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Freeze Casting: A Review of Processing, Microstructure and Properties via the Open Data Repository, FreezeCasting.net

Kristen L. Scotti, David C. Dunand

arXiv:1710.00037v1physics.app-phcond-mat.mtrl-sci

TL;DR

Freeze-casting can produce application-relevant porous materials, but its complex templating process and partially understood processing–structure–property relationships limit systematic interpretation. The paper constructs an open repository from over 800 papers and analyzes the extracted data. The repository supports database-based testing of literature relationships and shows broad, variable ranges of attainable microstructures and properties.

  • Problem

    Freeze-casting offers tunable three-dimensional pore structures, but complex processing variables and incomplete understanding make systematic processing–structure–property analysis difficult.

  • Method

    The authors systematically extract and standardize literature data, organize it in a relational repository, and analyze processing, microstructure, and property relationships through web-accessible tools.

  • Results

    The repository contains data from over 800 papers, and its analysis summarizes attainable porosity, pore widths, wall widths, and processing–structure relationships across freeze-cast materials.

  • Takeaways & Limitations

    FreezeCasting.net is intended to support data dissemination, better informed experimental design, industrial use, and modeling of freeze-casting materials.

  • Takeaways & Limitations

    Extending elastic-buckling relations from elastomeric honeycombs to ceramic freeze-cast materials involves at least two identified issues.

Abstract

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Freeze-casting produces materials with complex, three-dimensional pore structures which may be tuned during the solidification process. The range of potential applications of freeze-cast materials is vast, and includes: structural materials, biomaterials, filtration membranes, pharmaceuticals, and foodstuffs. Fabrication of materials with application-specific microstructures is possible via freeze casting, however, the templating process is highly complex and the underlying principles are only partially understood. Here, we report the creation of a freeze-casting experimental data repository, which contains data extracted from ~800 different freeze-casting papers (as of August 2017). These data pertain to variables that link processing conditions to microstructural characteristics, and finally, mechanical properties. The aim of this work is to facilitate broad dissemination of relevant data to freeze-casting researchers, promote better informed experimental design, and encourage modeling efforts that relate processing conditions to microstructure formation and material properties. An initial, systematic analysis of these data is provided and key processing-structure-property relationships posited in the freeze-casting literature are discussed and tested against the database. Tools for data visualization and exploration available through the web interface are also provided.

1. Introduction

Freeze-casting creates tunable three-dimensional porous materials, but its many processing variables make processing–structure–property relationships difficult to establish systematically. The paper addresses this gap through a repository and database-based analysis of literature data.

  • Process and motivation: Freeze-casting templates pore structures by rejecting particles or solute during solidification, followed by removal of the solidified fluid.The resulting pores replicate the morphology of the solidified fluid.
  • Repository contribution: The repository contains data from over 800 papers linking processing conditions to microstructure and mechanical or physical properties.The paper uses the repository to test processing–structure–property relationships and provide more granular comparisons across processing states, structure types, and material classes.
  • Freezing modes: Anisotropic freezing produces aligned structures, whereas isotropic freezing produces nearly non-aligned porosity through randomly oriented nucleation and growth.Unidirectional solidification is more extensively investigated than isotropic freezing.
  • Pore structures: The most commonly reported anisotropic structures are lamellar (60%), dendritic (20%), and honeycomb (19%), while isotropic structures are mainly cellular (92%) and equiaxed (7%).Pore structure is categorized qualitatively, while porosity, wavelength, and pore and wall sizes provide quantitative descriptors.
  • Characterization limits: Two-dimensional characterization can misrepresent three-dimensional feature sizes and cannot readily quantify interconnectivity, percolation, surface curvature, or tortuosity.Sublimation and sintering can also modify microstructures after solidification.

2. Methods

The authors systematically searched, filtered, digitized, and standardized freeze-casting literature, then organized the extracted data in a relational repository exposed through web-based exploration and visualization tools.

