EXTENDED ENSEMBLE MOLECULAR-DYNAMICS METHOD FOR CONSTANT STRAIN-RATE UNIAXIAL DEFORMATION OF POLYMER SYSTEMS

We describe a novel molecular dynamics (MD) method to simulate the uni axial deformation of an amorphous polymer. This method is based on a r igorously defined statistical mechanics ensemble appropriate for descr ibing an isothermal, displacement controlled, uniaxial stress mechanic al test. The total number of particles is fixed and the normal stresse s in the direction normal to the applied strain are constant, i.e., an NTLx sigma(yy)sigma(zz) ensemble. By using the Lagrangian of the exte nded system (i.e., including additional variables corresponding to the temperature and cross-sectional area fluctuations), we derive a set o f equations of motion for the atomic coordinates and the additional va riables appropriate to this ensemble. In order to avoid the short MD t ime step appropriate for the stiff covalent bonds along the polymer ch ains, we introduce bond length constraints. This is achieved using a v ariation of the commonly used SHAKE [J. P. Ryckaert, G. Ciccotti, and H. J. C. Berendsen, J. Comp. Phys. 23, 327 (1977)] algorithm. A numeri cal method for integrating the equations of motion with constraints vi a 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)] algorit hm is presented. We apply this new algorithm to the constant strain ra te deformation of an amorphous polyethylene in a model containing seve ral distinct polymer chains. To our knowledge, this is the first time that bond length constraints were applied to a macromolecular system t ogether with an extended ensemble in which the simulation cell shape i s allowed to fluctuate. (C) 1997 American Institute of Physics.