Hole Dynamics in Polymer Langmuir Films

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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
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Why hole-closing is interesting?

• Phase coexistence
• Biological system, e.g. cell membrane

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A gas-phase hole in a 2D polymer liquid
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Fundamental Dynamics Equations

• Stokes Equation
• Continuity Equation

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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
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Assumptions on the subfluid

• Incompressible
• Bulk viscosity ?
• Velocity

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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.
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Derivation Result Vertical Motion

• Vertical Cross section of flow lines in the
  subfluid

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Experimental setup
Brewster Angle Microscope
PDMS Poly(dimethylsiloxane) Mw31600 N427
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Hole-closing images
0.27mm X 0.44mm

• Monolayer thickness 0.7 nm
• Surface vibration
• Hole Moving around
• Surface concentration 0.35 mg/m2
• Monolayer coverage 70
• Monolayer ? dark
• gaseous hole ? bright

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

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Complete Experiment Result
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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

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Tether Relaxation
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Thank you!
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outline

• Why interesting (BG and others work)
• Theory part model, assumptions, equations and
  prediction
• Experiment part setup, difficulties, data,
  result and explanation
• Conclusion and future work
• Acknowledgement

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Acknowledgement

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

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monolayer
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2 r
substrate
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n
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hole
monolayer
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substrate
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