Nonexponential relaxation

Jackson, T. A., Lim, M., and Anfinrud, P. A. 1994. Complex nonexponential relaxation in myoglobin after photodissociation of MbCO Measurement and analysis from 2 ps to... 

Often, one defines nonexponential relaxations in terms of a time-depen-dent rate coefficient k(t) through p(t) = exp(—k(t)t). For the fractional Kramers model one therefore obtains the rate coefficient k(t) = ln a(—r ta) /t which leads to two limiting cases, the short-time self-simi-... 

It has been claimed that reactions in proteins can, as an approximation, be formulated within the Kramers reaction theory of barrier crossing [106]. The highly nonexponential relaxation pattern can now be explained by our model,... 

Leisen, J., Schmidtrohr, K., and Spiess, H. W. (1993). Nonexponential relaxation functions above T(G) analyzed by multidimensional NMR and novel spin-echo decay techniques. Physica A 201,79-87. 

For many of the systems being studied, the relationship above does not sufficiently describe the experimental results. The Debye conjecture is simple and elegant. It enables us to understand the nature of dielectric dispersion. However, for most of the systems being studied, the relationship above does not sufficiently describe the experimental results. The experimental data are better described by nonexponential relaxation laws. This necessitates empirical relationships, which formally take into account the distribution of relaxation times. 

The dielectric relaxation properties in a sodium bis(2-ethylhexyl) sulfosuc-cinate (AOT)-water-decane microemulsion near the percolation temperature threshold have been investigated in a broad temperature region [47,143,147]. The dielectric measurements of ionic microemulsions were carried out using the TDS in a time window with a total time interval of 1 ps. It was found that the system exhibits a complex nonexponential relaxation behavior that is strongly temperature-dependent (Figure 8). 

In Section II.B we have classified several types of non-Debye relaxation and have mentioned a few particular approaches that have been developed in order to explain the origins of these relaxation patterns. We shall now discuss a model that considers one particular case of nonexponential relaxation. 

We first discuss the 2H NMR spin-lattice relaxation results of molecular glass formers at T< Tg. In Fig. 53, we present the mean relaxation time (7)), equal to the integral of the corresponding (nonexponential) relaxation function, for several glasses including a polymer (polybutadiene-d6). The temperature-... 

It is plausible that the deviation of /(f) from the Poisson condition generates the nonexponential relaxation of connection between [Pg.396]

MD simulations of supercooled liquids are revealing that the heterogeneous scenario is more likely to explain the nonexponential relaxation, and a bunch of articles on this subject were published even within the past few years. Dynamical heterogeneity is one of the central issues in the problem of glassforming liquids. 

Anomalous (nonexponential) relaxations have long been and still are a favorite topic in the physics of inhomogeneous media [179-204]. Broadly speaking, one... 

In like manner, it becomes easy to predict the pattern of anomalous, nonexponential relaxation at times, shorter than the relaxation time X at the lowest (i.e., 1-st) self-similarity level. This level may be considered as the primitive one (in a sense that it cannot be further tesselated into subclusters) hence, the relaxation should be of a classical, Debye-like type,... 

Therefore, in the present context, the Kramers escape rate can be best understood as playing the role of a decay parameter in the Mittag-Leffler functions governing the highly nonexponential relaxation behavior of the system. 

Another important characteristic of viscous liquids close to Tg is nonexponential relaxation. Consider the response of a system to a perturbation, such as the polarization in response to an applied electric field, the strain (deformation) resulting from an applied stress, the stress in response to an imposed deformation, the volume response to applied pressure, or the temperature response to a heat flux. It is found experimentally that the temporal behavior of the response function 0(t), following an initial instantaneous response, can often be described by the stretched exponential, or Kohlrausch-Williams-Watts (KWW) function (Kohlrausch, 1854 Williams and Watts, 1970),... 

The procedure described here is an example for combining theory (that relates rates and currents to time correlation functions) with numerical simulations to provide a practical tool for rate evaluation. Note that this calculation assumes that the process under study is indeed a simple rate process characterized by a single rate. For example, this level of the theory cannot account for the nonexponential relaxation of the v = 10 vibrational level of O2 in Argon matrix as observed in Fig. 13.2. 

Molinero, V., Cagin, T., and Goddard III, W.A. The mechanisms of nonexponential relaxation in supercooled glucose solutions The role of water facilitation, /. Phys. Ghent., 108, 3699, 2004. 

A basic feature of the response of fragile liquids to various perturbations is the pronounced nonexponential relaxation behavior. The relaxation function typically exhibits a two-step feature. The fast relaxation at short times is generally associated with vibrational degrees of freedom. The long-time decay of the relaxation function 4>(t), which is governed by the structural relaxation, can often be described by the stretched exponential or the Kohlrausch-Williams-Watts (KWW) function... 

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