第8讲 高分子晶态取向液晶态R
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Tm = 414.2(1-0.627/l)
g f T
0 m
0 h f Tm s f 0
s f
h f
0 Tm
Lauritzen-Hoffman equation
0 2 eTm l 0 h Tm Tm
g f Tm h f Tm s f
0 Tm Tm h f 0 Tm
Basic Morphology of Polymer Crystals
“Single crystals”单晶 have one lattice “Polycrystalline samples” 多晶 are aggregates of many single crystals
Crystal Habits: a: lamellar (片晶) b: platy c: tabular d: isometric e: prismatic f: acicular g: needle-like h: fibrous (纤维晶)
K gI K g II
4b0 eTm h f 2b0 eTm h f
K g I K g III 2 K g II
高分子总结晶速率
Overall Polymer Crystallization Rate Definition of crystallinity (结晶度)
Random coils (无规线团)
折叠链模型 Models
？
高分子折叠链结晶过程 Chain-Folded Lamellae of Polymers
Chain folding (链折叠) concept
Fold surface (折叠表面)
e
TC or T Crystallization
wc Wc/Wtotal; vc Vc/Vtotal wc: weight fraction; vc: volume fraction W: weights : density (g/cm3) : specific volume (cm3/g)＝1/
Isothermal crystallization Crystallinity T1 T2 T3
Under Polarized optical microscopy )
Banded spherulites (环带球晶)
片晶扭曲周期
球晶中的片晶 Lamellae in a spherulite
树枝晶 1. 片晶 Lamellae 2. 连接分子 Tie Molecules 3. 无定形区 Amorphous
l
Random coil
Lateral surface (侧表面)
Lamellar thickness
Folded chain (折叠链)
or fold length (片晶 厚度)
TC: crystallization temperature (结晶温度) T: supercooling (过冷度), T = Tm0 - TC e: fold surface free energy (折叠表面自由能) : lateral surface free energy (侧表面自由能), e 10
结晶的分子机理 Crystallization
How do the polymer chains pack in the lamellar crystals?
Crystallization
Random coil with the chain contour length (轮廓长度) longer than 1 m
Chain-folded Lamellae
Process of Polymer Crystallization
Two steps: Nucleation & Linear Growth
(1) Nucleation (成核) process
临界核生成前后自由能随核尺寸 的变化示意
诱导期
稳定期
Homogeneous (均相成核) and heterogeneous nucleation(异相成核)
G a 2 lg f 4al 2a 2 e
自由能与表面能竞争
l a a
临界状态：
g f Tm h f Tm s f 0
s f
h f Tm
g f
a* 4
g f
g f Tc h f Tc s f h f
For secondary nucleus
球晶的小角激光光散射
Hv
qmax~1/R
Vv
Positive spherulites
2
negative spherulites
1 q cos I Hv AV0 3 sin
3 2
3 I Vv AV02 3 t s 2sin q q cos q Siq r s Siq sin q q
t
（2）球晶的交叠 Dilatometric (膨胀计法) vt 1/ t ht
h0 ht
ht h h h 1 0 t 1 vc va h0 h h0 h
v0 v
e
n
vt v ln ln v v 0
晶核形成的三个区域 I, II, and III
C G n
* QD
* QD exp RT
K g exp k T T B I , II , III
蠕动活化能 Regime 的成核常数
K g
第八讲
高分子有序态 结晶、取向和液晶
内容提要
长链分子的结晶 折叠链结晶的表现与原因 结晶过程 多尺度取向 取向结晶 应用例子：聚丙烯纺丝与成膜过程 • 液晶形态 • 液晶流动 • • • • •
Chain Crystallization
Requisites for polymer crystallization 原子有序
Overall crystallization rate (总结晶速率)
Overall rate
‘Bell’ curve IV III II I
of overall crystallization rate
Tm0
32
t1/2
Time Tg TMAX
总体结晶动力学
•
Overall Crystallization Kinetics Avrami equation （1）自由生长模型 v v kt
