τ τ

1 1 1.1 1.1.1 τ τ

2 1 1.1.2 1.1 1.1 µ ν M φ ν end ξ µ ν end ψ ψ = µ + ν end φ ν = 1 2 (µφ + ν end) ξ = ν (µ + ν end ) + 1

1.1 3 6.18 a b 1.2 a b 1.1.3 1.1.3.1 f R{A f } A f 1 B R{AB f 1 } COOH A OH B 1.3 A 3 B 2 C O H + HO CH 2 C O CH 2 + H 2 O O O ph 1839 C.Goodyear C-S-S-C

4 1 1.3 1.4 R{A 3 } 1.4 3 1.1.3.2

1.1 5 1.5 a 1.5 b C n H 2n+1 n = 12 25 ABA 1.5 c 1.5 d κ- 1.5 e

6 1 1.5 1.2 M w = (1.1) 1.2.1 R{AB f 1 } A B m m- m- 1.6

1.2 7 Cayley 1.6 AB 3 B p B α A p B (f 1)α α 0 α 1/(f 1) m- m A (f 1)m B m 1 A m 1 B B (f 1)m (m 1) = fm 2m + 1 m- A 1.6 A m- A m- A m- f m N m / j N j N m m- f m = ω mα m 1 (1 α) fm 2m+1 (1.2) ω m m m- m 1 m fm m B m 1 B fm m C m 1 = (fm m)!/(m 1)!(fm 2m + 1)! A (m 1)! m! ω m = (fm m)! m!(fm 2m + 1)! (1.3)

8 1 f m = 1 α α ω mβ m (1.4) β = α(1 α) f 2 (1.5) M N m = N (f 1)αN = N[1 (f 1)α] (1.6) A 1.4 < m > n = 1 1 (f 1)α (1.7) < m > w = 1 (f 1)α2 [1 (f 1)α] 2 (1.8) α = α 1/(f 1) A 1 A 1.2.2 R{A f } 1940 P.J.Flory W.H.Stockmayer N m- A 2(m 1) A fm 2(m 1) = fm 2m + 2 1.7 fn(1 α) m- P m = [(f 2)m + 2]N m /[fn(1 α)] (1.9) l 1 ω m P m = ω mα m 1 (1 α) fm 2m+1 (1.10) N m = N f(1 α)2 ω m β m (1.11) α

1.2 9 1.7 A 3 β 1.5 ω m ω m (fm m)!/m!(fm 2m + 2)! (1.12) A (fn)α/2 1 M N m M = N (fn)α/2 = N(1 fα/2) (1.13) f m N m /M f m = f(1 α)2 α(1 fα/2) ω mβ m (1.14) < m > n = 1 1 fα/2 (1.15) w m mn m / mn m w m = f(1 α)2 mω m β m (1.16) α < m > w = 1 + α 1 (f 1)α (1.17) α α = 1/(f 1) α (1.18)

10 1 < m > n = 2(f 1)/(f 2) 1.8 α 1.8 A f ω m ω m k X S k m k ω mβ m, m=1 S k X m k ω m β m m S 0 = S 0 = α 1 α, S 1 = α(1 fα/2) f(1 α) 2, S 1 = α (1 α)[1 (f 1)α], S 2 = α f(1 α) 2, S 2 = α[1 (f 1)α 2 ] (1 α)[1 (f 1)α] 3 α(1 + α) f(1 α) 2 [1 (f 1)α] 1.16 1.17 m m α = lim 2(m 1)/fm = 2/f (1.19) m α α α w G

1.2 11 α = (2/f)w G + α (1 w G ) w G = (f 1)α 1 1 2/f (1.20) α = 1/(f 1) α = 2/f 1 α = 1 α = α 1.9 S 1.9 S F w G = 1 (1 α)2 α (1 α ) 2 α (1.21) α α α β α(1 α) f 2 α α β = α(1 α) f 2 = α (1 α ) f 2 (1.22) α 1.16 β α α w m w S = m 1 w m = (1 α)2 α (1 α ) 2 α (1.23) 1.21 α α α α = α w S + α w G (1.24)

12 1 α 2/f 1.9 1.10 w G α = 0.5 z- 1.8 1.10 A 3 1.2.3 f R{A f } N f 1.11 f = 1, 2, N f N fn f Ψ w f fn f / fn f (1.25) f n fn f / N f = ( wf /f) 1 (1.26) f w f 2 N f / fn f = fw f (1.27) m = (m 1 m 2 ) f m f

1.2 13 1.11 m= (1, 1, 1, 2, 3, 0, 1) 1.11 1.11 m = (1, 1, 1, 2, 3, 0, 1) m N(m) α ( ) ( fm f m f )! N(m) = fnf ( fm f 2 m f + 2)! α Σm f 1 (1 α) Σfm f 2Σm f +2 (w f ) m f m f! f 1 (1.28) fm fm f 1/m! (wf ) m f /m f! fmf w = f w(1 + α) 1 (f w 1)α (1.29) (f w 1)α = 1 (1.30) f = 2 1 f( 3) (m 2, m f ) m 2 = l m f = n N lm = ( fnf ) (l + fm m)! (fm 2n + 2)! αl+m 1 (1 α) fm 2m+2 wl 2 w m f l! m! (1.31) w f w 2 = 1 ρ N lm = ( (1 α)2 fn f ) ρα = ρ ω lm η l ζ m (1.32)

