28 28 3 PRO GRESS IN P H YSICS Vol. 28 No. Mar. 28 :2542 (28) 222 NMR, (,, 437) :, (NMR) (Rouse, / Rouse ) NMR NMR, :; Rouse ; / ; NMR ; NMR : O48 :A (soft2condensed matter) [,2 ],,,,,, :,,() ( soft matter), (complex fluids), ( ),,, de Gennes 99 [3 ] de Gennes,,,, :2728224 : (:4746,67452) ( ) 4 5 (),,,, (), ( ) ; (2) :, (3),,,
2 28,, ( t ube) (primitive) [4,5 ] ( ),,,, [6 ] 97, De Gennes [7 ] (reptating) Brown, Doi Edwards [ 8 ], /, ( ),, (NMR), NMR [9 ] De Gennes [7 ], NMR, NMR 2, : Rouse, / Rouse ; NMR NMR,NMR 2NMR ( ),,. Rouse, Rouse 953 [2 ] N (Kuhn ),,,,, (), () : K = 3 kb T/ b 2 () 2, ah,b,, Stokes : = 6 a h (2) kb Boltzmann, T, b,, ah ( ), n Langevin : f L n ( t) Langevin, :, f L n ( t) = f L n( t) f L m( t ) = 2 kb T mm ( t - t ) s - 2-9 s, < nm (3), Rouse, 5 rn 5t - K 52 rn 5 n 2 = f L n ( t) (3)
, : NMR 3 Xp ( t) N N N cos p n (3) : 5 Xp ( t) 5t r n ( t) d n ( p =,,2, ) = X p ( t) + f p ( t) (4) p p Rouse N p = s p s N Rouse s = 2 b 2 3 2 kb T (5) (6),Rouse p =,, Rouse,, R = s N 2 (7) Xp ( t) ( NMR ) : cp ( t) 5cp ( t) 5t Xp ( t) Xp () = c p ( t) (8) p cp ( t) Xp ( t) Xp () = Nb2 t exp - (9) 2 2 p 2 p Rouse n : ( rn ( t) - rn () ) 2 =( X ( t) - Xn () ) 2 + N - 8 [ cp ( t) - cp () ]cos 2 p = N p n () ( Kuhn ),,Gaussian -,, e s N 2 e, n n cos 2 N p n = / 2, (9) R 2 ( t) ( r( t) - r () ) 2 =( X ( t) - N - X () ) 2 + 4 [ cp ( t) - cp () ] = p = 6 D R t + 2 Nb2 : R 2 ( t) = 2 p p 2 - exp - (2b 2 / 3 ) t/ s s ν T ν R 6 D Rt t µ R D R = b 2 3 2 N N - s t () p (2a) (2b) (3) Rouse,( t µ R ), Einstein R 2 N - t ; Rouse,, R 2 N t / 2,. 2 / Rouse,Rouse, t = s N 33. 4 D N - 22. 5 [3 ],Rouse R = s N 2 D N - Rouse Edwards [6 ] de Gennes [7 ],Doi Edwards [8 ], / D E :,,, d = bn / 2 e,57 nm, N e 2 d (),,, Doi2Edwards, ( 2) : s, e, Rouse R, d