Intercrystalline links in spherulites
连接分子所占比例对聚合物性能很重要！
片晶生长
Growth of spherulites
poly(bisphenol A octane ether) BA -C8
均相成核 homogenously nucleated
异相成核 heterogeneously nucleated
G G a l 0 0
T Tm
l*
4 e 4 eTm g f h f T
4 Tm a* h f T
G abl g f 2bl 2ab e
l*
2 e 2 eTm g f h f T
a*
2 Tm 2 g f h f T
b
分子动力学模拟
Yamamoto, T., Adv in Polym Sci, 191, 37(2005)
50K
300K
温度影响结晶
成核过程的分子理论
Molecular model - Lauritzen-Hoffman (LH) Theory
(1)成核位垒的变化
假定： (1)无序相是无规线团 (2)链的扩散是管式的 (3)解缠结比较快
大分子结晶常常是层状或者纤维状
Lamellae Crystallized from Dilute Solution
Keller, 1957
Polyethylene (聚乙烯)
Tc ~ 70 C Tc ~ 80 C
Polyoxymethylene (聚甲醛)
PEO(聚氧乙烯)-b-PS(聚苯乙烯) diblock copolymer
isotactic Hydrogen bonding syndiotactic
Zig-zag Conformations
H21
聚丙烯为什么形成螺旋结构？
0.12 nm
PE
H
H
0.25 nm PP CH3: 0.2 nm
Chain packing in crystal lattices
LH RH LH
单晶片晶结构
PE链垂直于片晶表面 注: 片晶的厚度 ~10 nm, 高分子链长 > 1000 nm. PE 链必须在片晶中来回的 折叠
尾端
Melting and Stretching of lamellae
连接分子
从熔体中结晶 Spherulites (球晶) of polymers 偏光显微镜
Classic Nucleation Theory –
临界核的尺寸 critical nucleus size
For primary nucleus
G G a l 2al g f 4l 4a e 0 a 2 g f 4a 0
l* 4 e
Chemical regularity Homopolymer Copolymer block copolymer random copolymer Stereoregularity (立构规整度) Isotactic (等规) Syndiotactic (间规) Atactic (无规)
Lamella with the thickness of 550 nm and lateral size of microns.
Macroconformations (巨构象):
Fringed Fringed micelle (缨状微束) Extended chains (伸展链)
Folded chains (折叠链)
RH LH RH
LH RH LH
密堆砌，低能量
Chain packing in crystal lattices
PE
斜方晶 orthorhombic
Nylon 66 三斜晶 triclinic
Hydrogen bonding
i-Poly-1-butene
三角晶 Trigonal 单斜晶 Monoclinic
G 0
2 e 0 1 Tm Tm l h
线性聚乙烯 的熔点变化：从熔体和溶液
Similar to critical nucleus size
lineargrowth?1nucleation成核process临界核生成前后自由能随核尺寸的变化示意homogeneous均相成核andheterogeneousnucleation异相成核诱导期稳定期classicnucleationtheory临界核的尺寸criticalnucleussizeg?forprimarynucleus4??4??eemtfflght???efaalgla??2224????????0fmfm?fgthts????forsecondarynucleusga??gl??2??2??eemtfflght???2440fegalg?l?a?a????????240fgaga?l????????fga???4fegl???422fegablgblab????????2??2??mfftaght???4?mftaht???0??0????tfcfcfghts?????ffmhst???fmtht???aal自由能与表面能竞争b临界状态
1/2
ht’ h
k
ln 2 n t1/ 2
t1/2
t
lnt
熔化过程 Melting of Lamellar Crystals
热力学分析
片晶的熔点 Melting point of l
Gibbs-Thomson extrapolation
T
0 m
Tm
G a 2l g f 2a 2 e 4al
Chain Conformations in Crystals
Helix Conformations
21 31 32 31 41 52 72 91 61 73 92
42= 21 51 62= 31 71 重复一周的主链原子数
H31
repeating unit
达到重复的周数
81
83
CHCH 3 CH 2 CHCH 3
Microscopic model - Lauritzen-Hoffman (LH) Theory
(2) Linear growth rate G
过冷度增加
Regime III: 真实加工过程的淬冷 很短的侧向铺展，不超过几个链段, 存在多种形式的链折叠 Hoffman, J. D., Polymer, 38(13), 3151(1997)