14 1 η ζ η (1 ρ)α (1.33) ζ ρα(1 α) f 2 (1.34) ρ = 0 ρ = 1 f M N lm M = N 2 + N f α }{{} 2 (2N 2 + fn f ) }{{} monomers cross links (1.35) f w = fρ + 2(1 ρ) = (f 2)ρ + 2 1.30 [(f 2)ρ + 1]α = 1 1.2.4 n f = n n 1 αn γ (1.36) γ α 0 γ crosslink index β α(1 α) n 2 γe γ n 1 ω m = (nm m)! m!(nm 2m + 2)! nm w m n2 γ m(γe γ ) m (1.37) γe γ γ γ = 1 (1.38) 1 1

1.3 15 1.23 w m = m 1 f(1 α)2 S 1 (α ) (1.39) α w S = γ /γ, w G = 1 γ /γ (1.40) α γ β α β = α (1 α ) f 2 γ n e γ S 1 (α ) = α f(1 α ) 2 γ n 2 1.3 1.3.1 f A R{A f } g B R{B g } A B R{A f }/R{B g } A B A B 1.12 1.12

16 1 α 1.13 1.13 f (f 1) (f 1)α = 1 (1.41) 1.14 1.14 R{A f }/R{B g } AB 1.15 A f /B g

1.3 17 A p B q 1.15 A A α = p(g 1)q (f 1)p(g 1)q = 1 (1.42) R{A f }/R{A 2 }/R{B 2 } AB 1.16 A f /A 2 /B 2 1.16 R{A f } A A ρ R{A f } R{A f } α = p{q(1 ρ)p} i qρ = i=0 p q ρ 1 p q(1 ρ) (1.43) (f 1)α = 1 [(f 2)ρ + 1]p q = 1 (1.44) A A 2 A f A f w f w = 2(1 ρ) + fρ = (f 2)ρ + 2 (f w 1)p q = 1 (1.45) A 2 ρ = 1 α = p q (f 1)p q = 1 A B p = q α = p 2 ρ/[1 p 2 (1 ρ)]

18 1 1.3.2 A f /B g f R{A f } N A g R{B g } N B Ψ A = fn A Ψ B = gn B A B 1952 A l B m λn l,m = (fl l)!(gm m)! l!m!(fl l m + 1)!(gm l m + 1)! xl y m (1.46) λ 1.48 (l, m) = (1, 0) (0, 1) x y x = λfn 10, y = λgn 01 (1.47) A B fn 10 p Ψ A (1 p) f x x = λψ A (1 p) f y = λψ B (1 q) g x y p q A Ψ A p B Ψ B q γ λ A + B A B λ = Ψ A p Ψ A (1 p)ψ B (1 q) = Ψ B q Ψ A (1 p)ψ B (1 q) λψ A = q/(1 p)(1 q) (1.48) x = y = q (1 p)(1 q) (1 q(1 p)f p)f 1 = 1 q p (1 p)(1 q) (1 p(1 q)g q)g 1 = 1 p (1.49) (1.50) γ γ = λψ A Ψ B (1 p)(1 q) (1.51) A B λ p = γ/ψ A q = γ/ψ B γ = λψ A Ψ B (1 γ/ψ A )(1 γ/ψ B ) (1.52) γ γ λγ = 1 {1 + λ(ψ A + Ψ B ) [1 2λ(Ψ A + Ψ B ) + λ 2 (Ψ A Ψ B ) 2 ] 1/2} 2

1.3 19 λ 0 λψ A C A λψ B = C B λγ = 1 2 { 1 + C A + C B [1 2(C A + C B ) + (C A C B ) 2 ] 1/2} w(c A, C B ) γ N S lm N lm = Ψ A /f + Ψ B /g γ (1.53) N lm M A M B A B M w (M A l + M B m) 2 N lm / A l + M B m)n lm (1.54) lm l,m(m [ (f 1)pM 2 B + (g 1)qMA 2 M w = + 2M ] pq AM B 1 (f 1)(g 1)pq + q f M A 2 + p g M B 2 q f M A + p g M B (1.55) 1.42 (f 1)(g 1)pq = 1 (1.56) 1.3.3 A B f R{A f } N A f B N B g Ψ A = fn A f Ψ B = gn B g (f = 1, 2, ) g (g = 1, 2, ) A B w A f fna f /Ψ A w B g gn B g /Ψ B p, q 1952 ( fl f l f )!( gm g m g )! λn(l, m) = ( fl f l f m g + 1)!( gm g l f m g + 1)! ( l x f ) f ( m y g ) g (1.57) l f! m f g g!

20 1 x f y g x f w A f q(1 p) f 1, y g wg B 1 q p(1 q) g 1 1 p (1.58) λ λ p Ψ A Ψ A (1 p)ψ B (1 q) = q Ψ B Ψ A (1 p)ψ B (1 q) (1.59) f w fw A f, g w gw B g (1.60) M A M f w A f, M B M g w A g (1.61) 1.55 f g f w g w M A /f M B /g M A /f M B /g MA 2 /f M B 2 /g Mf 2wA f /f Mg 2 wg B /g (f w 1)(g w 1)p q = 1 (1.62) 1.3.4 1.17 B R{B g } g B A g B A B

1.3 21 k m g j k wf A w f wg B p k p k A k A g w = kp k µ w µ w k 1.18 lf = (k 1)j k + 1 flf = kj k (1.63a) (1.63b) 1.57 p(1 p)q(1 q) q 1 N(j, l) = ( ( ) ( ) fn f ) jk 1! lf 1! f (w f ) l f l f! k (p k ) j k j k! (1.64) 1962 (f w 1)(µ w 1) = 1 (1.65) A/B α = (g w 1)pq 1.42 q = 1 (g w 1)p (k 1)p k α = µ w 1 k k 1 α = k 1(k 1)p k = µ w 1 (1.66) 1.181.65

22 1