Atomistic Monte Carlo simulation of steady-state uniaxial, elongational flow of long-chain polyethylene melts: dependence of the melt degree of orientation on stress, molecular length and elongational strain rate

Full Paper: Following our recent work on the simulation of elasticity and b irefringence of linear polyethylene (PE) melts [Mavrantzas and Theodorou, 1 998; 2000], new : results are presented for PE melts of chain length up to C-1000, modelled in atomistic detail. The simulations have been performed w ith the End-Bridging Monte Carlo (EBMC) method, allowing large numbers of s trained polymer melt configurations, thoroughly equilibrated at all length scales, to be sampled. These strained configurations are representative of the structure of PE melt systems under conditions of low-Deborah number ste ady- state uniaxial elongational flow in the x direction. The degree of ori entation at the level of individual bonds and of entire chains and the melt anisotropic refractive index (birefringence) are presented and analyzed fo r a collection of PE melt systems of mean chain length C-24 up to C-1000 an d polydispersity index 1.05 to 1.09 over a wide range of imposed stresses. The simulations demonstrate: a) a linear dependence of the conformation ten sor component (c) over tilde (xx), I quantifying the overall chain orientat ion and deformation, and of the bond order parameter S-x on the imposed str ess difference tau (xx) - tau (yy), for all systems and strain-rates invest igated, except for the shortest C-24 system at stress levels exceeding abou t 350 atm, and b) conformity to the stress optical law (linearity between t he anisotropy of the refractive index and the anisotropy of stress) in all cases except for the C-24 system at the highest stress levels. The stress o ptical coefficient C is seen to go through a maximum at : around C-100 and to reach an asymptotic value beyond C-500, which is predicted within 30% of the experimental value : for high-molecular weight linear PE melts. The li near I relationship between S-x and (c) over tilde (xx) borne out of the me lt simulations is in excellent agreement with Flory's theoretical treatment based on single freely-jointed chains. Results are also presented for the elongational viscosity eta (E) of the (u nentangled) C-24 and C-78 PE melts and for its dependence on elongational s train rate. Values of eta (E) are calculated from the dependence-of stress on the orienting field employed in the EBMC simulations. This field is conv erted to a strain rate by mapping the atomistic model onto the Hookean dumb bell, FENE dumbbell and Rouse : models of viscoelasticity so that the unper turbed chain dimensions and chain self-diffusivity (obtained through: equil ibrium molecular dynamics studies of the same systems, Harmandaris et al., 1998) are preserved. The results obtained with all models: a) respect Trout on's law and b) display a continuous increase of eta (E) for these short PE melt systems with the applied elongational strain rate.