Effective eigenmode description of dynamical processes in dense classical fluids and fluid mixtures

Influence of cholesterol on the collective dynamics of the phospholipid acyl chains in model membranes

We have studied the packing and collective dynamics of the phospholipid acyl chains in a model membrane composed of 1,2-dimyristoyl-sn-glycero-3-phosphatidylcholine (DMPC) and cholesterol in varied phase state. After a structural characterization of this two-component model bilayer using X-ray reflectivity, we have carried out coherent inelastic neutron scattering to investigate the chain dynamics. Both DMPC/cholesterol membranes exhibited much sharper and more pronounced low-energy inelastic excitations than a pure DMPC membrane. In the high-energy regime above 10 meV, the insertion of cholesterol into the membrane was found to shift the position of the inelastic excitation towards values otherwise found in the pure lipids gel phase. Thus, the dissipative collective short-range dynamics of the acyl chains is strongly influenced by the presence of cholesterol.

Analysis of inelastic x-ray scattering spectra of low-temperature water

We analyze a set of high-resolution inelastic x-ray scattering (IXS) spectra from H2O measured at T=259, 273, and 294 K using two different phenomenological models. Model I, called the "dynamic cage model," combines the short time in-cage dynamics described by a generalized Enskog kinetic theory with a long-time cage relaxation dynamics described by an alpha relaxation. This model is appropriate for supercooled water where the cage effect is dominant and the existence of an alpha relaxation is evident from molecular-dynamics (MD) simulation data of extended simple point charge (SPC/E) model water. Model II is essentially a generalized hydrodynamic theory called the "three effective eigenmode theory" by de Schepper et al. 11. This model is appropriate for normal liquid water where the cage effect is less prominent and there is no evidence of the alpha relaxation from the MD data. We use the model I to analyze IXS data at T=259 K (supercooled water). We successfully extract the Debye-Waller factor, the cage relaxation time from the long-time dynamics, and the dispersion relation of high-frequency sound from the short time dynamics. We then use the model II to analyze IXS data at all three temperatures, from which we are able to extract the relaxation rate of the central mode and the damping of the sound mode as well as the dispersion relation for the high-frequency sound. It turns out that the dispersion relations extracted from the two models at their respective temperatures agree with each other giving the high-frequency sound speed of 2900+/-300 m/s. This is to be compared with a slightly higher value reported previously, 3200+/-320 m/s, by analyzing similar IXS data with a phenomenological-damped harmonic oscillator model 22. This latter model has traditionally been used exclusively for the analysis of inelastic scattering spectra of water. The k-dependent sound damping and central mode relaxation rate extracted from our model analyses are compared with the known values in the hydrodynamic limit.

Model for dynamics in supercooled water

We propose a phenomenological model for the intermediate scattering function (ISF) associated with density fluctuation in low temperature water. The motivation is twofold: to extract various physical parameters associated with the ISF computed from extended simple-point-charge model water at supercooled temperatures, and to apply this model to analyze high resolution inelastic x-ray scattering data of water in the future. The ISF of the center of mass of low temperature water computed from 10 M-step molecular dynamics (MD) data shows clearly time-separated two-step relaxation with a well-defined plateau in-between. We interpret this result as due to the formation of a stable hydrogen-bonded, tetrahedrally coordinated cage around a typical molecule in low temperature water. We thus model the long-time cage relaxation by the well-known Kohlrausch form exp[-(t/tau)(beta)] with an amplitude factor which is a k-dependent Debye-Waller factor A(k), and treat the short-time relaxation as due to molecular collisional motions within the cage. The latter motions can be described by the generalized Enskog equation, taking into account the confinement effect of the cage. We shall show that the effect of the confinement changes the collisional dynamics by modifying certain input parameters in the kinetic theory by a factor [1-A(k)](1/2). We solve the generalized Enskog equation approximately but analytically by a Q-dependent triple relaxation time kinetic model. This kinetic model was previously shown to account for the large k behavior of Rayleigh-Brillouin scattering from moderately dense, simple fluids. We find that our model fits well with the MD generated collective as well as single-particle ISFs. For the short-time collisional dynamics, we fix values of the hard sphere diameter sigma and pair correlation function at contact g(sigma), without introducing any adjustable parameters. The calculated ISFs reproduce the correct Brillouin peak frequencies at low k values. From the long-time dynamics, we deduce values of the Debye-Waller factor A(k), the Kohlrausch exponent beta(k), and the cage relaxation time tau(k).