# Operational Variables on the Processing of Porous Titanium Bodies by Gelation of Slurries with an Expansive Porogen

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}O

_{2}[20], freeze-casting [21], replication [22] or robocasting [23].

_{3}and CO

_{2}according to the equation:

_{4}) HCO

_{3}→ H

_{2}O + NH

_{3}+ CO

_{2}

_{2}bubbles leading to a porous Ti structure. The weight of the different processing variables in the characteristics of the green Ti sponge was analyzed by an experimental design method, and the sintered properties of the Ti open sponge cell were determined. The methodology presented in this paper provides processing tools to design green porous bodies with variables sizes and porosity by controlling the interlaced initial composition and processing temperature.

## 2. Materials and Methods

#### 2.1. Slurry Formulation and Characterization

^{−1}in 120 s, keep at 1000 s

^{−1}for 60 s and decreased to 0 s

^{−1}in 120 s. In the case of CS mode tests, the stress was increased from 0 to the desired value and back to 0 Pa at up and down rate of 2 Pa/min. The applied high-shear rates during up-ramps are enough to achieve a reproducible suspension microstructure, dependent only on the suspension composition, but not on the slurry preparation history [16]. Then the flow curves presented are the down-ramps in the log–log plot and fitting following the Cross model (1):

_{0}and η

_{∞}are the extrapolation of the viscosity to zero (zero-shear viscosity) and infinity (infinite shear viscosity), respectively, C is a time constant and n is the rate constant, and it is a parameter which is related with the dependence of viscosity on the shear rate. The Cross model describes the limit behavior of the standing suspension and at an infinite shear rate, therefore not only gives information about which suspension is more viscous but which is more stable.

#### 2.2. Ti Sponges Processing and Characterization

^{3}.

^{−5}atm at 1100 °C for 30 min. The characterization of sintered parts consisted in the measurement of their density at room temperature by the Archimedes method using an analytical balance with a resolution of ±0.1 mg, He pycnometry (MonosorbMultipycnometer, Quantachrome Instruments Co., Boynton Beach, FL, USA) and MIP. Compressive mechanical tests were carried on using a universal testing machine (Microtest S.A., Madrid, Spain) with steel plates. The pressure was applied using a load frame displacement rate of 0.02 mm/min. Load and displacement of the load frame were recorded during pressing. The microstructure of the sintered samples was registered by a scanning electron microscope (Philips Model XL30, Eindhoven, The Netherlands). The oxygen content, which is an interstitial element and has the greatest effect on the mechanical properties of Ti was measured using an inert gas fusion technique. For these measurements, a LECO TC-500 (MI, USA) was used.

#### 2.3. Experimental Design Method

^{n}factorial design was used. This experimental design works with a series of points (experiments) around a point of central composition (central experiment), for the estimation of constant for the mathematical models tested. This design satisfies the general requirements and therefore all parameters of the mathematical models can be estimated without an excessive number of experiments. The design used is defined by three parameters: number of variables, k; constant p, which takes the values 0 for k < 5 and 1 for k > 5; and number of central points, nc.

- -
- 2
^{k−p}points of the factorial design. - -
- 2·k axial points.
- -
- n
_{c}central points.

_{n}is the normalized value of gelation agent (X

_{G}), porogen (X

_{p}) or temperature (X

_{T}); X is the absolute experimental value of the variable concerned; X

_{m}is the mean of the extreme values of X; and X

_{max}and X

_{min}are its maximum and minimum values, respectively.

_{G}is the concentration of MC and takes values of 8, 10 and 12 g/L, X

_{P}is the concentration of ammonium bicarbonate and takes values of 15, 20 and 25 wt.% related to the solid content of the slurry and X

_{T}is gelation/drying temperature and takes values of 60, 70 and 80 °C.

## 3. Results

#### 3.1. Study of the Influence of the Operation Variables on the Properties of the Ti Sponges

_{G}), the porogen concentrations (X

_{P}) and temperature (X

_{T}).

