Biomedical Engineering Reference
In-Depth Information
molecules, enters into conflict with torsion, which tends to disrupt this alignment.
This conflict of topological nature, or frustration, arises because of the flatness of
the Euclidean space, but does not exist in the curved space of the three-sphere
where particular lines, its fibers, can be drawn which are parallel and nevertheless
twisted. As these fibrations conciliate compactness and torsion, they can be used
as geometrical templates for the analysis of organizations in the Euclidean space
[240].
1.3.9
Polymer Thermodynamics
The first experiments suggested that TC molecules are rigid, rod-shaped structures.
However, on the basis of hydrodynamic methods and transmission electron
microscopy (TEM), it was found that TC molecules demonstrate some flexibility,
which can be measured by the persistence length [241].
1.3.9.1
Thermodynamics
From the first law of thermodynamics, the increase in internal energy d
U
during
any change in a system is equal to the sum of the elementary amount of heat d
Q
added to it and the elementary amount of work d
L
performed on it.
d
U
=
d
Q
+
d
L
The second law states that the increase in heat d
Q
is expressed in any reversible
process by the relation
d
Q
=
T
d
S
where d
S
denotes the entropy differential and
T
denotes the (absolute) temperature.
Hence, for a reversible process
d
U
=
T
d
S
+
d
L
The Helmholtz free energy is defined by
A
=
U
−
TS
Its change at constant temperature is given by
d
A
=
T
d
U
+
T
d
S
which means that
=
d
A
d
L
The work done on the system by a tensile force
F
in a displacement d
x
is
d
L
=
F
d
x
Then,
∂
A
∂
x
=
F
τ
