**4.1 Composite foams/foams with guest phases with preload of new phases in the preform**

## *4.1.1 Magnesium/diamond composite foams*

*Foams - Emerging Technologies*

*3.2.4 Monolithic finned foams*

*3.2.5 Composite finned foams*

matrix can be obtained (**Figure 5**).

continuous matrix is obtained (**Figure 6**).

*structure of the final material (b) for monolithic finned foams.*

integrated into a material with a layered structure and a noncontinuous matrix

Another way to fabricate finned foams is to perform a casting of a liquid precursor into a mold where preexistent self-standing porous leachable preforms are conveniently located. As a result, monolithic finned foam materials with continuous

Loading of new phases is achieved by building an assembly consisting of packed or self-standing porous leachable preforms alternated with packed beds of the new phases in finely divided form (inclusions). After infiltration and removal of the leachable materials, a final material with a layered distribution of components and

*Schematic drawings showing a mold with preexistent self-standing porous leachable preforms (a) and the* 

(a) (b)

*Schematic drawings showing an assembly consisting of packed or self-standing porous leachable preforms alternated with packed beds of finely divided inclusions (a) and the structure of the final material (b) for* 

(joints are present in between components) (**Figure 4**).

**8**

**Figure 6.**

*composite finned foams.*

**Figure 5.**

Open-pore magnesium foams, which have traditionally been discarded for active thermal management due to their low thermal conductivity values, can be appropriate for heat dissipation applications if they incorporate thermal inclusions such as diamond particles coated with a TiC layer of nanometric dimensions. These multiphase open-pore composite foams can be manufactured by the replication method following a strict processing control. First, a correct distribution of the preform components (NaCl and diamond particles) has to be achieved to ensure homogeneity and complete connectivity of the pores after dissolution. For this purpose, the selection of the composition of bimodal particle mixtures has been studied in detail following a predictive method described in [8, 34–37]. The results of these calculations are depicted in **Figure 7a** for the entire spectrum of NaCl particle fraction in the bimodal mixtures. The complete pore connectivity is achieved when the composition of NaCl in the bimodal (NaCl-diamond) mixture falls in the region of interest represented in **Figure 7a**. In this region the large NaCl particles are touching each other, and the smaller diamond particles are filling the voids left by the sodium chloride particles.

Another critical processing step is the proper control of TiC coating on diamond particles, which allows for high thermal conductance at the interface between the diamond particles and the matrix. The scanning electron microscopy (SEM) images in **Figure 8** illustrate some microstructural features of Mg/diamond composite foam. **Figure 8a** shows the diamond particles homogeneously distributed in the struts of the Mg matrix. **Figure 8b** depicts Si and Fe precipitates on diamond surfaces. During the metal solidification, traces of Si and Fe present in the nominal composition of magnesium segregate toward the interface, enhancing together with the TiC coating the magnesium-diamond interfacial thermal conductance.

### **Figure 7.**

*Contour diagram of the total volume fraction of inclusions (considering diamond and salt particles mixtures) over the whole range of NaCl particle fraction (XNaCl) as a function of R (ratio of the diameters of coarse NaCl particles to small diamond particles) (a); (b) is a magnification of the region of interest show in (a). Reproduced with permission from [8].*

**Figure 8.**

*SEM micrographs of TiC-coated diamond particle distribution in the foam struts (a) and fine precipitates of silicon and iron on the TiC-coated diamond particles (b). Sample (a) was prepared by fracture, while sample (b) was prepared by fracture followed by magnesium electro-etching. Reproduced with permission from [8].*

The thermal conductivity of these materials was both measured and estimated with analytical methods. The measurement of the thermal conductivity was carried out by the so-called comparative stationary method, which provides accurate and relatively fast measurements. It consists of comparing the thermal conductivity of an unknown material (the sample) with that of a reference, connecting the sections of both and establishing a thermal gradient.

