One calculation tracks PMMA's stiffness from terahertz vibrations down to millihertz lab rates

Deform an ordered solid and you can picture every atom moving along with the imposed macroscopic strain. A polymer glass is structurally disordered, so its atoms do not all follow that deformation, and many of them make additional local rearrangements that collectively soften the material ^[9]. Non-affine lattice dynamics calculates that softening by connecting the vibrational modes of the atomic structure with the forces generated when the material is deformed, and the quantity it returns is the macroscopic shear modulus ^[10]. The author says he helped develop the framework with his longtime collaborator Dr. Tim Sirk at the U.S. Army Research Laboratory ^[8].

Vibrations alone do not reach laboratory timescales. In a simple friction model the resistance an atom feels depends only on what is happening at that instant, while a glassy polymer's response retains information about what happened before, which makes the dynamics non-Markovian ^[11]. The power-law memory kernel put into the equations for the non-affine motions is what carries the broad spectrum of relaxation processes ^[12]. How the exponent of that kernel was set goes unreported in the write-up, and that determines how much of the low-frequency curve is computed and how much is fitted ^[18].

A terahertz is 10^12 hertz and a millihertz is 10^-3 hertz, so the two frequencies quoted bracket 15 orders of magnitude, not the more than 20 the account reports ^[13][16]. Twenty decades above a millihertz floor would put the ceiling near 10^17 hertz ^[17]. The account describes the top of its range only as above the terahertz regime ^[13].

"The result surprised even us in terms of the range of scales that could be connected," wrote the researcher who described the work for phys.org ^[15]. The comparisons run down the frequency axis in order: direct molecular dynamics at the fastest scales, Brillouin light scattering in the gigahertz range, high-rate mechanical tests below that, and dynamic mechanical analysis at conventional laboratory frequencies ^[14]. All of those PMMA datasets existed before the calculation. Matching them tests the chain of reasoning.

The cost the approach avoids is simulation time. Molecular dynamics resolves the fastest atomic motions, and the shortness of the time step is what makes ordinary mechanical timescales so hard to reach ^[3]. Here the vibrational modes come out of one atomistic model and the frequency sweep happens in the theory ^[7]. Between those two ends, Brillouin scattering, ultrasonic measurement and high-strain-rate testing each fill portions of the gap ^[4].