The liquid structure

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

As the temperature is decreased, free-volume is lost. If the molecular shape or cross-linking prevent crystallisation, then the liquid structure is retained, and free-volume is not all lost immediately (Fig. 22.8c). As with the melt, flow can still occur, though naturally it is more difficult, so the viscosity increases. As the polymer is cooled further, more free volume is lost. There comes a point at which the volume, though sufficient to contain the molecules, is too small to allow them to move and rearrange. All the free volume is gone, and the curve of specific volume flattens out (Fig. 22.8c). This is the glass transition temperature, T . Below this temperature the polymer is a glass. 

Since amorphous alloys can be regarded as metallic solids with a frozen-in melt structure, the liquid structure freezes at different temperatures... 

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. 

The correlation between mobility and sphericity has given rise to different speculations relating molecular shape and physical properties that could influence electron transport. However, it should be stressed that the liquid structure is important as well (Stephens, 1986). For example, although the electron mobility in liquid NP is several orders of magnitude larger than that in liquid... 

In solution, although solute contributions can generally be singled out, difficulties arise sometimes solvent-solute interactions may induce a shift of the solute absorption and consequently of its susceptibility or hydrogen bonded molecular complexes may modify the liquid structure. This situation has been studied both theoretically and experimentally by Zyss and Berthier (10) and by Ledoux and Zyss (13) in the case of urea derivatives in various solvents and in crystal showing the importance of environment considerations and thus the limitations of an oriented gas model for crystals. 

Contributing to Ajj are, in addition to the solvent structural effects explicitly considered, contributions from dielectric saturation, from the liquid structure effects one has even in simple fluids, from solvent-mediated dispersion interactions of the ions, from charge-polarizability interactions of the ions, and so on. It is difficult to tell a-priori which effects are dominant or how big they are. However the collection of A 5 coefficients has characteristics that are consistent with the first named effect being dominant. 

With the Structural information obtained from the crystals, we are now in a position to discuss the liquid structure of bmimX ionic liquids. Raman spectra of liquid bmimX (X = Cl, Br, 1, BF4, PFg) are shown in Fig. 10. The Raman spectra of bmimCl Crystal (1) and bmimBr are also shown as references. All Raman spectra were measured at room temperature. The Raman spectra of liquid bmimCl and bmimBr were obtained from their supercooled states. 

Fig. 2. Plot, as a function of the inverse of temperature, of the average of ln(Ti) for all protonated carbons in quinazoline. The break indicates a change in the liquid structure and...

Transient Nucleation If a liquid is cooled continuously, the liquid structure at a given temperature may not be the equilibrium structure at the temperature. Hence, the cluster distribution may not be the steady-state distribution. Depending on the cooling rate, a liquid cooled rapidly from 2000 to 1000 K may have a liquid structure that corresponds to that at 1200 K and would only slowly relax to the structure at 1000 K. Therefore, Equation 4-9 would not be applicable and the transient effect must be taken into account. Nonetheless, in light of the fact that even the steady-state nucleation theory is still inaccurate by many orders of magnitude, transient nucleation is not discussed further. 

The information obtained from the study of the [C4CjIm]Cl crystals can be used as a basis to better understand the liquid structure of the [C4CiIm]X... 

This value of 3.54 A is somewhat less than the diameter of a nitrogen molecule based upon the cross-sectional area of 16.2 A. This is as it should be since the liquid structure is considered to be close-packed hexagonal and each nitrogen molecule sits in the depression between three molecules in the layers above and below. Equation (8.20) can now be written as... 

Another way of explaining why tiny suspended particles should be important for boiling is that these motes represent cracks or imperfections in the liquid structure. The tensile strength of the liquid will be reduced because of these flaws. 

Fig. 6.77. Calculations done using the statistical mechanical theory of electrolyte solutions. Probability density p(6,r) for molecular orientations of water molecules (tetrahedral symmetry) as a function of distance rfrom a neutral surface (distances are given in units of solvent diameter d = 0.28 nm) (a) 60H OH bond orientation and (b) dipolar orientation, (c) Ice-like arrangement found to dominate the liquid structure of water models at uncharged surfaces. The arrows point from oxygen to hydrogen of the same molecule. The peaks at 180 and 70° in p(0OH,r) for the contact layer correspond to the one hydrogen bond directed into the surface and the three directed to the adjacent solvent layer, respectively, in (c). (Reprinted from G. M. Tome and G. N. Patey, ElectrocNm. Acta 36 1677, copyright 1991, Figs. 1 and 2, with permission from Elsevier Science.

Typical forms of the radial distribution function are shown in Fig. 38 for a liquid of hard core and of Lennard—Jones spheres (using the Percus— Yevick approximation) [447, 449] and Fig. 44 for carbon tetrachloride [452a]. Significant departures from unity are evident over considerable distances. The successive maxima and minima in g(r) correspond to essentially contact packing, but with small-scale orientational variation and to significant voids or large-scale orientational variation in the liquid structure, respectively. Such factors influence the relative location of reactants within a solvent and make the incorporation of the potential of mean force a necessity. 

These equations were developed further using similar techniques to those already discussed. The more detailed analysis of liquid structures required to describe the recombination process, than the homogeneous reaction, requires higher-order equations for the liquid structure to be used. This necessarily means that approximations have to be made [286]. 

Considering local equilibrium, the liquid structure in a small portion of space around a point r is determined at time t by the local thermodynamical variables T(r,t) and P(r, t). If further the variation of temperature ST(r,t) and pressure SP(r, t) with respect to the reservoir temperature To and pressure Po is small, the x-ray scattering signal of a small volume tfir at r, which contains dn r) molecules, can be written to first order ... 

In some polymers, addition of very small amounts of diluent seems to fill up the holes in the liquid structure and the dynamics actually slow down. This antiplasticizer effect has not yet been examined with PCS, but this technique should prove very useful. The whole area of the effect of dilution on the PCS of bulk polymers is very promising and virtually unexplored. 

---