Transport of water in high T polymers: A comparison between interacting and non-interacting systems - Polyimides and Other High Temperature Polymers - page 280

diffusivity. Good curve fittings of sorption kinetics data are obtained, for both
PMDA-ODA and TGDDM-DDS, by assuming a Fickian behaviour with constant
mutual diffusivity (D). In fact, the time evolution of absorbed mass, normalized
by the equilibrium mass uptake, is described for sorption in a plane sheet by the
following relationship [29]:

( )

M

2

8

∞

1 − D 2 m + 1 π

2

t

t

= 1 − exp

(3)
where M t is the amount of penetrant absorbed at time t, M ∞ is the amount of pene-
trant absorbed at equilibrium and

( )

M π

2 2 2

2 m + 1

m =

∞ 0

is the thickness of the sheet. This equation
has been used to fit sorption data to determine the values of diffusivity. It is worth
noting that the values of D determined in this way are actually averages over the
ranges of water concentration in each sorption test. The diffusion coefficients
evaluated in this way are reported, as a function of water vapour activity, in Fig-
ure 12. Consistent with the previous discussion, the dependence is more pro-
nounced in the case of epoxy. The lower values of D measured for the TGDDM-
DDS resin are partly due to the lower test temperature and partly to the strong
molecular interactions between the penetrant and the matrix.

Figure 12. Water diffusivity evaluated from sorption tests reported as a function of water vapour ac-
tivity for the case of epoxy matrix at 24°C and of polyimide matrix at 30°C.