Modeling of Sol-Gel Transition with Loop Network Formation and its Implications on Mechanical Properties
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Modeling of Sol-Gel Transition with Loop Network Formation and its Implications on Mechanical Properties Hang-Shing Ma1, Jean-H. Prévost2, Rémi Jullien3, George W. Scherer4 1 Dept of Chemical Engineering, Princeton University, Princeton NJ 08544, USA 2 Dept of Civil and Environmental Engineering, Princeton University, Princeton NJ 08544, USA 3 Laboratoire des Verres, UMR 5587, CNRS, Université Montpellier II, CC069, Place E. Bataillon, 34095 Montpellier, France 4 Dept of Civil and Environmental Engineering/Princeton Materials Institute, Princeton University, Princeton NJ 08544, USA ABSTRACT Certain classes of sol-gel transition have been modeled as diffusion-limited cluster-cluster aggregation (DLCA), but it produces excessive dangling branches on the resulting network that underestimates the rigidity of gels. The “dangling bond deflection” (DEF) model was developed to simulate spatial fluctuation of the dangling branches under thermal energy. Collision and sticking of two dangling branches within the same cluster turns these branches into a loop. Combination of the DLCA and DEF models creates network that possesses extensive loop structure and negligible dangling mass. The networks are substantially stiffened by the loop structure, and successfully reproduce the empirical scaling relationship between linear elastic modulus and density exhibited by real aerogels. The gel structure can be represented by the “blob-and-link” model, in which blobs refer to dense, rigid collections of particles, interconnected by tenuous links of particle chains. When the network is deformed, only these few weak links contribute to the stiffness, leaving the blobs unstrained. The gel modulus drops significantly as porosity increases because more particles reside in the blobs and fewer particles carry the strain. INTRODUCTION Sol-gel process is an important class of reaction for synthesizing organic and inorganic materials from liquid phase reaction. An example of the sol-gel derived products is silica aerogel [1]. Its unique characteristic features, including high porosity (> 90%), small pore radii (~ 1 nm), high specific surface area (~ 1000 m2/g SiO2) and percolating pore and solid network structure, give aerogel immense potential in a wide range of applications [2]. For example, the thermal conductivity of silica aerogel is only half of that of polystyrene foam, therefore it can be used as a high performance insulating material. However, one of the biggest challenges blocking the development of aerogel applications is its lack of mechanical integrity which leads to costly processing and difficult handling. Before any breakthrough methods of making stiff gels can be developed, it is our belief that we have first to understand how the sol-gel transition shapes the gel structure which in turn determines the mechanical properties, and this is the goal of the project. Diffusion-limited cluster-cluster aggregation (abbreviated DLCA) is one of the models to simulate the sol-gel transition process [3,4]. In a cubic lattice of length L, n sphe
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