A Fractal Model for Effective Thermal Conductivity of Isotropic Porous Silica Low-k Materials  

作　　者：董锡杰 胡一帆 吴玉莹 赵军 万珍珠 

机构地区：[1]Wuhan High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074 [2]School of Physics, Huazhong University of Science and Technology, Wuhan 430074 [3]5310 Army, 25 Zhongnan Road, Wuhan 430071 [4]School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074

出　　处：《Chinese Physics Letters》2010年第4期163-166,共4页中国物理快报（英文版）

基　　金：Supported by the National Natural Science Foundation of China under Grant No 60476011.

摘　　要：We establish a new model based on fractal theory and cubic spline interpolation to study the effective thermal conductivity of isotropic porous silica low-k materials. A 3D fractal model is introduced to describe the structure of the silica xerogel and silica hybrid materials （such as methylsilsesquioxane, MSQ）. Combined with fractal structure, a more suitable medium approximation is developed to study the isotropic porous silica xerogel and MSQ materials. Cubic spline interpolation for fitting discrete predictions from the fractal model is used to obtain the continuous function of the effective thermal conductivity versus porosity. Compared with other common models, the effective thermal conductivity predicted by our model presents better agreement with the experimental data for all porosity. These results indicate that the proposed model is valid.We establish a new model based on fractal theory and cubic spline interpolation to study the effective thermal conductivity of isotropic porous silica low-k materials. A 3D fractal model is introduced to describe the structure of the silica xerogel and silica hybrid materials （such as methylsilsesquioxane, MSQ）. Combined with fractal structure, a more suitable medium approximation is developed to study the isotropic porous silica xerogel and MSQ materials. Cubic spline interpolation for fitting discrete predictions from the fractal model is used to obtain the continuous function of the effective thermal conductivity versus porosity. Compared with other common models, the effective thermal conductivity predicted by our model presents better agreement with the experimental data for all porosity. These results indicate that the proposed model is valid.

关 键 词：Soft matter liquids and polymers Condensed matter: electrical magnetic and optical Condensed matter: structural mechanical & thermal Chemical physics and physical chemistry 

分 类 号：O413.1[理学—理论物理] TN47[理学—物理]