Templating porous materials with ice
Freeze-casting, also known as ice-templating, is an environmentally friendly materials processing technique that can be utilized to create a diverse array of materials. As a result of the large range of materials (ceramics, metals, polymers, composites), in addition to the range of pore shapes and sizes that are attainable using the freeze-casting technique, applications for freeze-cast materials are numerous. In recent years, the technique has been investigated as a prossessing route for applications that include: structural materials , cocoa tablets , fuel cell electrodes , biomaterials [4-6], dye-sensitized solar cell electrodes [7,8], pharmaceuticals [9,10], stretchable circuits , and lithium ion battery electrodes ; just to name a few! As a result of the broad aplicability of the technique, freeze-casting has gained a considerable amount of attention over the past decade (Fig. 1).
Fig. 1. Number of freeze-casting papers published in peer-reviewed journals FY2001 to 2016.
Freeze-casting was first used as a materials processing technique by NASA in 1954 . The original work consisted of bulk freezing aqueous particle suspensions. After freezing, ice removal, and sintering, near net-shaped refractory materials were obtained (Fig. 2). Then, in the late 1970's freeze-casting was used in the food processing industry to produce imitation meat . It wasn't until the early 2000's that materials scientists rediscovered it [15-17], this time, assigning ice the additional role of inducing particle assembly to form walls surrounding elongated, aligned pores. The basic procedure is still very simple, the only major change being the induction of a temperature gradient during freezing.
Fig. 2. Freeze-cast turbocharger blade. Extracted from: Maxwell, W.G., RS; Francisco, AC, Preliminary investigation of the'freeze-casting'method for forming refractory powders. 1954.
The freeze-casting process can generally be described in terms of four main steps. As depicted in Fig. 3, particles are first dispersed in a fluid and the resulting suspension is frozen. When directional freezing techniques are employed, a temperature gradient is induced by placing the suspension on a cold plate. Ice nucleates preferentially at the cold surface and colonies of ice dendrites, oriented perpendicular to the freezing substrate and parallel to each other, propagate along the direction imposed by the temperture gradient. As ice dendrites advance, particles are rejected from the moving front, forming a region of accumulated particles ahead of the interface. As solidification progresses, ice dendrites break through the accumulation region and particles are forced to concentrate within the spaced between the ice dendrites.
Fig. 3. Freeze-casting processing steps. An aqueous suspension of particles (a) is placed onto a cold plate; ice crystals propagate in the direction of the temperature gradient, while pushing particles away from the moving freeze front (b). A region of accumulated particles develops ahead of the freeze front and particles are forced to assemble inbetween the ice crystals (c). After complete solidification (d), ice crystals are removed via freeze-dring (e). Lastly, the particle scaffold is heat-treated to densify particle-packed walls (f).
Although aqueous suspensions are most commonly used, it's important to note suspensions may also be non-aqueous. Indeed, since the morphology of the frozen fluid templates the pore structure in resulting materials, the range of fluids that may be employed offers much diversity in terms of attainable pore structures. Camphene has been used extensively and results in highly dendritic pore structures [18,19]. Dendrite to rod-ike structures can be obtained by adjsuting the naphthalene-camphor ratio from hypo- to hypereutectic . Tertiary-butyl alcohol has been employed to obtain long pore channels parallel to the freezing direction . Although the terms are often used interchangeably, when non-aqueous suspensions are used, the technically-correct term for the method is "freeze-casting," as opposed to "ice-templating."
The microstructural characteristics of freeze-cast materials are largely determined by the "morphology," or the shape, of the frozen fluid, which depends largely on the nature of the interactions between particles within the suspension and the solid/liquid interface. As a result of complex, interdependent relationships in the freeze-casting process, material properties can vary widely even within seemingly similar systems, making predictive control difficult. A sound theoretical understanding is necessary to gain predictive control.
Fig. 4. Depending on the speed of the freezing front, particle size and solids loading there are three possible morphological outcomes: (a) planar front where all particles are pushed ahead of the ice, (b) lamellar/cellular front where ice crystals template particles or (c) particles are engulfed producing no ordering.
Figure and figure caption reprinted without modification under CC BY 4.0.
Image credit: Aaron Lichtner
Experimentally, it has been shown that particles are rejected by the advancing interface if the velocity of the interface is below a critical value; above this value, particles are engulfed [22,23]. For freeze-casting, the velocity of the solidification interface must be kept below the so-called “critical velocity” such that particles are first pushed by the interface and may later self-assemble within interdendritic space (Fig. 4).
Theoretical models attempt to predict critical velocity by balancing the forces exercised on a particle within the vicinity of the solid/liquid interface [24-30]. Numerous possible forces are considered, though the combination of forces included in any given model varies (Fig. 5). These include: forces resulting from molecular interactions between a particle and the solid/liquid interface (e.g. van der Waals, or disjoining pressure, and interfacial ), forces exercised on the particle by the liquid medium (viscous drag ; buoyancy [34, 35]); Brownian [36, 37] and convective forces [38, 39] are also sometimes considered. Additional considerations include heat diffusivity  and latent heat . For some systems, thermal conductivity mismatches between the solid and liquid induce interface shape distortions [42, 43]. In these systems, the effect is so strong that entire models have been built on this consideration alone . However, it has been shown that even in systems where conductivity mismatch behavior seems to dominate the system, it merely complicates it. At the instant before a particle is rejected/engulfed by the interface, it is the magnitude of the attractive and repulsive forces that are determinant .
Fig. 5. Schematic of a particle within the liquid phase interacting with an oncoming solidification front.
Figure and figure caption reprinted without modification under CC BY 4.0.
Image credit: Aaron Lichtner
In very dilute suspensions, critical velocity can be estimated fairly well using theoretical models. However, in suspensions containing higher particle fractions, critical velocity cannot be determined based on discrete treatments of force magnitudes alone, because the solidification velocity fluctuates in response to transient thermal gradient shifts , associated with varying local particle fractions. Indeed, as observed experimentally in ice-templating systems , global and local instabilities during solidification correspond to sudden interface jumps which are associated with decreases in local concentration and temperature. For ice-templating systems, theoretical models serve as a starting point in estimating an appropriate solidification velocity, but experimental verification is always necessary. Chino et al. found a solidification velocity of 2 to 12 µm/s was sufficiently slow to allow particle pushing of 45 µm titanium particles, but within the same velocity range, titanium particles of 125 µm were engulfed .
Ice-templating models that attempt to tackle multiple particle interactions employ the “Colloids as Big Atoms” approach , wherein colloid particles are taken as atoms that can be directly observed in real space. Nevertheless, due to the inherent complexity of the system, computational models contain inevitable simplifications, making a priori predictions impossible. The basic principles of freezecasting rely on the induction and exploitation of non-equilibrated behavior for the formation of desired microstructures. However, attempts to model the system out of equilibrium with a nonplanar interface are extremely complex. It should also be noted that very few models consider commonly employed nanometric particles; those that do suggest increased fluctuations in the thermal gradient inconsistent with previous models [37, 48, 49].
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