Chemistry Reference
In-Depth Information
4.3.6 Thermodynamics of Cationic Polymerization
Sawada [
406
] described the thermodynamics' of cationic polymerization as follows: The process of
protonic acid initiation of cationic polymerization starts with heterolytic bond dissociation of the
acid. The energy of this process can be designated by the quantity
e
2
, the affinity of the proton for the
olefin. The potential energy between ion pairs separated at a distance
r
is
2
e
3
¼ e
=rD
where
e
is the unit of electronic charge and
D
the dielectric constant. The total entropy change of the
system is
DH ¼ e
1
e
2
e
3
where,
e
1
is the acid strength of the initiator,
e
2
is the proton affinity of the monomer, and
e
3
is the
solvating power of the solvent.
The change in free energy of initiation is,
DF
i
¼ DH TDS
By substituting the above values, the free energy change of initiation, can be written as
2
DF
i
¼ e
1
e
2
e
=rD TDS
The entropy change and the enthalpy change are negative for the free energy change to be
negative.
In the propagation process, the change in activation entropy is based on two phenomena: (a) the entropy
change of immobilization of a free-moving monomer into a polymeric chain and (b) the difference of
entropy in the solvation between the reactants and the transition state, which can be written as
DS
¼ DS
ð
ÞþDS
ð
immobilization of monomer
solvation
Þ
DS
* solvation is a positive term because in the transition state the electric charge is more diffuse and
the degree of solvation is lower than that of the more compact dipolar species corresponding to
reactants.
The propagation constant, based on Eyring theory,
ðDE
p
=RTÞ
¼ðkT=hÞ
k
p
¼ A
p
exp
ðDS
=RÞ
ðDE
p
=RTÞ
exp
exp
the activation entropy is
DS
p
* is the function of
f
t
and
f
i
, the partition functions of the transition and
initial states of the propagation step, respectively,
DS
p
¼ R
ln
ðf
t
=f
i
ÞþRT d
ln
ðf
t
=f
i
Þ=dT
f
t
and
f
i
can be assigned, according to Sawada [
406
] to be the partition functions of the monomer in
the transition sate (
f
i
(m)), because other parts of
the growing chain are common in the transition and initial states of the propagation reaction.
f
t
(m)) and that of the monomer in the initial state (
