Brownian dynamics simulations of Lennard-Jones gas/liquid phase separation and its relevance to gel formation

Abstract

Brownian dynamics computer simulations have been used to follow the phase separation behaviour of model adhesive colloidal systems quenched in temperature from a supercritical state into the two-phase coexistence region, CR, of the phase diagram. The systems studied consisted of monodisperse spherical particles interacting through either 12–6, 24–12 or 36–18 pair potentials. Systems quenched to state points just inside the two-phase boundary initially exhibit negligible domain growth or a period of ‘latency’ before slow decomposition, a feature associated with phase separation by nucleation. Systems quenched further into the two-phase region are characterised by immediate decomposition and more rapid growth of a characteristic length scale, behaviour characteristic of phase separation via a spinodal decomposition mechanism. Both domain size and peak height followed a power law growth with time over a period of the separation and some systems exhibit dynamic scaling of the structure factors. For systems at a volume fraction in excess of ca. 0.1 percolating interconnecting networks formed which manifested gel-like properties such as an increasing infinite frequency shear modulus, the appearance of a low-frequency shear modulus and more pronounced power-law behaviour of the stress time autocorrelation functions. The LJ clusters consist of compact regions separated by thin branches, whereas the shorter ranged potentials formed more tenuous gel-like structures. Phase separation was slower for the shorter range attractive potentials.

