464-8602 (Dated: March 14, 2008) Abstract () PACS numbers: 81.10.-h, 64.60.Qb, 82.20.-w Electronic address: uwaha@nagoya-u.jp 1
I. [1] [2] 20 L [3] D D D BCF Frank [4] D L [5] 2 D L D L [6] D L [7] SiO 2 SiO 4 2
? II. Kondepudi NaClO 3 [8] D L D L D L 50 D L D L NaClO 3 NaBrO 3 [9] 1,1 - (binaphthyl) [9 11] 2 2 [12] 2 (whisker) 2 [13] Kondepudi [14] [15] A B A B A B D L 3
Α x 2 FIG. 1: x A+B D, A+B L, (1) A+B+D 2D, A+B+L 2L, (2) D L S S ( ABDLS ) D+L S (3) D L D L D xl y α = x y x + y D L (enantiomeric excess) α AB xy = x 2 2 α ( 1) NaClO 3 Viedma [16] D L 200μm D L 1 4 (4)
D L DL 1 D L D L 2 Ising (Gibbs-Thomson ) NaClO 3 III. [17]5 : AD D L L, D u L u NaClO 3 4 [16] 2 A+A D u, A+A L u, (5) 2 D u +D u D, L u +L u L, (6) A+D D, A+L L, D u +D D, L u +L L, (7) 5
z x xu yu y (a) 1 x y z (b) 0 100 200 300 FIG. 2: k 0 =0.1, k 1 = k u =1,k c =0.01, λ 0 =0.1λ 1 = λ u =0.05 x(0) = 0.001y(0) = x u (0) = y u (0) = 0z(0) = 0.999 (a) (b) [17] D L ADD u LL u zxx u yy u dx dt = k 1zx + k u x u x + k c x 2 u λ 1x λ u x, (8) dy dt = k 1zy + k u y u y + k c yu 2 λ 1y λ u y, (9) dx u dt = k 0z 2 k u x u x k c x 2 u + λ ux λ 0 x u, (10) dy u dt = k 0z 2 k u y u y k c yu 2 + λ uy λ 0 y u, (11) dz dt = 2k 0z 2 k 1 zx k 1 zy +λ 1 x + λ 1 y + λ 0 x u + λ 0 y u. (12) (5)-(7) k λ 6
1 x y xu,yu z (a) 0 10 20 30 1 x z y xu yu 0 1000 500 (b) FIG. 3: 2 x(0) = 0.101, y(0) = 0.100x u (0) = y u (0) = 0 z(0) = 0.799 [17] Ostwald [20] (8)-(12) k 0 =0.1k 1 = k u =1k c =0.01, λ 0 =0.1λ 1 = λ u =0.05 x(t)+x u (t)+y(t)+y u (t)+z(t) =1 2 D x(0) = 0.001y(0) = x u (0) = y u (0) = 0z(0) = 0.999 x u y u 7
L y, yu U x, xu R FIG. 4: (x(t),y(t)) (x u (t),y u (t)) () 1 2 2 3 [17] xy t 20 D L 5 t 200 L y L y u 3 x(0) = 0.101, y(0) = 0.100x u (0) = y u (0) = 0 L 1 t 10 t 100 t 900 L D u L u A 4 x(0) >y(0)x u (0) = y u (0) = 0 (x(t),y(t)) (x u (t),y u (t)) (8)-(12) RLU 3 [19] R L U 3 x = yx u = y u U R L R L x =0 y =0x y 8
IV. III () 2 D i L i i (5) D u L u D 2 L 2 i 2 A +D i D i+1, A+L i L i+1 (13) 2 6 2 D 2 +D 2 D 4, L 2 +L 2 L 4 (14) D 6 3D 2, L 6 3L 2 (15) 7 (12) 13 2 (14) D 6 L 6 3 Cartwright [21] A D 1, A L 1, (16) A +D i D i+1, A+L i L i+1, (17) D i D i s + sd 1, L i L i s + sl 1, (18) D 1 L 1 (16) Ostwald (18) D 1 L 1 2 2 2 (17) (18) 2 A 2 100 Ostwald III 9
L D k1 ku Lu A Du FIG. 5: (?) (16) Ostwald V. III IV [22] (2-- ) NaClO 3 () A 2 A d A l [23] III (D u +D u DL u +L u L) (A + A D u A+A L u ) McBride Tully [24]( 5) 4 (8)-(12) k 1 k u λ 0 λ u 3 D 10
L D L L D - IIIIV [1] [2] Chiral [3] d D (dextrorotatory) L (levorotatory) dl D L RS DL DL [4] F. C. Frank: Biochim. Biophys. Acta, 11 (1953) 459. [5] :?? [6] :?? [7] :?? [8] D. K. Kondepudi, R. Kaufman and N. Singh: Science 250 (1990) 975. [9] D. K. Kondepudi and K. Asakura, Acc. Chem. Res. 34 (2001) 946. [10] R. E. Pincock, R. R. Perkins, A. S. Ma and K. R.Wilson, Science 174 (1971) 1018. 11
[11] D. K. Kondepudi, J. Laudadio, K. Asakura, J. Am. Chem. Soc. 121 (1999) 1448. [12] R.-U. Qian and G. D. Botsaris: Chem. Eng. Sci. 53 (1998) 1745. [13] J. H. E. Cartwright, J. M. Garcia-Ruiz, O. Piro, C. I. Sainz-Diaz, and I. Tuval: Phys. Rev. Lett. 93 (2004) 035502. [14] D. K. Kondepudi and G. W. Nelson: Phys. Rev. Lett. 50 (1983) 1023. [15] : 34 (2007) 63. [16] C. Viedma: Phys. Rev. Lett. 94 (2005) 065504. [17] M. Uwaha: J. Phys. Soc. Jpn. 73 (2004) 2601. [20] Y. Saito and H. Hyuga: J. Phys. Soc. Jpn. 73 (2004) 33. [19] 4 [20] Y. Saito and H. Hyuga: J. Phys. Soc. Jpn. 74 (2005) 535. [21] J. H. E. Cartwright, O. Piro, and I. Tuval: Phys. Rev. Lett. 98 (2007) 165501. [22] W. L. Noorduin, T. Izumi, A. Millemaggi, M. Leeman, H. Meekes, W. J. P. Van Enckevort, R. M. Kellogg, B. Kaptein, E. Vlieg, and D. G. Blackmond: J. Am. Chem. Soc. 130 (2008) 1158. [23] J. M. McBride, J. C. TullyNature 452 (2008) 161. [22] Ostwald [24] J. M. McBride, NORDITA Origins of homochirality (2008 2 ) http://nordita.org/programs/homochirality Chiral Symmetry Breaking in Crystallization Makio Uwaha Department of Physics, Nagoya University Spontaneous chiral symmetry breaking in crystallization is briefly reviewed. Experimentally crystallization of several substances such as NaClO 3 from supersaturated solution with stirring produces strong chiral symmetry breaking. In addition, stiring and grinding of racemic mixture of chiral crystals in solution results in chirality transformation, and complete symmetry breaking is realized. Several models to explain these experiments are introduced, and the mechanism of autocatalytic processes is discussed at a phenomenological level. 12