RESUMO
Electron mobility in superfluid helium is modeled between 0.1 and 2.2 K by a van der Waals-type thermodynamic equation of state, which relates the free volume of solvated electrons to temperature, density, and phase dependent internal pressure. The model is first calibrated against known electron mobility reference data along the saturated vapor pressure line and then validated to reproduce the existing mobility literature values as a function of pressure and temperature with at least 10% accuracy. Four different electron mobility regimes are identified: (1) Landau critical velocity limit (T ≈ 0), (2) mobility limited by thermal phonons (T < 0.6 K), (3) thermal phonon and discrete roton scattering ("roton gas") limited mobility (0.6 K < T < 1.2 K), and (4) the viscous liquid ("roton continuum") limit (T > 1.2 K) where the ion solvation structure directly determines the mobility. In the latter regime, the Stokes equation can be used to estimate the hydrodynamic radius of the solvated electron based on its mobility and fluid viscosity. To account for the non-continuum behavior appearing below 1.2 K, the temperature and density dependent Millikan-Cunningham factor is introduced. The hydrodynamic electron bubble radii predicted by the present model appear generally larger than the solvation cavity interface barycenter values obtained from density functional theory (DFT) calculations. Based on the classical Stokes law, this difference can arise from the variation of viscosity and flow characteristics around the electron. The calculated DFT liquid density profiles show distinct oscillations at the vacuum/liquid interface, which increase the interface rigidity.
RESUMO
An exact model aimed at describing uniaxial rotational motions, based on a rotational adapted Gaussian statistics, is presented. In its simplest form, it depends on only two parameters, an order parameter which can vary from 1 (perfect order) to 0 (isotropic diffusion) and a time-dependent correlation parameter rho which varies from 1 to 0 between initial and infinite times. This model yields closed form expressions for the correlation functions relevant to the main spectroscopic techniques (dielectric absorption, light and neutron scattering, NMR line shape, spin-lattice relaxation, etc.) for all values of the two parameters. According to the functional form postulated for rho(t), in particular forms decaying as power laws at long times, one obtains shapes for the spectroscopic correlation functions and spectra that are similar to those experimentally observed in a large variety of complex systems (liquid crystals, polymers, gels, and amorphous and glassy materials), especially in confined geometries, which often resemble "stretched" exponentials. A simple way to introduce time coherent effects through a modification of rho(t) is proposed. Examples of theoretical correlation functions and spectra are presented. Important remarks concerning the application of this model to the analysis of real data are made. This model is the rotational analogue of the Gaussian translational model developed recently (Volino et al. J. Phys. Chem B 2006, 110, 11217).
RESUMO
A simple model based on Gaussian statistics, aimed at describing localized diffusive translational motion in one, two, and three dimensions is presented and used to calculate the corresponding incoherent neutron scattering laws. In the time domain, these laws are closed form mathematical functions. In the frequency domain, some of these laws can be expressed as an infinite series depending on one single index. Owing to this relative simplicity, such a model can advantageously replace previous models such as diffusion on a segment, inside a circle and inside a sphere with an impermeable surface, to analyze neutron quasielastic scattering data associated with molecular motions in confined media. It may also be more realistic when the confinement is defined by soft, ill-defined boundaries.
