Modulus profiles in Figure 4.17b show that the modulus in the bulk is not affected during ageing at 120°C even for long durations such as 27 days. This is a clear validation of the fact that thermal degradation (without oxygen) can be neglected and all modulus changes are induced by oxidation. At the same time large modulus increases, up to several GPa, are observed at the edges; these observations confirm measurements performed in homogeneous conditions. The question now is whether the model can predict quantitatively these profiles. In order to perform such modelling oxygen diffusion has to be taken into account, so first it is necessary to measure the actual oxygen diffu- sion coefficient in this material.
4.4.1.2 Oxygen permeability
Permeation of oxygen through a rubber sheet has been measured at dif- ferent temperatures; results are plotted in Figure 4.18. Permeability has been measured using a stabilized sample and at relatively low temperature, in or- der to avoid any oxidation of the rubber during the test. Oxygen diffusivity is calculated from this permeability measurement considering that the solubility coefficient is equal to 3.10−8 mol.l−1.Pa−1 [1] and temperature independent.
This last point could be refined, in fact it seems that solubility might be slightly influenced by temperature [113] but this effect is considered to be of second order here. Oxygen diffusivity can be expressed as follows:
D=D0·exp(−EPox
R·T ) (4.7)
With Do equal to 3 10−4 m2.s−1 and EPox equal to 39 kJ/mol. Then at 120°C, oxygen diffusivity is equal to 1.9 10−9 m2.s−1. This value is in accordance with data available in the literature ([69], [1]).
It has to be noted that oxygen diffusion has been characterized on unaged polychloroprene and it has been postulated that this value does not change with oxidation. This point is an assumption that could be discussed, in fact because of the increase in crosslink density and the appearance of possible glassy areas with oxidation the value of oxygen diffusivity might be affected.
This point would need further experiments in order to take it into account in the modelling.
Figure 4.18: Oxygen permeability coefficient as a function of temperature.
4.4.2 Modelling
The model used with thick samples is exactly the same as for homogeneous oxidation except for the fact that the oxygen concentration depends on time due to both consumption by the oxidation and increase due to diffusion from external media. These phenomena can be written in mathematical terms us- ing the following equation that has been added to the entire model described previously:
∂[O2]
∂t =−k2·[Po]·[O2] +k6·[P Oo2]2+D·∂2[O2]
∂z2 (4.8)
Where D is oxygen diffusion coefficient (in m2.s−1), [O2] is the oxygen con- centration and zthe position in the sample thickness and tthe time.
Considering this differential equation with the value of diffusivity measured on the unaged sample it is possible to model oxidation as a function of time and position in a thick polychloroprene rubber. Results obtained at 120°C for both double bond consumption and modulus changes are plotted in Figure 4.19. As expected a strong DLO is observed with large double bond consump- tion coupled with a large modulus increase localized at the sample edges. A comparison between experimental data and predicted values (in Figure 4.20) shows that both are in agreement, indicating that the kinetic model is suit- able for prediction of heterogeneous degradation. However for low degradation levels, i.e. modulus under 10 MPa, the results are not exactly the same; the measured profile is sharper than the predicted one. This means that oxidation is more localized on the surface than predicted by the model; this behaviour
could be due to a decrease of the oxygen diffusivity with ageing. In fact the effect of the value of oxygen diffusion coefficient D on the predicted profile shape is plotted in Figure 4.21, a higher value of D leads to a sharper profile.
This means that if oxidation leads to a reduction of the oxygen diffusivity (through an increase of the crosslink density), the degradation profile will be more localized close to the surface. By taking into account this potential evo- lution of diffusivity with oxidation a better description of experimental results might be possible. This would require measurements of oxygen permeability at several oxidation levels. It is important to note that a modification of the oxygen solubility might also occur during degradation. This effect of oxidation on both oxygen solubility and diffusion is still an open field for research and would also require time dependent DLO models.
Figure 4.19: Typical modelling results with evolution of double bonds (left) and increase in modulus (right) as a function of time and position at 120°C.
Figure 4.20: Comparison between predicted and measured modulus profile through thickness after 6 days of ageing at 120°C.
Figure 4.21: Effect of the oxygen diffusivity value on the modulus profile at 120°C.
The comparison between experiments and modelling is limited to one age- ing time; in fact for longer durations the modulus of the oxidized layer is considerably higher than 50 MPa, which was taken as the upper limit in terms of prediction. It would be useful to perform ageing for shorter durations in order to make comparisons at different ageing times. Prediction for very high oxidation levels needs to consider more reactions and physical phenomena such as formation of glassy regions in the rubber. This is out of the scope of this work but would be interesting for the future.