Distribution functions for reversibly self-assembling spherocylinders

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Abstract
We consider an equilibrium solution of hard spheres undergoing reversible self-assembly into spherocylinders. Our main interest is the distribution of cylinder orientations and lengths in the nematic phase. Over a limited range of concentrations, we find accurate numerical results for the distribution using an iterative equation. Based on trends in this regime, a trial distribution function is introduced that allows an efficient calculation of accurate thermodynamic data over the entire concentration range. In agreement with previous authors, we find a first-order transition from a dilute, weakly polymerized, isotropic phase to a concentrated, highly polymerized, nematic phase.