2. Huggin,s Enthalpy of minong hxt A Different pairs in solution solvent-solvent molecule: [1-1,6 solute-solute segment: [2-2,E2 solvent-solute: [1-21,612 Mixing process:1-1]+-[2-2]=[1-2] ●→0● N, v and o xN,L AE2=612-(E1+82) N,+xN. y N+xN. y △H P24812 P12 total pairs of[1-2 AH=(2-2)N中24E12 Inning (Z-2)xN24E1 =[(z-2)x+19N2=(z-2)N2 kTxN中2=R7xn2 cells surrounding number of polymers im-kTxpa2=Vm928-82/N a polymer volume fraction of solvent- Possibility 2(z-2)△ 12-V(82-82 of the cell occupied by solvent. RT Flory-Huggins parameter
2. Huggin’s Enthalpy of mixing Mixing process: 1 [2 2] 2 1 [ 2 1 1] [ 2 1 ] 12 12 11 22 1 2 'H H H H Different pairs in solution: solvent-solvent molecule: [1-1], H11 solute-solute segment: [2-2], H22 solvent-solute: [1-2], H12 ' 'H H P mixing 12 12 1 2 12 ( 2) ' I H ZN mixing 'H 12 ( 2) Z kT F 'H ' H kT N mixing F 1 2 I Flory-Huggins parameter: (interaction parameter) P Zx 12 >( 2) 2@ volume fraction of solvent ~ Possibility of the cell occupied by solvent. cells surrounding a polymer number of polymers P12 total pairs of [1-2] 1 1 1 1 2 s m N V N N xN V I 2 2 2 1 2 s m xN xN V N xN V I and N1 N2 10 I1 1 2 N2 ( 2) Z N I RT n F 1 2 I = 1 2 m s V kT V FI I > @ 2 12 1 2 / V N m II G G 2 Vs 1 2 RT G G 2 1 12 ( 2) Z xN I 'H V V s ps with x segments
另类导法 B1==6()=()(-4( 4()÷J4()()==(6-61) 62p=2(-)=2(24-862) 12 8120, B2 △H mning H12-(H1+H2) F(2-2(21+62)+cO xd: D2tconst
ਖ㊫ሬ⌅ 11 2 11 11 1 1 s H r dr V H I ³ 11 1 2 1 s r r dr V H I I ³ 11 11 1 12 s s r dr r r dr V V H H I II ³ ³ 2 22 22 2 m s V H V H I 22 2 1 1 m s V V HI I 22 2 22 1 2 m s V V H I H II 12 12 1 2 m s V H V H II 12 11 22 1 2 ' H H HH mixing 11 1 11 1 2 m s V V H I H II 12 11 22 1 2 1 . 2 m s V const V H H H II § · ¨ ¸ © ¹ 1 2 . m s V const V FI I
另类导法 ∫(M=()(-=( 2j4(0b24()()(G一E1) H2=E292 22(1-)m=2m(=2-62) N 12 8120, B2 HO E1 △m=H12+(H1+H2)-(H1+HB) E 四62(E1+/n=R7x9 0+0=V m 12
ਖ㊫ሬ⌅ 12 2 11 11 1 1 2 s H r dr V H I ³ 11 1 2 1 2 s r r dr V H I I ³ 11 11 1 12 2 2 s s r dr r r dr V V H H I II ³ ³ 2 22 22 2 2 m s V H V H I 22 2 1 1 2 m s V V HI I 22 2 22 1 2 2 m s V V H I H II 12 12 1 2 m s V H V H II ' H H HH mixing 12 11 22 11 1 11 1 2 2 m s V V H I H II 12 11 22 1 2 1 2 m s V V H H H II § · ¨ ¸ © ¹ 1 2 m s V kT V FI I 0 0 H H 11 22 0 0 1 11 11 11 2 2 s s V N H V H H 0 0 2 22 22 22 2 2 p s V xN H V H H 0 0 VVV s pm 1 1 s m V N V I 2 2 s m xN V V I
3.3 Thermodynamics of Polymer Solutions s。°·x Sam(M)、3,h+C 链构象保持不变 △S=0 cont 与溶剂混合会产生各种排列组合状态即混合熵ASm>0n
3.3 Thermodynamics of Polymer Solutions 13 ߣґܴЉՊ Њ䇎ӷࢌՠѫфࣿ՟य़ӧুՠہࣙԯ ,ࢌՠ䒤οܵ> 0 + 0 conf ' S 2 2 3 (, ) 2 conf g B g SN k C N l h h ?
3.3 Thermodynamics of Polymer Solutions (1)Entropy of mixing for ideal solution △ k(NIn x, +NIn x (2) Entropy of mixing for polymer solutions The lattice model assumes that the yo回 volume is unchanged during mixing. l l己d oo Each repeating unit of the polymer (segment)occupies one position in the p。ooro lattice and so does each solvent molecule p olololoJoooryo >The mixing entropy is strongly onto- influenced by the chain connectivity of ooooooLog the polymer component
3.3 Thermodynamics of Polymer Solutions (1) Entropy of mixing for ideal solution 1 12 2 ln ln i mix ' S kN X N X (2) Entropy of mixing for polymer solutions ¾The lattice model assumes that the volume is unchanged during mixing. ¾Each repeating unit of the polymer (segment) occupies one position in the lattice and so does each solvent molecule. ¾The mixing entropy is strongly influenced by the chain connectivity of the polymer component. 14