Skip to main content
SpringerLink
Log in

Simulation and Modelling of Polymers

  • Chapter
  • First Online:
Applied Polymer Science

  • 1408 Accesses

Abstract

Theory and experiment are historically the two main tools of material science, but during the last few decades, computer simulation has emerged as an increasingly important complement. In polymer science, simulations can be used to develop polymeric materials with improved properties, to optimize the geometries of macroscopic constructions, to study polymeric materials under experimentally inaccessible conditions, to explain experimentally observed phenomena and to reduce the number of required experiments. Many simulation techniques exist, and the choice of simulation strategy depends on the characteristic time and length scales of the computational problem. Some phenomena are preferably simulated with atomistic simulation techniques, whereas others are better modelled with macroscopic methods. Multiscale modelling combines simulation methods on different time and length scales. The aim of this chapter is to provide a brief overview of the simulation techniques used in material science.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Alder, B. J., & Wainwright, T. E. (1959). Studies in molecular dynamics. I. General method. The Journal of Chemical Physics, 31(2), 459–466.

    Article  ADS  MathSciNet  Google Scholar 

  • Alexandrowicz, Z. (1998). Simulation of polymers with rebound selection. The Journal of Chemical Physics, 109(13), 5622–5626.

    Article  ADS  Google Scholar 

  • Allen, M., & Tildesley, D. (1989). Computer Simulation of Liquids. Oxford: Oxford University Press.

    MATH  Google Scholar 

  • Andersen, H. C. (1980). Molecular dynamics simulations at constant pressure and/or temperature. The Journal of Chemical Physics, 72(4), 2384–2393.

    Article  ADS  Google Scholar 

  • Andersen, M., Panosetti, C., & Reuter, K. (2019). A practical guide to surface kinetic Monte Carlo simulations. Frontiers in Chemistry, 7, 202.

    Article  ADS  Google Scholar 

  • Auhl, R., Everaers, R., Grest, G. S., Kremer, K., & Plimpton, S. J. (2003). Equilibration of long chain polymer melts in computer simulations. The Journal of Chemical Physics, 119(24), 12718–12728.

    Article  ADS  Google Scholar 

  • Ayers, P., Yang, W., & Bartolotti, L. (2009). Fukui function. In P. K. Chattaraj (Ed.), Chemical reactivity theory: A density functional view (pp. 255–268). Boca Raton: CRC Press.

    Google Scholar 

  • Becke, A. D. (1988). Density-functional exchange-energy approximation with correct asymptotic behavior. Physical Review A General Physics, 38(6), 3098.

    Article  ADS  Google Scholar 

  • Bingham, R. C., Dewar, M. J., & Lo, D. H. (1975). Ground states of molecules. XXVI. MINDO/3 calculations for hydrocarbons. Journal of the American Chemical Society, 97(6), 1294–1301.

    Article  Google Scholar 

  • Blumers, A. L., Tang, Y.-H., Li, Z., Li, X., & Karniadakis, G. E. (2017). GPU-accelerated red blood cells simulations with transport dissipative particle dynamics. Computer Physics Communications, 217, 171–179.

    Article  ADS  Google Scholar 

  • Bock, F. E., Aydin, R. C., Cyron, C. J., Huber, N., Kalidindi, S. R., & Klusemann, B. (2019). A review of the application of machine learning and data mining approaches in continuum materials mechanics. Frontiers in Materials, 6, 110.

    Article  ADS  Google Scholar 

  • Bondi, A. A. (1968). Physical properties of molecular crystals liquids, and glasses. New York: Wiley.

    Google Scholar 

  • Born, M., & Oppenheimer, R. (1927). Zur quantentheorie der molekeln. Annalen der Physik, 389(20), 457–484.

    Article  ADS  MATH  Google Scholar 

  • Brenner, S., & Scott, L. (2008). The mathematical theory of finite element methods texts in applied mathematics. Berlin: Springer.

