Dynamics of polydisperse polymer mixtures

Macromolecules

Volumn 36, Issue 3, 2003, Pages 934-949

  Pagonabarraga, I ^a,b   Cates, M E ^c  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

^b UNIVERSITY OF BARCELONA   (Spain)

^c NONE

Author keywords

[No Author keywords available]

Indexed keywords

POLYDISPERSE MIXTURES;

ENTHALPY; QUENCHING; SOLVENTS;

MACROMOLECULES;

EID: 0038190853     PISSN: 00249297     EISSN: None     Source Type: Journal    
DOI: 10.1021/ma020690m     Document Type: Article

References (21)

1. Sollich, P.; Warren, P. B.; Cates, M. E. Adv. Chem. Phys. 2001, 116, 265.
2. Pagonabarraga, I.; Cates M. E. Europhys. Lett. 2001, 55, 348.
3. Huang, C.; Olvera de la Cruz, M. Macromolecules 1994, 27, 4231.
4. Clarke, N. Eur. Phys. J. E 2001, 4, 327.
5. Warren, P. B. Phys. Chem. Chem. Phys. 1999, 1, 2397.
6. Evans, R. M. L.; Holmes, C. B. Phys. Rev. E 2001, 64, 011404.
7. Nesarikar, A.; Olvera de la Cruz, M.; Crist, B. J. Chem. Phys. 1993, 98, 7385.
8. Brochard, F. Molecular Conformation and Dynamics of Macromolecules in Condensed Systems; Nasagawa, M., Ed.; Elsevier: Amsterdam, 1988; p 249; see also ref 10.
9. Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics; Clarendon Press: Oxford, England, 1989.
10. Doi, M.; Onuki, A. J. Phys. II 1992, 2, 1631.
11. 1/2. In the text, we are interested in the low q expansion of the Debye function g(q); see ref 2. g(q) also depends on the polymer length through the gyration radius.
12. In the present formulation, the determination of the diffusive flux is done neglecting the spatial extent of the polymeric chains, and this is introduced only in this section to describe the thermodynamics. This description follows in spirit what is done in ref 4, and in Cahn-Hilliard theory for polymeric systems generally. However, a more systematic approach would be to consider the nonlocal relation between the monomer and the chain density when deriving the diffusion fluxes (see, e.g.: Pincus, P. J. Chem. Phys. 1981, 75, 1996). The nonlocal dependence derived in this reference for the blend mobility suggests that to leading order in the wave vector the results we report will not be affected, while the subsequent dependence in wave vector will have modified amplitudes; however, we do not expect that the general trends of our results will be affected by the disregarded nonlocal effects in the mobility matrix.
13. The use of dynamical mean field theory (variable effective χ) in treating random copolymers requires that the monomeric interactions are sufficiently weak that these do not present barriers to the diffusion of any individual chain. See, e.g. Bouchaud, J.-P.; Cates, M. E. J. Phys. (Paris) II 1993, 3, 1171.
14. j(q) in Fourier space.
15. nt).
16. 1, the matrix of coefficients that defines the linear dynamics of this system is lower triangular.
17. n(with n being a moment).
18. Kramer, E. J.; Green, P.; Palstrom, C. J. Polymer 1984, 25, 473.
19. The fact that Brochard's model is a fast mode theory can be appreciated in the expressions for the diffusive fluxes, eq 26. The contribution of species j to the flux of species i is inverserly proportional to its friction coefficient (which in turn is proportional to its polymerization length). Hence, the longer the chain the smaller the cooresponding contribution to the diffusive flux of the rest of the species.
20. n+1(r).
21. The perturbative analysis around the monodisperse limit should be analyzed carefully, since it has a singular character depending how it is performed. Moreover, an incomplete treatment of the dynamics based on a finite subset of moments may give rise to spurious oscillatory modes. We thank M. R. L. Evans for an enlightening discussion of this point.