# Elastic Properties of Polychloroprene Rubbers in Tension and Compression during Ageing

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{10}, C

_{01}and K are the material parameters, K being in particular the bulk modulus of the elastomer; I

_{1}and I

_{2}the first and second invariants of the deformation gradient tensor; J the Jacobian which can be written as the volume ratio V/V

_{0}, with J = 1 for perfectly incompressible materials.

_{0}where l

_{0}is the initial sample length.

_{10}, C

_{01}), bulk modulus (K) and elastic properties at small strain (Young’s modulus E and Poisson’s ratio ν) can then be summarized as follows:

## 2. Materials and Methods

#### 2.1. DSC/OIT

#### 2.2. Tensile Tests

#### 2.3. Hardness Tests (Shore A)

#### 2.4. Oedometric Compression Test

## 3. Results

#### 3.1. Chemical Stability: OIT Changes

_{r}) which is defined equal to the actual OIT for the filled samples, and for the unfilled values as OIT − 0.6 (which is the OIT difference at t = 0 h between unfilled (1.7) and filled (1.1) samples). Thus, Figure 1b shows the relative OIT for the three temperatures of exposure and allows to compare both elastomers in terms of OIT decrease. It clearly appears that the relative OIT decrease rate (i.e., the slope of the “linear” region shown as dotted lines in Figure 1b) follows the same trend for both elastomers whatever the exposure temperature. As a result, filled and unfilled elastomers show the same ageing kinetic and differ only by their initial state.

_{a}the activation energy (J/mol), R the gas constant = 8.314 J/mol/K and T the temperature (in kelvin). E

_{a}is then considered as a characteristic of the process and its activation by temperature. Here, the temperature of exposure activates the OIT drop rate with an activation energy close to 78 kJ/mol considering such behavior.

#### 3.2. Tensile Tests

^{3}for carbon black and 1.2 g/cm

^{3}for the elastomer [22], the volume fraction of fillers here is about 0.2, which yields a value of 2 for the modulus ratio using Equation (5).

_{n}= OIT(t)/OIT(t = 0)) for both filled and unfilled rubbers at the three ageing temperatures. All the data display a similar trend and fall within the same envelope (see dotted lines in Figure 5): starting from high normalized OIT values (unaged rubbers), normalized Young’s modulus increases as normalized OIT decreases until a limit value of OIT which corresponds to a total consumption of stabilizers (OIT

_{n}reaching values close 0).

#### 3.3. Hardness Tests (Shore A)

#### 3.4. Bulk Modulus

## 4. Discussion

#### 4.1. Structure-Properties Relationships

^{3}) [28]. As a consequence, the crosslink density modifications which can be deduced from E measurements may be linked to OIT, elongation at break and hardness changes. Although FTIR measurements only slightly evidence oxidation products in the timeframe of the ageing experiments (see infrared spectra in Appendix B), it is well known that oxidation leads to crosslinking in the case of polychloroprene rubbers during long-term exposure in air, due to addition reactions between alkyl/peroxyl radicals and double bonds [6,8]. This is consistent with the fact that OIT decreases when E increases.

_{A}) are proposed in the literature [29,30]. In [30], a finite element simulation study leads to a linear relation between the logarithm of the elastic modulus and the hardness values (see Equation (8)):

_{1}and c

_{2}empirical constants determined from the best fit as c

_{1}= 0.0235 and c

_{2}= 0.6403 for 20 < S

_{A}< 80 [30].

_{A}. According to the previous approach, our experimental results lead to c

_{1}= 0.0245 and c

_{2}= 1.075 for both filled and unfilled samples, independently of ageing, in the 40 < S

_{A}< 85 range, which is in good agreement with the values reported previously [30].

