At temperatures well below the Tg of the conditioned material, water absorption of most polymers correlates well with Fick’s laws (see Annex A of BS EN ISO 62 [1]). The diffusion coefficient, independent of time and moisture concentration (i.e. humidity level) can be calculated from the Fickian diffusion curve (Figure 4). Figure 5 shows a typical diffusion curve for an epoxy resin sample.
Figure 4: Fickian diffusion curve
Figure 5: Fickian curve fit to moisture absorption of an epoxy resin
The diffusion coefficient D is determined from the initial linear region of the Fickian diffusion curve using the following relationship [3]:
(2)
where M ¥ is the equilibrium moisture concentration (or content), M1 is the moisture uptake after time t1 , M2 is the moisture uptake after time t2 and h is the thickness. The moisture equilibrium concentration corresponds to the final asymptotic value on the diffusion curve.
The fractional moisture content gain G can be approximated by [4-6]:
(3)
where Mi is the initial moisture content of the sample and M = M(t) the percent moisture content of the composite at any time t . When only one side of the sample is exposed, the thickness h is replaced by 2h .
The analysis used to derive D assumes that the specimen is an infinite rectangular plate with no moisture diffusion from the specimen edges. In practice, moisture diffusion occurs from all six surfaces. Shen and Springer [4] derived a correction factor to account, which enables the true one-dimensional diffusion coefficient Dx to be determined as follows:
(4)
where l and b are the sample length and width, respectively.
If the moisture entering through the specimen edges is neglected then Dx the diffusivity of the material in the direction normal to the surface is:
(5)
Note: Diffusion in an adhesive joint may be 10 as high as that measured for bulk adhesive samples as a result of capillary action along the adhesive/adherend interface. Moisture diffusion may differ between the unstressed and stressed states with the diffusion rate increasing with applied stress.
Diffusivity D can be expressed as a function of absolute temperature T by the following Arrhenius relationship [5]:
(6)
Do and k are constants determined from a linear regression fit to log D versus 1/T graph (see Figure 6).
Figure 5: Typical diffusivity versus temperature plot
Next: Moisture Control
