The bijel is a soft composite material with unusual characteristics that make it suitable, for example, for catalysis, filtration and electrode/electrolyte applications. The name is an acronym for bicontinuous interfacially jammed emulsion gel; it is a member of the family of emulsions with interfaces stabilized by colloidal particles. Conventional particle-stabilized (Pickering–Ramsden) emulsions have a dispersed liquid phase in the form of droplets and a continuous liquid phase that surrounds them. A bijel has two continuous liquid phases that are mutually entangled in a tortuous pattern, with a particle-stabilized interface between. Bijels were originally conceived in silico and conventionally fabricated by arresting the spinodal pattern of phase-separating liquids. The purpose of this chapter is to present the bijel concept as initially developed. This provides the foundation for the more recent innovations covered in subsequent chapters. We begin by putting the bijel idea in the context of the liquid-crystal research that immediately preceded it. We then explain the practicalities of making bijels, the processing route and the characteristics of the final samples. We briefly mention related research on freeze-casting porous ceramics, which occurred in parallel and is another example of using a phase transition in a host solvent to structure colloidal particles. Finally, we highlight some very recent research on carboxysomes, where self-organization driven by phase transition kinetics is being used in a very different context.
1.1 Background
Self-assembly of colloidal components is an important means of building materials and objects from the micrometre scale upwards. It is often achieved by controlling the chemical bonds formed between the components.1 Most spectacularly, this has been implemented via the use of carefully chosen DNA segments that are attached to solid particle or droplet surfaces.2 In this case, the DNA can be directly bonded to complementary strands or via the use of linker molecules.3 The topic of this chapter is a profoundly different approach: organizing particles by using the phase transition kinetics of the host solvent. This has two advantages: firstly, the pattern of organization comes from the solvent and not from the building blocks. Hence, the same approach will work for a broad variety of starting materials. Secondly, because the approach relies on the host solvent being driven out of thermodynamic equilibrium, it is history-dependent. This makes it possible to tune the formation route via changes to parameters such as composition, quench depth, quench rate, etc. Organizing particles, by using the phase transition kinetics of the host solvent, makes it possible to achieve the same result using different particles and to controllably achieve different results using the same particles. This is a versatile approach. Towards the end of the chapter, we will see how organization via phase separation is being used to explain carboxysome formation in cyanobacteria. In this case, both specific interactions between components and generic phase separation are important.
The bijel forms when liquids that demix via spinodal decomposition are used to assemble particles. This research rose to prominence with the publication of computer simulations4 in 2005 and their subsequent experimental realization in 2007.5 However, the idea of structuring liquids using complex host solvents had been explored previously, for example, by working with composites of liquid crystals and colloidal particles. The soft matter group at the University of Edinburgh, led in turn by Pusey, Cates and then Poon, had spent many years studying dispersions of sterically stabilized poly(methyl methacrylate) colloidal particles (PMMA): firstly, as model hard spheres and, secondly, with non-adsorbing polymers as a model of colloidal depletion interactions. Meeker, Poon and collaborators went on to examine the behaviour of PMMA particles in a highly unconventional solvent.6 Meeker et al. used a low-molecular-weight liquid crystal 4-n-pentyl-4′-cyanobiphenyl (5CB) that exhibits an isotropic to nematic phase transition at TIN ≈ 35 °C. The experiments using ∼5 vol% of particles revealed that a particle network formed during the temperature quench and that this conveyed great mechanical strength to the liquid crystal (Figure 1.1). Subsequent research explored the details of the network, its properties and its formation.7
Network formation in a sample of 5CB with φw = 0.05 of σ = 0.7 µm PMMA particles cooled through the isotropic–nematic transition at TIN down to T = 15 °C. After five minutes at this temperature, the samples were removed from the temperature stage. The resulting network structure was studied via fluorescence confocal microscopy using a Nikon microscope and the 488 nm line of an Ar-ion laser.
Network formation in a sample of 5CB with φw = 0.05 of σ = 0.7 µm PMMA particles cooled through the isotropic–nematic transition at TIN down to T = 15 °C. After five minutes at this temperature, the samples were removed from the temperature stage. The resulting network structure was studied via fluorescence confocal microscopy using a Nikon microscope and the 488 nm line of an Ar-ion laser.
The research on 5CB–PMMA composites set the scene for the bijel project. The phase transition kinetics of the host solvent and the relationship between the particles and the ordered and disordered phases play crucial roles in structure self-organization. In the isotropic phase, molecular orientation is random, whereas, in the nematic phase, the molecules have a preference for alignment along a specific axis. On cooling, nuclei of ordered nematic appear and begin to confine the PMMA particles in the residual isotropic phase due to the elastic energy penalty of leaving a PMMA particle in a well-ordered nematic region. The nuclei progressively coarsen, which ultimately confines the particles in high volume fraction strands with disordered liquid crystal in the interstices.
At a conceptual level, the isotropic–nematic transition is characterized by a non-conserved order parameter. Once the phase transition has gone to completion, none of the high temperature disordered (isotropic) phase remains. Hence, particle network formation is what occurs as the particles are excluded from the ordered regions. The bijel project was then launched as the result of Cates (then also at the University of Edinburgh) asking the question: what would happen to particles dispersed in the disordered phase of a system characterized by a conserved order parameter? He then articulated some of the ideas subsequently researched and described in this book as claims in a patent filed in 2006.8 At a transition with a conserved order parameter the aspects of the system that will go on to form the ordered phase already exist in the disordered phase. Phase-separating liquids are an example of just such a system.4
Whether the order parameter is conserved or non-conserved has profound implications for the dynamics of the phase transition and this, in turn, is important when the transition is being employed to organize dispersed particles. When an order parameter is conserved through a phase transition, components have to move around within the sample for the order to develop.9 In phase-separating liquids, this occurs via diffusion at an early stage and is then driven by Laplace pressure gradients during late-stage coarsening.10 As a bijel begins to form, this is crucial because the incipient arrangement of particles must allow material to diffuse across the interface. Likewise, at a later stage during bijel formation the jammed particles must finally prevent large-scale flow parallel to the interface. By contrast, in a system characterized by a non-conserved order parameter, the phase transition dynamics do not involve components moving. However, this does not mean that nothing moves during the formation of, for example, liquid-crystal particle composites. As regions of the sample order, and as the order grows, the particulate component will be swept along by the ordering front. A crucial characteristic in this case is whether the particles have too much inertia to be moved by this ordering front.11
As an aside, it is important to note that it is also possible to create cellular networks, such as those observed in 5CB–PMMA composites, in partially miscible binary fluid systems (see Figure 1.2), i.e., via a transition with a conserved order parameter.12 In this case, emulsions are created via nucleation and growth following an off-critical quench of a dispersion of silica particles in an oil/alcohol mixture. Droplets of the minority phase form and particles are both swept up onto the liquid interface and trapped between the droplets. Here, the tuning of the particle wettability is not crucial and the emulsion has long-term stability from a combination of interfacial particles and a surplus population in the continuous phase. Network formation then occurs on re-warming the system towards the mixed phase. Due to creaming of the droplets, a change in (local) sample composition has occurred, with much of the continuous phase separated at the base of the sample. Hence, during warming the droplets expand, largely due to coalescence, and the particles become increasingly concentrated in the space between the droplets. A faceted network is found to form (see Figure 1.2).A similar change in sample composition, leading to network formation, can also be achieved via evaporation of one of the liquid phases from a particle-stabilized emulsion.13
Three-dimensional structure from two-photon fluorescence images of the formation of a cellular network by step-wise heating of a creamed hexane–methanol/silica emulsion: (a,c,e) vertical xz slices and (b,d,f) horizontal xy slices; the latter were taken at the heights indicated by white arrows in panels a,c,e. Sample temperature was constant for ≥3 min prior to imaging; heating rates were ∼0.1 °C min−1. Scale bars: 200 µm. Reproduced from ref. 12 with permission from the Royal Society of Chemistry.
