Senichev V.Yu., Tereshatov V.V., Makarova M.A., Yakushev R.M., Vnutskikh Z.A., Fedoseev M.S. , Volkova E.R.

Institute of Technical Chemistry of Ural Branch of the RAS, Perm, Russia.

Strain-stress dependencies of real polymer networks on the base of polybutadiene liquid rubbers

One of the main problems of high-elasticity theory is an adequate understanding of stress-strain relationship over the entire range of strain values. Usually, strain-stress plots for elastomer on simple stretching are convex, but sometimes these plots are with inflection. The last curves contain initial a concave-shaped part and a part exceedingly marked by convexity-shaped at the last strain stages of a material on its essential hardening. The description of such curves is complicated [1].

Modification of the elasticity theory, while taking into account steric constraints in the strain process (the Erman-Monnerie MCC-model) and the finite chain extensibility conception has allowed to describe strain-stress dependencies with abrupt rise in stress under high strain values (usually λ>5). This approach was recently used for describing simple extension of polyurethane samples [2]. The task of this work is to show applicability of the developed approach for cross-linked elastomers that does not contain urethane bonds.

Two elastic materials on the base of liquid oligomers with two terminal carboxylic groups were investigated. Polybutadiene-nitrile SKN-10-KTR (Mn~3000, nitrile groups), and polybutadiene SKD-KTR (Mn~3000) were obtained from FSUE NIISK(Russia, Saint Petersburg). Compositions based of these oligomers were obtained via mixes of the Epotec YD 127 epoxy resin from Aditya Birla Chemicals (Thailand), 4,6-tris(N,N-dimethylaminomethyl)phenol and zinc oxide.

Cross-linked elastomers were obtained using one-stage process. The following components weight ratios were used (phr): SKN-10-KTR 100, Epotec YD 127-13.9 , 2,4,6-tris(N,N-dimethylaminomethyl) phenol -0.53, and zinc oxide – 1.53, for SKN-1; SKD-KTR 100, Epotec YD 127-11.1, 2,4,6-tris(N,N-dimethylaminomethyl) phenol -0.53, and zinc oxide 1.53 for SKD-1. The compositions were cured for 2 days at 100 ^oC.

Glass transition temperature Tg of the elastomers was determined by means of the DSC 822^e calorimeter (Mettler-Toledo) at the heating rate 0.08K·s^-1. Mechanical tests were performed on the Instron 3365 tensile-testing machine at low strain rate 0.0028 s^-1, 25±1 ^oC. The values of effective network density N_C resulting from chemical cross-linking were determined by the Cluff-Gladding-Pariser method using toluene as a solvent.

Preliminary evaluation of the equilibrium swelling value was conducted in toluene and dioxane-1,4 using samples before strain and after strain and relaxation. Experimental results have shown that equilibrium swelling values do not vary after the strain, that excluding the necessity to take into account the Mullins effect. The glassing temperatures values were -65^oC (for SKN-1), and -74^oC (for SKD-1). They were significantly lower than the temperature of mechanical tests.

Stress values σ under simple strain for polyurethane samples were calculated as per the following equation using data on effective network density (Table) [2]:

(1)

where k-Boltzmann constant, b-parameter of corrected MCC-model [3], λ –strain ratio, d=0.2- parameter of corrected MCC-model [3], g_s-structural parameter, related with the part of chains that are overstressed under high strain ratios, a-

inextensibility parameter,.

Comparison of calculated and experimental data shows (Fig.1) that the proposed combined approach describes the s=f(l) dependence practically adequately in the entire strain range at parameters values given in Table.

Fig. 2 presents visualization of the contribution of the MCC-model and the contribution of the finite chain extensibility effect to the total stress of SKN-1 sample under strain. The shaded area shows the contribution of this effect to the free energy of high elasticity.

Fig. 1 Strain-stress plots for the sample SKN-1 and SKD-1. line – experiment, calculated data (dots) produced as per equation(1).		Fig. 2 Strain-stress plots for the sample SKN-1. line – experiment, calculated data (dots) obtained as per equation(1): 1–the contribution of the MCC-model, 2–the contribution of the finite chain extensibility effect, 3–total stress values for the combined model.

Table. Values of parameters in equation (1) for investigated elastomers

sample	NC×10^-24, m^-3	gs	a	b
SKN-1	5.0	0.1	0.09	0.11
SKD-1	6.0	0.1	0.09	0.11

This work was financially supported by the Ural Branch of the Russian Academy of Science, the program “Creation and investigation of macromolecules and macromolecular structures of new generation” (project 12-T-3-1005), and the Russian Fund for Basic Research (projects 13-03-00101, 13-03-96000).

References

1. Christenson E.M.; Anderson J.M.; Hiltner A.; Baer E. Relationship between nanoscale deformation processes and elastic behavior of polyurethane elastomers. Polymer 2005, 46, 11744–11754.

2. Tereshatov V.V.; Senichev V.Yu. A generalized approach for describing curves stress versus strain for cross-linked elastomers. In: Materials of the IX Conference “Advanced science news”. BialGRAD BG. Sofia, Bulgaria. 2013, 8-10.

3. Tereshatov, V.V.; Senichev, V.Yu. Stress-strain behavior of cross-linked polybutadiene urethanes. Polym. Sci. 1995, A37, 702-705.