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To obtain Equation (5) we have taken the limit L_Z/σ_T→∞ of the corresponding equation for slab-like systems (see Equation (2.53) in [34]).

has been cited by the following article:

• TITLE: Dimensionality Effects in Dipolar Fluids: A Density Functional Theory Study

  AUTHORS: Remi Geiger, Sabine H. L. Klapp

  KEYWORDS: Dipole-Dipole Interactions; Dimensionality; Phase Diagram; Density Functional Theory; Long-Range Correlations

  JOURNAL NAME: Journal of Modern Physics, Vol.4 No.3A, March 29, 2013

  ABSTRACT: Using classical density functional theory (DFT) in a modified mean-field approximation we investigate the fluid phase behavior of quasi-two dimensional dipolar fluids confined to a plane. The particles carry three-dimensional dipole moments and interact via a combination of hard-sphere, van-der-Waals, and dipolar interactions. The DFT predicts complex phase behavior involving first- and second-order isotropic-to-ferroelectric transitions, where the ferroelectric ordering is characterized by global polarization within the plane. We compare this phase behavior, particularly the onset of ferroelectric ordering and the related tri-critical points, with corresponding three-dimensional systems, slab-like systems (with finite extension into the third direction), and true two-dimensional systems with two-dimensional dipole moments.