Hole density fluctuations

Figure 2 shows the transient absorption spectrum of PB in CI%H at 5.7 MPa. The pattern of the transient sp>ectrum is almost the same as those in methanol. The hole broadening occurs mostly within 0.8 ps, and the bleach is recovered with two different time constants in a similar manner as in the liquid solvents, although the recovery after 2 ps is much slower in the fluid near the critical density (about 40 ps). It is also to be noted that the bleach signal after 2 ps is narrow banded in comparison with the equilibrium absorption. This can be interpreted by the overlapping of the excited state absorption, and/or, the small inhomogeneity remained after 2 ps due to the long time density fluctuation. 

The perspective upon which the concept of a superheat limit emerges is based on random molecular density fluctuations within the hulk of a liquid producing hole-like regions of moleculardimensions that act as bubbles. A phase transition occurs when abubble, formed by these molecular processes, grows to a size such that it is in unstable equilibrium (i.e.. a critical size nucleus ) with the surrounding liquid. The "nucleation rate ,/, refers to the mean rate of forming such vapor nuclei in units of nuclei/(volume time). 

Because of the poorer packing of protofibrils at band locations, these should be more readily invaded by foreign substances. Large invading molecules may actually increase the distortions of protofibrils at bands or actually pry open the structure to increase the spread of distortion along the fibril. On the other hand, molecules which are small compared to protofibril diameters may serve to smooth out the kinks and increase perfection, or perhaps to fill in the holes and reduce the electron-density fluctuations at the imperfect cross sections, thus causing similar reduction in the diffraction evidence of imperfection. Chemical attack on the fibril should most easily be accomplished at band locations. 

This study shows that none of the various forms of relaxation function used to describe ageing are completely satisfactoiy and TRS is inappropriate. Correlation between results, (Figure 9) indicates the inherent connectivity between the processes. Curro et al (24,25) have studied the change in density fluctuation with temperature and annealing time for PMMA (25) and compared it with specific volume data. Positron annihilation data on PMMA (27,28) has been interpreted in terms of free volume. For a distribution of hole sizes there will exist many decaying exponentials each with a different characteristic lifetime. The composite of these many exponentials can itself be approximated to an exponential, and it is this decay constant that is used to represent the mean lifetime, and therefore mean hole size. 

Isobaric density fluctuations entropy fluctuations, i.e. fluctuations in Frenkel s holes in the structure of a liquid (Frenkel, 1955). They lead to the density fluctuations which do not depend on pressure fluctuations. Their evolution proceeds quite slowly and causes a much lower frequency shift on scattering. These fluctuations are related to the central component of scattered light called Rayleigh s component. 

Fujita (Fujita and Kishimoto, 1961), and those of Vrentas and Duda (1977, 1982). They all consider the free volume per molecule as the volume within the cage of a molecule minus the volume of the molecule itself, i.e., as a hole opened up by density fluctuations of the molecules. According to Cohen and Turnbull (1959), diffusion occurs not as a result of activation in the ordinary sense, but as a result of redistribution of free volume within the liquid. With this, they derive an expression for mobility, similar to the Doolittle equation (1951, 1952) ... 

For the exchange and correlation terms we thus obtain two contributions, namely from the homogeneous electron density no = Z I q outside the core region (since inside the core the orthogonalization hole repels the valence electrons), and a contribution from the density fluctuations. The first term thus gives a contribution ... 

The hole model may serve as a basis in the tmderstanding of the decrease of the first coordination number with decreasing density in the liquid state. However it seems imable to account for the extra-entropy which exists in the liquid state. Ihis is due to the excessively schematic representation of the density fluctuations. Furthermore the problem of correlations in the motions of molecules is not solved, the hole model being a one-particle model exactly as the original Leimard-Jones and Devonshire model. 

Nucleation in a pure liquid. According to the kinetic theory for pure gases and liquids, there are local fluctuations of densities, which are clusters of molecules in a gas and holes (or vapor clusters) in a liquid. Frenkel (1955) established the population distribution of such holes of phase B in a liquid of continuum phase A by Boltzmann s formula,... 

It was found that normal zero-point oscillations lie on top of large gluon fluctuations - instantons and anti-instantons with random positions and sizes. The left column - action density and the right column - topological charge density. Here instantons are peaks and anti-instantons are holes. 

The Perez model comes from an approach in which the source of mobility is the existence of quasi-punctual defects characterized by positive or negative fluctuations of packing density, whereas classical free volume theories take into account only the domains of low packing density, e.g., the holes. The model leads to the following equation for the complex modulus ... 

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