Fluid-solid phase separation in hard-sphere mixtures is unrelated to bond percolation

In a recent Letter, Buhot [1] proposes that entropy driven phase separation in hard-core binary mixtures is directly related to a bond-percolation transition. In particular, Buhot suggests that a phase instability occurs when the coordination number n b , defined as n b ෇ r l Z s l #r#s l ͑11R͒ g ll ͑r͒ dr , (1) is equal to zp c , where z is the coordination number of a particular crystal lattice, and p c is its bond-percolation threshold. Here r l is the number density of the larger particles , g ll ͑r͒ is the radial distribution function of the larger particles, and R ෇ s s ͞s l , 1 is the ratio of the diameters s i. However, for binary hard-sphere mixtures, calculations based on an accurate approximation to g ll ͑r͒ demonstrate that n b varies widely along the phase boundaries calculated directly by simulations, implying that bond percolation is unrelated to the phase separation in these systems. For highly asymmetric binary hard-sphere systems, Dijkstra et al. [2] conclusively demonstrated that an effective one-component description based on a depletion potential picture quantitatively describes the fluid-solid transition. This in turn implies that the one-component description should give a fair representation of the radial distribution function g ll ͑r͒. Recent simulations [3] of the Asakura-Oosawa (AO) depletion potential [4] show that the Percus-Yevick (PY) approximation quantitatively describes the pair correlations along the fluid-solid transition line. In the inset of Fig.