1 Chain Structure of Polymer

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1 Polymer Physics 高分子物理 1 hain Structure of Polymer 高分子的链结构

2 Structure and Property of Polymer 高分子结构与性能 1.1 高分子结构的 特点和分类 haracteristic and classification of polymer structure

3 1.1.1 高分子的结构特点 haracteristics of polymer structure Polymer is composed of many structural units, which can be viewed as small molecules and linked by chemical bonds. The molecular weight of polymer is very high and has polydispersity. The main chains of polymer can rotate, leading to flexibility of polymer chains. Due to thermal motion, the shape (conformation) of polymer chains change with time. The van de Waals force among structural units is very important. rosslinking may greatly change properties of polymers. The aggregate state of polymer may be crystalline or amorphous. The order of polymer in crystalline state is smaller than that of crystalline small molecules,but the order in amorphous state is higher than that of amorphous small molecules.

4 1.1.2 高分子的结构层次 classification of polymer structure onfiguration 高分子结构 链结构 hain structure 近程结构 ( 一次结构 ) Short range structure 远程结构 ( 二次结构 ) Long range structure 聚集态结构 ( 三次结构 ) Aggregate structure chemical composition regioisomerism stereoisomerism branching & crosslinking bonding sequence in copolymer size (molecular weight and distribution) onformation (flexibility and rigidity) crystalline state liquid crystalline amorphous state rientation state textural structure 高次结构 textural structure ( 织态结构 )

5 Short range structure ( 近程结构 ) structural unit or local chain segment is involved Long range structure ( 远程结构 ) entire single polymer chain is involved Aggregate structure ( 聚集态结构 ) different polymer chains are involved

6 Polymer structures at different levels are different but correlated. Polymer structure is the sum of structures at different levels, which contribute to apparent polymer properties. Regulation and improvement of polymer properties can be achieved by change of polymer structures at different levels. synthesis:short range structure processing:long range structure and aggregate structure blending:textural structure

7 1.2 高分子链的近程结构 Short-range structure of polymer chain onfiguration ( 构型 ) 近程结构 ( 一次结构 ) Short range structure chemical composition regioisomerism stereoisomerism branching & crosslinking bonding sequence in copolymer

8 1.2.1 结构单元的化学组成 omposition of structural unit Structural unit Main chain H 2 H n Side chain group or substituent l Polymerization degree e.g. Polyvinyl hloride - PV

9 碳链高分子 arbon chain polymer The polymer main chain ( 主链 ) are totally composed of carbon atoms linked by chemical bonds ( most are prepared by addition polymerization) 特点 :Difficult to hydrolyze, good processibility, poor thermal stability, easy to flame and age.

10 聚丙烯 H 3 PP Polypropylene H 2 H n 聚异丁烯 PIB Polyisobutylene H 2 H 3 H 3 n 聚丙烯酸 H Polyacrylic acid H 2 H n 聚甲基丙烯酸甲酯 PMMA H 3 Polymethyl methacrylate H 2 H 3 n

11 聚醋酸乙烯酯 PVAc Polyvinyl acetate H 2 H n H 3 聚乙烯基甲基醚 PVME Polyvinyl methyl ether H 2 n H 3 H 聚丁二烯 PB Polybutadiene H 2 H H H 2 n 聚异戊二烯 PIP Polyisoprene H 2 H H 2 n H 3

12 聚氯乙烯 PV Polyvinyl chloride H 2 H l n 聚偏二氯乙烯 PVD Polyvinylidene chloride H 2 l l n 聚四氟乙烯 PTFE Polytetrafluoroethylene (Teflon) 聚丙烯腈 PAN Polyacrylonitrile F 2 F 2 n H H 2 n N

13 杂链高分子 Heterochain polymer The polymer main chains are composed of carbon atoms and other atoms (for example:, N, S, P et al.) linked by chemical bonds. 特点 : Prepared by condensation or ring-opening polymerization. The main chains has polarity. Advantages:good thermal stability, high strength Disadvantages:easy to hydrolyze and decompose in alcohol or acid. Applications: engineering plastics.