The thermal conductivity was estimated with the differential effective medium (DEM) scheme, which has been extendedly applied with success to model and interpret thermal conduction in different composite materials consisting of randomly distributed monodispersed particles in a metal matrix [8, 34, 35, 37, 38]. The leading equation is expressed as the following integral:

$$\begin{aligned} & \text{Performance parameter} \text{ in a mean matrix } \{\mathbf{p}\} \sim \eta \text{ } \text{yes, } m \text{, } \text{sex}^{\dagger}. \text{ Here} \\ & \text{Based as the following integral:} \\ & \int\_{K\_m}^{K\_C} \frac{dK}{K \sum\_i X\_i \frac{-(K - K\_r^{\text{eff}})}{(K - K\_r^{\text{eff}})p - K}} = -\ln\left(1 - V\right) \tag{1} \end{aligned} \tag{1}$$

where *K* is thermal conductivity and subscripts *C* and *m* refer to composite and matrix, respectively. *Xi* is the fraction of the *i* inclusion type in the total amount of inclusions of the composite (in composites containing only one type of inclusions *i* = 1; hence, *X1* = 1). *V* is the total volume fraction of inclusions, and *p* is the polarization factor of an inclusion (equal to one-third for spheres). *Kr eff* is the effective thermal conductivity of an inclusion which, for spherical geometries, is related to its intrinsic thermal conductivity, *Kr in*, the matrix/inclusion interface thermal conductance *h*, and the radius of the inclusion *r*, by *eff* = *Kr* \_

$$K\_r^{eff} = \frac{K\_r^{in}}{\mathbf{1} + \frac{K\_r^{in}}{hr}} \tag{2}$$

In general, the integral on the left-hand side of Eq. (1) has no analytical solution and needs to be solved numerically with appropriate mathematical software.

Foam materials can be considered composites where pores are inclusions of zero nominal thermal conductivity (*Kr in* = 0 W/mK). Eq. (1) then becomes

$$K\_C = K\_{fam} = K\_m \left(1 - V\_p\right)^{\frac{1}{1-p}} \tag{3}$$

**11**

**Figure 9.**

*from [8].*

*Open-Pore Foams Modified by Incorporation of New Phases: Multiphase Foams for Thermal…*

the pore structure of the foam was derived, since the replication method maintains the morphological characteristics of the leachable particles in the pores of the final material). For spherical particles again *p* = 1/3 [8]; in more complicated particle geometries, the value of p can be derived from the slope of a plot of log(*Kfoam*) vs. log(1 − *Vp*) for foam materials in which *Vp* is varied. *Km* is the thermal conductivity of the matrix in the foam material, which can be in turn calculated with Eq. (1) by considering that the matrix is an effective composite material of pure magnesium

The calculated thermal conductivities of Mg/diamond composite foams according to Eqs. (1)–(3) are plotted in **Figure 9a** against the experimental results [8]. In general, large fractions and large average sizes of diamond particles in the matrix generate higher thermal conductivities, and the presence of nano-coated TiC diamond is necessary to overcome the thermal conductivity of magnesium foam, reaching values up to 82 W/mK when the material contains 30% of nano-coated

Since there is no standardized methodology for testing heat sinks in inducedconvection active thermal management, the author of [8] proposed a new experimental setup inspired by that reported in [39] to measure power dissipation density of open-pore materials. Results obtained with this setup showed that composite foams achieved excellent performance in active thermal management with values up to 100% higher than their equivalent magnesium foams and 20% superior than

These multiphase foam materials were inspired by the recently developed family of highly anisotropic thermally conductive ternary composites formed by the combination of graphite flakes (Gf), ceramic particles, and a metal matrix [40, 41]. Aluminum/graphite flake (Al/Gf) composite foams combine the appeal of using Gf to improve thermal conductivity with the advantages of metal foams and configure a new family of foam materials with great potential for active thermal management applications. These materials are fabricated using the replication method, replacing the ceramic particles of the ternary composites with

*Experimental vs. calculated thermal conductivities for Mg/diamond composite foams developed in [8] (a) and a comparison of power density as a function of airflow between Mg-TiC/diamond composite foam and conventional metal foams (b). In (a), MBD4 refers to the quality of the diamond particles; in (b), XD is the diamond particles fraction in the original bimodal particle mixture preform. Reproduced with permission* 

*DOI: http://dx.doi.org/10.5772/intechopen.88977*

with diamond particles as thermal inclusions.

conventional aluminum foams (**Figure 9b**).

*4.1.2 Aluminum/graphite flake composite foams*

TiC diamond.

where *Vp* refers to the volume fraction of pores and p is now the polarization factor of the pores (equal to the polarization factor of the NaCl particles from which *Open-Pore Foams Modified by Incorporation of New Phases: Multiphase Foams for Thermal… DOI: http://dx.doi.org/10.5772/intechopen.88977*

the pore structure of the foam was derived, since the replication method maintains the morphological characteristics of the leachable particles in the pores of the final material). For spherical particles again *p* = 1/3 [8]; in more complicated particle geometries, the value of p can be derived from the slope of a plot of log(*Kfoam*) vs. log(1 − *Vp*) for foam materials in which *Vp* is varied. *Km* is the thermal conductivity of the matrix in the foam material, which can be in turn calculated with Eq. (1) by considering that the matrix is an effective composite material of pure magnesium with diamond particles as thermal inclusions.

