34
at any time, and can only be temporarily preserved by quenching the relatively
unstable system. The thermodynamic function of the system can be defined as
follows:
G U PV TS
= +
-
(3.2)
The heating, stretching and cooling processes of shape memory materials are
completed under isobaric pressure, whose volume change could be neglected. Thus,
G could also be defined as follows:
dG dU Tds SdT
=
-
-
(3.3)
Depending on the nature of the thermodynamic functions, the change in function
of the process for the preparation of SMPs can be shown as follows:
D
D
D
D
G
G
G
=
+
+
1
2
3
G
(3.4)
ΔG 1 is the change in the thermodynamic function caused by the temperature
from T 0 to T 1 , and ΔG 3 is the change in the thermodynamic function caused by the
temperature from T 1 to T 0 , while the effect of volume change on the thermodynamic
function can then be ignored:
DG 1
3
= G
(3.5)
Thus,
D
D
G
G
=
2
(3.6)
ΔG 2 is the change in thermodynamic function induced by stretching in the high
strain state. In this context, under low strain-at-break conditions, the change in internal energy caused by the stress is insignificant, which mainly causes the entropic
change, due to the isothermal process, thus obtaining Eq. 3.3.
DG
G
T dS
=
=D 2
1
(3.7)
The above equation indicates: dS > 0, ΔG < 0, and dS < 0, ΔG > 0.
Therefore, following the first and second laws of thermodynamics, the polymer
in a state of high elasticity when subjected to reversible stress at high temperature,
the relationship between the ΔG and the work done by the external force could be
expressed as follows:
dW dU TdS
=
-
(3.8)
where dW is the work done by external force; dU the change in the energy of the
system; dS the entropy change of the system.
Z. Gao and G. Gao