    Google Scholar 

  • Buckingham, R. A. (1938). The classical equation of state of gaseous helium, neon and argon. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 168(933), 264–283.

    ADS  Google Scholar 

  • Chatterjee, A., & Vlachos, D. G. (2007). An overview of spatial microscopic and accelerated kinetic Monte Carlo methods. Journal of Computer-Aided Materials Design, 14(2), 253–308.

    Article  ADS  Google Scholar 

  • Cook, R. D. (2007). Concepts and applications of finite element analysis. New York: John Wiley & Sons.

    Google Scholar 

  • Coulomb, C. A. (1785). Second mémoire sur l’électricité et le magnétisme. Histoire de l’Académie Royale des Sciences, 579, 578–611.

    Google Scholar 

  • Courant, R. (1943). Variational methods for the solution of problems of equilibrium and vibrations. Bulletin of the American Mathematical Society, 49, 1–23. https://doi.org/10.1090/S0002-9904-1943-07818-4.

    Article  MathSciNet  MATH  Google Scholar 

  • Cramer, C. J. (2004). Essentials of computational chemistry: theories and models (2nd ed.). Chichester: John Wiley & Sons.

    Google Scholar 

  • Deuflhard, P., & Bornemann, F. (2002). Scientific computing with ordinary differential equations. New York: Springer Science & Business Media.

    Book  MATH  Google Scholar 

  • Dijkstra, M. (1997). Confined thin films of linear and branched alkanes. The Journal of Chemical Physics, 107(8), 3277–3288.

    Article  ADS  Google Scholar 

  • Einstein, A. (1905). On the motion of small particles suspended in liquids at rest required by the molecular-kinetic theory of heat. Annalen der Physik, 17(549–560), 208.

    Google Scholar 

  • Eriksson, G. (2002). Kompendium i tillämpade numeriska metoder. Stockholm: KTH Department of Numerical Analysis and Computer Science.

    Google Scholar 

  • Evans, L. (2010). Partial differential equations (2nd ed.). Providence, R.I: American Mathematical Society.

    MATH  Google Scholar 

  • Fermi, E., Pasta, J., & Ulam, S. (1955). Los alamos report la-1940. Fermi. Collected Papers, 2, 977–988.

    Google Scholar 

  • Flory, P. J. (1989). Statistical mechanics of chain molecules (Vol. 5). Munich: Hanser Publishers.

    Google Scholar 

  • Fock, V. (1930). Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems. Zeitschrift für Physik, 61(1–2), 126–148.

    Article  ADS  MATH  Google Scholar 

  • Fredenslund, A., Jones, R. L., & Prausnitz, J. M. (1975). Group-contribution estimation of activity coefficients in nonideal liquid mixtures. AICHE Journal, 21(6), 1086–1099.

    Article  Google Scholar 

  • Frenkel, D., & Smit, B. (2002). Understanding molecular simulation: from algorithms to applications (2nd ed.). San Diego: Academic Press.

    MATH  Google Scholar 

  • Galerkin, B. (1915). Rods and plates. Series occurring in various questions concerning the elastic equilibrium of rods and plates. Eng. Bull(Vestnik Inzhenerov) 19:897–908 (in Russian), (English Translation: 863–18925, Clearinghouse Fed. Sci. Tech. Info. 11963

    Google Scholar 

  • Gartner, T. E., & Jayaraman, A. (2019). Modeling and simulations of polymers: A roadmap. Macromolecules, 52(3), 755–786.

    Article  ADS  Google Scholar 

  • Gedde, U. W., & Hedenqvist, M. S. (2019). Fundamental polymer science (2nd ed.). Cham: Springer.

    Book  Google Scholar 

  • Gedde, U. W., & Hedenqvist, M. S. (2019a). Introduction to polymer science (Chap. 1). In Fundamental Polymer Science. Cham: Springer Nature Switzerland AG.

