Technique for Measurement of Inter-Phase Line Tension in Langmuir Films Lu Zou and Elizabeth K. Mann Kent State University Jacob M. Pugh and Andrew J. Bernoff Harvey Mudd College James C. Alexander and J. Adin Mann, Jr. Case Western Reserve Unviersity

2 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

3 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% ?

4 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)

5 Phase coexistence of 8CB 8CB Molecule At room temperature Surface pressure ~6.5mN/m

6 Experimental set-up Brewster Angle Microscope Stepper Motor 4-Roll Mill

7 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 beam a b domain

8 Experimental video At 30 frames per second

9 Simulation T best 90%T best 110%T best λ = Inter-phase line tension T = Characteristic relaxation time η’= Subfluid viscosity A = Total area Relative standard deviation Δλ/λ < 5%

10 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.

11 Profile of 8CB layers at air/water interface [Ref] L. Lejcek and P. Oswald, J. Phys. II France, 1 (1991) Line tension: λ= (5.90 mN/m) ΔL

12 Result Small perturbation technique Mean value Symmetric Difference Metric Relative Standard deviation in area Relative standard deviation

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