Enabling three-dimensional real-space analysis of ionic colloidal crystallization

(a) Negatively charged homopolymer particles are synthesized in batch conditions with a single-step monomer injection initiated by KPS as described in the Methods section; representative SEM images across the achievable size range are included. (b) Diameter is tuned by adjusting the monomer concentration while holding all other parameters constant. (c) Scheme to synthesize positively charged copolymer particles initiated with AIBA in batch conditions as described in the Methods section; too little or too much qMA comonomer results in aggregated or size disperse particles, respectively. (d) Time-course of measured Zeta potential for an AIBA initiated homopolymer and a stable copolymer recipe stored in deionized water shows that the former loses charge rapidly over the course of days while the copolymer remains unchanged. (e) Mole ratio qMA C_qMA relative to monomer C_M vs. total monomer concentration with identified regions of stable, uniform size (blue), stable size disperse (yellow), and aggregated (red). (f, g) SEM images of aggregated (f) and size disperse (g) particles. (h) SEM images of selected stable and uniform copolymer particles made by single step batch conditions as well as those seeded with 290 nm particles that afford particles larger than 400 nm. (i) Colloid diameter as measured by SEM plotted against relative qMA feed showing a marked decrease in size with qMA; inset shows a much weaker size relationship to monomer concentration when the qMA ratio is held constant. (j) qMA feed vs. particle radius normalized by concentration of PFPMA to the 1/3 power showing good agreement with a qMA monomer directed nucleation in stable recipes. (k) qMA incorporation vs. feed concentration measured by ¹H NMR; best linear fit gives a slope of 0.33 suggesting that about 30% of comonomer fed remains in the colloids after purification. (l) ¹H NMR of qMA in D₂O (top) and PFPMA (middle) monomers, poly(PFPMA-co-qMA) (bottom, solid) and poly(PFPMA) (bottom, broken) in acetone-d6. Peaks labeled with an asterisk are from solvent. Scale bars are all 1 μm.

(a) Comparative visualization and turbidity measurements of PS and PFPMA colloidal suspensions in water at varying particle concentrations. (b) To enhance the transparency of our samples, PFPMA particles were suspended in an H₂O:DMSO binary mixture. The refractive index matching point was determined by measuring transmittance against DMSO concentration for a 1.5 wt% PFPMA suspension, revealing an optimal solvent composition of 40% DMSO. (c,d) Confocal volumetric scans were conducted on bulk crystals formed from regular PS particles in water and PFPMA particles in the matched solvent, respectively. These scans highlight the enhanced depth penetration in the PFPMA system, allowing the confocal laser to effectively probe particle positions up to a depth of ~80 μm, whereas the PS system’s signal diminishes by 5 μm. Scale bars are 1 μm.

Molecular dynamics simulations of CsCl and Cu₃Au forming systems were performed as described in Methods. Particles with crystalline environments are found using Ovito’s common neighbor analysis (CNA) function³⁵ with a cutoff of 550 nm, and snapshots shown have particles with low crystallinity are set to be semi-transparent. The largest cluster size, which corresponds approximately to the size of the crystal, was computed using the Freud software³⁷ with a cutoff of 550 nm (ref. ³⁶). (a) Particles of size r_N=185 nm and r_P=200 nm were simulated with Debye length λ=5.5 nm and volume fraction Φ=0.009. The plot shows the resulting number of particles in the largest cluster versus time. Snapshots show representative images of the initial gas phase, a crystal nucleus, two intermediate structures during the crystal growth, and the final structure. In the final state, almost all free particles are exhausted into a single CsCl crystal exhibiting rhombic dodecahedral habits. (b) A seed Cu₃Au crystal with r_N=240 nm and r_P=187.5 nm was placed in a box of those particles at volume fraction Φ=0.007 and simulated with λ=5.4 nm. The seed particle had 658 total particles, with N_P=450 and N_N=208, with each edge of the cube ~3126 nm long. Snapshots show a magnified image of the initial seed, an intermediate, and a final state where the growth of the seed has plateaued after growing in volume by almost five times. During the growth process, the seed is coated in a disordered shell, which eventually transforms back into a structure with cubic habits.

(a) Particle coordinates, derived from experiments or simulations, are shifted, rotated, and scaled to align with a candidate lattice. These adjusted coordinates are then input into the Mercury software to simulate the corresponding diffraction pattern. The resulting spectra can be compared with the theoretical spectra of the candidate compound. Panels (b) and (c) depict this comparison for three different candidate compounds, with crystals assembled using particle size ratios of 0.88 and 0.78, respectively.

(a) A 3D-reconstructed snapshot capturing a CsCl crystal as it undergoes melting. Within this image, the red layers highlight the volume of interest where vacancy clusters are identified and tracked. (b) Confocal data (left) and the corresponding reconstruction (right) depict a vacancy cluster that spans three particle layers. The scale bar represents 2 μm. (c) The position of each vacancy within the volume of interest is tracked over time, unveiling a substantial degree of particle movement. Each reconstructed frame highlights newly emerged vacancies in color, while vacancies that have disappeared are indicated by a semitransparent wire-frame. (d) Utilizing the data from particle tracking, we created a heat map that illustrates the probability of encountering a vacancy at each lattice point within the volume of interest.

(a) 3D confocal images alongside their reconstructed models depict Cu₃Au crystals with two consecutive twin planes, shown in parallel (left) and non-parallel (right) orientations. Digital slicing of these crystals facilitates the identification of twin boundaries, reaffirming adherence to the {111} twin law. (b) Through similar internal analysis, we’ve characterized stacking faults, a frequent 2D defect in Cu₃Au crystals. The accompanying cartoon illustrates how stacking faults arise from interruptions in the regular sequence of particle planes. The (010) planes of two crystal segments (blue and purple) are connected by a (020) plane (green) made of small particles only, which results in a plane shift along the vector (0.5, 0, 0.5) (black arrows). The scale bars represent 2 μm.