Liquid structure density fluctuations

Spp(A) which is the liquid structure factor discussed earlier in section A2.2.5.2. The density fluctuation spectrum is... 

For a one-component fluid, the vapour-liquid transition is characterized by density fluctuations here the order parameter, mass density p, is also conserved. The equilibrium structure factor S(k) of a one component fluid is... 

The Phenomenon. In existing materials the electron density is not even constant inside a single phase. This is obvious for the liquid structure of amorphous regions. Nevertheless, even in crystalline phases lattice distortions and grain boundaries result in variations of the electron density about its mean value. In analogy to the sunlight scattered from the fluctuations of air density, X-rays are scattered from the fluctuations of electron density. 

In a supercooled liquid the static structure factor 5(q) is nearly zero for small wavenumbers (because of very low compressibility) hence density fluctuation can take place only at intermediate wavenumbers where S(q) is large. For example, a fluctuation at qa = 1 would imply a length scale approximately comparable to 2na, which is of the same order as estimated by Cicerone et al. [86]. 

In supercritical fluids, the possibility of local composition enhancements of cosolvent about a solute suggests that we should see enhancement of anion fluorescence if the water cosolvent clusters effectively about the 2-naphthol solute. Although in liquids the water concentration must be >30% to see anion emission, the higher diffusivity and density fluctuations in SCFs could allow stabilization of the anion at much lower water concentrations provided that the water molecules provide sufficient structure. Therefore the purpose of these experiments was to investigate 2-naphthol fluorescence in supercritical CO 2 with water cosolvent in the highly compressible region of the mixture to probe the local environment about the solute. 

When two such surfaces approach each other, layer after layer is squeezed out of the closing gap (Fig. 6.12). Density fluctuations and the specific interactions then cause an exponentially decaying periodic force the periodic length corresponds to the thickness of each layer. Such forces were termed solvation forces because they are a consequence of the adsorption of solvent molecules to solid surfaces [168], Periodic solvation forces across confined liquids were first predicted by computer simulations and theory [168-171], In this case, however, the experimental proof came only few years afterwards using the surface forces apparatus [172,173]. Solvation forces are not only an important factor in the stability of dispersions. They are also important for analyzing the structure of confined liquids. 

The restriction to dense hquids and, in some respects, to one-component systems deserves further comment. Such restrictions follow from the physical assumption here that thermal fluctuations in are negligible. If a one-component liquid is sufficiently dense, then variety in the structures that occur with reasonable frequency during the thermal motion will be limited. Since density fluctuations may be gauged with the compressibility dp/dfip j, see Eq. (2.24) p. 27, these approximations are expected to be better where the compressibility is (or more generally, susceptibilities are) smaller. The compressibility is likely to be smaller for the higher density fluid states. 

Of these models, the mode-coupling theory has the clearest direct coimection to liquid-state structure it attempts to describe nonhnear density fluctuations in dense liquids. 

MCT is a popular liquid viscosity theory (Gee, 1970 Gotze et al., 1981 Leutheuser, 1984, Jackie, 1989). It is based on the description of the dynamical properties of density fluctuations in terms of a dynamical structure factor. There are inherent density fluctuations in liquids, which decay with characteristic relaxation times. The decay becomes slower as the temperature is lowered due to increase of viscosity. It is controlled by dynamically correlated collisions. The equations governing the decay are non-linear. Analysis of the non-linear equation of motion of the density fluctuations gives a density correlation function of the type... 

The discrete level structure is crucial for the lowest energy excitations, whose wavelength is comparable to Rq, and which represent collective excitations of the entire cluster. The eigenmomenta k e are defined by boundary condition (i) for the LDM, with je kneRo) = 0, where j -) are the spherical Bessel functions. The compressional density fluctuations in a liquid drop give a phonon-like discrete spectrum for all clusters sizes [84, 85, 128]... 

The supercooled liquid catastrophe, if it exists, would necessarily be associated with diverging fluctuations in the structural order parameter F. This stems from the fact that the Y surface develops a vanishing curvature in the F direction as this endpoint is approached. Because the bicyclic octamer elements are bulky, fluctuations in their coiKentration amount to density fluctuations. Diverging density fluctuations then imply diverging isothermal compressibility. Furthermore the infinite slope of the metastable liquid locus at its endpoint implies the divergence of thermal expansion. Potential energy fluctuations remain essentially normal, so constant-volume heat capacity remains small. But the volumetric divergence creates an unbounded constant-pressure heat capacity. 

Reference has also been made to clean or purified water. In fact, all the numbers shown in Table 1 and Figure 7 are based on the homogeneous nucleation model, according to which the generation of nuclei is solely the result of random density fluctuations within the liquid phase. It is, however, well known that nucleation can be catalysed by internal and external factors, in which case the growth and persistence, possibly also the dimensions and structures, of critical clusters are... 

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