Molecular dynamics simulations of dipolar fluids in orientationally ordered phases Dong-Qing Wei, 1, * Ying-Jie Wang, 1,2 Lu Wang, 1,2 Jin-He Hu, 1,2 Zi-Zheng Gong, 3 Yong-Xin Guo, 2 and Yi-Sheng Zhu 1 1 College of Life Science and Biotechnology, Shanghai Jiaotong University, China 200240 2 Physics Department, Liaoning University, Shenyang, China 3 China Academy of Space Technology, Beijing, China Received 8 November 2006; revised manuscript received 29 March 2007; published 6 June 2007 It has been established that the strongly interacting dipoles form orientationally ordered liquid phases. However, most of the computer simulations adapt the point dipole model. In this paper, we report molecular dynamics simulations of orientationally order phases formed by extended dipoles, where the potential energy consists of the site-site Lennard-Jones potential and electrostatic contribution of partial charges. The calcula- tions were performed for a range of densities along an isotherm and for different temperatures at the same reduced densities. It is found that orientationally ordered phases are present in the wide density regime, the extended dipole tends to form chains at low density, and the isotropic liquid phase is not seen in the density regime studied for a specific temperature. DOI: 10.1103/PhysRevE.75.061702 PACS numbers: 64.70.Md, 61.25.Em, 61.20.Ja I. INTRODUCTION In recent years there has been renewed interest in the thermodynamic and structural properties of dipolar fluids, which consist of spherical particles with embedded point di- poles. In 1916, Born conjectured that dipolar forces alone can create an orientationally ordered fluid. In the early 1990s, the molecular dynamics MD simulations of Wei and Patey 1,3 for the model of soft spheres with electric point dipoles embedded at their centers represents the first contri- bution which shows that the dipolar interaction alone is ca- pable of bringing about the formation of an orientationally ordered phase. Moreover, they showed that this phase is a ferroelectric liquid crystal, becoming a stable ferroelectric solid at high density. The Monte Carlo MC simulations of Weis et al. 4 for a system of strongly interacting dipolar hard spheres have revealed that dipolar hard spheres can also form an orientationally ordered phase. Levesque, Weis, and co-workers 5–8 also extended their previous MC calcula- tions to lower densities and temperatures. The systems of spheres with point dipoles are highly ide- alized ones. In order to search for the thermodynamic and molecular parameters that the ferroelectric liquid states are stable we have to consider more complex and more realistic systems. Ballenegger and Hansen 9 performed extensive MD simulations for systems of extended dipoles formed by two opposite charges + / -q separated by a distance d dipole moment  = qd in the liquid state. The strengths and short- comings of the point dipole model for polar fluids of spheri- cal molecules are illustrated. The dependence of the pair structure, dielectric constant and dynamics on the charge separation is analyzed. However, the ferroelectric phase was not the focus of their studies. In 1997, Kachel and Gburski 10,11 performed MD simulations for a model system which consists of elongated molecules with three embedded inter- action sites XY 2 placed on the major axis of the molecule. The sites Y -X-Y are responsible for the nondipolar intermo- lecular interaction of atomic groups united atoms or pseudoatoms located inside the molecule 8. Their simula- tions have shown that the simple protoplasts of elongated molecules can form spatially ordered, chainlike structures. Subsequently, Patey et al. 12–14 considered fluids of hard spheres each carrying two parallel point dipoles using constant-volume Monte Carlo computer simulations, and the results show that both ferroelectric and antiferroelectric fluid phases can be stabilized at high density and low temperature by dipolar interactions alone, if the separation between the dipoles on each sphere was sufficiently large. In the present paper, we performed MD simulations for a model system which consist of rigid polyatomic molecules with electric extended dipole; the dipole moment was along the prime axis in the molecular fixed frame. Our molecules have two effective charges q 0.5,-0.5 located on the z axis 0.05 and -0.05 nm, respectively and with the distance d = 0.1 nm between them. In other words, the molecule has the dipole moment   = | | = qd, q = 0.5. In the following sec- tions, we shall describe the model, computational methods, and results. II. COMPUTATIONAL METHODS The model that we use is a common one for the rigid polyatomic molecules 15,16 where the intermolecular forces consist of short range Lennard-Jones LJ site-site forces combined with electrostatic long range forces. The potential energy for any two sites i , j is given by U ij r =  ij  ij /r 12 -  ij /r ij  6  + q i q j /r . 1 There are two sites like diatomic molecule on each mol- ecule.  ij is the Lennard-Jones well depth and  ij is the dis- tance at the Lennard-Jones minimum, q i is the partial atomic charge, and r is the distance between atomic sites i and j , which belong to different molecules. The Lennard-Jones pa- rameters between pairs of different atoms are obtained from the Lorentz-Berthelodt combination rules, in which  ij values are based on the geometric mean of  i and  j and  ij values are based on the arithmetic mean between  j and  j . The *Corresponding author; dqwei@sjtu.edu.cn PHYSICAL REVIEW E 75, 061702 2007 1539-3755/2007/756/0617025 ©2007 The American Physical Society 061702-1