The calculated thermal conductivities of Mg/diamond composite foams according to Eqs. (1)–(3) are plotted in **Figure 9a** against the experimental results [8]. In general, large fractions and large average sizes of diamond particles in the matrix generate higher thermal conductivities, and the presence of nano-coated TiC diamond is necessary to overcome the thermal conductivity of magnesium foam, reaching values up to 82 W/mK when the material contains 30% of nano-coated TiC diamond.

Since there is no standardized methodology for testing heat sinks in inducedconvection active thermal management, the author of [8] proposed a new experimental setup inspired by that reported in [39] to measure power dissipation density of open-pore materials. Results obtained with this setup showed that composite foams achieved excellent performance in active thermal management with values up to 100% higher than their equivalent magnesium foams and 20% superior than conventional aluminum foams (**Figure 9b**).

### *4.1.2 Aluminum/graphite flake composite foams*

These multiphase foam materials were inspired by the recently developed family of highly anisotropic thermally conductive ternary composites formed by the combination of graphite flakes (Gf), ceramic particles, and a metal matrix [40, 41]. Aluminum/graphite flake (Al/Gf) composite foams combine the appeal of using Gf to improve thermal conductivity with the advantages of metal foams and configure a new family of foam materials with great potential for active thermal management applications. These materials are fabricated using the replication method, replacing the ceramic particles of the ternary composites with

### **Figure 9.**

*Foams - Emerging Technologies*

**Figure 8.**

*from [8].*

The thermal conductivity of these materials was both measured and estimated with analytical methods. The measurement of the thermal conductivity was carried out by the so-called comparative stationary method, which provides accurate and relatively fast measurements. It consists of comparing the thermal conductivity of an unknown material (the sample) with that of a reference, connecting the sections

*SEM micrographs of TiC-coated diamond particle distribution in the foam struts (a) and fine precipitates of silicon and iron on the TiC-coated diamond particles (b). Sample (a) was prepared by fracture, while sample (b) was prepared by fracture followed by magnesium electro-etching. Reproduced with permission* 

The thermal conductivity was estimated with the differential effective medium

= −*ln*

(1 − *V*) (1)

*in*, the matrix/inclusion interface thermal

(2)

1−*<sup>p</sup>* (3)

*eff* is the effective

(DEM) scheme, which has been extendedly applied with success to model and interpret thermal conduction in different composite materials consisting of randomly distributed monodispersed particles in a metal matrix [8, 34, 35, 37, 38]. The

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ *dK*

(*K* − *Kr eff*) \_\_\_\_\_\_\_\_\_\_\_\_ (*<sup>K</sup>* <sup>−</sup>*Kr eff*)*p* − *K*

thermal conductivity of an inclusion which, for spherical geometries, is related

*Kr*

and needs to be solved numerically with appropriate mathematical software.

*KC* = *Kfoam* = *Km*

where *K* is thermal conductivity and subscripts *C* and *m* refer to composite and matrix, respectively. *Xi* is the fraction of the *i* inclusion type in the total amount of inclusions of the composite (in composites containing only one type of inclusions *i* = 1; hence, *X1* = 1). *V* is the total volume fraction of inclusions, and *p* is the polar-

> *eff* = *Kr* \_ *in*

1 + *Kr in* \_ *hr*

In general, the integral on the left-hand side of Eq. (1) has no analytical solution

Foam materials can be considered composites where pores are inclusions of zero

where *Vp* refers to the volume fraction of pores and p is now the polarization factor of the pores (equal to the polarization factor of the NaCl particles from which

*in* = 0 W/mK). Eq. (1) then becomes

\_1

(1 − *Vp*)

*<sup>K</sup>* <sup>∑</sup>*i Xi* <sup>−</sup>

ization factor of an inclusion (equal to one-third for spheres). *Kr*

of both and establishing a thermal gradient.

to its intrinsic thermal conductivity, *Kr*

nominal thermal conductivity (*Kr*

leading equation is expressed as the following integral:

∫

conductance *h*, and the radius of the inclusion *r*, by

*Km KC* 

**10**

*Experimental vs. calculated thermal conductivities for Mg/diamond composite foams developed in [8] (a) and a comparison of power density as a function of airflow between Mg-TiC/diamond composite foam and conventional metal foams (b). In (a), MBD4 refers to the quality of the diamond particles; in (b), XD is the diamond particles fraction in the original bimodal particle mixture preform. Reproduced with permission from [8].*

sodium chloride particles, which act as templates and can be removed by dissolution to obtain a material with an interconnected porous structure. The preforms were prepared by packing under external pressure a homogeneous distribution of oriented Gf and NaCl particles.

