Introduction For domains within Langmuir monolayers the line

Introduction For domains within Langmuir monolayers, the line tension plays a very important role to determine the equilibrium size and shape, as well as the dynamics and the stability. However, it is hard to be either predicted or controlled, so there are few systematic experimental studies performed. We applied a new, simplified model of the dynamics of molecular layers to derive the line tension of 8 CB multilayers from the relaxation of elongated domains towards circles, driven by line energy minimization.

Fig. 1. 8 CB molecule structure Previous work [1] estimated line tension for the lowest two layers. We extend these results to as many as 10 multilayers. When the temperature is increased, a phase transition of the multilayers, which behaves different from the bulk case, is also observed.

Experimental setup • Langmuir trough with symmetric movable barriers • 8 CB in hexane, concentration = 0. 3 mg/ml • Deposit for monolayer/trilayer coexistence • 2 compression/decompression cycles isolated domains in different thicknesses for • Observed with Browster Angle Microscope (BAM).

Fig. 2. Schematics of Browster Angle Microscope (BAM). L 1 and L 2 are lens. P is a polarizer and A is an analyzer.

Relaxation Model For small distortions, line tension λ is estimated by Relaxation Model. Fig. 3. Schematics of Langmuir domain on air/water interface. Surface and bulk viscosities are ηs and ηb respectively. • At the domain boundary, the line tension λ balances with the pressure change Δπ, Δπ = λ / Rc (Rc is the local radius)

• For small distortion, exponential decay, Θ= L / W - 1 = exp(-t / Tc) • For 2 -D impressible liquid, when ηs<< ηb. R, TC = 5 πηb R 2 / 16λ [2] Fig. 4. Schematics of an elongated domain. From Θ(t) Characteristic time Tc Line Tension λ

Comparison: Model/Exp. Experiments show that the relaxation model works for the small distortions. Fig. 5. Plot of the experimental distortion: exponential-decay with time for aspect ratio less than 3.

Based on the experiments on different sizes of domains, the characteristic time Tc is proportional to the domain area R 2. Fig. 6. Plot of the linear dependence of the characteristic time Tc on domain area R 2.

Result When compressing the 8 CB layers, monolayers and then trilayers appear in turn. (Fig. 7. [3]) After trilayers cover all the air/water interface, multilayers in different thicknesses form on the top of trilayers. The reflectivity is proportional to the square of the thickness. [4] a b Fig. 7. Schematics of collapse of an 8 CB a) monolayer to a trilayer, b) trilayer to a nine-layered stacked interdigitated bilayer structure.

Fig. 8. CCD image of 8 CB multi-layers on trilayer. The brightest domain is elongated and relaxing. The white bar in photo stands for 1 mm. Fig. 9. Relaxation of 8 CB multi-layer domain. The time interval in every two continuous images is 0. 5 sec.

Experimental result (Fig. 10. ) shows that within the error range, the line tension increases with the thickness. We extend the previous work [1] and our result is consistent with other’s for the line tension of the trilayer. Fig. 10. Plot of line tension vs. relative thickness of 8 CB multilayers. Here, the thickness of trilayer is 1 unit.

The real thickness is estimated by X-ray reflectivity experiment [5]. The line tension is linearly dependent on the thickness difference ΔL. The slope is (5. 90 ± 0. 59) m. N/m. } ΔL Fig. 11. Plot of line tension vs. the difference of thicknesses ΔL. The inset is a schematics of a multilayer domain (pink) on a trilayer. Light blue stands for pure water substrate.

A phase transition of 8 CB multilayers on air/water interface is observed when temperature is increased from 20 o. C to 40 o. C. More experiments is being carried on. Bulk: K 20. 5 o. C Sm. A 33. 3 o. C N 41. 5 o. C Fig. 12. CCD Images of phase transition of 8 CB multilayers on air/water interface. a) at 26. 6 o. C, domains are flat and uniform; b) at 27. 4 o. C, the coexistence of flat domains and droplets; c) at 34. 5 o. C, only droplets.

Conclusion • Line tension of 8 CB multilayers in different thicknesses were measured. • For trilayers, previous work was confirmed. • For multilayers, line tension is proportional to the thickness difference λ = (5. 90 m. N/m) / ΔL • Phase transition of 8 CB multilayers under study

Reference [1] J. Langer, C. R. Robertson, C. W. Frank, G. G. Fuller, Langmuir, 12: 5630 (1996). [2] H. A. Stone, H. M. Mc. Connell, Proc. R. Soc. London, Ser A, 558, 97(1995) [3] M. N. G. De Mul, J. A. Mann Jr. , Langmuir, 10: 2311 (1994) [4] M. N. G. De Mul, J. A. Mann Jr. , Langmuir, 14: 2455 (1998) [5] S. Bardon, R. Ober, etc. , PRE, 59: 6808 (1999)

Acknowledgement This material is based upon work supported by the national Science Foundation under Grant No. 9984304 For further information Please contact: Lu Zou lzou@kent. edu Dr. Elizabeth K. Mann emann@kent. edu