Understanding the Vogel–Fulcher–Tammann law in terms of the bond strength–coordination number fluctuation model

• An expression of viscosity similar to the VFT equation is derived analytically.
• Physical meanings of the parameters of the VFT equation are given.
• The strength parameter D includes information of the fluctuations.

It is shown that an expression similar to the Vogel–Fulcher–Tammann (VFT) equation of viscosity can be derived from the bond strength–coordination number fluctuation (BSCNF) model. The parameters BVFT and T0 of the VFT equation, η = η0exp[BVFT / (T − T0)], are related directly to the parameters of the BSCNF model; BVFT ≅ E0Z0 / R and T0 ≅ |ΔE||ΔZ| / R, where E0 and Z0 are the mean values of the bond strength and the coordination number of the structural units, and ΔE and ΔZ are their fluctuations and R is the gas constant. According to the BSCNF model, the viscous flow occurs by breaking or twisting the bonds that connect the structural units of the melt. From the analytical expression obtained in the present study, an expression for the strength parameter D can be also derived. Namely, D is written as D = BVFT / T0 ≅ (E0Z0) / (|ΔE||ΔZ|). This relation indicates that D includes information of the fluctuations that characterize the disorder of glass-forming materials.