    Google Scholar 

  • Gedde, U. W., & Hedenqvist, M. S. (2019b). Conformations in Polymers (Chap. 2). In Fundamental Polymer Science. Cham: Springer Nature Switzerland AG

    Google Scholar 

  • Gibson, J., Goland, A. N., Milgram, M., & Vineyard, G. (1960). Dynamics of radiation damage. Physical Review, 120(4), 1229.

    Article  ADS  Google Scholar 

  • Gottlieb, D., & Orszag, S. A. (1977). Numerical analysis of spectral methods: Theory and applications. Philadelphia: SIAM. https://doi.org/10.1137/1.9781611970425.

    Book  MATH  Google Scholar 

  • Hairer, E., & Wanner, G. (1996). Solving ordinary differential equations II stiff and differential-algebraic problems (2nd ed.). Berlin: Springer Berlin Heidelberg.

    MATH  Google Scholar 

  • Hairer, E., Nørsett, S. P., & Wanner, G. (1993). Solving ordinary differential equations I. Nonstiff problems (2nd ed.). Berlin: Springer Series in Computational Mathematics.

    MATH  Google Scholar 

  • Hall, G. (1951). The molecular orbital theory of chemical valency VIII. A method of calculating ionization potentials. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 205(1083), 541–552.

    ADS  MATH  Google Scholar 

  • Hansen, C. (2007). Hansen solubility parameters: A user’s handbook (2nd ed.). Boca Raton: CRC/Taylor & Francis.

    Book  Google Scholar 

  • Hansen, J., & McDonald, I. (1986). Theory of simple liquids (2nd ed.). London: Academic Press.

    MATH  Google Scholar 

  • Hartree, D. R. (1928). The wave mechanics of an atom with a non-coulomb central field. Part II. Some results and discussion. In: Mathematical Proceedings of the Cambridge Philosophical Society, vol 1. Cambridge University Press, pp 89–110.

    Google Scholar 

  • Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1), 97–109.

    Article  MathSciNet  MATH  Google Scholar 

  • Heath, M. (1997). Scientific computing: An introductory survey (2nd ed.). New York: McFraw-Hill Companies.

    MATH  Google Scholar 

  • Hehre, W. J., Stewart, R. F., & Pople, J. A. (1969). Self-consistent molecular-orbital methods. i. Use of gaussian expansions of Slater-type atomic orbitals. The Journal of Chemical Physics, 51(6), 2657–2664.

    Article  ADS  Google Scholar 

  • Hoffmann, R. (1963). An extended Hückel theory. I. hydrocarbons. The Journal of Chemical Physics, 39(6), 1397–1412.

    Article  ADS  Google Scholar 

  • Hohenberg, P., & Kohn, W. (1964). Inhomogeneous electron gas. Physical Review, 136(3B), B864.

    Article  ADS  MathSciNet  Google Scholar 

  • Hoogerbrugge, P., & Koelman, J. (1992). Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. EPL (Europhysics Letters), 19(3), 155.

    Article  ADS  Google Scholar 

  • Hoover, W. G. (1985). Canonical dynamics: Equilibrium phase-space distributions. Physical Review A, General Physics, 31(3), 1695.

    Article  ADS  Google Scholar 

  • Hückel, E. (1931). Quantentheoretische beiträge zum benzolproblem. Zeitschrift für Physik, 70(3–4), 204–286.

    Article  ADS  MATH  Google Scholar 

  • in’t Veld, P. J., & Rutledge, G. C. (2003). Temperature-dependent elasticity of a semicrystalline interphase composed of freely rotating chains. Macromolecules, 36(19), 7358–7365.

    Article  ADS  Google Scholar 

  • Kanazawa, T., Asahara, A., & Morita, H. (2019). Accelerating small-angle scattering experiments with simulation-based machine learning. Journal of Physics: Materials, 3(1), 015001.

