Multistep Heterogeneous Nucleation in Binary Mixtures of Charged

Letter pubs.acs.org/JPCL

Multistep Heterogeneous Nucleation in Binary Mixtures of Charged Colloidal Spheres Jianing Liu,*,†,‡ Tong Shen,†,‡ Zhao Hua Yang,† Shu Zhang,† and Guang Yu Sun† †

School of Physics and Optoelectronic Engineering, Nanjing University of Information Science & Technology, Nanjing 210044, China ‡ Jiangsu Key Laboratory for Optoelectronic Detection of Atmosphere and Ocean, Nanjing University of Information Science & Technology, Nanjing 210044, China ABSTRACT: Nucleation plays a decisive role in determining the crystal structure and size distribution; however, understanding of the fundamentals of nucleation is quite limited. In particular, it is unclear whether a nucleus forms spontaneously from solution via a single- or multiple-step process. Here we show how a binary mixture of charged colloidal spheres nucleates heterogeneously on a flat substrate by means of Bragg microscopy, laser diffraction, and laser microscopy. In contrast with the conventional one-step and two-step nucleation mechanisms, a novel pathway of multistep heterogeneous nucleation under certain experimental conditions is highlighted by four steps: initial homogeneous fluid → prenucleation clusters → preordered prenucleation clusters → intermediate ordered phase → final crystal. It is expected that the obtained results would be helpful in rationalizing the rich phase behavior exhibited by the binary mixture systems and in developing better and broadly applicable nucleation models as well as in designing defect-free single-crystal alloys.

N

atomic and molecular systems in real and reciprocal space. In particular, charged colloids, as compared with sterically stabilized colloids, do have certain advantages. First, they exhibit much richer crystallization phenomena and polymorphism. Second, the long-range order appears at much lower volume fractions, even in extremely dilute dispersions under exhaustively deionized condition. Third, their particle− particle interaction is density-dependent; any change of particle density will significantly alter the surface potential and the screening length.24,25 Furthermore, when different charged colloidal particles are mixed, the particle interactions can be further tailored, and this leads to more complex spatiotemporal behavior than in the pure case.26 From this perspective, this Letter is devoted to studying the pathway of heterogeneous nucleation of binary mixtures of charged colloidal spheres on a flat substrate by conditioning particle number density and mixing ratio, which is specified by their fluid-to-crystal phase transition, the morphologies, and the growth kinetics of heterogeneous crystallization, and identifying each step of the nucleation pathway in both real-space and reciprocal-space by means of Bragg microscopy, laser diffraction, and laser microscopy. The nucleation and crystallization experiments are online performed in a closed Teflon tubing circuit system. (See Experimental Methods.) Phase Transition and Crystallization. The fluid-to-crystal phase transition is characterized by means of Bragg microscopy.

ucleation plays an important role in condensed matter physics and materials science, but its detailed nature about how a nucleus emerges from a metastable liquid has not yet been well characterized. In the context of classical nucleation theory (CNT), nucleation, in which a metastable crystalline nucleus reaches a critical size and grows into a stable crystal, occurs in a simple one-step process. However, CNT often fails in quantitative predictions of some nucleation phenomena and cannot provide more details of their pathway leading from fluids to solids owing to the simplifying assumptions.1,2 In recent years, there has been an increasing awareness that the formation of crystal phases involves nonstandard nucleation and growth processes,1−23 the most influential of which is the two-step nucleation model, dating back at least to the classical works of Ostwald in 1897.12 Such a sequential pathway, according to ten Wolde and Frenkel,13 would correspond to the formation of a highly disordered liquid droplet, followed by the formation of a crystalline nucleus inside the droplet. The alternative approaches to representing two-step or multistep nucleation model have also been discussed, such as via stable prenucleation clusters.2−4,7,14−19 So far, the nonstandard nucleation is found mostly in homogeneous nucleation, a direct experimental probing of heterogeneous nucleation, which is induced by container walls or additional particles acting as seeds, has rarely been realized not only in pure but also particularly in mixed system,7,19,20,23 despite it being usually accepted that heterogeneous nucleation will follow the kinetic law for homogeneous nucleation. Colloidal systems have proven to be very useful experimental models to understand the solidification due to the fact that their kinetics and dynamics are more accessible than those complex © XXXX American Chemical Society

Received: August 10, 2017 Accepted: September 11, 2017 Published: September 11, 2017 4652

