Crystal-to-Crystal Transitions in Binary Mixtures of Soft Colloids

Abstract

In this article, we demonstrate a method for inducing reversible crystal-to-crystal transitions in binary mixtures of soft colloidal particles. Through a controlled decrease of salinity and increasingly dominating electrostatic interactions, a single sample is shown to reversibly organize into entropic crystals, electrostatic attraction-dominated crystals, or aggregated gels, which we quantify using microscopy and image analysis. We furthermore analyze crystalline structures with bond order analysis to discern between two crystal phases. We observe the different phases using a sample holder geometry that allows both in situ salinity control and imaging through confocal laser scanning microscopy and apply a synthesis method producing particles with high resolvability in microscopy with control over particle size. The particle softness provides for an enhanced crystallization speed, while altering the re-entrant melting behavior as compared to hard sphere systems. This work thus provides several tools for use in the reproducible manufacture and analysis of binary colloidal crystals.

Keywords: binary colloidal crystals; colloidal particles; crystal transitions; phase transitions; soft colloids; tunable materials.

Figure 1

Cross-section of the sample holder design, not to scale.

Figure 2

Analysis of one sample at different salinities. (A–D) CLSM images with their corresponding radial distribution functions (RDFs) of pN-to-pN, pM-to-pM, and pN-to-pM. (A) 2 × 10^–3 M KCl, showing entropy-driven crystallinity. (B) 1.5 × 10^–3 M KCl, in a fluid phase. (C) 1.25 × 10^–3 M KCl, showing electrostatic forces-driven crystallinity. (D) Sample at 1 × 10^–3 M KCl, in an electrostatically aggregated gel. (E) Mean-square displacements (MSDs) of pN particles for all salinities, together with a line with a slope proportional to t¹ to guide the eye. The MSDs for pM are highly similar to the MSDs of pN. (F) Corresponding P(Z_eq) for all salinities. Dashed lines indicate the theoretical values corresponding to AuCu (0.33) and FCC (0.5) crystal values. Each scale bar length is 10 μm.

Figure 3

CLSM images of the same sample at different salinities, with their corresponding radial distribution functions (RDFs). (A) CLSM image at 2 × 10^–3 M KCl. (B) Corresponding RDFs of pN-to-pN, pM-to-pM, and pN-to-pM. The overlapping RDFs illustrate the random distribution of particles throughout the lattice. The RDF peaks are in accordance with the positions and relative magnitudes of those in an FCC lattice (blue, rescaled magnitudes by arbitrary factor for visibility). (C) CLSM image at 1.25 × 10^–3 M KCl. (D–F) Corresponding RDF at 1.25 × 10^–3 M KCl of (D) pN-to-pN, (E) pM-to-pM, and (F) pN-to-pM. Each RDF is shown with the corresponding peaks for AuCu-type crystals. The scale bar length is 10 μm.

Figure 4

Unit cells of (A) a single particle type FCC and (B) a AuCu crystal. The red particles represent the larger Au atoms.

Figure 5

CLSM image slices from a 3D stack, compared with Voronoi cells colored according to their q̅_l. (A, B) FCC crystal at 2.0 × 10^–3 M KCl. (C, D) AuCu crystal at 1.25 × 10^–3 M KCl. If q̅₄(equal) > 0.45 or q̅₈(equal) > 0.45, AuCu crystallinity is denoted by a blue cell; if q̅₆(all) > 0.35, but q̅₄(equal) < 0.45 and q̅₈(equal) < 0.45, FCC crystallinity is denoted by a red cell; and if q̅₆(all) < 0.35 and q̅₄(equal) < 0.45 or q̅₈(equal) < 0.45, the cell was left white, denoting an amorphous local surrounding.