Complex modulus: As Solid σ=nsin(ot+δ o(t=o sin ot cos+o cos tsin S synchronization asynchronism Modulus of Modulus of 8=8 sin(ot synchronization part asynchronism part E ECOSSE"oo sin d E E≠E+E E E=E+E or e*=etiE I E 内耗的量度 tan d E 偏向液体的程度 E
Complex Modulus: As “Solid” VV ZG 0 sin t 0 0 V t VZG sin t cos V ZG cos s n t i HH Z 0 sin t synchronization asynchronism Modulus of synchronization part Modulus of asynchronism part 0 0 E ' cos V G H § · ¨ ¸ © ¹ 0 0 E" sin V G H § · ¨ ¸ © ¹ E’ E” G E z E ' E" E E E E ' E iE " " * ' G G G ' an " t E E G 㙇Ⲵ䟿ᓖ փⲴ〻ᓖੁ⏢ٿ or 0 0 * i E e V G H § · ¨ ¸ © ¹ 16
Complex viscosity: AS" Liquid E=Eo sin(on) o()=oo sin ot cos& +Oo cos ot sin 8 da o cos(ot asynchronism synchronization Viscosity of Viscosity of asynchronism part synchronization part cos& SIn SoC soC (2)8↓-( E E
Complex Viscosity: As “Liquid” 0 0 V t VZG sin t cos V ZG cos s n t i 0 HH Z sin t 0 cos d t dt H J HZ Z asynchronism synchronization Viscosity of synchronization part Viscosity of asynchronism part 0 0 ' sin V K G H Z § · ¨ ¸ © ¹ 0 0 " cos V K G H Z § · ¨ ¸ © ¹ 0 0 E ' cos V G H § · ¨ ¸ © ¹ 0 0 E" sin V G H § · ¨ ¸ © ¹ ' " E K Z " ' E K Z 17
For dynamic mechanics Model i-Maxwell model g t 8 1 do a 0=0e dt Em dt n d( 合 E -=1oe+-0elor -10+ =0 ∫4(=gm-+|e-d E k=1 E*=△()Eno2z2 △E(1)1+2*、EnOr 1+2r v=1 E Model lI-Voigt-Kelvin model g=E 8+nm dt Ot oe Complex compliance D E* 1+2τ E Fn/E
For dynamic mechanics Model I - Maxwell model 0 i t e Z V V 0 0 00 it it it m m mm d t ie e i e dt E E ZZ Z H V V VV Z Z K K § · ¨ ¸ © ¹ 0 0 i t m m d t dt i e dt E V V Z H Z K § · ¨ ¸ © ¹ ³ ³ 2 2 22 22 * 1 1 m m t E E E i t V Z W ZW H ZW ZW ' ' W=Km/Em l nE ( Z) lnZ E’ E” tanG ZW=1 k=2 k=1 k=-1 k=0 18 Model II - Voigt-Kelvin model 0 i t e Z H H Complex compliance 22 22 1 1 * * 1 1 m m D i E E E ZW ZW ZW 1 m m d d dt E dt H VV K m m d E dt H V HK
ternal friction高聚物的内耗与温度、频率的关系 可用力学损耗角的正切tanδ来表示内耗的大小 tand tand 粘弹态 橡胶态 玻璃态 loga 玻璃化转变区域是粘弹性表现最强烈的区域
internal friction ਟ⭘࣋ᆖᦏ㙇䀂Ⲵ↓࠷tanGᶕ㺘⽪㙇Ⲵབྷሿ 儈㚊⢙Ⲵ㙇оᓖǃ仁⦷Ⲵޣ㌫ Tg Tf tanG logZ tanG ₑ㜦ᘱ ㋈ᕩᘱ ⧫⪳ᘱ ⧫⪳ॆ䖜ਈ४ฏᱟ㋈ᕩᙗ㺘⧠ᴰᕪ⛸Ⲵ४ฏ 19
单松弛与多松弛时间与性能的关系 10 polymer 86 G()=∑G le :G(o=Gge- -303691215 og
অᶮᕋоཊᶮᕋᰦ䰤оᙗ㜭Ⲵޣ㌫ 20 single W polymer / 0 t G t Ge W / i t i i G t Ge W ¦