_{G}variable) determines the polymerization degree and the gel structure during the gelation process, being also the responsible of changes in the rheological behavior of the suspensions. For this reason, the addition of different amounts of MC to the Ti slurries was firstly studied in terms of its rheological behaviour. Methylcelluloses are common thickeners for liquids used in food industries, biotechnology and materials processing. Rheological modification depends on intrinsic characteristic properties such as the molecular weight and substitutions of the anhydroglucose repeat unit as well as concentration of additive. Amounts can range from a few grams per litter [28] to tens of grams [29]. Figure 2a shows the viscosity vs. the shear rate for slurries of Ti with 50 vol.% of solids contents in DI water (without gelation agent or porogen) and in an aqueous media containing 8, 10 and 12 g/L of MC (X

_{G}8, X

_{G}10 and X

_{G}12). For each of the slurries the curves were made overlapping the decreasing shear rate of the CR and CS experiments. It should be noted that for the thicker slurries the CR and CS curves do not coincide on the overlapping zone, as the CR experiment shears the slurry more energetically leaving no time for rearrangement of interparticle forces, while the CS experiment is less energetic allowing a faster formation of the mentioned interparticles forces and consequently higher viscosity values.

_{0}) and the infinite shear viscosity (η

_{∞}). High values of zero-shear viscosity are indicative of the capacity of samples to keep the shape and avoid segregation of phases in a resting state (out of external forces or stirring). On the other hand, low infinite shear viscosity values are indicative of efficiency on the mixing and milling processes. These values are collected in Table 1 together to the values of viscosity at shear rates of 10 and 100 s

^{−1}which are reference values for casting.

_{∞}below 100 mPa·s which indicates a higher homogenization capability. The viscosity values of all MC slurries in the shear range of 10–100 s

^{−1}fulfilled the requirements to be processed by gel casting.

^{−1}containing MC with the temperature was plotted. Two sections were identified on these plots. In the low temperature zone, the viscosity decreases with the raise of the temperature. This behavior was also observed in slurries dispersed with polyelectrolytes of both ceramic [30] and metallic powders [31]. As the temperature achieves the 50 °C, this decreasing in the viscosity is compensated and starts to increase as the MC already dissolved into the liquid medium starts to gel. The gelation process of MC occurs during heating due to the hydrophobic association between methyl groups on cellulose chains [32,33]. The points where derivate of the curves included in Figure 2b equals to 0 indicate the temperature where gelation process become predominant on the rheological behavior of the slurries. This temperature is 51, 49 and 47 °C, respectively, for the concentrations of MC of 8, 10 and 12 g/L.

_{G}−15X

_{P}), (8X

_{G}−20X

_{P}) and (8X

_{G}−25X

_{P})). Similar rheograms for MC concentrations of 8 and 10 g/L were measured (no show here) with similar results and evolution of the slurries viscosity.

_{0}), infinite shear viscosity (η

_{∞}) and viscosity at 100 s

^{−1}(η

_{100}).

_{G}−15X

_{P}−60X

_{T}) and 7 (8X

_{G}−15X

_{P}−80X

_{T}), (b) samples 5 (8X

_{G}−25X

_{P}−60X

_{T}) and 3 (8X

_{G}−25X

_{P}−80X

_{T}), (c) samples 8 (12X

_{G}−15X

_{P}−60X

_{T}) and 6 (12X

_{G}−15X

_{P}−80X

_{T}), (d) samples 4 (12X

_{G}−25X

_{P}−60X

_{T}) and 2 (12X

_{G}−25X

_{P}−80X

_{T})). Similar pore size distributions were determined for other samples in Table S1 (data and plots can be found as supplementary material) with similar results that those discussed below.