_{b}and E. As a first approximation, the elongation at break can be related to the chain dimensions [1]: assuming an initial Gaussian conformation ${\mathit{R}}_{\mathbf{0}}\mathbf{=}\sqrt{\mathit{n}}\mathit{l}$ with R

_{0}the chain end-to-end distance, n the average number of repeating units in the chain and l the monomer typical size, and fracture occurring when the chain extension reaches a maximal value ${\mathit{R}}_{\mathit{max}}\mathbf{=}\mathit{n}\mathbf{l}$, we can write Equation (9):

_{c}the molar mass between crosslinks (in kg/mol), which is proportional to n. Hence, ${\mathit{\lambda}}_{\mathit{b}}$ should scale as $\mathbf{1}\mathbf{/}\sqrt{\mathit{E}}$ which is indeed observed in Figure 10. Interestingly, this simple scaling remains valid whatever the ageing conditions and for both filled and unfilled materials.

^{3}, and with a molar mass M

_{0}of 88 g/mol for the polychloroprene monomer, the calculated prefactor is $\sqrt{\frac{3\rho \mathrm{R}T}{{M}_{0}}}\approx 10$ MPa

^{−1/2}. This is in very good agreement with the value obtained from the fit. Note the calculated value is obtained by assuming the typical molar mass between crosslinks is the molar mass of the whole chain, which explains the slightly underestimated value obtained.

_{b}and hardness shore A show a direct relation according to simple physical relations from rubber elasticity theory. Interestingly, these correlations are valid for the filled and unfilled rubbers during ageing. From a practical purpose, the choice of a critical value for one of these three properties can be simply translated in terms of crosslink density changes during ageing.

#### 4.2. Poisson’s Ratio

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Evolution/profile of modulus through the thickness measured by microindentation of a 2 mm-thick sample aged at 90 °C for different durations.

## Appendix B

^{−1}region with a resolution of 4 cm

^{−1}and 16 scans.

^{−1}is of particular interest when studying polychloroprene degradation due to the presence of bands attributed to oxidation products [4,5,32]. It should be noted that unfilled neoprene has been aged up to 6000 h for this analysis, while in the rest of the study the longest ageing time was 3000 h. The intensity of the band centered at 1590 cm

^{−1}clearly increases with ageing, but the change becomes only significant after 4900 h. This band can be attributed to carboxylate species. Their presence results from the conversion of acid chlorides and carboxylic acids during ageing in the presence of a small amount of metal oxides such as ZnO, classically used as an activator for the sulfur vulcanization of rubbers [33].

