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

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.

Colloids are often used as model systems in order to study various phenomena in condensed matter physics.[1] Particular attention has been devoted to the effects that interaction potentials have on the phase behavior of colloids[2,3] and to processes such as crystallization[4−8] or the mechanisms and kinetic pathways of fluid–crystal and crystal–crystal transitions.[9−11] In these contexts, colloids have been employed as an analogue of atomic systems, so that the relevant length and time scales are in a range that makes experimental investigation much simpler. The earliest investigations primarily used standard “hard” colloids such as sterically stabilized PMMA spheres.[12,13] Later, more complex particles have been studied, to explore for instance the influence of long-range electrostatic repulsions[14,15] or the effect of a short-range attraction resulting, for example, from depletion interactions in colloid–polymer mixtures.[2,16,17]

The majority of these investigations were performed with approximately monodisperse particles. Inspired by analogies with “real” atomic materials such as alloys and salts, numerous attempts have also been made to investigate binary mixtures.[18−27] However, investigating equilibrium structures in dense binary mixtures of hard spheres remains difficult, as nucleation and crystal growth may be very slow or hindered due to vitrification of the sample.[28,29] Moreover, the lack of simple annealing mechanisms and the resulting formation of crystals with many small domains make a determination of the 3D crystal structure more difficult with diffraction experiments.[30,31]

Here, the recent development of using soft particles as model systems[32−34] provides us with tools that can overcome several of these hurdles. Their weak repulsions temporarily allow particle overlap, allowing particles to overcome local energy minima and promoting crystal growth speed compared to hard spheres.[28,35] Crystallization involving soft particles has been shown to possess a larger tolerance for polydispersity,[36] and many soft particle types have inherently tunable interaction potentials,[37,38] some as a function of externally controllable parameters such as temperature.[39] Furthermore, many soft systems can be extensively modified to tailor particle behavior or simplify analysis.[40−43] For example, modifying particles with fluorescent labels allows for direct imaging using confocal scanning laser microscopy, which provides sufficient information to determine phase behavior and specific organizations and to quantify kinetics.[44,45]

In this article, we describe several crystalline phases and a crystal-to-crystal transition. We employ oppositely charged microgel particles synthesized via a synthesis method that emphasizes discernibility between particles in confocal scanning laser microscopy (CLSM). The softness of the particles allows for crystallization at very high concentrations,[3] and the thermoresponsiveness of the particles allows for additional annealing mechanisms.[46] Furthermore, these systems allow for precise fine-tuning of volume fraction and size ratio. In the absence of electrostatic interactions, i.e., at sufficiently high salt concentrations, the particles interact via soft repulsive forces.[47,48] We employ a sample geometry that allows in situ salinity control during CLSM imaging, and thus a tuning of the electrostatic contributions to the interaction potential. By applying this geometry we can easily control and analyze the phase behavior of these systems as a function of electrostatic attraction strength. Our work experimentally demonstrates the existence of multiple binary soft crystal phases and how the transition between them can be controlled using in situ control over the electrostatic interactions.

Results and Discussion

We synthesized core–shell particles with a small fluorescent core and several undyed cross-linked shells. By growing multiple shells, we achieve a thick shell with controllable size that allows good discernibility between individual particles in CLSM, while retaining the corona density distribution similar to a traditional microgel.[48] Particle characteristics can be found in Table , with negatively charged pNIPAm particles abbreviated by pN and positively charged pNIPMAm particles by pM.

Table 1

Particles Used in Experiments, with Their Polymer, Dye Type, Colors, Charge Signs, and Hydrodynamic Diameters σH at 20 °C for Final Core–Shell Particles and for Cores Only

polymer	abbreviation	dye	color	charge	σH(particle) [nm]	σH(core) [nm]
pNIPAm	pN	PM546	green	negative	280	73
pNIPMAm	pM	PM605	red	positive	336	103

Samples were prepared with partial number densities of ρpN = ρpM = 4 × 1018m–3 and were inserted in a sample cell as in Figure , designed to allow controlled in situ variation of the ionic strength during microscopical imaging. Details on design and manufacture can be found in the Materials and Methods section. The reservoir was filled with a KCl solution and left to equilibrate for at least 24 h, kept at a constant temperature of 20 °C.