14 聚甲醛 PM Polyformaldehyde 聚氧化乙烯 PE Poly(ethylene oxide) H 2 n H 2 2 n 聚己二酰己二胺 Polyhexamethylene adipamide (Nylon6-6) H N H H 2 6 N H 2 4 n Poly(- 聚己内酰胺 caprolactam) i.e Nylon 6 H 2 5 H N n

15 聚苯醚 PP Polyphenylene oxide, or Polyphenylene ether H 3 H 3 n 聚对苯二甲酸乙二酯 PET Polyethylene terephthalate H 2 H 2 n H 3 聚碳酸酯 P Polycarbonate n H 3

16 聚醚醚酮 PEEK Polyether ether Ketone n 对苯二甲酰对苯二胺 PPTA Kevlar Poly(p-phenyleneterephthalamide) H N H N n 聚酰亚胺 Polyimide N N n

17 H 3 S n 聚砜 H 3 polysulfone R R' n polyester 聚酯 NH R NH R' n polyurethane 聚氨酯

18 元素有机高分子 Elementary organic polymer There is no carbon atom in the polymer main chains, but the side chains contain carbon atom. H 3 Si H 3 n Possessing both thermal stability of inorganic element and elasticity and plasticity of organics, but the strength is low.

19 无机高分子 Inorganic polymer The polymer are composed of non-carbon atoms. S S S S Si Si Si P P S S S S 二硫化硅 silicon disulfide l l P N P N nly partial non-metal elements in Ⅲ A, ⅣA, ⅤA, ⅥA can form inorganic polymers 聚偏磷酸 ( 盐 ) polyphosphoric acid (or polyphosphates) l l 聚二氯一氮化磷 poly(dichloro phosphazene)

20 1.2.2 分子构造 Molecular architecture 单链 Single chain H 2 H Polystyrene

21 梯型聚合物 Ladder chain arbon fiber H H 2 N H H 2 N H H 2 N 聚合 H H 2 N H H 2 N H H 2 N 脱氢 环化 H N H N H N Features of ladder polymers: excellent thermal stability. When single chain in a ladder ring is broken upon heating, the molecular weight of the polymer is unaffected.

22 H 2 N NH 2 + H 2 N NH 2 N N N N n

23 Branching Effects on polymer properties: crystallinity, flexibility, hardness, density, melting temperature, etc. short branches regularity, crystallinity, density, melting temperature long branches dissolving property and rheology in the melt

24 Influence of grafting and crosslinking on the properties of polyethylene Type Properties HDPE LDPE XPE rystallinity, % 95 60~70 Density, g/ml 0.95~ ~ ~1.40 Melting point, Working temperature, ~ ~135 Tensile Strength, MPa 20~40 10~20 10~100 Elongation, % 50~400 50~800 50~600

25 交联 crosslinking rosslinking polymers:undissolvable, unmeltable strength thermal stability Thermoset resin and vulcanized rubber are crosslinking polymer materials.

26 Vulcanization of rubber H 3 H 3 S H H H 2 H 2 H H 2 S S H 3 H H H 2 ure of thermoset plastics A A B BA A A A B BA A A A B BA AB BA A rosslinking of saturated polyolefins: radical attack (for example:irradiation crosslinking)

27 1.2.3 键接异构 Bond order isomer Regioselectivity of structural units in polymerization ( 区域选择性 ) vinyl monomers (H 2 =HR) head-head tail-tail head-tail affecting crystallizability, mechanical properties and thermal stability

28 H 2 H l 头尾 Head-to-tail H 2 H H 2 H H 2 H* l H 2 H 头头 Head-to-head H H 2 l l l l H 2 H H H 2 + Zn Znl 2 86% H 2 H H H 2 Head-tail structure is the majority in polymers of vinyl monomers.

29 H 3 H 3 H 2 H 2 H 3 H 3 H 2 H 2 H H H H H H H H head-to-tail head-to-head H 3 H 3 H 2 H 2 H 3 H 3 H 2 H 2

30 PVA H H H H + H 维尼纶 Head-head and tail-tail structures leading to more hydroxyl left, thus the ability of water absorption increases and strength is reduced.