_{0}, η

_{∞}and η

_{100 s−1}), the apparent densities (D) and the mean pore diameter (P) resulting from the characterization of Ti sponges obtained at the 15 proposed experiments. Reported values show that viscosity in resting conditions varies from 1720 to 250 mPa·s and the mean pore size diameters range from 6.09 to 9.93 µm while the green density of Ti sponges varies from 1.77 to 2.56 g/cm

^{3}(from 39.25% to 56.76%).

_{G}, X

_{P}and X

_{T}) in the apparent density, data in Table S2 and the plots in Figure 4 and similar (show as Supplementary Material, Figure S1) were analyzed. As a function of the ammonium bicarbonate concentration (when X

_{G}and X

_{T}were fixed varying the X

_{P}) and the MC concentration (X

_{P}and X

_{T}are fixed), whatever it is the values of other two variables, the apparent density decreases due to the higher amount of gas generated by the ammonium bicarbonate decomposition and the stronger gel structure formed by the slurry which is retaining the gas bubbles. In fact, from the microstructural inspection, pores in the green samples obtained with higher MC contents are lower in size and better distributed (Figure 3). However, the increment of the process temperature promotes the increase of the apparent density. This could be due to the faster gas formation when temperature increases that promotes the coalescence of the bubbles at low gel concentrations and high porogen contents, avoiding an effective formation of the gel. In those cases, even the full structure of the green sponge can collapse.

_{P}at the same X

_{T}or X

_{G}. (not show here, but in the Supplementary Material, Figure S2) were also analyzed. As a function of the ammonium bicarbonate concentration (when X

_{G}and X

_{T}were fixed varying the X

_{P}), although the full width at half maximum for the main peak in the pore size distribution graphs ranges between 4 and 10 µm in all the cases, for the higher concentration of porogen a second broad area of porosity over the 10 µm is detected (Figure 5b,d). Similarly occurs if the temperature is considered as the variable (when X

_{G}and X

_{P}were fixed varying the X

_{T}), the higher is the temperature the wider is the population of pores with diameters higher than 10 µm. An in both cases, the higher is the concentration of the gelation agent (when X

_{P}and X

_{T}are fixed being X

_{G}the variable) the lower is the extension of this second population of pores. Those results indicate that the gel strength prevents the coalescence of pores. However, for the highest gelation temperature tested, even the highest concentration of MC is not enough to keep the pores isolated, and then they coalesce to generate pores of bigger sizes.

_{G}samples provide a plastic binder between particles, what allows higher strain (and stress) without breaking. The second zone (Zone II) consists in a stress plateau where multiple cracks grow and propagate easily throughout the materials collapsing the structure. The transition from the Zone I to the Zone II define a yield point which depends on the size, connectivity and number of pores. The final evolution of the force-strain curve (Zone III) can be identified with a densification process forced by the uniaxial pressure that compression plates exert onto the broken sample. As the broken pieces are not confined into a die, the Zone III can’t be clearly identified [40]. In this study we were focused on the Zones I and II where the structural integrity of green sponges is mainly conditioned by the porosity and then by the selected operation variables (X

_{G}, X

_{P}and X

_{T}).

_{G}−15X

_{P}−80X

_{T}) and 3 (8X

_{G}−25X

_{P}−80X

_{T}), and samples. 6 (12X

_{G}−15X

_{P}−80X

_{T}) and 2 (12X

_{G}−25X

_{P}−80X

_{T}), respectively, which illustrate the mechanical response of Ti sponges obtained formulating slurries with 8 g/L and 12 g/L of MC, respectively, when the content of porogen change from 15 to 25 wt.% for a similar thermal treatment at 80 °C.

