Modifying Fragility and Collective Motion in Polymer Melts with Nanoparticles

We investigate the impact of nanoparticles (NP) on the fragility and cooperative string-like motion in a model glass-forming polymer melt by molecular dynamics simulation. The NP cause significant changes to both the fragility and the average length of string-like motion, where the effect depends on the NP-polymer interaction and the NP concentration. We interpret these changes via the Adam-Gibbs (AG) theory, assuming the strings can be identified with the "cooperatively rearranging regions" of AG. Our findings indicate fragility is primarily a measure of the temperature dependence of the cooperativity of molecular motion.Comment: To appear in Physical Review Letter

A quantitative theoretical model of the boson peak based on stringlet excitations

The boson peak (BP), a low-energy excess in the vibrational density of states over the phonon Debye contribution, is usually identified as one of the distinguishing features between ordered crystals and amorphous solid materials. Despite decades of efforts, its microscopic origin still remains a mystery and a consensus on its theoretical derivation has not yet been achieved. Recently, it has been proposed, and corroborated with simulations, that the BP might stem from intrinsic localized modes which involve string-like excitations ("stringlets") having a one-dimensional (1D) nature. In this work, we build on a theoretical framework originally proposed by Lund that describes the localized modes as 1D vibrating strings, but we specify the stringlet size distribution to be exponential, as observed in independent simulation studies. We show that a generalization of this framework provides an analytically prediction for the BP frequency $\omega_{BP}$ in the temperature regime well below the glass transition temperature in both 2D and 3D amorphous systems. The final result involves no free parameters and is in quantitative agreement with prior simulation observations. Additionally, this stringlet theory of the BP naturally reproduces the softening of the BP frequency upon heating and offers an analytical explanation for the experimentally observed scaling with the shear modulus in the glass state and changes in this scaling in cooled liquids. Finally, the theoretical analysis highlights the existence of a strong damping for the stringlet modes at finite temperature which leads to a large low-frequency contribution to the 3D vibrational density of states, as observed in both experiments and simulations

Parallel Emergence of Rigidity and Collective Motion in a Family of Simulated Glass-Forming Polymer Fluids

The emergence of the solid state in glass-forming materials upon cooling is accompanied by changes in both thermodynamic and viscoelastic properties and by a precipitous drop in fluidity. Here, we investigate changes in basic elastic properties upon cooling in a family of simulated polymer fluids, as characterized by a number of stiffness measures. We show that $\tau_{\alpha}$ can be expressed quantitatively both in terms of measures of the material ``stiffness'', $G_p$ and $\langle u^2 \rangle$, and the extent $L$ of cooperative particle exchange motion in the form of strings, establishing a direct relation between the growth of emergent elasticity and collective motion. Moreover, the macroscopic stiffness parameters, $G_p$, $B$, and $f_{s, q^*}$, can all be expressed quantitatively in terms of the molecular scale stiffness parameter, $k_{\mathrm{B}}T / \langle u^2 \rangle$ with $k_{\mathrm{B}}$ being Boltzmann's constant, and we discuss the thermodynamic scaling of these properties. We also find that $G_p$ is related to the cohesive energy density $\Pi_{\mathrm{CED}}$, pointing to the critical importance of attractive interactions in the elasticity and dynamics of glass-forming liquids. Finally, we discuss fluctuations in the local stiffness parameter as a quantitative measure of elastic heterogeneity and their significance for understanding both the linear and nonlinear elastic properties of glassy materials.Comment: 69 pages, 18 figure