31 Diene monomers 1,4-addition ( H 2 -H=H-H 2 ) n n H 2 =H-H=H 2 1,2-addition ( H 2 -H ) n H=H 2 2? H 2 H H H 3

32 Determination of regioregularity: NMR, IR, chemical reaction

33 1.2.4 立体异构 Stereoisomerism After polymerization, a chiral ( 手性 ) carbon atom is produced for vinyl monomers, thus there are two optical isomers. 旋光异构 ptical isomerism R H R H H H meso (m) ( 内消旋 ) X H H R * H Y X H H H * Due to co-existence of meso- and racemic isomers, the whole polymer material exhibits no optical activity. R Y H H R R H H R H H H H R racemic (r) ( 外消旋 ) (For single polymer chain, the optical activity is very weak due to the small difference between the two long chain group.)

34 三种类型 Isotactic 全同立构 Polymer chains are composed of single optical isomers. uniform and crystallizable. Syndiotactic 间同立构 Polymer chains are composed of two alternative optical isomers, uniform and crystallizable. Atactic 无规立构 Polymer chains are randomly composed of two optical isomers. non-uniform and non-crystallizable The former two are stereoregular PP, and the last one is stereoirregular PP.

35 Stereoconfiguration affects polymer properties PS: isotactic PS:crystallizable,T m =240,uneasy to dissolve atactic PS:soft temperature 80,soluble in benzene PP: isotactic PP: T m =175,high strength, used as fiber and engineering plastic atactic PP:soft, additive for paving asphalt

36 Is stereoregularity the necessary condition for polymer crystallization? Under most cases it is, but some exceptions: H H H H l l n n H F H H n l F poly(fluoroethylene) poly(vinyl alcohol) poly(trichloro fluoroethylene) similar sizes of F and H strong H bond l is slightly larger than F, But strong repulsion between F atoms.

37 几何 ( 顺反 ) 异构 Geometrical (cis-/trans-) isomerism For 1,4-addition of diene monomers cis-1,4-butadiene, rubber trans-1,4-butadiene, crystalline, plastics H 3 H 3 天然橡胶 Natural rubber H 3 H 3 杜仲胶 Gutta-percha

38 Stereo-isomerism and regio-isomerism may occur simultaneously!

39 1.2.5 共聚物的序列结构 Sequence structure of copolymers copolymerization can improve some specific properties of polymers PMMA exhibits strong intermolecular interaction due to polar ester group, so the flow behavior in the melt is poor and not suitable for injection-molding. MMA+S copolymer: improved flow behavior, suitable for injection molding S+AN copolymer: impact resistance, thermal stability and chemical resistance are improved. (can be used as oilresistant parts)

40 无规共聚物 (random copolymer) Two or more monomer units distribute along the polymer chain randomly ABAABABBAAABABBAAA The interaction among structural units and the intermolecular interaction are altered. The solution properties, crystallizability and mechanical properties of the copolymer are different from the corresponding homopolymers ( 均聚物 ).

41 For example: PE and PP are plastics, but EP random copolymer is rubber. PTFE( 聚四氟乙烯 )is a plastics. Molten processing is impossible, but copolymer of tetrafluoroethylene and hexafluoropropylene is a thermoplastic.

42 嵌段共聚 (block copolymer) AAAAAAAAABBBBBBBBB polya-b-polyb or poly(a-b-b) SBS (styrene-b-butadiene-b-styrene) is prepared by living anionic polymerization, and is a thermoplastic elastomer. Hard Soft Hard

43 SBS:It is melted at 120 and can be processed by injection molding. At room temperature, PS chains at both ends are glassy, but the PB in the middle is rubbery, so it is like crosslinking rubber. However, the crosslinker is glassy PS, and the crosslinking is physical instead of chemical. (thermoplastic elastomer) PS PB

44 接枝共聚 (graft copolymer) B B B B B B B AAAAAAAAAAAAAAAAAAA B B B B B B polya-g-polyb

