•Review of experimental, numerical, and theoretical advances in emulsion rheology•Disordered monodisperse emulsions: exemplary glassy and jammed deformable colloids•Quantitative models for key rheological properties of repulsive emulsions•Influence of composition, flow history, and structure on emulsion rheology•Material memory: shear-induced elastification, ordering, and disorderingWe review advances that have been made in the rheology of concentrated emulsions and nanoemulsions, which can serve as model soft materials that have highly tunable viscoelastic properties at droplet volume fractions near and above the glass transition and jamming point. As revealed by experiments, simulations, and theoretical models, interfacial and positional structures of droplets can depend on the applied flow history and osmotic pressure that an emulsion has experienced, thereby influencing its key rheological properties such as viscoelastic moduli, yield stress and strain, and flow behavior. We emphasize studies of monodisperse droplets, since these have led to breakthroughs in the fundamental understanding of dispersed soft matter. This review also covers the rheological properties of attractive emulsions, which can exhibit a dominant elasticity even at droplet volume fractions far below maximal random jamming of hard spheres.Download high-res image (235KB)Download full-size image

Proteins can self-assemble into a variety of exquisitely organized structures through hierarchical reaction pathways. To examine how different core shapes of proteins and entropy combine to influence self-assembly, we create systems of lithographically fabricated proteomimetic colloids, or ‘proteoids’, and explore how Brownian monolayers of mobile proteoids, which have hard interactions, self-assemble as they are slowly crowded. Remarkably, chiral C-shaped proteoids having circular heads on only one side form enantiopure lock-and-key chiral dimers; these dimers have corrugated, shape-complementary perimeters, so they, in turn, form lock-and-key arrangements into chiral dimer crystals. Time-lapse video microscopy reveals the expulsion of monomers from the growing dimer crystals through tautomerization translocation reactions which expedite the crystallization kinetics. By lithographically mutating proteoids, we also tune the types and structures of the resulting dimer crystals. Thus, rational design of sub-particle features in hard-core colloidal shapes can be used to sterically select desired self-assembly pathways without introducing any site-specific attractions, thereby generating a striking degree of hierarchical self-ordering, reminiscent of protein crystallization.

We explore the electrophoretic propagation of charged colloidal objects, monodisperse anionically stabilized polystyrene spheres, in large-pore agarose gels that have been passivated using polyethylene glycol (PEG) when a radial electric field is applied in a cylindrical geometry. By contrast to standard Cartesian gel-electrophoresis geometries, in a cylindrical geometry, charged particles that start at a ring well near the central axis propagate outward more rapidly initially and then slow down as they move further away from the axis. By building a full-ring cylindrical gel electrophoresis chamber and taking movies of scattered light from propagating nanospheres undergoing electrophoresis, we experimentally demonstrate that the ring-like front of monodisperse nanospheres propagates stably in PEG-passivated agarose gels and that the measured ring radius as a function of time agrees with a simple model that incorporates the electric field of a cylindrical geometry. Moreover, we show that this cylindrical geometry offers a potential advantage when performing electrophoretic separations of objects that have widely different sizes: smaller objects can still be retained in a cylindrical gel that has a limited size over long electrophoretic run times required for separating larger objects.

Colloidal annular sectors are a broad class of shapes that offer the interesting possibility of dimerization when osmotically compressed to high densities while undergoing Brownian motion in two dimensions (2D). Here, we lithographically create and form a stable aqueous dispersion of many microscale prismatic 270° annular sectors, and we explore their near-equilibrium behavior in a tilted 2D gravitational column. Near the top of the column where the 2D gravitational osmotic pressure Π2D is low, we observe a gas-like phase composed almost entirely of monomers. However, below the surface and deeper into the column where Π2D is higher, we observe a reaction zone where monomers and dimers coexist, followed by an arrested region containing a very high percentage of interpenetrating, lock-and-key dimers that are a racemic mixture of positive and negative chiralities. We determine particle area fractions of monomers and dimers as a function of depth and use these to obtain the system’s 2D osmotic equation of state. In the reaction zone, where dimers transiently form and break up, we also use these to calculate the equilibrium constant K associated with the monomer–dimer reaction, which increases exponentially with Π2D. This dependence can be attributed the reduction in number of accessible microstates for dimers as they become more tightly compressed.

