Modulus

1.3.3 Consequences of oxidation for mechanical properties of

Because Natural Rubber is an unsaturated rubber and has been widely studied in the past (much more than CR) it is interesting to focus on changes of mechanical properties of this material during oxidation. During NR oxida- tion, the change in modulus is not simple: in a first stage a decrease of the modulus is observed and then a large increase occurs. The initial decrease is usually attributed to scission of intermolecular sulfur-sulfur bonds that have been created during vulcanization. The following large increase is attributed to the reaction of free radicals on the double bonds that creates new inter- molecular bonds and so increases crosslink density [66]. This rapid description of the natural rubber behaviour during oxidation highlights the fact that both reactions on sulfur-sulfur bonds and double bonds have to be considered in order to describe network evolution. Because these reactions do not have the same activation energy, the temperature dependence of the mechanical prop- erties is non-monotonic, as shown by Shelton [67] who found the modulus to increase at 40°C, decrease at 110°C and to vary non-monotonically at 90°C.

The role of sulfur in rubber oxidation will be detailed in Chapter 4. But here the question is: how to predict this behaviour?

Usually two main approaches are used in literature, the first one is mainly used by ‘mechanics’ researchers and considers the evolution of parameters of a con- stitutive model. As an example, Ha-Anh proposed a prediction of the modulus based on the evolution of the two parameters of the Mooney Rivlin equation as a function of oxidation conditions. This approach could appear interest- ing because it is simple, however there is no consideration of the chemistry involved in the degradation and it could lead to a relativly poor prediction.

In fact, at high temperature in thick samples, oxidation is not homogeneous because it is diffusion limited, meaning that the actual measured behaviour is the resultant of the different local behaviours of elementary thickness layers.

Moreover, the prediction is made using Arrhenius law that could not be used a priori (see previous section). And finally, it is worth noting that this method has to be performed again if there is a small change in the formulation of the material.

The second approach that is more used by ‘chemistry’ researchers is based on a correlation between the build-up of oxidative products and modulus changes [68] [69], so if we are able to determine this correlation and then predict oxida- tion product formation it will be possible to make a prediction of the modulus.

This approach has been used by Wise and Celina on polychloroprene to predict the increase of modulus, assuming the increase to be linked to the quantity of oxygen absorbed by the oxidation process by measuring experimentally the oxygen consumed by oxidation in the non DLO regime [61] [62]. Since a cor- relation between oxygen absorbed and modulus (at the edge of the sample) has been established in the case where oxidation is not controlled by oxygen diffusion, the authors are able to simulate modulus profiles through the sam- ple thickness thanks to their analytical kinetic model coupling oxidation and oxygen diffusion. This methodology is very interesting because it is based on the chemistry of oxidation and moreover the actual acceleration factor is

measured over a large temperature range in order to perform reliable predic- tions. However, the actual correlation between the concentration of oxygen absorbed and modulus lacks the physical insights needed to build a complete non empirical model.

From the literature it appears that modulus prediction during rubber oxi- dation is a complex subject and existing methodologies are based either on quantitative consideration but without any chemistry involved or on qualita- tive predictions when chemistry is considered. Because the mechanistic model allows the prediction of chain scission and crosslinking, it should be possible to establish a quantitative relationship between oxidation chemistry and network evolution at the macromolecule scale. But now the question is: is it possible to quantitatively link the evolution of the network to the rubber modulus?

Fortunately and thanks to the theory of rubbery elasticity the modulus of an unfilled elastomer is directly linked to the crosslink density as shown below.

In fact based on thermodynamic considerations, assuming that deformations occur at constant volume and that macroscopic deformations are affine of mi- croscopic ones, it is possible to show [70] that the stress/strain behaviour at low deformation of unfilled rubber is, in simple extension, given by:

σ=R.T.ρ.ν.(λ−λ⁻²) (1.14) withσ the stress in Pa defined as F/S_o with F the load and S_o initial section, R the perfect gas constant, T the absolute temperature, ρ the density of the material, ν the crosslink density, i.e. the concentration of elastically active chains, andλthe extension ratio.

From this equation it appears that the Young’s modulus of an unfilled rubber in ideal conditions is directly linked to the crosslink density of the rubber.

E = 3.R.T.ρ.ν (1.15)

At reasonably low conversions, the actual crosslink density changes with time can be written as:

ν(t) =ν₀−δ·s(t) +γ·x(t) (1.16) Whereν₀is the initial crosslink density, s(t) and x(t) are respectively the num- bers of chain scission and crosslinking events at time t, theδ andγcoefficients depend on the nature of the rubber and will be discussed later (Chapter 4).

So it appears that, in theory, by using the mechanistic approach coupled with theoretical considerations on structure-property relationships it is possi- ble to predict quantitatively the evolution of rubber modulus during oxidation.

This approach will be applied in Chapter 4 on vulcanized polychloroprene.

As a conclusion, oxidation induces a large increase of polychloroprene mod- ulus due to crosslinking by free radical addition on double bonds. Although the origin of this modulus increase is well known the prediction of change in

modulus as a function of oxidation in rubber is not straightforward. Exist- ing methodologies are interested in either quantitative evolution without any consideration of oxidation mechanisms and could be partially wrong, or on qualitative evolutions. Using a mechanistic approach coupled with the theory of rubber elasticity a quantitative prediction of modulus considering chemistry involved during oxidation seems to be possible and will be developed in this study. At the same time, most lifetime predictions of rubbers are based on fracture properties, so the next section will be dedicated to changes in fracture properties of rubber with oxidation.