45 ABS (acrylonitrile-butadiene-styrene) is a ternary copolymer of acrylonitrile, butadiene and styrene. It is prepared by combination of random copolymerization and grafting polymerization. ABS is composed of P(BS) rubber main chain grafted by P(SA) side chain, or P(AB) main chain grafted by PS side chain, or P(SA) main chain grafted by P(AB) side chain. -H 2 -H=H-H 2 - hemical resistance, high tensile strength and hardness Rubber-like elasticity. High impact resistance Good formability

46 交替共聚物 (alternating copolymer) ABABABAB An example: Styrene-maleic anhydride alternating copolymer

47 short range structure configuration structural unit molecular architecture bond order isomerism stereoisomerism sequence of copolymer carbon chain polymer heterochain polymer elementary organic polymer Inorganic polymer single chain ladder chain branching crosslinking vinyl monomer:h-t; H-H; T-T diene monomer:1,2; 1,4; 3,4 vinyl monomer:optical isomerism (isotactic, syndiotactic, atactic) diene monomer:geometric isomer random copolymer block copolymer grafting copolymer alternating copolymer

48 1.3 高分子链的远程结构 Long-range structure of polymer chain

49 Strength 分子量 Molecular Weight Small molecule:definite molecular weight for a specific substance Polymer:distribution of molecular weight (polydispersity) For the details, see hapter 4 nly when MW reaches a certain value (critical MW), polymer materials exhibit useful mechanical strength. polar polymer: DP cri 40 non-polar polymer: DP cri 80 Polar When MW is very high (DP>600~700),strength reaches a limit, but melt viscosity is too high to process. Fiber: narrow MW distribution Nonpolar Molecular Weight Plastics and rubber: broad MW distribution (high MW parts contribute to strength, low MW parts improve processability.)

50 1.3.2 内旋转构象 onformational State Due to rotation of - single bond, polymer chain can change its conformation The number of conformation of a polymer chain is considerable. Polymer chains are usually flexible. TEM of bacteria s DNA The repeating units in the main chain are connected by covalent bonds no independent motion for single unit polymer chains are poor in entropy. 链段 hain segment consisting in many units, which can move independently.

51 Due to presence of H and other substituents, energy barrier must be overcome for rotation of single bond. larger distance smaller repulsion lower energy stability: trans > gauche > cis cis 正丁烷或聚乙烯内旋转位能图 trans gauche t g- g+

52 Flexibility mechanisms Polyethylene molecule: Distance between carbon atoms l=1.54å Angle between neighboring bonds-tetrahedral angle =68 Main source of polymer flexibility is the variation of torsional angles

53 For linear PE chain, the energy level of all-trans conformation is the lowest T=0 K: planar zig-zag conformation T > 0K: gauche conformation appear due to thermal motion

54 If all torsion angles of the whole chain are in the trans state, the chain as the largest possible value of its end-to-end distance R max. ontour length of the chain Rmax nl cos 2

55 For a with 10,000 bonds, The number of arrangements 3 10,000 =10 4,771

56 1.3.3 分子链的柔顺性 hain Flexibility for polyethylene at room temperature is 0.8kT The energy barrier E between trans and gauche states determines the dynamic of conformational rearrangements.

57 Static flexibility ( 静态柔顺性 ) flexibility of polymer chain at thermodynamic equilibrium determined by the difference in the potential energy of trans and gauche conformation () <kt large amount of gauche conformation, and the shape of polymer chain is random coils ( 无规线团 ) kt trans conformation is the majority (the whole polymer chain is flexible, but local is rigid.) >>kt The polymer chain is rigid.

58 Dynamic flexibility ( 动态柔顺性 ) the transition rate between different conformations determined by the energy barrier between different conformations (E) p : time for transition from trans to gauche conformation p exp E 0 kt small p : good dynamic flexibility large p : poor dynamic flexibility E<< kt transition from trans to gauche conformation can be completed in s.