Three-dimensional structure from two-photon fluorescence images of the formation of a cellular network by step-wise heating of a creamed hexane–methanol/silica emulsion: (a,c,e) vertical xz slices and (b,d,f) horizontal xy slices; the latter were taken at the heights indicated by white arrows in panels a,c,e. Sample temperature was constant for ≥3 min prior to imaging; heating rates were ∼0.1 °C min−1. Scale bars: 200 µm. Reproduced from ref. 12 with permission from the Royal Society of Chemistry.
Returning to bijels, there are important experimental results that pre-date the fabrication of bijels from low-molecular-weight liquids. In 1994,Gubbels et al. used carbon black particles to stabilize a blend of polyethylene and polystyrene polymers.14 They needed the carbon black particles to percolate through the sample to give good electrical conductivity. Unsurprisingly, the best blend stabilization and conductivity properties were achieved with the particles trapped at the interface between two tortuous polymer domains. In 2005, Composto and his team prepared two-dimensional bijels in thin polymer films (see Chapters 3 and 4). This geometry allowed them to explore the relationship between the morphology and the wettability of the external surfaces of the samples. While both of these projects resulted in the formation of polymer blend-based composites, the work on three-dimensional samples described below prepared bijels from low-molecular-weight liquids.5,15
1.2 Bijel Structure Formation and Particle Organization
1.2.1 Phase Transition Kinetics
The host solvent for bijel fabrication is a mixed pair of partially miscible liquids. Such liquids have a phase diagram (Figure 1.3) where a binodal line separates a mixed phase from a region where the liquids are phase separated.16 The kinetic pathway associated with phase separation depends on the proportion of the two liquids and the size of the temperature change,16 due to the existence of a spinodal line inside the demixed region. On one side of the spinodal line, the mixed phase is totally unstable; on the other side the mixed phase remains stable in response to small local fluctuations in composition. The spinodal line meets the binodal line at the critical point. A temperature change, which takes partially miscible liquids from the mixed phase across both the binodal and the spinodal lines, results in phase separation via spinodal decomposition. This can be achieved either by passing through the critical point or via a deep and fast quench at a different composition (Figure 1.3). A small change in temperature, which only takes the system across the binodal line, results in phase separation via nucleation and growth.16
Schematic of the water–lutidine phase diagram. The solid line is the binodal, the dot-dash line is the spinodal and CP indicates the critical point. Above the binodal line, the liquids phase separate; for example, heating a sample along the line of the vertical arrow results in phase separation into domains of composition A and composition B. In the presence of interfacially active particles, different heating routes will lead to the formation of different types of emulsions, as pictured above.
Schematic of the water–lutidine phase diagram. The solid line is the binodal, the dot-dash line is the spinodal and CP indicates the critical point. Above the binodal line, the liquids phase separate; for example, heating a sample along the line of the vertical arrow results in phase separation into domains of composition A and composition B. In the presence of interfacially active particles, different heating routes will lead to the formation of different types of emulsions, as pictured above.
For bijel fabrication, spinodal decomposition provides the bicontinuous arrangement of liquid domains. Lattice Boltzmann simulations were used in Edinburgh to explore phase transition dynamics in partially miscible liquids.17 This research did not initially include added particles, and was focused on establishing whether evidence existed for a cross-over between a regime of viscosity-dominated dynamics and inertia-dominated dynamics. The simulations can model the actual motion of the liquid rather than the resulting changes in the domain organization. Both were explored over an unprecedented range of length and time scales via combining the results of many different simulations.
As outlined above, the ‘spinodal’ regime can be accessed using sample compositions close to critical, or for deep and fast quenches. Here, the mixture is locally unstable to small composition fluctuations and a bicontinuous arrangement of liquid domains separated by an interface results from a phase of diffusive separation. After further separation, the local composition of the liquid domains corresponds to that of the two bulk phases found on the binodal line at this temperature. Further liquid motion is driven by variations in Laplace pressure due to interfacial curvature with location along the interface.17 The flow can result in changes in the morphology of the liquid domains via pinch-off events. The motion of the interfaces, which results from pinch-off events, changes significantly depending on whether the system is in the viscous or inertial regimes.18 Spinodal decomposition was first described mathematically by Cahn and Hilliard19 and it results in a bicontinuous arrangement of liquid domains only if the volumes of the two phases are not too different. It is thought that bicontinuity will be lost if the smallest domain occupies less than 30% of the sample volume (see Section 1.3.4).20 Without added particles, the end state is macroscopic phase separation, with the less dense phase sitting on top of the more dense phase separated by a flat interface.
It should be noted that the symmetry of the (volume fraction, temperature) phase diagram is also an important consideration in bijel fabrication. In the case of a symmetric phase diagram, the quench path in the phase diagram is vertical, and so is the symmetry line, ensuring that the volume ratio of phase-separating phases remains close to 1 : 1.21 In the case of an asymmetric phase diagram, the symmetry line is off-vertical, while the quench path remains vertical. According to the Lever rule,22 this must mean that the volume ratio of the phase-separating phases moves away from 1 : 1. In extreme cases, the volume ratio of the phase-separating phases may be so far from 1 : 1 that bicontinuity becomes hard to maintain.20,23,24 Presumably, this is why Clegg et al. struggled to produce bijels using methanol–hexane and ethanol–dodecane mixtures.25
1.2.2 Particle Trapping and Jamming
A colloidal particle that exhibits partial wettability with a pair of immiscible liquids can become trapped at the interface between them.26 For example, a particle whose surface chemistry is partially hydrophobic is likely to become trapped at an interface between a hydrocarbon liquid and water. The mechanism is that the particle removes a region of shared interface between the two liquids. If the energy cost of the particle surface in both liquids is roughly equal, then there is no additional penalty for the particle having contact with both liquids rather than just one. The depth of the energy well for a single particle at a flat interface is:
A cartoon of a particle, radius r, trapped at a liquid–liquid interface; θw is the wetting angle.
A cartoon of a particle, radius r, trapped at a liquid–liquid interface; θw is the wetting angle.