4 28,Doi2 Edwards ( ) DE ( ) DE ( ) DE ( s ν t ν e ) Rouse,( ),Rouse (2a) : R 2 ( t) M t / 2 (2a) ( e ν t ν d ),,, (), Rouse n s n Langevin [8,4 ] : 5sn 5t - K 52 sn 5 n 2 = f L n ( t) (4) (3) : s 2 ( sn ( t) - sn () ) 2 = 2 Nb2 3 2 p p 2 - exp - ( kb Tb2 t/ ) / 2 t ν R 2 kb Tt N + p 2 t R (5) kb Tb/ N t µ R Gassian, R 2 = d(sn ( t) - sn () ) 2 / 2 : ( ) DE : ( e ν t ν R ) : R 2 ( t) d ( kb Tb 2 t/ ) / 4 M t / 4 (6), ( ) DE : ( R ν t ν d ) :R 2 ( t) d ( kb Tt/ N ) / 2 M - / 2 t / 2 (7) ( ) d 2 (R 2 ( t) N b 2 (7) ) : d = 3 s N 3 / N e = 3 R N / N e (8) ( ) DE,,, s 2 t ;, (), s 2 M - R 2 s 2 / 2,, ( ) DE ( t µ d ) :R 2 ( t) 6 Dct (9) Dc N e = kb T 3N 2 M - 2 (2),,,, Einstein, / Dc N - 2 d N 3, D N - 2-2. 5 tn 3. 5, /, ( d = bn / 2 e ),/ [4,5 ], 57 nm, / [622 ] [2326 ], [27,28 ] / 2( ) ( from refs ) ( ) R 2 (/ T) ( ) DE s ν ( t,/ ) ν e M t / 2 M ln ( s ) ( ) DE e ν ( t,/ ) ν R M t / 4 M - 3/ 4 ( ) DE R ν ( t,/ ) ν d M - / 2 t / 2 M / 2 - / 2 ( ) DE ( t,/ ) µ d M - 2 t M 2
, : NMR 5. 3 /,,, [2937 ], Langvevin. 3. Langevin Langevin [28,29,37 ] 5 Xp ( t) 5t + : 5cp ( t) 5t p ( t - ) 5 Xp 5 d= p2 X p ( t) + f p ( t) R + (2) p ( t - ) 5cp p2 d= c p ( t) (22) 5 R Rouse (4), (22),, p ( t - ),, ( t - ) =, Rouse : (22) Fourier/ Laplace : cp ( ) = cp ( ) = cp () R 2 ( t) ( r( t) - N - cp ( t) e i t dt (23) cp () / - i p = Nb 2 / (2 2 p 2 ) = R [ + p ( ) ]/ p 2 p (24) p ( ) = p ( t) e i t dt (25) r () ) 2 = 4 Re ( - cos t) cp ( ) d (26) p = - [29,3 ] Schweizer p ( t) = 6 b 3 3 5/ 2 R 2 ( t) 3/ 2 Q R 2 Q / 3b 2 q 6 exp ( - q 2 ) q 4 + 2pR2 2 dq (27) ( t) Q N = m d 6 g 2 ( d) S () / b 3 m, d, g ( r), S ( k), (27), (27), R 2 ( t). 3. 2 Rouse R 2 ( t) R (26) R 2 ( t) Q, R 2 ( t) Q =R 2 ( t) R = (2 b 2 / 3 ) t/ s [,3739 ],: () ( t ν s/ ),, Rouse (2) (: p > N/ 6 ), s/ (. 9) ν t ν (6 ) 4. 9 s,, R 2 n ( t). 5b 2 ( t/ s ) / 4 (28) (3) ( p < N/ 6 ),. 5 (6 ) 4 ν t ν : R 2 ( t). 23b 2 ( t/ s ) 2/ 5 (29) t µ = 2. 4 s N 2. 5 (3) R 2 ( t) = 6 D t (3). 2 kb T D = (32) 3 2 s N 3/ 2 2 D N -. 5 N 2. 5, DN - 2-2. 5 tn 3. 5 Rouse,