59 Factors affecting flexibility of polymer chain (1) Structure of main chain (2) Substitutes Internal Factors External Factors (3) Branching and cross-linking (4) Length of polymer chain (5) Intermolecular force (6) rystallization (1)Temperature (2)Force (3)Solvent

60 Main chain structure length of single bond isolated double bond flexibility conjugated ( 共轭 )double bond rigidity Si- > -N > - > - 顺丁胶 -H=H-H=H-H=H 聚乙炔聚苯 H bond rigidity NH NH = = 尼龙

61 Side group polarity interaction flexibility PAN < PV < PP number of polar side group Hl Hl < poly(1,2-dichloroethylene) flexibility H 2 Hl PV polarity: 1,1- di-substituents < 1-mono-substituents) H 2 l 2 PVD size of side group PS < PP < PE non-polar 1,1-di-substituent flexibility > flexibility poly(iso-butene) (PIB)> PE H 2 Hl PV distance of polymer chains

62 hain length length of main chain number of conformation flexibility length of side chain interaction flexibility But when the side chain is too long, it hinders rotation of the main chain and flexibility decreases. H 3 H 2 n: 0<1<2< <18 >19>20> (H 2 ) n H 3

63 1.4 高分子链的构象统计 onformational statistics of polymer chain

64 1.4.1 自由连接链 Freely Jointed hain The polymer chain consists in n equal one-dimensional links of length l ( with no occupied volume). There is no restriction on the angles between the links. No energy is required to change the angles. The probability of each bond at any direction is equal and the contour or fully extended length of the chain is nl. Freely jointed chain is just used for theoretical calculation, and it does not correspond to any real polymer chain.

65 ther two terms: random walk ( 无规行走 ) one-dimensional freely jointed chain random flight ( 无规飞行 ) three-dimensional freely jointed chain

66 Simulation of freely jointed chain N = 10 4 The trace is like that of Brownian particles. The volume fraction of the units is very small. There are lot of holes inside the random coil.

67 End-to-end distance ( 末端距 ) r l l l... l l f, j r f, j n i1 l i 0 n n i1 i

68 Mean-square of end-to-end distance ( 均方末端距 ) n n 2 f, j i j n n i1 j1 r l l ( l l l... l )( l l l... l ) l l i i l 2 Total n 0 terms l i l j ij r 2 nl 2 f, j f, j f, j r nl r r n l extended chain The conformation of freely jointed chain is far from that of extended chain!

69 rigin of rubber elasticity

70 Radius of gyration The square radius of gyration is defined as the average square distance between monomers in a given conformation (position vector R i ) and the polymer s centre of mass (position vector R 0 )

71 Radius of gyration ( 旋转半径 ) mass of unit: m i coordinate of ith unit: coordinate of center of mass r 0 r i 1 n ri n i 质心 r 0 r i i 2 R g 2 g 1 n n i 1 2 R r r i 0 freely jointed chain R ( n 1)( n 1) l / 6n 2 2 g 1 n 时 also applicable to freely Rg nl /6 rf, j 6 rotating chain and Gaussian chain Radius of gyration is suitable for polymer chains with multiple chain ends.

72 1.4.2 自由旋转链 Freely Rotating hain Model with fixed valency angle The angle are restricted to lie on a cone, but the bond can rotate freely on the surface of the cone.

73 Mean-square of end-to-end distance n n 2 f, r i j n n i1 j1 r l l ( l l l... l )( l l l... l ) l l i i l 2 Total n terms 2 2 l l cos(180 ) cos ii1 l l Total 2(n-1) terms 2 m 2 l l l cos (180 ) l cos i im m Total 2(n-m) terms

74 2 f, r r =l 2 {n+2[(cos+cos 2 +cos 3 + +cos n-1 ) (cos + cos 2 + +cos n-2 ) (cos + + cos n-3 ) +.. n 2 2 1cos 1cos rf, rl { n( ) 2cos } 2 1cos (1 cos ) n r nl 2 2 f, r 1 cos 1 cos + cos ]} 四面体构型 cos = 1/ f, r f, j r l n r

75 1.4.3 受阻内旋转链 Hindered Rotation hain For a real polymer chain, the rotation of the bonds on the cones is not free. Energy barrier must be overcome for rotation of the bonds. The energy barrier for rotation is not a constant, but it varies with rotation angle. r 2 nl 2 rr, 1cos1 cos 1cos1 cos Bond angle 键角 onformation angle 构象角