DOI: 10.1021/acs.jpclett.7b02096 J. Phys. Chem. Lett. 2017, 8, 4652−4658

Letter

The Journal of Physical Chemistry Letters

Figure 1. Fluid-to-crystal phase transition. (a) Side-view of Bragg microscopic showing fluid-to-crystal phase transition with increasing the particle number density n. (1) homogeneous fluid, (2) freezing transition, (3) coexistence of fluid and crystal, (4) melting transition, (5) heterogeneous nucleated crystals within the moderate supersaturation zone, and (6) competitive growth of crystals from homogeneous and heterogeneous nucleation. (b) Distribution of freezing point nf and melting point nm versus mixing ratio p, respectively. Here p = nA/n = nA/(nA + nB), where nA and nB, respectively, denote the particle number density of PnBAPS68 and PS100.

Figure 2. Time-dependent crystal morphology in side view and corresponding scaling in L ≈ t α relations. (a,c) At moderate supersaturation n > nm, where growth height of crystals L depends linearly on t. (b,d) At lower supersaturation n ≤ nm, where α ≈1/2. The crystal growth kinetics. (e) v versus n at different p, where nf, nm, and v∞ correspond to p = 20%. The solid lines are the WF fitting. (f) v versus p at different n derived from the WF fitting, where the closeness of v at p = 20% for different n is marked by a dashed circle.

Figure 1a displays such a process with slightly rising particle number density n in the closed Teflon tubing circuit system. As it turns out, the heterogeneous nucleated wall crystals shine brightly. It arises because of the special nature of the Bragg scattering of visible light; that is, the interstitial spacing between Bragg reflecting planes is of the same order of magnitude as the wavelength of incident visible light. In contrast, the fluid is opaque and even dark. It can be also seen from Figure 1a that the freezing transition exhibits tiny cap-like crystallites that

locate above the walls of the sample cell and coexist with bulk fluid. This is consistent with the classical hemispherical cap model.27,28 In the case of melting transition, the tooth-like wall crystals with flaws grow from bottom-up and top-down until they fill the whole sample cell. From the characteristic morphologies, one can distinguish the freezing transition from the melting transition. The freezing and melting distribution is depicted in Figure 1b. It is worth noting that when the mixing ratio of particle number density p ≈ 20%, both 4653


Letter


20% are much smaller than that at other p. The sensitive dependence of v on p at a given n and the insensitive dependence of v on n at p = 20% is inconsistent with a fundamental view of classical crystal growth theory that crystallization proceeds via attachment of the basic monomers.36 The physical reason behind it can be attributed to the fact that, as is well known, heterogeneous crystallization is usually facilitated by foreign small seeds under certain conditions; the seeds should be compatible with the thermodynamically favored crystal structure, otherwise they would induce elastic distortions and thus impede crystal growth.37 Likewise, the seeds from the system itself, tiny clusters of a few particles, can also do the same job when they are spatially arranged into ordered structures.38,39 Hence, it seems appropriate to predict that at p = 20%, within moderate supersaturation, there may exist prenucleation clusters that behave like prestructured seeds or precursors prior to nucleation and initial crystal growth.19,20 Prenucleation Clusters and Their Preordering. Laser diffraction, laser microscopy, and Bragg microscopy techniques make it easy to study how a crystal nucleus emerges from initial homogeneous fluid. Figure 3a shows laser diffraction patterns at