6 28 Rouse ( Rouse : R = s N 2 DN - ) p ( t) ( Rouse, ),. 3. 3 R 2 ( t) R 2 ( t) Q,, 3,, ( ) T,, /, : ThR R p 3 s N 3. 5 (33) D ThR R - 3 - s N - 2. 5 (34) R 2 M t 2/ 7 ( e ν t ν ThR R ) (35) 2 2( ) ( from refs, Rouse 3739) ( ) R 2 (/ T) s ν t,/ν s/ M t / 2 - ln ( s ) / M ( ) p > N/ 6 s/ (. 9 ) ν t ν (6 ) 4. 9 s M t / 4 M - / 2 ( ) p < N/ 6. 5 (6 ) 4 s ν t ν M t 2/ 5 M - / 5 ( ) p < N/ 6t µ ( = 2. 4 s N 2. 5 ) M - 3/ 2 t M - 2 + ( / 2) 2 3 2( ) ( from refs, Rouse 3739) ( ) R 2 (/ T) s ν t,/ν s/ M t / 2 - ln ( s ) / M ( ) T p > N/ 6 s/ (. 9 ) ν t ν (6 ) 4. 9 s M t / 4 M - / 2 ( ) T p < N/ 6. 5 (6 ) 4 s ν t ν M t / 3 M - / 3 ( ) T p < N/ 6t µ (5. 52 2 s N 3 ) M - 2 t M - 2 + ( / 2) 2 2 NMR NMR,, NMR (), NMR, ( ),NMR () - s ( Hz), NMR,NMR,NMR - ( ) T (NMR relaxometry) ; ( NMR diff usometry) ; ( dipolar correlation) NMR 2 ( ) [4 ] NMR,T NMR, : - - 3 s
, : NMR 7 3 rad Hz,: - 4 4 rad Hz s A diff ( T E) exp ( - 2 k 2 D ( ) / 3) (39) : () DM (2) () R 2 t 2. NMR,: R 2 ( t) M t (36), NMR ( NMR ), 2.. NMR NMR 2.. 2 DM NMR / () [442 ] NMR, Z B,z Gz ( G, z ),B ( z) = B + Gz : DM /, ( t µ t d ), D M - 2 ( PDMS) [52 ], ( PS) ( PE) [5355 ] A diff ( T E) =e i<( T E ) (37) ( PEO) [56 ], T E, <T E, DM - 2 [5258 ], 4, (a) (3 ( a) ), <= kz (b) = Gz = G( z2 - z ),z [52,53 ] z2 DM - 2, 2 NMR,Ds M -, [435 ], Hahn (3 ( a) ), (5 (a) ) 5 (a) [59 ] : (37) 3 ( a) Hahn, Mcross, Rouse DsM - ; : Mcross,/ DsM - 2. 4, A diff ( T E) =e i<( T E ) exp ( - kr 2 2 () / 6) = Mcross exp ( - k 2 D ()/ 6) (38) ( R 2 (), D () ), A diff, M - 3. 4,D s R 2 D D sm - 2. 4 M - 3 Ds ( ) ( 3 (b),, M - 2 : DsM - 2 NMR 3 2Hahn, ( (a) (b) )
8 28 4 (a) (b) ( PDMS) ( PS) [52,53 ],M 3? [662 ] [6367 ] : - 2. 4 Ds M. (4) (5 (a) ) (5 (b) ) NMR [ 6268 ], [ 69 ], /, DsM - 2 t µ d, ( 2 ),, NMR Ds M - 2, MW = 2. 5 5 5 (a), 2. 4,MCross = 3. 7 3 g/ mol (3 C),29 3 g/ mol (45 C, 65 C 85 C) (b) (75 C), [59 ],3 ms 2 nm ( < 25 nm) NMR 22, NMR ( 2 ms) 2 flip2flop ( - 5 m 2 / s), 2,,,, 2 D, 2 D, NMR,
, : NMR 9 2 T NMR, [772 ] 2.. 3 R 2 t,m - 2 /, R 2 ( = 3Z 2 ) (D) t, / 6,6 (a) ( PEO) 353 K [49 ],,, D ( t) t - / 2, Z 2 t / 2 ;,, flip2 flop 6 (b) CCl4 [ 53 ], :Z 2 t / 4, t / 2 t, / ( ) DE, ( ) DE( ) DE 2. 2 NMR 2 ( ) NMR,NMR 2, 2: T ( ) ( M Hz ), (7) T ( k Hz2M Hz) T, H - H 2 6 (a) ( Polyethylene oxide) (5 6 ) ; ( b) CCl4 ( PS) Z 2 t ( : 2. 2 % 5 6 daltons ; : 9 % 3. 6 daltons ; : 9 % 3. 6 daltons ; : 9 % 5 6 daltons) [49,53 ] 7 NMR relaxometry B : B,B2 ( B2, T,T,T ),B3 2. 2. 2 I I2 d2 Hamiltonian [9,3739 ] : H D = I gd I2 (4) gd, : gd= 2 g ( d 3-3 2 n n) (42) x, y, z n n n = d 2 / d2 (), Hamiltonian : Gm ( t) =H D ( t) H D () (43), / T ( ) I ( ), Fourier :
