Physical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 64

defined with the same certainty as the transition temperatures between the equilib-
rium phases.
Another important difference between the glass transition and other transitions
presented in Fig. 3.1 is that at T g the G versus T curve for glass merges smoothly
with the curve for liquid, whereas the G versus T curves for other transitions demon-
strate a change in the slope at the transition temperature. Mathematically, a change
in the slope is equivalent to discontinuity of the first derivative of G with respect to
T, which, in turn, means discontinuity in the entropy, S, and enthalpy, H:

=− ∂
∂

G
T

(3.1)

S

P

∂
∂

(/)
(/ )

GT
T

(3.2)

H = .

1

P

Per Ehrenfest's classification [ 5 ], the phase transitions that show discontinuity in
the first derivative of the Gibbs energy are defined as transitions of first order. The
glass transition does not show discontinuity in the first but in the second derivative
of G with respect to T, which means discontinuity in the heat capacity:

2

CT G
T

∂
∂

∂
∂

H
T

(3.3)

=− = .

P

2

P

P

Discontinuity in the second derivative classifies a phase transition as being of sec-
ond order. Although the glass transition reveals this feature of a second-order transi-
tion, it is not the classical second-order transition that occurs between two phases
coexisting in equilibrium with each other.
The aforementioned difference between the glass and first-order transitions has
direct implication for experimental measurements of these processes by differential
scanning calorimetry (DSC). The instrument measures the heat flow that has two
principal contributions:

d H d T d α

(3.4)

Φ ≡ = C +∆ H .

P

d t d t d t

The first term in the right-hand side represents a contribution from the sensible heat
flow. This is the heat produced by substance of finite heat capacity in response to
changing temperature. The second term is a contribution from the latent heat flow.
This heat arises from a change in the enthalpy, Δ H, due to a phase transition or
chemical reaction. Per Eq. 3.2, first-order transitions are accompanied by the latent
heat. In DSC, they manifest themselves as peaks because as seen from Eq. 3.4, the
heat is released in proportion to the processes rate (d ʱ /d t ), which under the condi-
tions of continuous heating (or cooling) always starts from and finishes at zero,
passing some nonzero value in between. On the other hand, the glass transition is