76 cos cos exp U / kt d exp U / kt d i i For PE,trans: =0, U(t)=0; gauche (g or g') =±120, U(g or g')=3.34kj mol -1, 298K o N(0 ) exp(0) 1 N J mol 8.31J K mol 298K 1 o o (120 ) N( 120 ) exp( ) o o o 1cos(0 ) [cos(120 ) cos( 120 )] cos

77 1.4.4 高斯链 Gaussian hain Equivalent chain: (1) The polymer chain comprises N hypothetical segments. (2) Each segment has a length of l and is rigid. (3) Segments are freely jointed and there is no restriction on angles. The distribution of equivalent chain obeys Gaussian distribution. Gaussian chain

78 *The same contour length: L=N e l e =nlcos(/2)) *The same <R 2 >: <R 2 >=N e l e 2 l e =<R 2 >/L

79 For PE freely jointed chain freely rotating chain under condition extended chain <R 2 > Nl 2 2Nl Nl 2 2/3 N 2 l 2 Kuhn length l (bond length) 2.45l 8.28 l 0.82Nl For freely rotating chain: contour length: N e l e =Nlcos[(180-)/2]=Nlsin(/2) <R 2 >=N e l e2 =2Nl 2 l e =2Nl 2 /Nlsin(/2)=2.45l (Note: nly for freely jointed chain the contour length is Nl. For other chains, the contour length is Nlsin(/2).

80 Equivalent freely jointed chain obey Gaussian distribution; the motion unit is a segment; correspond to real polymer chain Free jointed chain obey Gaussian distribution; the motion unit is a single bond; only used for theoretical study

81 End-to-end distance of Gaussian chain from statistical method Probability distribution function of end-to-end distance for freely jointed chain in one-dimensional space W(x) Start from zero point (one end of the chain) Each step l (bond length), n steps of random walk (number of bonds) Where is the last step (the other end of the chain) located?

82 The probability distribution function for other end W(x) is:

83 Probability distribution function in three dimension 三维空间几率分布函数 W(xyz) ne end is fixed at x=0, y=0, z=0 P is the probability of the other end located in the space dxdydz Z Y dxdydz X

84 Probability P W ( xyz) dxdydz W ( x) dxw ( y) dyw ( z) dz x y e dx e dy e z dz e ( x y z ) dxdydz 3 e 2 2 ( ) R dxdydz

85 The probability distribution function in three-dimensional space W(xyz): 3 3 W ( xyz) e e ( x y z ) R

86 Usually only the distance of the ends is cared, and the direction of the ends is ignored. radiant distribution function W(R) R dr Meaning of W(R): When one end of the chain is fixed at the zero point, W(R) is the probability density for the other end appearing in the spherical shell from radius R to R+dR. W( R) W( xyz)4 R 均方末端距 R R W( xyz)4 R dr 0 2 R Nl 2 2

87 R

88 Three types of end-to-end distance The most probable end-to-end distance R* W( R) R 0 R Mean end-to-end distance 2n l 3 R 40 Å For PE, n=1000, l=1.54å 8n R RW ( R) dr l 3 0 Mean square root end-to-end distance R 45 Å ( ) 2 0 R R W R dr nl R 49 Å

89 1.4.5 柔顺性的表征 haracterization of Flexibility 1) characteristic ratio ( 特征比 ) r r f, j Undisturbed mean square end-to-end distance under condition 2) 空间位阻参数 ( 刚性因子 ) flexibility 2 r r r f, r flexibility 3) undisturbed dimension A ( 无扰尺寸 ) r 2 / M 1/ 2 0 A A flexibility

90 4) Kuhn 链节长度 Kuhn Segment Length 2 L 高分子链围线尺寸 le r0 L ontour length of the chain Kuhn segment length l e is usually larger than contour length of a single bonds l 0. l e /l 0 can be used to characterize flexibility of polymer chain. l e /l 0 flexibility

