Chapter 8
Molecular Glasses
8.1 Glass as Frozen-in State
8.1.1 Simple View on Glass Transitions
8.1.1.1 Relaxation and Dispersion
When a macroscopic system is brought slightly out of its equilibrium by changing an
external parameter (such as electric field), the system usually exhibits a continuous
change into a new equilibrium under the condition. This change is called relaxation.
A typical example is the relaxation of the electric polarization of dielectric material
after the magnitude of applied electric field E is suddenly changed, e.g., E 0 → 0
at t = 0. Assume that the stationary polarization is p 0 before the sudden change
(t < 0), and p 0 = χ 0 E 0 , in which χ 0 is a (static) electric susceptibility. Since the
polarization relaxation is driven by the deviation in polarization from the equilibrium
one, it is reasonable to write
d
dt
p = −τ
−1 p,
(8.1)
where τ is a time constant known as a relaxation time. This equation is easily integrated as
p(t) = p 0 exp
−
t
τ
.
(8.2)
The relaxation, in this case, obeys an exponential decay with a time constant τ . Note
that the relaxation of a system does not always exhibit an exponential decay.
To get an idea of the relation between the microscopic dynamics of particles
(molecules) and the relaxation of the system, let us consider the particles having
© The Editor(s) (if applicable) and The Author(s), under exclusive license
to Springer Nature Singapore Pte Ltd. 2020
K. Saito, Chemical Physics of Molecular Condensed Matter,
Lecture Notes in Chemistry 104,
https://doi.org/10.1007/978-981-15-9023-8_8
161
Molecular Glasses
8.1 Glass as Frozen-in State
8.1.1 Simple View on Glass Transitions
8.1.1.1 Relaxation and Dispersion
When a macroscopic system is brought slightly out of its equilibrium by changing an
external parameter (such as electric field), the system usually exhibits a continuous
change into a new equilibrium under the condition. This change is called relaxation.
A typical example is the relaxation of the electric polarization of dielectric material
after the magnitude of applied electric field E is suddenly changed, e.g., E 0 → 0
at t = 0. Assume that the stationary polarization is p 0 before the sudden change
(t < 0), and p 0 = χ 0 E 0 , in which χ 0 is a (static) electric susceptibility. Since the
polarization relaxation is driven by the deviation in polarization from the equilibrium
one, it is reasonable to write
d
dt
p = −τ
−1 p,
(8.1)
where τ is a time constant known as a relaxation time. This equation is easily integrated as
p(t) = p 0 exp
−
t
τ
.
(8.2)
The relaxation, in this case, obeys an exponential decay with a time constant τ . Note
that the relaxation of a system does not always exhibit an exponential decay.
To get an idea of the relation between the microscopic dynamics of particles
(molecules) and the relaxation of the system, let us consider the particles having
© The Editor(s) (if applicable) and The Author(s), under exclusive license
to Springer Nature Singapore Pte Ltd. 2020
K. Saito, Chemical Physics of Molecular Condensed Matter,
Lecture Notes in Chemistry 104,
https://doi.org/10.1007/978-981-15-9023-8_8
161