Effects of polydispersity on hard sphere crystals

See Eng Phan, William B. Russel, Jixiang Zhu, Paul M. Chaikin

    Research output: Contribution to journalArticle

    Abstract

    We use simple models and molecular dynamics simulations to determine the effects of polydispersity δ on the equation of state for hard sphere crystals. Experiments show that the osmotic pressure for poly-(methyl methacrylate) (PMMA) spheres with a poly-(12-hydroxy stearic acid) (PHSA) layer with a 5% polydispersity exceeds the value expected for hard spheres as the volume fraction φ increases, particularly for φ>0.60. Mean field theory predicts a higher osmotic pressure with increasing polydispersity, but the effects are only significant for δ>0.10. Molecular dynamics simulations with δ=0.05 bound the equation of state between a metastable disordered upper limit and a crystalline organized polydisperse (possibly) lower limit. The pressure for the PMMA-PHSA spheres lies close to the organized polydisperse limit, indicating a preference for a crystalline ordered arrangement where smaller particles surround larger ones. Thus, the higher osmotic pressure seen in the equation of state of PMMA-PHSA spheres is a direct effect of polydispersity, manifest as a pronounced reduction in the crystalline close packed volume fraction from φmax(FCC, δ=0)=0.7404 to φmax(FCC, δ=0.1)=0.665. The random close packing φmax(RCP) is almost independent of polydispersity. This leads to a crossing of values of φmax(FCC) and φmax(RCP) and hence a possible terminal polydispersity of 0.12±0.01, consistent with other simulations, theories, and experiments. Since our results do not include size fractionation of the liquid and solid, the exact meaning of this crossing is unclear and its agreement with previously reported terminal polydispersities may be coincidental.

    Original languageEnglish (US)
    Pages (from-to)9789-9795
    Number of pages7
    JournalJournal of Chemical Physics
    Volume108
    Issue number23
    StatePublished - Jun 15 1998

    Fingerprint

    Polydispersity
    osmosis
    Crystals
    polymethyl methacrylate
    equations of state
    Polymethyl Methacrylate
    crystals
    Equations of state
    acids
    Crystalline materials
    molecular dynamics
    Molecular dynamics
    Volume fraction
    simulation
    fractionation
    dynamic models
    Mean field theory
    Computer simulation
    Fractionation
    Experiments

    ASJC Scopus subject areas

    • Atomic and Molecular Physics, and Optics

    Cite this

    Phan, S. E., Russel, W. B., Zhu, J., & Chaikin, P. M. (1998). Effects of polydispersity on hard sphere crystals. Journal of Chemical Physics, 108(23), 9789-9795.

    Effects of polydispersity on hard sphere crystals. / Phan, See Eng; Russel, William B.; Zhu, Jixiang; Chaikin, Paul M.

    In: Journal of Chemical Physics, Vol. 108, No. 23, 15.06.1998, p. 9789-9795.

    Research output: Contribution to journalArticle

    Phan, SE, Russel, WB, Zhu, J & Chaikin, PM 1998, 'Effects of polydispersity on hard sphere crystals', Journal of Chemical Physics, vol. 108, no. 23, pp. 9789-9795.
    Phan SE, Russel WB, Zhu J, Chaikin PM. Effects of polydispersity on hard sphere crystals. Journal of Chemical Physics. 1998 Jun 15;108(23):9789-9795.
    Phan, See Eng ; Russel, William B. ; Zhu, Jixiang ; Chaikin, Paul M. / Effects of polydispersity on hard sphere crystals. In: Journal of Chemical Physics. 1998 ; Vol. 108, No. 23. pp. 9789-9795.
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