  • Literature search: Literature published from 1998 to 2017 was identified through Google Scholar and Web of Science searches using freeze-casting and related terms.More than 2,000 keyword-related studies were initially retrieved.
  • Study selection: Studies were excluded when they lacked a solidification step, used a non-sacrificial second phase, or lacked relevant experimental data.Numerical, theoretical, and review papers were retained in a general literature table but not extracted to avoid overrepresenting data subsets.
  • Data extraction: Data were manually extracted from papers, digitized from plots when necessary, converted into consistent units, and entered into the repository.Plot Digitizer was used when values were unavailable in text or tables.
  • Database design: The database uses a modified relational model with primary tables for authors, papers, and samples and secondary tables organized by processing or characterization categories.Sample identifiers distinguish results obtained under varying processing conditions within individual papers.
  • Repository access: A public web interface provides background information, downloadable database formats, interactive plotting, and interactive tables for data exploration.Plots support filtering, transformations, regressions, citation access, and CSV export.
  • Statistical analysis: Python and SciPy were used for statistical analysis and curve fitting, with analysis code supplied as a Jupyter notebook.Power-law analyses used logarithmic transforms before fitting or regression.

3.1. Templating pore structures using fluids and additives

Freeze-casting fluids, additives, and solidification conditions provide multiple routes for tuning pore morphology, aspect ratio, interconnectivity, and pore size. The literature includes transitions among lamellar, dendritic, cellular, honeycomb, and equiaxed structures.

  • Lamellar structures: Lamellar structures arise predominantly during anisotropic freezing because hexagonal ice grows anisotropically, producing plate-like pores with high aspect ratios.The mean literature aspect ratio for lamellar structures is 5.5±3.2 (N=212).
  • Dendritic transitions: Increasing interconnectivity can be achieved by inducing lamellar-to-dendritic transitions through additives, higher particle volume fraction, or increased solidification velocity.Greater interconnectivity is desirable for load-bearing materials because it improves compressive response by helping prevent internal wall buckling.
  • Binder effects: Binder concentration can drive lamellar-to-dendritic and dendritic-to-cellular transitions in materials including Al2O3, WS2, and hydroxyapatite.Examples include increasing PVA in Al2O3 suspensions and increasing gelatin in WS2 or hydroxyapatite suspensions.
  • Sugar additives: Sucrose and trehalose promote dendritic or cellular morphologies by introducing interfacial instability during solidification.Al2O3 structures were dendritic with 5 wt.% sucrose and cellular with 10 wt.% sucrose or 8 wt.% trehalose.
  • Alcohol-containing fluids: At approximately 10, pore aspect ratios were highest with 5 vol.% IPA, representing a three-fold increase from the ratio without IPA.The comparison concerns sintered TiO2 microstructures obtained with 0, 1, 5, and 30 vol.% IPA relative to fluid volume.
  • Glycerol effects: Five wt.% glycerol produces bridges between lamellar walls, and bridge number density increases with glycerol concentration.Glycerol also decreases pore width, with cryoprotectant effects suggested to dominate over viscosity changes in reducing ice-crystal size.
  • Mechanistic uncertainty: Glycerol’s effects on suspension rheology and ice morphology remain unclear because both increased and decreased viscosities have been reported under comparable conditions.The reported viscosity behavior varies especially with particle volume fraction and dispersant interactions.
  • Other morphologies: Zirconium acetate complexes can produce honeycomb structures, while isotropic freezing or temporary space-holders can produce equiaxed pores.These morphology-control strategies have been demonstrated across several material systems.

3.2. Suspension stabilization

Suspension stabilization is a prerequisite for controlling particle packing and solidification morphology. The repository organizes stabilization data around particle, fluid, additive, concentration, size, and additive-role variables.

  • Stability and defects: Particle–particle interactions affect both particle packing and the morphology of the solidified fluid, while unstable suspensions promote defects such as ice lenses.Stabilization can be non-trivial for suspensions containing charged particles.
  • Zeta potential: Zeta potential quantifies electrostatic repulsion between particles, and larger absolute values indicate greater suspension stability.A suspension can therefore be stable at either positive or negative zeta-potential values.
  • Dispersants: Dispersants are added to charged-particle suspensions to prevent flocculation and coagulation.Carboxylic-acid-containing dispersants are commonly used for aqueous Al2O3 suspensions.
  • Repository guidance: Stabilization procedures depend on the selected particle, fluid, and additives, so database filtering can guide choices across these variables.Relevant filters include concentrations, particle sizes, and additive roles.

3.3. Controlling porosity via solid fraction

Porosity generally decreases as initial solid fraction increases, but the relationship depends strongly on sample processing and material group. Regression fits improve when data are separated by fluid type, sintering state, or narrowly defined material systems.

