Phase behavior of bidisperse ferrocolloids

The phase behavior of bidisperse ferrocolloids consisting of binary mixtures of dipolar hard spheres (DHS’s) with different particle diameters and different dipole moments is investigated using density-functional theory in a modified mean-field approximation. We focus on the fluid phase regime, where we consider both isotropic and anisotropic states. Depending on the parameter $\Gamma$—measuring the asymmetry of the dipolar couplings—the systems display complex fluid-fluid phase behavior involving demixing transitions, as well as first- and second-order isotropic-to-ferromagnetic phase transitions. The topology of the resulting phase diagrams turns out to be similar to those corresponding to monodisperse DHS mixtures investigated previously by us [Phys. Rev. E 69, 041201 (2004)]. However, additional size asymmetry has a strong impact on the relative importance of the various types of phase transitions. In particular, the demixing transition of bidisperse ferrocolloids is strongly destabilized compared to that of monodisperse DHS’s in the sense that demixing critical points are significantly shifted towards lower temperatures.

Figure 1

MMF phase diagram of a monodisperse DHS fluid containing only $A$ particles in the packing fraction-temperature plane $[T^{*}=k_{\mathrm{B}}T{\sigma }_A^3∕m_A^2,\eta =(\pi ∕6){\rho }_A{\sigma }_A^3]$. The inset shows the $\eta$ dependence of $P_{A,1}$ at $T^{*}=0.65$. For an explanation of the lines and symbols, see the main text.

Figure 2

Packing fraction-concentration phase diagram for a bidisperse ferrocolloid with $\Gamma =0.75$ at various temperatures. For explanation of the various lines, see the main text. The pairs of open symbols denote coexisting states at $T^{*}=0.50∕{\Delta \mu }^{*}=-\infty$ (circles), $T^{*}=0.50∕{\Delta \mu }^{*}=0.6$ (triangles), $T^{*}=0.50∕{\Delta \mu }^{*}=0.9$ (diamonds), and $T^{*}=0.30∕{\mu }^{*}=-5.5$ (squares). The solid circle denotes a demixing critical point.

Figure 3

Same as Fig. 2, but for $\Gamma =0.60$. The pairs of open symbols denote coexisting states at $T^{*}=0.45∕{\Delta \mu }^{*}=1.0$ (triangles), $T^{*}=0.45∕{\Delta \mu }^{*}=1.42$ (diamonds), and $T^{*}=0.37∕{\mu }^{*}=4.0$ (squares).

Figure 4

Same as Fig. 2, but for $\Gamma =0.40$. The pairs of open symbols denote coexisting states at $T^{*}=0.60∕{\mu }^{*}=3.0$ (triangles) and $T^{*}=0.60∕{\mu }^{*}=17.9$ (diamonds).

Figure 5

Same as Fig. 2, but for $\Gamma =0.30$. The pairs of open symbols denote coexisting states at $T^{*}=0.55∕{\mu }^{*}=0.0$ (triangles) and $T^{*}=0.55∕{\mu }^{*}=20.0$ (diamonds).

Figure 6

${\mu }^{*}\text{−}{\Delta \mu }^{*}$ phase diagrams for bidisperse ferrocolloid with (a) $\Gamma =0.75$, (b) $\Gamma =0.60$, (c) $\Gamma =0.40$, and (d) $\Gamma =0.30$, at different temperatures $T^{*}$. Solid (dotted) lines denote two-phase coexistence (critical) lines. Solid circles, triangles, and squares denote CP’s, TCP’s, and CEP’s, respectively.

Figure 7

(a) Same as Fig. 4 and (b) $\eta \text{−}{c}_A$ phase diagram of a monodisperse DHS mixture at $\Gamma =0.4$ [13].

Figure 8

Comparison of the ${\mu }^{*}\text{−}{\Delta \mu }^{*}$ phase diagrams of a bidisperse ferrocolloid (solid line) and a monodisperse DHS mixture (dashed line) at $\Gamma =0.4$ and $T^{*}=0.5$. The solid circle denotes a CP and the solid squares denote CEP’s.

Figure 9

Temperatures $T^{*}$ (left) and concentrations $c_A$ (right) related to the TCP’s, CEP’s, and CP’s as functions of the packing fraction for a bidisperse ferrocolloid (solid lines) and a monodisperse DHS mixture (dashed lines) at $\Gamma =0.4$.