Reaction-field and Ewald summation methods in Monte Carlo simulations of dipolar liquid crystals

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Abstract
The treatment of the long-range dipolar interactions in simulations of mesogens is examined. After a brief reformulation of the standard Ewald summation and reaction-field methods in the general context of electrostatics using Green functions, we report the results of Monte Carlo simulations of liquid crystalline phases for L/D = 5 hard spherocylinders (cylinder length Land diameter D) with central point dipoles oriented along the main axis of the cylinder. In the case of N = 1020 particles an equivalent description of the thermodynamic properties and the structure of the phases is obtained with both techniques. A good description of the dielectric constant of the surrounding continuum is achieved by using a simple selfconsistent iterative method based on the calculation of the dielectric constant within the cell. The reaction-field method allows a systematic study of the phase behaviour of the system to be made with relatively modest computational requirements. We make a preliminary assessment of the phase behaviour for this system. In the case of molecules with central longitudinal dipoles, the nematic phase is destabilized relative to the isotropic (I) and the smectic-A (SmA) phases when compared with the non-polar system; the nematic (N) phase disappears altogether when the temperature is lowered below an I–N–SmA triple point. Furthermore, there is no evidence of ferroelectricity although some short-range antiferroelectric ordering is seen. The destabilization of the nematic phase relative to the smectic phase is also seen for systems with central transverse dipoles, but contrasts with that for molecules with terminal longitudinal dipoles where the smectic-A phase is destabilized.