Equal wettability of the particle surfaces by the two liquid phases (neutral wetting) is especially important for bijel formation. As particles are pushed close to one another on a liquid–liquid interface, the particle wettability tends to bias the liquid interface towards adopting a particular curvature. Typically, this results in the interface bending away from the liquid that most readily wets the particle surfaces.26 In order for particles to be packed closely together on the interface between two tortuous liquid domains, the interface must be able to meander around in space.21
During bijel fabrication, a population of particles is dispersed at the critical liquid composition in the mixed phase. Phase separation via spinodal decomposition is induced via a change in temperature, leading to the appearance of a huge amount of liquid–liquid interface (relative to the total cross-sectional area of the particles). The particles begin to be swept up and irreversibly trapped; early on, the neutral wetting criterion is easily met because the compositions of the two liquid domains are very similar (Figure 1.5). As phase separation proceeds, the liquid domain size steadily expands and the amount of interface steadily decreases. Consequently, the amount of area available for the particles slowly reduces. In addition, during coarsening, the interfacial tension is steadily increasing; due to the high trapping strength, the particles cannot escape from the interfaces. Instead, they are forced into close contact, creating a jammed two-dimensional sheet28 that percolates through the bulk sample (Figure 1.5). The presence of this solidified interface prevents any further phase separation between the two liquid phases.29 The result is a permanent bicontinuous arrangement of liquid domains: the bijel.
Time series of fluorescence confocal microscopy images of a 2,6-lutidine–water sample at critical composition, with Φv = 2% particles, slowly quenched from 33.5 to 35.3 °C. Only images around the separation are shown. The Δt between images is 0.7 s. Particles appear white, whereas liquids appear dark; the difference in the shade of grey for the two domains indicates that the lighter phase contains a substantial population of residual particles (scale bar, 100 µm). The separation via spinodal decomposition is clearly visible. Reproduced from ref. 5 with permission from Springer Nature, Copyright 2007.
Time series of fluorescence confocal microscopy images of a 2,6-lutidine–water sample at critical composition, with Φv = 2% particles, slowly quenched from 33.5 to 35.3 °C. Only images around the separation are shown. The Δt between images is 0.7 s. Particles appear white, whereas liquids appear dark; the difference in the shade of grey for the two domains indicates that the lighter phase contains a substantial population of residual particles (scale bar, 100 µm). The separation via spinodal decomposition is clearly visible. Reproduced from ref. 5 with permission from Springer Nature, Copyright 2007.
The mesoscopic size of the colloidal particles (neither molecular nor macroscopic) leads to the enormous trapping strength described above, but it also has other implications. For example, the particles are relatively monodisperse spheres and hence they cannot completely cover the interface between the two liquids. The two liquid domains are permanent but are still in contact over roughly 10% of the interfacial area. This good liquid–liquid contact over an extended area has important implications for a host of potential applications.
The domain size for the final bijel is controlled via the size and concentration of the particles.30 This is because the interface is arrested in a configuration with just enough area to accommodate all of the trapped particles, i.e., more numerous particles or a fixed volume fraction of smaller particles will require greater interfacial area. As the interfacial area increases, the liquid domain size becomes correspondingly diminished. The scaling relationship between these quantities has been demonstrated for domain sizes from 1 µm to 100 µm,21 and up to 500 µm if bridged bijels are included.31 At the larger end of this range, any imperfection in the particle wettability may become increasingly difficult to avoid5 (see ref. 32 for a theoretical exploration of this behaviour).
In practice, particles interact before coming into direct contact. This can be due to familiar colloidal forces, e.g., electrostatic repulsion, van der Waals attraction and steric repulsion.33 Additionally, there are also capillary forces between particles due to the presence of the liquid–liquid interface. These result from inevitable roughness and/or heterogeneity in the particle surfaces, which lead to the liquid–liquid contact line undulating.34 Attractive interactions result from particles moving together to reduce the corresponding undulations in the liquid surface.
1.2.3 Effect of Deviations of Wettability from Neutral
A standard and effective way to achieve neutral wetting is chemical surface modification, e.g., using hexamethyldisilazane (HMDS), which has been successfully demonstrated for nitromethane–ethanediol bijels by Tavacoli et al.21 This silanization treatment replaces relatively hydrophilic Si–OH (silanol) groups on the surface of the silica particle with relatively hydrophobic Si–O–Si-(CH3)3 groups.35 This chemical modification has the benefit that the degree of silanization can be reproducibly controlled via the HMDS concentration and/or the treatment duration. Note that the reaction seems to have an early stage ∼1 h and a slower stage of the order of days,36 which means the HMDS starting concentration and treatment time must be carefully controlled in order to achieve reproducible results. Moreover, strict adherence to the drying protocol is advised, as the treatment in the case of bijel preparation typically ends with drying the particles in a vacuum oven to remove residual solvent,31 and any variation in that part of the treatment may translate into contact-angle variations (see Section 1.3.2). Furthermore, there are some indications that the HMDS treatment impedes monogellation37–39 (see Section 1.3.1). More recently, adsorbed surfactants and polymers have been used to control particle wettability in the context of Pickering emulsions and bijels (see Chapters 6, 7 and 9).
The wettability that we are attempting to control is important for both Pickering emulsions and bijels. In Pickering emulsions, transitional inversion can occur, in which, for example, a water-in-oil emulsion becomes an oil-in-water emulsion when the particle surfaces are made increasingly hydrophilic. In bijels, the wettability of the surface controls whether structure formation is possible. When the particle wettability deviates from neutral, liquid–liquid demixing results in droplet formation, i.e., spinodal decomposition alone is insufficient to give bijel formation.40 However, nanoparticles are less influenced by wettability imperfections than are microparticles.41 It turns out that this effect can be best explored via the quench rate (Figure 1.6). There is a minimum heating rate for bijel formation; heating slightly too slowly results in secondary phase separation, going more slowly still leads to complete collapse of the structure. Reeves et al. demonstrated that the minimum heating rate for bijel fabrication became two orders of magnitude slower for nanoparticles compared with microparticles.41 Figure 1.6 shows the structures formed for two different particle sizes and three different heating rates. Slow heating results in droplet formation for microparticles. Bijels continue to form with nanoparticles at slow heating rates; however, there is an increasing prevalence of thin necks. Time-resolved imaging suggests that bijels begin to form in the microparticle case but that necks begin to pinch-off within a couple of seconds thus destroying connectivity. No such pinch-off events are observed for nanoparticles. The results suggest that microparticles fail to produce bijels via slow heating because depercolation via pinch-off events occurs before the interfacial particles jam and lock-in the bicontinuous structure.
Fluorescence confocal micrographs of final-state emulsions of water and lutidine (magenta) formed using various heating rates (dT/dt), stabilized by (nearly) neutrally wetting particles (yellow) of radius r. Particle volume fraction is (a) 2.6%, (b,c) 2.2% and (d–f) 0.7%. Scale bars: 100 µm. Adapted from ref. 41, http://dx.doi.org/10.1103/PhysRevE.92.032308 with permission from American Physical Society, Copyright 2015.
Fluorescence confocal micrographs of final-state emulsions of water and lutidine (magenta) formed using various heating rates (dT/dt), stabilized by (nearly) neutrally wetting particles (yellow) of radius r. Particle volume fraction is (a) 2.6%, (b,c) 2.2% and (d–f) 0.7%. Scale bars: 100 µm. Adapted from ref. 41, http://dx.doi.org/10.1103/PhysRevE.92.032308 with permission from American Physical Society, Copyright 2015.