freezing point nf and the melting point nm reach a minimum value. This means that at p ≈ 20% the supersaturation Δμ of solution is sufficiently promoted at a given n > nm, and thus the free-energy barrier needed for heterogeneous nucleation is most effectively reduced and nucleation will be substantially enhanced. Because the effects of a substrate on nucleation are supersaturation-dependent, if the supersaturation is too high, then substrates, in fact, exert a negative impact on the surface integration. The so-called shadow effect of the substrate on nuclei growth will slow the nucleation kinetics and weaken the effect of reduced nucleation barrier, resulting in a supersaturation-driven interfacial structural mismatch.29 As is commonly suggested, the thermodynamic supersaturation is directly reflected in Δμ = B(n − nf)/nf, where B is the fitting constant.30−32 Therefore, it is necessary, by controlling n, to determine an appropriate supersaturation condition for heterogeneous nucleation and crystal growth to achieve a better structural match and synergy between colloidal melt and substrate and thus to obtain an ordered crystal structure. From the direct observations above, one can pick out a moderate supersaturation zone where n ranges from 6 to 8 μm−3. Within this range, only heterogeneous nucleation occurs (Figure 1a (5)), while beyond the upper limit of the range, a highly competitive growth of crystal resulting from homogeneous nucleation and heterogeneous nucleation is inevitable (Figure 1a (6)). Indeed, as soon as the suspension is prepared in such a zone, the crystal surface appears to be sufficiently smooth (Figure 2a). Crystal Growth Kinetics. Figure 2a,b displays the timedependent morphologies and kinetics of wall crystal growth when n > nm and nf < n < nm, respectively, from which it can be derived that the time t-dependent crystal height L typically grows in a power law fashion L ∝ tα, where α is the growth exponent. By the experimental fits, a direct description of concrete aspects of the kinetics of crystal growth is brought out. In the case where n > nm, there is α ≈ 1; as shown in Figure 2c, an interface-limited mechanism is responsible for crystal growth,33 while for nf < n < nm, the L is linearly dependent on the square-root of time (Figure 2d); it can be concluded that when the system is quenched into the fluid and crystal coexistence region, the growth becomes interface diffusive. From the L ≈ t relations, one can further deduce the crystal growth rate v by the v = ΔL/Δt, as illustrated in Figure 2c, and the v distributions over n at different p are shown in Figure 2e. Theoretically, the dependence of v on n and p can be modeled by the Wilson−Frenkel (WF) law34,35

Figure 3. Prenucleation clusters and their preordering under sample condition p = 20% and n ≈ 6.8 μm−3. (a) Laser diffraction pattern of prenucleation clusters at t ≈ 10s. The four spots marked in the circle correspond to a tetrahedral cluster, as schematically depicted in the inset. (b) Laser microscopy at t ≈ 10s showing cubic-like structures, highlighted by white cubic lines. (c) Bragg microscopy in top view at t ≈ 12s, indicating the coexistence of preordered cubic-like clusters and fluid phase. Scale bar is 1 μm.

time t ≈ 10s after cessation of shear under sample condition p = 20% and n ≈ 6.8 μm−3. The visible four diffraction spots that are marked in the circle determine the appearance of a shortrange ordered cluster, and the nearly symmetrical distribution of these clusters indicates that they are arranged in a long-range ordered layer structure, which is very similar to the diffraction from a 2D grating. Because the geometric arrangement of the spots in the pattern reflects the surface crystallographic structure, the four spots, which correspond to four lattice planes, designate a simplest tetrahedral cluster, as schematically depicted in the inset of Figure 3a, in which the four charged colloidal spheres are bonded to each other into a stable growth unit with a comparatively high density of packing and consequently low energy. It is tempting to interpret the stable tetrahedral cluster as an elementary structural building block40 or a prenucleation cluster with “molecular” characterization in solution14 in studying short-range order and transition to longrange order of condensed phases. Because the cluster−cluster interaction is essentially controlled and stabilized by the Yukawa repulsion, such a prenucleation cluster cannot grow into larger aggregate, but how the clusters are tetrahedrally

v = v∞(1 − exp(Δμ/kBT ))

where v∞ is the limiting growth rate corresponding to infinite supersaturation and kBT is the thermal energy. Figure 2e shows a numerical calculation of how WF law matches the data on the v distributions over n. As we have seen, when n > nm, it fits nicely with them, but for nf < n < nm, apparently, it is not the case. From such a result it seems reasonable to ascertain that WF law is more appropriate for the treatment of interfacecontrolled growth rather than diffusion-controlled growth. Furthermore, to justify the dependence of v on p, the WF fits in Figure 2e can be easily converted into v−p plots in some specified n within moderate supersaturation. Figure 2f features the correlation between v and p. There are two important observations. On the one hand, for a given n, the v at p = 20% increases more dramatically than that at other p. The other involves that, as n increases, the differences between v at p = 4654


