A comparison between the bond-strength-coordination number fluctuation model and the random walk model of viscosity

Abstract

We have studied the temperature dependence of the viscosity of some polymeric materials by using both, the bond strength-coordination number fluctuation model and the random walk model. The results reveal that both models show an excellent agreement with the experimental data. For the random walk model, two equations corresponding to two temperature regimes (low-T and high-T) separated by the critical temperature c T , which is difficult to determine, are needed to describe the temperature dependence of the viscosity of a fragile system, whereas for the bond strength-coordination number fluctuation model, a single equation with clear physical meaning describes the temperature dependence of the viscosity of both, the fragile and strong systems. We have also studied the relationship between the normalized temperature range of cooperativity and the fragility index. A theoretical expression for the relationship has been derived based on the bond strength-coordination number fluctuation model. The comparison with the experimental data shows a good agreement, leading to the conclusion that the kinetic properties of glass forming liquids and the cooperativity of molecular relaxations are correlated.

Bond Strength—Coordination Number Fluctuation Model of Viscosity: An Alternative Model for the Vogel-Fulcher-Tammann Equation and an Application to Bulk Metallic Glass Forming Liquids

“…Furthermore, we have compared and discussed the interrelation between the VFT equation and the BSCNF model [25,26]. It has been found that in the case of γ = 1, the viscosity behavior described by Equation 1 with the set of parameters ( B , C ) obeying the relation Equation 3, perfectly follows the behavior described by the VFT equation, $\text{log}\eta =A_{\text{VFT}}+\frac{B_{\text{VFT}}}{T-T_0}\text{,}$ where A VFT is the logarithm of the viscosity at the high temperature limit, A VFT = log η 0 , and B VFT , T 0 are the free fitting parameters of the VFT equation.…”

“…From the BSCNF model of the viscosity given in Equation 1, we obtain the fragility index m [23,24,25,26]. $m=\frac{1}{\text{ln}\left(10\right)}\left\{\frac{B-C+2\left[\text{ln}\left(\frac{{\eta }_{T\text{g}}}{{\eta }_0}\right)+\frac{1}{2}\text{ln}(1-B)\right]}{1-B}\right\}\text{.}$…”

“…In other words, if the value of fragility index m is given, the set of ( B * , C * ) can be determined uniquely by calculating the intersection. The applicability of Equation 10 has been discussed by applying it to some polymeric [25] and metallic materials [27]. The characteristic temperature ratio T 0 / T g , is related to the fragility [14,19,43,44,45].…”

“…In this article, it is shown that under certain conditions, the BSCNF model reproduces exactly the same viscosity behavior as the VFT equation [ 25 , 26 , 35 ]. The prerequisite is that the normalized bond strength fluctuation |Δ E |/ E 0 equals the normalized coordination number fluctuation |Δ Z |/ Z 0 .…”

“…The model which is called Bond Strength—Coordination Number Fluctuation (BSCNF) model, describes the viscosity behavior in terms of the mean values of the bond strength E 0 , the coordination number Z 0 , and their fluctuations, Δ E , Δ Z , of the structural units that form the melt. In our previous works, the model has been applied to investigate the viscosity of many kinds of glass forming liquids such as covalent, ionic, molecular, metallic, and polymeric materials [ 24 , 25 , 26 , 27 ]. It has been shown that the model reproduces experimental data well, and characterizes many kinds of glass forming liquids extending from strong to fragile systems.…”