^{1,a)}, Jun-Ichi Saito

^{1}, Nobuyuki Kato

^{1}and Yuka Tabe

^{1}

### Abstract

Orientational correlations in Langmuir monolayers of nematic and smectic-C liquid crystal(LC) phases are investigated by molecular dynamics simulation. In both phases, the orientational correlation functions decay algebraically yet with the different exponents of 1.9 and 0.2 for the nematic and the smectic-C monolayers, respectively. The power law decay, i.e., the absence of long-range orientational order, means the both monolayers should be the ideal 2D system with a continuous symmetry, whereas the large difference in the exponents of power law gives rise to the crucial difference in their optical properties; the nematic monolayer is optically isotropic while the smectic-C monolayer exhibits an anisotropy on the length scale of visible light. Since the exponent is inversely proportional to the molecular exchange energy, the averaged molecular interaction in the nematic monolayer should be an order of magnitude smaller than that in the smectic-C monolayer, which is ascribed to the low molecular density and the weak molecular dipole due to the water molecule. The relation between the molecular interaction and the orientational correlation calculated for the 2D LC system offers much information not only about the 2D LCs but also on the bulk system.

We are thankful to Professor Hiroshi Yokoyama (Kent State University, USA), Dr. Makoto Yoneya (AIST, Japan), and Dr. Keiko M. Aoki (Toho University, Japan) for their helpful and useful discussions.

The computations were mainly carried out using the computer facilities at Research Institute for Information Technology, Kyushu University.

I. INTRODUCTION

II. MODELS AND METHODS

III. RESULTS AND DISCUSSIONS

IV. CONCLUSION

### Key Topics

- Monolayers
- 51.0
- Liquid crystals
- 17.0
- Atomic and molecular interactions
- 12.0
- Molecular dynamics
- 11.0
- Correlation functions
- 9.0

## Figures

The molecular structure and phase sequence of simulated LC compound: 4^{′}-pentyloxy-phenyl-2-(5-heptyl)pyrimidine (P-5O7)

The molecular structure and phase sequence of simulated LC compound: 4^{′}-pentyloxy-phenyl-2-(5-heptyl)pyrimidine (P-5O7)

MD simulation snapshot of the nematic monolayer at the water interface after 6 ns viewed from the layer normal. The equilibrated structure of P-5O7 laying on the water layer is shown.

MD simulation snapshot of the nematic monolayer at the water interface after 6 ns viewed from the layer normal. The equilibrated structure of P-5O7 laying on the water layer is shown.

MD simulation side-viewing snapshot of the smectic-C monolayer after 6 ns. The equilibrated structure of the smectic monolayer consisting of P-5O7 molecules at the water interface is shown. The molecules tend to be tilted to one particular direction from the layer normal.

MD simulation side-viewing snapshot of the smectic-C monolayer after 6 ns. The equilibrated structure of the smectic monolayer consisting of P-5O7 molecules at the water interface is shown. The molecules tend to be tilted to one particular direction from the layer normal.

Time evolution of the 2D order parameter for the 2D nematic system (blue line) and order parameter of c-director for the 2D smectic-C system (red line). Both systems reach the equilibrated state after 4 ns. Averaged order parameter for the 2D smectic-C is much larger than that for the 2D nematics.

Time evolution of the 2D order parameter for the 2D nematic system (blue line) and order parameter of c-director for the 2D smectic-C system (red line). Both systems reach the equilibrated state after 4 ns. Averaged order parameter for the 2D smectic-C is much larger than that for the 2D nematics.

Radial distribution functions for the 2D nematic system and smectic system. Blue curve shows the distribution of the molecular positions for the 2D nematics and red curve is the one for the 2D smectics. These functions are continuous with soft decaying peaks and reaching one constant value. It indicates that both systems behave as liquid not solid.

Radial distribution functions for the 2D nematic system and smectic system. Blue curve shows the distribution of the molecular positions for the 2D nematics and red curve is the one for the 2D smectics. These functions are continuous with soft decaying peaks and reaching one constant value. It indicates that both systems behave as liquid not solid.

Mean square displacement as a function of time for the 2D nematic system (a) and smectic system (b) in the equilibrated state. The fact that MSDs grow linearly with time reveals that both systems behave as fluids. The slope of linear approximation line possibly gives us the diffusion constant for the system; 0.82 for the 2D nematic system, and the one for the 2D smectic system is 0.16.

Mean square displacement as a function of time for the 2D nematic system (a) and smectic system (b) in the equilibrated state. The fact that MSDs grow linearly with time reveals that both systems behave as fluids. The slope of linear approximation line possibly gives us the diffusion constant for the system; 0.82 for the 2D nematic system, and the one for the 2D smectic system is 0.16.

Orientational correlation functions *g* _{2}(*r*) with molecular distance *r* for the 2D nematic and the 2D smectic systems in the thermally equilibrated state. The obtained values for the 2D nematics are plotted as blue circle points and red square plots are ones for the 2D smectics. The solid lines show that OCFs decay according to the power law of molecular distance: the value of exponent for the nematic monolayer is −1.9 and for the smectic system is −0.20. The inset graph is a log–log plot of *g* _{2}(*r*) indicating that correlation functions decay algebraically.

Orientational correlation functions *g* _{2}(*r*) with molecular distance *r* for the 2D nematic and the 2D smectic systems in the thermally equilibrated state. The obtained values for the 2D nematics are plotted as blue circle points and red square plots are ones for the 2D smectics. The solid lines show that OCFs decay according to the power law of molecular distance: the value of exponent for the nematic monolayer is −1.9 and for the smectic system is −0.20. The inset graph is a log–log plot of *g* _{2}(*r*) indicating that correlation functions decay algebraically.

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