Letter

The Journal of Physical Chemistry Letters brought into being is not quite clear. It has been suggested that they may be driven to such configuration in a variety of ways, for instance, short-range attractive interactions being complemented by long-range repulsive interactions,41,42 spherical symmetrical packing,43 depletion-induced attraction,44 and dynamic arrest.45,46 Phenomenologically, the formation of the clusters takes at least two successive stages. First, by spinodal decomposition, the homogeneous suspension of the binary mixture, after cessation of shear, spontaneously fluctuates into two coexisting phases. One is richer in the condensable component, and the other is poorer. From p = 20% and n ≈ 6.8 μm−3, one can then get the particle number density of PnBAPS68 and PS100: nA = 1.36 μm−3 and nB = 5.44 μm−3. It follows that nA is much lower than the nf of PnBAPS68 and nB is higher than the nf of PS100 (Figure 1b). The asymmetric supersaturation leaves the system at an unstable equilibrium state, from which it phase-separates into domains of two locally stable phases. That is to say, PS100 will be segregated out from PnBAPS68, resulting in a higher PS100-rich domain, in which prenucleation clusters are triggered. By contrast, in PnBAPS68rich domain the fluid phase is predominant. Second, because the overlap volume of the depletion layers of a wall and a sphere is almost twice as large as that of two spheres,47 such prenucleation clusters grow preferentially on the unstructured flat substrate and, subsequently, are densified and then construct the ordered layer structure by intercluster interactions, where they will act, in effect, as seed-like precursors and promote nucleation. Such a result is shown in Figure 3b, where the laser microscopy at t ≈ 10s verifies the existence of the preordered layer of cubic-like constructions. Furthermore, from Bragg microscopy at t ≈ 12s in Figure 3c, one can still observe that prenucleation clusters coexist with fluid phase, where these clusters have been self-assembled into a network. Principally, the substrate-induced cubic-like structures will largely dominate the course of future nucleation. After sedimentation of PS100 particle is finished, PnBAPS68 particles start to precipitate on top of the interface between preordered PS100 and fluid parts and couple themselves to the preordered structure and no longer remain suspended in the solution. Just like the substrateinduction effect, the surface of preordered structure also plays a seed-like role in PnBAPS68 orientation selection, giving rise to a “right” structure of PnBAPS68, which is similar to the preordering of PS100 cluster. It can easily be shown from the laser microscopy at t ≈ 20s (Figure 4a) that the two cubic-like metastable phases coexist, in which the two different colors that originate from Bragg diffraction reflect their different lattice constants. As discussed above, the binary mixture typically undergoes a doubled heterogeneous nucleation; that is, first it happens at the vicinity of flat wall and then at the preordered structure−liquid interface.48 Intermediate Phase and Single-Crystal Alloy. Figure 4b displays two symmetric diffraction stripes with different scattering angles θ1 ≈ 70° and θ2 ≈ 79.5°. Theoretically, the scattering angle can be used to determine the facet of precritical nuclei.49 According to Bragg’s law, the modulus of the scattering vector q is associated closely with the scattering angle θ and the wavelength λ and satisfies

Figure 4. Multistep heterogeneous nucleation of binary mixtures under sample condition p = 20% and n ≈ 6.8 μm−3. (a) Laser microscopy of two coexisting metastable cubic-like phases at t ≈ 20s. (b) Two symmetric diffraction stripes with scattering angles θ1 ≈ 70° and θ2 ≈ 79.5° at t ≈ 20s. (c) Laser microscopy of single crystal at t ≈ 60s. (d) Scattered image of the single-crystal alloy at t ≈ 60s. (e) Bragg microscopy of the bcc alloy in top view at t ≈ 63s. (f) Schematic of the AB4 bcc-alloy and corresponding lattice structure. Scale bar is 1 μm.

where h, k, and l are the three Miller indices that determine lattice planes and g is the lattice constant of the crystalline. Therefore sin(θ /2) = (λ /2g )(h2 + k 2 + l 2)1/2

In general, there are three most fundamental lattice constants that associate with the particle number density, n ⎧(1/n)1/3 for simple cubic ⎪ ⎪ g = ⎨(2/n)1/3 for bcc ⎪ ⎪(4/n)1/3 for fcc ⎩

Thus, at n ≈ 6.8 μm−3, the facets of nuclei (hkl) can be easily specified by giving θ: θ1 ≈ 70° for (100) of the simple cubic and θ2 ≈ 79.5° for (110) of the bcc. This result implies that nuclei have a mixed character of simple cubic and bcc. The coexistence of phases persists until the formation of final crystals. The laser microscopy at t ≈ 60s displays a rearrangement of the lattice planes; the two different colors shown in Figure 4a have now changed into one color (Figure 4c). It means that the two different cubic-like structures fluctuate, squeeze, and interpenetrate each other into a stable single-crystal structure. This can be made clearer by the scattered image at t ≈ 60s (Figure 4d), obtained by injecting the laser beam (red arrows) through the 2 mm × 100 mm plane into sample cell with a tilted angle. Those apparent multiple parallel lines, marked by white arrows, reflect two typical features of the internal order of colloidal arrangements. First, the direction and the periodic repetitions of the scattering lines signify that colloids are spatially arranged in a proper order. Second, the multiple overlapping of the scattering lines indicates that the crystal nuclei have two types of colloids that locate on their respective parallel planes with certain spacing. This means that the crystal nuclei take the form of an alloy structure.