References

1. J. E. Martin, Phys. Rev. A, 1987, 36, 3415.
2. J. E. Martin, J. Wilcoxon and J. Odinek, Phys. Rev. A, 1991, 43, 858.
3. J. E. Martin and J. Wilcoxon, Phys. Rev. Lett., 1988, 61, 373.
4. D. F. Hodgson and E. J. Amis, Phys. Rev. A, 1990, 41, 1182.
5. S. Z. Ren and C. M. Sorenson, Phys. Rev. Lett., 1993, 70, 1727.
6. A. P. Gast, C. K. Hall and W. B. Russel, J. Colloid Interface Sci., 1983, 96, 251.
7. H. Verduin and J. K. G. Dhont, J. Colloid Interface Sci., 1995, 172, 425.
8. S. Hayward, D. W. Heermann and K. Binder, J. Stat. Phys., 1987, 49, 1053.
9. W. C. K. Poon, A. D. Pirie and P. N. Pusey, Faraday Discuss., 1995, 101, 65.
10. M. H. G. M. Penders and A. Vrij, Adv. Colloid Interface Sci., 1991, 36, 185.
11. J. D. Gunton, M. San Miguel and P. S. Sahni, in Phase Transitions and Critical Phenomena, ed. C. Domb and J. L. Lebowitz, Academic, London, 1983, vol. 8, ch. 3, pp. 267–482.
12. M. D. Haw, M. Sievwright, W. C. K. Poon and P. N. Pusey, Physica A, 1995, 127, 231.
13. M. R. Mruzik, F. F. Abraham and G. M. Pound, J. Chem. Phys., 1978, 69, 3462.
14. A. J. Bray, Adv. Phys., 1994, 43, 357.
15. K. Binder, Rep. Prog. Phys., 1987, 50, 783.
16. S. M. Illett, A. Orrock, W. C. K. Poon and P. N. Pusey, Phys. Rev. E, 1995, 51, 1344.
17. K. Binder and D. Stauffer, Phys. Rev. Lett., 1974, 33, 1006.
18. P. N. Pusey, A. D. Pirie and W. C. K. Poon, Physica A, 1993, 201, 322.
19. W. C. K. Poon, J. S. Selfe, M. B. Robertson, S. M. Illett, A. D. Pirie and P. N. Pusey, J. Phys. II (France), 1993, 3, 1075.
20. P. N. Pusey, W. C. K. Poon, S. M. Illett and P. Bartlett, J. Phys. A: Condens. Matter, 1994, 6, 29.
21. M. Carpineti and M. Giglio, Phys. Rev. Lett., 1992, 68, 3327.
22. M. Carpineti and M. Giglio, Phys. Rev. Lett., 1993, 70, 3828.
23. M. Carpineti and M. Giglio, J. Phys. A: Condens. Matter, 1994, 6, 329.
24. M. Carpineti, M. Giglio and V. Degiorgio, Phys. Rev. E, 1995, 51, 590.
25. D. Asnaghi, M. Carpineti, M. Giglio and A. Vailati, Physica A, 1995, 213, 148.
26. B. H. Bijsterbosch, M. T. A. Bos, E. Dickenson, J. H. J. van Opheusden and P. Walstra, Faraday Discuss., 1995, 101, 51.
27. S. W. Koch, R. C. Desai and F. F. Abraham, Phys. Rev. A, 1983, 27, 2152.
28. B. D. Butler, H. J. M. Hanley, D. Hansen and D. J. Evans, Phys. Rev. Lett., 1995, 74, 4468.
29. E. Velasco and S. Toxvaerd, Phys. Rev. Lett., 1993, 71, 1993.
30. M. T. A. Bos and J. H. J. van Opheusden, Phys. Rev. E, 1996, 53, 5044.
31. D. A. Kofke, J. Chem. Phys., 1993, 98, 4149.
32. R. Agrawal and D. A. Kofke, Mol. Phys., 1995, 85, 43.
33. D. Duh and D. Henderson, J. Chem. Phys., 1996, 104, 6742.
34. D. L. Ermak, J. Chem. Phys., 1975, 62, 4189.
35. G. C. Ansell and E. Dickinson, Faraday Discuss. Chem, Soc., 1987, 83, 167.
36. P. J. Mitchell, D. M. Heyes and J. R. Melrose, J. Chem. Soc., Faraday Trans., 1995, 91, 1975.
37. C. F. Tejero, A. Daanoun, H. N. W. Lekkerkerker and M. Baus, Phys. Rev. Lett., 1994, 73, 752.
38. C. F. Tejero, A. Daanoun, H. N. W. Lekkerkerker and M. Baus, Phys. Rev. E, 1995, 51, 558.
39. T. Coussaert and M. Baus, Phys. Rev. E, 1995, 52, 862.
40. M. H. J. Hagen, E. J. Meijer, G. C. A. M. Mooij, D. Frenkel and H. N. W. Lekkerkerker, Nature (London), 1993, 365, 425.
41. R. I. Tanner, Engineering Rheology, Oxford Science Publ., Oxford, 1992.
42. J. H. R. Clarke, J. Chem. Soc., Faraday Trans. 2, 1978, 74, 1371.
43. H. Tanaka, T. Yokawa, H. Abe, T. Hayashi and T. Nishi, Phys. Rev. Lett., 1990, 65, 3136.
44. D. A. Weitz and M. Oliveria, Phys. Rev. Lett., 1984, 52, 1433.
45. P. Meakin, Phys. Rev. Lett., 1983, 51, 1119.
46. M. Kolb, R. Botet and R. Jullien, Phys. Rev. Lett., 1983, 51, 1123.
47. P. W. Rouw, A. T. J. M. Woutersen, B. J. Ackerson and C. G. De Kruif, Physica A, 1989, 156, 876.
48. H. Furukawa, Adv. Phys., 1985, 34, 703.
49. M. Carpineti, F. Ferri, M. Giglio, E. Paganini and U. Perini, Phys. Rev. A, 1990, 42, 7347.
50. D. Asnaghi, M. Carpineti, M. Giglio and M. Sozzi, Phys. Rev. A, 1992, 45, 1018.
51. D. M. Heyes and P. J. Mitchell, J. Chem. Soc., Faraday Trans., 1994, 90, 1931.
52. C. Michon, G. Cuvelier and B. Launay, Rheolog. Acta, 1993, 32, 94.
53. D. M. Heyes, Mol. Phys., 1990, 69, 559.
54. A. L. R. Bug, S. A. Safran, G. S. Grest and I. Webman, Phys. Rev. Lett., 1985, 55, 1896.
55. H. Tanaka, Phys. Rev. Lett., 1996, 76, 787.