Handbook of Solvents - George Wypych - ChemTech - Ventech!

344 George Wypych
Self-diffusion coefficient, 10 -8 cm 2 s -1
surface appears dry (this stage ends when
the surface is dry) and the diffusion rate becomes
very low; in the third stage solvent
diffuses from the cured film. This is a slow
process during which diffusion rate drops to
zero. These changes are shown in Figure
7.1.8. The diffusion rate during drying decreases
as the concentration of polymer
(phenol resin) in varnish increases. Also,
the time to reach the slope change point in
diffusion/time relationship increases as the
concentration of polymer increases. 8
Two methods have been used to measure
the diffusion coefficient of toluene in
mixtures of polystyrenes having two different
molecular weights: one was dynamic
light scattering and the other, fluorescence
recovery after bleaching. 10 The data show
that the relationship between the diffusion
coefficient and polymer concentration is not linear. The crossover point is shown in Figure
7.1.9. Below a certain concentration of polymer, the diffusion rate drops rapidly according
to different kinetics. This is in agreement with the above theory (see Figure 7.1.1 and explanations
for equation [7.1.2]). The slope exponent in this study was -1.5 which is very close
to the slope exponent predicted by the theory of reptation (-1.75).
The above data show that theoretical predictions are accurate when modelling diffusion
phenomena in both simple and complicated mixtures containing solvents.
7.1.2 SWELLING
Polymers differ from other solids because they may absorb large amounts of solvents
without dissolving. They also undergo large deformations when relatively small forces are
involved. 12 Swelling occurs in a heterogeneous two phase system a solvent surrounding a
swollen body also called gel. Both phases are separated by the phase boundary permeable to
solvent. 13
The swelling process (or solvent diffusion into to the solid) occurs as long as the
chemical potential of solvent is large. Swelling stops when the potentials are the same and
this point is called the swelling equilibrium. Swelling equilibrium was first recognized by
Frenkel 14 and the general theory of swelling was developed by Flory and Rehner. 15,16
The general theory of swelling assumes that the free energy of mixing and the elastic
free energy in a swollen network are additive. The chemical potential difference between
gel and solvent is given by the equation:
where:
10
1
0.1 1
Polymer concentration, g cm
10
-3
Figure 7.1.9. Self-diffusion coefficient vs. polystyrene
concentration. [Adapted, by permission, from
L Meistermann, M Duval, B Tinland, Polym. Bull., 39,
No.1, 101-8 (1997).]
0
0
0
( μ − μ ) = ( μ − μ ) + ( μ −μ
)
1 1
μ 1
0
μ 1
Light scattering
Fluorescence recovery
1 1
mix 1 1 el [7.1.5]
chemical potential of gel
chemical potential of solvent