Correlations short-range molecular

Thus, the structure factor of the liquid with a short-range periodicity is the two Lorentzians centered Aq = q =2% a and q = -qo, Fig. 5.19b. Their positions are a measure of the molecular size a and their widths are a measure of the characteristic distance for the short range molecular correlations. The total intensity of scattering for positive q is shown in Fig. 5.20a. Note that the curve for the total intensity is slightly asymmetric because this function is a product of the form factor and the structure factor according to Eq. 5.25. 

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. 

QuantlogP, developed by Quantum Pharmaceuticals, uses another quantum-chemical model to calculate the solvation energy. As in COSMO-RS, the authors do not explicitly consider water molecules but use a continuum solvation model. However, while the COSMO-RS model simpUfies solvation to interaction of molecular surfaces, the new vector-field model of polar Uquids accounts for short-range (H-bond formation) and long-range dipole-dipole interactions of target and solute molecules [40]. The application of QuantlogP to calculate log P for over 900 molecules resulted in an RMSE of 0.7 and a correlation coefficient r of 0.94 [41]. 

Packing efficiency can also be described by the extent of short-range order in the amorphous state. Mitchell has shown through X-ray scattering studies that, while the local molecular organization of noncrystalline polymers is random, in many cases, there are additional correlations that do not perturb the chain trajectory but will impact polymer properties.15 These correlations have a limited spatial range (<50A) but will have a particular impact on bulk properties... 

The molecular approach, adopted throughout this book, starts from the statistical mechanical formulation of the problem. The interaction free energies are identified as correlation functions in the probability sense. As such, there is no reason to assume that these correlations are either short-range or additive. The main difference between direct and indirect correlations is that the former depend only on the interactions between the ligands. The latter depend on the maimer in which ligands affect the partition function of the adsorbent molecule (and, in general, of the solvent as well). The argument is essentially the same as that for the difference between the intermolecular potential and the potential of the mean force in liquids. 

The pair correlation function is a short range quantity in liquids, decaying to unity after a few molecular diameters, the correlation length However, in supercritical fluids g(r) has a much longer range and t, becomes considerably larger than the mean inter-molecular separation at the critical density. For instance, for carbon dioxide , = 5.5 nm at Tc compared to the mean intermolecular separation of 0.55 nm (Eckert, Knutson and Debenedetti 1996). 

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