Composite colloidal assembly by critical Casimir forces

TL;DR

This work shows that particle-pair-specific critical Casimir forces in a near-critical binary solvent can drive binary colloidal alloys withTuneable phase behavior around $T_c$ and a critical composition $c_{L,c}$. By surface-tuning two particle types (A and B), the authors map a rich phase diagram and observe alloy-like crystallization into A-rich and B-rich domains, with limited mixing and a reversible, temperature-controlled interaction strength. A minimal four-component mean-field ABCD model captures the observed phase behavior and predicts additional critical and triple points, highlighting the role of explicit solvent in mediating many-body effects near criticality. The ability to anneal the crystal microstructure via controlled temperature cycling offers a route to tailor colloidal alloys and solid-solution-like phases at the nanoscale, with potential applications where DNA-mediated or patchy interactions are not feasible.

Abstract

We investigate the phase behaviour of mixtures of two populations of colloidal particles dispersed in a binary solvent system near its critical composition. The surfaces of particles are chemically modified to elicit a specific solvent affinity for one of the solvents. In this way, fluid-mediated interactions, which involve the critical Casimir effect, become particle population specific. As a result, the colloidal mixture shows a complex crystallization behavior reminiscent of the crystallization of atomic alloys. We show that the exquisite temperature dependence and reversibility of the critical Casimir interaction allows sampling the entire phase diagram of the binary system, and can be even used to anneal the crystalline microstructure analogous to temperature cycling of atomic alloy phases.

Figures (7)

• Figure 1: Temperature and solvent composition dependent aggregation diagram for a dilute composite system of colloidal particles A and B at equal particle number $N_\mathrm{A} = N_\mathrm{B}$. The total volume fraction of colloids $\eta=\eta_A + \eta_B = 0.01$. Four aggregation boundaries are observed: $T_{AA}(c_L)$ marks the onset of the self-aggregation for $P_\mathrm{A}$; $T_{AB}(c_L)$ the onset of the hetero-aggregation for $P_\mathrm{A}$ and $P_\mathrm{B}$; $T_{BB}(c_L)$ the onset of the self-aggregation for $P_\mathrm{B}$. $T_{x}(c_L)$ is the solvent phase separation curve of the bulk solvent. The point $T_{cx}$ is the critical composition and temperature ($x_{r,c}$ = 0.5). Symbols correspond to the experimental data whereas solid lines are theoretical predictions (see SI for details of the theoretical model). From the fit of the solvent coexistence curve around the critical temperature of the solvent $T_\mathrm{c}$ to $\phi=c_\mathrm{L}-c_\mathrm{L,c} = \mathcal{B}|t|^{\beta}$, where $t=\Delta T/T_\mathrm{c}=(T_\mathrm{c} - T)/T_\mathrm{c}$ and $\beta$ is the critical exponent, we have determined the non-universal amplitude $\mathcal{B}$.
• Figure 2: Temperature dependent $P_\mathrm{A}$ phase changes from colloidal gas, #1, to colloidal liquid, #2, to finally a colloidal crystal #3 at $c_L = 32$wt%. Note: upon $P_\mathrm{A}$ crystallite formation, sedimentation also occurs, resulting in an apparent compositional change.
• Figure 3: Compositionally dependent phases observed close to $T_\mathrm{c}$ at $\Delta T<T_\mathrm{BB}$ at $c_\mathrm{L} = 32$wt% corresponding to particle composition number indicated in the phase diagram shown in Fig.\ref{['composition_phase_diagram']}.
• Figure 4: Temperature and particle composition ($\eta_B/\eta$) phase diagram with representative phase boundaries for all three composite phases: $L_{B}$+$\alpha_A$, $L_A$+$\beta_B$, and $\alpha_A$+$\beta_B$. Composition values are directly calculated by particle counting within images #1-7 shown in Fig. \ref{['Temperature']} and Fig. \ref{['Composition']}.
• Figure 5: Theoretical phase diagram of an ABCD mixture in the plane $(\Delta T/T_c, \eta)$ for a pure solvent composition of $x_\mathrm{r}=0.4$, representing the gas (G), liquid (L), and solid (S) phases. (a) Color coding indicates different fixed fractions of $\eta_\mathrm{B}/\eta$ in the liquid phase: black, green, red, blue, cyan, and gray for $\eta_B/\eta=$0, 0.1, 0.187, 0.5, 0.73, and 1, respectively. Full circles indicate stable upper critical points, while full triangles indicate triple points. Metastable G-L phase boundaries are indicated by dashed lines. For equal fractions of both colloid types (blue line), the upper critical point is metastable (open blue circle). The vertical magenta line shows the value of the experimental significant total packing fraction $\eta=0.4$ for which we present the phase behavior in Fig. \ref{['fig:mf_2']}. (b) The phase diagram for the fraction $\eta_\mathrm{B}/\eta$ fixed in the gas phase at the value of 0.187 (red line) and 0.5 (blue line) showing broad coexistence of G-S phases. Metastable G-L phase boundaries with the same value of $\eta_\mathrm{B}/\eta$ are indicated by dashed lines. Note that the triple points differ from those in (a), where the $\eta_\mathrm{B}/\eta$ ratio is fixed in the liquid phase.