Katsumi Hagita

Estimation of relaxation modulus of polymer melts by molecular dynamics simulations: Application of relaxation mode analysis

A framework for estimating the linear relaxation modulus of polymer melts by molecular dynamics (MD) simulations is presented on the basis of relaxation mode analysis (RMA). Conventional calculations of the relaxation modulus based on the Green–Kubo formula are computationally very expensive owing to long relaxation times and poor convergence of stress autocorrelation functions: In practice, reliable calculations usually require a time average over (mathcal{O}(10tau _{1}{text{--}}100tau _{1})), where τ1 is the longest relaxation time of a chain in the melt. RMA is a method that systematically extracts relaxation modes and rates of a polymer chain from the time correlation functions of coordinates of polymer segments. In the present method, the relaxation modulus is evaluated by fitting the data of the stress autocorrelation functions to the generalized Maxwell model whose relaxation times are determined from the relaxation rate spectrum obtained by RMA. It is demonstrated that the stress relaxation ...

Thinning Approximation for Two-Dimensional Scattering Patterns from Coarse-Grained Polymer Melts under Shear Flow

We proposed a thinning approximation (TA) for estimation of the two-dimensional (2D) wide-angle scattering patterns from Kremer–Grest polymer melts under shear. In the TA, extra particles are inserted at the middle of bonds for fine-graining of the coarse-grained polymers. For the case without the TA, spots corresponding to the orientation of bonds at a high shear rate are difficult to observe because the bond length of successive particles is comparable to the distance between neighboring particles. With the insertion of the extra particles, a ring pattern originating from the neighboring particles can be moved to a wide-angle region. Thus, we can observe the spots at high shear rates. We also examined the relationship between 2D scattering patterns and the Weissenberg number, which is defined as the product of the shear rate and the longest relaxation time. It is confirmed that the relationship for coarse-grained polymers with the TA is consistent with that of the all-atomistic model of polyethylene.

Filler Network Model of Filled Rubber Materials to Estimate System Size Dependence of Two-Dimensional Small-Angle Scattering Patterns

We proposed a filler network toy (FN-toy) model in order to approximately forecast changes in two-dimensional scattering patterns (2DSPs) of nanoparticles (NPs) in crosslinked polymer networks in ultrasmall-angle X-ray scattering (USAXS) experiments under uniaxial elongation. It enables us to estimate the system size dependence of the 2DSP of the NPs. In the FN-toy model, we considered NPs connected by harmonic springs with excluded-volume interactions among the NPs. In this study, we used the NP configurations estimated by reverse Monte Carlo (RMC) analysis for USAXS data observed in SPring-8 experiments on filler-filled styrene butadiene rubber (SBR). In the FN-toy model, we set a bond between every pair of NPs whose distance is less than Cd, where d is the diameter of an NP and C is a parameter that characterizes network properties. We determined the optimal value of C by comparison with 2DSPs of the NPs at 200% elongation for end-modified and unmodified SBR. These 2DSPs are obtained from the results o...