It is assumed that the bijels are failing for microparticles at slower quench rates because of the particle wettability being slightly suboptimal. This condition then results in the microparticles inducing a preferred curvature in the liquid interface during jamming. This curvature then leads to pinch-off events and the formation of a droplet emulsion (Figure 1.7). Nanoparticles, with the same wettability, demand a more strongly curved interface, but the driving force towards that curvature is smaller. Reeves et al. conclude that this provides mechanical leeway for the organization of smaller particles using an interface.41
Time sequences of confocal fluorescence micrographs showing water–lutidine mixtures containing (nearly) neutrally wetting particles of radius r (white) during slow heating (1 °C min−1). The particle volume fractions ϕ are (a–d) 2.1% and (e–h) 1.8%. Note (c,d) the depercolation via (encircled) pinch-off events and (e–h) the formation of a bijel (also verified down to ϕNP = 0.7%). Scale bars: 100 µm. Adapted from ref. 41, http://dx.doi.org/10.1103/PhysRevE.92.032308 with permission from American Physical Society, Copyright 2015.
Time sequences of confocal fluorescence micrographs showing water–lutidine mixtures containing (nearly) neutrally wetting particles of radius r (white) during slow heating (1 °C min−1). The particle volume fractions ϕ are (a–d) 2.1% and (e–h) 1.8%. Note (c,d) the depercolation via (encircled) pinch-off events and (e–h) the formation of a bijel (also verified down to ϕNP = 0.7%). Scale bars: 100 µm. Adapted from ref. 41, http://dx.doi.org/10.1103/PhysRevE.92.032308 with permission from American Physical Society, Copyright 2015.
Clearly, a population of particles with a very broad spread of wetting characteristics will also be a problem. Measurements of the variance in contact angle in a single batch of colloidal particles have demonstrated that this may well be a common scenario.42 In this case, a bijel will form, however, surplus particles and particle-stabilized droplets are then found in each of the liquid domains. Much recent research has focused on relaxing the demands on the particle surfaces via the combined use of colloidal particles and molecular/polymeric surfactants (see Chapters 6, 7 and 9).
In the initial bijel studies, Herzig et al. made use of adsorption to control the particle wettability of silica with respect to water and lutidine.5 Lutidine (2,6-dimethyl pyridine) is a small molecule that phase separates from water on warming above about 34 °C. The silica particles, used in these and many other experiments, typically have a layer of physi-adsorbed water on their surfaces.40 The extent of this water layer has a profound influence on the wettability of the particle surfaces. Hence, a systematic programme of drying can be used to temporarily fine-tune the particle wettability. The drying of silica surfaces has been explored extensively in the literature.43,44 At about 25 °C,the silica surface is covered with a complete layer of physically adsorbed water and there is no modification to the chemistry of the silanol groups. The silanol groups remain unmodified up to about 190 °C; however, the adsorbed layer of water is driven off by the time this temperature is reached. On further heating to 400 °C the underlying chemistry of the surfaces changes. Siloxane bridges form via a condensation reaction between silanol groups. There is disagreement in the literature concerning the temperature at which this reaction starts.
The adsorption to silica surfaces of molecules that are very similar to lutidine (both di- and tri-methylpyridines) has also been studied. The surfaces used in these studies were comparable to those employed in the above-mentioned bijel research.45,46 NMR was used to explore the molecule–surface interactions, evidencing π-bonding between the pyridine rings and the oxygen of the silanol groups or siloxane groups. This research ruled out interactions between the nitrogen lone pair and the silanol groups. Hence, the lutidine rings can be thought of as lying flat on the silica surfaces. The adsorption isotherms have characteristic steps indicating that successive layers form, presumably via π-stacking. In the absence of methyl groups the behaviour is quite different; the lone pair of the nitrogen does dominate the interaction with the surface and the rings stand up on their edge.47
It is important to note that the details of the silica drying behaviour and the adsorption of lutidine will also be modified by the presence of other chemical groups at the silica surface. When Herzig et al. prepared water–lutidine bijels, Stöber silica particles were used with no additional modification to the surface chemistry beyond that required for adding a fluorescent dye.5 Crucially, bijel formation in the water–lutidine/silica system does require functionalization of the silica particles with 3-(aminopropyl)triethoxysilane (APTES), the dye linker molecule; stable water–lutidine bijels could not be produced with plain silica.40
1.2.4 Pre-transitional Effects
1.2.4.1 Changes to the Phase Diagram
One assumption of bijel research, which has been successfully demonstrated up to volume fractions of 11.5%,21 is that it will be possible to add a large population of colloidal particles into a binary liquid system close to its binodal line, without anything changing with the equilibrium phase behaviour or the phase transition kinetics. At the most basic level, once the sample has been taken over the binodal line, the particles will act as nucleation centres for phase separation. This effect would become more pronounced if the particle surfaces are preferentially wetted by a minority phase. For a quench over the spinodal line, with neutrally wetting particles it is hoped, and presumably observed, that heterogeneous nucleation is suppressed.
1.2.4.2 Wetting, Pre-wetting and Clustering
If two partially miscible liquids are in contact with a solid surface, then at a temperature close to the critical temperature, the system will undergo a wetting transition. Between the wetting transition temperature and the critical temperature one of the liquids will perfectly wet the solid surface, i.e., the contact angle is zero and a layer of the liquid of macroscopic thickness forms. This transition occurs closer to the critical temperature (i.e., it is somewhat suppressed) on the surface of a solid sphere (the colloidal particles), compared with a flat surface, because the surface area of the wetting layer has to increase as it becomes thicker.
Combining this wetting transition with the adsorption effects described in Section 1.2.3, we find that the adsorption behaviour at silica surfaces is complex.40 At temperatures below demixing it is the lutidine that is preferentially adsorbed. This is a particularly strong effect for low lutidine concentrations, but still occurs at the critical composition. Once the critical point is crossed, one phase will completely wet the silica surface due to the wetting transition. All reports suggest that it is the water-rich phase that wets a flat silica surface. The handling of the surface can modify the temperature range of complete wetting (the upper limit reported for flat surfaces is 15 °C above the critical temperature). The wetting transition on particles in water–lutidine mixtures has been explored for polystyrene spheres.48 Here, complete wetting only occurs for a very small temperature range above phase separation, and the wetting phase changes depending on the detailed chemistry of the particle surfaces. Once the wetting transition has been left behind, the silica surfaces exhibit partial wettability with the two phases. This implies that our particle surfaces may well go through a sequence of first adsorbing lutidine, then being completely wet by water, before finally becoming partially wettable in the bijel structure.
Furthermore, while still on the mixed side of the binodal line, bijel creation can be adversely influenced by a pre-wetting transition that will result in the particles destabilizing the liquid mixture before reaching the binodal line. The coated particles then aggregate to reduce the surface area of the liquid–liquid interface. This effect has been investigated in great detail, most notably by Beysens.49 It is particularly curious because the pre-wetting is observed in a temperature range that is well beyond theoretical expectations.50 For bijel production, the important point is that, at compositions to either side of the critical point, particle aggregation due to pre-wetting can be anticipated; this is another reason that slow, off-critical quenches are typically detrimental to bijel formation. At the critical composition, aggregation via this mechanism is not expected.
