Technique for Measurement of Inter-Phase Line Tension in

Langmuir Films

Lu Zou and Elizabeth K. MannKent State University

Jacob M. Pugh and Andrew J. BernoffHarvey Mudd College

James C. Alexander and J. Adin Mann, Jr.Case Western Reserve Unviersity

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Introduction• Line tension = free energy per unit length

• Line tension (2D) Surface tension (3D)

• Determine the shape, size and relaxation of surface domains

• Help us to understand the function of biological membrane systems

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Previous experiments & limitations• Small perturbations

(oval shape)– Theory: Two surface phases have identical properties

– Exp: Hard to measure accurately

• Large perturbations

(bola shape)– Theory: Exact shape does NOT matter.

– Exp: Measured line tensions scatter ~20%-30%?

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Our theory model

• Considering the coupling between the surface phases and the substrate

[Ref] J. C. Alexander, A. J. Bernoff, E. K. Mann, J. A. Mann Jr., J. M. Pugh, and L. Zou, J. Fluid Mech. (2006)

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Phase coexistence of 8CB

8CB Molecule

At room temperature

Surface pressure ~6.5mN/m

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Experimental set-upBrewster Angle

Microscope StepperMotor

4-Roll Mill

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Experimental set-up (cont’)

M

a = 6.6 mm, b = 10.5 mm

4-Roll Mill

• Running speed ~0.2 revolutions per second

• Running time ~5 seconds

• Reynolds number ~16

5mm

Laser beama

b

domain

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Experimental video

At 30 frames per second

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Simulation

Tbest90%Tbest 110%Tbest

λ = Inter-phase line tension

T = Characteristic relaxation time

η’= Subfluid viscosity

A = Total area

Relative standard deviation

Δλ/λ < 5%

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Conclusion

• We develop a new technique to measure the line tension of two surface-fluid phases at air/water interface.

• Compared with other models, it provides a more accurate and stable solution.

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Profile of 8CB layers at air/water interface

[Ref] L. Lejcek and P. Oswald, J. Phys. II France, 1 (1991) 931-937

Line tension: λ= (5.90 mN/m) ΔL

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Result

Small perturbation technique

Mean value

Symmetric Difference

Metric

Relative Standard deviation in area

Relative standard deviation

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