Extended ensemble molecular dynamics method for constant strain rate uniaxial deformation of polymer systems

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Original languageEnglish
Pages (from-to)4396-4407
Journal / PublicationJournal of Chemical Physics
Issue number11
Publication statusPublished - 15 Sept 1997
Externally publishedYes


We describe a novel molecular dynamics (MD) method to simulate the uniaxial deformation of an amorphous polymer. This method is based on a rigorously defined statistical mechanics ensemble appropriate for describing an isothermal, displacement controlled, uniaxial stress mechanical test. The total number of particles is fixed and the normal stresses in the direction normal to the applied strain are constant, i.e., an NTLxσyyσzz ensemble. By using the Lagrangian of the extended system (i.e., including additional variables corresponding to the temperature and cross-sectional area fluctuations), we derive a set of equations of motion for the atomic coordinates and the additional variables appropriate to this ensemble. In order to avoid the short MD time step appropriate for the stiff covalent bonds along the polymer chains, we introduce bond length constraints. This is achieved using a variation of the commonly used SHAKE [J. P. Ryckaert, G. Ciccotti, and H. J. C. Berendsen, J. Comp. Phys. 23, 327 (1977)] algorithm. A numerical method for integrating the equations of motion with constraints via a modification of the velocity Verlet [W. C. Swope, H. C. Andersen, P. H. Berens, and K. R. Wilson, J. Chem. Phys. 76, 637 (1982)] algorithm is presented. We apply this new algorithm to the constant strain rate deformation of an amorphous polyethylene in a model containing several distinct polymer chains. To our knowledge, this is the first time that bond length constraints were applied to a macromolecular system together with an extended ensemble in which the simulation cell shape is allowed to fluctuate.