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高分子科学·聚合物
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高分子科学·聚合物
12
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聚合度 DP = Mn / M0
Degree of polymerization DP = Mn / M0
DP=Mn/M0 · 每链重复单元数 · PE Mn28k→DP1000
From number-average and repeat-unit molar mass to chain length
分子量分布 · Mn、Mw 与 PDI
Molecular-weight distribution · Mn, Mw, PDI
Mn/Mw · PDI=Mw/Mn≥1 · 分布曲线 · 单分散PDI=1
Number- and weight-average molar mass, and the polydispersity index PDI = Mw / Mn
无规线团 · 端到端距离与回转半径
Random coil · end-to-end distance and radius of gyration
无规线团 · 末端距l√N · Rg=l√(N/6) · R0/Rg=√6
Ideal (freely-jointed) chain: √⟨r²⟩ = l√N, Rg = l√(N/6)
逐步聚合 · Carothers 方程
Step-growth polymerization — Carothers equation
Carothers DP=1/(1−p) · p=0.99→DP100 · 需高转化率
How the degree of polymerization DP depends on extent of reaction p and stoichiometric ratio r
自由基链式聚合 · 稳态动力学
Free-radical chain polymerization — steady-state kinetics
Rp=kp[M](fkd[I]/kt)^½ · Rp∝[I]^½ · 动力学链长ν
How the polymerization rate Rp and kinetic chain length ν depend on [M] and [I]
共聚物组成 · Mayo–Lewis 方程
Copolymer composition — Mayo–Lewis equation
Mayo-Lewis · 竞聚率r1/r2 · 恒比点 · 组成漂移
Instantaneous copolymer composition F1 from feed f1 and reactivity ratios r1, r2
Flory–Huggins 聚合物溶液理论
Flory–Huggins theory of polymer solutions
ΔGmix/RT=φ1lnφ1+(φ2/n)lnφ2+χφ1φ2 · χc=½(1+1/√n)²
Free energy of mixing, the χ parameter and critical demixing: why long chains barely dissolve
Mark–Houwink 方程与黏均分子量
Mark–Houwink equation and viscosity-average molar mass
[η]=K·Mᵃ · a反映构象(0.5θ/0.8良溶剂/1棒) · Mv
Intrinsic viscosity [η] = K·Mᵃ: the exponent a reveals chain conformation, and solving back for Mv
玻璃化转变与 WLF 方程(时温等效)
Glass transition & the WLF equation (time–temperature superposition)
WLF log aT=−17.44(T−Tg)/(51.6+T−Tg) · 时温等效 · 自由体积
Shift factor log aT = −C₁(T−Tg)/(C₂+(T−Tg)): collapsing curves at different temperatures onto one master curve
橡胶弹性(熵弹性)
Rubber elasticity (entropic elasticity)
熵弹性σ=G(λ−1/λ²) · G=nkT · 应力随温升
Nominal stress σ = G(λ − 1/λ²) of a crosslinked network; the modulus G = nkT rises with temperature
结晶度(密度法)
Degree of crystallinity (density method)
Xc=ρc(ρ−ρa)/[ρ(ρc−ρa)] · HDPE ρ0.96→75% · 半结晶
Crystallinity of a semicrystalline polymer from measured density: Xc = ρc(ρ − ρa) / [ρ(ρc − ρa)]
立构规整度(等规 / 间规 / 无规)
Tacticity (isotactic / syndiotactic / atactic)
等规/间规/无规 · 控结晶度Tm力学 · iPP晶aPP胶
How stereochemical arrangement of substituents sets crystallinity, melting point and properties