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Distribution of the Distance Between Receptors of Ordered Micropatterned Substrates

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Part of the book series: Lecture Notes in Electrical Engineering ((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.

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References

  1. See, e.g. Intelligent Substrate Inc., Micropatterned substrates: Highlights from the literature. Available: www.intelligentsubstrates.com/Applications/Applications.html

  2. Crosby AJ, Hageman M, Duncan A (2005) Controlling polymer adhesion with ‘Pancakes’. Langmuir 21:11738–11743

    Article  Google Scholar 

  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):572–577

    Article  Google Scholar 

  4. Zheng H, Lee I, Rubner MF, Hammond PT (2002) Two component particle arrays on patterned polyelectrolyte multilayer template. Adv Mater 14(8):569–572

    Article  Google Scholar 

  5. Azioune A, Capri N, Tseng Q, Théry M, Piel M (2010) Protein micropatterns: a direct protocol using deep UVs. Methods Cell Biol 97:133–146

    Article  Google Scholar 

  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. 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 6:485–490

    Article  Google Scholar 

  8. Lee I, Wool RP (2000) Polymer adhesion vs. substrate receptor group. Macromolecules 33:2680–2687

    Article  Google Scholar 

  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. Raghavan S, Chen ChS (2004) Micropatterned Environments in Cell Biology. Adv Mater 16(15):1303–1313

    Article  Google Scholar 

  11. Amin R, Hwang S, Park SH (2011) Nanobiotechnology: an interaction between nanontechnology and biotechnology. NANO 6(2):101–111

    Article  Google Scholar 

  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):511–522

    Article  Google Scholar 

  13. Grünbaum B, Shepard G (1986) Tilings and patterns. W. H. Freeman, New York

    Google Scholar 

  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–R61

    Article  MathSciNet  MATH  Google Scholar 

  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):147–159

    Article  MathSciNet  MATH  Google Scholar 

  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 296–304

    Google Scholar 

  17. Rakenburg IC, Zieve RJ (2001) Influence of shape on ordering of granular systems in two dimensions. Phys Rev E 63(6):61303

    Article  Google Scholar 

  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. 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 604–608

    Google Scholar 

  20. Domański Z (2011) Efficiency of two-dimensional microfilters. AIP Conf Proc 1373:211–220

    Article  Google Scholar 

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Correspondence to Zbigniew Domański .

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Domański, Z., Sczygiol, N. (2013). Distribution of the Distance Between Receptors of Ordered Micropatterned Substrates. In: Kim, H., Ao, SI., Rieger, B. (eds) IAENG Transactions on Engineering Technologies. Lecture Notes in Electrical Engineering, vol 170. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4786-9_24

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  • DOI: https://doi.org/10.1007/978-94-007-4786-9_24

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-4785-2

  • Online ISBN: 978-94-007-4786-9

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