Density oscillations

For water, organic and water-organic metal salts mixtures the dependence of integral and spectral intensities of coherent and non-coherent scattered radiation on the atomic number (Z), density, oscillator layer thickness, chemical composition, and the conditions of the registering of analytical signals (voltage and tube current, tube anode material, crystal-analyzer) was investigated. The dependence obtained was compared to that for the solid probes (metals, alloys, pressed powder probes). 

Valence electrons also can be excited by interacting with the electron beam to produce a collective, longitudinal charge density oscillation called a plasmon. Plas-mons can exist only in solids and liquids, and not in gases because they require electronic states with a strong overlap between atoms. Even insulators can exhibit... 

The principal effect of the presence of a smooth wall, compared to a free surface, is the occurrence of a maximum in the density near the interface due to packing effects. The height of the first maximum in the density profile and the existence of additional maxima depend on the strength of the surface-water interactions. The thermodynamic state of the liquid in a slit pore, which has usually not been controlled in the simulations, also plays a role. If the two surfaces are too close to each other, the liquid responds by producing pronounced density oscillations. 

Fig. 5(a) contains the oxygen and hydrogen density profiles it demonstrates clearly the major differences between the water structure next to a metal surface and near a free or nonpolar surface (compare to Fig. 3). Due to the significant adsorption energy of water on transition metal surfaces (typically of the order of 20-50kJmoP see, e.g., [136]), strong density oscillations are observed next to the metal. Between three and four water layers have also been identified in most simulations near uncharged metal surfaces, depending on the model and on statistical accuracy. Beyond about...

Judging by these results the angular momentum relaxation in a dense medium has the form of damped oscillations of frequency jRo = (Rctc/to)i and decay decrement 1/(2tc). This conclusion is quantitatively verified by computer experiments [45, 54, 55]. Most of them were concerned with calculations of the autocorrelation function of the translational velocity v(t). However the relation between v(t) and the force F t) acting during collisions is the same as that between e> = J/I and M. Therefore, the results are qualitatively similar. In Fig. 1.8 we show the correlation functions of the velocity and force for the liquid state density. Oscillations are clearly seen, which point to a regular character of collisions and non-Markovian nature of velocity changes. 

Figure 2.5 Density oscillations of water close to the solid surface, as reported in [54].

Cheng, L, Fentee, P., Nagy, K. L, SCHLEGEL, M. L, StURCHIO, N. C., Molecular-scale density oscillations in water adjacent to a mica surface, Phys. Rev. Lett. 87, 15 (2001) 6103-6104. 

Within the classically allowed region, the wave function and the probability density oscillate with n nodes outside that region the wave function and probability density rapidly approach zero with no nodes. 

Strictly speaking, additionally the particles must be convex (i.e., without indentations or holes) and homogeneous (i.e., without density oscillations)... 

We first examined the density distribution near the solid-melt interface vs. depth from the surface. Figure 19 shows typical density profiles in a relatively small system of 8000 atoms (80 chains of Cioo). It is readily noticed that even at 500 K marked density oscillation is present near the solid surface, though... 

Fig. 19 Profiles of the atomic densities averaged in the x-y plane, at 500 K ( ) and at 300 K (o), both after 1.28 ns. Even in the melt at 500 K, marked layer structure in the density distribution is quite evident near the solid-melt interfaces. The increase in the density oscillation at 300 K is an indication of the onset of crystallization...

With decreasing temperature, the density oscillation becomes very pronounced and grows into a deeper melt region. At 300 K, for example, we can see at least 5 layers after 1.28 ns. Within the layers, as will be shown later, definite order in chain orientation and chain packing is observed suggesting the growth of polymer crystals. 

It is difficult to make a quantitative estimate of the uncertainty in the result coming from the model dependence of the approach. In the analysis several assumptions must be made, such as the radial shape of the density oscillations and the actual values of the optical model parameters. 

The results in Table V illustrate that MD studies, compared to the MC results in Table IV, facilitate the investigation of transport and time-dependent properties. Also, they show that use of the MCY potential leads to very large density oscillations and increasing water density near the surfaces. This appears to be a serious drawback to the use of the MCY potential in simulations of interfacial water. Results from the investigations using the ST2 potential show that interfacial water density is approximately 1.0 g/cc, with a tendency for decreased density and hydrogen bonding near the surfaces. As in the MC simulations, orientations of the water dipole moment are affected by the presence of a solid/liquid interface, and an... 

Monte Carlo and Molecular Dynamics simulations of water near hydrophobic surfaces have yielded a wealth of information about the structure, thermodynamics and transport properties of interfacial water. In particular, they have demonstrated the presence of molecular layering and density oscillations which extend many Angstroms away from the surfaces. These oscillations have recently been verified experimentally. Ordered dipolar orientations and reduced dipole relaxation times are observed in most of the simulations, indicating that interfacial water is not a uniform dielectric continuum. Reduced dipole relaxation times near the surfaces indicate that interfacial water experiences hindered rotation. The majority of simulation results indicate that water near hydrophobic surfaces exhibits fewer hydrogen bonds than water near the midplane. 

These results reflect the point made earlier that the structure of water is determined by the competition between the water-metal and water-water interactions. When the former are weak with no underlying lattice structure, the water structure near the metal is similar to the bulk structure. When the water-metal interactions are stronger, the water is much more structured. This was clearly demonstrated by Lee et who observed much more pronounced density oscillations when the water hydrogen-bonding interactions were turned off. 

Without the external field, the Stockmayer fluid near the wall exhibits symmetric density oscillations that die out as they reach the middle of the film. Near the surface, the fluid dipoles are oriented parallel to the walls. Upon turning on the electric field, the density profile of the Stockmayer fluid exhibits pronounced oscillations throughout the film. The amplitude of these oscillations increases with increasing field strength until a saturation point is reached at which all the fluid dipoles are oriented parallel to the field (perpendicular to the walls). The density profile remains symmetric. The dipole-dipole correlation function and its transverse [] and longitudinal [] com-... 

Lastly, non-elementary several-stage reactions are considered in Chapters 8 and 9. We start with the Lotka and Lotka-Volterra reactions as simple model systems. An existence of the undamped density oscillations is established here. The complementary reactions treated in Chapter 9 are catalytic surface oxidation of CO and NH3 formation. These reactions also reveal undamped concentration oscillations and kinetic phase transitions. Their adequate treatment need a generalization of the fluctuation-controlled theory for the discrete (lattice) systems in order to take correctly into account the geometry of both lattice and absorbed molecules. As another illustration of the formalism developed by the authors, the kinetics of reactions upon disorded surfaces is considered. 

Balian, R. and Bloch, C. (1972). Distribution of eigenfrequencies for the wave equation in a finite domain III. Eigenfrequency density oscillations, Annals of Physics 69, 76-160. 

W. Kohn, L.J. Sham, Quantum density oscillations in an inhomogeneous electron gas. Phys. Rev. 137, A1697-A1705 (1965)... 

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