High frequency dynamics of fluid binary mixtures
Izzo, Maria Grazia
This thesis is aimed to the study of dynamics in binary fluid mixtures by means of inelastic scattering spectroscopies. Nowadays the understanding of these dynamics is still unsatisfactory. In particular, any model is able to adequately describe collective dynamics beyond the hydrodynamic limit. In such a low momentum (k) and frequency () transfer limit, the collective dynamics is characterized by a single (adiabatic) longitudinal acoustic mode accounting for sound propagation. At frequencies above the hydrodynamics ones a transition towards a decoupled dynamic regime is expected. This is characterized by two distinct modes, namely the slow (low-) and fast (high-) sounds. The microscopic mechanisms driving such a transition, so as the related macroscopic quantities, are still unclear, even in an heuristic point of view. In this work the collective dynamics of neutral and ionic mixtures are investigated with the aim to shed light in this debated issue. He/Ne mixtures have been studied by means of Inelastic X-ray Scattering (IXS) spectroscopy. Exploiting the lack of kinematic limitations peculiar of this technique, the high frequency (>THz) dynamics has been analyzed from the mesoscopic up to the high-k range, where the dynamic response of the system can be described using the Impulse Approximation (IA). This kind of study is of particular interest for disparate mass mixtures, since inefficient kinetic energy exchanges between light and heavy particles taking place on very short time scales are expected to greatly influence the phenomenology of the aforementioned dynamic decoupling. The prototype ionic mixture, RbF, also, has been investigated by means of Inelastic Neutron Scattering (INS) spectroscopy. Ionic mixtures are particularly suited to investigate the role played by optic-like excitations (related to concentration fluctuations) in the transition from the hydrodynamics to the decoupled regime. Indeed, these kind of excitations are expected to be emphasized because of the long range Coulomb interactions. Conversely at k’s enough high, i.e. k>k* with k* dependent on the values of the electric conduction coefficient and the adiabatic sound velocity, they are expected to behave like neutral binary mixtures. The study of molten RbF has been, then, focused on the characterization of collective dynamics in the transition region, which is more difficultly accessible by IXS because of instrumental limitations. IXS data on He0.8Ne0.2 mixture have been analyzed using a generalization of the viscoelastic function, which, in our knowledge, has been applied for the first time to this purpose. This kind of data analysis permitted to extrapolate the partial dynamical structure factors related to He-He, Ne-Ne and He-Ne density fluctuations. The adiabatic and high frequency sound velocity as well as the relaxation time associated to each mixture component has been calculated from fitting parameters. The analysis of the extrapolated relaxation times permitted to define, in the probed range, two k-region depending on the behavior of such quantity. At the higher k probed the relaxation times of single components can be well described by the respective single specie collision time, indicating a complete dynamics decoupling. At lower k, conversely, the relaxation times show a deviation to respect the collisional times. The study of the same mixture in three different thermodynamic conditions, revealed a common k trend of the single component relaxation times once proper normalization, made by means of kinetic parameters, has been done. An empirical expression has then been proposed. The result can be interpreted in the framework of ‘two temperature theory’, based on the assumption that in disparate mass binary mixtures inefficient kinetic energy exchanges induce a two step process for the relaxation of density fluctuations towards the thermodynamic equilibrium. These processes are characterized by two distinct timescales: the intra-specie collision time, where each specie subsystem reaches a condition of ‘local’ equilibrium associated with a ‘local’ temperature and a characteristic time for the equilibration of the microscopic temperatures to the thermodynamic temperature trough inter-specie collisions. A further corroboration of the above picture has been found from the analysis of IXS spectra in the IA region, which allowed extrapolating the momentum distribution functions of the specie subsets. An anomalous behavior has been noticed on the He momentum distribution function, i.e. the apparent temperature associated to the momentum distribution is about 40 K higher than the macroscopic one. This striking result can be straightforwardly interpreted as a fingerprint of the peculiar ‘two temperature’ equilibration process. INS experiment on molten RbF permitted to reveal the simultaneous presence of two dispersive collective modes in the transition region. The dispersive behavior (linear with k) and the characteristic energies permitted to exclude an optic-like nature for both excitations. The performed data analysis permitted also to extrapolate the value of the electrical conduction coefficient, founding a quite low value as compared with typical values of molten salts. An estimation of k* for the studied system emphasize the possibility that at the probed k it may be isomorphous to a neutral mixture. The observed phenomenology can be thus interpreted in terms of double sound propagation phenomenon, observed in rarefied non-ionic gaseous mixtures. Finally, an alternative interpretation of these experimental results can be qualitatively provided within the frame of the generalized collective mode approach. In this case the high frequency mode is identified with the extension of the adiabatic longitudinal sound mode beyond hydrodynamic limit that, in analogy to what observed in several fluids, follows a linear dispersion with an associated sound velocity larger than the adiabatic one. The low frequency mode could instead be associated with a propagating kinetic mode related to energy fluctuations (heat waves). In conclusion, an extensive analysis of high-frequency dynamics in binary mixtures has been reported. Particular emphasis has been devoted to the study of the sound decoupling phenomenon manifesting beyond the hydrodynamic region. The experimental results indicate that such a phenomenon is manifested in both neutral and ionic disparate mass binary mixtures. It can be related to microscopic dynamics, e.g. thermalization effects related to the inefficient kinetic exchange between lighter and heavier particles.