    ADS  Google Scholar 

  • Karatrantos, A., Clarke, N., & Kröger, M. (2016). Modeling of polymer structure and conformations in polymer nanocomposites from atomistic to mesoscale: A review. Polymer Reviews, 56(3), 385–428.

    Article  Google Scholar 

  • Karayiannis, N. C., Giannousaki, A. E., & Mavrantzas, V. G. (2003). An advanced Monte Carlo method for the equilibration of model long-chain branched polymers with a well-defined molecular architecture: Detailed atomistic simulation of an H-shaped polyethylene melt. The Journal of Chemical Physics, 118(6), 2451–2454.

    Article  ADS  Google Scholar 

  • Kim, K., & Jordan, K. (1994). Comparison of density functional and MP2 calculations on the water monomer and dimer. Journal of Physical Chemistry, 98(40), 10089–10094.

    Article  Google Scholar 

  • Kmiecik, S., Gront, D., Kolinski, M., Wieteska, L., Dawid, A. E., & Kolinski, A. (2016). Coarse-grained protein models and their applications. Chemical Reviews, 116(14), 7898–7936.

    Article  Google Scholar 

  • Kohn, W., & Sham, L. J. (1965). Self-consistent equations including exchange and correlation effects. Physical Review, 140(4A), A1133.

    Article  ADS  MathSciNet  Google Scholar 

  • Kremer, K., & Binder, K. (1988). Monte Carlo simulation of lattice models for macromolecules. Computer Physics Reports, 7(6), 259–310.

    Article  ADS  Google Scholar 

  • Kremer, K., & Grest, G. S. (1990). Dynamics of entangled linear polymer melts: A molecular-dynamics simulation. The Journal of Chemical Physics, 92(8), 5057–5086.

    Article  ADS  Google Scholar 

  • Ladd, A. J. (1993). Short-time motion of colloidal particles: Numerical simulation via a fluctuating lattice-Boltzmann equation. Physical Review Letters, 70(9), 1339.

    Article  ADS  Google Scholar 

  • Larson, M. G., & Bengzon, F. (2013). The finite element method: theory, implementation, and applications (Vol. 10). Berlin Heidelberg: Springer Science & Business Media.

    Book  MATH  Google Scholar 

  • Leach, A. R. (2001). Molecular modelling: principles and applications (2nd ed.). Harlow: Pearson Education.

    Google Scholar 

  • Lee, T. S., York, D. M., & Yang, W. (1996). Linear-scaling semiempirical quantum calculations for macromolecules. The Journal of Chemical Physics, 105(7), 2744–2750.

    Article  ADS  Google Scholar 

  • Leibniz, G. (1697). Communicatio suae pariter, duarumque alienarum ad adendum sibi primum a Dn. Jo. Bernoullio, deinde a Dn. Marchione Hospitalio communicatarum solutionum problematis curvae celerrimi descensus a Dn. Jo. Bernoullio geometris publice propositi, una cum solutione sua problematis alterius ab eodem postea propositi. Acta Eruditorum, 16, 201–205.

    Google Scholar 

  • Lemarchand, C., Bousquet, D., Schnell, B., & Pineau, N. (2019). A parallel algorithm to produce long polymer chains in molecular dynamics. The Journal of Chemical Physics, 150(22), 224902.

    Article  ADS  Google Scholar 

  • Lennard-Jones, J. E. (1924). On the determination of molecular fields. Proceedings of the Royal Society of London A, 106, 463–477.

    ADS  Google Scholar 

  • Lennard-Jones, J. E. (1929). The electronic structure of some diatomic molecules. Transactions of the Faraday Society, 25, 668–686.

    Article  MATH  Google Scholar 

  • LeVeque, R. J. (2002). Finite volume methods for hyperbolic problems. Cambridge: Cambridge University Press.

    Book  MATH  Google Scholar 

  • Levitt, M., & Warshel, A. (1975). Computer simulation of protein folding. Nature, 253(5494), 694–698.

