Application of the Adam-Gibbs equation to the non-equilibrium glassy state
Application of the Adam-Gibbs equation to the non-equilibrium glassy state
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Adam-Gibbs方程在非平衡玻璃态中的应用
DOI：
10.1021/ma992015r
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发表时间：
2000
期刊：
影响因子：
5.5
通讯作者：
P. Cortés
中科院分区：
文献类型：
--
作者：
J. Hutchinson;S. Montserrat;Y. Calventus;P. Cortés
本文比较了TNM方程和非线性形式的AG方程，并讨论了TNM方程的温度和假想温度对玻璃态材料弛豫时间的影响。结果表明，Narayanaswamy参数x与构型熵降为零的温度T2之间的关系，即x1-T2/Tf，导致许多聚合物玻璃的T2值不切实际.这个问题通过将构型熵表示为T和Tf的函数来解决，其中分区参数xs（0 ≤ xs ≤ 1）控制它们各自的贡献。比较TNM与这个新的非线性AG表达式纳入Sc（T，Tf）导致一个明确的关系x和xs涉及T，T2，和Tf，其中一些预测可能会作出。(1)对于T T f，即，对于接近平衡的弛豫，1 -T2/Tf被认为是x的最小可能值，这意味着T2 ≥ Tf（1 - x），其量取决于xs的值。这解决了T2的明显异常值。(2)对于远离平衡的弛豫，具有常数x的TNM方程变得越来越不合适。(3)随着退火温度和退火时间的增加，分析预测x值增加，如文献中经常报道的那样。起源的依赖性的Sc T和Tf被认为是从吉布斯和DiMarzio的理论，它认为，实验观察到的典型值ofx可能与冻结在只有一定比例的弯曲的债券和/或空晶格位点（孔）在玻璃化转变。因此，它是可能的，以确定X s，并间接地x，与物理上有意义的参数，如分子间和分子内的键能，冻结过程的相对贡献。
The Tool-Narayanaswamy-Moynihan (TNM) equation for the temperature (T) and fictive temperature (T f ) dependence of the relaxation time in glassy materials is compared with the usual nonlinear form of the Adam-Gibbs (AG) equation. It is shown that the relationship derived between the Narayanaswamy parameter x and the temperature T 2 at which the configurational entropy reduces to zero, namely x 1 - T 2 /T f , leads to unrealistic values of T 2 for many polymer glasses. This problem is resolved by expressing the configurational entropy as a function of both T and T f , with a partitioning parameter x s (0 ≤ x s ≤ 1) controlling their respective contributions. Comparing TNM with this new nonlinear AG expression incorporating S c (T,T f ) leads to an explicit relationship between x and x s involving T, T 2 , and T f , from which a number of predictions may be made. (1) For T T f , i.e., for relaxations close to equilibrium, the quantity 1 - T 2 /T f is identified as the minimum possible value for x, implying that T 2 ≥ T f (1 - x), by an amount depending on the value of x s . This resolves the apparently anomalous values of T 2 . (2) For relaxations further from equilibrium, the TNM equation with constant x becomes increasingly inappropriate. (3) With increasing annealing temperature and increasing annealing time, the analysis predicts increasing values of x, as has often been reported in the literature. The origin of the dependence of S c on T and T f is considered from the theory of Gibbs and DiMarzio, and it is argued that typical values ofx observed experimentally may be associated with the freezing-in of only a certain fraction of either flexed bonds and/or vacant lattice sites (holes) at the glass transition. Thus, it is possible to identify X s , and indirectly x, with the relative contributions of physically meaningful parameters, such as intermolecular and intramolecular bond energies, to the freezing-in process.