Abstract
The stiffness of a simple planar polymeric chain is modeled using analogies of mechanical springs arranged in series and in parallel assemblies. The stiffness of chemical bonds is resolved into two perpendicular axes defined by the longitudinal and transverse axes in the molecular plane. Using Hooke's definition of spring stiffness, the molecular stiffness of polyethylene is obtained along the longitudinal and transverse directions. This paper demonstrates the use of physical analogies and mathematical approximations for obtaining an analytical form for the stiffness of a simple single-molecule.
Similar content being viewed by others
References
J.F. Marko and E.D. Siggia, Stretching DNA, Macromolecules 28 (1995) 8759–8770.
S.B. Smith, Y. Cui and C. Bustamante, Overstretching B-DNA: The elastic response of individual double-stranded andsingle-stranded DNA molecules, Science 271 (1996) 795–799.
M.D. Wang, H. Yin, R. Landick, J. Gelles and S.M. Block, Stretching DNA with optical tweezers, Biophys. J. 72 (1997) 1335–1346.
J.C. Meiners and S.R. Quake, Femtonewton forcespectroscopy of single extended DNA molecules, Phys. Rev. Lett. 84 (2000) 5014–5017.
A.D. Mehta, M. Reif, J.A. Spudich, D.A. Smith and R.M. Simmons, Single-molecule biomechanics with optical methods, Science 283 (1999) 1689–1695.
A.F. Oberhauser, P.E. Marszalek, H.P. Erickson and J.M. Fernandez, The molecular elasticity of the extracellular matrix proteintenascin, Nature 393 (1998) 181–185.
T. Fujii, Y.L. Sun, K.A. An and Z.P. Luo, Mechanical properties of single hyaluronan molecules, J. Biomech. 35 (2002) 527–531.
R.H. Boyd and P.V.K. Pant, Simulation of glassy polyethylene starting from the equilibrated liquid, Macromolecules 24 (1991) 4078–4083.
Z. Sun, R.J. Morgan and D.N. Lewis, Calculation of crystalline modulus of syndiotactic polystyrene using molecular modeling, Polymer 33 (1992) 725–727.
Y. Jin and R.H. Boyd, Subglass chain dynamics andrelaxation in polyethylene: A molecular dynamics simulation study, J.Chem. Phys. 108 (1998) 9912–9923.
K. Fukui, B.G. Sumpter, M.D. Barnes and D.W. Noid, Molecular dynamics studies of the structure and properties of polymer nano-particles, Comput. Theor. Polym. Sci. 9 (1999) 245–254.
D.W. Noid, R.E. Tuzun and B.G. Sumpter, On the importance of quantum mechanics for nanotechnology, Nanotechnology 8 (1997) 119–125.
S.L. Mayo, B.D. Olafson and W.A GoddardIII, DREIDING: A generic force field for molecular simulations, J. Phys. Chem. 94 (1990) 8897–8909.
K. Tashiro, Molecular dynamics calculation to clarify the relationship between structure and mechanical properties of polymer crystals: the case of orthorhombic polyethylene, Comput. Theor. Polym. Sci. 11 (2001) 357–374.
D.W. Noid and G.A. Pfeffer, Short time molecular dynamics simulations: stressed polyethylene results, J. Polym. Sci. B Polym. Phys. 27 (1989) 2321–2335.
D.W. Noid, B.G. Sumpter and B. Wunderlich, Molecular dynamics simulation of twist motion in polyethylene, Macromolecules 24 (1991) 4148–4151.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lim, TC. Spring Constant Analogy for Estimating Stiffness of a Single Polyethylene Molecule. Journal of Mathematical Chemistry 34, 151–161 (2003). https://doi.org/10.1023/B:JOMC.0000004065.34221.47
Issue Date:
DOI: https://doi.org/10.1023/B:JOMC.0000004065.34221.47