    Article  ADS  Google Scholar 

  • Liu, Y., Zhao, T., Ju, W., & Shi, S. (2017). Materials discovery and design using machine learning. Journal of Materiomics, 3(3), 159–177.

    Article  Google Scholar 

  • Liu, Y., Niu, C., Wang, Z., Gan, Y., Zhu, Y., Sun, S., & Shen, T. (2020). Machine learning in materials genome initiative: A review. Journal of Materials Science and Technology, 57, 113–122.

    Article  Google Scholar 

  • Lyubartsev, A. P. (2017). Inverse Monte Carlo methods. In G. Papoian (Ed.), Coarse-grained modeling of biomolecules (pp. 29–54). Boca Raton: CRC Press.

    Google Scholar 

  • Maday, Y., & Patera, A. T. (1989). Spectral element methods for the incompressible Navier-Stokes equations. In A. Noor (Ed.), State-of-the-art surveys on computational mechanics (pp. 71–143). New York: ASME.

    Google Scholar 

  • Malevanets, A., & Kapral, R. (2000). Solute molecular dynamics in a mesoscale solvent. The Journal of Chemical Physics, 112(16), 7260–7269.

    Article  ADS  Google Scholar 

  • Martin, M. G., & Siepmann, J. I. (1999). Novel configurational-bias Monte Carlo method for branched molecules. Transferable potentials for phase equilibria. 2. United-atom description of branched alkanes. The Journal of Physical Chemistry B, 103(21), 4508–4517.

    Article  Google Scholar 

  • Masubuchi, Y., & Uneyama, T. (2018). Comparison among multi-chain models for entangled polymer dynamics. Soft Matter, 14(29), 5986–5994.

    Article  ADS  Google Scholar 

  • Mattice, W. L., & Suter, U. W. (1994). Conformational theory of large molecules: the rotational isomeric state model in macromolecular systems. New York: Wiley-Interscience.

    Google Scholar 

  • McCammon, J. A., Gelin, B. R., & Karplus, M. (1977). Dynamics of folded proteins. Nature, 267(5612), 585–590.

    Article  ADS  Google Scholar 

  • Meirovitch, H. (1988). Statistical properties of the scanning simulation method for polymer chains. The Journal of Chemical Physics, 89(4), 2514–2522.

    Article  ADS  Google Scholar 

  • Metropolis, N. (1987). The beginning of the Monte Carlo method. Los Alamos Science, 15(15 Special Issue, Stanislaw Ulam 1909–1984), 125–130.

    MathSciNet  Google Scholar 

  • Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953). Equation of state calculations by fast computing machines. The Journal of Chemical Physics, 21(6), 1087–1092.

    Article  ADS  MATH  Google Scholar 

  • Moore, T. C., Iacovella, C. R., & McCabe, C. (2014). Derivation of coarse-grained potentials via multistate iterative Boltzmann inversion. The Journal of Chemical Physics, 140(22), 06B606_601.

    Article  Google Scholar 

  • Morse, P. M. (1929). Diatomic molecules according to the wave mechanics. II. Vibrational levels. Physical Review, 34(1), 57.

    Article  ADS  MATH  Google Scholar 

  • Mountain, R. D., & Thirumalai, D. (1994). Quantative measure of efficiency of Monte Carlo simulations. Physica A: Statistical Mechanics and its Applications, 210(3–4), 453–460.

    Article  ADS  Google Scholar 

  • Moyassari, A., Unge, M., Hedenqvist, M. S., Gedde, U. W., & Nilsson, F. (2017). First-principle simulations of electronic structure in semicrystalline polyethylene. The Journal of Chemical Physics, 146(20), 204901.

    Article  ADS  Google Scholar 

  • Müller-Plathe, F. (2002). Coarse-graining in polymer simulation: from the atomistic to the mesoscopic scale and back. ChemPhysChem, 3(9), 754–769.

