Linear Free Energy Relationships in Extraction of Rare Earths by Acidic Organophosphorus Extractants

The correlation relationships of apparent extraction equilibrium constant (1gK(ex)) with the electronic effect parameter( Sigma sigma(Phi)) and the steric effect parameter ( Sigma upsilon ) of the substituents in extractant molecules are investigated by linear regression analysis in the extraction of rare earths by various classes and structures of monoacidic organophosphorus extractants. The results indicate that in Linear free energy relationship formula 1gK(ex) = rho Sigma sigma(Phi) + psi Sigma upsilon + h generally follows for this kind of extraction systems. Accordingly, the quantitative structure-behaviour relationships of extractants are discussed. These relationships can be preliminarily applied to predict the 1gK(ex) values of rare earth extraction with definite structures of this class of extractants, and thus can provide some directions for the design of new RE extractants.

Effect of Ionic Liquid on Retention of Solutes on C_(18) Column Based on Linear Solvation Energy Relationships

Several chromatography systems with ionic liquids and a mixture of water with the modifier as mobile phase were characterized via the linear solvation energy relationships（LSER） model. The effects of the ionic liquids and modifier（methanol） concentrations on the retention of 10 solutes（caffeine, pyridine, aniline, phenol, methylparaben, acetopenone, m-cresol, p-cresol, o-cresol, and benzene） were discussed. The LSER model demonstrated high potential to predict retention factors with high squared correlation coefficients（r^2〉 0.97）. A comparison of predictable and experimental retention factors revealed that LSER can adequately reproduce the experimental retention factors of the solutes under different investigated experimental conditions. This model is a helpful tool to evaluate the retention characteristics of ionic liquid systems and to understand the interactions of solutes and ionic liquids.

Energy relationship and the polarization of C_(60) cage in the endohedral complexes (X@C_(60))

In this paper, we carry out the calculation on the system (X@C60)(X=Li, Na, K, Kb, Cs; F, Cl, Br, I), where the position of X changes along 5 typical symmetry directions. For the calculation of quantum chemistry we use EHMO/ASED method, for the calculation of molecular mechanics we use Buckingham potential (exp-6-1) function, and for the calculation of thermo-chemical cycle we use individually isolating the processes such as the structure variation, charge transfer and charge distribution, and their interactions etc. The calculation results show that (1) In the region of radius r≈0.2 nm of the Ceo cage, the potential field is nearly spherical; (2) Except for Li and Na, the systems are the most stable with minimum energies at the center of C60 cage. For Li and Na, the systems are the most stable with minimum energies at r≈0.16 nm and r≈0.13 nm, respectively. In view of the interactive region of chemical bonds, the interactions between X and the C60 cage do not belong to the classical chemical bonds; (3) The non-bonding interaction between the X and C60 cage are not purely electro-static, in which the electro-static interactions only occupy -90% at most on an average. The repulsion owing to the overlap of the electron cloud and the attraction owing to the dispersion can not be neglected. These two interactions determine the variations of size and trend of the system energies with r; (4) The polarization due to the position of X deviating from the center of C60 cage plays an important role at the most stable positions of Li and Na.

Application of TLSER method in predicting the aqueous solubility and n-octanol/water partition coefficient of PCBs,PCDDs and PCDFs

The theoretical linear solvation energy relationship(TLSER) approach was adopted to predict the aqueous solubility and n -octanol/water partition coefficient of three groups of environmentally important chemicals-polychlorinated biphenyls(PCBs), polychlorinated dibenzodioxins and dibenzofurans(PCDDs and PCDFs). For each compound, five quantum parameters were calculated using AM1 semiempirical molecular orbital methods and used as structure descriptors: average molecular polarizability(α), energy of the lowest unoccupied molecular orbit( E _ LUMO ), energy of the highest occupied molecular orbit( E _ HOMO ), the most positive charge on a hydrogen atom( q _+), and the most negative atomic partial charge( q _-) in the solute molecule. Then standard independent variables in TLSER equation was extracted and two series of quantitative equations between these quantum parameters and aqueous solubility and n -octanol/water partition coefficient were obtained by stepwise multiple linear regression(MLR) method. The developed equations have both quite high accuracy and explicit meanings. And the cross-validation test illustrated the good predictive power and stability of the established models. The results showed that TLSER could be used as a promising approach in the estimation of partition and solubility properties of macromolecular chemicals, such as persistent organic pollutants.

Intrinsic physical relationships between rotor modal shapes and instantaneous vibrational energy flow transmission characteristics:Theoretical and numerical analysis and application

The modal vibration of the rotor is the main cause of excessive vibration of the aeroengine overall structure.To attenuate the vibration of the rotor under different modal shapes from the perspective of energy control,the intrinsic physical relationships between rotor modal shapes and instantaneous vibrational energy flow transmission characteristics is derived from the general equation of motion base on the structural intensity method.A dual-rotor-support-casing coupling model subjected to the rotor unbalanced forces is established by the finite element method in this paper.The transmission,conversion and balance relationships of the vibrational energy flow for the rotors in the first-order bending modal shape,the conical whirling modal shape and the translational modal shape are analyzed,respectively.The results show that the vibrational energy flow transmitted to the structure can be converted into the strain energy,the kinetic energy and the energy dissipated by the damping of the structure.The vibrational energy flow transmission characteristics of rotors with different modal shapes are quite different.Especially for the first-order bending modal shape,the vibrational energy flow and the strain energy are transmitted and converted to each other in the middle part of the rotor shaft,resulting in large deformation at this part.To attenuate this harmful vibration,the influences of grooving on the shaft on the first-order bending vibration are studied from the perspective of transmission control of vibrational energy flow.This study can provide theoretical references and guidance for the vibration attenuation of the rotors in different modal shapes from a more essential perspective.

Relationships among group delay,energy storage,and loss in dispersive dielectric mirrors

We show that absorbed and stored electromagnetic energy are proportional to the reflection group delay in highly reflective dispersive dielectric mirrors over the high-reflectivity band. Our theoretical considerations are verified by numerical simulations performed on different dielectric mirror structures. The revealed pro- portionality between group delay and absorbed energy sets constraint on the application of ultrabroadband and/or dispersive dielectric mirrors in broadband or widely tunable, high-power laser systems.