Liquid correlations

S. H. Vosko, L. Wilk and M. Nusair, Accurate spin-dependent electron liquid correlation energies for local spin density calculations a critical analysis, Canadian J. Phys., 58,1200 (1980). 

Vosko, S. J., Wilk, L., Nusair, M., 1980, Accurate Spin-Dependent Electron Liquid Correlation Energies for Local Spin Density Calculations A Critical Analysis , Can. J. Phys., 58, 1200. 

Electron Liquid Correlation Energies for Local Spin Density Calculations A Critical... 

When estimating the stirrer power requirements for non-Newtonian liquids, correlations of the power number versus the Reynolds number (Re see Figure 7.8) for Newtonian hquids are very useful. In fact, Figure 7.8 for Newtonian liquids can be used at least for the laminar range, if appropriate values of the apparent viscosity are used in calculating the Reynolds number. Experimental data for various non-Newtonian fluids with the six-blade turbine for the range of (Re) below 10 were correlated by the following empirical Equation 12.1 [1] ... 

This fugacity ratio correction is critically important and can have an enormous effect on solubility. Since chemicals in solution are in the liquid state they behave as if, in the limit, they were pure liquids, and the reference fugacity or vapor pressure must be of the liquid. Correlations of partition coefficients such as octanol-water with solubility must include this "correction."... 

Electron spin resonance (ESR) studies of radical probe species also suggest complexity. Evans et al. [250] study the temperature dependence of IL viscosity and the diffusion of probe molecules in a series of dissimilar IL solvents. The results indicate that, at least over the temperature range studied, the activation energy for viscous flow of the liquid correlates well with the activation energies for both translational and rotational diffusion, indicative of Stoke-Einstein and Debye-Stokes-Einstein diffusion, respectively. Where exceptions to these trends are noted, they appear to be associated with structural inhomogeneity in the solvent. However, Strehmel and co-workers [251] take a different approach, and use ESR to study the behavior of spin probes in a homologous series of ILs. In these studies, comparisons of viscosity and probe dynamics across different (but structurally similar) ILs do not lead to a Stokes-Einstein correlation between viscosity and solute diffusion. Since the capacities for specific interactions are... 

Unfortunately, there is no good theory equivalent to the kinetic theory that is applicable to liquids. Thus liquid correlations tend to be more empirical than the equivalent ones for the gas phase. 

In Section 1.7.2, we will see that the weight-average molar mass can be measured by light scattering from a dilute polymer solution. The viscosity of polymer liquids correlates well with the weight-average molar mass. 

Ueno K, Tokuda H, Watanabe M (2010) lonicity in ionic liquids correlation with ionic structure and physicochemical properties. Phys Chem Chem Phys 12 1649-1658... 

Vosko S H, L Wilk and M Nusair 1980. Accurate Spin-dependent Electron Liquid Correlation Energies for Local Spm Density Calculations- A Critical Analysis Canadian journal of Physics 58-1200-1211. 

The unusually small volume ratio of gas to liquid makes stripping plate efficiencies low. Yokota s model of the process assumes that liquid travels across a plate in uniform flow with no transverse mixing but that vertical mixing is perfect. He then characterizes a plate by the length of linear travel of the liquid. Correlation of the experimental data is in terms of the length of a transfer unit. This is the distance that liquid must travel to undergo an amount of mass transfer equivalent to one transfer unit. A plate then provides a (normally fractional) number of transfer units given by... 

Miran MS, Yasuda T, Susan MA, Dokko K, Watanabe M (2013) Electrochemical properties of protic ionic liquids correlation between open circuit potential for H2/O2 cells under non-humidified conditions and ApKa. RSC Adv 3 4141-4144... 

Vosko SL, Wilk L, Nusair M (1980) Accurate spin-dependent electron liquid correlation energies for local spin density calculations a critical analysis. Can J Phys 58 1200-1211 Wagman DD, Evans WH, Parker VB, Schumm RH, Halow I, Bailey SM, Chumey KL, Nuttall, RL (1982) The NBS Tables of chemical thermodynamic properties, selected values for inorganic and cl and c2 organic substances in SI units. J Chem Phys Ref Data (Supplement 2) 11 1-329 Wallen SL, Palmer BJ, Fulton JL (1998) The ion-pairing and hydration stracture of NP in supercritical water at 425 degrees C determined by X-ray absorption fine stracture and molecular dynamics studies. J Chem Phys 108 4039-4046... 

RI is related to molecular-physical properties of the substance. Thus, RIs of crystalline alkali halides decrease linearly as their melting temperamres increase (Eig. 11.3) [34], while RIs of organic liquids correlate similarly with their boiling temperatures [35]. 

The mean field (Landau) theory erf block copolymers developed by Leibler [87] is based on an IRPA treatment of the liquid correlations. Enfordng the latter constraint on PRISM theory in a post facto maimer yields for an AB block... 

The combination of polymeric density functional methods and PRISM theory for the liquid correlations allow a wide range of closure and inhomogeneous material problems to be studied [109]. Present research involves using this approach to treat at an atomistic level the crystallization of the entire alkane series, and the structure of hydrocarbon fluids near surfaces and interfaces [109]. An alternative, purely integral equation approach to the latter problem is to employ the wall-PRISM theory of Yethiraj and Hall [37]. 

Figure 1. Atomic correlation energi as a function of atomic number Z, Circles show the results of Clementi [18], essentially as extracted from experiment. Upper dashed curve shows results based on local density use of homogeneous electron liquid correlation energy. Lowest dashed curves show the results using the He-atom based result of CoUe and Salvetti [19]. Plainly atoms are not described quantitatively by local density electron liquids. (Redrawn from March and Wind [17])...

Foam breaking difficulty quantitatively related to intrinsic foamabiUty of liquid. Correlations given for critical disc speed for foam breaking with foamability Sparging/bubble Correlations for critical disc speed... 

The main area per paraffinic chain increases with temperature and chain length, corresponding to an increase of the curvature between the aromatic and the paraffinic moieties. For this reason columnar mesomorphism is always the high temperature one and is obtained directly from the isotropic liquid. Correlatively, with two dense paraffinic ends (phasmids and pentacatenars) a columnar phase occurs, while smectic and nematic phases appear as the number of paraffinic chains is decreased [50]. 

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