    Article  Google Scholar 

  • Nairn, J. (2003). NairnFEAMPM A Macintosh application. Salt Lake City: Department of materials science and engineering, University of Utah.

    Google Scholar 

  • Nakamura, K., Ankyu, S., Nilsson, F., Kanno, T., Niwano, Y., von Steyern, P. V., & Örtengren, U. (2018). Critical considerations on load-to-failure test for monolithic zirconia molar crowns. Journal of the Mechanical Behavior of Biomedical Materials, 87, 180–189.

    Article  Google Scholar 

  • Nanda, D., & Jug, K. (1980). SINDO1. A semiempirical SCF MO method for molecular binding energy and geometry I. Approximations and parametrization. Theoretica Chimica Acta, 57(2), 95–106.

    Article  Google Scholar 

  • Newton I (1687). Philosophiae naturalis principia mathematica. Reg Soc Praeses, London, 2, 1–4.

    Google Scholar 

  • Nilsson, F., Gedde, U. W., & Hedenqvist, M. S. (2009). Penetrant diffusion in polyethylene spherulites assessed by a novel off-lattice Monte-Carlo technique. European Polymer Journal, 45(12), 3409–3417.

    Article  Google Scholar 

  • Nilsson, F., Krueckel, J., Schubert, D. W., Chen, F., Unge, M., Gedde, U. W., & Hedenqvist, M. S. (2016). Simulating the effective electric conductivity of polymer composites with high aspect ratio fillers. Composites Science and Technology, 132, 16–23.

    Article  Google Scholar 

  • Nosé, S. (1984). A unified formulation of the constant temperature molecular dynamics methods. The Journal of Chemical Physics, 81(1), 511–519.

    Article  ADS  Google Scholar 

  • Orszag, S. A. (1972). Comparison of pseudospectral and spectral approximation. Studies in Applied Mathematics, 51(3), 253–259.

    Article  MathSciNet  MATH  Google Scholar 

  • Páll, S., Abraham, M. J., Kutzner, C., Hess, B., & Lindahl, E. (2014). Tackling exascale software challenges in molecular dynamics simulations with GROMACS. In International conference on exascale applications and software (pp. 3–27). Cham: Springer.

    Google Scholar 

  • Pallon, L., Hoang, A., Pourrahimi, A., Hedenqvist, M. S., Nilsson, F., Gubanski, S., Gedde, U., & Olsson, R. T. (2016). The impact of MgO nanoparticle interface in ultra-insulating polyethylene nanocomposites for high voltage DC cables. Journal of Materials Chemistry A, 4(22), 8590–8601.

    Article  Google Scholar 

  • Pallon, L. K., Nilsson, F., Yu, S., Liu, D., Diaz, A., Holler, M., Chen, X. R., Gubanski, S., Hedenqvist, M. S., & Olsson, R. T. (2017). Three-dimensional nanometer features of direct current electrical trees in low-density polyethylene. Nano Letters, 17(3), 1402–1408.

    Article  ADS  Google Scholar 

  • Pangali, C., Rao, M., & Berne, B. (1978). On a novel Monte Carlo scheme for simulating water and aqueous solutions. Chemical Physics Letters, 55(3), 413–417.

    Article  ADS  Google Scholar 

  • Park, J., & Paul, D. (1997). Correlation and prediction of gas permeability in glassy polymer membrane materials via a modified free volume based group contribution method. Journal of Membrane Science, 125(1), 23–39.

    Article  Google Scholar 

  • Pople, J., & Beveridge, D. (1970). Approximate molecular orbital theory. New York: McGraw-Hill.

    Google Scholar 

  • Pople, J. A., Santry, D. P., & Segal, G. A. (1965). Approximate self-consistent molecular orbital theory. I. Invariant procedures. The Journal of Chemical Physics, 43(10), S129–S135.

    Article  ADS  Google Scholar 

  • Pople, J., Beveridge, D., & Dobosh, P. (1967). Approximate self-consistent molecular-orbital theory. V. Intermediate neglect of differential overlap. The Journal of Chemical Physics, 47(6), 2026–2033.

