Atomistic simulation of the birefringence of uniaxially stretched polyethylene melts

The birefringence of uniaxially stretched, long-chain polyethylene (PE) melts is predicted through detailed atomistic simulations by employing the end-bridging Monte Carlo method. The method involves two steps: First, a large number of well-equilibrated, uniaxially stretched polymer configurations are sampled by invoking the methodology developed in our recent work on the simulation of polymer melt elasticity. A key feature in this step is the tensorial field a_xx which orients and, under certain conditions, deforms the polymer chains in the x direction, inducing anisotropy in the melt. Second, the structural characteristics of the oriented polymer configurations are analyzed and a description of their anisotropy at the monomer level is obtained. By transforming the polarizability tensor of each individual skeletal bond (or united atom group) from the coordinate frame of its principal axes to the laboratory frame, the ensemble average polarizability tensor per methylene group 〈α〉 of the uniaxially stretched polymer melt is calculated as a function of the segment order parameter S_x. The anisotropic melt refractive index Δn(≡n_xx−n_yy) is obtained from 〈α〉 by using the Clausius–Mossoti and Lorentz–Lorenz relationships. Results obtained for two linear PE melts (average chain length C₇₈ and C₂₀₀) verify the validity of the stress optical law for small enough imposed elongational flow rates a_xx. The calculated stress optical law coefficient C is found to be equal to (3.15±0.20)×10⁻⁹ Pa⁻¹ for the C₇₈ melt and equal to (2.35±0.10)×10⁻⁹ Pa⁻¹ for the C₂₀₀ melt. The experimentally measured value for high-molecular weight, linear, high-density PE melts is 2.20×10⁻⁹ Pa⁻¹.