Hole Dynamics Hole Dynamics in Polymer Langmuir Filmsin Polymer Langmuir Films

Lu ZouLu Zou++, James C. Alexander, James C. Alexander**, Andrew , Andrew J. BernoffJ. Bernoff&&, J. Adin Mann, Jr., J. Adin Mann, Jr.##, Elizabet, Elizabeth K. Mannh K. Mann++

++ Department of Physics, Kent State University Department of Physics, Kent State University* Department of Mathematics, Case Western Reserve University* Department of Mathematics, Case Western Reserve University&& Department of Mathematics, Harvey Mudd College Department of Mathematics, Harvey Mudd College## Department of Chemical Engineering, Case Western Reserve Univers Department of Chemical Engineering, Case Western Reserve Universityity

Partially under NSF Grant No. 9984304

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Why hole-closing is Why hole-closing is interesting?interesting?• Phase coexistencePhase coexistence

• Biological system, e.g. cell membraneBiological system, e.g. cell membrane

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A gas-phase hole in a 2D polymer A gas-phase hole in a 2D polymer liquidliquid

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Fundamental Dynamics Fundamental Dynamics EquationsEquations

• Stokes EquationStokes Equation

• Continuity EquationContinuity Equation

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Assumptions on the surfaceAssumptions on the surface

• 2D liquid phase + very dilute 2D gas2D liquid phase + very dilute 2D gas– surface viscosity surface viscosity 0 0

• Liquid phase: Liquid phase: – High elasticity (incompressible)High elasticity (incompressible)

• Gas phase:Gas phase:– Null compressibility Null compressibility Elasticity = 0 Elasticity = 0

– Circular holeCircular hole

II

II

II

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Assumptions on the subfluidAssumptions on the subfluid

• IncompressibleIncompressible•Bulk viscosity Bulk viscosity

ηη’ ’ •VelocityVelocity

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Derivation Result – Derivation Result – closing closing raterate

[Ref]: J. C. Alexander, A. J. Bernoff, E. K. Mann, J. A. Mann Jr., L. Zou, [Ref]: J. C. Alexander, A. J. Bernoff, E. K. Mann, J. A. Mann Jr., L. Zou, ““Hole Dynamics in Polymer Langmuir FilmsHole Dynamics in Polymer Langmuir Films”, ”, Physics Of FluidPhysics Of Fluid, , to be published.to be published.

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Vertical Cross section of flVertical Cross section of flow lines in the subfluidow lines in the subfluid

Derivation Result – Derivation Result – Vertical Vertical MotionMotion

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Experimental setupExperimental setup

Brewster Angle Brewster Angle MicroscopeMicroscope

PDMS = Poly(dimethylsiloxanPDMS = Poly(dimethylsiloxane)e)

MMww=31600=31600 N=427N=427

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0.27mm X 0.27mm X 0.44mm0.44mm

Hole-closing imagesHole-closing images

• Monolayer thickness ~ 0.7 nmMonolayer thickness ~ 0.7 nm• Surface vibrationSurface vibration• Hole Moving aroundHole Moving around

• Surface concentration 0.35 mg/mSurface concentration 0.35 mg/m22

• Monolayer coverage ~ 70%Monolayer coverage ~ 70%• Monolayer Monolayer dark dark • gaseous hole gaseous hole bright bright

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Experimental result (linear)Experimental result (linear)

[Ref[Ref]]

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

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ConclusionConclusion

• Develop a model for the closing of a Develop a model for the closing of a gaseous hole in a liquid domaingaseous hole in a liquid domain within a within a 2D fluid layer, coupled to a fluid bulk 2D fluid layer, coupled to a fluid bulk substratesubstrate

• Experimental result supports the Experimental result supports the prediction on the hole-closing rateprediction on the hole-closing rate

• Suggest an independent means of Suggest an independent means of determining the determining the line tensionline tension

• Predict the Predict the vertical motionvertical motion of the of the underlying incompressible fluidunderlying incompressible fluid

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Complete Experiment ResultComplete Experiment Result

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Future workFuture work

• Improvement on the current experimentImprovement on the current experiment– How to make a better hole?How to make a better hole?– How to obtain better images?How to obtain better images?

• Observation on the vertical motion of thObservation on the vertical motion of the subfluide subfluid

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Tether RelaxationTether Relaxation

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outlineoutline

• Why interesting (BG and other’s work)Why interesting (BG and other’s work)

• Theory part – model, assumptions, Theory part – model, assumptions, equations and predictionequations and prediction

• Experiment part – setup, difficulties, Experiment part – setup, difficulties, data, result and explanationdata, result and explanation

• Conclusion and future workConclusion and future work

• AcknowledgementAcknowledgement

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AcknowledgementAcknowledgement

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

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