Figure 1

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

In Figure A–D, we show CLSM images and their 3D radial distribution functions (RDFs) for four different salinities. The calculated RDFs are split into three components, pN-to-pN, pM-to-pM, and pN-to-pM (equal to pM-to-pN). At relatively high salt concentrations (2.0 × 10–3 M and up, Figure A), charges on the particles are sufficiently screened and the system crystallizes into a hexagonal lattice due to entropic forces. The three corresponding RDFs overlap, confirming a random distribution of pN and pM particles in the lattice. It is important to note that this crystal forms despite the size ratio of 0.83 between pN and pM, highlighting the permissiveness of crystallization in soft colloids when it comes to polydispersity[36] as compared to that in hard spheres.[49] Interestingly, the first peak of all RDFs of the high-salt crystal, and thus its lattice spacing, appears at approximately σH(pN), the hydrodynamic diameter of the smaller particle. This implies that for soft binary crystals the smaller particles govern the lattice spacing, especially when considering that the total volume fraction is significantly above the volume fraction of a hexagonal packing of spheres: based on hydrodynamic radii and number densities, the total volume fraction is ∼1.0. This confirms earlier findings, where it has been shown that dopant-quantity microgels with large radii can adopt highly compressed conformations to fit into a crystal with a much smaller lattice spacing.[36]

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(Zeq) 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.

A decrease in salinity leads to behavior increasingly dominated by electrostatic interactions, ultimately yielding aggregation and phase separation. Reducing salinity to 1.5 × 10–3 M KCl leads to melting of the entropic crystal (Figure B), caused by weak electrostatic forces driving oppositely charged particles to interpenetrate, opening free space resulting in fluid behavior. It is interesting to note here that, while colloidal attractions have been shown to lead to re-entrant melting behavior,[50] the particles’ soft repulsive potential and resulting interpenetration will cause such behavior to be enhanced, as compared to incompressible hard sphere systems. Further removal of salt to 1.25 × 10–3 M KCl allows electrostatic forces to overtake entropic contributions and causes the system to recrystallize with a specific pN–pM ordering (Figure C). An even further removal of salt induces an additional increase of electrostatic attraction and yields aggregated systems (1.0 × 10–3 M KCl, Figure D). The pN-to-pM RDF reflects the increasing electrostatic attractions, with its initial peak appearing at decreasing separations r, reflecting the larger particle interpenetration that occurs upon increasing the electrostatic attraction strength.

Mean square displacements (MSDs) for pN particles at different salinities are shown in Figure E and follow the trends as described above. MSDs for pM are highly similar to those of pN and are therefore left out for clarity. At high salinities, particles are strongly caged, with apparent particle motion below the noise threshold for this analysis method; removal of salt to 1.5 × 10–3 M KCl causes cage breaking and fluid-like behavior. The slightly subdiffusive behavior is due to the high density and electrostatic attractions. At 1.25 × 10–3 M KCl, particles are once again caged, but in larger cages than at high salinities due to pN–pM interpenetration. Further removal of salt to 1.0 × 10–3 M KCl causes irreversible aggregation, where displacement is caused by cluster diffusion.

We define Zeq as the total number of nearest neighbors of equal type divided by the total number of nearest neighbors, with P(Zeq) its probability distribution, plotted in Figure F. At high salinity, P(Zeq) is symmetric around 0.5, once again reflecting the random distribution of pN and pM particles. The weak attractions at 1.5 × 10–3 M KCl cause a preference for Zeq < 0.5. The electrostatic crystal structure at 1.25 × 10–3 M KCl, as will be discussed later, has four neighbors of equal type and eight neighbors of unequal type, reflected in the P(Zeq) peak at Zeq = 0.33. A further removal of salt and subsequent aggregation leads to a partial loss of preference for unequal particle types, caused by the amorphous nature of the aggregates.

Finally, we note that this behavior is fully reversible: bringing a sample from 2.0 × 10–3 M KCl to 1.0 × 10–3 M KCl and back to 2.0 × 10–3 M KCl causes an entropic crystal to melt, electrostatically aggregate, and re-form into entropic crystals via all described phases at intermediate salinities. Since the return to entropic crystals involves a transition via a fluid phase, remixing occurs while raising salinity, and a random distribution is obtained upon reaching 2.0 × 10–3 M KCl.