28 I ( T ) = - Gm ( t) e i t dt (44),2 : int ra / T = / T + / T inter (45),, 2 D,, 2 D,, A B A Kuhn (8), ( - 2-9 s) ( t s l b),, (),,,, -, A [9 ] GA ( t) = ga ( t) + GA ( ) (46),( PIP) 38 K [ ], m. 8-9 s 8, ( A) ( B), re 2 9 ( PIP) - [,76 ] B ( ), Kuhn, s d, Rouse,() ga ( t) (t µ s, ga ( t) = ) GA ( ) GA ( ) NMR ( t µ s ), GA ( ) / ga () - 3-2 Kuhn (, ),NMR, [9 ] : T GA ( t) = ga ( t) + GA ( ) GB ( t) (47), : ga ( t > s ) ; GB ( t s ) = GB () = H, NMR T 2T A ( 3 << rad Hz, 9) T m, B m /( )
, : NMR 2. 2. 2 2 NMR 2 T, t µ s,, Kuhn rij, t µ s,( ), Kuhn, rn n (Kuhn ) [9 ] : bn ( t) 5 rn ( t) 5 n = - N - 2 Xp p sin N p n (48) N p = bn ( t) bn () 2 2 N 2 N - p = p 2 cp ( t) (49), (4) (44) [3739 ] Gm ( t) =H D ( t) H D () n ( t) n () n ( t) n () b n ( t) b n () b n ( t) b n () =b n ( t) b n () 2 (5) : b T n ( t) b n () 2 e - i t dt ( s ν ) (5) -, b n ( t) b n (), 2 () Rouse Rouse, cp ( t) (9), () : bn ( t) bn () = ( b2 / 2) (5) : T - sln ( s ) sln N s/ t s ν t ν R ( b 2 / N) exp ( - t/ R ) t µ R (52) s ν ( t,/ ) ν R ( t,/ ) µ R (53a) (53b),NMR s - µµ - R, NMR (/ T ), Rouse (2) / ( ) DE : s ν ( t, / ) ν e, Rouse, 2 (53a) :/ T- M ln ( s ) ( ) DE : e ν ( t, / ) ν R, Gm ( t) Kuhn t (44) Gm ( t) R 2 ( t) = M t - / 4 (54) / T M - 3/ 4 (55) de Gennes, NMR [7 ] ( ) DE : R ν ( t,/ ) ν d, (7), / T M / 2 - / 2 (56) ( ) DE : ( t,/ ) µ d,/ T M 2 (57), 2,,( ) 2 () / (5) [73,74 ], Kimmich Weber [75 ] Gp ( t) t,: Gp ( t) = 2 D d dt R2 s ( t) ( t µ s ) (58) R 2 s ( t), D (2), (6), (7) (44) : ( ) DE : ( ) DE : / T M - / 2 ( s ν t ν e ) (59) / T M - / 4 ( e ν t ν R ) (6) ( ) DE : / T M / 2 - / 2 ( R ν t ν d ) (6) (59) (6) (53) (55)
