Freeze-casting , also frequently referred to as ice-templating , is a technique that exploits the highly anisotropic solidification behavior of a solvent (often, but not exclusively, water) in a well-dispersed solution or slurry to controllably template directionally porous ceramics , [ 1 ] [ 2 ] [ 3 ] [ 4 ] polymers, [ 5 ] [ 6 ] metals [ 7 ] and their hybrids. [ 8 ] By subjecting a slurry to a directional temperature gradient, ice crystals will nucleate on one side and grow along the temperature gradient. The ice crystals will redistribute the dissolved substance and the suspended particles as they grow within the slurry, effectively templating the ingredients that are distributed in the slurry. [ 9 ]
Once solidification has ended, the frozen, templated composite is placed into a freeze-dryer to remove the ice. The resulting green body contains anisotropic macropores in a replica of the sublimated ice crystals and structures from micropores to nacre -like packing [ 10 ] between the ceramic or metal particles in the walls. The walls templated by the morphology of the ice crystals often show unilateral features. [ 11 ] These together build a hierarchically structured cellular structure. [ 12 ] This structure is often sintered for metals and ceramics, and crosslinked for polymers, to consolidate the particulate walls and provide strength to the porous material. The porosity left by the sublimation of solidified fluid is typically between 2–200 μm. [ 13 ]
The first observation of cellular structures resulting from the freezing of water goes back over a century, [ 14 ] but the first reported instance of freeze-casting, in the modern sense, was in 1954 when Maxwell et al. [ 15 ] attempted to fabricate turbosupercharger blades out of refractory powders. They froze extremely thick slips of titanium carbide , producing near-net-shape castings that were easy to sinter and machine. The goal of this work, however, was to make dense ceramics. It was not until 2001, when Fukasawa et al. [ 16 ] created directionally porous alumina castings, that the idea of using freeze-casting as a means of creating novel porous structures really took hold. Since that time, research has grown considerably with hundreds of papers coming out within the last decade. [ 17 ]
The principles of freeze casting are applicable to a broad range of combinations of particles and suspension media. Water is by far the most commonly used suspension media, and by freeze drying is readily conducive to the step of sublimation that is necessary for the success of freeze-casting processes. Due to the high level of control and broad range of possible porous microstructures that freeze-casting can produce, the technique has been adopted in disparate fields such as tissue scaffolds , [ 18 ] [ 19 ] photonics , [ 20 ] metal-matrix composites , [ 21 ] dentistry , [ 22 ] materials science , [ 23 ] [ 24 ] [ 25 ] and even food science . [ 26 ]
There are three possible end results to uni-directionally freezing a suspension of particles. First, the ice-growth proceeds as a planar front, pushing particles in front like a bulldozer pushes a pile of rocks. This scenario usually occurs at very low solidification velocities (< 1 μm s −1 ) or with extremely fine particles because they can move by Brownian motion away from the front. The resultant structure contains no macroporosity. If one were to increase the solidification speed, the size of the particles or solid loading moderately, the particles begin to interact in a meaningful way with the approaching ice front. The result is typically a lamellar or cellular templated structure whose exact morphology depends on the particular conditions of the system. It is this type of solidification that is targeted for porous materials made by freeze-casting. The third possibility for a freeze-cast structure occurs when particles are given insufficient time to segregate from the suspension , resulting in complete encapsulation of the particles within the ice front. This occurs when the freezing rates are rapid, particle size becomes sufficiently large, or when the solids loading is high enough to hinder particle motion. [ 4 ] To ensure templating, the particles must be ejected from the oncoming front. Energetically speaking, this will occur if there is an overall increase in free energy if the particle were to be engulfed (Δσ > 0) .
Δ σ = σ p s − ( σ p l + σ s l ) {\displaystyle \Delta \sigma =\sigma _{ps}-(\sigma _{pl}+\sigma _{sl})}
where Δσ is the change in free energy of the particle, σ ps is the surface potential between the particle and interface, σ pl is the potential between the particle and the liquid phase and σ sl is the surface potential between the solid and liquid phases. This expression is valid at low solidification velocities, when the system is shifted only slightly from equilibrium. At high solidification velocities, kinetics must also be taken into consideration. There will be a liquid film between the front and particle to maintain constant transport of the molecules which are incorporated into the growing crystal. When the front velocity increases, this film thickness (d) will decrease due to increasing drag forces. A critical velocity (v c ) occurs when the film is no longer thick enough to supply the needed molecular supply. At this speed the particle will be engulfed. Most authors express v c as a function of particle size where v c ∝ 1 R {\displaystyle v_{c}\propto {\tfrac {1}{R}}} . The transition from a porous R (lamellar) morphology to one where the majority of particles are entrapped occurs at v c , which is generally determined as: [ 3 ]
v c = Δ σ d 3 η R ( a 0 d ) z {\displaystyle v_{c}={\frac {\Delta \sigma d}{3\eta R}}\left({\frac {a_{0}}{d}}\right)^{z}}
where a 0 is the average intermolecular distance of the molecule that is freezing within the liquid, d is the overall thickness of the liquid film, η is the solution viscosity , R is the particle radius and z is an exponent that can vary from 1 to 5. [ 28 ] As expected, v c decreases as particle radius R goes up.
