Raman-Scattering Measurements of the Vibrational Density of States of a Reactive Mixture During Polymerization: Effect on the Boson Peak

Abstract

Raman-scattering measurements are used to follow the modification of the vibrational density of states in a reactive epoxy-amine mixture during isothermal polymerization. Combining them with Brillouin light and inelastic x-ray scattering measurements, we analyze the variations of the boson peak and of the Debye level while the system changes from liquid to glass upon increasing the number of covalent bonds among the constituent molecules. The shift and intensity variation of the boson peak are explained by the modification of the elastic properties throughout the reaction, and a master curve for the boson peak can therefore be obtained. Surprisingly, bond-induced modifications of the structure do not affect this master curve.

Stress-Induced Modification of the Boson Peak Scaling Behavior

“…Without exception, available results are all in agreement [3,4,[13][14][15][16][17][18][19][20][21][22]: the BP shifts towards higher frequencies and decreases in intensity when the sample becomes stiffer (increase of elastic constants). Recently, it has been proposed to quantitatively test the role played by the changes in the elastic properties by scaling the BP data with the Debye frequency, a quantity defined by the elastic medium.…”

“…As shown in ref. 19, throughout the isothermal reaction the BP scaling law remains Debye-controlled and the elastic moduli follow (within the errors) the Cauchy-like relation. At any time during the polymerization, however, the system -as a usual glass former -can also be forced to reach the glassy phase by decreasing the temperature.…”

“…The question of whether such a scaling is able to generate a master curve of the data, and hence, the variations of g(ω) can be explained in terms of elastic medium transformations is still highly debated. So far, the accumulated evidence is apparently in favor of opposite views: on one hand, the BP evolution in sodium silicate glasses (cooled [13], compressed [16], hy-perquenched [3] and permanently densified samples [4]) and in an epoxy-amine mixture during chemical vitrification [19] is controlled by changes in the system's elasticity, according to the Debye scaling law; on the other hand, the BP variations in network forming glasses like silica and GeO 2 upon cooling [14,15,23], in permanently densified silica [17], and in few polymers under pressure [20,21] are stronger than the elastic medium transformation, and the Debye scaling does not work. In light of such controversial results the question we face is the following: Do these results really conflict, or rather there is a general explanation in terms of the elastic properties of the systems?…”

Elastic anomalies at terahertz frequencies and excess density of vibrational states in silica glass

“…However, controversial results have been reported on the connection between the BP modification and the change in the elastic medium properties. In some systems, 14,18,19 it appears that the BP variation is solely associated with the change in the Debye frequency, which accounts for the modifications of the elastic continuum medium. In other cases, 13,[15][16][17] the BP shifts more strongly than suggested by the simple variation of the macroscopic medium.…”

“…Among them we may recall the soft potential model, 4 the mode-coupling theory applied to the vibrations in glasses, 5 models on a lattice 6 or on the continuum 7 with randomly fluctuating elastic constants, and harmonic models where the atoms vibrate around topologically disordered configurations. 8,9 Experimentally the BP has been studied as a function of macroscopic parameters such as the temperature, 10,11 the density, [12][13][14][15] and the pressure 16,17 or during chemical vitrification 18 or as a function of the quenching rate. 19 It is observed that the BP shifts to higher frequencies and decreases in intensity when the pressure or the density is increased.…”