q = (4π /λ)sin(θ /2) With respect to crystal structure, the Bragg peaks are given by q = (2π /g )(h2 + k 2 + l 2) 4655


Letter

The Journal of Physical Chemistry Letters Finally, the structure of the alloy is determined by means of Bragg microscopy. In Figure 4e, when t ≈ 63s, the angle ϕ between a stripe of the pattern and a shear direction matches well with the angle 54.7° between (110) plane and direction in the bcc. Therefore, it turns out as a whole that the crystal shares the geometric feature of the bcc structure, as schematically depicted in Figure 4f, left. From this fact it can be inferred that such an ordered bcc structure typically consists of two interpenetrating simple-cubic lattices, with prenucleated clusters of PS100 occupying one sublattice and PnBAPS68 the other, attached to each other (Figure 4f, right), and the stoichiometric composition in this crystal alloy structure can be given as AB4, where A and B represent PnBAPS68 and PS100, respectively. A common effect of the long-ranged Yukawa repulsion and short-ranged attraction should be responsible for the stability of the single crystal alloy. To summarize, in the work presented here, given the fixed charge ratio and the size ratio, by specifying the mixing ratio of binary charged colloidal systems, we reveal a nonclassical multistep heterogeneous nucleation, which follows four different stages. These are (1) initial homogeneous fluid → (2) prenucleation clusters → (3) preordered prenucleation clusters → (4) intermediate ordered phase → (5) final crystal. There are, however, crucial differences from the two-step mechanism. On the one hand, step (2) replaces homogeneous disordered dense liquid clusters in the conventional scenario. Indeed, the dense liquid cluster is a metastable phase with respect to the solution as well as the final crystals, while prenucleation clusters are thermodynamically stable solute with “molecular” character in aqueous solution. On the other hand, it is important to note that, according to the two-step nucleation model, crystal nucleation usually occurs within the metastable dense liquid clusters, but the preordered prenucleation clusters are quite different, they can act as nucleation seeds and thus not only promote crystal nucleation but also, more importantly, give rise to heterogeneous dynamics. In this sense, the common mechanism of two-step nucleation cannot be simply transferred to the nucleation of crystals forming via prenucleation clusters. In particular, after spinodal decomposition, we find the occurrence of a doubled heterogeneous crystal nucleation process from step (2) to step (3). First, the prenucleation clusters are formed at vicinity of flat wall, and the secondary heterogeneous nucleation occurs close to the preordered structure−liquid interface. Furthermore, it is shown in step (4) that there exists a structure transformation; the two intermediate ordered phases that take the form of very similar cubic-like structures fluctuate, squeeze, and interpenetrate each other into a final stable single-crystal bcc alloy. As such, the entire system exhibits an asynchronous fluctuation of density, composition, and structure during the nucleation. We hope that the results presented here will be helpful in rationalizing the rich phase behavior exhibited by the binary mixture systems and in developing better and broadly applicable nucleation models as well as design methods for defect-free single-crystal alloys.