Waschkies et al. [ 29 ] studied the structure of dilute to concentrated freeze-casts from low (< 1 μm s −1 ) to extremely high (> 700 μm s −1 ) solidification velocities. From this study, they were able to generate morphological maps for freeze-cast structures made under various conditions. Maps such as these are excellent for showing general trends, but they are quite specific to the materials system from which they were derived. For most applications where freeze-casts will be used after freezing, binders are needed to supply strength in the green state. The addition of binder can significantly alter the chemistry within the frozen environment, depressing the freezing point and hampering particle motion leading to particle entrapment at speeds far below the predicted v c . [ 29 ] Assuming, however, that we are operating at speeds below v c and above those which produce a planar front, we will achieve some cellular structure with both ice-crystals and walls composed of packed ceramic particles. The morphology of this structure is tied to some variables, but the most influential is the temperature gradient as a function of time and distance along the freezing direction.
Freeze-cast structures have at least three apparent morphological regions. [ 30 ] At the side where freezing initiates is a nearly isotropic region with no visible macropores dubbed the Initial Zone (IZ). Directly after the IZ is the Transition Zone (TZ), where macropores begin to form and align with one another. The pores in this region may appear randomly oriented. The third zone is called the Steady-State Zone (SSZ), macropores in this region are aligned with one another and grow in a regular fashion. Within the SSZ, the structure is defined by a value λ that is the average thickness of a ceramic wall and its adjacent macropore.
Although the ability of ice to reject suspended particles in the growth process has long been known, the mechanism remains the subject of some discussion. It was believed initially that during the moments immediately following the nucleation of the ice crystals, particles are rejected from the growing planar ice front, leading to the formation of a constitutionally super-cooled zone directly ahead of the growing ice. This unstable region eventually results in perturbations, breaking the planar front into a columnar ice front, a phenomenon better known as a Mullins-Serkerka instability. After the breakdown, the ice crystals grow along the temperature gradient, pushing ceramic particles from the liquid phase aside so that they accumulate between the growing ice crystals. However, recent in-situ X-ray radiography of directionally frozen alumina suspensions reveal a different mechanism. [ 31 ]
As solidification slows and growth kinetics become rate-limiting, the ice crystals begin to exclude the particles, redistributing them within the suspension. A competitive growth process develops between two crystal populations, those with their basal planes aligned with the thermal gradient (z-crystals) and those that are randomly oriented (r-crystals) giving rise to the start of the TZ. [ 30 ] [ 32 ] [ 33 ]
There are colonies of similarly aligned ice crystals growing throughout the suspension. There are fine lamellae of aligned z-crystals growing with their basal planes aligned with the thermal gradient. The r-crystals appear in this cross-section as platelets but in actuality, they are most similar to columnar dendritic crystals cut along a bias. Within the transition zone, the r-crystals either stop growing or turn into z-crystals that eventually become the predominant orientation, and lead to steady-state growth. There are some reasons why this occurs. For one, during freezing, the growing crystals tend to align with the temperature gradient, as this is the lowest energy configuration and thermodynamically preferential. Aligned growth, however, can mean two different things. Assuming the temperature gradient is vertical, the growing crystal will either be parallel (z-crystal) or perpendicular (r-crystal) to this gradient. A crystal that lays horizontally can still grow in line with the temperature gradient, but it will mean growing on its face rather than its edge. Since the thermal conductivity of ice is so small (1.6 - 2.4 W mK −1 ) compared with most every other ceramic (ex. Al 2 O 3 = 40 W mK −1 ), the growing ice will have a significant insulative effect on the localized thermal conditions within the slurry. This can be illustrated using simple resistor elements. [ 30 ] [ 34 ]
When ice crystals are aligned with their basal planes parallel to the temperature gradient (z-crystals), they can be represented as two resistors in parallel. The thermal resistance of the ceramic is significantly smaller than that of the ice however, so the apparent resistance can be expressed as the lower R ceramic . If the ice crystals are aligned perpendicular to the temperature gradient (r-crystals), they can be approximated as two resistor elements in series. For this case, the R ice is limiting and will dictate the localized thermal conditions. The lower thermal resistance for the z-crystal case leads to lower temperatures and greater heat flux at the growing crystals tips, driving further growth in this direction while, at the same time, the large R ice value hinders the growth of the r-crystals. Each ice crystal growing within the slurry will be some combination of these two scenarios. Thermodynamics dictate that all crystals will tend to align with the preferential temperature gradient causing r-crystals to eventually give way to z-crystals, which can be seen from the following radiographs taken within the TZ. [ 35 ]
When z-crystals become the only significant crystal orientation present, the ice-front grows in a steady-state manner except there are no significant changes to the system conditions. It was observed in
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