2 28 (3) :. 3. 2,Rouse bn ( t) bn (), N - bn ( t) bn () = 2 Re N 2 cp ( ) cos td p = p 2 - (62) ( 5) 2 / T ( t ν s/ ),Rouse [38,39 ] : bn ( t) bn () = ( b 2 / 2) ( s/ t) / 2 / T - M ln ( s ) ( p > N/ 6 ), s/ (. 9) ν t ν (6 ) 4. 9 s, [37 ] : bn ( t) bn (). 4b 2 ( s/ t) / 4 (63) 2 : / T = M - / 2 (64) ( p < N/ 6 ), [,37,38 ] : bn ( t) bn () = 2 : M - / 5 b 2 ( s/ t) 2/ 5. 5 (6 ) 4 s ν t ν ( b 2 / N) exp ( - t/ ) t µ. 5 (6 ) 4 ν t ν / T M - 2 / [ + ( / 2) 2 ] t µ (65) (66) 2 (2) :,, ( (3) ) (2) (3),Rouse ( ), ( ) ( ) 2. 2. 3 () Rouse,NMR ( B),,, Rouse, 2 (53a) (a) ( b) ( PDMS) [38,75 ] [76 ] 2 PDMS ( MW = 47 < Mc5 ), 2 (4) ( MW = 423 µ Mc),, 2 (53a) Rouse, Rouse,, NMR 2 ( ), 2 / NMR 2 A ( PDMS) (a) (b) 2 (4) [ 52, 53 ] (2) NMR
, : NMR 3 : Rouse,,NMR - (2 ), (DE ),, NMR, H 2 D 2 (a2d) H - [,76 ],, : T M w / 2 region M w / 4 region M w. 4. 5 region, ( ), M w, NMR, () NMR, NMR, ( PDMS) ( PIB),NMR 2 ;,( PEO) ( PIP) NMR DOI/ Ed2 wards : () ( ) DE ( Rouse ) ; (2), T / 4,/ 4 /
4 28 ; (3) T,/ ( ) DE( ) DE T, ( ), T ( ), T ( ) T. 4. 5 ( (b) ),/ ( ) T,,, 2 D H, [,77 ] 2 ( PE O) ( PB) 2 D H [77 ], H, / 4 - / 3 ; 2 D,/ 3, 2 D,,, H H - H, T inter. 4. 5,. 4. 5 [,77 ], ( d) ( PDES) ( me2 sop hase),. 73. 45, / 3/ 4 / 2 T 3/ 4 ( ) NMR [78 ] DOI/ Edwards, DOI/ Edwards (), Rouse 2 PEOD ( MW = 48, ) PEO H ( MW = 438, ) 2 D H (a) PBD ( MW = 36, ) PB H ( MW = 4, ) 2 D H (b) [77 ] 2. 3 NMR 2 ( ) 2. 3. NMR 2 [42,79,8 ] M ( t) = M () exp ( i t)exp{ i t ( t) dt} (67) Larmor ; ( t) : ( t) = H D/ g= (3cos 2 ( t) - ) (68) = 3 2 g/ 4 d 3 (69) ( t) d ( 3 (b) )
, : NMR 5 (68) H D,Larmor,( ),Zeeman, H D Larmor ( - ) M ( t) ( t) Gussian, = M () exp ( i t) exp{ - dt t ( t - t ) c( t ) } (7) c( t ) =( t )() (7),, M ( t) = M () exp ( i t) exp{ - M2 = c() =() 2 = 9 2 2 M2 t2 } (72) 2 2 g d 3 (73),,NMR ( CH2,M2 5 c ν Hz),M2 M ( t) = M () exp ( i t) exp ( - M2 c t) (74) c = M2 dt c ( t ) (75), M R x ( t) = exp{ - d ( t - ) Lorentz l ( ) } (82),,,,,,, ( ),,,, ( ), ( ) : 2 ( t) =(( t) -( t) s) 2 s +( t) 2 s (76) s, re ( 3 (a) ) ( t) ( - 9-5 cs ( ) = s ( ) +( t) 2 s s) s ( ) =( t)( t + ) s -( t) 2 s (77), s,( t) s,re ( t) s l cl ( ) = l ( ) =( t) s( t + ) s (78) [798 ] : M x ( t) = M R x ( t) m R x ( t) (79) m R x ( t),, : m R x ( t) = exp ( - t/ T s 2 ) (8) / T2 s = d s ( ) (8) M R x ( t),: 2. 3. 2 Rouse t Rouse d 2 R d, Rouse,NMR,