  • Processing state: ~40% of variance in total porosity is predicted by solid fraction for sublimated, unsintered samples, versus only ~1% across all data.The all-data regression uses N=2,855 and is dominated by sintered samples, which comprise ~82% of the dataset.
  • Processing state: Sintering lowers the regression intercept from 92%±3% for unsintered samples to 82%±10% for sintered samples.The lower intercept is attributed to volumetric shrinkage during sintering, while varying sintering conditions increase data scatter.
  • Fluid type: Water and camphene data explain 43% and 37% of porosity variance, respectively, whereas the TBA fit is not statistically significant.For aqueous samples, correlation strengthens when sintered and green samples are considered separately.
  • Material specificity: ~93% of porosity variance is explained for sintered TiO2 from aqueous suspensions, compared with broader ceramic datasets having larger prediction ranges.The TiO2 model has coefficients a=-1.7±0.2 and b=99.1%±0.7%.
  • Material group: At a given solid fraction, average porosity is highest for polymers and lowest for metals, with significant differences among ceramics, metals, and polymers.Regression slopes are -1.6±0.3 for metals and -0.8±0.2 for polymers; fluid type shows no significant differences within material groups.
  • Processing state: Sintering shrinkage is greatest for metals, intermediate for ceramics, and lowest for polymers.Shrinkage is measured from changes in diameter, height, and/or volume.

3.4. Tuning microstructures during unidirectional solidification

Unidirectional freeze-casting tunes microstructure through solidification velocity, cooling strategy, and undercooling, but measured relationships vary with material, processing route, and sample position.

  • Solidification velocity: Higher solidification velocity generally corresponds to smaller lamellar spacing, with λ = 184±52 μm and k = -0.5±0.1 across the database.Equation 2 predicts ~58% of λ variance for green ceramic samples but only ~7% for sintered ceramics.
  • Solidification velocity: Velocity-dependent pore-width fits are strong for polymers (~88% variance explained) but weak for ceramics (~12%), despite an excellent 96% fit for six in-situ ceramic samples.The in-situ result is based on a small sample count (N=6).
  • Solidification velocity: Wall-width fits are statistically weaker than λ or pore-width fits, and some in-situ aqueous alumina data suggest wall width may increase with velocity.Particle accumulation at the solidification interface is proposed as a possible explanation.
  • Cooling techniques for unidirectional solidification: Constant-temperature one-sided cooling produces a velocity gradient and pore widths that increase by 236% on average from the sample bottom to the top.The large standard deviation is 182%, and the gradient may be useful for tissue engineering and biomedical implants.
  • Cooling techniques for unidirectional solidification: Double-sided cooling reduces the average top-to-bottom pore-width increase to 88%±49%, indicating greater control over the thermal gradient than constant one-sided cooling.The comparison is reported for double-sided cooling versus constant cooling temperature.
  • Cooling techniques for unidirectional solidification: Cooling rate is an imperfect proxy for solidification velocity, and only eleven papers report both variables, with correlation r=0.65 across 82 observations.Direct velocity measurement is described as more generalizable, while feature size also depends strongly on sample position.

3.5. Summary of attainable microstructures

Freeze-casting spans broad microstructural ranges, with attainable porosity and feature sizes depending strongly on structure type and processing conditions. Porosity alone does not tightly determine pore width.

  • 65±14%, 66±18%, and 82±18% mean porosity are reported for sintered lamellar, dendritic, and honeycomb structures, respectively.Green samples show higher means of 80±18%, 80±15%, and 87±17% for the same structures.
  • Anisotropic structures show approximate lower porosity bounds of 22% for lamellar, 15% for dendritic, and 28% for honeycomb patterns.Below these values, the corresponding patterns are often lost or become cellular.
  • Most pore and wall width observations are below 100 and 30 μm, respectively, across sintered and green anisotropic samples.The distributions are highly skewed, so the majority of observations cluster below these thresholds.
  • Sintered cellular structures have a mean pore diameter of 42±87 μm, with reported diameters below 5 μm and up to 580 μm.The broad range reflects the different solidification techniques used to create cellular structures.
  • At 60% porosity, pore widths range from <1 to ~400 μm, demonstrating weak dependence of pore width on total porosity.Solidification conditions, especially velocity, are identified as better predictors of pore width than porosity.

