Steepness index

Steepness index - Ratio between the ID 50 and MFD50. A high steepness index indicates that the magnitude of effects will increase more rapidly as the dose is increased. 

Specifically, the general approximation / 0.079 m has been suggested [142] for a wide range of both polymer and small molecule liquids. This relation implies that high molar mass F-S polymers should have steepness index m of about m 100, which is consistent in order of magnitude with estimates [142] for the representative F-S polymer, polystyrene (PS). 

V. N. Novikov and A. P. Sokolov, Nature 431, 961 (2004). Actually, they specifically claim that a closely related quantity to fragility, the steepness index m, is proportional to Zg. 

The steepness index or the fragility index m is defined as follows [105] ... 

The coefficient D is the steepness index of the supercooled and within the framework of the random first-order transition it is given by [39]... 

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... 

This representation actually gives the steepness index - a measure of the rapid rise in rj close to Tg. Some typical values of F, determined this way are given in Table 3.6. 

Figure 5 shows this plot for 3 different binary mixtures, as well as for a neat system (the epoxy resin PPGE). A good superposition for the a-relaxation frequency is obtained, as it is expected, since the steepness index of Za(T) m (fragility according to Angell definition ) is almost constant under pressure... 

However, in this case the change of the definition of the steepness index may be not important since for the typical range of experimental data the condition Tgp >Tg is well fulfilled. Corrected definitions of steepness indexes are a clear consequence of corrected VFT-t5q)c equations for r(r), r(/ ), t(f) and t p) dependences. The Angell plot, logjo vs. TgjT, is probably the most... 

From the VFT fit one can calculate the glass transition temperature Tg=334 K (Tg is defined as a temperature at which = 100s ) and the steepness index m=78 estimated from the following equation... 

Fig. 15). Furthermore, to facilitate the comparison, the glass-transition temperature Tg is operationally defined as a temperature corresponding to the most probable relaxation time of 100 s. There is a pronounced variation of the curvature or the steepness index which is defined as... 

Fig. 16. Steepness index m [=dlc xlA(TglT), extracted from the initial slopes in the previous figure, plotted as a function of the number of carbon atoms (1) on the side chain of poly(re-alkyl methacrylates). In the same plot the dependence of the LVDW peak in the waxs spectra Qi is shown. There is a one-to-one correspondence between the structural properties and the steepness index, which implies the relation of the fragility to the intersegmental correlations.

The slope corresponding to the glass transition has been quantitatively treated by Aklonis and co-workers (61-63) for relaxation phenomena. Aklonis defined a steepness index (SI) as the maximum of the negative slope of a stress relaxation curve in the glass transition region. They found that while... 

Comparison of temperature dependences of r of polymers on a plot of log versus TJT shows a pattern [163-165]. The pattern can be characterized by a single parameter, which is the steepness index, S, or... 

A correlation between or 1 — j6a(7g) and the steepness index m has been found to... 

While the viscosity-temperature plots provide a clear visual estimate of fragility, it is more convenient to establish a single parameter that provides a quantitative measure of fragility. Several measures have been proposed, but the most commonly used fragility index is the "m fragility" or "steepness index" defined as [52, 55] ... 

---