An ideal parallelogram platelet, although achiral in 3D, has an identifiable chirality when confined in a 2D monolayer. We lithographically fabricate microscale parallelogram platelets, disperse them in an aqueous surfactant solution, and allow them to settle towards a lower glass wall. To reduce the thermal-gravitational height, we add polystyrene nanospheres as a depletion agent to create a depletion attraction between the parallelograms and the wall. Surprisingly, by increasing the volume fraction of the depletion agent, we show that a nearly enantiopure monolayer can be created. We explain this by developing a model of 2D monolayer formation based on anisotropic facial attractions; one face of a platelet is more strongly attracted to the wall than the other as a consequence of an anisotropy introduced by the lithographic process. We study enantiopure Brownian systems of parallelograms as a function of particle area fraction and show that oblique chiral crystals form at high densities. By mixing parallelogram platelets printed in opposite senses, we also dictate the chiral ratio in the monolayer over the entire possible range. This approach is not limited to parallelograms and provides a means for tuning the chiral ratio in fluctuating 2D monolayers composed of a wide variety of chiral shapes.

We show that hard, convex, lithographic, prismatic kite platelets, each having three 72° vertices and one 144° vertex, preferentially form a disordered and arrested 2D glass when concentrated quasi-statically in a monolayer while experiencing thermal Brownian fluctuations. By contrast with 2D systems of other hard convex shapes, such as squares, rhombs, and pentagons, which readily form crystals at high densities, 72° kites retain a liquid-like disordered structure that becomes frozen-in as their long-time translational and rotational diffusion become highly bounded, yielding a 2D colloidal glass. This robust glass-forming propensity arises from competition between highly diverse few-particle local polymorphic configurations (LPCs) that have incommensurate features and symmetries. Thus, entropy maximization is consistent with the preservation of highly diverse LPCs en route to the arrested glass.

Gel electrophoresis (gel–EP) has been used for decades to separate charged biopolymers, such as DNA, RNA, and proteins, yet propagation of other charged colloidal objects, such as nanoparticles, during gel–EP has been studied comparatively little. Simply introducing anionic nanoparticles, such as sulfate–stabilized polystyrene nanospheres, in standard large-pore agarose gels commonly used for biomolecules does not automatically ensure propagation or size-separation because attractive interactions can exist between the gel and the nanoparticles. Whereas altering the surfaces of the nanoparticles is a possible solution, here, by contrast, we show that treating a common type I–A low-electroendoosmosis agarose gel with a passivation agent, such as poly-(ethyleneglycol), enables charged nanoparticles to propagate through large-pore passivated gels in a highly reproducible manner. Moreover, by taking advantage of the significant optical scattering from the nanoparticles, which is not easily measurable for biopolymers, relative to scattering from the gel, we perform real-time, light-scattering, video-tracking gel–EP. Continuous optical measurements of the propagation of bands of uniformly sized nanospheres in passivated gels provides the propagation distance, L, and velocity, v, as a function of time for different sphere radii, electric field strengths, gel concentrations, and passivation agent concentrations. The steady-state particle velocities vary linearly with applied electric field strength, E, for small E, but these velocities become non-linear for larger E, suggesting that strongly driven nanoparticles can become elastically trapped in the smaller pores of the gel, which act like blind holes, in a manner that thermal fluctuations cannot overcome. Based on this assumption, we introduce a simple model that fits the measured v(E) in both linear and non-linear regimes over a relevant range of applied voltages.Graphical abstractPassivation of a large-pore agarose gel by polyethylene glycol enables charged nanospheres to propagate electrophoretically through the passivated gel when an electric field is applied. Video tracking analysis of scattered visible light from bands of differently sized nanospheres provides the propagation distance and steady-state velocity as a function of time after applying the electric field.

