Equations tool narayanaswamy moynihan

Equation 13.6 is referred to as the Tool-Narayanaswamy-Moynihan (TNM) equation to acknowledge the contributions of different authors to the theoretical model. Both Ah and x have no clear physical meaning. However, in their treatment of the glassy state, Gibbs and DiMarzio (1958) (GD) postulated that a second thermodynamic transition T2 existed below Tg at which the configurational entropy Sc is zero. The concept of a temperature at which Sc = 0 was introduced by... 

Nonlinearity is accounted for in the Tool-Narayanaswamy-Moynihan (TNM) model by replacing r in the linear equations (2.1) and (2.2) by r given by the so-called Tool-Narayanaswamy (TN) equation ... 

In addition to controlling the magnitude of structural relaxation, fragility also affects the kinetics of the relaxation process. This is easily seen by inspection of the Tool-Narayanaswamy-Moynihan (TNM) equation [53] ... 

Moynihan s formulation [5] of the Tool-Narayanaswamy [7] model is used in tins woilc. In Moynihan s equations, the Active temperature, Tf, originally d ned by Tod [78], is used as a measure of the structure of the glass. The evdution of Active temperature is represented by the generalized stretched exponential Kohlrausch-William-Watts(KWW) function [76,77] ... 

Models of structural recovery include the Kovacs-Aklonis-Hutchinson-Ramos (KAHR) model (119), Moynihan s model (120), and Ngai s coupling model (121). These models are based on work done originally by Narayanaswamy (122), incorporating the ideas of Tool (13). The models of stnictiual recovery reflect the nonlinear and nonexponential effects observed experimentally. The historical development of these equations has been detailed (7,8) only a brief description follows. The KAHR formulation (119), which is written in terms of a departure from equilibrium S rather than in terms of Tf, is conceptually easier to use when the full three-dimensional PVT surface is considered ... 

---