_{P}= 15 wt.%), that means to the structures with a lower level of porosity. In fact, samples 7 (8X

_{G}−15X

_{P}−80X

_{T}) and 6 (12X

_{G}−15X

_{P}−80X

_{T}) have similar apparent densities (2.44 and 2.37 g/cm

^{3}, respectively) and mean pore sizes (6.22 and 6.62 µm, respectively). However, the comparative examination of the whole curve evolution of both samples suggests a structure reinforcement achieved by the incorporation of a higher amount of the MC. At the plots, the higher is the amount of CM in the slurry formulation the higher is the compressive force required to achieve the plateau at the Zone II. Moreover, the tensile drops are less abrupt in the sponge num. 6 (12X

_{G}−15X

_{P}−80X

_{T}). Those effects can be related to the joining effect of the gelation agent over the particles and that the porosity generated by the ammonium bicarbonate decomposition is clearly trapped by a stiffer and stronger gel structure, respectively.

_{G}−25X

_{P}−80X

_{T}) and 2 (12X

_{G}−25X

_{P}−80X

_{T}) have dissimilar apparent densities (2.15 and 1.77 g/cm

^{3}, respectively) and mean pore sizes (7.17 and 6.27 µm, respectively). A low stiffness is observed for these sponges since they show a higher displacement for the application of smaller compressive forces. However, it is important to note that the whole behavior of the force-strain curves is similar to the curves measured for lower porogen contents (samples 7 and 6 Supplementary Material). So we can intuit that MC concentration influences the pore size and the porosity distribution, being both values higher as more porogen is added.

#### 3.2. A Multiple Regression Analysis of the Experimental Data

_{0}, D and P) with the operational variables (X

_{T}, X

_{G}and X

_{P}), resulting in:

_{T}, X

_{G}and X

_{P}) in each of the output variables (η

_{0}, D and P).

_{0}) fits the experimental measured values with errors lower that 9%, the average value of the errors being lower than the rest of the variables, which indicates a good adjustment of the experimental results. Finally, the fitting values for the mean pore size (P) adjust to the experimental values with error lower than 15%. In this case, there is a greater disparity in the errors calculated on this variable from this model.

_{0}, D and P) were estimated from Equations (5)–(7), and the values of the corresponding operational variables (X

_{T}, X

_{G}and X

_{P}) were determined, and collected in Table 4.

_{G}, X

_{P}and X

_{T}, respectively. The viscosity values only depend on two variables, X

_{G}and X

_{P}, as the temperature was applied after the determination of the slurry viscosity. To determine the influence of the input variables on the properties considered it is necessary to determine the optimum conditions for each of the mentioned properties. For that, a non-linear programming as implemented in the More and Toraldo method was used. The values of two of the input variables were fixed and the other one was varied until the maximum and minimum value of each output parameter was reached, and with them the error was calculated. The maximum error corresponds to the most influential operational variable on the output parameter (η

_{0}, D or P).

_{G}was fixed and X

_{P}was the variable, the maximum and minimum viscosity values are 0.36 and 2.05, respectively, with error values of the 82.18%. Otherwise, when X

_{P}was fixed and X

_{G}was the variable, the values were 1.34 and 2.05 with and error of 34.38%. Consequently, the most influential variable in the zero-shear viscosity is X

_{P}.

_{G}and X

_{P}were fixed and X

_{T}was varied, the maximum and minimum density values were 1.73 and 1.94 g/cm

^{3}with an error of 10.80%. When X

_{G}and X

_{T}were fixed and X

_{P}was varied, there are obtained minimum and maximum density values of 1.73 and 2.04 g/cm

^{3}with an error of 15.00%. In addition, when X

_{P}and X

_{T}were fixed and X

_{G}was varied, there were obtained minimum and maximum values of 1.73 and 2.16 g/cm

^{3}with an error of 19.66%. So, the most influential variable in the density is X

_{G}, followed by the X

_{P}and the lower influential was X

_{T}.

_{G}and X

_{P}and changing the X

_{T}, the maximum and minimum pore sizes were 9.4 and 8.0, respectively, with error of 14.92%. Fixing X

_{G}and X

_{T}and changing the X

_{P}, the maximum and minimum pore sizes were 9.4 and 7.2 µm, respectively, with an error value of 22.98%. In addition, fixing X

_{P}and X

_{T}and changing the X

_{G}, the maximum and minimum mean pore sizes were 9.4 and 7.93 µm, respectively, with an error value of 15.77%. Based on this data the most influential variable in the mean pore size is X

_{P}, followed by X

_{G}and X

_{T}.

