Heat Transfer via the Solid Backbone

The heat transfer via the solid backbone of aerogels depends on the backbone stmcture and connectivity (Chap. 21), and its chemical composition. For a given temperature gradient within an aerogel, heat is transferred by diffusing phonons via the chains of the aerogel backbone, where the mean free path of the phonons is far below the dimensions of the mostly amorphous, dielectric primary particles. Within the primary particles, the thermal conductivity is a property of the backbone material and is described in terms of the phonon diffusion model by Debye [7], i.e.,  

The strongly density-dependent factor G considers the effects of the ineffective dead ends of the solid backbone, the increase in the specific heat due to the enhanced specific surface of an aerogel, the meandering chains along a temperatme gradient and the constriction of heat flow at the connecting area between the primary particles within the chains. A proper approach to the description of the density dependence is provided by the 

For porous media and under the assumption that the phonon diffusion model is valid, the sohd thermal conductivity can be derived by way of an analogy conclusion measuring the sound velocity of the porous media [8, 14]  

---

Figure 23.1. Diagram of an aerogel structure and the heat transfer mechanisms involved. Heat is transferred via chains of primary particles forming the solid backbone (indicated by the red particle chain), by thermal radiation (wavy yellow arrows), and by gas molecules present in the porous structure of the aerogel blue dots).

---