Determination of viscoelastic properties by analysis of probe-particle motion in molecular simulations

Abstract

We present a technique for the determination of viscoelastic properties of a medium by tracking motion of an embedded probe particle by using molecular dynamics simulations. The approach involves analysis of the simulated particle motion by continuum theory; it is shown to work in both passive and active modes. We demonstrate that for passive rheology, an analysis based on the generalized Stokes-Einstein relationship (GSER) is not adequate to obtain the values of the viscoelastic moduli over the frequency range studied. For both passive and active modes, it is necessary to account for the medium and particle inertia when analyzing the particle motion. For a polymer melt system consisting of short chains, the values calculated from the proposed approach are in good quantitative agreement with previous literature results that were obtained using completely different simulation approaches. The proposed particle rheology simulation technique is general and could provide insight into the characterization of the mechanical properties in biological systems such as cellular environments and polymeric systems such as thin films and nanocomposites that exhibit spatial variation of properties over the nanoscale.3

Temperature dependent micro-rheology of a glass-forming polymer melt studied by molecular dynamics simulation

“…7 (top) extends beyond both of these values (for the low frequencies similar behavior was found in Ref. 8).…”

“…At first glance, this is astonishing, considering limiting frequencies for the applicability of the microrheological method, which can be derived from the frequency dependent penetration depth of the shear waves generated by the particle motion. 7,8 A high frequency cutoff can be defined by the frequency at which this penetration depth is equal to the particle size (ω = 1.1 for T = 1.06), a low frequency cutoff can be defined by the frequency where the penetration depth is equal to half the system size (ω = 0.1 for T = 1.06). The agreement in Fig.…”

“…The underlying theories for the analysis of the Brownian motion range from a rather simple Generalized Stokes-Einstein relation [1][2][3] to full hydrodynamic approaches. [4][5][6][7][8][9] When approaching the glass transition temperature, the mobility of polymeric liquids decreases by orders of magnitude. The glass transition itself is still not fully understood and has found much theoretical and experimental interest.…”

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

“…Rigorous data analysis for singe-point passive microrheology utilizes the generalized Stokes-Einstein relation (GSER), or at sufficiently high frequencies, the inertial GSER (IGSER) [18]. This relation assumes that (1) the probe particle sees the medium as a continuum, (2) that deformations of the medium due to the particle displacement are sufficiently small that the medium can be treated in the linear viscoelastic regime, (3) the fluctuation-dissipation theorem applies, and (4) the probe particle experiences no hydrodynamic interaction with nearby surfaces.…”

“…In our previous work [18], we studied probe rheology in a model unentangled polymer melt by analyzing the molecular dynamics (MD) simulation data using continuum mechanics.…”