scholarly journals Anomalies in the low frequency vibrational density of states for a polymer with intrinsic microporosity – the Boson peak of PIM-1

2018 ◽  
Vol 20 (3) ◽  
pp. 1355-1363 ◽  
Author(s):  
Reiner Zorn ◽  
Huajie Yin ◽  
Wiebke Lohstroh ◽  
Wayne Harrison ◽  
Peter M. Budd ◽  
...  
Keyword(s):  
Density Of States ◽  
Low Frequency ◽  
Boson Peak ◽  
Vibrational Density Of States ◽  
First Time ◽  
Intrinsic Microporosity ◽  
Vibrational Density

For the first time the low frequency vibrational density of states is reported for a polymer with intrinsic microporosity.

Low frequency vibrational density of state of highly permeable super glassy polynorbornenes – the Boson peak

2020 ◽  
Vol 22 (33) ◽  
pp. 18381-18387
Author(s):  
Reiner Zorn ◽  
Paulina Szymoniak ◽  
Mohamed A. Kolmangadi ◽  
Marcell Wolf ◽  
Dmitry A. Alentiev ◽  
...  
Keyword(s):  
Density Of States ◽  
Time Of Flight ◽  
Low Frequency ◽  
Boson Peak ◽  
Density Of State ◽  
Neutron Time ◽  
Incoherent Neutron ◽  
Vibrational Density

Inelastic incoherent neutron time-of-flight scattering was employed to measure the low frequency density of states for a series of addition polynorbornenes with bulky side groups.

scholarly journals Universal law for the vibrational density of states of liquids

2021 ◽  
Vol 118 (5) ◽  
pp. e2022303118
Author(s):  
Alessio Zaccone ◽  
Matteo Baggioli
Keyword(s):  
Density Of States ◽  
Normal Modes ◽  
Low Frequency ◽  
Average Lifetime ◽  
Vibrational Density Of States ◽  
Lennard Jones ◽  
Average Relaxation Time ◽  
Universal Law ◽  
Infinite Set ◽  
Vibrational Density

An analytical derivation of the vibrational density of states (DOS) of liquids, and, in particular, of its characteristic linear in frequency low-energy regime, has always been elusive because of the presence of an infinite set of purely imaginary modes—the instantaneous normal modes (INMs). By combining an analytic continuation of the Plemelj identity to the complex plane with the overdamped dynamics of the INMs, we derive a closed-form analytic expression for the low-frequency DOS of liquids. The obtained result explains, from first principles, the widely observed linear in frequency term of the DOS in liquids, whose slope appears to increase with the average lifetime of the INMs. The analytic results are robustly confirmed by fitting simulations data for Lennard-Jones liquids, and they also recover the Arrhenius law for the average relaxation time of the INMs, as expected.

scholarly journals Vibrational density of states and boson peak in two-dimensional frictional granular assemblies

2016 ◽  
Vol 65 (3) ◽  
pp. 036301
Author(s):  
Niu Xiao-Na ◽  
Zhang Guo-Hua ◽  
Sun Qi-Cheng ◽  
Zhao Xue-Dan ◽  
Dong Yuan-Xiang
Keyword(s):  
Density Of States ◽  
Boson Peak ◽  
Two Dimensional ◽  
Vibrational Density Of States ◽  
Granular Assemblies ◽  
Vibrational Density

scholarly journals Vibrational density of states of amorphous solids with long-ranged power-law-correlated disorder in elasticity

2020 ◽  
Vol 43 (11) ◽  
Author(s):  
Bingyu Cui ◽  
Alessio Zaccone
Keyword(s):  
Internal Stress ◽  
Density Of States ◽  
Power Law ◽  
Elastic Constants ◽  
Boson Peak ◽  
Internal Stresses ◽  
Logarithmic Correction ◽  
Spatial Correlations ◽  
Vibrational Density Of States ◽  
Vibrational Density

Abstract. A theory of vibrational excitations based on power-law spatial correlations in the elastic constants (or equivalently in the internal stress) is derived, in order to determine the vibrational density of states D($\omega$ ω ) of disordered solids. The results provide the first prediction of a boson peak in amorphous materials where spatial correlations in the internal stresses (or elastic constants) are of power-law form, as is often the case in experimental systems, leading to a logarithmic enhancement of (Rayleigh) phonon attenuation. A logarithmic correction of the form $ \sim -\omega^{2}\ln\omega$ ∼ - ω 2 ln ω is predicted to occur in the plot of the reduced excess DOS for frequencies around the boson peak in 3D. Moreover, the theory provides scaling laws of the density of states in the low-frequency region, including a $ \sim\omega^{4}$ ∼ ω 4 regime in 3D, and provides information about how the boson peak intensity depends on the strength of power-law decay of fluctuations in elastic constants or internal stress. Analytical expressions are also derived for the dynamic structure factor for longitudinal excitations, which include a logarithmic correction factor, and numerical calculations are presented supporting the assumptions used in the theory. Graphical abstract

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