Kovacs-Aklonis- Hutchinson-Ramos KAHR model

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 ... 

The Kovacs-Aklonis-Hutchinson-Ramos (KAHR) model... 

Concurrently with experimental investigations, structural relaxation has also received a great deal of interest from theoretical studies. Several kinetic or thermodynamic models were developed to capture the three essential ingredients of structural relaxation. Among these models, the most famous two are the Tool-Narayanaswamy-Moynihan (TNM) model [96-98] and the Kovacs-Aklonis-Hutchinson-Ramos (KAHR) model [99]. 

A similar equation can be derived for the enthalpy. It turned out that this modification to give the retardation time a free volume dependence, was successful in describing one-step isothermal recovery but unsuccessful in describing memory effects. Kovacs, Aklonis, Hutchinson and Ramos (1979) attributed the latter to the contributions of at least two independent relaxation mechanisms involving two or more retardation times. These authors proposed a multiparameter approach, the so-called KAHR (Kovacs-Aklonis-Hutchinson-Ramos) model. The recovery process is divided into N subprocesses, which in the case of volumetric recovery may be expressed as ... 

KAHR Kovacs, Aklonis, Hutchinson, and Ramos (model of kinetics of... 

Modeling of relaxation behaviour in the glass can be done using either phenomenological models or models that attempt to describe bulk behaviour using thermodynamic or molecular arguments. An example of the former is the transparent mulitparameter model of Kovacs, Aklonis, Hutchinson, and Ramos (29), now commonly referred to as the KAHR model. They used a sum of exponentials and a normalized departure from equilibrium, 8 = (v-v ,)/vco, where v is the volume at time t and Voo is the volume at equilibrium. The distribution of relaxation or retardation times is a function of 6 and can be written ... 

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