Determination of linear viscoelastic properties of an entangled polymer melt by probe rheology simulations

M Karim and T Indei and JD Schieber and R Khare, PHYSICAL REVIEW E, 93, 012501 (2016).

DOI: 10.1103/PhysRevE.93.012501

Particle rheology is used to extract the linear viscoelastic properties of an entangled polymer melt from molecular dynamics simulations. The motion of a stiff, approximately spherical particle is tracked in both passive and active modes. We demonstrate that the dynamic modulus of the melt can be extracted under certain limitations using this technique. As shown before for unentangled chains Karim et al., Phys. Rev. E 86, 051501 (2012), the frequency range of applicability is substantially expanded when both particle and medium inertia are properly accounted for by using our inertial version of the generalized Stokes-Einstein relation (IGSER). The system used here introduces an entanglement length d(T), in addition to those length scales already relevant: monomer bead size d, probe size R, polymer radius of gyration R-g, simulation box size L, shear wave penetration length Delta, and wave period Lambda. Previously, we demonstrated a number of restrictions necessary to obtain the relevant fluid properties: continuum approximation breaks down when d greater than or similar to Lambda; medium inertia is important and IGSER is required when R greater than or similar to Lambda; and the probe should not experience hydrodynamic interaction with its periodic images, L greater than or similar to Delta. These restrictions are also observed here. A simple scaling argument for entangled polymers shows that the simulation box size must scale with polymer molecular weight as M-w(3). Continuum analysis requires the existence of an added mass to the probe particle from the entrained medium but was not observed in the earlier work for unentangled chains. We confirm here that this added mass is necessary only when the thickness L-S of the shell around the particle that contains the added mass, L-S > d. We also demonstrate that the IGSER can be used to predict particle displacement over a given timescale from knowledge of medium viscoelasticity; such ability will be of interest for designing nanoparticle-based drug delivery.

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