Two restrictions were found according to the preparation of these preforms. The first one was related with the dissolution of the template. To ensure complete and effective dissolution, the NaCl particles must achieve a coordination number for each particle of at least 3. This restriction defined a so-called percolation limit that is shown in **Figure 10a** as a dotted straight line. The second restriction has to do with the existence of a minimum volume fraction attained when particles are subjected to the sole action of gravity. This second restriction, the so-called compaction limit, is represented in **Figure 10a** by the line corresponding to a nominal zero pressure. As a consequence, preforms with compositions falling in regions below these two limits of **Figure 10a** cannot be manufactured.

For these microstructures where Gf are oriented and distributed homogeneously in a matrix, we can take the following expression for the longitudinal thermal conductivity of composite foams *KC L* [13, 41]:

$$\begin{array}{l}\text{we the following expression for the longitudinal thermal} \\ \text{positive forms } K\_C^{\perp L} \text{ [13, 41]:} \\\\ K\_C^{\perp} = K\_{foam} + K\_{foam} \frac{V'f}{\frac{\pi t}{4D} (1 - V'f) + \frac{K\_{foam}}{K\_f^{\perp} - K\_{foam}}} \\ \end{array} \tag{4}$$

where *Kf L* is the longitudinal thermal conductivity of Gf, *V´f* is the volume fraction of Gf in the composite material, and *t* and *D* are the thickness and diameter of Gf, respectively. *Kfoam* can be calculated with Eq. (3).

The calculated vs. the experimental results of longitudinal thermal conductivity for these composite foams are represented in **Figure 11a**. **Figure 11b** depicts the power dissipation densities of two Al/Gf composite foams (one with *V´f* = 0.54 and another one with *V´f* = 0.34) and a conventional aluminum foam (with a porosity volume fraction of 0.78) vs. airflow, obtained with the setup described in [8]. It is clear that proper designs of Al/Gf composite foams can reach power dissipation densities three times higher than those achieved with conventional aluminum foams.

### **Figure 10.**

*(a) Preform composition ternary phase diagram as a function of compaction pressure (in MPa) and (b) photograph of an Al/Gf foam with homogeneous distribution of oriented Gf along the porous material. In (b) the pores were infiltrated with epoxy resin for a better polishing. Reproduced with permission from [13].*

**13**

**Figure 12.**

*(b). Reproduced from [15, 16].*

*Open-Pore Foams Modified by Incorporation of New Phases: Multiphase Foams for Thermal…*

Open-pore foams containing guest phases in porous cavities is one of the latest developments in the design of foam materials that brings specific functionalities and opens niches for new applications [15, 16]. Depending on the nature of the guest phases or the combination of them, several applications can be considered for these materials such as adsorption of gases, adsorption of liquids or species in solution, catalysis, filters of inorganic or biological substances, and medical implantology. The processing route involves the generation of preforms by packaging particles coated with a sacrificial material (e.g., NaCl), their subsequent infiltration with a suitable precursor, and finally the dissolution of the sacrificial material. This results in open-pore foams in which the cavities contain other phases that provide certain functionalities. A distinctive feature is that there is no bond between the matrix and the guest phases, except for a simple contact generated by gravity, so that the interconnectivity of the pores remains assured. **Figure 12** shows SEM images of a guest particle coated with a sacrificial material (NaCl in this case) (a)

*(a) Calculated vs. experimental thermal conductivities for different Al/Gf composite foams and (b) a comparison of power dissipation density as a function of airflow between some selected Al/Gf composite foams and a conventional aluminum foam. Graphit flakes dimensions: 1000 μm average diameter and 20–45 μm* 

and the same guest particle inside the pore cavity of a metal foam (b).