## References

- Rubinstein, M.; Colby, R. Polymer Physics; Oxford University Press: Oxford, UK, 2003. [Google Scholar]
- Mark, J. Rubber Elasticity. J. Chem. Educ.
**1981**, 58, 98. [Google Scholar] [CrossRef][Green Version] - Nagdi, K. Rubber as an Engineering Material: Guideline for User; Hanser: Munich, Germany, 1993. [Google Scholar]
- Celina, M.C.; Wise, J.; Ottesen, D.; Gillen, K.; Clough, R. Correlation of chemical and mechanical property changes during oxidative degradation of neoprene. Polym. Degrad. Stabil.
**2000**, 68, 171–184. [Google Scholar] [CrossRef][Green Version] - Shelton, R. Aging and oxidation of elastomers. Rubber Chem. Technol.
**1957**, 30, 1251–1290. [Google Scholar] [CrossRef] - Delor, F.; Lacoste, J.; Lemaire, J.; Barrois-Oudin, N.; Cardinet, C. Photo-and thermal ageing of polychloroprene: Effect of carbon black and crosslinking. Polym. Degrad. Stabil.
**1996**, 53, 361–369. [Google Scholar] [CrossRef] - Celina, M.C. Review of polymer oxidation and its relationship with materials performance and lifetime prediction. Polym. Degrad. Stabil.
**2013**, 98, 2419–2429. [Google Scholar] [CrossRef] - Le Gac, P.-Y.; Roux, G.; Verdu, J.; Davies, P.; Fayolle, B. Oxidation of unvulcanized, unstabilized polychloroprene: A kinetic study. Polym. Degrad. Stabil.
**2014**, 109, 175–183. [Google Scholar] [CrossRef][Green Version] - Bergström, J. Mechanics of Solid Polymers; Elsevier: Amsterdam, The Netherlands, 2015. [Google Scholar]
- Peng, S.; Landel, R. Stored energy function and compressibility of compressible rubberlike materials under large strain. J. Appl. Phys.
**1975**, 46, 2599. [Google Scholar] [CrossRef] - Laufer, Z.; Diamant, Y.; Gill, M.; Fortuna, G. A Simple Dilatometric Method for Determining Poisson’s Ratio of Nearly Incompressible Elastomers. Int. J. Polym. Mater.
**1978**, 6, 159–174. [Google Scholar] [CrossRef] - Kugler, H.; Stacer, R.; Steimle, C. Direct Measurement of Poisson’s Ratio in Elastomers. Rubber Chem. Technol.
**1990**, 63, 473–487. [Google Scholar] [CrossRef] - Elektrova, L.; Melent’ev, P.; Zelenev, Y. Influence of fillers on the poisson ratios of rubber-like polymers. Polym. Mech.
**1973**, 8, 308–309. [Google Scholar] - Robertson, C.; Bogoslovov, R.; Roland, C. Effect of structural arrest on Poisson’s ratio in nanoreinforced elastomers. Phys. Rev. E
**2007**, 75, 051403. [Google Scholar] [CrossRef] [PubMed][Green Version] - Planes, E.; Chazeau, L.; Vigier, G.; Fournier, J. Evolution of EPDM networks aged by gamma-irradiation—Consequences on the mechanical properties. Polymer
**2009**, 50, 4028–4038. [Google Scholar] [CrossRef][Green Version] - Le Gac, P.-Y.; Broudin, M.; Roux, G.; Verdu, J.; Davies, P.; Fayolle, B. Role of strain induced crystallization and oxidative crosslinking in fracture properties of rubbers. Polymer
**2014**, 55, 2535–2542. [Google Scholar] [CrossRef][Green Version] - Le Gac, P.-Y.; Albouy, P.-A.; Petermann, D. Strain-induced crystallization in an unfilled polychloroprene rubber: Kinetics and mechanical cycling. Polymer
**2018**, 142, 209–217. [Google Scholar] [CrossRef][Green Version] - Le Gac, P.-Y.; Albouy, P.-A.; Sotta, P. Strain-induced crystallization in a carbon-black filled polychloroprene rubber: Kinetics and mechanical cycling. Polymer
**2019**, 173, 158–165. [Google Scholar] [CrossRef][Green Version] - Bouaziz, R.; Ahose, K.; Lejeunes, S.; Eyheramendy, D.; Sosson, F. Characterization and modeling of filled rubber submitted to thermal aging. Int. J. Solids Struct.
**2019**, 169, 122–140. [Google Scholar] [CrossRef] - Guth, E. Theory of Filler Reinforcement. J. Appl. Phys.
**1945**, 16, 596–604. [Google Scholar] [CrossRef] - Fukahori, Y.; Hon, A.A.; Jha, V.; Busfield, J.J.C. Modified GUTH–GOLD Equation for Carbon Black-Filled Rubbers. Rubber Chem. Technol.
**2013**, 86, 218–232. [Google Scholar] [CrossRef] - Mark, J. Polymer Handbook; Oxford University Press: Oxford, UK, 1999. [Google Scholar]
- Mullins, L.; Tobin, N. Stress softening in rubber vulcanizates. Part I. Use of a strain amplification factor to describe the elastic behavior of filler-reinforced vulcanized rubber. J. Appl. Polym. Sci.
**1965**, 9, 2993–3009. [Google Scholar] [CrossRef] - Anandakumaran, K.; Seidl, W.; Castaldo, P. Condition Assesment of Cable Insulation Systems in Operating Nuclear Power Plants. IEEE T. Dielect. El. In.
**1999**, 6, 376–384. [Google Scholar] [CrossRef] - Burns, J.; Dubbelday, P.; Ting, R. Dynamic Bulk Modulus of Various Elastomers. J. Polym. Sci. B Polym. Phys.
**1990**, 28, 1187–1205. [Google Scholar] [CrossRef] - Diani, J.; Fayolle, B.; Gilormini, G. Study on the temperature dependence of the bulk modulus of polyisoprene by molecular dynamics simulations. Mol. Simul.
**2008**, 34, 1143–1148. [Google Scholar] [CrossRef][Green Version] - Seitz, J. The estimation of mechanical properties of polymers from molecular structure. J. Appl. Phys.
**1993**, 49, 1331–1351. [Google Scholar] [CrossRef] - Flory, P. Principles of Polymer Chemistry; Cornell University Press: Ithaca, NY, USA; London, UK, 1953. [Google Scholar]
- Gent, A.J. On the relation between indentation hardness and Young’s modulus. Rubber Chem. Technol.
**1958**, 31, 896–906. [Google Scholar] [CrossRef] - Qi, H.J.; Joyce, K.; Boyce, M.C. Durometer hardness and the stress-strain behavior of elastomeric materials. Rubber Chem. Technol.
**2003**, 76, 419–435. [Google Scholar] [CrossRef] - Wise, J.; Gillen, K.; Clough, R. Quantitative model for the time development of diffusion-limited oxidation profiles. Polymer
**1997**, 38, 1229–1244. [Google Scholar] [CrossRef] - Le Gac, P.-Y.; Celina, M.; Roux, G.; Verdu, J.; Davies, P.; Fayolle, B. Predictive ageing of elastomers: Oxidation driven modulus changes for polychloroprene. Polym. Degrad. Stabil.
**2016**, 130, 348–355. [Google Scholar] [CrossRef][Green Version] - Heideman, G.; Datta, R.; Noordermeer, J.; van Baarle, B. Influence of zinc oxide during different stages of sulfur vulcanization. Elucidated by model compound studies. J. Appl. Polym. Sci.
**2005**, 96, 1388–1404. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) Oxidation induction time (OIT) and (

