, equations and prediction Theory part – model, assumptions, equations and prediction Experiment part – setup, difficulties, data, result and explanation Experiment part – setup, difficulties, data, result and explanation Conclusion and future work Conclusion and future work Acknowledgement Acknowledgement

'06 CSSS18 Acknowledgement Dr. Elizabeth K. Mann Dr. Elizabeth K. Mann Dr. James C. Alexander Dr. James C. Alexander Dr. Andrew J. Bernoff Dr. Andrew J. Bernoff Dr. J. Adin Mann, Jr. Dr. J. Adin Mann, Jr.

'06 CSSS19 n holemonolayer 2 r substrate ẑ ρ θ

'06 CSSS20

'06 CSSS21 holemonolayer r substrate ẑ

'06 CSSS22 4) 5) 8) 44) 45)

'06 CSSS23 9)