**4.2. Air content and wet foam stability**

**Figure 10.** Contact angle of suspension with respect to different concentrations of amphiphiles.4

**Figure 9.** Contact angle and surface tension of Al2O3-TiO2equimolar suspension, with respect to different vol% of 3:2

mole ratio of Al2O3-SiO2 suspension added for the mullite phase32

68 Advanced Ceramic Processing

The total porosity of directly foamed ceramics is proportional to the amount of air incorporated into the suspension or liquid medium during the foaming process. The pore size, on the other hand, is determined by the stability of the wet foam. High-volume foams are formed upon mechanical frothing which strongly indicates the stabilization of air bubbles due to the attachment of particles to the air-water interface.

In Fig. 12, a relationship between the air content and the different concentration of amphiphiles has been plotted. It can be seen that for all three amphiphiles, the air content gradually increases until it achieves the highest value. This is because the particles were not sufficiently hydro‐ phobized below this concentration (i.e., 0.15 m/mol for propionic acid and 0.10 m/mol for valeric acid). All the investigated suspension reports highest air content (i.e., 69% in case of propionic acid and 58-60% in case of butyric acid and valeric acid) upon achieving sufficient hydrophobization. The decrease in air content at high amphiphile concentration is due to increase of suspension viscosity which resists the air incorporation to the suspension.

In Fig. 13, the influence of the amphiphile concentration on the wet foam stability is displayed. At very low amphiphile concentrations, no stable foams are obtained since the alumina particles are not sufficiently hydrophobized to stabilize the air-water interface of freshly formed air bubbles. Using 0.10 mol/L of amphiphile results in rather unstable foam with wet foam stability of about 72-77%. At a certain point between 0.15 and 0.2 mol/L of amphiphile concentration, wet foams with highest stability are obtained. Propionic acid having the shortest hydrophobic chain requires more concentration (0.20 mol/L) to result sufficient hydrophobi‐ zation. However, the middle and long chain amphiphiles, i.e., butyric acid and valeric acid, respectively, produce effective hydrophobicity at around 0.15 mol/L. More concentrations of them increase the suspension viscosity results from increasing hydrophobicity of the particles, which prohibits the suspension to be foamed by mechanical stirring.

Fig. 14 establishes the air contents and foam stability of Al2O3-TiO2equimolar suspension, with respect to different vol% of 3:2 mole ratio of Al2O3-SiO2 suspension added for the mullite phase. High-volume foams with air content up to 83% form upon mechanical frothing, which strongly indicates the stabilization of air bubbles, due to the attachment of particles to the air-water interface. We measured the foam stability and observed that on the addition of 10 vol% suspension for the mullite phase, the foam stability suddenly decreased. This is probably due to the high viscosity of the suspension, due to higher particle concentration. However, 20, 30, and 50 vol.% of addition enhanced the foam stability, which might be explained by the optimum surface hydrophobicity being achieved, due to the increased particle concentration.

**Figure 12.** Air content of suspension with respect to different concentration of amphiphiles.4

In Fig. 15, the wet foam stability can be determined by observing the average bubble size with respect to the time after foaming. The foams stabilized with butyric acid and valeric acid show no significant bubble growth unlike the foam stabilized with propionic acid which shows a little coarsening. We can attribute the first two cases of remarkable resistance to the irreversible adsorption of the partially hydrophobized particles at the air-water interface. Therefore, the bubble size remains almost constant with the increase of time up to 6 hours of foaming. The foams stabilized with propionic acid are prone to bubble coarsening due to the pressure

**Figure 13.** Wet foam stability of suspension with respect to different concentration of amphiphiles.4

hydrophobic chain requires more concentration (0.20 mol/L) to result sufficient hydrophobi‐ zation. However, the middle and long chain amphiphiles, i.e., butyric acid and valeric acid, respectively, produce effective hydrophobicity at around 0.15 mol/L. More concentrations of them increase the suspension viscosity results from increasing hydrophobicity of the particles,

Fig. 14 establishes the air contents and foam stability of Al2O3-TiO2equimolar suspension, with respect to different vol% of 3:2 mole ratio of Al2O3-SiO2 suspension added for the mullite phase. High-volume foams with air content up to 83% form upon mechanical frothing, which strongly indicates the stabilization of air bubbles, due to the attachment of particles to the air-water interface. We measured the foam stability and observed that on the addition of 10 vol% suspension for the mullite phase, the foam stability suddenly decreased. This is probably due to the high viscosity of the suspension, due to higher particle concentration. However, 20, 30, and 50 vol.% of addition enhanced the foam stability, which might be explained by the optimum surface hydrophobicity being achieved, due to the increased particle concentration.

which prohibits the suspension to be foamed by mechanical stirring.

