Comparison of Friction Parametrization from Dynamics and Material Properties for a Coarse-Grained Polymer Melt

Abstract

In this work, we extend an approach to coarse-grained (CG) modeling for polymer melts in which the conservative potential is parametrized using the iterative Boltzmann inversion (IBI) method and the accelerated dynamics inherent to IBI are corrected using the dissipative Langevin thermostat with a single tunable friction parameter (J. Chem. Phys. 2021, 154, 084114). Diffusive measures from picoseconds to nanoseconds are used to determine the Langevin friction factor to apply to the CG model to recover all-atom (AA) dynamics; the resulting friction factors are then compared for consistency. Here, we additionally parametrize the CG dynamics using a material property, the zero-shear viscosity, which we measure using the Green-Kubo (GK) method. Two materials are studied, squalane as a function of temperature and the same polystyrene oligomers previously studied as a function of chain length. For squalane, the friction derived from the long-time diffusive measures and the viscosity all strongly increase with decreasing temperature, showing an Arrhenius-like dependence, and remain consistent with each other over the entire temperature range. In contrast, the friction required for the picosecond diffusive measurement, the Debye-Waller factor, is somewhat lower than the friction from long-time measures and relatively insensitive to temperature. A time-dependent friction would be required to exactly reproduce the AA measurements during the caging transition connecting these two extremes over the entire timespan at this level of coarse-graining. For the polystyrene oligomers for which we previously characterized the diffusive friction, the viscosity-parametrized frictions are consistent with the diffusive measures for the smallest chain length. However, for the longer chains, we find different trends based on measurement method with friction derived from rotational diffusion remaining nearly constant, friction derived from translational diffusion showing a modestly increasing trend, and viscosity-derived friction showing a modest decreasing trend. This seems to indicate that there is some sensitivity of the friction measurement method for systems with increased relaxation times and that in particular, the unsteady dynamics of the individual parametrization schemes plays a role in this. Increased difficulty in applying the GK method with increasing relaxation time of the longer chain systems is also discussed. Overall, we find that when the material is in a high-temperature melt state and the viscosity measurement is reliable, the friction parametrization from the diffusive friction measures is consistent and the lower cost diffusive parametrization is a reliable means for modeling viscosity. Our data give insight into the time-dependent friction one might compute using a non-Markovian approach to enable the recovery of AA dynamics over a wider range of time scales than can be computed using a single friction.

Figure 1.

Illustration of a single molecule of each (a) squalane and (b) PS11 shown with the CG representation superimposed over the AA representation. Images were generated using Visual Molecular Dynamics (VMD)^, and TopoTools. A single CG type, representing roughly one monomer per CG, is utilized for each molecule.

Figure 2.

Early time monomer MSD $g_1(t)$ as a function of time for squalane at (a) 100 °C, (b) 65 °C, and (c) 40 °C. The AA reference simulations are shown as solid black curves. The CG systems with varying friction ${\mathrm{\Gamma }}^{\prime }$ are shown as a series of curves, as noted in the legend in units of ps⁻¹.

Figure 3.

Chain MSD $g_3(t)$ as a function of time for squalane at (a) 100 °C, (b) 65 °C, and (c) 40 °C. The AA reference simulations are shown as solid black curves. The CG systems with varying friction ${\mathrm{\Gamma }}^{\prime }$ are shown as a series of curves, as noted in the legend in units of ps⁻¹.

Figure 4.

End-to-end vector autocorrelation function $⟨\hat{\mathbf{u}}(t)\cdot \hat{\mathbf{u}}(0)⟩$ as a function of time for squalane at (a) 100 °C, (b) 65 °C, and 40 °C. The AA reference simulations are shown as solid black curves. The CG systems with varying friction ${\mathrm{\Gamma }}^{\prime }$ are shown as a series of curves, as noted in the legend in units of ps⁻¹.

Figure 5.

Stress relaxation modulus $G(t)$ as a function of time for squalane at (a) 100 °C, (b) 65 °C, and (c) 40 °C. The AA reference simulations are shown as solid black curves. The CG systems with varying friction ${\mathrm{\Gamma }}^{\prime }$ are shown as a series of curves, as noted in the legend in units of ps⁻¹.

Figure 6.

Viscosity $\eta (t)$ as a function of time for squalane at (a) 100 °C, (b) 65 °C, and 40 °C, for the AA and CG representations, with applied friction ${\mathrm{\Gamma }}^{\prime }$ shown in the legend in units of ps⁻¹. The dashed curves represent the fitting approach described by Zhang et al. which we summarize in the Supporting Information.

Figure 7.

Dimensionless groups $Z_1,Z_2,Z_3$, and $Z_4$ represent the relative magnitude of the CG measurement compared to the AA target value plotted as a function of the applied friction, ${\mathrm{\Gamma }}^{\prime }$, for squalane at varying temperatures, (a) 100 °C, (b) 65 °C, and (c) 40 °C. Fittings shown are double exponential.

Figure 8.

Values of ${\mathrm{\Gamma }}^{\prime }$ extracted from curves of best fit, ${\mathrm{\Gamma }}_{\mathrm{D}\mathrm{W}\mathrm{F}}{}^{\prime },{\mathrm{\Gamma }}_{\text{chain}}{}^{\prime },{\mathrm{\Gamma }}_{\text{rot}}{}^{\prime }$, and ${\mathrm{\Gamma }}_{\text{visc}}{}^{\prime }$, as a function of inverse temperature for squalane.

Figure 9.

Stress relaxation modulus $G(t)$ as a function of time for (a) PS11, (b) PS21, and (c) PS41. The AA reference simulations are shown as solid black curves. The CG systems with varying friction ${\mathrm{\Gamma }}^{\prime }$ are shown as a series of curves, as noted in the legend in units of ps⁻¹.

Figure 10.

Viscosity $\eta (t)$ as a function of time for (a) PS11, (b) PS21, and (c) PS41 systems for the AA and CG representations with the applied friction ${\mathrm{\Gamma }}^{\prime }$ defined in the legend in units of ps⁻¹. The dashed curves represent the fitting approach described by Zhang et al. which we summarize in the Supporting Information.

Figure 11.

Dimensionless groups $Z_1,Z_2,Z_3$, and $Z_4$ as a function of the applied friction factor ${\mathrm{\Gamma }}^{\prime }$ for each chain length for (a) PS11, (b) PS21, and (c) PS41. Fittings shown are double exponential. $Z_1,Z_2$, and $Z_3$ were calculated as a function of ${\mathrm{\Gamma }}^{\prime }$ in ref and are replotted here.

Figure 12.

Values of ${\mathrm{\Gamma }}^{\prime }$ extracted from curves of best fit, ${\mathrm{\Gamma }}_{\mathrm{D}\mathrm{W}\mathrm{F}}{}^{\prime },{\mathrm{\Gamma }}_{\text{chain}}{}^{\prime },{\mathrm{\Gamma }}_{\text{rot}}{}^{\prime }$, and ${\mathrm{\Gamma }}_{\text{visc}}{}^{\prime }$, as a function of chain length $N$ for PS. ${\mathrm{\Gamma }}_{\mathrm{D}\mathrm{W}\mathrm{F}}{}^{\prime },{\mathrm{\Gamma }}_{\text{chain}}{}^{\prime }$, and ${\mathrm{\Gamma }}_{\text{rot}}{}^{\prime }$ were derived from data presented in ref and are replotted here.