4. Mechanical properties

Mechanical strength is related to relative density, pore structure, material orientation, specimen geometry, and testing conditions. Database analyses show that micromechanical models can explain substantial variance, but unreported impurities, morphology, defects, and failure modes limit prediction.

  • Density and micromechanical models: For relative density below 0.5, regression gives β1=1.7±0.5, near the open-cell prediction β1=1.5; above 0.4, β1=1.1±0.4 agrees better with the honeycomb prediction β1=1.The open-cell model is a better fit below relative density 0.5, whereas honeycomb behavior becomes more consistent at higher relative density.
  • Density and micromechanical models: σc*/σ0 follows relative-density scaling, with regression coefficients C2=0.69±0.10 and β1=2.2±0.1; the open-cell model fits better than the honeycomb model.The open-cell model predicts ~67% of variance across the full relative-density range, compared with ~57% for the honeycomb model.
  • Anisotropy and pore structure: Anisotropic ceramics exhibit, on average, higher compressive strength-to-density ratios than isotropic structures above relative density ≈0.18 when loads are applied parallel to the walls.The reported intersection of anisotropic and isotropic regression fits occurs at relative density ≈0.18.
  • Model limitations: The models provide upper-bound strength estimates because they assume defect-free materials with fully densified walls; microporosity and other defects lower attainable strength.The paper also notes that predicted strengths commonly exceed experiments, especially below relative density 0.5.
  • Anisotropy and pore structure: Regression fits for β1 decrease from 3.1±0.2 for TBA to 2.2±0.2 for water and 1.8±0.3 for camphene, corresponding to different predominant pore structures.TBA, water, and camphene predominantly produce honeycomb, lamellar, and dendritic structures, respectively.
  • Specimen geometry: For TBA, adding aspect ratio to relative density raises explained variance from ~88% to 96%, with σc*/σ0 ∝ (ρ*/ρ0)^2.5·A^-1.0.The BIC decreases from 187 for relative density alone to 64 for the combined model, indicating improved prediction for TBA specimens.

5. Concluding remarks

The paper establishes FreezeCasting.net as an open repository linking freeze-casting processing conditions with microstructure and material properties. It also reviews and tests reported processing–structure–property relationships against the database.

  • 5. Concluding remarks: FreezeCasting.net contains experimental data from over 800 freeze-casting papers published by August 2017.The repository covers processing conditions, microstructure, and material properties.
  • 5. Concluding remarks: The repository and paper aim to disseminate relevant data, improve experimental design, and encourage industrial use of freeze-casting.
  • 5. Concluding remarks: The paper summarizes freeze-cast microstructures and reviews and tests key processing–structure–property relationships using repository data.

All materials

Across materials, porosity depends minimally on suspension-fluid type but is strongly correlated with material type. Sintering shrinkage further affects how porosity depends on initial solid fraction.

  • All materials: Porosity's relationship with suspension solid-particle fraction depends minimally on fluid type.
  • All materials: Porosity is highly correlated with material type, including metal, ceramic, and polymer classes.
  • All materials: Materials with the lowest sintering-shrinkage rates, such as polymers, show greater porosity dependence on initial solid fraction.

Anisotropic materials derived from aqueous suspensions

For anisotropic materials from aqueous suspensions, structure wavelength correlates with solidification velocity, with the relationship depending on measurement and post-processing conditions.

  • Anisotropic materials derived from aqueous suspensions: Structure wavelength, defined as adjacent lamellar pore and wall widths combined, correlates with solidification velocity.
  • Anisotropic materials derived from aqueous suspensions: The structure-wavelength correlation is statistically weaker for pore width or wall width considered separately.
  • Anisotropic materials derived from aqueous suspensions: The correlation is strongest for sublimated rather than sintered samples.

Metals

For anisotropic freeze-cast sintered metals, the best compressive-strength model changes with relative density. The open-cell model fits below 0.5, while the out-of-plane honeycomb model fits better above that threshold.

  • Metals: Below relative density 0.5, compressive strength is best described by the Gibson–Ashby open-cell model.
  • Metals: Above relative density 0.5, the out-of-plane honeycomb model provides the better fit.
  • Metals: The model transition applies to anisotropic freeze-cast, sintered metals relating compressive strength to relative density.

Ceramics

For freeze-cast ceramics, the Gibson and Ashby open-cell model fits compressive-strength data better than the honeycomb model for both anisotropic and isotropic structures. Adding specimen aspect ratio to relative density improves regression models, but its predicted effect depends on fluid type.