#### 3.3. Sintering and Characterization of Ti Sponges

_{supra-macro}) to the surface of the piece and burst lowering the porosity. Category B (samples 6, 7 and 11 in Table S1) is associated to the materials with bigger pores in which the pores can internally merge into big pores but has only a limited capability to move up to the surface and once they burst, do not lose the shape. This porosity was opened, tubular and directional to the surface. Category C (samples 1, 4, 13 and 14 in Table S1) corresponds to structures with a higher amount of pores, homogeneously distributed in the structure. In these cases, the viscosities were higher enough to keep the size of the pores without merges them in bigger ones but with open junctions. Finally, the Category D (samples 2, 3, 5, 10, 12 and 15 in Table S1) corresponds to the higher values of the operational variables. The processing of these slurries is complicated due to both, the high viscosity and porosity, promotes the structure collapse. Those materials are hardly handling and then category D has not been considered for further characterizations. Figure 7 shows the pictures and micrographs of the materials which represents the categories A, B and C, while Table 6 collects the characterization of the porosity and oxygen content (O

_{2}) of these materials after sintering.

_{macro}ranging 50 nm < P < 200 µm) the more representative pore size in the Ti sponge microstructure. Samples on group A are denser than others and mainly present macroporosity. Materials on group B exhibit higher porosities which correspond mainly to the macro and supra-macro porosity. The high value on the supra-macro porosity was due to the coalescence of pores in the conditions where the gelation agent does not provide enough strength. Finally, materials of group C present the higher porosity, mainly macro porosity. The oxygen content ranges from 1.31 to 2.22 wt.%, close to the values of Ti processed by other aqueous colloidal techniques [19,22], being the structures on group C have the higher oxygen content, as a consequence of the higher total porosity.

^{3}corresponding to 51.40–54.23%) and a narrow pore size distribution with mean size ranging 6–7 µm. After sintering, these samples have the lowest closed porosity (0.2%) denoting the homogeneous and high degree of particles packing achieved during shaping. Moreover, these sponges exhibit the best compressive behavior (Figure 6) as a result of the homogeneous distribution of the generated porosity in the stiff green structure. Finally, the macro porosity in this category of sponges is balanced between macro- and supra-macro pores leading to sintered Ti sponges with 39% of open porosity and almost null close porosity.

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**(

**a**) Flow curves of Ti slurries with 50 vol. % of solid contents formulated without MC and with 8, 10 and 12 g/L of MC. (

**b**) Viscosity values vs. Temperature for 50 vol.% slurries with 8, 10 and 12 g/L of MC.

**Figure 3.**Porous Ti green sample, (

**left**) dome shaped by gelation and drying and (

**right**) a detail of the internal porous structure observed after breaking apart the sample.

**Figure 4.**Evolution of the viscosity with the shear rate of 50 vol.% Ti slurries with 15, 20 and 25 wt.% of ammonium bicarbonate and 12 g/L of MC.

**Figure 5.**Pore distributions by Mercury Intrusion Porosimetry (MIP), for samples in Table S1. Grouping operational variables by fixing X

_{G}and X

_{P}and variable X

_{T}: (

**a**) sample 9 (8X

_{G}−15X

_{P}−60X

_{T}) and sample 7 (8X

_{G}−15X

_{P}−80X

_{T}); (

**b**) sample 5 (8X

_{G}−25X

_{P}−60X

_{T}) and sample 3 (8X

_{G}−25X

_{P}−80X

_{T}); (

**c**) sample 8 (12X

_{G}−15X

_{P}−60X

_{T}) and sample 6 (12X

_{G}−15X

_{P}−80X

_{T}); (

**d**) sample 4 (12X

_{G}−25X

_{P}−60X

_{T}) and sample 2 (12X

_{G}−25X

_{P}−80X

_{T}).