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**Figure 12.** Air content of suspension with respect to different concentration of amphiphiles.4

In Fig. 15, the wet foam stability can be determined by observing the average bubble size with respect to the time after foaming. The foams stabilized with butyric acid and valeric acid show no significant bubble growth unlike the foam stabilized with propionic acid which shows a little coarsening. We can attribute the first two cases of remarkable resistance to the irreversible adsorption of the partially hydrophobized particles at the air-water interface. Therefore, the bubble size remains almost constant with the increase of time up to 6 hours of foaming. The foams stabilized with propionic acid are prone to bubble coarsening due to the pressure

**Figure 14.** Air content and foam stability of Al2O3-TiO2equimolar suspension, with respect to different vol% of 3:2 mole ratio of Al2O3-SiO2 suspension added for the mullite phase.32

difference between two bubbles of different radius which leads to Ostwald ripening. This thermodynamically driven spontaneous process occurs because the internal pressure of a particle is indirectly proportional to the radius of the particle. Large particles, with their lower surface to volume ratio, result in a lower energy state, whereas the smaller particles exhibit higher surface energy. As the system tries to lower its overall energy, molecules on the surface of a small particle tends to detach. It diffuses through colloidal solution and attaches to the surface of larger particle. Therefore, the number of smaller particles continues to shrink, while larger particles continue to grow [17].

**Figure 15.** Relative average bubble size of suspension with respect to time after foaming.4

### **4.3. Adsorption free energy**

The adsorption free energy plays an important role in stabilizing foams. Particles attached to the gas-liquid interfaces of foams lower the system free energy, by replacing part of the gasliquid interfacial area. According to Equation (1), G (the Gibbs free energy) is greatest when *θ* is 90º; however, the foam stabilization of particles readily occurs when *θ* is between 50º and 90º.

Fig. 16 shows the change in the adsorption energy corresponding to the different mole ratio of SiO2 content used to stabilize the suspension.An Al2O3 loading of 30 vol.% in the suspension was taken as a standard, and experiments were performed with 0.01 mol L-1 amphiphiles for stabilization of the particles. The calculations show that the energy level decreases with the nanoparticle size and with increase in SiO2 content. However, after the middle value (0.75) of the SiO2 loading, the van der Waals attraction force between the particles gradually increases, forcing the suspension to destabilize and finally decrease the wet foam stability from 87% to

**Figure 16.** Free energy and wet foam stability with respect to the different mole ratio of SiO2.

68%. A higher energy of adsorption of 1.7×108 kTs could be achieved in the initial suspension without SiO2 content. The adsorption free energy decreases with the increasing concentration. Higher contact angle of 62°-75° with a lower interfacial energy of 1.7×108 kTs were seen at SiO2 mole ratio of 0.25 giving an interfacial tension of 42-45 mNm-1.

Fig. 17 establishes the relationship between adsorption free energy corresponding to the foam stability, with respect to the different vol.% of suspension added for the mullite phase. Low adsorption free energy resulting from the spontaneous bubble growth leads to foam instability. The investigated samples exhibit much higher adsorption free energy of about 2.2×10-13 J to 2.7×10-13 J at the interface, resulting in irreversible adsorption of particles at the air-water interface, which leads to outstanding stability.

In Fig. 18, a relationship between adsorption free energy corresponding to the concentrations of different chain length of amphiphile has been established. Stable and unstable zones have been described relating to the data obtained by the wet foam stability graph. Low adsorption free energy (e.g., 2.05×10-13 J to 3.78×10-13 J) results from the spontaneous bubble growth leads to foam instability. However, higher adsorption free energy of about 4.52×10-13 J to 8.22×10-13 J at the interface results in irreversible adsorption of particles at the air-water interface which leads to outstanding stability.