91 1.4.6 蠕虫状链 Wormlike hain ~ 持续长度 l Proposed by Porod and Kratky to describe rigid polymer chains. N bonds of length b; free rotation; bond angle: (180-) Average of projection of polymer chain in the first bond cos <1 ~ l z b bcos bcos z b When N, cos N 0 lim N z Persistence Length b 1 cos N 1 cos 1 cos 2 bcos N 1 ~ 持续长度 l: Average of projection in the first bond of polymer chain with infinite length. ~ l R

92 ~ l lim N z 1 cos b 1 cos ~ b / l When 0, cos 1 z b ln(cos ) cos 1 ~ N cos 1 cos l (1 cos 1cos exp{ b N ) ~ l / ~ l } (1 exp{ Nb / ~ l })

93 Mean square end-to-end distance Flexible chain Rigid chain ~ ~ l 2 Nb R 2l Nb 1 1 exp ~ Nb l R ~ l 2 ~ ~ Nb >> l exp{-nb/l} 0 2 R 2 ~ l Nb Half of the bond length in freely jointed chain ~ Nb << l ~ ~ 2 2 Nb / l ( Nb / l) ( Nb) (1 ) ( Nb 3 12 ) 2

94 持续长度 ( 自由旋转链 ) s=kb 为两个结构单元间的围线长度 ~ R << l 高分子链为刚形 ~ R >> l 高分子链为半刚形 (DNA).

95 Advantage of l k : it can be directly experimentally measured. Advantage of l : it has a direct microscopic meaning.

96 1.4.7 真实链 : 排斥体积 excluded volume In real polymer chain, the repeating units have occupied volume and they can not interpenetrate. (Rotation of single bond is further restricted, leading to increase of R g.

97 自规避行走 (Self-avoiding walks) ne-dimensional: Two-dimensional: <R 2 >=N 0.75 l

98 Three dimensional: <R 2 > 0.5 =N 0.6 l In general: <R 2 > 0.5 SAW=constant*N where =3/(d+2) d is the dimension of space

99 Excluded volume onsider the energy cost U(r) of bringing two monomers from to within distance r of each other in a solvent Athermal solvent: monomers are chemically identical to the solvent and there is no energy difference between their interactions. Effective interaction potential between two monomers in a solution of other molecules The hare-core potential prevents monomers from overlapping

100 Excluded volume The probability of finding two monomers separated by a distance r in a solvent at temperature T is proportional to the Boltzmann factor exp[-u(r)/(kt)] Boltzmann factor is equal to one at large distances if there are no long-range interactions The Mayer f-function: f r exp U r / kt 1

101 Excluded volume f r exp U r / kt 1 The Mayer f-function: The excluded volume: v 1 exp / 3 3 f r d r U r kt d r A net attraction v<0, A net repulsion v>0. The Mayer f-function and its integration (shaded regions) to determine excluded volume

102 Excluded volume v 1 exp / 3 3 f r d r U r kt d r only valid for spherical monomers. Particularly because of the monomer being defined as a Kuhn monomer, the monomer is better described as a cylinder of length equal to the Kuhn length b, but smaller diameter d. Excluded volume describes the two-body (pairwise) monomer-monomer interaction in solution.

103 本章重点 : 1. 不同层次的结构内容 2. 键接异构, 立体异构, 几何异构 3. 分子链柔顺性与结构的关系 4. 自由连接链, 自由旋转链和内旋转受阻链 5. 高斯链,Kuhn 长度, 持续长度 6. 真实链与排斥体积

104 近程 (shot range) 远程 (long range) 研究对象大分子的一个链节整个大分子链 研究范围 10-4 m 10-2 m 研究手段 涉及的重要概念 区别 它的改变影响什么性能 IR NMR MS 等微观结构的研究手段 构型 : 结构单元在空间的排布与化学键有关 与化学键的破坏有关, 与时间无关 物理性能 : 强度 结晶性 弹性化学性能 : 热稳定性 化学反应及裂解反应的方式和产物 溶液法 热力学 统计学等宏观研究方法 单键相连的原子内旋转造成的分子内各原子的空间排布 与原子的内旋转有关, 与时间无关, 而与外部环境有关 影响大分子的柔顺性影响聚合物的高弹性

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