Handbook of Solvents - George Wypych - ChemTech - Ventech!

346 George Wypych
Temperature, K
310
300
290
280
270
260
0.25 0.3 0.35 0.4 0.45 0.5 0.55
A comparison of equations [7.1.7]
and [7.1.8] shows that the slope and sign of
swelling curve are determined by the quan-
g/lorcr
tity ΔH1 . Since the melting enthalpy of
water is much larger than the transfer
enthalpy of water, the swelling curves of
gel in liquid water are very steep. The sign
of the slope is determined by the heat transfer
of the solvent which may be negative,
positive or zero depending on the quality of
solvent. The melting enthalpy is always
positive and therefore the swelling curve in
the presence of crystalline solvent is flat
with a positive slope. A positive slope in
temperatures below zero (for ice) means
that gel has to deswell (release water to its
surrounding, or dry out) as temperature
decreases. 13 Figure 7.1.10 illustrates this.
For practical purposes, simple equations
are used to study swelling kinetics.
The degree of swelling, α, is calculated from the following equation: 17
V −V
α=
V
1 0
0
where:
V1 volume of swollen solid at time t=t
V0 volume of unswollen solid at time t=0
The swelling constant, K, is defined by:
K k1
α
= =
k 1−α
2
PEO/water
PEO/ice
Mass fraction of water
Figure 7.1.10. Swelling of crosslinked polyurethane in
water and ice. [Adapted, by permission, from B Hladik,
S Frahn, W Borchard, Polym. Polym. Compos., 3, No.1,
21-8 (1995).]
[7.1.9]
[7.1.10]
where:
k1 rate constant of swelling process
k2 rate constant of deswelling process
This shows that the swelling process is reversible and in a dynamic equilibrium.
The distance of diffusion is time-dependent:
distance (time) n
∝ [7.1.11]
The coefficient n is between 0.5 for Fickian diffusion and 1.0 for relaxation-controlled
diffusion (diffusion of solvent is much faster than polymer segmental relaxation). 18 This
relationship is frequently taken literally 19 to calculate diffusion distance from a measurement
of the change of the linear dimensions of swollen material.
The following equation is used to model changes based on swelling pressure measurements: