橡胶老化的化学应力松弛数学模型

MATHEMATICAL MODEL FOR CHEMICAL STRESS RELAXATION OF RUBBERS IN AGING

以Maxwell数学模型为基础,从老化机理及化学流变学观点出发,并考虑到橡胶的粘度与老化时间的关系。推导出橡胶老化的化学应力松弛数学模型:σ/σ_0=Bexp[-A(1+K_ct)~a]。参数α与橡胶的粘度和老化机理有关。参数A反映了老化时发生物理松弛的能力,参数B是发生物理松弛和化学应力松弛的相对常数。通过测试未加防老剂的NBR-26硫化胶老化过程中的化学应力松弛和时数据进行计算机处理,证实此数学模型是正确的。通过时NBR-26硫化胶和BR硫化胶老化时化学应力松弛的参数分析可知,温度较低时,老化以氧化和交联为主,温度较高(200℃)时则以降解反应为主。

The stress relaxation of rubbers in aging is a kind of chemical stress relaxation . The Li' s mathematical model is an experiential equation . The Maxwell mathematical model is effective only when both Yong's modulus E and vicosity η are constants . Indeed , the variation of E is so muchsmaller than that of η in aging due to high molecular weigth M of rubbers that E is regarded as a constant . Which η varies largely with the variations of M and molecular structure of rubbers . Combination of aging mechanism of rubbers and Staudinger-Kuhn equation η=KMm yields η=η0(1+kct)βwhere η is the vicosity at t time , η0 is the initial vicosity at t=0 ,kc is the constant for chemical reaction rate ,t is aging time, -m<β<m+ 1 . For β=0 , it shows that there are no chemical reaction or the effects of three kinds of chemical reaction on η are counteracted ; for β<0 , it shows that the aging of rubbers give priority to degradation ; for β>0 , it shows that the aging give priority to oxidation and crosslinking .The equation 1 is combined with equation dσ/σ= -Edt/η to yield an integral ,which on integration lead toσ/σ0=B exp [-A(1+kct)α] [2]where α= 1 -β ,A = E/η0kcα,B= exp(E/η0kcα). The equation 2 is the mathematical model for chemical stress relaxation of rubbers in aging . The parameter α ,A and B reflect the dependance of η on aging mechanism , ability of relative physical stress relaxation and ability of relative chemical stress relaxation of rubbers in aging respectively .When α= 1 , equation 2 becomes Maxwell mathematical model ; when kct(?) 1 , then l + kct≈kct,let Akcα =k , equation 2 is simpfied to Li 's experiential equation . These describle that Maxwell mathematical model and Li 's experiential equation are two special cases of equation 2.The chemical stress relaxation of NBR-26 vulcanizate without antioxidants at 85°C was determined . The stochastic selection on B and linear regression with experimental data yield themodel parameter A =8.158 × 10-2, B= 1.085 , kc = 3.01 × 10-4s-1 , and α=0.5869 .The chemical stress relaxation of NBR-26 vulcanizate without antioxidants at 85°C was simulated by equation 2 with above-mentioned parameter values used computer . The experimental data and computer simulating results are identical . It presents that equation 2 has reflected the chemical stress relaxation of rubbers in aging and the model parameters yielded by stochastic selection on B and linear regression are trustworthy .According to Maxwell mathematical model , the curves of chemical stress relaxations of distinct vulcanizates can not intersect due to different k and the curve with larger k is under the curve with smaller k . But it was found that the curves might intersect in some cases. The computer simulating results show that the phenomenon is not experimental error and is normal chemical stress relaxation phenomenon . That α of NBR-26 vulcanizate at 115°C and 2001 are 0.613 2 and 1.146 respectively show that the aging of NBR-26 at 115°C give priority to oxidation and crosslinking and the aging at 200 °C give priority to degradation . Thus , the equivalent of time-temperture in rubber aging is incorrect .