| Abstract: | New scaling laws for chain networks are derived to describe the fundamental relationships between the viscosity exponent (k), viscoelastic exponent (m), stretched exponent (β), spatial dimension (d). fractal dimension (df), and a universal constant (γ). The scaling of the total number of monomers and the radius of gyration is defined by df. We have discovered γ = m/β to be a universal constant which relates the shear modulus of a polymer gel melt to the shear modulus near the glass transition. Analyzing the size-dependent shear viscosity, we have determined γ = 3dfcd/(7d?5dfc) = 2.647 for d = 3 where dfc is the fractal dimension of critical clusters at the gel point. By using γ, the present theory extends previous work pertaining to systems near the sol-gel transition, and shows how properties far from the critical point can be explained. The theoretical prediction is in good agreement with viscoelastic measurements. |
