Disappearance of the Gas-Liquid Phase Transition for Highly Charged Colloids

We calculate the full phase diagram of spherical charged colloidal particles using Monte Carlo free energy calculations. The system is described using the primitive model, consisting of explicit hard-sphere colloids and point counterions in a uniform dielectric continuum. We show that the gas-liquid critical point becomes metastable with respect to a gas-solid phase separation at colloid charges $Q\ge 20$ times the counterion charge. Approximate free energy calculations with only one and four particles in the fluid and solid phases, respectively, are used to determine the critical line for highly charged colloids up to $Q=2000$. We propose the scaling law $T_c^{*}\sim Q^{1/2}$ for this critical temperature.

Figure 1

Phase diagrams for colloid charges (a) $Q=2$, (b) $Q=10$, (c) $Q=20$, and (d) $Q=50$. The circles (∘) are phase coexistence points, and the filled circles (•) are phase coexistence points based on approximate calculations, see text. The stars (*) are critical points, the squares are inflection points, and the triangles (△) are triple points. The critical points in (a) and (b) are from Ref. 8, and they are rescaled such that counterions are pointlike. The lines are a guide to the eye.

Figure 2

Effective colloid-colloid pair potential for (a) $Q=10$ and (b) $Q=50$. The arrow indicates the direction of increasing temperature.

Figure 3

Critical temperature $T_c^{*}$ as a function of colloid charge $Q$. The squares are the critical temperatures. The solid line is Eq. (3), and the dashed line is the scaling from 9, 18. Critical temperature for $Q=1$ is from Ref. 5, $Q=2$ and 3 from Ref. 6, $Q=5$ from Ref. 7, and $Q=10$ from Ref. 8, and they are all rescaled such that counterions are pointlike.