《高分子物理》教学中WLF方程的系数求解与分析  

The Solution and Analysis on Parameters of WLF Equation in Teaching the Course Polymer Physics

作　　者：郑强[1] 林宇[1] 叶一兰[1] 张小虎[1] 上官勇刚[1] 左敏[1] 

机构地区：[1]浙江大学高分子科学与工程学系,杭州310027

出　　处：《高分子通报》2010年第6期99-105,共7页Polymer Bulletin

摘　　要：Williams-Landel-Ferry方程(简称WLF方程)是高分子物理中一个非常重要的经验公式。其中,C1、C2作为两个经验参数,取决于参考温度Tr的取值,且其乘积为定值(C1.C2≈900),与自由体积热膨胀系数αf有关。本文分析讨论了C1、C2参数的物理意义及C1、C2参数的两种不同求解方法,发现与由-1/logαT对1/(T-Tr)作图的方法I相比较,由-(T-Tr)/logαT对(T-Tr)作图的方法II的灵敏度更高,平均相对残差更小;正是由于对(T-Tr)变化的更高的敏感响应,导致方法II作图的线性相关性(相关系数)较低。综合C1、C2解析值的合理性和作图求解的平均相对残差,推荐采用方法II。Williams-Landel-Ferry equation（WLF equation） is one of the most significant experimental equations in polymer physics,in which two parameters C_1 and C_2 are empirical constants,depending on the value of the reference temperature T_r selected.It is proven theoretically and experimentally that the product of C_1 and C_2 is also a constant（C_1·C_（2）≈ 900） involving the thermal expansion coefficient α_f.In this paper, the physical significance of C_1 and C_2 is emphasized,and two numerical calculating methods（I and II） to obtain C_1 and C_2 are discussed.It is found that the plotting-（T^T_r）/logα_T vs.（T-T_r）（referred to as II） exhibits higher sensitivity and less average relative residual,compared with the plotting-1/logα_T vs.1/（T-T_r）（referred to as I）.Moreover,it is due to higher sensitivity of Method II that it has poorer linear correlation than that of Method I.Concerning the reliability of numerical results of C_1 and C_2,together with average relative residual of plots,it is proposed that Method II is prior to Method I.

关 键 词：WLF方程 位移因子αT 粘弹性 灵敏度 平均相对残差 

分 类 号：O561-4[理学—原子与分子物理]