A dynamical model of molecular monolayers why tethers don t snap
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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

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


Relaxation of 8CB on Water/Air Interface

Why Don’t Tethers Snap?


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


Rayleigh Instability [1878]

  • Pure, cylindrical 3D fluid

  • Varicose mode fluctuations

  • Decrease area/surface energy

  • Break into droplets


Hele shaw cell
Hele-Shaw Cell

constrains

Height of gap


Evolution of a long, narrow bubble

Ref: Glasner, Karl

A diffuse interface approach to Hele-Shaw flow NONLINEARITY 16 (1): 49-66 JAN 2003


A dynamic model of molecular monolayers
A dynamic model of molecular monolayers

Z

Ω

Z = 0

Subphase fluid

Fundamental Hydrodynamic Equations

  • Stokes Equation

  • Continuity Equation


Assumptions on the subphase fluid
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


Assumptions on the surface
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


Result on small distortion limit for 2d
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


Lubrication theory
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


Simulation result
Simulation result

Initial state:


Discussion on the simulation
Discussion on the Simulation

  • Periodic Boundary condition

  • No ends

What constrains should be applied at the ends of the tether?


Hole closing
Hole Closing

Poly(dimethyl)siloxane (PDMS) monolayer on water/air interface


Conclusion
Conclusion

  • A simplified model with assumptions close to the real experimental conditions

Prospect

  • Line tension determination

  • Entire range of the relaxation behavior


Acknowledgement
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


Frequent questions
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


Brewster angle microscope set up

CCD

L1

L2

Ei

P

A

B

Water Surface

Brewster Angle Microscope (set-up)



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