ZPS100 = 530 ± 28. For all experiments the size ratio and the effective charge ratio remain unchanged. Sample Preparation. Under room temperature and standard atmosphere pressure, the binary mixtures of charged colloidal sphere suspensions are prepared and diluted in double-distilled water with conductivity σ = 65 nS. The heterogeneous nucleation and subsequent crystallization are performed in a closed Teflon tubing circuit system including measuring cells and preparation units.50 The suspension is pumped unidirectionally through the circuit system connecting (1) an ion exchange chamber, which is filled with ion-exchange resin (Amberlite UP 604, Rohm & Haas, Chancy, France) secluded by two nylon film (0.2 to 0.5 μm filters, Millipore, USA) at the two ends and a parallel bypass to delete air bubbles, (2) an observable 2 mm × 10 mm × 100 mm rectangular quartz glass sample cell for optical microscopies, (3) a conductivity (electrode LTA01 and bridge WTW 531, WTW, Germany), and (4) a reservoir under Argon gas atmosphere to add further suspension or water. Within this system the samples can be exhaustively deionized during 1 h. Under this condition the particle number density n is linearly dependent on the conductivity and can be online monitored by conductivity meter. Furthermore, for binary mixtures, by controlling the total particle number density n and the corresponding mixing ratio p, one can online tune the phase behavior of system. In the circuit system, application of unidirectional shear may destroy the underlying equilibrium crystalline structure and can also lead to a reentrance ordering, which is mainly due to the fact that the elastic constants of charged spheres are about 10 orders of magnitude smaller than in conventional solids, and the colloidal solids are fragile and easily destroyed by slightest mechanical perturbation. After cessation of shear, the system will relax back to equilibrium, and nucleation and subsequent crystal growth can be studied instantaneously. Measurements. All experiments are performed by means of Bragg microscopy, laser microscopy, and laser diffraction. The first has a collimated cold light source MI-150 from Edmund Optics, Germany, whereas the last two use a laser source λ = 635 nm, 4 mW helium-neon uniphase laser from 1096 Mellon Ave., Manteca, CA. The samples are illuminated under an angle fulfilling the Bragg condition, such that the Bragg reflected light is scattered in the direction of the optical axis of the microscope. Scattering and diffraction images are recorded by a CCD camera (EHD kampro04, 1/2” SVHS, EHD Physikalische Technik, Germany) attached to an inverted microscope with a low-resolution objective (Laborlux 12, Leitz, Wetzlar, Germany). Incident light penetrates through the 2 mm × 100 mm plane or a 10 mm × 100 mm plane of the quartz sample cell; correspondingly, the images are observed from the side-view or top-view.

EXPERIMENTAL METHODS Material. The aqueous suspension of highly charged soft sphere polystyrene−poly-n-butylacrylamide copolymer with a nominal diameter of 68 nm (PnBAPS68) and carboxyl-modified polystyrene with a diameter of 100 nm (PS100) were obtained from BASF, lot no. ZK2168/7387 and Bangs lab, lot no. 3067, respectively. Their transported effective charges Z are derived from conductivity measurements: ZPnBAPS68 = 450 ± 16 and

ORCID

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

■

Jianing Liu: 0000-0001-8820-7011 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grant No. 11174075) and the Talent 4656