The system is thus capable of forming two different crystal structures (Figure A and C), and a change of salinity can reversibly induce a switch between these crystal phases. For the high-salt crystal at 2 × 10–3 M (shown in Figures A and 3A), a comparison with a theoretical FCC RDF confirms the FCC structure of the crystal, as seen in Figure B. In contrast to the high-salt crystal, the particles in the low-salt crystal (shown in Figures C and 3C) are no longer randomly distributed throughout the lattice, but preferentially interact with the oppositely charged particles. Accordingly, the different RDFs seen in Figures D–F, no longer overlap. These RDFs correspond well with the theoretically predicted AuCu crystal structure, with poor agreement with other AB-type binary crystal structures. A comparison between theoretical RDFs of several AB-type crystals and the experimental RDFs can be found in the Supporting Information. Note that the first peak height for the pN-to-pM RDF is significantly higher than its two equal counterparts, reflecting the strength of the electrostatic interactions that drive AuCu crystallization, overtaking entropic forces that drive FCC crystallization. In Figure , unit cells of FCC-type and AuCu-type crystal structures are depicted, made using the visualization software OVITO.[51] The AuCu lattice parameters are identical to FCC lattices (given identical particle sizes), but particle type distributions differ. Our observation of AuCu crystallinity corresponds with theoretical predictions for binary systems of weakly attracting, soft particles with size ratios between approximately 0.75 and 0.85.[52]

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.

A common method of determining the crystal phase that a particle belongs to is by calculating local bond order parameters q.[44,53] This method analyzes the local surrounding of a particle and quantifies its symmetry, with q being a measure of the local l-fold symmetrical order around a given particle. It is obtained by[54,55]where Z(i) is the number of nearest neighbors of particle i, l and m are integer indices, with l ≥ 0 and m = −l, −l + 1, ..., l – 1, l, Y(r) are the spherical harmonics, and r is a vector pointing from particle i to particle j. q(i) is transformed into q through

The FCC and AuCu lattice parameters are nearly identical, and the unit cells differ mostly by distribution of particle type; we therefore extend the analysis method by discerning three bond order parameters per particle: q(all), q(equal), and q(unequal), which are the q calculated considering respectively all particles, only equal-type particles, and only unequal-type particles in the local surrounding. The obtained experimental values were further refined by calculating the average bond order parameter q̅,[55] given byfollowed by the transformation in eq . This step suppresses individual FCC particles that randomly have surroundings similar to AuCu-type crystallinity to be designated as a particle in an AuCu phase. Order parameters for perfect FCC and AuCu crystals with identical lattice parameters are given in Table .

Table 2

Theoretical 3D Local Bond Order Parameters for FCC and AuCu Crystalsa

crystal	q4	q6	q8
FCC	0.19	0.57	0.40
AuCu (all)	0.19	0.57	0.40
AuCu (equal)	0.82	0.59	0.79
AuCu (unequal)	0.44	0.57	0.53

q for AuCu is split into q(all), q(equal), and q(unequal).

We calculate q̅ for particles in 3D CLSM volumes and visualize this by coloring the corresponding Voronoi cells. Average q̅ and standard deviations of FCC and AuCu crystals can be found in the Supporting Information. Slices from this 3D volume are shown in Figure , with Figure A,B corresponding to 2.0 × 10–3 M KCl and Figure C,D corresponding to 1.25 × 10–3 M KCl. While it is clear that this method works well for discerning between crystal phases, it is still sensitive to local ordering and defects. The quality of the bond order analysis benefits from the statistics provided by 3D CLSM data, and 2D microscopy imaging is not sensitive enough to discern between these two crystal structures. One point of interest is the fact that AuCu cells in the FCC lattice (Figure B) are generally isolated or only a few cells, while FCC cells in the AuCu lattice (Figure D) tend to be connected to other FCC cells. We attribute this to the fact that a single-particle defect in a AuCu lattice affects the local ordering for all surrounding particles, whereas several particles need to cooperate to provide the local organized surrounding of one particle in our FCC lattice. Here, one should consider that varying the ionic strength also changes the free energy landscape, as the interaction potentials change from soft repulsive to attractive, which should also influence the distribution and lifetime of defects.

