that relaxation time would be infinite. If two configurations only were available for an entire liquid volume, mass transfer would require a simultaneous displacement of all structural entities. The probability for such a cooperative event would be extremely small, but not zero, and the relaxation times would be extremely high, but no longer infinite. When configurational entropy increases, the cooperative rearrangements of the structure required for mass transfer can take place independently in smaller and smaller regions of the liquid.
Within this picture, relaxation is determined by the topology of potential energy wells in an n‐dimensional space and, particularly, by the density and relative depths of these wells as may be illustrated in a 1‐d representation of such a potential‐energy landscape (Figure 18, insets). A simple distinction can then be made between strong and fragile liquids [43, 50]. For the former, a low density of wells translates into a small configurational heat capacity and entropy and thus, in small departures from an Arrhenian temperature‐dependence of relaxation times as given by Eq. (7); for the former, the high density of wells is in contrast associated with high configurational heat capacities and entropies, and marked deviations from Arrhenian temperature dependences.
Owing to the simple proportionality between relaxation times and viscosity, this difference may be simply visualized in plots of viscosities as a function of Tg /T where Tg is the standard glass‐transition temperature [51]. A well‐known sketch (Figure 21) illustrates the point for a variety of inorganic and organic glass‐forming liquids [52]. As particularly exemplified in Chapter 4.1, this duality between fragile and strong liquids will be a recurrent theme in many other chapters of the Encyclopedia to which the reader is thus referred.
Figure 21 Fragility as a measure of the extent of temperature‐induced configurational changes in inorganic and organic glass‐forming liquids: correlations between relative Cp increases at the glass transition and deviations of viscosities from Arrhenius laws
(Source: After [52]).
Lower panel, from top to bottom: SiO2, GeO2, BeF3, ZnCl3, LiCH3COO, 4 Ca[(NO3)]2·4 H2O, o‐terphenyl, glycerol (C3H8O3), and H2SO4·3 H2O.
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26 Sipp,
