Onsager's missing steps retraced

Abstract

Onsager's paper on phase transition and phase coexistence in anisotropic colloidal systems is a landmark in the theory of lyotropic liquid crystals. However, an uncompromising scrutiny of Onsager's original derivation reveals that it would be rigorously valid only for ludicrous values of the system's number density (of the order of the reciprocal of the number of particles) Based on Penrose's tree identity and an appropriate variant of the mean-field approach for purely repulsive, hard-core interactions, our theory shows that Onsager's theory is indeed valid for a reasonable range of densities.

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Cited by in corpus (5)

• Solution landscape of the Onsager model identifies non-axisymmetric critical points
• Asymptotic expansions for the incomplete gamma function in the transition regions
• Cavity volume and free energy in many-body systems
• Nematic first order phase transition for liquid crystals in the van der Waals-Kac limit
• Contributions of Repulsive and Attractive Interactions to Nematic Order