Moisture absorption measurement and modelling of a cellulose acetate
S. Khoshtinat1, V. Carvelli2, C. Marano1*
1 Department of Materials, Chemistry and Chemical Engineering “Giulio Natta”
2 Department of Architecture, Built environment and Construction engineering Politecnico di Milano, Piazza Leonardo Da Vinci 32, 20133 Milan, Italy
*Corresponding Author E-mail: claudia.marano@polimi.it
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Online Resource 1: Parametric study of the “variable surface concentration model”
Parametric study by the analytical model (Error: Reference source not found) to elucidate the effect of each single parameter on the concentration evolution in time. For this purpose, default values for each parameter has been considered as follows:
ha=0.1(mm), Csat=1×10−4(g/mm3), D=1×10−6(mm2/s), β=0.01(1/s)
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(a) Effect of the thickness (ha)
Default values for β, D, and Csat have been considered. The values of thickness have been varied from 0.01 to 1 (mm). As expected by the increase of the membrane thickness, the slope decreases, and the needed time to reach the concentration at saturation increases.
(b) Effect of the concentration at saturation (Csat)
since concentration at saturation has a linear relation with relative humidity, this plot represents the effect of relative humidity on the absorption curve trend, as well. Default values for β , D , and ha have been considered. The values of Csat have been investigated in the range of 2×10−5 and 1×10−4 for each 2×10−5
(
g/mm3)
. An increase in both slope and the needed time to reach the saturation concentration is evident when the relative humidity is increased.(c) Effect of the relaxation factor (β)
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Default values for ha , D , and Csat have been considered. The concentration at the surface reaches its concentration at saturation exponentially by Error: Reference source not found), which causes the toe part in the sigmoidal curve. Therefore, for a better perception of the effect of this parameter, the change of the order of the magnitude is more effective. As it can be seen, parameter β affects mostly the short-time moisture absorption (the toe of the curve). This corresponds to the time at which the surface level of the membrane reaches its concentration at saturation. Comparing the curves corresponding to β=0.001 and β=0.01(1/s) , we can see a sudden difference between the end of the short-time absorption (β=0.001→
√
t=25, β=0.01→√
t=10) . While this difference decreases by the increase of this parameter between β=0.01 and β=0.1(1/s) . Finally, we can see that the curves for β=0.1 and β=1(1/s) show a negligible difference before 100 seconds and coincide perfectly after this time.(d) Effect of the diffusion coefficient (D)
Default values for ha , β , and Csat have been considered. For cellulose acetate, we expect D is within the range 1×10−6÷1×10−5
(
mm2/s)
, depending on the degree of acetylation. Therefore, for this part of the parametric study, the values have been varied in this range with a step of 2×10−6(
mm2/s)
. It can be observed that the diffusion coefficient affects mostly the long-time of the moisture absorption process.As expected by the increase of the diffusion coefficient, the slope of the curve in the long-time absorption increases.
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