Effective-liquid approach to the generalized Onsager theories of the isotropic-nematic transition of hard convex bodies

摘要: Recent attempts to generalize the classical Onsager theory of nematic ordering finite-density systems finite-length hard convex bodies are related and compared. It is pointed out that, although good results can be obtained in three-dimensions (3D), two dimensions (2D) underlying factorization approximation radial angular variables always implies a second-order isotropic-nematic transition instead crossover from weakly first-order continuous (Kosterlitz-Thouless) as seen simulations. The quantitative agreement with simulations also much poorer 2D than 3D. On contrary, for large spatial these theories become exact.