**Figure 6.**Force-strain curves recorded in the compression tests of green samples: (

**a**) 7 (8X

_{G}−15X

_{P}−80X

_{T}) and 3 (8X

_{G}−25X

_{P}−80X

_{T}); (

**b**) samples 6 (12X

_{G}−15X

_{P}−80X

_{T}) and 2 (12X

_{G}−25X

_{P}−80X

_{T}) in Table S1.

**Figure 7.**Pictures and micrographs of the porous titanium sintered bodies representing the different processing categories (

**A**–

**C**).

**Table 1.**Characteristic viscosity values for 50 vol.% Ti slurries formulated without MC and with 8, 10 and 12 g/L of MC.

Formulation | η_{0} (mPa·s) | η_{∞} (mPa·s) | η_{10 s−1} (mPa·s) | η_{100 s−1} (mPa·s) |
---|---|---|---|---|

without MC | 430 | 10 | 410 | 61 |

8X_{G} | 760 | 95 | 620 | 396 |

10X_{G} | 900 | 108 | 735 | 458 |

12X_{G} | 1370 | 121 | 1070 | 515 |

**Table 2.**Statistical parameters values of polynomial models found for the processing of Ti porous structures.

Equation | Multiple-R | R^{2} | Adjusted R^{2} | p < | F > |
---|---|---|---|---|---|

D [Equation (3)] | 0.86 | 0.73 | 0.59 | 0.16 | 2.34 |

P [Equation (4)] | 0.85 | 0.73 | 0.52 | 0.24 | 1.61 |

η_{0} [Equation (5)] | 0.99 | 0.99 | 0.99 | 1.12 × 10^{−8} | 381.20 |

**Table 3.**Statistical parameters values of polynomial models found for the processing of Ti porous structures.

Num. | D (g/cm^{3}) | D (g/cm^{3})Estimated | Error (%) | η_{0} (Pa·s) | η_{0} (Pa·s)Estimated | Error (%) | P (μm) | P (μm) Estimated | Error (%) |
---|---|---|---|---|---|---|---|---|---|

1 | 2.38 | 2.29 | 3.78 | 1.72 | 1.69 | 1.48 | 7.33 | 7.13 | 2.79 |

2 | 1.77 | 1.99 | 12.53 | 0.35 | 0.36 | 4.15 | 6.13 | 6.53 | 6.32 |

3 | 2.15 | 2.17 | 0.92 | 1.34 | 1.34 | 0.15 | 7.11 | 8.00 | 12.53 |

4 | 1.85 | 1.78 | 3.68 | 0.35 | 0.36 | 4.15 | 7.24 | 7.55 | 4.30 |

5 | 1.98 | 1.96 | 1.02 | 1.35 | 1.34 | 0.59 | 9.28 | 9.04 | 2.64 |

6 | 2.37 | 2.25 | 5.07 | 0.28 | 0.28 | 1.62 | 6.20 | 5.80 | 4.93 |

7 | 2.44 | 2.43 | 0.50 | 0.26 | 0.24 | 8.48 | 6.27 | 5.90 | 5.85 |

8 | 1.95 | 2.04 | 4.61 | 0.28 | 0.28 | 1.62 | 6.98 | 6.83 | 2.10 |

9 | 2.24 | 2.22 | 0.99 | 0.26 | 0.24 | 8.48 | 7.07 | 6.94 | 1.88 |

10 | 2.46 | 2.31 | 6.24 | - | - | - | 9.93 | 8.59 | 13.54 |

11 | 2.50 | 2.56 | 2.58 | 1.32 | 1.40 | 5.78 | 6.23 | 7.18 | 15.21 |

12 | 2.56 | 2.39 | 6.59 | 1.72 | 1.69 | 1.48 | 6.41 | 5.80 | 9.53 |

13 | 2.22 | 2.18 | 1.74 | 1.72 | 1.69 | 1.48 | 6.62 | 6.83 | 3.22 |

14 | 1.99 | 1.87 | 6.20 | 0.34 | 0.32 | 5.88 | 6.48 | 6.73 | 3.84 |

15 | 2.01 | 2.04 | 1.72 | 0.74 | 0.79 | 6.76 | 7.17 | 7.52 | 4.92 |

**Table 4.**Operational variables values in the processing of Ti sponges to obtain maximum and minimum values of the dependent variables.

