Goodyear's Invention of Vulcanization FICA 1839 invention of vulcanization o Rendition of Charles Goodyears (Rubber and Plastics News, August 1984)
Goodyear’s Invention of Vulcanization 11
Rubber elasticity Energy-driven VS entropy-driven elasticity Energy-driven elasticity Entropy-driven elasticity of typical of crystalline solids rubber materials A stretched rubber sample subjected to a constant uniaxial load contracts reversibly on heating A rubber sample gives out heat Energy(U) reversible when stretched Entropy (s) f=∞(-T△Sor Elongation (r) 12
Rubber Elasticity ¾ Energy-driven vs entropy-driven elasticity ¾ Energy-driven elasticity typical of crystalline solids ¾ Entropy-driven elasticity of rubber materials ¾ A stretched rubber sample subjected to a constant uniaxial load contracts reversibly on heating ¾ A rubber sample gives out heat reversible when stretched 12
Thermodynamics of rubber Elasticity d=oQ-W,δW=pdV-fall 80=Tds Thermo-elastic behavior du= Tas-pdv + fal Measured at constant pressure G=H-TS=u+pv -ts dG=fdl+Vap-SdT 人(m)()/-(m-1 R.g. positive 0.2 al a(ar丿 aT (al 1.13 aH or af negative Slope intercept slope 0 275300325350375 Temperature (K) Thermoelastic effects 6Q=7as<0 Thermoelastic inversion(热弹转变) aH aH or small elongation a7) =T //OH for large elongation(10%), 13 p, but not for very large elongation
Thermodynamics of Rubber Elasticity negative slope positive slope Thermoelastic inversion (✝ᕩ䖜ਈ) ¾ Thermo-elastic behavior Measured at constant pressure , , p T p l H f f l T T § · w ¨ ¸ § · w © ¹ w ¨ ¸ © ¹ w p T, H f l § · w ! ¨ ¸ © ¹ w p T, H f l § · w ¨ ¸ © ¹ w for small elongation for large elongation (>10 %), but not for very large elongation Thermoelastic effects GQ=TdS<0 13 du TdS pdV fdl G H TS u pV TS dG fdl Vdp SdT , , l p G S T § · w ¨ ¸ , © ¹ w , p T G f l § · w ¨ ¸ © ¹ w , , , , pT l p pl pT G G T l lT § ·§ · w w ww §· §· ¨ ¸¨ ¸ ¨¸ ¨¸ w w ww ©¹ ©¹ © ¹© ¹ l p pT , , f S T l §· §· w w ¨¸ ¨¸ ©¹ ©¹ w w pT pT pT , ,, G HS f T l ll § · § · §· w ww ¨ ¸ ¨ ¸ ¨¸ © ¹ © ¹ ©¹ w ww pT pl , , H f f T l T § · §· w w ¨ ¸ ¨¸ © ¹ ©¹ w w intercept slope Tv lv , , u f f T l T §· § · w w ¨¸ ¨ ¸ ©¹ © ¹ w w or du Q W W pdV fdl GG G , GQ TdS , 0 T v u l § · w ¨ ¸ | © ¹ w
The statistical mechanics of rubber elasticity Affine network(仿射网络) The chain segments between crosslinks can be represented by Gaussian statistics of unperturbed Affine network model (L/Lo= 2) chains The network consists of N-chains per unit volume. The entropy of the network is the sum of the entropies of the individual chains All different conformational states have the same energy. Undeformed network The deformation on the molecular level is the same as that on the Phantom network model (L/Lo= 2) macroscopic level, i. e. deformation is affine The unstressed net work is isotropic. The volume remains constant during
The statistical mechanics of rubber elasticity Affine network (ԯሴ㖁㔌) ¾The chain segments between crosslinks can be represented by Gaussian statistics of unperturbed chains. ¾ The network consists of N-chains per unit volume. The entropy of the network is the sum of the entropies of the individual chains. ¾All different conformational states have the same energy. ¾The deformation on the molecular level is the same as that on the macroscopic level, i.e. deformation is affine. ¾The unstressed net work is isotropic. ¾The volume remains constant during deformation. 14
Stretching of an Ideal chain s=kIn p Φ=乎/g Φ'=Y/Q △S=klnΦ/d 3 ①(h,N exp ①(nN)=()?(N) 2丌Nl 2N l y(h, N)=(h, N)2(N) 3 2N12 2M//<2(N g S(h,M2)=-k )+kB InQ2(N G(h,N=U-TS2 N22+G(ND) oG(. N Nl 相当于拉一根弹黉,弹性系数=??2
Stretching of an Ideal Chain 15 3/2 2 2 2 3 3 , exp 2 2 g g g g g N Nl Nl ) S § ·§ · ¨ ¸¨ ¸ © ¹© ¹ h h 3/2 2 2 2 3 3 , , exp 2 2 g gg g g g N NN N Nl Nl < ): : S § ·§ · ¨ ¸¨ ¸ © ¹© ¹ h h h 2 2 2 3 33 ( , ) ln( ) ln 2 22 g B B Bg g g SN k k k N Nl Nl : S h h 2 (, ) 3 g B g G N h k T N l w w h f h 2 2 3 (, ) ( ) 2 g Bg g G N U TS k T G N N l h h )<: h h , ,/ N NN g gg Sk h ln< ???=ރۅڟmচڟ߿▲ܞйڢब f x k ' )) S k ln / ' / ' '/ ) < : ) < :