Distribution of the Distance Between Receptors of Ordered Micropatterned Substrates

Chapter
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 170)

Abstract

We study the statistics of equally spaced pairs of receptors on a family of ordered flat microsubstrates whose adhesive centers form regular tessellations. We establish relationship between the symmetry of substrates and the probability density of the end-to-end polymer separation in terms of the so-called Manhattan distance.

Keywords

Distance distribution Micropatterned substrates Polymer adhesion Surface chemistry Tessellations Zigzag path statistics 

References

  1. 1.
    See, e.g. Intelligent Substrate Inc., Micropatterned substrates: Highlights from the literature. Available: www.intelligentsubstrates.com/Applications/Applications.html
  2. 2.
    Crosby AJ, Hageman M, Duncan A (2005) Controlling polymer adhesion with ‘Pancakes’. Langmuir 21:11738–11743CrossRefGoogle Scholar
  3. 3.
    Lee I, Zheng H, Rubner MF, Hammond PT (2002) Controlled cluster size in patterned particle arrays via directed adsorption on confined surfaces. Adv Mater 14(8):572–577CrossRefGoogle Scholar
  4. 4.
    Zheng H, Lee I, Rubner MF, Hammond PT (2002) Two component particle arrays on patterned polyelectrolyte multilayer template. Adv Mater 14(8):569–572CrossRefGoogle Scholar
  5. 5.
    Azioune A, Capri N, Tseng Q, Théry M, Piel M (2010) Protein micropatterns: a direct protocol using deep UVs. Methods Cell Biol 97:133–146CrossRefGoogle Scholar
  6. 6.
    Otsuka H (2010) Nanofabrication of nonfouling surfaces for micropatterning of cell and microtissue. Molecules 15:5525–5546. Available: www.mdpi.com/1420-3049/15/8/5525/pdf Google Scholar
  7. 7.
    Tikhomirov G, Hoogland S, Lee PE, Fisher A, Sargent EH, Kelly SO (2011) DNA-based programming of quantum dot valency, self-assembly and luminescence. Nat Nanotechnol 6:485–490CrossRefGoogle Scholar
  8. 8.
    Lee I, Wool RP (2000) Polymer adhesion vs. substrate receptor group. Macromolecules 33:2680–2687CrossRefGoogle Scholar
  9. 9.
    Rana N, Kossow C, Eisenbraun ET, Greer RE, Koloyeros AE (2011) Controlling interfacial adhesion of self-assembled polypeptide fibrils for novel nanoelectromechanical systems (NEMS) applications. Micromachines 2:1–16. Available: www.mdpi.com/2072-666X/2/1/1/pdf Google Scholar
  10. 10.
    Raghavan S, Chen ChS (2004) Micropatterned Environments in Cell Biology. Adv Mater 16(15):1303–1313CrossRefGoogle Scholar
  11. 11.
    Amin R, Hwang S, Park SH (2011) Nanobiotechnology: an interaction between nanontechnology and biotechnology. NANO 6(2):101–111CrossRefGoogle Scholar
  12. 12.
    Pannier AK, Anderson BC, Shea LD (2005) Substrate-mediated delivery from self-assembled monolayers: effect of surface ionization, hydrophilicity, and patterning. Acta Biomater 1(5):511–522CrossRefGoogle Scholar
  13. 13.
    Grünbaum B, Shepard G (1986) Tilings and patterns. W. H. Freeman, New YorkGoogle Scholar
  14. 14.
    Janse van Rensburg EJ (2003) Statistical mechanics of directed models of polymer in the square lattice. J Phys A: Math Gen 36(15):R11–R61MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Bender CM, Bender MA, Demaine ED, Fekete SP (2004) What is the optimal shape of a city? J Phys A: Math Gen 37(1):147–159MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Leung VJ et al (2002) Processor allocation on Cplant: achieving general processor locality using one-dimensional allocation strategies. In: Proceedings of the 4th IEEE international conference on cluster computing. Willey-Computer Society Press, Chicago, pp 296–304Google Scholar
  17. 17.
    Rakenburg IC, Zieve RJ (2001) Influence of shape on ordering of granular systems in two dimensions. Phys Rev E 63(6):61303CrossRefGoogle Scholar
  18. 18.
    Domański Z (2011) Geometry-induced transport properties of two dimensional networks. In: Schmidt M (ed) Advances in Computer Science and Engineering. InTech, Rijeka, 2011, pp 337–352. Available: www.intechweb.org/books
  19. 19.
    Domański Z, Sczygiol N (2011) Distribution of the End-to-End Distance of Polymers Trapped onto Ordered Substrates. Lecture Notes in Engineering and Computer Science 2011, WCECS 2011, 19–21 October, 2011, San Francisco, pp 604–608Google Scholar
  20. 20.
    Domański Z (2011) Efficiency of two-dimensional microfilters. AIP Conf Proc 1373:211–220CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Institute of MathematicsCzestochowa University of TechnologyCzestochowaPoland
  2. 2.Institute of Computer and Information SciencesCzestochowa University of TechnologyCzestochowaPoland

Personalised recommendations