g f T
0 m
0 h f Tm s f 0
s f
h f
0 Tm
Lauritzen-Hoffman equation
0 2 eTm l 0 h Tm Tm
g f Tm h f Tm s f
0 Tm Tm h f 0 Tm
Basic Morphology of Polymer Crystals
“Single crystals”单晶 have one lattice “Polycrystalline samples” 多晶 are aggregates of many single crystals
Crystal Habits: a: lamellar (片晶) b: platy c: tabular d: isometric e: prismatic f: acicular g: needle-like h: fibrous (纤维晶)
K gI K g II
4b0 eTm h f 2b0 eTm h f
K g I K g III 2 K g II
高分子总结晶速率
Overall Polymer Crystallization Rate Definition of crystallinity (结晶度)
Random coils (无规线团)
折叠链模型 Models
？
高分子折叠链结晶过程 Chain-Folded Lamellae of Polymers
Chain folding (链折叠) concept
Fold surface (折叠表面)
e
TC or T Crystallization
wc Wc/Wtotal; vc Vc/Vtotal wc: weight fraction; vc: volume fraction W: weights : density (g/cm3) : specific volume (cm3/g)＝1/
Isothermal crystallization Crystallinity T1 T2 T3
Under Polarized optical microscopy )
Banded spherulites (环带球晶)
片晶扭曲周期
球晶中的片晶 Lamellae in a spherulite
树枝晶 1. 片晶 Lamellae 2. 连接分子 Tie Molecules 3. 无定形区 Amorphous
l
Random coil
Lateral surface (侧表面)
Lamellar thickness
Folded chain (折叠链)
or fold length (片晶 厚度)
TC: crystallization temperature (结晶温度) T: supercooling (过冷度), T = Tm0 - TC e: fold surface free energy (折叠表面自由能) : lateral surface free energy (侧表面自由能), e 10
结晶的分子机理 Crystallization
How do the polymer chains pack in the lamellar crystals?
Crystallization
Random coil with the chain contour length (轮廓长度) longer than 1 m
Chain-folded Lamellae
Process of Polymer Crystallization
Two steps: Nucleation & Linear Growth
(1) Nucleation (成核) process
临界核生成前后自由能随核尺寸 的变化示意
诱导期
稳定期
Homogeneous (均相成核) and heterogeneous nucleation(异相成核)
G a 2 lg f 4al 2a 2 e
自由能与表面能竞争
l a a
临界状态：
g f Tm h f Tm s f 0
s f
h f Tm
g f
a* 4
g f
g f Tc h f Tc s f h f
For secondary nucleus
球晶的小角激光光散射
Hv
qmax~1/R
Vv
Positive spherulites
2
negative spherulites
1 q cos I Hv AV0 3 sin
3 2
3 I Vv AV02 3 t s 2sin q q cos q Siq r s Siq sin q q
t
（2）球晶的交叠 Dilatometric (膨胀计法) vt 1/ t ht
h0 ht
ht h h h 1 0 t 1 vc va h0 h h0 h
v0 v
e
n
vt v ln ln v v 0
晶核形成的三个区域 I, II, and III
C G n
* QD
* QD exp RT
K g exp k T T B I , II , III
蠕动活化能 Regime 的成核常数
K g
第八讲
高分子有序态 结晶、取向和液晶
内容提要
长链分子的结晶 折叠链结晶的表现与原因 结晶过程 多尺度取向 取向结晶 应用例子：聚丙烯纺丝与成膜过程 • 液晶形态 • 液晶流动 • • • • •
Chain Crystallization
Requisites for polymer crystallization 原子有序
Overall crystallization rate (总结晶速率)
Overall rate
‘Bell’ curve IV III II I
of overall crystallization rate
Tm0
32
t1/2
Time Tg TMAX
总体结晶动力学
•
Overall Crystallization Kinetics Avrami equation （1）自由生长模型 v v kt