•Size distributions of nanospheres are measured using passivated gel electrophoresis.•An adaptive asymmetric point spread function is used to deconvolve optical images.•Multimodal mixtures of nanospheres and broadly polydisperse nanoemulsions are studied.•Electrophoretic mobility distributions of charged nanoparticles can be obtained.We image visible light scattered from dispersions of charged spherical nanoparticles propagating through a passivated agarose gel during electrophoresis. By analyzing one-dimensional light intensities along different lanes, we measure the mobility distributions of the nanoparticles and thereby infer their size distributions, which become time-independent after adequate propagation and separation have occurred. For a given large-pore passivated agarose gel, experiments using monodisperse, surfactant-free, sulfate-stabilized, polystyrene nanopheres establish the propagation distance as a function of time for a range of different sphere radii having known surface charges. As bands of monodisperse nanospheres propagate through the gel, the bands become smeared, developing asymmetric tails as some nanospheres experience additional delays compared to others of the same size. After background subtraction, these bands, including their tails, can be fit well using a modified log–normal distribution, yielding deconvolution parameters that vary with propagation distance and transit time. To demonstrate the approach for complex nanosphere dispersions, such as a multi-modal mixture or a broadly polydisperse nanoemulsion, we measure scattered light intensities as a function of propagation distance and time during gel-EP. Iterative deconvolution using a modified log–normal point-spread function, which changes shape according to propagation distance and time, directly yields unsmeared, high-resolution electrophoretic mobility distributions, from which detailed particle size distributions are inferred.

Oil-in-water emulsions composed of colloidal-scale droplets are often stabilized using ionic surfactants that provide a repulsive interaction between neighboring droplet interfaces, thereby inhibiting coalescence. If the droplet volume fraction is raised rapidly by applying an osmotic pressure, the droplets remain disordered, undergo an ergodic–nonergodic transition, and jam. If the applied osmotic pressure approaches the Laplace pressure of the droplets, then the jammed droplets also deform. Because solid friction and entanglements cannot play a role, as they might with solid particulate or microgel dispersions, the shear mechanical response of monodisperse emulsions can provide critical insight into the interplay of entropic, electrostatic, and interfacial forces. Here, we introduce a model that can be used to predict the plateau storage modulus and yield stress of a uniform charge-stabilized emulsion accurately if the droplet radius, interfacial tension, surface potential, Debye screening length, and droplet volume fraction are known.

We make an oil-in-water emulsion, which is initially stabilized using a first ionic surfactant, and mix it with a solution of a second ionic surfactant having the opposite charge, thereby inducing massively parallel droplet fusion. A transient disruption of the screened-charge repulsive barrier between interacting droplets, caused by the second ionic surfactant, arises from significant yet temporary charge neutralization of the first ionic surfactant on the surfaces of the oil droplets while mixing occurs. Interestingly, if a moderate molar excess of one surfactant exists, then the resulting emulsion re-stabilizes after limited droplet fusion. By adjusting the droplet volume fraction, concentrations of first and second surfactants, and volumes of the emulsion and the solution of the second surfactant, we control the degree of droplet coalescence and achieve a self-limiting droplet fusion process. Using optical microscopy, we observe that flat, thin, crystalline films can form between the two oil compartments after fusion of two or more immiscible microscale droplets. However, no such crystalline films are seen on the highly curved oil–oil interfaces inside nanoscale droplets that are composed of two or more immiscible oils and have been fused in the same manner, as revealed by cryogenic transmission electron microscopy.

Long-range chiral symmetry breaking (CSB) has been recently observed in 2D self-organized rhombic crystals of hard, achiral, 72 degree rhombic microparticles. However, purely entropic selection of a CSB crystal in an idealized system of hard achiral shapes, in which attractions are entirely absent and the shape does not dictate a chiral tiling, has not yet been quantitatively predicted. Overcoming limitations of a purely rotational cage model, we investigate a translational–rotational cage model (TRCM) of dense systems of hard achiral rhombs and quantitatively demonstrate that entropy can spontaneously drive the preferential self-organization of a chiral crystal composed of achiral shapes that also tile into an achiral crystal. At different particle area fractions, ϕA, we calculate the number of accessible translational–rotational microstates, Ω, of a mobile central rhomb in a static cage of neighboring rhombs, which can have different orientation angles, γ, relative to the bisector of the crystalline axes. As we raise ϕA, two maxima emerge in Ω(γ) at non-zero cage orientation angles, ±γmax. These maxima correspond to additional translational microstates that become accessible in the CSB crystalline polymorph through reduced translational tip–tip interference. Thus, entropy, often associated with structural disorder, can drive CSB in condensed phase systems of non-attractive achiral objects that do not tile into chiral structures. The success of the TRCM in explaining the entropic origin of CSB in systems of hard rhombs indicates that the TRCM will have significant utility in predicting the self-organized behavior of dense systems of other hard shapes in 2D.

