# Investigation of the Thermal Conductivity of Resin-Based Lightweight Composites Filled with Hollow Glass Microspheres

^{*}

## Abstract

**:**

^{3}. The relationship between the effective thermal conductivity of HGM/EP LWTI composites and material parameters (sizes and contents together) has been studied systematically. A three-phase prediction model was built using the self-consistent approximation method to predict the effective thermal conductivity of HGM/EP LWTI composites, and the resin matrix, the wall thickness, the HGM particle size, and other parameters (such as air) were fully considered during the derivation of this three-phase thermal conductivity model. Finally, the insulation mechanism of HGM/EP LWTI composites was systematically analyzed. The thermal conductivities of HGM/EP LWTI composites with different diameters and HGM contents calculated by the three-phase prediction model agreed well with the experimental test results, with a minimum error of only 0.69%. Thus, this three-phase thermal conductivity model can be used to theoretically simulate the thermal conductivity of epoxy resin-based LWTI composites and can be the theoretical basis for the design and prediction of the thermal conductivity of other similar hollow spheres filled materials.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

^{3}was purchased from Sinopec Baling Petrochemical Co., Ltd. (Yueyang, China). Methyl Tetrahydrophthalic Anhydride (MTHPA) (Zhejiang Alpharm Chemical Technology Co., Ltd, Zhengjiang, China) was used as a hardener. 3-Triethoxysilylpropylamine (KH550) was purchased from Yaohua chemical plant (Shanghai, China). The HGMs (HGMs) were provided by 3M China Ltd (Shanghai, China) and their properties are listed in Table S1.

#### 2.2. Preparation of HGM/EP LWTI Composites

#### 2.3. Characterization and Measurements

_{th}is the theoretical density, ${\rho}_{HGM}$ is the HGM density, ρ

_{m}is the density of the epoxy resin, and ${\varnothing}_{HGM}$ is the HGM volume fraction.

_{exp}is the measured density. The samples were cut into the standard dimension of 10 × 10 × 10 mm. Five specimens for each sample were tested in series to obtain the final results.

_{R}is the maximum load; L is the spacing between the two supports; and b and d are the specimen width and thickness, respectively.

_{t}is the deformation and F

_{t}is the corresponding load.

## 3. Results

#### 3.1. The Morphology and Density of HGM/EP LWTI Composites

^{3}to 0.930 g/cm

^{3}, 0.979 g/cm

^{3}to 0.826 g/cm

^{3}, 0.912 g/cm

^{3}to 0.709 g/cm

^{3}, and 0.845 g/cm

^{3}to 0.591 g/cm

^{3}, respectively. The theoretically calculated density values and the experimental test results for the HGM/EP LWTI composites showed the same change behavior, but the theoretically calculated values were slightly higher than the test results, owing to residual bubbles during the preparation steps including mechanical mixing, molding, and curing of the EP and HGMs. From the void volume fraction calculation, when the HGM content is 20 vol.%, the void volume fraction of HGM/EP LWTI composites increases from 2.41% to 5.18% as the HGM diameter increases from 30 μm to 55 μm. The HGM/EP LWTI composites with 30 vol.% HGMs increased from 3.2% to 5.86% and further increased from 4.33% to 8.39% and 5.50% to 11.71% for HGM/EP LWTI composites with 40 vol.% HGMs and 50 vol.% HGMs, respectively. As the HGM content increases, EP may not surround the HGM very well, resulting in increased gap formation in the composites. On the other hand, the increasing HGM content also makes it more difficult to mix the HGMs with the EP, and insufficient resin mixture can cause the HGMs to stick together, and bubbles to form in the composite.

#### 3.2. The Flexural Properties of HGM/EP LWTI Composites

#### 3.3. The Thermal Conductivity of HGM/EP LWTI Composites

#### 3.3.1. Thermal Conductivity Model for HGM/EP LWTI Composites

- (1)
- The HGMs, epoxy resin, and the LWTI composites formed using them are all isotropic.
- (2)
- The HGMs are evenly dispersed throughout the resin matrix, and the matrix resin evenly surrounds the surface of the HGMs.
- (3)
- The effect of bubbles on the composite properties is ignored (excluding the hollow interior of the HGMs).

_{z}

^{(12)}can be obtained from the interface temperature discontinuity between material 1 and material 2, as follows:

#### 3.3.2. The Experimental Thermal Conductivity Results

#### 3.4. Insulation Mechanism of HGM/EP LWTI Composites

#### 3.4.1. The Gaseous Convection within the HGMs

#### 3.4.2. The Thermal Radiation on the Surface of the HGMs

#### 3.4.3. The Solid and Gaseous Conduction

## 4. Conclusions

^{3}. Then, we presented a three-phase prediction model for the effective thermal conductivity by considering the resin matrix, the wall thickness, the HGM particle size, and other parameters (such as air) fully. The prediction results of our HGM/EP LWTI composites were further compared with experimental data, showing that this three-phase thermal conductivity model provides accurate thermal conductivity prediction of HGM/EP LWTI composites with different HGM diameters and content. All error rates of the experimental data and the theoretical predictions were below 5% and the minimum error was only 0.69%. Lastly, the heat transport in the HGM/EP LWTI composites is mainly governed by solid and gaseous conduction in this study, and the HGM/EP LWTI composites presented low thermal conductivity and good thermal insulation performance owing to the effective blocking of heat conduction by HGMs. More importantly, this work presents insights into this type of hollow sphere-filled material design through parametric studies; the prediction model and method are also easy to use to predict the thermal conductivity of other hollow sphere-filled materials.