Intercrystalline links in spherulites
连接分子所占比例对聚合物性能很重要！
片晶生长
Growth of spherulites
poly(bisphenol A octane ether) BA -C8
均相成核 homogenously nucleated
异相成核 heterogeneously nucleated
G G a l 0 0
T Tm
l*
4 e 4 eTm g f h f T
4 Tm a* h f T
G abl g f 2bl 2ab e
l*
2 e 2 eTm g f h f T
a*
2 Tm 2 g f h f T
b
分子动力学模拟
Yamamoto, T., Adv in Polym Sci, 191, 37(2005)
50K
300K
温度影响结晶
成核过程的分子理论
Molecular model - Lauritzen-Hoffman (LH) Theory
(1)成核位垒的变化
假定： (1)无序相是无规线团 (2)链的扩散是管式的 (3)解缠结比较快
大分子结晶常常是层状或者纤维状
Lamellae Crystallized from Dilute Solution
Keller, 1957
Polyethylene (聚乙烯)
Tc ~ 70 C Tc ~ 80 C
Polyoxymethylene (聚甲醛)
PEO(聚氧乙烯)-b-PS(聚苯乙烯) diblock copolymer
isotactic Hydrogen bonding syndiotactic
Zig-zag Conformations
H21
聚丙烯为什么形成螺旋结构？
0.12 nm
PE
H
H
0.25 nm PP CH3: 0.2 nm
Chain packing in crystal lattices
LH RH LH
单晶片晶结构
PE链垂直于片晶表面 注: 片晶的厚度 ~10 nm, 高分子链长 > 1000 nm. PE 链必须在片晶中来回的 折叠
尾端
Melting and Stretching of lamellae
连接分子
从熔体中结晶 Spherulites (球晶) of polymers 偏光显微镜
Classic Nucleation Theory –
临界核的尺寸 critical nucleus size
For primary nucleus
G G a l 2al g f 4l 4a e 0 a 2 g f 4a 0
l* 4 e
Chemical regularity Homopolymer Copolymer block copolymer random copolymer Stereoregularity (立构规整度) Isotactic (等规) Syndiotactic (间规) Atactic (无规)
Lamella with the thickness of 550 nm and lateral size of microns.
Macroconformations (巨构象):
Fringed Fringed micelle (缨状微束) Extended chains (伸展链)
Folded chains (折叠链)
RH LH RH
LH RH LH
密堆砌，低能量
Chain packing in crystal lattices
PE
斜方晶 orthorhombic
Nylon 66 三斜晶 triclinic
Hydrogen bonding
i-Poly-1-butene
三角晶 Trigonal 单斜晶 Monoclinic
G 0
2 e 0 1 Tm Tm l h
线性聚乙烯 的熔点变化：从熔体和溶液
Similar to critical nucleus size
lineargrowth?1nucleation成核process临界核生成前后自由能随核尺寸的变化示意homogeneous均相成核andheterogeneousnucleation异相成核诱导期稳定期classicnucleationtheory临界核的尺寸criticalnucleussizeg?forprimarynucleus4??4??eemtfflght???efaalgla??2224????????0fmfm?fgthts????forsecondarynucleusga??gl??2??2??eemtfflght???2440fegalg?l?a?a????????240fgaga?l????????fga???4fegl???422fegablgblab????????2??2??mfftaght???4?mftaht???0??0????tfcfcfghts?????ffmhst???fmtht???aal自由能与表面能竞争b临界状态
1/2
ht’ h
k
ln 2 n t1/ 2
t1/2
t
lnt
熔化过程 Melting of Lamellar Crystals
热力学分析
片晶的熔点 Melting point of l
Gibbs-Thomson extrapolation
T
0 m
Tm
G a 2l g f 2a 2 e 4al
Chain Conformations in Crystals
Helix Conformations
21 31 32 31 41 52 72 91 61 73 92
42= 21 51 62= 31 71 重复一周的主链原子数
H31
repeating unit
达到重复的周数
81
83
CHCH 3 CH 2 CHCH 3
Microscopic model - Lauritzen-Hoffman (LH) Theory
(2) Linear growth rate G
过冷度增加
Regime III: 真实加工过程的淬冷 很短的侧向铺展，不超过几个链段, 存在多种形式的链折叠 Hoffman, J. D., Polymer, 38(13), 3151(1997)