  • Ceramics: The Gibson and Ashby open-cell model fits experimental compressive-strength data better than the honeycomb model for anisotropic and isotropic freeze-cast ceramics.This finding contradicts previous reviews.
  • Ceramics: Including specimen aspect ratio with relative density improves compressive-strength regression models for anisotropic ceramics made with water, camphene, or tert-butyl alcohol.The fitted models predict different aspect-ratio effects across fluids.
  • Ceramics: Increased specimen aspect ratio is predicted to decrease compressive strength for water- and tert-butyl-alcohol-derived materials but increase it for camphene-derived materials.Further testing is needed to clarify this relationship.

Tables

The tables define regression summaries for porosity, shrinkage, and microstructural dependence on solidification velocity, with coefficients, sample counts, correlations, fit quality, and significance indicators.

  • Tables: Table 1 summarizes slope, intercept, sample count, correlation, determination coefficient, confidence intervals, and significance for porosity–solid-fraction regressions.The model is ϕp = a∙ϕs + b, with ϕp, ϕs, and b expressed as percentages.
  • Tables: The reported porosity regression includes N=2,855 samples, r=-0.12, and R2=0.02 for the all-data fit.The all-data slope and intercept are -1.0[-1.3,-0.7] and 86[80,92], respectively.
  • Tables: Table 2 reports mean sintering shrinkage as changes in diameter, height, and/or volume for metals, ceramics, and polymers.The table organizes shrinkage by material group and measurement dimension.
  • Tables: Tables 3 and 4 fit microstructural parameters against solidification velocity or cooling rate using coefficients C1, k, sample count, and R2.Table 3 defines the log-transformed form ln(λ) = C1 + k∙ln(v).

N R2 References C1 k STRUCTURE WAVELENGTH

The tables summarize freeze-cast morphology, dimensions, mechanical models, and material-property inputs, including regression parameters for density–strength relationships.

  • Microstructure: Table 5 summarizes porosity for anisotropic lamellar, dendritic, and honeycomb structures and isotropic cellular and equiaxed structures.It distinguishes solidification, green, frozen, and sintered samples and reports sample counts, means, and standard deviations.
  • Microstructure: Table 6 summarizes pore and wall widths using sample counts, means, and standard deviations across structure types and processing states.The categories include solidification, green, frozen, and sintered samples.
  • Mechanical properties: Tables 7–9 describe micromechanical regression models linking relative density to normalized compressive strength for metals and ceramics.Table 9 further categorizes anisotropic ceramic fits by fluid type.
  • Material properties: The repository includes bulk material property values used in mechanical comparisons, including flexural strengths for ceramics and other materials.Values were drawn from CES EduPack and literature sources.
  • Mechanical models: The reported model equations include density-based strength relations and an aspect-ratio extension for anisotropic ceramic materials.The aspect-ratio model is identified as Eq. 6–Eq. 8 in the supplied table excerpts.

Figures

The figures document freeze-casting processes, pore morphologies, database structure, and repository-wide analyses of porosity, shrinkage, and velocity–microstructure relationships.

  • Literature overview: The number of peer-reviewed freeze-casting papers published per year is plotted from 2000 onward.This figure provides a publication-history view of the field.
  • Process schematics: Unidirectional freezing drives dendrites along a thermal gradient, rejects particles ahead of the interface, and packs particles in interdendritic regions.The schematic follows suspension placement, nucleation, particle rejection, solidification, and subsequent processing.
  • Process schematics: Isotropic freezing nucleates and grows crystals in random orientations, producing nearly isotropic pores after sublimation and sintering.The suspension is cooled inside a thermally insulating mold.
  • Pore morphologies: The repository schematics distinguish common anisotropic lamellar, dendritic, and honeycomb structures from isotropic cellular and equiaxed structures.The solidified-fluid morphology largely defines the final pore structure after removal.
  • Processing effects: Binder, isopropyl alcohol, glycerol, fluid choice, and freezing mode are illustrated as variables associated with changes in freeze-cast microstructure.The figures include aqueous and non-aqueous systems and both directional and isotropic freezing.
  • Data exploration: Repository visualizations plot zeta potential, total porosity, sintering shrinkage, and microstructural dimensions against processing or material variables.The analyses include fluid- and material-specific categories and solidification-velocity dependence.
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