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Scanning electron microscopy (SEM) graphs of lightweight composites with different hollow glass microsphere (HGM) diameters and contents.

**Figure 2.**The flexural properties of HGM/EP LWTI composites with different HGM diameter and content. (

**a**) bending stress–strain curves; (

**b**) the flexural strength; (

**c**) the flexural modulus.

**Figure 4.**The thermal conductivity calculation of three-phase lightweight composites and actual test values.

**Table 1.**The relationship of porosity with different hollow glass microsphere (HGM) diameter and contents.

Diameter (μm) | Content of HGMs (vol.%) | ρ_{th}(g/cm ^{3}) | ρ_{exp}(g/cm ^{3}) | φ_{v}(%) |
---|---|---|---|---|

30 | 20 | 1.071 | 1.045 | 2.41 |

30 | 1.012 | 0.979 | 3.28 | |

40 | 0.953 | 0.912 | 4.33 | |

50 | 0.895 | 0.845 | 5.50 | |

40 | 20 | 1.005 | 1.027 | 2.17 |

30 | 0.946 | 0.915 | 3.33 | |

40 | 0.865 | 0.831 | 4.03 | |

50 | 0.785 | 0.743 | 5.34 | |

55 | 20 | 0.981 | 0.930 | 5.18 |

30 | 0.877 | 0.826 | 5.86 | |

40 | 0.773 | 0.709 | 8.39 | |

50 | 0.670 | 0.591 | 11.71 |

**Table 2.**Predicted thermal conductivity for the prepared HGM/epoxy resin (EP) lightweight thermal insulation composites.

Thermal Conductivity (W/(m·K)) | Volume Fraction | |||
---|---|---|---|---|

20% | 30% | 40% | 50% | |

D30 | 0.204 | 0.193 | 0.183 | 0.173 |

D40 | 0.190 | 0.174 | 0.158 | 0.143 |

D55 | 0.174 | 0.151 | 0.129 | 0.110 |

**Table 3.**A comparison of experimental data and calculated results from the thermal conductivity prediction model for HGM/EP LWTI composites.

HGMs Content (vol.%) | Type | Thermal Conductivity Theoretical Value (W/(m·K)) | Thermal Conductivity of Actual Value (W/(m·K)) | Error (%) |
---|---|---|---|---|

20 | D30 | 0.204 | 0.209 | 2.532 |

D40 | 0.190 | 0.187 | 1.710 | |

D55 | 0.174 | 0.171 | 1.755 | |

30 | D30 | 0.193 | 0.197 | 1.918 |

D40 | 0.174 | 0.169 | 2.738 | |

D55 | 0.151 | 0.155 | 2.679 | |

40 | D30 | 0.183 | 0.181 | 1.137 |

D40 | 0.158 | 0.162 | 2.474 | |

D55 | 0.129 | 0.135 | 4.246 | |

50 | D30 | 0.173 | 0.172 | 0.685 |

D40 | 0.143 | 0.148 | 3.363 | |

D55 | 0.110 | 0.114 | 4.090 |

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## Share and Cite

**MDPI and ACS Style**

Xing, Z.; Ke, H.; Wang, X.; Zheng, T.; Qiao, Y.; Chen, K.; Zhang, X.; Zhang, L.; Bai, C.; Li, Z.
Investigation of the Thermal Conductivity of Resin-Based Lightweight Composites Filled with Hollow Glass Microspheres. *Polymers* **2020**, *12*, 518.
https://doi.org/10.3390/polym12030518

**AMA Style**

Xing Z, Ke H, Wang X, Zheng T, Qiao Y, Chen K, Zhang X, Zhang L, Bai C, Li Z.
Investigation of the Thermal Conductivity of Resin-Based Lightweight Composites Filled with Hollow Glass Microspheres. *Polymers*. 2020; 12(3):518.
https://doi.org/10.3390/polym12030518

**Chicago/Turabian Style**

Xing, Zhipeng, Hongjun Ke, Xiaodong Wang, Ting Zheng, Yingjie Qiao, Kaixuan Chen, Xiaohong Zhang, Lili Zhang, Chengying Bai, and Zhuoran Li.
2020. "Investigation of the Thermal Conductivity of Resin-Based Lightweight Composites Filled with Hollow Glass Microspheres" *Polymers* 12, no. 3: 518.
https://doi.org/10.3390/polym12030518