    Article  ADS  Google Scholar 

  • Pyzer-Knapp, E. O., Li, K., & Aspuru-Guzik, A. (2015). Learning from the harvard clean energy project: The use of neural networks to accelerate materials discovery. Advanced Functional Materials, 25(41), 6495–6502.

    Article  Google Scholar 

  • Quateroni, A., Sacco, R., & Saleri, F. (2000). Numerical mathematics. In Applied mathematics (Vol. 37). New York: Springer.

    Google Scholar 

  • Rahman, A. (1964). Correlations in the motion of atoms in liquid argon. Physical Review, 136(2A), A405.

    Article  ADS  Google Scholar 

  • Rao, M., & Berne, B. (1979). On the force bias Monte Carlo simulation of simple liquids. The Journal of Chemical Physics, 71(1), 129–132.

    Article  ADS  Google Scholar 

  • Rapaport, D. C. (1996). The art of molecular dynamics simulation. Cambridge: Cambridge University Press.

    MATH  Google Scholar 

  • Rayleigh, J. (1877). The theory of sound, (edition of 1945). London: Macmillan and co.

    Google Scholar 

  • Reddy, J. N. (1993). An introduction to the finite element method. New York: McGraw-Hill.

    Google Scholar 

  • Reith, D., Pütz, M., & Müller-Plathe, F. (2003). Deriving effective mesoscale potentials from atomistic simulations. Journal of Computational Chemistry, 24(13), 1624–1636.

    Article  Google Scholar 

  • Ritz, W. (1909). Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik. Journal für die reine und angewandte Mathematik (Crelles Journal), 1909(135), 1–61.

    Article  MATH  Google Scholar 

  • Roothaan, C. C. J. (1951). New developments in molecular orbital theory. Reviews of Modern Physics, 23(2), 69.

    Article  ADS  MATH  Google Scholar 

  • Rosenbluth, M. N., & Rosenbluth, A. W. (1955). Monte Carlo calculation of the average extension of molecular chains. The Journal of Chemical Physics, 23(2), 356–359.

    Article  ADS  Google Scholar 

  • Rossky, P. J., Doll, J., & Friedman, H. (1978). Brownian dynamics as smart Monte Carlo simulation. The Journal of Chemical Physics, 69(10), 4628–4633.

    Article  ADS  Google Scholar 

  • Schellbach, K. (1851). Probleme der Variationsrechnung. Journal fur die Reine und Angewandte Mathematik, 1851(41), 293–363.

    Article  MathSciNet  Google Scholar 

  • Schrödinger, E. (1926). An undulatory theory of the mechanics of atoms and molecules. Physical Review, 28(6), 1049–1070.

    Article  ADS  Google Scholar 

  • Seifert, G., Eschrig, H., & Bieger, W. (1986). An approximation variant of LCAO-X-ALPHA methods. Zeitschrift Fur Physikalische Chemie-Leipzig, 267(3), 529–539.

    Google Scholar 

  • Siepmann, J. I., & Frenkel, D. (1992). Configurational bias Monte Carlo: A new sampling scheme for flexible chains. Molecular Physics, 75(1), 59–70.

    Article  ADS  Google Scholar 

  • Slater, J. C. (1929). The theory of complex spectra. Physical Review, 34(10), 1293.

    Article  ADS  MATH  Google Scholar 

  • Sliozberg, Y. R., Kröger, M., & Chantawansri, T. L. (2016). Fast equilibration protocol for million atom systems of highly entangled linear polyethylene chains. The Journal of Chemical Physics, 144(15), 154901.

    Article  ADS  Google Scholar 

  • Stein, E. (2014). History of the finite element method–mathematics meets mechanics–part I: Engineering developments. In The history of theoretical, material and computational mechanics-mathematics meets mechanics and engineering (pp. 399–442). Berlin, Heidelberg: Springer.

