Introduction We applied a new, simplified model of the dynamics of molecular layers to derive the line tension of 8CB multilayers from the relaxation of elongated domains towards circles, driven by line energy minimization. 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.

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. Fig. 1. 8CB molecule structure

Experimental setup Langmuir trough with symmetric movable barriers 8CB in hexane, concentration = 0.3 mg/ml Deposit for monolayer/trilayer coexistence 2 compression/decompression cycles for isolated domains in different thicknesses 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 Fig. 3. Schematics of Langmuir domain on air/water interface. Surface and bulk viscosities are η s and η b respectively. At the domain boundary, the line tension λ balances with the pressure change Δπ, Δπ = λ / R c (R c is the local radius) For small distortions, line tension λ is estimated by Relaxation Model.

For small distortion, exponential decay, Θ= L / W - 1 = exp(-t / T c ) For 2-D impressible liquid, when η s << η b R, T C = 5 πη b R 2 / 16λ [2] Fig. 4. Schematics of an elongated domain. From Θ(t)  Characteristic time T c  Line Tension λ

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

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

When compressing the 8CB 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 8CB a) monolayer to a trilayer, b) trilayer to a nine-layered stacked interdigitated bilayer structure. Result

Fig. 8. CCD image of 8CB multi-layers on trilayer. The brightest domain is elongated and relaxing. The white bar in photo stands for 1mm. Fig. 9. Relaxation of 8CB 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 8CB multilayers. Here, the thickness of trilayer is 1 unit.

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. } ΔL 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) mN/m.

A phase transition of 8CB 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. Fig. 12. CCD Images of phase transition of 8CB 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. Bulk: K 20.5 o C SmA 33.3 o C N 41.5 o C

Conclusion Line tension of 8CB 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 mN/m) / ΔL Phase transition of 8CB 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. McConnell, 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 For further information Please contact: Lu Zou Dr. Elizabeth K. Mann