1.2.4.3 Critical Casimir Effect
Critical fluctuations of the liquid composition are expected to induce particle–particle interactions approaching the critical point from the mixed phase. This is a direct analogue of the attractive interactions induced by electromagnetic fluctuations of the vacuum. The interaction is attractive if the wetting character of both particle surfaces is the same. Careful experiments by Hertlein et al. have probed this interaction for the water–lutidine system;51 furthermore, this interaction has been harnessed to enable organization of particles at a flat surface and as a model system for active colloids.52 For bijel fabrication, this effect can be minimized by moving rapidly from deep in the mixed phase to deep in the demixed phase; this avoids spending any significant time in a region of the phase diagram where particle aggregation can be anticipated.
1.3 Bijel Morphology and Characteristics
1.3.1 Appearance and Macroscopic Stability
The bijel formation route places well-defined demands on the mechanics of the particle-coated interfaces.53 This compares with the more complex mixture of shear, dilation and breakup that occurs during droplet formation during energetic mixing. To understand the mechanics of bijel formation, Thijssen and Vermant considered the behaviour of interfaces under compression, both in a trough and on the surface of a pendant drop (Figure 1.8a,b), under shear and during bending. For compression in a Langmuir trough (Figure 1.8a), both experimental data with model colloids and computer simulations are available for comparison. Particles are unlikely to be ejected from these interfaces, which begin flat. Instead, crumpling of the entire interface occurs at elevated surface pressures (Figure 1.8c). Experiments and simulations using a pendant drop geometry (Figure 1.8b) demonstrate that particle ejection can occur in this case, but tends to be localized in regions of high curvature. Under less extreme circumstances, it is found that the packing fraction needs to become very high before appreciable differences to isotropic behaviour are observed from the composite interface. Interfacial shear studies are useful for understanding the relationship between microscopic motion and macroscopic flow and for probing the emergence of solidity. Unfortunately, their relevance to bijel stability is less obvious. Bending is the final mode of distortion; as described, it has been shown to be important to bijel formation for the case of variation of mechanical leeway with particle size. Nonetheless, the bending moduli are shown to be relatively small compared with the dilational and shear moduli.
(a,b) Schematics for some interfacial rheology measurement techniques: (a) Langmuir trough and (b) pendant drop. (c) ‘Crumpling’ of a monolayer of 2.6 micrometre diameter polystyrene particles at a water–octane interface following compression in a Langmuir trough. Scale bar represent 100 micrometres. (a), (b) Reproduced from ref. 72 with permission from the Royal Society of Chemistry. (c) Adapted from ref. 71 with permission from American Chemical Society, Copyright 2000.
(a,b) Schematics for some interfacial rheology measurement techniques: (a) Langmuir trough and (b) pendant drop. (c) ‘Crumpling’ of a monolayer of 2.6 micrometre diameter polystyrene particles at a water–octane interface following compression in a Langmuir trough. Scale bar represent 100 micrometres. (a), (b) Reproduced from ref. 72 with permission from the Royal Society of Chemistry. (c) Adapted from ref. 71 with permission from American Chemical Society, Copyright 2000.
The mechanical demands placed on an interface during formation and coating with particles can be considered in the context of emulsions undergoing limited coalescence.53 This is a situation, like bijel formation, in which a partially covered interface progresses towards jamming. As droplets coalesce, there comes a point where the mechanical properties of the interfaces begin to dominate the behaviour. In addition to conventional jamming on contact, particle–particle interactions can remove the drive towards further coarsening before the interfaces become fully covered.
In the early stages of bijel formation, the interfacial tension is initially very low, in contrast to droplets undergoing limited coalescence; nonetheless, it remains quite likely that the mechanical properties of the interface are initially irrelevant.53 Imperiali et al. demonstrated, via bijel fabrication and trough studies, that in the late stages, the mechanical properties of the interface are sufficient to resist further coarsening.54 Given that the particles have significant attractive interactions in this case, this demonstration is not yet the final word. While there is evidence for some slow reorganization of the particle–laden interfaces, there is no evidence for particle ejection.37 This suggests that the keystone mechanism, in which a keystone particle is pushed off the interface due to the collective force of a large patch of particles acting upon it,55 is not important for the case of surfaces with an average mean curvature of zero.
By eye, bijel samples are opaque, homogeneous and stable for months in the terrestrial gravitational field.5 As discussed in Section 1.3.6, using a centrifuge it is possible to destroy the macroscopic homogeneity;56 furthermore, even without increasing the gravity, there is some evidence that slow local rearrangements of particle packing on the interface do occur. This was demonstrated using the water–lutidine pair by reversing the temperature quench a little while after the bijel has formed57 (see also ref. 58). The initial idea was that if the interfacial tension is holding the particles in place, presumably, once it vanishes and the liquids remix, the particles will redisperse (Remixing of liquids can occur via the interstices between particles; hence, it is not unreasonable to imagine this occurring with the particles still in place.) The observed behaviour turns out to be more complex than might initially be anticipated and it gives important insight into the nature of the particle–particle interactions.57
Sanz et al. created bijels from water–lutidine mixtures using Stöber silica particles. Once formed, the samples could be recooled to room temperature. If this cooling is carried out immediately, the particles were found to redisperse as the liquids remix. This is exactly as expected. Surprisingly, when the bijel sample is held at elevated temperature for an hour or more, recooling no longer collapses the structure. Instead, the sample is characterized by a web of locally two-dimensional colloidal monolayers.57 This is the arrangement from the bijel interfaces, but it now exists within a single-phase solvent. We call this structure the monogel.
The cause of monogel stability was explored via computer simulations. Sanz et al. took colloidal coordinates from the end-point of a lattice Boltzmann bijel simulation (Figure 1.9). The question of which particle–particle interactions would maintain this arrangement, in the absence of an interfacial tension, were then investigated using Monte Carlo simulations. Specifically, short-range isotropic interactions were compared with the combination of a short-range attraction and a long-range repulsion. It was found that the long-range repulsion was essential to the stability of the monogel. This feature of the interaction potential is essential to prevent the two-dimensional colloidal sheets from ‘rolling up’ and becoming three-dimensional clusters (Figure 1.9). It was assumed that the attraction was due to van der Waals interactions and that the repulsion was electrostatic in origin.
A slab of the initial configuration is compared with those obtained after simulating both short-range attraction/long-range repulsion (SRA/LRR) and short-range attraction (SRA) interactions and different attractive ranges λ. Adapted from ref. 57, https://doi.org/10.1103/PhysRevLett.103.255502, with permission from American Physical Society, Copyright 2009.
A slab of the initial configuration is compared with those obtained after simulating both short-range attraction/long-range repulsion (SRA/LRR) and short-range attraction (SRA) interactions and different attractive ranges λ. Adapted from ref. 57, https://doi.org/10.1103/PhysRevLett.103.255502, with permission from American Physical Society, Copyright 2009.
Further to this, Sanz et al. demonstrated that coarsening due to liquid–liquid interfacial tension, i.e., the capillary attraction, during the late stage of bijel formation would be sufficient to overcome a typical electrostatic repulsion for particles in a locally hexagonal geometry. This suggests that the waiting time for monogel formation is associated with particles rearranging locally to overcome a remnant repulsive electrostatic barrier. The formation of these permanent structures strongly depends on the choice of binary liquid.39
1.3.2 Curvature of the Particle-stabilized Interface
In order to isolate the essential physics of bijel formation, Stratford et al. simulated cylinders of liquid stabilized by a layer of interfacial particles.4 Without the rigid interface, a liquid cylinder would normally undergo the Rayleigh–Plateau instability: the cylinder breaks up into a line of spherical droplets. Bidisperse particles were used in the computer simulations to demonstrate long-term stability of this motif in the absence of crystallization of the interface (Figure 1.10).
