Kohlrausch exponent

An intimate connects exists between the shape of the relaxation function and steepness index [3,5,48,89,116,117], Strong liquids have less broad relaxation functions compared with fragile glass formers. The degree of nonexponentiality is reflected in the Kohlrausch exponent [1... 

However, in order for this explanation to be consistent with the observed monotonic increases of the products A and Dttc as the temperature is lowered toward A the breadth of the relaxation time distribution has to increase (or the Kohlrausch exponent, l-n, has to decrease) correspondingly. However, for two glassformers, ortho-terphenyl (OTP) and tni naphthylbenzene (TNB) which show the breakdown of the SE and DSE relations, Richert and coworkerss recently reported that their dielectric spectra are characterized by a temperature independent width (e.g. l-rid is constant and is equal to 0.50) from 345-417 K in the case of TNB. The Tg of TNB is 342 K. Photon correlation spectroscopic and NMR measurements all indicate a temperature-independent distribution of relaxation times. Thus, the data of TNB and OTP contradicts the explanation based on spatial heterogeneities. On the other hand, an alternative explanation based on intermolecular coupling (originating from many-molecule relaxation) continues to hold. ... 

To support this point, we propose also considerations based on experimental research of dymethacrylates post-polymerization kinetics, that is, dark, after turning off f/F irradiation, process of pol5mierization [4. It was foimd, that the chain termination is linear, and its kinetics submits to the law of stretched Kohlrausch exponent ... 

The model considerations outlined above permit one to clarify the results presented in Table XI. For example, from the explicit definition of the Kohlrausch-Williams-Watts stretched exponent on the barrier height... 

This ansatz can be rationalized by some theoretical considerations [325,326]. It is also supported by the experimental data at very low concentrations of the component A where the study is reduced to the dynamics of the probe A in host B. Each probe molecule experiences the same environment, which eliminates the complications from concentration fluctuations. We have mentioned in Section III, paragraph 4, that the probe rotational correlation function indeed has the Kohlrausch form. The differential between the probe rotational time xA and the host a-relaxation time xaB is gauged by their ratio, xA/xaB. As expected, the slower the host B compared with the probe A, the larger the coupling parameter, nA = (1 — pA), obtained from the stretch exponent (3A of the measured probe correlation function. The experimental data are shown in Fig. 52. For more details, see Ref. 172. 

Although glass transition is conventionally defined by the thermodynamics and kinetic properties of the structural a-relaxation, a fundamental role is played by its precursor, the Johari-Goldstein (JG) secondary relaxation. The JG relaxation time, xjg, like the dispersion of the a-relaxation, is invariant to changes in the temperature and pressure combinations while keeping xa constant in the equilibrium liquid state of a glass-former. For any fixed xa, the ratio, T/G/Ta, is exclusively determined by the dispersion of the a-relaxation or by the fractional exponent, 1 — n, of the Kohlrausch function that fits the dispersion. There is remarkable similarity in properties between the JG relaxation time and the a-relaxation time. Conventional theories and models of glass transition do not account for these nontrivial connections between the JG relaxation and the a-relaxation. For completeness, these theories and models have to be extended to address the JG relaxation and its remarkable properties. 

Not only does the magnitude of Ta uniquely defrne the dispersion, as shown herein, but also many properties of are governed by or correlated with the width of the dispersion of the structural relaxation or the fractional exponent n of the Kohlrausch function, (t) = exp[-(t/r ) "], frequently used to fit the... 

This equation has been used as the basis to explain the T-P superposition of the O -relaxation of a component in mixtures of van der Waals glass-formers and polymer blends as discussed in Capaccioli and Ngai (2005). Concentration fluctuations in the mixture or blend create a distribution of environments /. Each environment, i, has its own coupling parameter, tii, primitive relaxation time, Toi, and the corresponding Kohlrausch function with stretch exponent, (1 — ,), which determines the relaxation time t, by the CM equation rai =. In the same manner as shown earlier for neat glass-... 

To, as in experiments. (4.) In addition, the relaxation of J(t) at times before and after the j8-relaxation window can be fitted by the Rouse-theory and by a Kohlrausch function with a temperature independent exponent (time-temperature superposition principle), respectively (39 40). 

The response function is chosen, according to Moynihan et at. [50], in a manner of a Kohlrausch function [51], which is also called the stretched exponential function and is often used as a phenomenological description of relaxation in disordered systems. The value of p, which is called the stretching exponent and describes the nonexponential characteristic of the relaxation process, is defined as... 

Experimental signatures of this peculiar transition has been found essentially in chalcogenide glasses fi om Raman scattering [18], stress relaxation and viscosity measurements [19], vibrational density of states [17], Brillouin scattering [20], Lamb-Mossbauer factors [21], resistivity [22], and Kohlrausch fractional exponents [23]. 

In the Kohlrausch-Wilhams—Watts equation the exponent /3k typically ranges between 0.3 and 0.8 for structural glasses and is often found to be temperature-independent, which means that the structural relaxation time Tie carries the whole temperature dependence in the Kohlrausch formula. A plot of the correlation function versus the reduced variable i/tic... 

Privalko V P (1999) Glass transition in polymers dependence of the Kohlrausch stretching exponent of kinetic free volume fraction, J Non-Cryst Solids 255 259-263. Tant M R, Mauritz K A and Wilkes G L (Eds.) (1997) lonomers. Chapman and Hall, London. 

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