The topological constrains (entanglements) are created when the centers of mass of two adjacent chains move apart or together. The entanglement interactions slow the relative movement of center of mass of the chains and even draw them back.
The radial distribution function g(r) for both systems with and without entanglements. The circles are for the entangled system and the solid line is for the system without entanglements.
Distribution of the number of entanglements Z per chain computed by our model in equilibrium state. Symbols: simulation data; line: fitted curve.
The P t of the entanglements as a function of t age .
The distribution of the deviation of the distance of centers of mass of two entangled chains from the initial states with different strengths of entanglement interactions. The k* is the harmonic force constant in reduced unit.
The mean square displacement g(t) of the system with (scatted cycles) and without (full line) entanglements.
The stress auto-correlation G(t) of entangled PE system.
Shear viscosity as a function of shear rate. Linear fitting the data and extrapolating to zero shear rate gives the zero shear viscosity.
The input parameters for the model of C 1000 H 2002 at 450 K. The mass density ρ M is taken from Ref. 36, the isothermal compressibility κ T from Ref. 38, and the radius of gyration R G from Ref. 29. r c is the cutoff radius. Δt and Δt* are the integration time step in real units and in reduced units, respectively. ρ* is the reduced number density, and k* is the entanglement interaction force constant in reduced units. Pc 0 and Pa 0 are the probabilities of creation and annihilation of entanglements, respectively. Parameters A and B are calculated from Eq. (12) for MDPD.
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