Fusion of two critical points and accelerated phase dynamics in orientational ternary mixtures

Abstract

Motivated by intracellular phase separation, we theoretically investigate how molecular orientation and multi-component nature affect phase behavior. We construct a minimal model for a ternary mixture composed of isotropic (I), anisotropic (A), and solvent (s) components by combining the Flory-Huggins and Maier-Saupe theories. We obtain two main results from evaluating the phase behavior and the time evolution of the density fields. First, for certain interaction parameters, two distinct binodal lines appear in the plane of the volume fractions of the I- and A-components, and merge through their respective critical points. Second, rapid droplet formation emerges due to a weakly first-order phase transition, characterized by a discontinuity of the spinodal surface. The first result indicates the possibility of continuous transformation between the two phase-separated states. The second result suggests that anisotropic molecules can regulate phase separation kinetics. These findings might be physically general beyond biological systems.

Figures (11)

• Figure 1: Color plot of the orientation order parameter $S$ for $\chi \in[0.60:0.79]$. The horizontal and vertical axes indicate $\phi_{\rm I}$ and $\phi_{\rm A}$, respectively.
• Figure 2: Binodal lines on the $\phi_{\rm I}$ -$\phi_{\rm A}$ plane for $\chi \in[0.42:0.60]$. The horizontal and vertical axes indicate $\phi_{\rm I}$ and $\phi_{\rm A}$, respectively. Purple symbols indicate the binodal points; the black dashed line indicates the tie line for the I-I phase separation, and the purple dashed line shows the tie line for isotropic–nematic coexistence. The black solid line corresponds to $\phi_{\rm I} + \phi_{\rm A} = 1$.
• Figure 3: Binodal lines for $\chi \in [0.76, 0.79]$. Axes and symbols are the same as in Fig. \ref{['fig:phase_diagram_small_chi']}. For $\chi > 0.76$, two binodal lines appear: an upper one (I-rich and A-rich) and a lower one (I-rich and s-rich).
• Figure 4: Spinodal surface. (A) Color map of spinodal surface $\chi_{\rm s}$ on the $\phi_{\rm I}$-$\phi_{\rm A}$ plane. The red color specifies high $\chi_{\rm s}$, while blue color means its low value. (B) 3D view around the merged critical point. (C) Full 3D view of the spinodal surface. Black arrows indicate discontinuity in $\chi_{\rm s}$.
• Figure 5: Time evolution of the A-component density field $\phi_{\rm A}$. The upper panels show the full system; the lower panels show magnified views highlighting droplet formation.