    Chapter  MATH  Google Scholar 

  • Stillinger, F. H., & Rahman, A. (1974). Improved simulation of liquid water by molecular dynamics. The Journal of Chemical Physics, 60(4), 1545–1557.

    Article  ADS  Google Scholar 

  • Strang, G. (1986). Introduction to applied mathematics. Wellesley: Wellesley-Cambridge Press.

    MATH  Google Scholar 

  • Szabo, A., & Ostlund, N. S. (1996). Modern quantum chemistry: Introduction to advanced electronic structure theory. Mineola: Dover Science Books.

    Google Scholar 

  • Thomas, J. W. (1999). Numerical partial differential equations: conservation laws and elliptic equations – Conservation Laws and Elliptic Equations, Vol 33. Springer Science & Business Media

    Google Scholar 

  • Urey, H. C., & Bradley, C. A., Jr. (1931). The vibrations of pentatonic tetrahedral molecules. Physical Review, 38(11), 1969.

    Article  ADS  MATH  Google Scholar 

  • van der Giessen, E., Schultz, P. A., Bertin, N., Bulatov, V. V., Cai, W., Csányi, G., Foiles, S. M., Geers, M. G., González, C., & Hütter, M. (2020). Roadmap on multiscale materials modeling. Modelling and Simulation in Materials Science and Engineering, 28(4), 043001.

    Article  ADS  Google Scholar 

  • Van Gunsteren, W. F., & Berendsen, H. J. (1990). Computer simulation of molecular dynamics: methodology, applications, and perspectives in chemistry. Angewandte Chemie International Edition in English, 29(9), 992–1023.

    Article  Google Scholar 

  • Van Krevelen, D. W., & Te Nijenhuis, K. (2009). Properties of polymers: their correlation with chemical structure; their numerical estimation and prediction from additive group contributions (4th ed.). Amsterdam: Elsevier.

    Google Scholar 

  • Verdier, P. H., & Stockmayer, W. (1962). Monte Carlo calculations on the dynamics of polymers in dilute solution. The Journal of Chemical Physics, 36(1), 227–235.

    Article  ADS  Google Scholar 

  • Verlet, L. (1967). Computer “experiments” on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Physical Review, 159(1), 98.

    Article  ADS  Google Scholar 

  • Versteeg, H. K., & Malalasekera, W. (2007). An introduction to computational fluid dynamics: the finite volume method (2nd ed.). Harlow: Pearson Education.

    Google Scholar 

  • Warshel, A., & Levitt, M. (1976). Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. Journal of Molecular Biology, 103(2), 227–249.

    Article  Google Scholar 

  • Widom, B. (1963). Some topics in the theory of fluids. The Journal of Chemical Physics, 39(11), 2808–2812.

    Article  ADS  Google Scholar 

  • Young, W., & Elcock, E. (1966). Monte Carlo studies of vacancy migration in binary ordered alloys: I. Proceedings of the Physical Society, 89(3), 735.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fibre and Polymer Technology, KTH Royal Institute of Technology, Stockholm, Sweden

    Ulf W. Gedde, Mikael S. Hedenqvist, Minna Hakkarainen & Fritjof Nilsson

  2. Structural and Fire Engineering Division, Department of Civil, Environmental and Natural Resources Engineering, Luleå University of Technology, Luleå, Sweden

    Oisik Das

Authors
  1. Ulf W. Gedde
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mikael S. Hedenqvist
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Minna Hakkarainen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Fritjof Nilsson
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Oisik Das
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ulf W. Gedde .

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Gedde, U.W., Hedenqvist, M.S., Hakkarainen, M., Nilsson, F., Das, O. (2021). Simulation and Modelling of Polymers. In: Applied Polymer Science. Springer, Cham. https://doi.org/10.1007/978-3-030-68472-3_5

Download citation

Publish with us

Policies and ethics

Search

Navigation