Figure 5

CLSM image slices from a 3D stack, compared with Voronoi cells colored according to their q̅. (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.

Conclusions

In this work, we have demonstrated the feasibility of binary mixtures of soft colloids for forming multiple crystal phases, including a crystal-to-crystal transition. Combining soft particles with opposite charges yields a pathway to a sequence of structural transitions that can be controlled externally via the ionic strength of the system through a re-entrant crystal transition, i.e., from an entropic crystal, via an intermediate fluid regime, to an electrostatic attraction-driven crystal, and into an amorphous aggregated gel state at even stronger mutual attraction. Control over ionic strength is facilitated by the sample cell design, allowing for in situ access to the effective interaction potential. Particles used in this study were synthesized according to a method that enhances discernibility in CLSM compared to other synthesis procedures, while allowing control over particle size during synthesis. We benefit from the softness of these particles, as they are less prone to becoming trapped in nonequilibrium arrested states at high densities and because of their enhanced nucleation and crystal growth that facilitate in situ studies of liquid–solid and solid–solid transitions. In addition to that, the softness and interpenetrability of the particles alter the re-entrant melting behavior as compared to hard sphere systems. Finally, we have analyzed our results using local bond order parameters adapted for discerning between systems with strong crystal similarity.

It is important to note that the use of these types of binary mixtures allows for an extra dimension of tunability: heating these mixtures has the effect that pN particles decrease in size, whereas pM particles are only slightly affected.[56] By thus manipulating the size ratio, even more crystal phases are expected, and our system provides exceptional control over both temperature and salinity. Thus, the systems introduced here are a good candidate for observing multiple in situ crystal-to-crystal transitions and, therefore, help to bring about a deeper understanding of the kinetics and mechanisms of such transitions.

Materials and Methods

Chemicals

The monomers used were styrene (99%, contains 4-tert-butylcatechol as polymerization inhibitor, Sigma-Aldrich), N-isopropylacrylamide (97%, NIPAm, Sigma-Aldrich), and N-isopropylmethacrylamide (97%, NIPMAm, Sigma-Aldrich). The inhibitor was removed with active basic Al2O3 (for chromatography, VWR Chemicals). Surfactants used were sodium dodecyl sulfate (99%, SDS, Duchefa) and cetyltrimethylammonium bromide (99%, CTAB, Sigma-Aldrich). Dyes used were pyrromethene 546 (PM546, Exciton) and pyrromethene 605 (PM605, Exciton). Initiators used were potassium persulfate (99%, KPS, Sigma-Aldrich) and 2,2-azobis(2-methylpropionamidine) dihydrochloride (97%, V50, Sigma-Aldrich). Cross-linker was N,N′-methylene-bis-acrylamide (99%, BIS, Sigma-Aldrich).

Synthesis

A core–multishell particle synthesis method was developed combining elements from previous work,[48,57,58] yielding a small fluorescent core and an undyed soft shell, with a corona similar to traditional microgels.[48]

pNIPAm-interlaced polystyrene cores (PS-pN) were synthesized by purging 100 mL of Millipore-quality water (MQ-H2O) with N2 gas for 30 min at room temperature in a round-bottom flask. 27 mL of styrene was run over an Al2O3 column to remove polymerization inhibitor and was added to the round-bottom flask together with 3 g of NIPAm, 200 mg of SDS, and 22 mg of pyrromethene 546. The mixture was stirred and purged for 45 min with N2 at 75 °C, while the mixture was shielded from ambient light. 50 mg of KPS was dissolved in 2 mL of MQ-H2O, degassed, and added instantaneously to the reaction mixture. The mixture was left stirring for 24 h, filtered through glass wool, and purified through dialysis against MQ-H2O over the course of 2 weeks. Concentration was performed by centrifugation at 104g and removal of supernatant. pNIPMAm-interlaced polystyrene (PS-pM) cores were synthesized identically but replacing NIPAm with 3 g of NIPMAm, SDS with 100 mg of CTAB, pyrrhomethene 546 with 22 mg of pyrrhomethene 605, and KPS with 50 mg of V50. Dialysis of PS-pM particles was performed against 0.01 M CTAB.