**b**) relative OIT (OIT

_{r}) evolution as a function of ageing time.

**Figure 2.**(

**a**) Tensile curves to failure of samples aged at 90 °C for unfilled and (

**b**) filled rubbers.

**Figure 3.**(

**a**) Evolution of Young modulus (E) with ageing time for unfilled and (

**b**) filled rubbers at 70 °C, 80 °C and 90 °C.

**Figure 4.**Ratio of the filled and unfilled moduli as a function of ageing time for three ageing temperatures.

**Figure 8.**(

**a**) Evolution of the bulk modulus (K) with ageing time for unfilled and (

**b**) filled rubbers at 70 °C, 80 °C and 90 °C.

**Figure 9.**Young’s modulus (E) versus hardness shore A for all samples (filled, unfilled) and temperatures.

**Figure 10.**${\mathit{\lambda}}_{\mathit{b}}$ versus $\mathbf{1}\mathbf{/}\sqrt{\mathit{E}}$ for all samples (filled, unfilled) and temperatures.

**Figure 11.**(

**a**) Poisson’s ratio versus ageing time for unfilled and (

**b**) filled rubbers at 70 °C, 80 °C and 90 °C.

E_{a} (kJ/mol) | E | OIT | λ_{b} | Hardness |
---|---|---|---|---|

Unfilled | 90 | 78 | 86 | 53 |

Filled | 84 | 78 | 74 | 72 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bouaziz, R.; Truffault, L.; Borisov, R.; Ovalle, C.; Laiarinandrasana, L.; Miquelard-Garnier, G.; Fayolle, B. Elastic Properties of Polychloroprene Rubbers in Tension and Compression during Ageing. *Polymers* **2020**, *12*, 2354.
https://doi.org/10.3390/polym12102354

**AMA Style**

Bouaziz R, Truffault L, Borisov R, Ovalle C, Laiarinandrasana L, Miquelard-Garnier G, Fayolle B. Elastic Properties of Polychloroprene Rubbers in Tension and Compression during Ageing. *Polymers*. 2020; 12(10):2354.
https://doi.org/10.3390/polym12102354

**Chicago/Turabian Style**

Bouaziz, Rami, Laurianne Truffault, Rouslan Borisov, Cristian Ovalle, Lucien Laiarinandrasana, Guillaume Miquelard-Garnier, and Bruno Fayolle. 2020. "Elastic Properties of Polychloroprene Rubbers in Tension and Compression during Ageing" *Polymers* 12, no. 10: 2354.
https://doi.org/10.3390/polym12102354