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

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.

Figure 1

Amplitude (top) and phase shift (bottom) of the forced oscillation of a tracer particle with size $R_0=2$ at two different coupling constants and two different temperatures as indicated. The amplitude of the external potential oscillations is $A=0.1$. Error bars show maximal and minimal values from subsets of oscillations.

Figure 2

Storage (top) and loss modulus (bottom) derived with oscillatory active one-particle microrheology based on the amplitude and phase shift of the forced oscillation of a tracer particle with size $R_0=2$ at two different coupling constants and two different temperatures as indicated. The amplitude of the external potential oscillations is $A=0.1$. The lines show the results from passive microrheology for the two temperatures $T=1.06$ (solid) and $T=0.50$ (dashed). Error bars show maximal and minimal values from subsets of oscillations.

Figure 3

Storage (top) and loss modulus (bottom) derived with oscillatory active one-particle microrheology based on the amplitude and phase shift of the forced oscillation of a tracer particle with size $R_0=2$ at $k_{\mathrm{ot}}=5000$ and $T=0.50$. The amplitude of the external potential oscillations is $A=0.1$. Crosses: Evaluation using only the stationary Stokes friction [Eqs. (12) and (13)]. Filled symbols: Evaluation using full hydrodynamic friction with real viscosity [Eqs. (26) and (27)]. Open symbols: Evaluation using full hydrodynamic friction with complex viscosity [Eq. (30)]. Circles and squares are for upper and lower sign in the corresponding equations. Some results are negative and cannot be seen in this log-log plot.

Figure 4

Storage (top) and loss modulus (bottom) derived with oscillatory active one-particle microrheology based on the amplitude and phase shift of the forced oscillation of a tracer particle with size $R_0=2$ at $k_{\mathrm{ot}}=5000$ and $T=0.50$. The amplitude of the external potential oscillations is $A=0.1$. Crosses: Evaluation using only the stationary Stokes friction [Eqs. (12) and (13)]. Filled symbols: Evaluation using full hydrodynamic friction with real viscosity. Open symbols: Evaluation using full hydrodynamic friction with complex viscosity. Circles, squares, and triangles are different solutions of the corresponding equations. Some results are negative and cannot be seen in this log-log plot.