Time evolution of a cylinder coated with bidisperse, neutrally wetting colloids. Left frame (particles shown translucent) shows the perturbed interfacial configuration shortly after initiation (5000 time steps). Instead of growing (as occurs for the particle-free cylinder via the Rayleigh–Plateau instability, culminating in pinch-off), the perturbation decays to a smaller amplitude and then arrests. Second frame, particles again translucent, after 100 000 time steps. Third frame, 200 000 time steps. There is almost no visible evolution between this and 600 000 time steps (right frame). Without particles, rupture occurs at t = tr ≈ 55 000 time steps. Reproduced from ref. 4 with permission from AAAS, Copyright 2005.
Time evolution of a cylinder coated with bidisperse, neutrally wetting colloids. Left frame (particles shown translucent) shows the perturbed interfacial configuration shortly after initiation (5000 time steps). Instead of growing (as occurs for the particle-free cylinder via the Rayleigh–Plateau instability, culminating in pinch-off), the perturbation decays to a smaller amplitude and then arrests. Second frame, particles again translucent, after 100 000 time steps. Third frame, 200 000 time steps. There is almost no visible evolution between this and 600 000 time steps (right frame). Without particles, rupture occurs at t = tr ≈ 55 000 time steps. Reproduced from ref. 4 with permission from AAAS, Copyright 2005.
Lee and Mohraz analysed stacks of confocal images to show how the mean curvature and Gaussian curvature vary, in practice, across bijel samples.59 The Gaussian curvature was found to be peaked at slightly negative values, whereas the mean curvature was centred on zero. These are the signatures of a spinodal surface. In particular, the zero mean curvature demonstrates that, on average, this is a minimal surface. The values of the mean curvature are spread over a range between ±1 µm−1, which implies that the surface is not minimal locally (Measurements using X-ray computed tomography (CT) scans confirmed these results with vastly improved statistical accuracy.58 ) To be able to sustain the variations in mean curvature, it is necessary either that the interface is jammed and solidified, or that the effective interfacial tension has vanished. An effective interfacial tension of zero results in highly dynamic, fluctuating samples; by contrast, we observe static, stable samples. Hence, the distribution of interfacial curvature is another indication of the jammed and solidified interfaces.28
1.3.3 Organization of Particles on the Interface
Compared with the stability of the structures and the curvature of the interface, the organization of the particles is relatively unexplored. Scanning electron microscopy reveals a monolayer of particles that is not well ordered. Random packing and holes are all in evidence.5,59 This presumably reflects the rapid jamming process and the possibility of ‘stickiness’ due to capillary and van der Waals attractions. This contrasts strongly with simulated particle arrangements. The lattice Boltzmann simulations, performed by Stratford et al., employed hard sphere particles, i.e., no attractions and no long-range repulsions.4
1.3.4 Demonstration that the Structure is Bicontinuous and the Distribution of Pore Sizes
Much recent work has been carried out to quantify the connectivity (and hence bicontinuity) and characteristic size distributions of the bijel structure. The bicontinuity was established, by Reeves et al., using X-ray CT data,58 which can survey a much larger volume of sample than has been possible traditionally using confocal microscopy. The sample surveyed was a polymerized water–lutidine bijel stabilized using 63 nm silica nanoparticles. The connectivity of the two fluid domains was demonstrated using a region-growing algorithm.60 A point was selected in each of the two domains in the lowest slice of the image stack. All connected pixels of the same colour were then labelled as belonging to the same domain (this process is illustrated in Figure 1.11). It was established that connectivity is maintained all the way across each slice and all the way through to the top surface of the sample. The proportion of pixels of either colour not connected to its domain is 0.03%. This establishes that the bicontinuity, characteristic of spinodal decomposition, is maintained when the pattern is jammed in place using interfacial particles.
Two-dimensional slices from a three-dimensional (3D) X-ray CT data set: (a)–(d) direct, i.e., channel A is white and (e)–(h) inverted, i.e., channel B is white. (a) and (e) Slice at bottom of 3D data set: the yellow/red arrow points to the initial yellow/red point before region growing of channel A and B. (b) and (f) Same as (a) and (e) but after region growing, showing (in red) all the points above the threshold connected to the initial point in (a) and (e). (c) and (g) Slice at top of 3D data set, and (d) and (h) same as (c) and (g) but after region growing, showing in red all the points above the threshold connected to the initial point in (a) and (e). Reproduced from ref. 58 with permission from the Royal Society of Chemistry.
Two-dimensional slices from a three-dimensional (3D) X-ray CT data set: (a)–(d) direct, i.e., channel A is white and (e)–(h) inverted, i.e., channel B is white. (a) and (e) Slice at bottom of 3D data set: the yellow/red arrow points to the initial yellow/red point before region growing of channel A and B. (b) and (f) Same as (a) and (e) but after region growing, showing (in red) all the points above the threshold connected to the initial point in (a) and (e). (c) and (g) Slice at top of 3D data set, and (d) and (h) same as (c) and (g) but after region growing, showing in red all the points above the threshold connected to the initial point in (a) and (e). Reproduced from ref. 58 with permission from the Royal Society of Chemistry.
Given this comprehensive display of connectivity it might be anticipated that the bijel structure is very regular. This is not the case. We have performed an assessment of the size distribution of channels in a (polymerized) water–lutidine bijel stabilized using 63 nm silica nanoparticles, via a ‘local thickness analysis’ of a corresponding X-ray CT scan. Figure 1.12a shows the resulting pore-size distribution in the polymer and air channels. First of all, note that the polymer channel is, on average, thinner than the air channel. This is because the lutidine-rich channel has been polymerized in this case59 and the volume ratio of lutidine-rich to water-rich channels is approximately 35 : 65. Secondly, the distributions are quite broad. This might reflect a range of jamming times for different regions of the interface: regions jamming fractionally later will have coarsened slightly more. Finally, the peak in the pore-size distribution between 5 and 10 µm is an artefact of the image analysis; the algorithm sometimes assigns a small local thickness to pixels (4.48 µm pixel size) at the edge of the channels (see Figure 1.12b).
(a) The pore-size distribution in the polymer and air channels in a (polymerized) water–lutidine bijel stabilized using 63 nm silica nanoparticles, via a ‘local thickness analysis’ of an X-ray CT scan. (b) Analysed image to show the artefact induced by the channel edges.
(a) The pore-size distribution in the polymer and air channels in a (polymerized) water–lutidine bijel stabilized using 63 nm silica nanoparticles, via a ‘local thickness analysis’ of an X-ray CT scan. (b) Analysed image to show the artefact induced by the channel edges.
