The multi-phases parallel model for blend polymer solids was applied to express the mechanical properties of polymer film in the course of sorption of small molecules; the following relations were obtained.
1) The following fundamental equations developed. With
X: film thickness,
x: distance from the film surface in the direction of the thickness, a: distance where the small molecules are diffused,
C(
x,
t): concentration distribution at time
t (mass/volume),
q (
t ): amount of absorbed small molecules at
t (mass/volume),
E: elastic modulus of polymer during the sorption process,
EA(
x,
t): elastic modulus distribution,
Ep: elastic modulus of pure polymer, F: function between
EA and
C at time
t.
2) When the relation between
EA and
C is linear, equation (9) is obtained by using the equations (3), (4) and (5).
3) Assuming the three typical distributions of concentration and elastic modulus, the relations between
E and
q(
t)/
q(∞) were calculated for various relations between
EA and
C (see fig. 3 and fig. 4).
4) The elastic modulus on the surface of film,
EA(O,
t) is given by following euqation. With
ka: reaction velocity constant.
5) Characteristic temperature dispersions of complex elastic modulus for polymer film during the sorption process were obtained by using the blend polymer theory (see fig. 6)
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