复旦大学：《高分子物理》课程电子讲义_Chapter 3 Polymer Solutions、Chapter 4 Multi-component Polymer Systems

Chapter 3 Polymer Solutions 3.1 Interactions in Polymer System 3.2 Criteria of Polymer Solubility 3.3 Thermodynamics of Polymer Solutions: Flory-Huggins Theory 3.4 Thermodynamics and Conformations of Polymers in Dilute Solution 35 Scaling law(标度律) of polymers 3.6 Conformations of Polymer in Semi-dilute solution 3.7 Thermodynamics of Gels 3.8 Polyelectrolytes Solution 3.9 Hydrodynamics of Polymer Solutions

Chapter 3 Polymer Solutions 0 3.1 Interactions in Polymer System 3.7 Thermodynamics of Gels 3.4 Thermodynamics and Conformations of Polymers in Dilute Solution 3.6 Conformations of Polymer in Semi-dilute Solution 3.3 Thermodynamics of Polymer Solutions: Flory-Huggins Theory 3.8 Polyelectrolytes Solution 3.9 Hydrodynamics of Polymer Solutions 3.5 Scaling Law(ḷᓖᖻ) of Polymers 3.2 Criteria of Polymer Solubility

Chapt. 3 Polvmer Solutions The solution process(linear Polymer) Swelled Sample Polymer Solution This process is usually slower compared with small molecules, and strongly dependent on the chemical structures and condensed states of the samples 先溶胀,后溶解

Chapt. 3 Polymer Solutions ¾ The solution process (linear Polymer) ¾ This process is usually slower compared with small molecules, and strongly dependent on the chemical structures and condensed states of the samples. 1 Swelled Sample Polymer Solution ݸⓦ㛰ˈਾⓦ䀓

Crosslinked polymers: only can be swelled 有溶胀,无溶解

Crosslinked polymers: only can be swelled 2 ᴹⓦ㛰ˈᰐⓦ䀓

「 Crystalline polymers 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. 先熔融,后溶解

Crystalline polymers 3 ݸ⟃㶽ˈਾⓦ䀓 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 Interactions in Polymer System van der Waals interactions 1. electrostatic interaction Keesom force Ek 3r6kRt between permanent charges 2. Induction(polarization interaction between a permanent multipole Debye force Ep (a1u2 +a2u2) on one molecule with an induced multipole on another 3. Dispersion interaction between a ny pair of 3/h1l2 molecules, including non London force EL 2(1+12 polar atoms, arising from the interactions of instantaneous multipoles A:Dipole moment a: Polarizability au 3kpT I: lonization energy

3.1 Interactions in Polymer System 4 van der Waals interactions 1. electrostatic interaction 2. Induction (polarization) interaction 3. Dispersion interaction Keesom force Debye force London force ܧ ௄ൌ െ 2 3 ଵߤ ଶߤଶ ଶ ݎ ଺݇஻ܶ between permanent charges between a permanent multipole on one molecule with an induced multipole on another ܧ= ஽ െ ߙଵߤଶ ଶ + ߙଶߤଵ ଶ ݎ ଺ = ఓߙ ߤ ଶ 3݇஻ܶ P: Dipole moment D: Polarizability between any pair of molecules, including non￾polar atoms, arising from the interactions of instantaneous multipoles. ܧ ௅ൌ െ 3 2 ଶܫଵܫ ଶܫ + ଵܫ ଶߙଵߙ ݎ ଺ I: Ionization energy

Long-range Coulomb interactions see 3.8 O, Oe (r) 4IEokBTr Hydrogen bond interactions

„ Long-range Coulomb interactions see 3.8 „ Hydrogen bond interactions 5   2 1 2 0 4 B QQe U r SH k Tr

The Lennard-Jones or Hard Core potential The L-j(6-12) Potential is often used as an approximate model for a total (repulsion plus attraction van der Waals force as a function of distance E Repulsive +A/r12 U Attractive-B/r6 A B U=0 r>ro 12 6 U=∞T≤10

