Abstract
Although the idea that entropy alone is sufficient to produce an ordered state is an old one in colloid science1, the notion remains counter-intuitive and it is often assumed that attractive interactions are necessary to generate phases with long-range order. The phase behaviour for both rods and spheres has been studied experimentally1,2,3,4,5,6,7, theoretically8,9 and by computer simulations10. Here we describe the phase behaviour of mixtures of colloidal rod-like and sphere-like particles (respectively viruses and polystyrene latex or polyethylene oxide polymer) under conditions in which they act like hard' particles2,3. We find a wealth of behaviour: bulk demixing into rod-rich and rod-poor phases and microphase separation into a variety of morphologies. One microphase consists of layers of rods alternating with layers of spheres11; in another microphase of unanticipated complexity, the spheres reversibly assemble into columns, which in turn pack into a crystalline array. Our experiments, and previous theory and computer simulations11, suggest that this phase behaviour is entropically driven by steric repulsion between particles. The phenomena are likely to be quite general, applying also for example to low-molecular-mass liquid crystals12. This kind of microphase separation might also be relevant to systems of amphiphiles13 and block copolymers14, to bioseparation methods and DNA partitioning in prokaryotes15, and to protein crystallization16,17 and the manufacture of composite materials.
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References
Forsyth, P. A. J, Marcelja, S., Mitchell, D. J. & Ninham, B. W. Ordering in colloidal systems. Adv. Coll. Int. Sci. 9, 37–60 (1978).
Fraden, S. in Observation, Prediction, and Simulation of Phase Transitions in Complex Fluids (eds Baus, M., Rull, L. F. & Ryckaert, J. P.) 113–164 (Kluwer Academic, Dordrecht, (1995)).
Poon, W. C. K. & Pusey, P. N. in Observation—Prediction, and Simulation of Phase Transitions in Complex Fluids (eds Baus, M., Rull, L. F. & Ryckaert, J. P.) 3–51 (Kluwer Academic, Dordrecht, (1995)).
Tang, J. & Fraden, S. Isotropic–cholesteric phase transition in colloidal suspensions of filamentous bacteriophage fd. Liq. Cryst. 19, 459–467 (1995).
Tang, J. & Fraden, S. Temperature dependence of the flexibility of fd: Behavior of the isotropic–cholesteric phase boundary and magnetic birefringence. Biopolymers 39, 13–22 (1996).
Dogic, Z. & Fraden, S. Smectic phase in a colloidal suspension of semiflexible virus particles. Phys. Rev. Lett. 78, 2417–2420 (1997).
Sato, T. & Teramoto, A. Concentrated solutions of liquid-crystalline polymers. Adv. Polym. Sci. 126, 85–161 (1996).
Onsager, L. The effects of shape on the interaction of colloidal particles. Ann. NY Acad. Sci. 51, 627–659 (1949).
Hosino, M., Nakano, H. & Kimura, H. Nematic-smectic transition in an aligned rod system. J. Phys. Soc. Jpn 46, 1709–1715 (1979).
Frenkel, D. in Liquids, Freezing, and Glass Transition (eds Hansen, J. P., Levesque, D. & Zinn-Justin, J.) Ch. 9, 689–762 (Elsevier Science, Amsterdam, (1991)).
Koda, T., Numajiri, M. & Ikeda, S. Smectic-A phase of bidisperse system of parallel hard rods and hard spheres. J. Phys. Soc. Jpn 65, 3551–3556 (1996).
Rieker, T. P. Organic lyotropic lamellar liquid crystals. Liq. Cryst. 19, 497–500 (1995).
Gelbart, W. M., Ben-Shaul, A. & Roux, D. (eds) Micelles, Membranes, Microemulsions, and Monolayers (Springer, New York, (1994)).
Bates, F. S. Polymer–polymer phase behavior. Science 251, 898–905 (1991).
Walter, H. & Brooks, D. E. Phase separation in cytoplasm, due to macromolecular crowding, is the basis for microcompartmentation. FEBS Lett. 361, 135–139 (1995).
ten Wolde, P. R. & Frenkel, D. Enhancement of protein crystal nucleation by critical density fluctuations. Science 277, 1975–1978 (1997).
Adams, M. & Fraden, S. Phase behavior of mixtures of rods (tobacco mosaic virus) and spheres (polyethylene oxide, bovine serum albumin). Biophys. J. 74, 669–677 (1998).
Asakura, S. & Oosawa, F. Interaction between particles suspended in solutions of macromolecules. J.Polym. Sci. 33, 183–192 (1958).
Flory, P. J. Statistical thermodynamics of mixtures of rodlike particles. 5. Mixtures with random coils. Macromolecules 11, 1138–1141 (1978).
Gast, A. P., Russel, W. B. & Hall, C. K. An experimental and theoretical study of phase transitions in the polystyrene latex and hydroxyethylcellulose system. J. Coll. Int. Sci. 109, 161–171 (1986).
1. Frenkel, D. in Proceedings of the Sitges Conference on Complex Liquids (ed. Garrido, L.) 137–148 (Springer, New York, (1993)).
Dinsmore, A. D., Yodh, A. G. & Pine, D. J. Entropic control of particle motion using passive surface microstructures. Nature 383, 239–242 (1996).
Lekkerkerker, H. N. W. & Stroobants, A. Phase behaviour of rod-like colloid + flexible polymer mixtures. Il Nuovo Cimento 16 D 949–962 (1994).
Bolhuis, P., Stroobants, A., Frenkel, D. & Lekkerkerker, H. N. W. Numerical study of the phase behavior of rodlike colloids with attractive interactions. J. Chem. Phys. 107, 1551–1564 (1997).
Herzfeld, J. Entropically driven order in crowded solutions: From liquid crystals to cell biology. Acc. Chem. Res. 29, 31–37 (1996).
Devanand, K. & Selser, J. C. Polyethylene oxide does not necessarily aggregate in water. Nature 343, 739–741 (1990).
Model, P. & Russel, M. in The Bacteriophages (ed. Calender, R.) Ch. 6, 375–456 (Plenum, New York, (1988)).
Chiruvolu, S., Naranjo, E. & Zasadzinski, J. A. Microstructure of Complex Fluids by Electron Microscopy (Am. Chem. Soc., Washington DC, (1994)).
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We acknowledge grant support from the NSF (D.M.R.)
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Adams, M., Dogic, Z., Keller, S. et al. Entropically driven microphase transitions in mixtures of colloidal rods and spheres. Nature 393, 349–352 (1998). https://doi.org/10.1038/30700
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DOI: https://doi.org/10.1038/30700
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