We present a study of the elastic alignment, accompanying director field distortions, and elastic pair interactions of star-shaped colloids suspended in aligned nematic liquid crystals. We design and fabricate lithographic colloids, “N-stars”, containing N rod-like protrusions (i.e. “rays” or “arms”) each having a constant angle between adjacent rays. N-star geometries contain concave regions while retaining the rotational and mirror symmetries of regular polygonal platelets having N sides. Planar anchoring of the nematic director at N-star surfaces induces elastic deformations of the uniform background director, resulting in distinct orientational states and pair interactions that depend upon N. Director fields around isolated N-stars are characterized using polarized optical microscopy. For each N-star, we observe long-lived metastable orientational states with accompanying metastable director configurations, which are topologically distinct from the ground state director field. We develop a model, based on a superposition of the elastic energy of rod-like inclusions at appropriate angles to the far-field director, to estimate the energies in both cases. Numerical calculations of the director field around an individual ray elucidate the effect of azimuthal degeneracy in the anchoring and cross-sectional shape of the ray. The analytical results agree with the simulations, however, we find that the total elastic energy must be rescaled to account for weaker anchoring. The long-range elastic pair interactions between N-stars are probed using optical tweezers and video microscopy. We observe a distinct multipole depending on whether N is even or odd, which dominates the distance-dependence for attractive elastic forces between pairs of N-stars. Finally, we discuss assemblies made up of mixtures of different types of N-stars that display a variety of aggregated states.

Through extreme flow-induced fusion and rupturing of microscale droplets within a mixture of two or more oil-in-water emulsions, each having a different type of mutually immiscible oil, we create complex oil-in-water nanoemulsions composed of multicomponent compartmentalized nanodroplets. The extreme flow temporarily overcomes the repulsive barrier between oil droplets, arising from stabilizing surfactant molecules on the droplet interfaces, thereby causing multidroplet fusion as well as droplet fission down to the nanoscale. After the droplets leave the vicinity of extreme flow, they remain stable against subsequent coarsening and coalescence. Using this highly parallel, top-down, nonequilibrium synthetic approach, we create bulk quantities of engulfed-linear Cerberus oil-in-water nanoemulsions. Each Cerberus nanodroplet contains three different immiscible oils that form complex-shaped internal compartments, as revealed by cryogenic transmission electron microscopy (cryo-TEM). Within a given Cerberus nanodroplet, depending upon the interfacial tensions and relative volume fractions of the different oils, the internal oil–oil interfaces can be significantly deformed. Such multicomponent compartmentalized oil nanodroplets have the capacity of holding different types of oil-soluble cargo molecules, including fluorinated drug molecules, which have a wide variety of functional capacities and the potential for local synergistic effects. Their size range is small enough to permit a wide variety of pharmaceutical applications. As such, Cerberus nanoemulsions open up possibilities for simultaneously delivering several different types of oil-soluble drug molecules, each of which is readily soluble in at least one of the different types of immiscible oils, to the same cell or tissue.

We observe twinning of two-dimensional (2D) rhombic colloidal crystals of hard Brownian rhombic platelets. By contrast to square particles, which have higher symmetry but can also form rhombic lattices at high densities, each rhombic particle has a distinguishable bidirectional pointing axis. This key feature, which is not readily seen in rhombic crystals of square colloids, facilitates observations of different types of twinning: contact, polysynthetic, and cyclic. Moreover, we find that the twinned crystals are slightly offset spatially along their shared mirror line. In addition, the average pointing axis of the particles in a single crystal is also offset on average by a small angle, either clockwise or counterclockwise, from the average pointing axis of the rhombic lattice yielding a form of nonlocal chiral symmetry breaking. Because mirror lines between contact twins introduce only a small reduction in the total number of accessible states, compared to a perfect single crystal, twinning and piecewise linear defects are commonly observed. Thus, twinning, which is usually associated with complex compositions in certain minerals, also emerges in a simpler 2D system of entropically driven, hard, achiral objects.