Letter


(22) Erdemir, D.; Lee, A. Y.; Myerson, A. S. Nucleation of Crystals from Solution: Classical and Two-step Models. Acc. Chem. Res. 2009, 42, 621−629. (23) Ganapathy, R.; Sood, A. K. Crystallization: Brought to the Surface. Nat. Phys. 2017, 13, 421−422. (24) Russel, W. B. Tunable Colloidal Crystals. Nature 2003, 421, 490−491. (25) Palberg, T. Crystallization Kinetics of Colloidal Model Suspensions: Recent Achievements and New Perspectives. J. Phys.: Condens. Matter 2014, 26, 333101. (26) Lorenz, N. J.; Schöpe, H. J.; Reiber, H.; Palberg, T.; Wette, P.; Klassen, I.; Holland-Moritz, D.; Herlach, D.; Okubo, T. Phase Behaviour of Deionized Binary mixtures of Charged Colloidal Spheres. J. Phys.: Condens. Matter 2009, 21, 464116. (27) Volmer, M. Particle Formation and Particle Action as a Special Case of Heterogeneous Catalysis. Z. Elektrochem. Angew. Phys. Chem. 1929, 35, 555. (28) Turnbull, D. Kinetics of Heterogeneous Nucleation. J. Chem. Phys. 1950, 18, 198−203. (29) Nishinaga, T. Handbook of Crystal Growth, 2nd ed.; Elsevier Link: Amsterdam, The Netherlands, 2015. (30) Zhang, K.-Q.; Liu, X. Y. In Situ Observation of Colloidal Monolayer Nucleation Driven by an Alternating Electric Field. Nature 2004, 429, 739−743. (31) Aastuen, D. J. W.; Clark, N. A.; Cotter, L. K.; Ackerson, B. J. Nucleation and Growth of Colloidal Crystals. Phys. Rev. Lett. 1986, 57, 1733−1736; 1986, 57, 2772. (32) Würth, M.; Schwarz, J.; Culis, F.; Leiderer, P.; Palberg, T. Growth Kinetics of Body Centered Cubic Colloidal Crystals. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 1995, 52, 6415− 6423. (33) Langer, J. S. Instabilities and Pattern Formation in Crystal Growth. Rev. Mod. Phys. 1980, 52, 1−28. (34) Wilson, H. A. On the Velocity of Solidification and the Viscosity of Supercooled Liquid. Philos. Mag. 1900, 50, 238. (35) Frenkel, J. Note on a Relation between the Speed of Crystallization and Viscosity. Phys. Z. Sowjetunion 1932, 1, 498. (36) Zettlemoyer, A. C. Nucleation Phenomena; Elsevier Link: Amsterdam, The Netherlands, 1977. (37) Allahyarov, E.; Sandomirski, K.; Egelhaaf, S. U.; Löwen, H. Crystallization Seeds Favour Crystallization only during Initial Growth. Nat. Commun. 2015, 6, 7110. (38) Jungblut, S.; Dellago, C. Crystallization on Prestructured Seed. Phys. Rev. E 2013, 87, 012305. (39) Hermes, M.; Vermolen, E. C. M.; Leunissen, M. E.; Vossen, D. L. J.; van Oostrum, P. D. J.; Dijkstra, M.; van Blaaderen, A. Nucleation of Colloidal Crystals on Configurable Seed Structures. Soft Matter 2011, 7, 4623−4628. (40) Ossi, P. M. Disordered Materials: An Introduction; Springer Link: Berlin, Germany, 2006. (41) Stradner, A.; Sedgwick, H.; Cardinaux, F.; Poon, W. C. K.; Egelhaaf, S. U.; Schurtenberger, P. Equilibrium Cluster Formation in Concentrated Protein Solutions and Colloids. Nature 2004, 432, 492− 495. (42) Sciortino, F.; Mossa, S.; Zaccarelli, E.; Tartaglia, P. Equilibrium Cluster Phases and Low-density Arrested Disordered States: The Role of Short-range Attraction and Long-range Repulsion. Phys. Rev. Lett. 2004, 93, 055701. (43) Schade, N. B.; Holmes-Cerfon, M. C.; Chen, E. R.; Aronzon, D.; Collins, J. W.; Fan, J. A.; Capasso, F.; Manoharan, V. N. Tetrahedral Colloidal Clusters from Random Parking of Bidisperse Spheres. Phys. Rev. Lett. 2013, 110, 148303. (44) Klix, C. L.; Murata, K.; Tanaka, H.; Williams, S. R.; Malins, A.; Royall, C. P. Novel Kinetic Trapping in Charged Colloidal Clusters due to Self-induced Surface Charge Organization. Sci. Rep. 2013, DOI: 10.1038/srep02072. (45) Niu, R.; Speck, T.; Palberg, T. Self-assembly of Colloidal Molecules due to Self-generated Flow. Phys. Rev. Lett. 2017, 119, 028001.

Founding of Nanjing University of Information Science & Technology (Grant No. S8113127001). We thank Prof. T. Palberg (Uni. Mainz, Germany) for constructive discussions and support. It is also our pleasure to acknowledge the gift of colloidal sample PnBAPS68 sent by BASF.