1.3.5 Conductivity Properties
Bijels have been explored as scaffolds for battery and fuel cell electrodes (see Chapter 2). Here, the two liquid channels are being repurposed to provide structural stability, together with connected pathways. Competitive values of the impedance for a solid electrolyte have been achieved, alongside improvements to the mechanical characteristics of the electrode. In spite of the acronym, the bijel is actually characterized by three continuous connected pathways, i.e., it is tricontinuous. This is because the particle layer on the interface also percolates. There are areas, especially in electrode/electrolyte applications for fuel cells and batteries, where being able to flow three different species is valuable. For example, in a Li–air battery, lithium ions, electrons and oxygen all need to flow through the electrode. Having a separate pathway for each, which meets at a three-phase contact line, is ideal. To date, research has primarily focused on using a single fluid channel as a host for a solid or liquid electrolyte.
1.3.6 Mechanical Properties, Including Tuning
The first serious investigations of the mechanical properties of the bijel were carried out by Lee et al. and involved preparing samples directly on the plate of a rheometer geometry.39 These investigations permitted a demonstration of the emergence of a yield stress during the temperature change (see Chapter 2). The yield stress was also shown to vary with the depth of the temperature quench: providing evidence for the dependence of the mechanical properties on the interfacial tension. Aspects of monogel formation and its variation with the choice of partially miscible liquids were also apparent from these experiments. Bijel rheology, in particular the annealing time and the formation of monogels, was further explored in non-polar bijels by Bai et al.61
The bijel structure is locked in place because the trapped particles become jammed on the interface as its area is reduced by coarsening. Creating more interfacial area in a bijel should unjam the particles and fluidize the sample. The process should be cyclical: if the bijel is allowed to relax, the domains will coarsen again and the interfaces should re-jam. This was first verified experimentally by Tavacoli et al. using a needle to locally perturb the bijel.21 Rumble et al. further investigated this phenomenon by studying the response of the bijel to compression in a centrifuge. This is an alternative approach to mechanical testing, which is compatible with high-resolution confocal imaging of very large regions of sample before and after perturbation.56 This makes it possible to probe in detail whether particles are being detached, and the nature of any reorganization of the structure. Rumble et al. used confocal microscopy to view the organization of the interfaces before and after compression for nitromethane–ethanediol bijels stabilized using silica particles in order to suppress monogel formation.
Centrifugal compression has previously been used to study dispersions of particles and droplets.62,63 In the case of polymeric beads, the samples were found to exhibit a maximum strain, beyond which no further compression was possible.62 With Pickering emulsion droplets, high levels of droplet deformation were induced by high centrifuge speeds.63 The droplets did not coalesce. Perhaps unsurprisingly, it is possible to destroy a bijel in a centrifuge. At speeds of 360g, the sample is transformed into two macroscopically phase-separated liquids, with a high volume fraction of particles at the base of the vial.56 It was not possible to tell whether there remained a liquid–liquid interface with the particles at the base of the vial.
At more modest centrifuge speeds (14–27g), the samples were not destroyed and more subtle effects could be interrogated. Rumble et al. used a total compression time of one hour with the sample height being measured every five minutes.56 One immediate difference compared with, for example, dispersions of droplets, is that there is no elastic recovery when the sample is removed from the centrifuge. This is presumably due to the combined influence of re-jamming of the interfaces and the existence of two continuous phases. In a dispersion, once the compression force is removed, the osmotic pressure pulls the continuous phase back down amongst the dispersed component. For the bijel, the two liquids sit above the channels with the more dense liquid in contact with the upper surface of the structure. While this liquid can potentially enter its own channels, the channels of the other solvent are closed off from it. The actual reorganization of the interfaces to close off contact with the unfavourable solvent is evident in confocal micrographs.
The sample height measurements show the bijels becoming strongly compressed initially, with the height becoming constant after ∼30 minutes. This has been explored as a function of the concentration of particles, and for a range of centrifuge speeds. For each sample, the liquid channel dimensions prior to compression, were determined. Rumble et al. analysed the height data using the theory of gels sedimenting in a gravitational field, due to Buscall and White.64 The permeability of the structure is proportional to the initial slope of the variation in height with compression duration. The empirical values are proportional to the square of the channel width, albeit with large error bars, i.e., the ease with which liquids can move through the structure depends on the interface separation.
Confocal micrographs of a bijel, compressed at 20g, show that there have been very significant changes to the organization.56 The particles remain trapped on the liquid–liquid interfaces, but the arrangement of liquid channels is now predominantly perpendicular to the axis of compression, and this anisotropy does not relax (Figure 1.13). This evidences the fact that the interfaces have unjammed, moved and re-jammed during compression. It is initially surprising that the liquid domains are not aligned with the compression direction. If they were, this would allow more ready movement of liquid out of the bijel. However, this is also the direction of the gradients in the compressive stress. By reorganizing into flat domains perpendicular to the compression, the system has minimized the variation of stress experienced by the liquid–liquid interface.
(a) Images of a compressed bijel with 5 vol% particles and an interface separation of 32 µm, which was centrifuged at 15g for 5 minutes with increasing depth in the sample, where the ethanediol rich phase is coloured magenta and the particles are coloured yellow. The scale bar is 50 µm. The bottom line is the fast-Fourier transform (FFT) of these images. (b) A graph showing the full width half maximum (FWHM) of the FFT peak obtained using a heuristic fit function versus the height from the cuvette base. The schematic shows the orientation within the sample. Inset: graph showing a peak from the FFT (red) and the respective fit functions (black). Reproduced from ref. 56 with permission from the Royal Society of Chemistry.
(a) Images of a compressed bijel with 5 vol% particles and an interface separation of 32 µm, which was centrifuged at 15g for 5 minutes with increasing depth in the sample, where the ethanediol rich phase is coloured magenta and the particles are coloured yellow. The scale bar is 50 µm. The bottom line is the fast-Fourier transform (FFT) of these images. (b) A graph showing the full width half maximum (FWHM) of the FFT peak obtained using a heuristic fit function versus the height from the cuvette base. The schematic shows the orientation within the sample. Inset: graph showing a peak from the FFT (red) and the respective fit functions (black). Reproduced from ref. 56 with permission from the Royal Society of Chemistry.
By systematically imaging many compressed samples at different heights along the sample, Rumble et al. were able to analyse changes to the structure over a small range of compressive stress. The anisotropy and characteristic length scale were found by taking the Fourier transform of the confocal micrographs.56 These consisted of a bright peak in the centre, which decayed away with increasing spatial wave vectors. The characteristic wave vector of this decay in the horizontal and vertical directions was used as a measure of the internal strain as a function of the height in the sample (Figure 1.13). The sample anisotropy was found to typically begin at a particular height in the sample, indicating that a yield stress for reorganization has been overcome. The availability of an internal length measurement also made it possible to demonstrate that the amount of liquid–liquid interfaces did not decrease during the unjamming and re-jamming process. This indicates that particles are not being stripped off the interface.
1.4 Related Research: Freeze-casting Ceramics
Creating new materials via dispersing colloids in a host solvent with a phase transition extends beyond the examples described above. This approach has been pioneered by Deville, to tailor the architecture of green bodies as precursor materials to porous ceramics, for example as fuel cells and as bone substitutes.65 Here, a very concentrated dispersion of particles is chosen; the host solvent then undergoes a freezing transition at a well-controlled rate and usually with an applied temperature gradient. This then yields the desired size and arrangement of host solvent crystals.
