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1、第三章 高分子溶液,3.1 高分子的溶解性判据,3.5 高分子凝胶的热力学,3.3 稀溶液的热力学性质和高分子构象,3.4 亚浓溶液的热力学性质和高分构象,3.2 高分子溶液的热力学-Flory-Huggins理论,3.6 聚电解质溶液,3.9 高分子溶液的流体力学性质,3.7 高分子共混物的热力学,3.8 嵌段共聚物的热力学初步,Chapt. 3 Polymer Solutions,The solution process,This process is usually slower compared with small molecules, and strongly dependent
2、on the chemical structures and condensed states of the samples. Crosslinked polymer: only can be swelled. Crystalline PE: dissolve at the temperature approached to its melting temperature. Crystalline Nylon 6,6: dissolved at room temperature by using the solvent with strong hydrogen bonds.,3.1 Crite
3、ria (判据) of Polymer Solubility,Solubility occurs only when the DGmix is negative.,Gibbs free energy of mixing,(DE/v) cohesive energy density (内聚能密度),d=(DE/v)1/2 : solubility parameter (溶度参数),1. Hildebrand enthalpy of mixing (混合焓),1: solvent; 2: polymer,P12,3.2 Thermodynamics of Polymer Solutions,(1)
4、 Entropy of mixing for ideal solution,(2) Entropy of mixing for polymer solutions,The lattice model assumes that the volume is unchanged during mixing. Each repeating unit of the polymer (segment) occupies one position in the lattice and so does each solvent molecule. The mixing entropy is strongly
5、influenced by the chain connectivity of the polymer component.,Flory-Huggins theory (Lattice Model (格子模型),体系中有N1个溶剂分子 + N2个链段数为x的高分子,总格子数: N=N1+xN2,已有j个高分子放入, 剩下N-xj个空格, 求第j+1个高分子的放置方式Wj+1 ?,1. 放置第j+1个高分子的第1个链段的概率,N-xj,2. 放置第j+1个高分子的第2个链段的概率,Z(N-xj-1)/N,3. 放置第j+1个高分子的第3个链段的概率,(Z-1)(N-xj-2)/N,.,(Z-1)
6、(N-xj-x+1)/N,x. 放置第x个链段的概率,Entropy of mixing from FH theory,Z Z 1,Entropy of solution:,总方式,Entropy of mixing from FH theory,Using Stirlings approximation (lnx! xlnx x), we have:,Entropy of the pure solvent and pure polymer:,(N1 = 0) and,Therefore,Free Energy of FH Theory,Huggins Enthalpy:,Gibbs Free
7、 Energy:,摩尔数,分子数,一般通式,For Polymer Solutions x1=1,Chemical potentials (化学位):,In the case of f2 1,c=1/2, 有热效应的“理想溶液”?,Osmotic pressure (渗透压):,当f21/x, 即f22 f2 /x,当f21/x(0.5-c)或c=1/2,second Virial coefficent,Appendix: Osmotic pressure,Polymer Shapes in Dilute Solutions,concentration,P /RTc,A2 1/2; poor
8、solvent,A2 0, 1/2; good solvent,A2 = 0, = 1/2; Q condition,Coil-globule transition,Expanded, unperturbed, and collapsed chains,The coil-globule transition in a solution of polystyrene in cyclohexane. The radius of gyration Rg and the hydrodynamic radius Rh of the polymer show a dramatic change as te
9、mperature passes through the Q temperature. (Sun, S.T.; etc. J. Chem. Phys. 1980, 73, 5971.),c1/kT !,3.3 Chain Conformations in Dilute Solutions,ideal chain,real chain in solutions,(1) P(h),一个链段占有的体积分数vc/h3,其他链段不与之发生重叠的概率(1-vc/h3),整条链两两链段都不发生重叠的总概率,体积排除修正,能量权重修正,溶液中真实单链的末端距概率分布函数W(h,x),当c=1/2, 理想高斯链
10、,1. Polymer chain in good solvents method I,W0(h,x)的极值h0*=(2xl2/3)1/2,c1/2, n=3/5,c=1/2, n=1/2,c1/2, n=?,2. Polymer chain in good solvents - method II,Two body interaction is very important,c1/2,hx3/5,two body interaction: excluded volume repulsion solvent-segment interaction,second Virial coefficen
11、t,conformation entropy,+,How to get ideal chain?,c=1/2,h2N1,Q Temperature,Q Solution,When does the freely jointed chain works等效自由连接链,(1) 调节溶剂-链节的作用屏蔽掉体积排除效应和链节-链节相互作用 达到Q温度的溶液, 测得无扰尺寸0N,溶剂排斥作用,3. Polymer chain in poor solvents-Method I,hh0,f2=xvc/h3,Three body interactions becomes important,c1/2,3.
12、Polymer chain in poor solvents-Method II,T,f2,f,f”,In Polymer rich Phase:,Concentration in Coil:,Polymer Shapes in Dilute Solutions,(1) Polymer in a good solvent N6/5 (2) Polymer in a Q solvent N1 (3) Polymer in a poor solvent N2/3,c1/kT !,Coil-globule transition,c,T,3.4 Semi-dilute Solutions of Pol
13、ymers,independent on M,pc9/4,Osmotic pressure measured for samples of poly(-methylstyrene) dissolved in toluene (25 C). Molecular weight vary between M = 7 104 (uppermost curve) and M = 7.47 106 (lowest curve). (Noda,I.; et al. Macromolecules 1981, 14, 668.),P/cc1,P/cc5/4,f21,f22 f2 /x,P/cc0,overlap
14、 concentration c*,Apparent correlation length (表观相关长度) apple,Semi-dilute regime: c c*,Semi-dilute regime: c = c*,1/2,For good solvent, v = 3/5,c,Scaling Law of semi-dilute solution,In semi-dilute regime, P is independent on N:,For good solvent, v = 3/5, therefore m = 5/4.,Osmotic pressure:,5/4,1,App
15、arent correlation length xapp:,xapp is independent on N:,For good solvent, v = 3/5, therefore m = -3/4.,app,Polymer Shapes in Semi-dilute Solutions,appc-3/4,串滴内有N”=g个链段单元, 串滴数N=N/g, 每个串滴大小l=app,blob model: 由N个串滴单元组成的理想链,串滴内- 由N”个单元组成的扩张(良溶剂下)的短链,The presence of monomers from the other chains begins
16、to “screen” (屏蔽) the intramolecular excluded volume interactions.,亚浓溶液: 串滴(blobs)在溶液中的分布达到均匀, 链段分布未达均匀,浓溶液: 链段在溶液中的分布完全均匀,实质:,3.5 Concentrated Solutions of Polymers,1. 高分子-增塑剂,2. 纺丝液,3. 凝胶和冻胶,Flory-Huggins free energy of a gel,V0,1/2,swelling,l3V0,l1/2,Basic Equation of Gel Swelling,Q=V/V0=1/f2,Volume Phase Transition of Gel
