复旦大学：《高分子物理》课程电子讲义_Chapt. 5 Amorphous State of Polymers

Chapt. 5 Amorphous State of Polymers 5.1 Molecular motions of polymers 特点,基本类型 5.2 Viscous flow of polymers 特点,表征,影响因素 5.3 Glass transition of polymers 意义,表征,理论

Chapt. 5 Amorphous State of Polymers 5.1 Molecular motions of polymers 5.3 Glass transition of polymers 5.2 Viscous flow of polymers ⢩⛩, สᵜ㊫ර ᜿ѹ, 㺘ᖱ, ⨶䇪 ⢩⛩, 㺘ᖱ, ᖡ૽ഐ㍐ 1

51高聚物的分子热运动 1.主要特点 运动单元的多重性 布朗运动/微布朗运动 与温度有关的松弛过程 T: relaxation time △ △x=△x (1)与运动单元有关 (2)与温度有关 a.指数形式t=roe AE/RT b.WLF方程(Tg附近) (3)与观察时的时间标尺有关 比如:升降温速度,振动频率

5.1 儈㚊⢙Ⲵ࠶ᆀ✝䘀ࣘ „ 1. ѫ㾱⢩⛩ „ 䘀ࣘঅݳⲴཊ䟽ᙗ ࣘᗞᐳᵇ䘀/ࣘᐳᵇ䘀„ „ о⑙ᓖᴹޣⲴᶮᕋ䗷〻 'x t / 0 t x xe  W ' ' W : relaxation time (1) о䘀ࣘঅݳᴹޣ (2) о⑙ᓖᴹޣ a. ᤷᮠᖒᔿ b. WLF ᯩ〻 (Tg䱴䘁) (3) о㿲ሏᰦⲴᰦ䰤ḷቪᴹޣ / 0 E RT W W e ' 2 ∄ྲ˖ॷ䱽⑙䙏ᓖˈᥟࣘ仁⦷

Time Dependent Behavior -Example: Silly putty

Time Dependent Behavior – Example: Silly Putty 3

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Stress relaxation 在恒定温度和形变保持不变的情况下,高分子材料内部的应 力随时间增加而逐渐衰减的现象 理想固体 g= Ea 交联高聚物 理想液体 线型高聚物 △E 7 7)=Eo exp(-t/T b

Stress relaxation d dt t H H VK K ' ' ൘ᚂᇊ⑙ᓖ઼ᖒਈ؍ᤱнਈⲴᛵߥлˈ儈࠶ᆀᶀᯉ޵䜘Ⲵᓄ ࣋䲿ᰦ䰤໎࣐㘼䙀⑀㺠߿Ⲵ⧠䊑 V ⨶ᜣപփ ⨶ᜣ⏢փ Ӕ㚄儈㚊⢙ 㓯ර儈㚊⢙ t t 0 t H t0 H1 H0     0   0 exp / t Et E t V W H  V H E 5

Creep 指一定温度和较小的恒定外力作用下,材料的形变随时间 的增加而逐渐变化的现象 E 理想液体 d - odt 线型高聚物 7 理想固体 g=EN 交联高聚物 蠕变松弛 蠕变发展 0=D()=D()(-e")()=()

Creep ᤷаᇊ⑙ᓖ઼䖳ሿⲴᚂᇊཆ࣋⭘֌лˈᶀᯉⲴᖒਈ䲿ᰦ䰤 Ⲵ໎࣐㘼䙀⑀ਈॆⲴ⧠䊑 H ⨶ᜣ⏢փ ⨶ᜣപփ V H E 㓯ර儈㚊⢙ Ӕ㚄儈㚊⢙ t0 t V t0 t V        / 0 1 t t Dt D e W H V  f     t / t e W H H  f 6 㹅ਈਁኅ 㹅ਈᶮᕋ

Relaxation Time Originates from Viscoelastic Properties of polymers Elasticity and viscosity > Hooke's law describes the behavior of a linear elastic solid and Newton's law that of a linear viscous liquid Spring as a model: Dashpot as a model: Modulus: E c粘度n Hooke's law:o= Ea Newton's law: o= n(da/dt) : stress(应力);E: strain(应变)

Relaxation Time Originates from Viscoelastic Properties of Polymers ¾ Elasticity and viscosity ¾Hooke’s law describes the behavior of a linear elastic solid and Newton’s law that of a linear viscous liquid: Spring as a model: Modulus: ( ¾ Hooke’s law: V = EH Dashpot as a model: Viscosity (㋈ᓖ): K V : stress (ᓄ࣋ ;(H: strain (ᓄਈ) ¾ Newton’s law: V = K(dHdt) 7

Phenomenological models for linear viscoelasticity Elasticity Viscosity iscoelasticity Es n(de/dt) Model I- Maxwell model Combining the spring and dashpot in series Model ll-Voigt-Kelvin model Combining the spring and dashpot in parallel Model IlI-Burger's Model Combining the Maxwell and Voigt elements in series

Phenomenological models for linear viscoelasticity V = EH V = K(dHdt) + = Viscoelasticity ? Elasticity Viscosity Model I - Maxwell model Combining the spring and dashpot in series Model II -Voigt-Kelvin model Combining the spring and dashpot in parallel Model III – Burger’s Model Combining the Maxwell and Voigt elements in series …. 8

Elasticity t Viscosity Viscoelasticity Model l: maxwell model da E1 d Emat dte dt d nu(de,/dr) E=81+E da 1 do dte dt de E For stress relaxation de/dt=0 At time t=0,0=oo Relaxation time: t=nm/em o(t=Ooexp 松弛模量E(=(

Elasticity + Viscosity = Viscoelasticity ? 1 m m d d dt E dt H VV K  dt d E m m V K V    0 exp m m E V V t t K § ·  ¨ ¸ © ¹   0 exp t V V t W § ·  ¨ ¸ © ¹ For stress relaxation, dH/dt = 0, At time t = 0, V = V0 , Relaxation time: W = Km/Em: Model I: Maxwell Model 2 m d dt H V K 1 1 m d d dt E dt H V 1 2 HH H  VV V 1 2 9 V1 = EmH1 V2 = Km(dH2 dt)     / 0 0 t t E t Ee V W H  ᶮᕋ⁑䟿

Maxwell Model fails to describe Creep de 1 do o For creep,o=oo de 1 door= dt Em dt nm, n the“ creep” behavior of viscous liquids

Maxwell Model fails to describe Creep 10 1 m m d d dt E dt H VV K  For creep, V = V0 , 00 0 1 m mm d d dt E dt H VVV K K  the “creep” behavior of viscous liquids.