■

REFERENCES

(1) Vekilov, P. G. The Two-step Mechanism of Nucleation of Crystals in Solution. Nanoscale 2010, 2, 2346−2357. (2) Karthika, S.; Radhakrishnan, T. K.; Kalaichelvi, P. A Review of Classical and Nonclassical Nucleation Theories. Cryst. Growth Des. 2016, 16, 6663−6681. (3) Myerson, A. S.; Trout, B. L. Nucleation from Solution. Science 2013, 341, 855−856. (4) Sear, R. P. The Non-classical Nucleation of Crystals: Microscopic Mechanisms and Applications to Molecular Crystals, Ice and Calcium carbonate. Int. Mater. Rev. 2012, 57, 328−356. (5) De Yoreo, J. Crystal Nucleation: More than One Pathway. Nat. Mater. 2013, 12, 284−285. (6) Loh, N. D.; Sen, S.; Bosman, M.; Tan, S. F.; Zhong, J.; Nijhuis, C. A.; Král, P.; Matsudaira, P.; Mirsaidov, U. Multistep Nucleation of Nanocrystals in Aqueous Solution. Nat. Chem. 2016, 9, 77−82. (7) Lee, S.; Wi, H. S.; Jo, W.; Cho, Y. C.; Lee, H. H.; Jeong, S.-Y.; Kim, Y.-I.; Lee, G. W. Multiple Pathways of Crystal Nucleation in an Extremely Supersaturated Aqueous Potassium Dihydrogen Phosphate (KDP) Solution Droplet. Proc. Natl. Acad. Sci. U. S. A. 2016, 113, 13618−13623. (8) Kawasaki, T.; Tanaka, H. Formation of a Crystal Nucleus from Liquid. Proc. Natl. Acad. Sci. U. S. A. 2010, 107, 14036−14041. (9) Russo, J.; Tanaka, H. Nonclassical Pathways of Crystallization in Colloidal Systems. MRS Bull. 2016, 41, 369−374. (10) Guo, C.; Wang, J.; Li, J.; Wang, Z.; Tang, S. Kinetic Pathways and Mechanisms of Two-step Nucleation in Crystallization. J. Phys. Chem. Lett. 2016, 7, 5008−5014. (11) Wedekind, J.; Xu, L.; Buldyrev, S. V.; Stanley, H. E.; Reguera, D.; Franzese, G. Optimization of Crystal Nucleation Close to a Metastable Fluid-fluid Phase Transition. Sci. Rep. 2015, DOI: 10.1038/ srep11260. (12) Ostwald, W. Studien über die Bildung und Umwandlung fester Körper. Z. Phys. Chem. 1897, 22, 289−330. (13) ten Wolde, P. R..; Frenkel, D. Enhancement of Protein Crystal Nucleation by Critical Density Fluctuations. Science 1997, 277, 1975− 1978. (14) Gebauer, D.; Cölfen, H. Prenucleation Clusters and Nonclassical Nucleation. Nano Today 2011, 6, 564−584. (15) Gebauer, D.; Kellermeier, M.; Gale, J. D.; Bergström, L.; Cölfen, H. Pre-nucleation Clusters as Solute Precursors in Crystallization. Chem. Soc. Rev. 2014, 43, 2348−2371. (16) Demichelis, R.; Raiteri, P.; Gale, J. D.; Quigley, D.; Gebauer, D. Stable Prenucleation Mineral Clusters are Liquid-like Ionic Polymers. Nat. Commun. 2011, 2, 590. (17) Gebauer, D.; Völkel, A.; Cölfen, H. Stable Prenucleation Calcium Carbonate Clusters. Science 2008, 322, 1819−1822. (18) De Yoreo, J. J.; Gilbert, P. U. P. A.; Sommerdijk, N. A. J. M.; Penn, R. L.; Whitelam, S.; Joester, D.; Zhang, H.; Rimer, J. D.; Navrotsky, A.; Banfield, J. F.; et al. Crystallization by Particle Attachment in Synthetic, Biogenic, and Geologic Environments. Science 2015, 349, aaa6760. (19) Dey, A.; Bomans, P. H. H.; Müller, F. A.; Will, J.; Frederik, P. M.; de With, G.; Sommerdijk, N. A. J. M. The Role of Prenucleation Clusters in Surface-induced Calcium Phosphate Crystallization. Nat. Mater. 2010, 9, 1010−1014. (20) Arai, S.; Tanaka, H. Surface-assisted Single-crystal Formation of Charged Colloids. Nat. Phys. 2017, 13, 503−509. (21) Tan, P.; Xu, N.; Xu, L. Visualizing Kinetic Pathways of Homogeneous Nucleation in Colloidal Crystallization. Nat. Phys. 2013, 10, 73−79. 4657


Letter

The Journal of Physical Chemistry Letters (46) Royall, C. P.; Williams, S. R.; Ohtsuka, T.; Tanaka, H. Direct Observation of a Local Structural Mechanism for Dynamic Arrest. Nat. Mater. 2008, 7, 556−561. (47) Koenderink, G. H.; Vliegenthart, G. A.; Kluijtmans, S. G. J. M.; van Blaaderen, A.; Philipse, A. P.; Lekkerkerker, H. N. W. Depletioninduced Crystallization in Colloidal Rod-sphere Mixtures. Langmuir 1999, 15, 4693−4696. (48) Löwen, H.; Allahyarov, E. Doubled Heterogeneous Crystal Nucleation in Sediments of Hard Sphere Binary-mass Mixtures. J. Chem. Phys. 2011, 135, 134115. (49) Zhu, J.; Li, M.; Rogers, R.; Meyer, W.; Ottewill, R. H.; STS-73 Space Shuttle Crew; Russel, W. B.; Chaikin, P M. Crystallization of Hard-sphere Colloids in Microgravity. Nature 1997, 387, 883−885. (50) Palberg, T.; Härtl, W.; Wittig, U.; Versmold, H.; Würth, M.; Simnacher, E. Continuous Deionization of Latex Suspensions. J. Phys. Chem. 1992, 96, 8180−8183.

4658


Multistep Heterogeneous Nucleation in Binary Mixtures of Charged

Recommend Documents