Packing Polydisperse Colloids into Crystals: When Charge-Dispersity Matters

Monte Carlo simulations, fully constrained by experimental parameters, are found to agree well with a measured phase diagram of aqueous dispersions of nanoparticles with a moderate size polydispersity over a broad range of salt concentrations, $c_s$, and volume fractions, $\varphi$. Upon increasing $\varphi$, the colloids freeze first into coexisting compact solids then into a body centered cubic phase (bcc) before they melt into a glass forming liquid. The surprising stability of the bcc solid at high $\varphi$ and $c_s$ is explained by the interaction (charge) polydispersity and vibrational entropy.

Figure 1

Colloidal crystallization in a polydisperse system can lead to (a) a set of distinct crystals of the same structure (e.g., fcc) and narrow monomodal size distributions, which together span the available range of particle sizes [6]; (b) more complex phases such as $A{B}_2$ [8] or $A{B}_{13}$ [9] structures, which utilize a bimodal subset of particles. These may coexist with simpler phases (e.g., as above, bcc [8]); (c) The appearance of crystals of different structures (e.g., bcc, fcc, hcp) and monomodal size distributions, as reported in this Letter. In all sketches, the shaded area shows the parent particle size distribution while the various open curves describe the particles found in any specific crystal structure and site.

Figure 2

As the dispersion is concentrated, colloidal crystals appear. The scattering intensities, $I$, of the spectra shown here, for $c_s=5\mathrm{mM}$, demonstrate the typical sequence of (a) fcc ($\varphi =19\%$), (b) a mixture of fcc and bcc ($\varphi =20\%$), and (c) bcc ($\varphi =21\%$) crystals, as $\varphi$ increases. A broad liquid peak is present in all spectra, and the most prominent crystal peaks are typically at least twice as intense as this liquid background. Additionally, a much weaker peak is often visible at lower $q$, consistent with an hcp structure of the same particle density, or stacking faults in an fcc lattice.

Figure 3

Phase diagram in the $c_s-\varphi$ plane of the TM50 silica dispersion at $p\mathrm{H}$ 9 as obtained from (a) SAXS analysis of dialyzed samples and (b) MC simulations of the MCM. For clarity, the hcp phase is not represented. The shaded areas of (a), (b) delimit the region where crystals are found in the simulations, and demonstrate the good correspondence with experiments.

Figure 4

Simulation results (at $p\mathrm{H}$ 9) show: (a) agreement of the simulated and measured equation of state (EOS) of the TM50 silica dispersion at various ionic strengths; (b) the predicted variation of the phase composition with $\varphi$ at $c_s=5\mathrm{mM}$; (c) and particle size distributions of the various crystalline phases in comparison with the parent size distribution (dashed curve) for the model silica dispersion at $\varphi =20.5\%$, $c_s=5\mathrm{mM}$.