Active one-particle microrheology of an unentangled polymer melt studied by molecular dynamics simulation

Abstract

We present molecular dynamics simulations for active one-particle microrheology of an unentangled polymer melt. The tracer particle is forced to oscillate by an oscillating harmonic potential, which models an experiment using optical tweezers. The amplitude and phase shift of this oscillation are related to the complex shear modulus of the polymer melt. In the linear response regime at low frequencies, the active microrheology gives the same result as the passive microrheology, where the thermal motion of a tracer particle is related to the complex modulus. We expand the analysis to include full hydrodynamic effects instead of stationary Stokes friction only, and show that different approaches suggested in the literature lead to completely different results, and that none of them improves on the description using the stationary Stokes friction.

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

“…Similar to our previous work for an unentangled polymeric system, we show that for the entangled system studied here, the inclusion of the particle and medium inertia in the continuum analysis leads to good agreement between the viscoelastic properties obtained by probe rheology and those obtained from the established simulation approaches, namely the Green-Kubo and the NEMD methods. Our observation is in contrast to recent work [38] which concluded that it was not possible to judge which of the different mathematical variants used for including inertial effects in probe rheology lead to the correct values of the medium viscoelasticity.…”

“…Inclusion of the inertial effects in the analysis not only removes these negative G (ω) values at high frequencies but also substantially enhances the agreement between the active probe rheology results and the results from the NEMD and the Green-Kubo techniques. As was the case for the unentangled polymers [18], this observation of ours for the entangled system also is opposite to that of Kuhnhold and Paul [38] who found that when inertia was not accounted for in the analysis, the storage modulus continued to exhibit positive values, whereas accounting for the inertia in their analysis led to unphysical values for the storage modulus in many instances. Fig.…”

“…Kuhnhold and Paul [37,38] also simulated both active and passive microrheology in a melt of unentangled bead-spring chains. However, they observed disagreement between the two approaches, and suggested that the inertial generalized Stokes relation (and by inference, the GSR) is incorrect, since it does not incorporate rheological memory effects.…”

“…First, their simulation box had edge length only one sixth of our simulation, so would contain artifactual hydrodynamic interaction between periodic images of the probe particle over a much greater frequency range. For the active rheology, they reported estimates of the dynamic modulus at very high frequencies at which these artifactual hydrodynamic interactions may not be significant, but at the same time, these frequencies (ω ≥ 1) are comparable or above the characteristic Lennard-Jones time scale [38]. In our previous simulations of an unentangled system [18], we observed a crossover from the Basset-force dominated motion to the ballistic motion of the probe on a very similar time range as that studied by Kuhnhold and Paul.…”

Microrheology of isotropic and liquid-crystalline phases of hard rods by dynamic Monte Carlo simulations

“…Introduced by the seminal works by Mason and Weitz in the 1990s [2,3], MR allows one to assess the viscoelastic behaviour of a soft material by tracking and analysing the dynamics of guest tracers (or probe particles) dispersed in it. The work by Mason and Weitz triggered further experimental and theoretical research [6,7,8,9] and eventually led to an important extension of the original MR technique, where a tracer is forced to displace upon application of constant, pulsed or oscillating external forces [10,11,12,13]. Such a technique, referred to as active MR, can capture both the linear and nonlinear viscoelastic regimes, including very intriguing phenomena, such as force thinning, where the effective friction coefficient decreases as the magnitude of the applied force increases [14,15,16,17].…”