Investigation of Thermal Conductivity for Liquid Metal Composites Using the Micromechanics-Based Mean-Field Homogenization Theory

For the facile use of liquid metal composites (LMCs) for soft, stretchable and thermal systems, it is crucial to understand and predict the thermal conductivity of the composites as a function of liquid metal (LM) volume fraction and applied strain. In this study, we investigated the effective thermal conductivity of LMCs based on various mean-field homogenization frameworks including Eshelby, Mori-Tanaka, differential and double inclusion methods. The double inclusion model turned out to make the prediction closest to the experimental results in a wide range of LM volume fractions. Interestingly, we found that the theoretical models based on the assumption of ideal LM dispersion and zero interfacial resistance underestimated the thermal conductivity compared to the experimental results in a low volume fraction regime. By considering the accompanied variations in the LM inclusion's aspect ratios under a typical size distribution of inclusions (∼μm), the change of effective thermal conductivity was predicted under a uniaxial 300% tensile strain. Our study will deepen the understanding of the thermal properties of LMCs and support the designs of stretchable thermal interfaces and packaging with LMCs in the future.