Short-range correlations

There has been much activity in the study of monolayer phases via the new optical, microscopic, and diffraction techniques described in the previous section. These experimental methods have elucidated the unit cell structure, bond orientational order and tilt in monolayer phases. Many of the condensed phases have been classified as mesophases having long-range correlational order and short-range translational order. A useful analogy between monolayer mesophases and die smectic mesophases in bulk liquid crystals aids in their characterization (see [182]). 

Equation (A3.3.57) must be supplied with appropriate initial conditions describing the system prior to the onset of phase separation. The initial post-quench state is characterized by the order parameter fluctuations characteristic of the pre-quench initial temperature T.. The role of these fluctuations has been described in detail m [23]. Flowever, again using the renomialization group arguments, any initial short-range correlations should be irrelevant, and one can take the initial conditions to represent a completely disordered state at J = xj. For example, one can choose the white noise fomi (i /(,t,0)v (,t, 0)) = q8(.t -. ), where ( ) represents an... 

As with SCRF-PCM only macroscopic electrostatic contribntions to the Gibbs free energy of solvation are taken into account, short-range effects which are limited predominantly to the first solvation shell have to be considered by adding additional tenns. These correct for the neglect of effects caused by solnte-solvent electron correlation inclnding dispersion forces, hydrophobic interactions, dielectric saturation in the case of... 

SALI compares fiivorably with other major surface analytical techniques in terms of sensitivity and spatial resolution. Its major advantj e is the combination of analytical versatility, ease of quantification, and sensitivity. Table 1 compares the analytical characteristics of SALI to four major surfiice spectroscopic techniques.These techniques can also be categorized by the chemical information they provide. Both SALI and SIMS (static mode only) can provide molecular fingerprint information via mass spectra that give mass peaks corresponding to structural units of the molecule, while XPS provides only short-range chemical information. XPS and static SIMS are often used to complement each other since XPS chemical speciation information is semiquantitative however, SALI molecular information can potentially be quantified direedy without correlation with another surface spectroscopic technique. AES and Rutherford Backscattering (RBS) provide primarily elemental information, and therefore yield litde structural informadon. The common detection limit refers to the sensitivity for nearly all elements that these techniques enjoy. 

Let us begin our discussion from the model of Cummings and Stell for heterogeneous dimerization a + P ap described in some detail above. In the case of singlet-level equations, HNCl or PYl, the direct correlation function of the bulk fluid c (r) represents the only input necessary to obtain the density profiles from the HNCl and PYl equations see Eqs. (6) and (7) in Sec. II A. It is worth noting that the transformation of a square-well, short-range attraction, see Eq. (36), into a 6-type associative interaction, see Eq. (39), is unnecessary unless one seeks an analytic solution. The 6-type term must be treated analytically while solving the HNCl... 

Correlation between Ionic Entropy and Viscosity. In Chapter 9, when we noticed that certain ions in aqueous solution cause a decrease in viscosity, and asked how this should be explained, it seemed natural to interpret the effect in terms of order and disorder. In pure water at room temperature there is a considerable degree of short-range order ... 

Surface force profiles between these polyelectrolyte brush layers have consisted of a long-range electrostatic repulsion and a short-range steric repulsion, as described earlier. Short-range steric repulsion has been analyzed quantitatively to provide the compressibility modulus per unit area (T) of the poly electrolyte brushes as a function of chain density (F) (Fig. 12a). The modulus F decreases linearly with a decrease in the chain density F, and suddenly increases beyond the critical density. The maximum value lies at F = 0.13 chain/nm. When we have decreased the chain density further, the modulus again linearly decreased relative to the chain density, which is natural for chains in the same state. The linear dependence of Y on F in both the low- and the high-density regions indicates that the jump in the compressibility modulus should be correlated with a kind of transition between the two different states. 

For (Li, Cs)Cl, the internal mobilities have been calculated from Eqs. (27) and (28), and are given in Table 8. The SEVs were calculated from the same MD runs and are plotted against the calculated internal mobilities in Fig. 17 with excellent correlation between these calculated quantities. The good correlation of the SEV with the calculated and experimental internal mobilities suggests that relatively short-range cation-anion interaction plays a role in internal mobilities and the separating motion of pairs, that is dissociation, is related to the internal mobilities. In other words, the result of the SEV supports the dynamic dissociation model. 

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