Handbook of Solvents - George Wypych - ChemTech - Ventech!

6.1 Modern views on kinetics of swelling 315
Figure 6.1.3. Kinetic curves of plane layer swelling at different values of concentration dependence of diffusion
coefficient (ε= 0.1, d = 2/9): a - power law mode (1-s=0;2-s=1;3-s=1.5; 4-s=2.5); b - exponential (5-s=5)
and blow-up mode (6 -s=5.5). [Adapted, by permission, from E. Ya. Denisyuk, V. V. Tereshatov, Vysokomol.
soed., A42, 74 (2000)].
following from Eqs. [6.1.38] and [6.1.41] we can estimate the concentration dependence of
the diffusion coefficient of a liquid fraction in elastomer. According to Eq. [6.1.40] the parameter
q is determined from the initial section of the kinetic swelling curve.
Experimental estimates of the parameter r can be obtained from the strain curve l(t) using
Eqs. [6.1.31] and [6.1.40]. Then by making use of the formula
d =1-q/r [6.1.46]
following from Eq. [6.1.41] we can evaluate the parameter d which characterizes the strain
dependence of the equilibrium swelling ratio of elastomer under symmetric biaxial extension
in Eq. [6.1.45]. Generally the estimation of this parameter in tests on equilibrium swelling
of strained specimens proves to be a tedious experimental procedure.
The value of diffusion coefficient in an equilibrium swelling state can be determined
from the final section of kinetic swelling curve using Eq. [6.1.44], which is expressed in
terms of dimensional variables as
2
2
g ( t) = 1−Cexp(
−α D t / h )
[6.1.47]
1 1
0
where α 1 is calculated from Eq. [6.1.43). For d = 2/9, α 1 ≈ 1.2220.
Note that all these relations are valid only for sufficiently high values of elastomer
swelling ratio.
The obtained theoretical predictions have been verified in experiments on real elastomers.
The elastomers tested in our experiments were amorphous polybutadiene urethanes
(PBU) with polymer network of different density: 0.3 kmol/m 3 (PBU-1), 0.05 kmol/m 3
(PBU-2), 0.2 kmol/m 3 (PBU-3), 0.1 kmol/m 3 (PBU-4). Oligooxypropylene triol - Laprol
373 was used as a crosslinking agent at the curing of prepolymer of oligobutadiene diol. The
elastomer specimens were manufactured in the form of disks, 35 mm in diameter and 2 mm
thick. The kinetics of specimen swelling was determined in low-molecular liquids: toluene,
dibutyl sebacate (DBS), dioctyl sebacate (DOS).
The typical kinetic and strain curves of free swelling are given in Figure 6.1.4. 6 The
S-shape of the kinetic swelling curves in terms of coordinates (t 1/2 ,g 1) is indicative of