Many types of colloids, including nanoemulsions, which contain sub-100 nm droplets, are dispersed in molecular and micellar solutions, especially surfactant solutions that confer stability. Since it would be desirable to measure the droplet volume fraction ϕ and surfactant concentration C of a nanoemulsion non-destructively, and since the droplet and surfactant structures are significantly smaller than the shortest wavelengths of visible light, optical refractometry could provide a simple and potentially useful approach. By diluting a silicone oil-in-water nanoemulsion having an unknown ϕ and C with pure water, measuring its refractive index n(ϕ,C) using an Abbé refractometer, and fitting the result using a prediction for n that treats the nanoemulsion as an effective medium, we show that ϕ and C can be deduced accurately over a relatively wide range of compositions. Moreover, we generalize this approach to other types of nanoemulsions in which a molecular constituent partitions in varying degrees between the dispersed and the continuous phases.

We discuss the formation, evolution, and stability of microfluidic flows involving two or more miscible fluids that have different viscosities. When two liquids that have widely different viscosities are injected into a rigid microfluidic device, their flow streams can naturally rearrange to form lubricated threads or stratified flows depending on the geometry and history of injection. An overview of two-fluid and three-fluid flow configurations in microchannels having square cross-sections is given for a variety of injection geometries. Miscible viscous fluid threads in confined microsystems can experience a range of viscous instabilities, such as folding and swirling. We show that microfluidics can be used to cause two or more instabilities to interact and co-evolve in diverging microchannels, thereby creating a variety of complex flow patterns.

Nanodroplets containing mixtures of silicone oil and squalene are dispersed in a simple aqueous surfactant solution, quenched in liquid ethane, and examined using cryogenic transmission electron microscopy (CTEM). Depending on the phase of ice that forms around the nanodroplets and on the composition of the oil mixture, nanoinclusions can be observed inside oil nanodroplets, independent of surfactant type. Our observations suggest that these nanoinclusions arise from nucleation of vapor cavities as the water freezes and expands while the oil remains liquid during the quench.

The structural evolution and rheology of dense nanoemulsion gels, which have been formed by creating strong attractions between slippery nanodroplets, are explored as a function of steady shear rate using rheological small-angle neutron scattering (rheo-SANS). For applied stresses above the yield stress of the gel, the network yields, fracturing into aggregates that break and reform as they tumble and interact in the shear flow. The average aggregate size decreases with increasing shear rate; meanwhile, droplet rearrangements within the clusters, allowed by the slippery nature of the attractive interaction, increase the local density within the aggregates. At the highest shear rates, all clusters disaggregate completely into individual droplets.

In thermal “passive” microrheology, the random Brownian motion of anisotropically shaped probe particles embedded within an isotropic viscoelastic material can be used to extract the material’s frequency-dependent linear viscoelastic modulus. We unite the existing theoretical frameworks for separately treating translational and rotational probe motion in a viscoelastic material by extending the generalized Stokes–Einstein relation (GSER) into a tensorial form that reflects simultaneous equilibrium translational and rotational fluctuations of one or more anisotropic probe particles experiencing viscoelastic drag. The tensorial GSER provides a formal basis for interpreting the complex Brownian motion of anisotropic probes in a viscoelastic material. Based on known hydrodynamic calculations of the Stokes mobility of highly symmetric shapes in a simple viscous liquid, we show simple examples of the tensorial GSER for spheroids and half-stick, half-slip Janus spheres.

We employ large-amplitude shear oscillation light scattering (SOLS) to study average droplet deformation and positional restructuring in concentrated uniform oil-in-water emulsions. Three dimensionless scattering intensity anisotropy factors, defined using the primary and secondary Bragg peaks, which can result from partial shear-induced ordering, reflect the phase-dependent droplet deformation and tilting. These factors distinguish the soft force-chain buckling regime, where shear disorders the droplets, from the sliding hexagonally-close-packed layer regime, where shear induces positional order. Near and above the jamming limit of spherical particles, the shear-induced structures depend sensitively on the droplet volume fraction and the shear history.

We have studied the transmission of visible and ultraviolet light through uniform silicone oil-in-water nanoemulsions stabilized by an anionic surfactant, sodium dodecyl sulfate (SDS), in the single-scattering limit. As the droplets become significantly smaller than 100 nm, the nanoemulsions still scatter noticeably in the ultraviolet region, yet they become progressively more transparent at visible wavelengths. This transparency can even be enhanced as the droplets are concentrated into a biliquid glass and the nanoemulsion becomes strongly elastic. From the measured transmission intensity as a function of wavelength, droplet radius, and volume fraction, I(λ,a,ϕ), we determine the extinction coefficient. Many qualitative features of the extinction coefficient can be identified using a modified structure factor based on disordered hard spheres and the Mie scattering form factor of isolated spheres. Due to the screened-charge repulsive interactions and the deformability of the droplets, there can be significant quantitative differences between the optical properties of glassy nanoemulsions and hard spheres.

