高分子物理-高分子溶液
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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
Mixing process: 1 [11] 1 [2 2] [1 2]
2
2
D12
12
1 2
11
22
DHmixing P12D12 P12 total pairs of [1-2]
P12 (Z 2)x 21N2 (Z 2)N12
cells surrounding a polymer
第三章 高分子溶液
3.1 高分子的溶解性判据 3.2 高分子溶液的热力学-Flory-Huggins理论 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 3.5 高分子凝胶的热力学 3.6 聚电解质溶液 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 3.9 高分子溶液的流体力学性质
= Vm
Vs
RT 12
Vm12
1 2
2
(Z 2)D12 Vs 1 2 2
kT
RT
Flory-Huggins parameter: 高分子物理-高分子溶液 (interaction parameter)
3.2 Thermodynamics of Polymer Solutions
(1) Entropy of mixing for ideal solution
高分子物理-高分子溶液
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 ….
x. 放置第x个链段的概率 高分子物(理Z--高1分)子(N溶液-xj-x+1)/N
Entropy of mixing from FH theory
W j1
高分子物理-高分子溶液
Chapt. 3 Polymer Solutions
➢ The solution process
solvent
polymer sample
swelled sample
polymer true solution
➢ This process is usually slower compared with small molecules, and strongly dependent on the chemical structures and condensed states of the samples.
the DGmix is negative.
1. Hildebrand enthalpy of mixing (混合焓)
1-1 + 2-2
1-2 + 1-2 1: solvent; 2: polymer
DHmix DE1 DE2 2 DE1DE2 P12 (DE/v) cohesive energy density
DSmi ix k N1 ln X1 N2 ln X2
(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 influenced by the chain connectivity of the polymer component.
2. Huggin’s Enthalpy of mixing
N1
N2
Different pairs in solution:
solvent-solvent molecule: [1-1], 11 solute-solute segment: [2-2], 22 solvent-solute: [1-2], 12
solvent with strong hydrogen bonds.
高分子物理-高分子溶液
3.1 Criteria (判据) of Polymer
➢SoGlibubbs firleietyenergy of mixing
DGmix DHmix TDSmix DSmix 0
➢ Solubility occurs only when
N
xj
Z
N
xj N
1 Z
1
Nቤተ መጻሕፍቲ ባይዱ
xj N
2 Z
1
N
xj N
3
Z 1 N xj x 1
number of polymers
volume fraction of solvent ~ Possibility of the cell occupied by solvent.
1
N1
N1 xN2
and
2
xN2 N1 xN2
DHmixing (Z 2)N12D12
DHmixing kT N12 RT n12
(内聚能密度)
DH mix
Vm1
N2v1 Vm
DE1 v1
1/ 2
DE2 v2
1/ 2
2
Vm12
DE1 v1
1/ 2
DE2 v2
1/ 2
Vm12 1 2 2
高分子物理-高分子溶液
=(DE/v)1/2 : solubility parameter (溶度参数)