Parameter | Maximum Values | Minimum Values | ||
---|---|---|---|---|

(X_{G}; X_{P}; X_{T}) | Results | (X_{G}; X_{P}; X_{T}) | Results | |

D (g/cm^{3}) | (−0.13; −1; 1) | 2.67 | (1; 0.43; −1) | 1.74 |

η_{0} (Pa·s) | (−0.2; 1) | 2.04 | (−1; −1) | 0.23 |

P (μm) | (−1; 1; −0.32) | 9.41 | (1; −0.24; 1) | 5.35 |

**Table 5.**Summary of the estimation of the influence of operational variables in the processing parameters of Ti sponges.

Parameter | Operational Variable | Errors | Influence |
---|---|---|---|

Apparent Density (D) | Fixed: X_{G}, X_{P}Variable: X _{T} | 10.80% | X_{G} > X_{P} > X_{T} |

Fixed: X_{G}, X_{T}Variable: X _{P} | 15.00% | ||

Fixed: X_{P}, X_{T}Variable: X _{G} | 19.66% | ||

Zero-shear Viscosity (η _{o}) | Fixed: X_{G}Variable: X _{P} | 82.18% | X_{P} > X_{G} |

Fixed: X_{P}Variable: X _{G} | 34.38% | ||

Mean Porous Size (P) | Fixed: X_{G}, X_{P}Variable: X _{T} | 14.92% | X_{P} > X_{G} > X_{T} |

Fixed: X_{G}, X_{T}Variable: X _{P} | 22.98% | ||

Fixed: X_{P}, X_{T}Variable: X _{G} | 15.77% |

**Table 6.**Porosity characterization of the sintered Ti sponges including their associated oxygen content.

Category | P_{Total} * | P_{closed} | P_{open} | P_{micro-meso}(<50 nm) | P_{macro}(<200 µm) | P_{supra-macro}(>200 µm) | O_{2}(wt.%) |
---|---|---|---|---|---|---|---|

A | 20.4% | 1.7% | 18.7% | <0.005% | 18.3% | 0.4% | 1.54% |

B | 39.4% | 0.2% | 39.2% | <0.005% | 20.3% | 18.9% | 1.31% |

C | 42.2% | 7.8% | 34.4% | <0.005% | 33.1% | 1.3% | 2.22% |

^{3}.

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**MDPI and ACS Style**

Sanchez-Herencia, A.J.; Gonzalez, Z.; Rodriguez, A.; Molero, E.; Ferrari, B.
Operational Variables on the Processing of Porous Titanium Bodies by Gelation of Slurries with an Expansive Porogen. *Materials* **2021**, *14*, 4744.
https://doi.org/10.3390/ma14164744

**AMA Style**

Sanchez-Herencia AJ, Gonzalez Z, Rodriguez A, Molero E, Ferrari B.
Operational Variables on the Processing of Porous Titanium Bodies by Gelation of Slurries with an Expansive Porogen. *Materials*. 2021; 14(16):4744.
https://doi.org/10.3390/ma14164744

**Chicago/Turabian Style**

Sanchez-Herencia, Antonio Javier, Zoilo Gonzalez, Alejandro Rodriguez, Esther Molero, and Begoña Ferrari.
2021. "Operational Variables on the Processing of Porous Titanium Bodies by Gelation of Slurries with an Expansive Porogen" *Materials* 14, no. 16: 4744.
https://doi.org/10.3390/ma14164744