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Atomistic Framework for Glassy Polymer Viscoelasticity Across 20 Frequency Decades

Ankit Singh, Vinay Vaibhav, Caterina Czibula, Astrid Macher, Petra Christöfl, Karin Bartl, Gregor Trimmel, Timothy W. Sirk, Alessio Zaccone

Abstract

Glassy polymers are central to engineering applications, yet their viscoelastic response over broad frequency and temperature ranges remains difficult to characterize. We extend non-affine deformation theory by incorporating a time-dependent memory kernel within the Generalized Langevin Equation for atomistic non-affine motions, yielding frequency-dependent mechanical response. Applied to poly(methyl methacrylate) (PMMA), the method captures the shear modulus and relaxation spectrum across more than twenty decades in frequency, from hundreds of terahertz down to the millihertz regime, thus bridging polymer mechanics from ordinary to extreme scales. Our predictions show quantitative consistency with independent estimates from oscillatory-shear molecular dynamics, Brillouin scattering, ultrasonic spectroscopy, Split-Hopkinson testing, and dynamic mechanical analysis (DMA), demonstrating a unified theoretical-computational route for multiscale characterization of polymer glasses.

Atomistic Framework for Glassy Polymer Viscoelasticity Across 20 Frequency Decades

Abstract

Glassy polymers are central to engineering applications, yet their viscoelastic response over broad frequency and temperature ranges remains difficult to characterize. We extend non-affine deformation theory by incorporating a time-dependent memory kernel within the Generalized Langevin Equation for atomistic non-affine motions, yielding frequency-dependent mechanical response. Applied to poly(methyl methacrylate) (PMMA), the method captures the shear modulus and relaxation spectrum across more than twenty decades in frequency, from hundreds of terahertz down to the millihertz regime, thus bridging polymer mechanics from ordinary to extreme scales. Our predictions show quantitative consistency with independent estimates from oscillatory-shear molecular dynamics, Brillouin scattering, ultrasonic spectroscopy, Split-Hopkinson testing, and dynamic mechanical analysis (DMA), demonstrating a unified theoretical-computational route for multiscale characterization of polymer glasses.

Paper Structure

This paper contains 2 equations, 3 figures.

Figures (3)

  • Figure 1: (a) Vibrational density of states $g(\omega)$ and (b) affine force field correlator $\Gamma(\omega)$ as a function of normal mode frequency $(\omega)$ at temperature $T=300$ K, for our simulated PMMA glass.
  • Figure 2: Temperature dependence of shear storage modulus $G'$ for PMMA calculated using NALD (close triangle) is compared with DMA experimental data (closed diamonds, at external frequency $\Omega=1$ Hz). The solid line represents the theoretical fit based on the equation described in SI supp, with a glass transition temperature of $T_g \approx 390~\mathrm{K}$. We also plot the affine modulus $G_{A}$ (open squares) as a function of temperature.
  • Figure 3: Low-frequency shear storage modulus $G^{\prime}$ as a function of external deformation frequency $\Omega$ at temperature $T=300$ K. The Solid line represents NALD calculations and symbols represent MD and experimental results that include DMA study in this work and other experiments from previous studies weishaupt1995pressureMikio_1995afifi2003ultrasonicafifi2003annealingMOTT2008572Sahraoui_1994davies1963dynamicmoy_paul_2003MULLIKEN20061331christofl2021comprehensive.