*Cobalt sphere with NaCl coating (a) and cobalt sphere as guest phase inside a cavity of an open-pore tin foam* 

*DOI: http://dx.doi.org/10.5772/intechopen.88977*

*4.1.3 Foams with guest phases*

*thickness. Partially reproduced from [13].*

**Figure 11.**

*Open-Pore Foams Modified by Incorporation of New Phases: Multiphase Foams for Thermal… DOI: http://dx.doi.org/10.5772/intechopen.88977*

### **Figure 11.**

*Foams - Emerging Technologies*

oriented Gf and NaCl particles.

conductivity of composite foams *KC*

*KC L*

Gf, respectively. *Kfoam* can be calculated with Eq. (3).

manufactured.

where *Kf*

aluminum foams.

*L*

sodium chloride particles, which act as templates and can be removed by dissolution to obtain a material with an interconnected porous structure. The preforms were prepared by packing under external pressure a homogeneous distribution of

Two restrictions were found according to the preparation of these preforms. The first one was related with the dissolution of the template. To ensure complete and effective dissolution, the NaCl particles must achieve a coordination number for each particle of at least 3. This restriction defined a so-called percolation limit that is shown in **Figure 10a** as a dotted straight line. The second restriction has to do with the existence of a minimum volume fraction attained when particles are subjected to the sole action of gravity. This second restriction, the so-called compaction limit, is represented in **Figure 10a** by the line corresponding to a nominal zero pressure. As a consequence, preforms with compositions falling in regions below these two limits of **Figure 10a** cannot be

For these microstructures where Gf are oriented and distributed homogeneously

<sup>4</sup>*D*(1 <sup>−</sup> *<sup>V</sup>*´ *<sup>f</sup>*) <sup>+</sup>

is the longitudinal thermal conductivity of Gf, *V´f* is the volume frac-

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \_

\_ *Kfoam Kf <sup>L</sup>* − *Kfoam* 

(4)

in a matrix, we can take the following expression for the longitudinal thermal

<sup>=</sup>*Kfoam* <sup>+</sup>*Kfoam <sup>V</sup>*´ *<sup>f</sup>*

[13, 41]:

*πt*

tion of Gf in the composite material, and *t* and *D* are the thickness and diameter of

*(a) Preform composition ternary phase diagram as a function of compaction pressure (in MPa) and (b) photograph of an Al/Gf foam with homogeneous distribution of oriented Gf along the porous material. In (b) the pores were infiltrated with epoxy resin for a better polishing. Reproduced with permission from [13].*

The calculated vs. the experimental results of longitudinal thermal conductivity for these composite foams are represented in **Figure 11a**. **Figure 11b** depicts the power dissipation densities of two Al/Gf composite foams (one with *V´f* = 0.54 and another one with *V´f* = 0.34) and a conventional aluminum foam (with a porosity volume fraction of 0.78) vs. airflow, obtained with the setup described in [8]. It is clear that proper designs of Al/Gf composite foams can reach power dissipation densities three times higher than those achieved with conventional

*L*

**12**

**Figure 10.**

*(a) Calculated vs. experimental thermal conductivities for different Al/Gf composite foams and (b) a comparison of power dissipation density as a function of airflow between some selected Al/Gf composite foams and a conventional aluminum foam. Graphit flakes dimensions: 1000 μm average diameter and 20–45 μm thickness. Partially reproduced from [13].*

### *4.1.3 Foams with guest phases*

Open-pore foams containing guest phases in porous cavities is one of the latest developments in the design of foam materials that brings specific functionalities and opens niches for new applications [15, 16]. Depending on the nature of the guest phases or the combination of them, several applications can be considered for these materials such as adsorption of gases, adsorption of liquids or species in solution, catalysis, filters of inorganic or biological substances, and medical implantology. The processing route involves the generation of preforms by packaging particles coated with a sacrificial material (e.g., NaCl), their subsequent infiltration with a suitable precursor, and finally the dissolution of the sacrificial material. This results in open-pore foams in which the cavities contain other phases that provide certain functionalities. A distinctive feature is that there is no bond between the matrix and the guest phases, except for a simple contact generated by gravity, so that the interconnectivity of the pores remains assured. **Figure 12** shows SEM images of a guest particle coated with a sacrificial material (NaCl in this case) (a) and the same guest particle inside the pore cavity of a metal foam (b).

### **Figure 12.**

*Cobalt sphere with NaCl coating (a) and cobalt sphere as guest phase inside a cavity of an open-pore tin foam (b). Reproduced from [15, 16].*

These materials have not yet been widely characterized, but it is intuited that they have a great potential in the following applications:

