Evolution from short time caged dynamics to long time cooperative
dynamics in supercooled liquids: inference from experimental data and the
coupling model
K.L. Ngai
Naval Research Laboratory, Washington DC 20375-5320 USA
Relaxations in supercooled liquids have properties that are difficult to explain because
the origin is the complex many-molecule dynamics, which is determined ultimately by the
intermolecular interaction. Workers in supercooled liquids often focus their attention mainly
on the variation of relaxation dynamics with changes in temperature or pressure, i.e., the glass
transition. Certainly entropy and specific volume are important factors that determine the
relaxation time. Recent studies at high pressures have shown often both factors contribute.
However, these thermodynamic “mean field” quantities alone cannot describe the timedependent complex molecular motions and explain properties such as dynamic heterogeneity,
non-Gaussianity and nonexponentiality, as well as lesser-known but perfectly general
anomalous properties found even at constant temperature and pressure. An example of the
latter is the anomalous Q-2/(1-n)-dependence of the -relaxation time found by quasi-elastic
neutron scattering, where Q is the scattering vector and (1-n) is the fractional exponent in the
Kohlrausch stretched exponential function, exp[-(t/)1-n], used to fit the intermediate
scattering function. For a more thorough explanation, one needs to consider another factor,
namely intermolecular interaction that determines the time dependent complex molecular
motions. The effect, intermolecular coupling (or cooperativity), that intermolecular interaction
has on the relaxation properties should provide a more complete explanation of all the
dynamic properties. Thus a viable strategy to build a thorough explanation is by first, in the
absence of intermolecular coupling, taking appropriately into account of the configurational
entropy, Sc and the free volume, Vf, in determining the intrinsic molecular mobility. Naturally,
the molecular dynamics considered at this level is simple, involving independent molecular
motions plausible only at shorter times. Finally in the second step, intermolecular coupling is
incorporated to capture the effects due to complex molecular motions at longer times.
Such a strategy is now implemented by using the coupling model (CM) of the author.
The independent relaxation rate, 1/0, of the CM is essentially the intrinsic mobility and it is
dependent on Sc and Vf. Through the Sc and Vf dependences, the temperature, T, and pressure,
P, dependences of 1/0 follow. Rigorous solution of simple analogue model systems suggests
intermolecular interaction is responsible for the emergence of exp[-(t/)1-n] for the relaxation
function at times longer than a temperature insensitive time tc, and its magnitude solely
depends on the strength of the intermolecular interaction. The magnitude of n increases with
intermolecular interaction strength and is an indicator of the degree of intermolecular
coupling. There are evidences of the crossover at tc from experimental data and from which
tc 2 ps for small molecule and polymeric glass-formers has been determined. Quasicontinuity of exp[-(t/)1-n] and exp(-t/0) at tc confers the relation,  = [tc-n0]1/(1-n), which has
proven useful to explain the properties of  especially the anomalous ones, unrivaled by any
other approach.
The new developments to be given are extension of the CM to address the dynamics at
short times when most molecules are caged and to intermediate times when an increasing
number of them are no longer caged. The crux of the extended CM is the quantitatively
determinable 0, which demarcates the short time and the intermediate time regimes and from
which the characteristics of the dynamics in the short and intermediate-times regimes can be
inferred. In many supercooled liquids, at temperatures above Tg, the “universal” JohariGoldstein (JG) -relaxation time, JG, is found nearly coincident with 0. These findings give
physical reality to the independent relaxation time of the CM through the JG relaxation time,
and validate its nature of a local independent relaxation. Several experimental facts indicate
that the JG relaxation, and hence the independent relaxation of the CM, is a function of
entropy and volume. These include the non-Arrhenius temperature dependences above Tg and
pressure dependence of JG, and the relatively abrupt increase of the derivative of the
dielectric strength of the JG relaxation, (dJG/dT), at Tg like the thermal expansion
coefficient and the heat capacity of a glass.
In the short time regime, t<<0JG, most of the molecules are caged and the low
probability of independent relaxation give rise to the “near constant loss” (NCL). There are
experimental evidences of the NCL from broadband dielectric relaxation measurements and
dynamics light scattering experiment at temperatures above Tg. In glass-formers with weaker
intermolecular coupling and at temperatures near Tg, the NCL has been observed over many
decades of frequency. The intensity of the NCL, NCL”, increases monotonically with
temperature but with different rates below and above Tg. There is again a relatively abrupt
increase of the derivative, (dNCL”/dT), at Tg like the thermal expansion coefficient and the
heat capacity of a glass. These properties are explained by the extended CM. The near
constant loss can be detected by elastic scan of neutron scattering with high energy resolution
like 1 eV in the form of the so-called “fast relaxation”, which is expressed as a factor,
exp[-Q2<u2(T)>/3], in the incoherent scattering law. Here <u2(T)> is the mean square
displacement. There is an observed change of rate of increase of <u2(T)> with T at Tg, a
previously puzzling result, and now can be explained by the extended coupling model through
the property of the NCL.