Journal of Mathematical Chemistry

, Volume 49, Issue 5, pp 1042–1053 | Cite as

Mathematical modelling for equilibrium configurations of concentric gold nanoparticles

  • Duangkamon Baowan
  • Kittisak Chayantrakom
  • Pairote Satiracoo
  • Barry J. Cox
Original Paper

Abstract

Nanotechnology is a promising research area, and it is believed that the unique properties of molecules at the nano-scale will benefit mankind especially in the medical exploration. Here we utilize an applied mathematical modelling to investigate spherical and cylindrical concentric structures of gold nanoparticles, with the aim of maximising the free space for which to improve amount of drug or gene to bind on the nanoparticle surfaces and deliver to the target cells. The energy between two gold molecules is modelled by the 6–12 Lennard-Jones potential function, and the total potential between two layers for such particles is calculated using the continuous approximation. On minimising the energy function, the radii for five layers for the concentric sphere and likewise for the cylinder are presented. Further, the equilibrium spacing between any two layers is predicted to lie in the range 2.94–2.96 Å, for both concentric structures. There are at present no experimental or simulation results for comparison with the theoretical equilibrium configurations for concentric gold nanoparticles predicted by this study.

Keywords

Gold nanoparticles Lennard-Jones potential Mathematical modelling 

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References

  1. 1.
    Mornet S., Vasseur S., Grasset F., Duguet E.: Magnetic nanoparticle design for medical diagnosis and therapy. J. Mater. Chem. 14, 2161–2175 (2004)CrossRefGoogle Scholar
  2. 2.
    Stella B., Arpicco S., Peracchia M.T., Desmaele D., Hoebeke J., Renoir M., D’Angelo J., Cattel L., Couvreur P.: Design of folic acid-conjugated nanoparticles for drug targeting. J. Pharm. Sci. 89(11), 1452–1464 (2000)CrossRefGoogle Scholar
  3. 3.
    Pissuwan D., Valenzuela S.M., Cortie M.B.: Therapeutic possibilities of plasmonically heated gold nanoparticles. Trends Biotechnol. 24(2), 62–67 (2006)CrossRefGoogle Scholar
  4. 4.
    Pissuwan D., Valenzuela S.M., Killingsworth M.C., Xu X., Cortie M.B.: Targeted destruction of murine macrophage cells with bioconjugated gold nanorods. J. Namopart. Res 9, 1109–1124 (2007)CrossRefGoogle Scholar
  5. 5.
    Pissuwan D., Valenzuela S.M., Cortie M.B.: Prospects for gold nanorod particles in diagnostic and therapeutic applications. Biotechno. Gen. Eng. Rev. 25, 93–112 (2008)Google Scholar
  6. 6.
    D. Pissuwan, T. Niidome, M.B. Cortie, The forthcoming applications of gold nanoparticles in drug and gene delivery systems. J. Control. Release. (2009). doi:10.1016/j.jconrel.2009.12.006
  7. 7.
    P. Ghosh, G. Han, M. De, C.K. Kim, V.M. Rotello, Cold nanoparticles in delivery applications. Adv. Drug Deliv. Rev. 60(11) (2008)Google Scholar
  8. 8.
    P.C. Chen, S.C. Mwakwari, A.K. Oyelere, Gold nanoparticles: from nanomedicine to nanosensing. Nanotech. Sci. Appl. 1(45–66) (2008)Google Scholar
  9. 9.
    Bhattacharya R., Patra C.R., Earl A., Wang S., Katarya K., Lu L., Kizhakkedathu J.N., Yaszemski M.J., Greipp P.R., Mukhopadhyay D., Mukherjee P.: Attaching folic acid on gold nanoparticles using noncovalent interaction via different polyethylene glycol backbones and targeting of cancer cells. Nanomedicine 3(3), 224–238 (2007)Google Scholar
  10. 10.
    Chithrani B.D., Ghazani A.A., Chan W.C.W.: Determining the size and shape dependence of gold nanoparticle uptake into mammalian cells. Nano Lett. 6(4), 662–668 (2006)CrossRefGoogle Scholar
  11. 11.
    Pu Q., Leng Y., Zhao X., Cummings P.T.: Molecular simulations of stretching gold nanowires in solvents. Nanotechnology 18, 424007 (2007)CrossRefGoogle Scholar
  12. 12.
    Lewis L.J., Jensen P., Combe N., Barrat J.-L.: Diffusion of gold nanoclusters on graphite. Phys. Rev. B 61(23), 16084–16090 (2000)CrossRefGoogle Scholar
  13. 13.
    Arcidiacono S., Walther J.H., Poulikakos D., Passerone D., Koumoutsakos P.: Solidification of gold nanoparticles in carbon nanotubes. Phys. Rev. Lett. 94, 105502 (2005)CrossRefGoogle Scholar
  14. 14.
    Bilalbegovic G.: Structures and melting in infinite gold nanowires. Solid State Commun. 115, 73–76 (2000)CrossRefGoogle Scholar
  15. 15.
    Andrews G.E., Askey R., Roy R.: Special Functions. Cambridge University Press, Cambridge (1999)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Duangkamon Baowan
    • 1
    • 2
  • Kittisak Chayantrakom
    • 1
    • 2
  • Pairote Satiracoo
    • 1
    • 2
  • Barry J. Cox
    • 3
  1. 1.Department of Mathematics, Faculty of ScienceMahidol UniversityBangkokThailand
  2. 2.Centre of Excellence in MathematicsBangkokThailand
  3. 3.Nanomechanics Group, School of Mathematical SciencesThe University of AdelaideAdelaideAustralia

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