To adopt this approach four ingredients are needed.66 Firstly, a ceramic powder, which can be chosen from a broad range of possibilities because the fabrication route is a physical process. The possible powders include some materials of value in a biological/medical context. The second ingredient is the solvent; here, water is often used due to its convenience, safety and toxicity considerations, compatibility with biological components and because the shape of ice crystals gives access to unique morphologies. The third ingredient is any functional/biological component required for the application. This includes, for example, enzymes and antibiotics. If these are included at the very start of the process (and they survive freezing) they will then be uniformly distributed throughout the final monolith. This can be of value in sustained-release applications. Finally, there are additives that are used to control the stability of the initial powder, the solidification/morphology of the solvent crystals and the handling properties of the green body during sublimation and/or prior to any sintering step.
It is important to emphasize that the porous ceramics form due to particles being excluded from growing solid crystals of solvent. This is primarily a physical interaction and hence is typically independent of the choice of materials. The porous structure is controlled to a significant extent by the combination of the morphology of the growing solvent crystals and the size of the particles (due to their ability to pack around the crystals). An aspect of this design motif, which is perhaps surprising, is the directionality of the pores obtained under the appropriate freezing conditions. Having a well-controlled solidification direction and, hence, aligned pores are the typical conditions for fabrication. In addition, there are other morphological features that are specific to ice. Under typical experimental conditions, highly anisotropic hexagonal ice crystals form (ice 1 h). This results in the powder being organized into lamellae. For many choices of solvent there are dendrites growing from the solid crystals, which add roughness to the porous material.
So far, the picture presented is a bit idealized. In practice, there is an unavoidable gradient in the porous materials fabricated (Figure 1.14). Each begins with an unavoidable dense region with no porosity; it is suggested that this region is where amorphous ice forms initially when the sample is supercooled.66 Then, there is a second region where the anticipated nucleation and growth of crystals occurs. There are two ways of controlling the pore size. A popular approach is to create smaller pores by solidifying more quickly. This works less well for templating large pores because the suspension stability requirements become quite punishing. Using camphene and related solvents in place of water can solve this problem. This host solvent also allows further pore growth via partial recrystallization. The second approach to controlling pore sizes is to change the solid loading. The disadvantage of this route is that the mechanical properties are sacrificed at the same time.
![Showing the cross-section parallel to the solidification direction in order to indicate the initial gradient. The displacement of the solidification interface occurred from bottom to top, leaving an amorphous region at the bottom. Scale bar: 100 µm. Adapted from ref. 66 [https://doi.org/10.3390/ma3031913] under the terms of the CC BY 4.0 license [https://creativecommons.org/licenses/by/4.0/].](/view-large/figure/7864660/BK9781788015202-00001-f14.jpg)
Showing the cross-section parallel to the solidification direction in order to indicate the initial gradient. The displacement of the solidification interface occurred from bottom to top, leaving an amorphous region at the bottom. Scale bar: 100 µm. Adapted from ref. 66 [https://doi.org/10.3390/ma3031913] under the terms of the CC BY 4.0 license [https://creativecommons.org/licenses/by/4.0/].
Showing the cross-section parallel to the solidification direction in order to indicate the initial gradient. The displacement of the solidification interface occurred from bottom to top, leaving an amorphous region at the bottom. Scale bar: 100 µm. Adapted from ref. 66 [https://doi.org/10.3390/ma3031913] under the terms of the CC BY 4.0 license [https://creativecommons.org/licenses/by/4.0/].
It is normal to create porous monoliths with between 40 and 60% porosity. Below 40%, the pores are no longer continuous or interconnected; above 60% the final ceramics are too weak. There is a final consideration about the size of the particles. Cracking defects appear, which are perpendicular to the solidification direction, due to the diffusion of small particles prior to sublimation of the solvent. If the particles reorganize, then secondary nucleation of solvent crystals can occur, resulting in substructure in the monolith. In general, this feature is unhelpful and puts a lower limit on the size of particles used.
1.5 Future Directions
We have shown examples of orientational ordering, phase separation and freezing being used to organize colloidal particles. Much more recently, a debate has begun about the occurrence of protein self-organization driven by the phase separation of a host solvent in nature.67 Carboxysomes are small capsules (organelles) that exist within cyanobacteria. These bacteria are involved in the oxygen-producing photosynthesis activity of land plants. This process leads to the synthesis of sugars from carbon dioxide; it is catalysed by the enzyme rubisco, which is notorious for being slow and non-specific. Rubisco can be made to perform more effectively by concentrating the carbon dioxide in its vicinity. Various solutions have evolved to address this problem; in the case of cyanobacteria, the solution involves assembling an organelle, the carboxysome, via phase separation.
Carboxysomes are less than half a micrometre in size and have an outer shell of protein (Figure 1.15). Unlike viral capsids, these structures are not equilibrium arrangements of the components; for example, the monomers of the shell do not fit together in a unique packing arrangement. Functionally, carbon dioxide and rubisco are concentrated within the carboxysome shell allowing the efficient synthesis of sugars. This is because the conversion product (carbonic anhydrase) can escape via diffusion through the protein shell, while carbon dioxide cannot.
Cartoon of the carboxysome showing the shell (blue blocks) around a dense protein drop. Note that the shell has a preference for being flat. Details of the transport and conversion processes are also included. Reproduced from ref. 67 with permission from the Royal Society of Chemistry.
Cartoon of the carboxysome showing the shell (blue blocks) around a dense protein drop. Note that the shell has a preference for being flat. Details of the transport and conversion processes are also included. Reproduced from ref. 67 with permission from the Royal Society of Chemistry.
Computer simulations have shown that liquid–liquid phase separation plays a crucial role in carboxysome formation.68 Indeed, live-cell imaging demonstrates that a liquid-like domain of rubisco forms at an early stage in the process and will coalesce if left uncovered. The size of the carboxysome is not controlled by the interfacial curvature preferred by the protein sheets; the protein prefers a flat arrangement and ultimately forms facets around the organelle. Instead, regularly sized capsules are found to emerge reliably in a simple model that includes a cargo species that is prone to aggregation, a shell species that spontaneously forms flat, hexagonally symmetric elastic sheets and an attractive interaction between the inside of the shell and the cargo. The attraction is required to overcome the elastic energy penalty of wrapping the flat protein sheet around a curved object, and experiments support its existence.69,70 Curiously, these interactions become weaker once shell formation is complete. The described process has clear similarities to Pickering droplet formation via phase separation, where the interface is stabilized using cuboidal particles. The change from the bijel research described here is that the particle shape would impose the preference of the particles for a flat interface (Figure 1.15). This is a fascinating direction to explore in experimental model systems in the future.
Much of the research outlined above would not have been possible without the generous support of EPSRC, including the Condensed Matter Doctoral Training Centre (CM-CDT) grant number EP/G03673X/1, Scottish Enterprise (grant SE/POC/8-CHM-002), the European Commission (Marie Curie Initial Training Network COMPLOIDS no. 234810) and personal fellowships (Royal Society Industry Fellowship, Royal Society of Edinburgh/BP Trust Personal Research Fellowship, The University of Edinburgh Chancellor's Fellowship).