The Lennard-Jones or Hard Core Potential „ The L-J (6-12) Potential is often used as an approximate model for a total (repulsion plus attraction) van der Waals force as a function of distance. ܷ௅௃ = 6 ܣ ݎ ଵଶ െ ܤ ݎ ଺ ଴ݎ < ݎ 0ܷ = ଴ݎ ൑ ݎ λܷ =

MayerfF-Function and Excluded Volume The Probability P(r of finding two monomers at distance r. Boltzmann factor P(r)a exp[-U (r)/(kBT) Mayer f-function difference of boltzmann factor for two monomers at r and at oo f(r)=exp (u (r/kB t)-1 0.5 Exclude volume v-I f(r)d3r=(1-exp[-U(r)/(kBT)Ddr

Mayer f-Function and Excluded Volume 7 The Probability P(r) of finding two monomers at distance r: Boltzmann factor Mayer f-function: difference of Boltzmann factor for two monomers at r and at λ ݂ ݎ = exp െܷ ݎ݇ Τ ஻ ܶ -1 Exclude Volume v: ݀ ݎ ݂න െ = ݒ ଷ ݎ = න 1 െ exp െܷ ݎ Τ ݇஻ܶ ݀ ଷ ݎ ܶ஻݇ Τ ݎ ܷെ exp ן ݎ ܲ

32 Criteria(判据) of polymer Solubility Gibbs free energy of mixing △G=△H-T△S Solubility occurs only when the 4G is negative △S>0 Entropy of mixing for ideal solution ASmix=k(N,In X1+N2 In X2)>0 △H??? X

3.2 Criteria (ࡔᦞ) of Polymer Solubility ¾ Solubility occurs only when the 'Gmix is negative. ' ! 0 mix S ' '  ' G H TS mix mix mix ¾ Gibbs free energy of mixing Entropy of mixing for ideal solution  1 12 2 ln ln 0  i mix '   ! S kN X N X 8 ??? 'Hmix

1. Hildebrand enthalpy of mixing (混合焓) 1-1+ 2-2- 1-2+ 1-2 1: solvent; 2: polymer △E,△E (AE/v) cohesive energy density △H △FN-2 P 12 (摩尔内聚能密度) l2 total pairs of「-2 △H nx ()(月)-6= l/2 1/2 l/2 △E 产=Vn △E1 △E2 V2 VI n[1-82] -(AE/v): solubility parameter (溶度参数)

1. Hildebrand enthalpy of mixing (␧ਸ❃) 9 2 1/ 2 1 2 2 / 1 2 1 mix E v H E v § · § ·§ · '  ¨ ¸ ¨ ¸¨ ¸ © ¹© ¹ © ' ¹ ' ('E/v) cohesive energy density (᪙ቄ޵㚊㜭ᇶᓖ) G=('E/v) 1/2 : solubility parameter (ⓦᓖ৲ᮠ) 1-1 + 2-2 1-2 + 1-2 1 1 2 2 1 2 1 2 2 mix E E E E v v v v H § ' · '   ¨ ¸ © ' ¹ ' ' 1: solvent; 2: polymer P12 2 2 2 1/2 1 1 2 1 / 1 2 m E v E v V I I ' § · § ·§ ·  ¨ ¸ ¨ ¸¨ ¸ © ¹© ¹ © ¹ ' > 2 @ 2 Vm 1 2 I 1  I G G 2 2 2 m n V V I1 I m m V V § · ¨ ¸ © ¹ P12 total pairs of [1-2] 2 2 n V 1 1 1 m nV V I 2 1/2 1 1 / 2 2 2 1 E v E v § · § ·§ ·  ¨ ¸ ¨ ¸¨ ¸ ' © ¹© ¹ © ¹ ' 1 1 nV I2 m m V V § · ¨ ¸ © ¹