6 28 :, - Gaussian, re,(3 (a) ) / 2 d ( 3 ( b) ),,,,, [798 ] : M R x ( t) ( - 2 ) M in x + 2 exp{ - t/ T2 e } (86) N s N s, T e 2 ; 3 (a) re, (b),d, (68) ( ), [ 79,8 ] : ( t) s = (3cos 2 - ) s = (/ ne) ( b 2 / N ea 2 ) (3cos 2 ( t) - ) = (/ n 2 e a 2 ) (2 z 2 - x 2 - y 2 ) (83) ne, a, b (b=x 2 + y 2 + z 2 = nea 2 ) 2, (68), ne, Rouse,Rouse [798 ] : l ( ) = t s( t + ) s =. 6 (/ N s) 2 E 2 ( ), E( ) = N - s P (84) exp ( - / P ) (85) N s (), 4 (cis,42polybutadiene ( PB) ) 25 [59 ], M c, 4 ( PB) 25 [59 ], t =, Mc = 485,9, : M ( t) m R x ( t) M R x = m R x { ( - 2/ N s) M in x + (2/ N s) exp ( - t/ T e 2 ) } (87) (2) Rouse M R x, ( ms ) ν, M R x,, ( ) 5 [883 ] M R x, m R x ( t)
, : NMR 7,, 5 M R x m R x ( t), m R x ( t) M R x (6) [8284 ], M R x, 6 (a) ( PEO) ;6 ( b) (c) (a) M R x 6 ( a),,,, ;,,, 6 ( b) M R x,(),t =, Mc = 22 K,5,, 6 (c) PEO ln ( M R x ) / tt,5 ms, M R x ( ( 87) ) 6 (c) M R x ( - 2/ N s ) M in x ( 6 (d) ) ( t =. 6 ms), Rouse, (82) (84) (85) 6 (d),,, Rouse 2. 3. 3 /
8 28 d R,,,,, ( t) t, 7 (2, ) [8 ] D E ( ) DE c( t) M / 2 t - / 2,, gm2 d gm2 =. 3 6 s - 2 d =. 9 s [8 ] c( t) =( t)() RA = gm2( t) gm2 =( t) 2 s ( t) t ( t) s 2 ( t) / 2 R 2 ( t) (89) / : (DE) :c( t) M t - / 4 ( e ν t ν R ) (9) (D E) :c( t) M t - / 2 ( R ν t ν d ) ( 9) NMR () NMR ( / 2 - - / 2 - - acq) [8 ] E(2 ) =cos[ ( <(, ) - <(,2 ) ) ]= exp{ 2 dt (- t ) c( t ) } exp{ dt c ( t ) + 2 dt (2- t ) c( t ) } (92),( t) =, =,,,, ( t) t,, Hahn ( / 2 - - - ), (2, ) =sin ( <(, ) sin<(,2 ) = exp{ - 2 dt (- t ) c( t ) } sinh{ dt c ( t ) + 2 dt (2- t ) c( t ) } (93) 7 3 K PDMS(5. 4 5 daltons) ((2, ) ) ( ) ( ) (o) [8 ] (3) NMR H [85,86 ] H 8 (a),texc t, t rec, 9, : I DQ t exc = t +2 t exc dt dt( t )( t ) t + t exc gm2 2 exc( t + exc ) (94) t ( = t + rec ), R 2 ( t) 8 9 [85, 86 ] t,t/ e e ( e ( T) ), t/ e,t/ e, :R 2 ( t) / t / 2 R 2 ( t) t / 4
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