Boson Peak Decouples from Elasticity in Glasses with Low Connectivity

We perform molecular-dynamics simulations of the vibrational and elastoplastic properties of polymeric glasses and crystals and the corresponding atomic systems. We evidence that the elastic scaling of the density of states in the low-frequency boson peak (BP) region is different in crystals and glasses. Also, we see that the BP of the polymeric glass is nearly coincident with the one of the atomic glasses, thus revealing that the former—unlike the elasticity—is controlled by nonbonding interactions only. Our results suggest that the interpretation of the BP in terms of the macroscopic elasticity, discussed in highly connected systems, does not hold for systems with low connectivity.

Figure 1

Correlation plot of the Steinhardt parameters $Q_6^{\text{local}}$ and $Q_6^{\text{global}}$ [37] of all of the samples under study at $T={10}^{-3}$, $P=0$. For ideal crystals, $Q_6^{\text{local}}=Q_6^{\text{global}}$. The global order is rather small in glasses, while their local order does not differ too much from the crystalline one.

Figure 2

Typical stress-strain curve for a single shear plane under athermal quasistatic shear deformation (the loaded system is a polymer crystal; the differences with the other systems are small). The curve is characterized by an initial linear elastic regime followed by a region with tiny, but apparent, sudden stress drops signaling plastic events which become much larger at higher strain; see, e.g., Ref. [36]. The elastic modulus $G_{x,y}$ is the slope for small deformations, $ϵ\le {ϵ}_{\mathrm{th}}={10}^{-4}$. (Inset) Distributions of the stress changes per particle $\mathrm{\Delta }{\tau }_{\alpha ,\beta }^i$ at $ϵ={ϵ}_{\mathrm{th}}$ for all samples in all of the deformation planes. The weak wing in the region of negative drops signals the presence of some local plastic events even in the macroscopic linear regime.

Figure 3

(Top panel) Distributions of the elastic modulus of the samples under study. The vertical dashed lines mark the average affine moduli $G_{\mathrm{A}}$ of the atomic solids (the corresponding narrow distributions are not plotted for clarity reasons). The affine moduli of the polymeric solids are about 1 order of magnitude larger, implying that the nonaffine effects taken as $G_{\mathrm{NA}}=G_{\mathrm{A}}-G$ are much larger. The modulus is affected by connectivity and, much less, by crystallinity. (Bottom panel) Corresponding distributions of the inverse reduced DW factor, a measure of the local stiffness. The latter is poorly affected by connectivity, and glasses are locally softer than crystals. (Inset) Distributions of the quantity $X=T{\rho }^{1/3}/G⟨u^2⟩$. Consistency requires that, if the changes of the reduced DW factor from crystals to glasses are driven by the corresponding elastic changes, their $X$ values must be equal, possibly depending only on the kind of solid, atomic, or polymeric.

Figure 4

Average DOS of the solids under study. Polymeric solids exhibit a high-frequency structure centered at about $\omega \sim 100$ with about 13% of the states [25, 48]. In spite of that, the low-frequency side of polymeric and atomic DOSs are nearly coinciding, and glasses exhibit an excess number of states with respect to crystals. The position of the low-frequency van Hove singularity of the bcc atomic crystal is indicated [40]. (Inset) Reduced DOS of the glasses in the BP region. The different Debye levels of the two glasses are marked as horizontal dashed lines.