#### **4.4. Laplace pressure and bubble size**

particle is indirectly proportional to the radius of the particle. Large particles, with their lower surface to volume ratio, result in a lower energy state, whereas the smaller particles exhibit higher surface energy. As the system tries to lower its overall energy, molecules on the surface of a small particle tends to detach. It diffuses through colloidal solution and attaches to the surface of larger particle. Therefore, the number of smaller particles continues to shrink, while

**Figure 15.** Relative average bubble size of suspension with respect to time after foaming.4

The adsorption free energy plays an important role in stabilizing foams. Particles attached to the gas-liquid interfaces of foams lower the system free energy, by replacing part of the gasliquid interfacial area. According to Equation (1), G (the Gibbs free energy) is greatest when *θ* is 90º; however, the foam stabilization of particles readily occurs when *θ* is between 50º and

Fig. 16 shows the change in the adsorption energy corresponding to the different mole ratio of SiO2 content used to stabilize the suspension.An Al2O3 loading of 30 vol.% in the suspension was taken as a standard, and experiments were performed with 0.01 mol L-1 amphiphiles for stabilization of the particles. The calculations show that the energy level decreases with the nanoparticle size and with increase in SiO2 content. However, after the middle value (0.75) of the SiO2 loading, the van der Waals attraction force between the particles gradually increases, forcing the suspension to destabilize and finally decrease the wet foam stability from 87% to

larger particles continue to grow [17].

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**4.3. Adsorption free energy**

90º.

Fig. 19 shows the wet foam stability corresponding to the pressure exerted by the bubbles (Laplace pressure) with respect to the different mole ratio of SiO2 content. The Laplace pressure increases with the increase in SiO2 concentration. This behavior can be attributed to the fact that high silica content requires a large volume of water in the suspension, which subsequently

**Figure 17.** Adsorption free energy and foam stability of Al2O3-TiO2 equimolar suspension, with respect to different vol % of 3:2 mole ratio of Al2O3-SiO2 suspension added for the mullite phase.32

**Figure 18.** Adsorption free energy of suspension with respect to different concentration of amphiphiles.4

lowers the outer pressure of the bubble. The wet foam stability suddenly decreases due to high Laplace pressure when the mole ratio of SiO2 reached at 0.60. The wet foams were stable at the pressure difference between 20 and 25 mPa, which corresponds to the SiO2 mole ratio content of 0.25-0.50. The stability increased to more than 80% at a SiO2 mole ratio of 0.75.

**Figure 19.** Laplace pressure and wet foam stability with respect to the different mole ratio of SiO2 content.

Fig. 20 plots the graph of the Laplace pressure and average bubble size of all evaluated suspensions, with respect to the various vol.% of suspension for the mullite phase. As we can see, instability occurs when the Laplace pressure is too low. Wet foam stability occurs when the Laplace pressure is about 1.5-2.2 mPa. The degree of particle hydrophobization influences the average bubble size of the resultant foams. Fig. 20 shows that the average bubble size decreases with increasing particle concentration and particle hydrophobicity. This is due to the decrease in surface tension and increase in foam viscosity that result from higher particle concentrations. This reduces the resistance of air bubbles against rupture and thus leads to the production of foams with average bubble sizes.

In Fig. 21, the Laplace pressure of all evaluated suspensions has been plotted in a graph with respect to the various concentration of different chain length of amphiphile. As we can see, the instability occurs when the Laplace pressure is too low as in case of 0.10 mol/L of amphiphile concentration. Wet foam stability occurs when Laplace pressure is about 0.8-1.4 mPa. Valeric acid, having the longest chain length, exhibits high Laplace pressure resulting in outstanding stability of wet foam.

The degree of particle hydrophobization, which is directly related to the concentration of amphiphile, influences the average bubble size of the resultant foams. Fig. 22 shows the bubble size of the suspension and the pore size by thin film or struts formed after the foaming of the particle stabilized suspension and sintering. The average bubble size for these types of stabilized foams was 98-140 μm. The required partial hydrophobization of the particles occurs at this point, which leads to porous ceramics with porosity greater than 80% and pore size of about 108 μm after sintering at 1300°C for 1 hour.

lowers the outer pressure of the bubble. The wet foam stability suddenly decreases due to high Laplace pressure when the mole ratio of SiO2 reached at 0.60. The wet foams were stable at the pressure difference between 20 and 25 mPa, which corresponds to the SiO2 mole ratio content

**Figure 17.** Adsorption free energy and foam stability of Al2O3-TiO2 equimolar suspension, with respect to different vol

% of 3:2 mole ratio of Al2O3-SiO2 suspension added for the mullite phase.32

74 Advanced Ceramic Processing

of 0.25-0.50. The stability increased to more than 80% at a SiO2 mole ratio of 0.75.