The pNIPAm shells were formed by purging 360 mL of MQ-H2O with N2 gas while stirring for 30 min at room temperature in a round-bottom flask. 2.0 g of NIPAm and 138.8 mg of BIS (5 mol %) were added to the flask, and 3.56 g of 15.9 wt % suspended PS-pN was added to the mixture. The mixture was stirred and purged for 45 min with N2 while stirring at 75 °C, while the mixture was shielded from ambient light. 74.0 mg of KPS was dissolved in 4 mL of MQ-H2O and added dropwise to the solution over the course of 5 min. After an additional 5 min, a solution of 69.4 mg of BIS (2.5 mol %) in 20 mL of MQ-H2O was added dropwise to the mixture over the course of 30 min. After 4 h, the sample was filtered through glass wool and purified. Consecutive shell growths were performed by preparing a degassed reaction mixture with all previously grown core–shell particles suspended in a volume of 80% of the previous reaction volume and addition of 80% of the previously added NIPAm, primary BIS addition (5 mol %), secondary BIS addition (2.5 mol %), and KPS, following identical steps. This is required to compensate for reaction yield and to prevent secondary nucleation. The final shell required no secondary BIS addition, only the addition of 5 mol % BIS. pNIPMAm shells were grown following an identical procedure, but on pS-pM particles with 3.0 g of NIPMAm instead of NIPAm, 123.3 mg of BIS (5 mol %), and 61.7 mg (5 mol %) and 74.0 mg of V50 instead of KPS. Hydrodynamic diameters were determined from dynamic light scattering using a modulated 3D cross-correlation instrument (LS Instruments) with a 660 nm diode-pumped laser.

Sample Preparation

Number densities of stock solutions were obtained through preparing single crystals at appropriate volume fractions, imaging a volume in CLSM, followed by particle counting. Binary microgel dispersions were prepared and mixed at 20 °C and 10–3 M KCl.

Sample holders were prepared as in Figure , similar to the ones described by Sato etal.[59] A rigid, composite material (FR-4, glass-reinforced epoxy laminate) slide of dimensions 25 × 75 × 1 mm was centrally perforated with a long, thin hole of 25 × 1 mm. The hole was covered with a dialysis membrane on one side. A capillary was created covering the dialysis membrane by placing two coverslips (5 × 50 × 0.1 mm) parallel on either side of the hole and topped with a third coverslip (25 × 50 × 0.1 mm). The coverslips were glued in place with an air- and water-resistant UV glue (Thorlabs UV glue 83). The opposite side of the composite slide was fitted with a solution reservoir of a volume at least 100 times the capillary volume, with inlet and outlet tubes, and was made air and water tight using hydrophobic, malleable wax. The capillary was rinsed with MQ-H2O and excess water removed before the sample was inserted. It was then sealed with UV glue, and the reservoir was filled. Measurements can be performed with a constant flow continuously refreshing the solution in the reservoir or equilibrated at a given salinity: in this work, the latter method is used, with a minimum equilibration time of 12 h. Reversibility was tested by slowly cycling samples between low and high salinities at least three times, while checking the appearance of all states shown in Figure ; this was successful for at least three cycles in three separately prepared samples. All samples were placed in a 0.02% (w/v) NaN3 solution for 24 h per week to prevent bacterial growth.

Imaging

Samples were mounted on an inverted CLSM (Leica TCS SP5 tandem scanner) and imaged using a 100×/1.4 NA oil immersion objective. The microscope was mounted in an enclosure that allows for temperature control with a 0.2 °C maximum variance using thermostated air circulation. Using standardized image analysis and particle tracking routines,[60] particle center coordinates were obtained for mean square displacements, radial distribution functions, and nearest-neighbor analyses. The uncertainty in these coordinates is approximately 14 nm, obtained by determining particle centers of immobilized polystyrene particles over time.[61] The particle geometry, with its small fluorescent core and large undyed shell, facilitates the enhanced particle center determination. Particle coordinates were determined using methods described in earlier work[62] for at least 10 z-stacks per different salinity.