高分子運動學的研究已經有很長的歷史，在自然環境中可以觀察到生物大分子的擴散行為，很多交互運動仍在研究中，例如DNA在細胞膜上的擴散係數與覆蓋率的關係呈一Λ型線，擴散係數隨覆蓋率上升的原因尚未被了解。我們的震動台和珠鏈實驗則可以藉由碰撞行為和已有的高分子動力學模型來說明這些現象。我們選擇垂直震動中的珠鏈來模擬分子鏈的運動，來探討珠鏈的質心在二維表面上，水平投影的運動特性，再藉由質心的位移來討論在不同鏈長、不同表面覆蓋率，以及不同表面材質下的運動行為。從改變表面材質的實驗，得到擴散係數與鏈長的指數率呈現不同的數值。我們發現震動中的珠鏈質心運動確實具有隨機行走的行為，也已經成功的重現高分子在膜表面的Λ型數據線。我們觀察到在表面覆蓋率0.08以下的區域，珠鏈之間相互碰撞使得珠鏈被瞬間加速的機會提高，增加表面覆蓋率會使得擴散係數明顯上升。擴散係數在覆蓋率0.08時達到最大值，而覆蓋率越高時，擴散係數的變化卻完全相反，過了最大值之後快速下降而後趨緩，在鋁板上得到擴散係數與鏈長有〖D∝N〗^(-１)的關係。在粗砂紙表面觀察到擴散係數變小，指數也是-1。在海綿上除了看到擴散係數變小之外，指數變為-0.76。在”non-slip”的表面觀察到指數率變為-1.51，並且完全看不到Λ型的趨勢，我們相信”non-slip” 的表面性質造成每一次碰撞後細微的位移變化就足以導致此現象消失。

[1] P. G. de Gennes, Scaling Concepts in Polymer Physics, Cornell Univ. Press:
Ithaca, NY (1979)
[2] M. Doi and S. F. Edwards, The Theory of Polymer Dynamics, Clarendon Press: Oxford, UK (1986)
[3] Debashish Mukherji and Martin H. Müser, Possible explanation of the Λ-shape anomaly in polymer surface diffusion, Phys. Rev. E 74, 010601(R) (2006) [4 pages]
[4] Debashish Mukherji, Guido Bartels, and Martin H. Müser, Scaling Laws of Single Polymer Dynamics near Attractive Surfaces, Phys. Rev. Lett. 100, 068301 (2008) [4 pages]
[5] Berenike Maier and Joachim O. Rädler, DNA on fluid membranes: a model polymer in two dimensions, Macromolecules, 33, 7185-7194 (2000)
[6] Wennan Chen and Kiwing To, Unusual diffusion in a quasi-two-dimensional granular gas, Phys. Rev. E 80, 061305 (2009) [4 pages]
[7] Hu-Jun Qian, Li-Jun Chen, Zhong-Yuan Lu*, and Ze-Sheng Li, Surface Diffusion Dynamics of a Single Polymer Chain in Dilute Solution, Phys. Rev. Lett. 99, 068301 (2007) [4 pages]
[8] Kevin Safford, Yacov Kantor, Mehran Kardar, and Arshad Kudrolli, Structure and dynamics of vibrated granular chains: Comparison to equilibrium polymers,
Phys. Rev. E 79, 061304 (2009) [4 pages]
[9] Debashish Mukherji and Martin H. Müser, Glassy Dynamics, Aging in Mobility, and Structural Relaxation of Strongly Adsorbed Polymer Films:  Corrugation or Confinement, Macromolecules, 40 (5), 1754–1762 (2007)
[10] Svetlana A. Sukhishvili, Yan Chen, Joachim D. Müller, Enrico Gratton, Kenneth S. Schweizer, and Steve Granick, Diffusion of a Polymer ‘pancake’, Nature, 406, 146 (2002)
[11] Berenike Maier and Joachim O. Rädler, Conformation and Self-Diffusion of Single DNA Molecules Confined to Two Dimension, Phys. Rev. Lett. 82, 1911–1914 (1999)
[12] Arshad Kudrolli, Concentration Dependent Diffusion of Self-Propelled Rods, Phys. Rev. Lett. 104, 088001 (2010)
[13] Svetlana A. Sukhishvili, Yan Chen, Joachim D. Müller, Enrico Gratton, Kenneth S. Schweizer, and Steve Granick, Surface Diffusion of Poly(ethylene glycol), Macromolecules, 35, 1776–1784 (2002)
[14] Matthew Mears, Drew S. Tarmey and Mark Geoghegan, Single Macromolecule Diffusion in Confined Environments, Macromol. Rapid Commun. 32, 1411-1418 (2011)
[15] Tapan G. Desai, Pawel Keblinski, Sanat K. Kumar and Steve Granick, Molecular-dynamics simulations of the transport properties of a single polymer chain in two dimensions, J. Chem.Phys., 124, 084904 (2006)
[16] Bas van der Vorst, E. Matthijs Toose, Dirk van den Ende, Rob J. J. Jongschaap and Jorrit Mellema, Generalized Rouse model for a dilute solution of clustered polymers, Rheol Acta 34, 274-280 (1995)
[17] Andrzej Sikorski and Piotr Adamczyk, Diffusion of polymer chains in porous media. A Monte Carlo study, Polymer 51, 581-586 (2010)
[18] Andrey Milchev and Kurt Binder, Static and Dynamic Properties of Adsorbed Chains at Surfaces: Monte Carlo Simulation of a Bead-Spring Model, Macromolecules, 29, 343–354 (1996)
[19] Gang He and Mark O. Robbins, Simulations of the kinetic friction due to adsorbed surface layers, Tribology Latters, 10, 1-2, (2001)
[20] P. G. de Gennes, Dynamics of entangled polymer solutions, Macromolecules, 9, 4 (1976)
[21] Bruno H. Zimm, Dynamics of polymer molecules in dilute solution : viscoelasticity, flow birefringence and dielectric loss, J. Chem.Phys., 24, 2 (1956)
[22] Tapan G. Desai, Pawel Keblinski, Sanat K. Kumar and Steve Granick, Modeling diffusion of adsorbed polymer with explicit solvent, Phys. Rev. Lett., 98, 218301 (2007)
[23] Liangfang Zhang and Steve Granick, Slaved diffusion in phospholipid bilayers, PNAS, 102, 26, 9118-9121 (2005)
[24] Jiang Zhao and Steve Granick, Polymer Lateral Diffusion at the Solid−Liquid Interface, J. Am. Chem. Soc., 126 (20), 6242–6243 (2004)