Physica A Precursors of long-range order and local disorder in colloids

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1976 M. Mayorga et al. / Physica A 388 (2009) 1973–1977Fig. 3. This image shows a rotation of Fig. 2 from which one can better observe the presence of orientational long range order. The packing fraction is alsoη = 0.545 which corresponds to the same conditions given in Fig. 2 but the figure has been slightly rotated to capture the corresponding view.Fig. 4. Pair correlation function for our model potential plotted versus reduced distance r ∗ , for two different β parameters. The continuous line is forβ = 11.910 and β = 11.905 for the dash line, for both cases α = 0.945 and η = 0.494. In this case, the shoulder is no longer flat. The particles becomearrested, giving rise to disordered configurations which have been found experimentally. The inset enhances the shoulder of the continuous plot whichshows qualitative agreement with the glassy precursor obtained experimentally in Refs. [17,21].fraction η = 0.494. The corresponding correlation functions are shown in Fig. 4. This function is similar to the one observedin experiments for PMMA particles immersed in a mixture of decalin and cycloheptylbromide, that were reported in theFigure 4(b) of Ref. [17]. The lower value of β corresponds to an increase of the diffusion of particles in comparison withthe ordered case. As a consequence, the shoulder in g appears at the right-hand side of the second maximum, leadingto the appearance of cages, one of the features of colloids close to glass transition [17,21], which can be considered asa sign of an amorphous-structure precursor. The above observation establishes that there is a crystallization window(i.e. β > 11.910) for which the crystallization can be induced, increasing the volume fraction. So, decreasing β belowthat value, the crystallization is frustrated, resulting in a disordered structure.4. ConclusionsWe have shown the existence of structural precursors of long-range order and local disorder in colloids, which can beidentified as shoulders around the second peak in the pair correlation function. The presence of a shoulder on the left (right)side is the signature of long-range order (local disorder) in colloidal suspensions. Its position depends on the value of asingle parameter that modulates the effective width of the attractive well in the interaction potential. These interestingfindings may contribute to a deeper understanding of the models that can be proposed to study phase transitions in colloidalsuspensions [22].
M. Mayorga et al. / Physica A 388 (2009) 1973–1977 1977AcknowledgmentsWe would like to thank S. Torquato, D. Frenkel and A. van Blaaderen for interesting discussions. We want to acknowledgefinancial support of PROMEP and grants UAEM 2263/2006, CONACyT P/49607 and by DGICYT of the Spanish Governmentunder Grant No. FIS2005-01299.References[1] K.H. Lin, et al., Phys. Rev. Lett. 85 (2000) 1770.[2] P.G. Vekilov, Cryst. Growth Des. 4 (2004) 671.[3] J.F. Lutsko, G. Nicolis, Phys. Rev. Lett. 96 (2006) 046102.[4] D. Frenkel, Nature Mater. 5 (2006) 85.[5] W.K. Kegel, A. van Blaaderen, Science 287 (2000) 290.[6] A. Yethiraj, J.H.J. Thijssen, A. Wouterse, A. Van Blaaderen, Adv. Mater. 16 (2004) 596.[7] T.F. Krauss, Nature Mater. 2 (2003) 777.[8] J. Gao, Z. Hu, Langmuir 18 (2002) 1360.[9] J. Wu, G. Huang, Z. Hu, Macromolecules 36 (2003) 440.[10] L.F. Filobelo, O. Galkin, P.G. Vekilov, J. Chem. Phys. 123 (2005) 014904;W. Pan, A.B. Kolomeisky, P.G. Vekilov, J. Chem. Phys. 122 (2005) 174905.[11] A. Ben-Naim, Hydrophobic Interactions, Springer, 1980.[12] J.N. Israelavichli, Intermolecular and Surface Forces, Academic Press, San Diego, 1995.[13] D. Kashchiev, Nucleation, Basic Theory and Applications, Butterworth-Heinemann, Oxford, 2000.[14] M. Mayorga, L. Romero-Salazar, J.M. Rubi, Physica A 307 (2002) 297.[15] D. Osorio-González, M. Mayorga, J. Orozco, L. Romero-Salazar, J. Chem. Phys. 118 (2003) 6989.[16] T.M. Truskett, S. Torquato, S. Sastry, P.G. Debenedetti, F.H. Stillinger, Phys. Rev. E 58 (1998) 3083.[17] E.R. Weeks, D.A. Weitz, Phys. Rev. Lett. 89 (2002) 095704.[18] R. Verberg, I.M. de Schepper, E.G.D. Cohen, Phys. Rev. E 61 (2000) 2967;R. Verberg, I.M. de Schepper, E.G.D. Cohen, Phys. Rev. E 55 (1997) 3143.[19] H.N.W. Lekkerkerker, W.C.K. Poon, P.N. Pusey, A. Stroobants, P.B. Warren, Europhys. Lett. 20 (1992) 559.[20] P. Bolhuis, D. Frenkel, Phys. Rev. Lett. 72 (1994) 2211.[21] E.R. Weeks, J.C. Crocker, D.A. Weitz, J. Phys. Cond. Matt. 19 (2007) 205131.[22] J.R. Savage, D.W. Blair, A.J. Levine, R.A. Guyer, A.D. Dinsmore, Science 314 (2007) 795.
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