2849
Macromolecules 1989,22, 2849-2851
Registry No. 111, 69496-25-9; IV, 119071-30-6; IV (homopolymer), 119071-35-1; metacryloyl chloride, 920-46-7.
References and Notes (1) Yao, Y.-F. Y.; Kummer, J. T. J . Jnorg. Nucl. Chem. 1967,29, 2453. (2) Alpen, U. V.; Muller, G. Ert. Abstr.-Int. SOC.Electrochem. 1977, 19, 77-2. (3) Fenton, D. F.; Parker, J. M.; Wright, P. V. Polymer 1973, 14, 589. (4) Wright, P. V. Br. Polym. J. 1975, 7, 319. (5) Armond, M. B.; Chabagno, J. M.; Duclot, M. J. In Fast Ion (6) (7) (8) (9)
Transport in Solids; Vashista, P., Mundy, J. M., Shenoy, G . K., Eds.; North Holland: New York, 1979; pp 131-136. Papke, B. L.; Ratner, M. A.; Shriver, D. F. J. Phys. Chem. Solids 1981, 42, 493. Lee, C. E.; Wright, P. V. Polymer 1982, 23, 681. Lee, Y. L.; Christ, B. J . Appl. Phys. 1986, 60(8), 2683. Nicholson, M. N.; Weismuller, T. P. J. Electrochem. SOC.1985,
132, 89. (10) Ferloni, P.; Chiodelli, G.; Magistris, A.; Sanesi, M. Solid State Ionics 1986, 18-19, 265-270. (11) Killis, A.; LeNest, J. F.; Cheradame, H.; Gandeni, A. Makromol. Chem. 1982, 183, 2835. (12) Watanabe, M.; Sanui, K.; Ogata, N.; Kobayashi, T.; Ohtaki, Z. J . Appl. Phys. 1985, 57, 123. (13) Watanabe, M.; Togo, M.; Sanui, K.; Ogata, N.; Kobayashi, T.; Ohdaki, Z. Macromolecules 1984, 17 2908. (14) Dupon, R.; Papke, B. L.; Ratner, M. A.; Shriver, D. F. J . Electrochem. SOC.1984, 131, 586. (15) Watanabe, M.; Rikukawa, M.; Sanui, K.; Ogata, N.; Koto, H.; Kabayashi, T.; Ohdaki, Z. Macromolecules 1984, 17, 2902. (16) Wintersgill, M. C.; Fontanella, J. J.; Calame, J. P.; Smith, M.
K.; Jones, T. B.; Greenbaum, S. G.; Adamic, K. J.; Shetty, A. N.; Andeen, C. G. Solid State Ionics 1986, 18-19, 326-331. (17) Harris, C. S.; Shriver, D. F.; Ratner, M. A. Macromolecules 1986, 19,987-89. (18) Harris, C. S.; Ratner, M. A.; Shriver, D. F. Macromolecules 1987, 20, 1778-81. (19) Clancy, S.; Shriver, D. F.; Ochrymowycz,L. A. Macromolecules 1986, 19,606-611. (20) Armstrong, R. D.; Clarke, M. D. Electrochim. Acta 1984, 29, 1443. (21) Blonsky, P. M.; Shriver, D. F.; Austin, P.; Allcock, H. R. J. Am. Chem. SOC.1984, 106, 6854-6855. (22) Spindler, R.; Shriver, D. F. Macromolecules 1988,21,648-654. (23) Vincent, C. A.; MacCallum, J. R. In Polymer Electrolyte Re-
views; MacCallum, J. R., Vincent, C. A., Eds.; Elsevier: London, 1987. (24) Paoke. B. L.: Ratner. M. A.: Shriver. D. F. J. Electrochem. SOC. 1 9 k , 129, 1694. ’ (25) Ratner, M. A. In Polymer Electrolyte Reoiews: MacCallum. J. R., Vincent, C. A., Eds.; Elsevier:- London, 1987. (26) Kamachi, M.; Fujii, M.; Ninomiya, S.; Katsuki, S.; Nozakura, S.; J . Polym. Sci., Polym. Chem. Ed. 1982, 20, 1489. (27) Tomoi, M.; Abe, 0.; Ikeda, M.; Kihara, K.; Kakiuchi, H. T. Tetrahedron Lett. 1978, 33, 3031. (28) Pedersen, C. J. J . Am. Chem. SOC.1967,89, 7017. (29) Cahen, Y. M.; Handy, P. R.; Roach, E. T.; Popov, A. I. J. Phys. Chem. 1975, 79(1), 80. (30) Smetana, A. J.; Popov, A. J. J . Solution Chem. 1980, 9(3), 183-96. (31) Brandrop, J., Immergut, E. H., Eds. Polymer Handbook; Wiley: New York, 1975; Chapter 111, p 148. (32) Kosaki, M.; Ohsima, H.; Ieda, M. J . Phys. SOC.Jpn. 1970, 29(4), 1012. (33) Tsuchida, E.; Kobayashi, N.; Ohno, H. Macromolecules 1988, 21, 96-100.
particular systems of that kind is a melt of diblock-copolymers A-B, incompatibility of A and B blocks being responsible for separation effects. It is well established that polymer melts are weakly fluctuating systems, so a mean-field approach (in a general sense) can be applied to the melts. The specific mean-field theories of blockcopolymer melts were proposed by Helfand and Wasserman1 for the case of narrow interphase width and by Leibler2 for the opposite case. The final results of these papers’ were obtained after some numerical work. More recent approaches3p4enable one to obtain essentially the same results in a purely analytical way. Moreover, a number of new analytical results were obtained in ref 3 and 4. In particular, it was shown that the interaction energy of two spherical domains (micelles) depends on the distance between them in a nonmonotonic manner. It was assumed that this prediction implied some special features of micelles formation and ordering. The aim of the present paper is to study quantitatively some equilibrium aspects of the process of formation and ordering of micelle^.^ Let us consider a melt of block-copolymers A-B,A being the minor component: f = NA/N > 1 is the number of links in a polymer chain). The radii of gyration of the blocks in a homogeneous melt are
RA = NA‘l2aA; RB = NB1I2UB (1) where aA and aB are the characteristic sizes of A and B links. Let us consider the simplest symmetric case: aA = a B = a and U A = U B = u, where U A and U B are the volumes per link in undiluted homopolymers A and B,respectively. The excess free energy of mixing can be written as’ pint
= x T l p A ( r ) ad-)d3r/u
(2)
where pA(r) and (og(r) are volume concentrations of A and B components relative to the pure polymers (an incompressibility condition, pA(r) + (pB(r)= 1 is assumed), and x is the (dimensionless) parameter of incompatibility.
Interaction of Micelles If x were sufficiently small, the melt would be homogeneous: = 1 -f ‘PA(r) = f ; As x increases, an effective repulsion of A and B blocks gives rise to aggregation of copolymer chains into spherical domains (micelles). The structure of a micelle was considered in ref 3 in detail: it includes a core filled by A blocks and a “coat” of B blocks “grafted” to the surface of the core (Figure 1). The size of the “coat” is of the order RB; the radius of the core is3
R = 2.l8(Xhr,)’l6R~, RA > 1
(8)
where
NA(X- x,) At larger concentrations, an interaction between micelles must be taken into account. The dependence of the interaction energy for two micelle^,^ Uint, on the distance between their centers, r, was obtained analytically in ref 3 (for the case f 0 is obtained for CC1, 0 1989 American Chemical Society