Virus-like particles are biomimetic delivery vehicles that cloak nanoscale cores inside coatings of viral capsid proteins, offering the potential for protecting their contents and targeting them to particular tissues and cells. To date, encapsidation has been demonstrated only for a relatively limited variety of core materials, such as compressible polymers and facetted nanocrystals, over a narrow range of cores sizes and of pH and ionic strength. Here, we encapsidate spherical nanodroplets of incompressible oil stabilized by adsorbed anionic surfactant using cationic capsid protein purified from cowpea chlorotic mottle virus. By imaging with transmission electron microscopy we show that, as the droplets become larger than the wild-type RNA core, the protein is forced to self-assemble into spherical shells that are not perfect icosahedra having special triangulation numbers characteristic of the Caspar−Klug hierarchy. Consequently, the distribution of protein conformations on larger droplets is significantly different than in the wild-type shell.Keywords: capsid; curvature; droplet; nanoemulsion; protein; self-assembly; virus

Water-in-oil-in-water emulsions are examples of double emulsions, in which dispersions of small water droplets within larger oil droplets are themselves dispersed in a continuous aqueous phase1, 2, 3. Emulsions occur in many forms of processing and are used extensively by the foods, cosmetics and coatings industries. Because of their compartmentalized internal structure, double emulsions can provide advantages over simple oil-in-water emulsions for encapsulation, such as the ability to carry both polar and non-polar cargos, and improved control over release of therapeutic molecules4, 5, 6. The preparation of double emulsions typically requires mixtures of surfactants for stability; the formation of double nanoemulsions, where both inner and outer droplets are under 100 nm, has not yet been achieved7, 8, 9. Here we show that water-in-oil-in-water double emulsions can be prepared in a simple process and stabilized over many months using single-component, synthetic amphiphilic diblock copolypeptide surfactants. These surfactants even stabilize droplets subjected to extreme flow, leading to direct, mass production of robust double nanoemulsions that are amenable to nanostructured encapsulation applications in foods, cosmetics and drug delivery.

Many types of colloids, including nanoemulsions, which contain sub-100 nm droplets, are dispersed in molecular and micellar solutions, especially surfactant solutions that confer stability. Since it would be desirable to measure the droplet volume fraction ϕ and surfactant concentration C of a nanoemulsion non-destructively, and since the droplet and surfactant structures are significantly smaller than the shortest wavelengths of visible light, optical refractometry could provide a simple and potentially useful approach. By diluting a silicone oil-in-water nanoemulsion having an unknown ϕ and C with pure water, measuring its refractive index n(ϕ,C) using an Abbé refractometer, and fitting the result using a prediction for n that treats the nanoemulsion as an effective medium, we show that ϕ and C can be deduced accurately over a relatively wide range of compositions. Moreover, we generalize this approach to other types of nanoemulsions in which a molecular constituent partitions in varying degrees between the dispersed and the continuous phases.

Proteins can self-assemble into a variety of exquisitely organized structures through hierarchical reaction pathways. To examine how different core shapes of proteins and entropy combine to influence self-assembly, we create systems of lithographically fabricated proteomimetic colloids, or ‘proteoids’, and explore how Brownian monolayers of mobile proteoids, which have hard interactions, self-assemble as they are slowly crowded. Remarkably, chiral C-shaped proteoids having circular heads on only one side form enantiopure lock-and-key chiral dimers; these dimers have corrugated, shape-complementary perimeters, so they, in turn, form lock-and-key arrangements into chiral dimer crystals. Time-lapse video microscopy reveals the expulsion of monomers from the growing dimer crystals through tautomerization translocation reactions which expedite the crystallization kinetics. By lithographically mutating proteoids, we also tune the types and structures of the resulting dimer crystals. Thus, rational design of sub-particle features in hard-core colloidal shapes can be used to sterically select desired self-assembly pathways without introducing any site-specific attractions, thereby generating a striking degree of hierarchical self-ordering, reminiscent of protein crystallization.