**Figure 18.** Adsorption free energy of suspension with respect to different concentration of amphiphiles.4

In Fig. 23, it can be seen that the average bubble size decreases with increasing amphiphile concentration and particle hydrophobicity. This is due to the decrease in surface tension and

**Figure 20.** Laplace pressure and bubble size of Al2O3-TiO2 equimolar suspension, with respect to different vol% of 3:2 mole ratio of Al2O3-SiO2 suspension added for the mullite phase.32

**Figure 21.** Laplace pressure of suspension with respect to different concentration of amphiphiles.4

increase in foam viscosity because of higher amphiphile concentrations. This decreases the resistance of air bubbles against rupture and thus leads to produce foams with average bubble sizes. It is interesting to note that valeric acid, having the longest amphiphilic chain, produces

**Figure 22.** Bubble size and pore size with respect to the SiO2 content of the wet foam before and after sintering at 1300°C for 1 hour.

very small sized bubbles of about 35-25 μm. This can be attributed to the greater hydropho‐ bicity, which results in enhanced stability of particle stabilized foams against bubble coales‐ cence and Ostwald ripening [see Fig. 26(c)].

#### **4.5. Microstructure analysis**

increase in foam viscosity because of higher amphiphile concentrations. This decreases the resistance of air bubbles against rupture and thus leads to produce foams with average bubble sizes. It is interesting to note that valeric acid, having the longest amphiphilic chain, produces

**Figure 21.** Laplace pressure of suspension with respect to different concentration of amphiphiles.4

**Figure 20.** Laplace pressure and bubble size of Al2O3-TiO2 equimolar suspension, with respect to different vol% of 3:2

mole ratio of Al2O3-SiO2 suspension added for the mullite phase.32

76 Advanced Ceramic Processing

The microstructures are described in Fig. 24, where tailored, open and closed, interconnected pores can be seen. Also, it can be seen that the larger and smaller pores are uniformly distrib‐ uted. In Fig. 24a-d, different compositions of Al2O3/SiO2 with well-developed and narrow pore size distribution can be seen. It shows a hierarchical pore distribution with porosities up to 80% from larger to smaller pores and thick struts (films in wet foams). It leads to produce more stable foams sintered to form porous ceramics with high mechanical strength.

Fig. 25 shows the microstructures of porous (a) AT, (b) ATM1, (c) ATM3, and (d) ATM5, sintered at 1500°C for 1 hour. The microstructures obtained generally consist of open, inter‐ connected pores with a narrow pore size distribution. The composition without addition of mullite (Fig. 25(a)) shows the characteristic microstructure of Al2TiO5: an open porous and microcracked Al2TiO5 matrix phase, with the presence of abnormal grain growth. These grains can be attributed to unreacted Al2O3 and TiO2 due to the formation reaction kinetics, which is a process led by the nucleation and growth of Al2TiO5 grains, and finally the diffusion of the reactants through the matrix. It is evident from Fig. 25b-d that the addition of mullite has a beneficial effect on grain growth control.

The scanning electron microscope images of 30 Vol% Al2O3-SiO2 porous ceramics sintered at 1300°C with different chain length amphiphile of concentration 0.15 mol/L are shown in Fig. 26. The microstructures obtained are generally consists of closed pores. It is interesting to note

**Figure 23.** Average bubble size of suspension with respect to different concentration of amphiphiles.4

that at the same concentration of amphiphile, the shortest chain carboxylic acid, i.e., propionic acid, produces relatively large pore size than the longest chain carboxylic acid, i.e., valeric acid. This can be attributed to the fact that greater hydrophobicity is achieved with the aid of long carbon chain present in valeric acid which results in small and uniform pore size. The smaller cell sizes result from the high stability of the foams in the wet state, which impedes bubble coarsening. The dense struts as shown in the inset of Fig. 26a-c plays vital role for improving the mechanical strength of the porous ceramics.
