Abraham Model Research Articles

Development of a Model to Predict Partition Coefficient of Organic Pollutants in Cloud Point Extraction Process

A quantitative structure property relationship (QSPR) study has been performed to establish a model to relate structural descriptors of 45 organic compounds to their partition coefficients in water-hexadecylpyridinium chloride (CPC) micelles at 298K using partial least squares (PLS). 510 of six different categories of structural descriptors were calculated by Dragon software. The descriptors with 0.9 mutually pair correlations and with less than 0.1 with dependent variables were excluded at the early stage of the preprocessing of the structural data matrix. The data set was randomly divided into two groups: training set (40 molecules) and test set (5 molecules). In the final model 50 of the most effective of the structural descriptors on the partition coefficient were remained to model building by PLS calibration method. The optimum number of latent variables 5, which spanned 80% of the original variations of data matrix, was selected using leave one out cross validation method. Prediction ability of the model was tested by prediction of the partition coefficients of five unknown compounds and the mean relative error of prediction was 3.6%. The outliers were treated using leverage and score plots of the first third principal components. The efficiency of the new model was compared with Abraham model and it was found that the proposed model has more prediction ability.

Extraction of selected pollutants in open tubular capillary columns

Extraction of selected phenol acetyl derivatives and polycyclic aromatic hydrocarbons in open tubular capillary columns was studied. It was found that open tubular extraction enables to extract phenols in 10 sorptive cycles with yields similar to those obtained in equilibrium solvent extraction. The sorptive properties of the stationary phase can be modified by the use of various solvents. The positive effect of toluene used as a swelling agent is especially strong for nitrophenols. Using the Abraham model, distribution coefficients are well correlated with the pollutant parameters. The hydrophobicity of the pollutants measured by the molar volume or octanol–water distribution coefficient, is the most important factor affecting extraction in open tubular extraction. The signs of other regression coefficients reflect well the effect of the stationary phase polarity.

Hopping transport in doped organic semiconductors: A theoretical approach and its application to p-doped zinc-phthalocyanine

A detailed approach to the complex hopping transport in organic semiconductors is presented and used to describe experimental data from Maennig et al. [Phys. Rev. B 64, 195208 (2001)] on the effect of doping on conductivity, mobility and thermopower. In this approach, the energetic distribution of the charge carriers in a Gaussian shaped density of states (DOS) is calculated under thermal equilibrium conditions and compared to the energetic distribution of the current. The description is based on the Miller–Abraham model for hopping in a disordered material and utilizes the so-called transport energy concept. To include also the case of higher electron concentrations in the tail states of the DOS the Fermi distribution was taken into account. Furthermore, additional trap states in the gap are considered to describe the experimental data at low doping concentration more correctly. In the framework of the model there is no indication of a thermally activated ionization of the dopants. In contrast to other descriptions, the position of the Fermi energy and transport energy are calculated from the model. It is demonstrated that the principal behavior of the transport parameter can be well explained in terms of classical semiconductor physics.

Abraham model in gas chromatography of phenol pollutants

Chromatographic data of some selected phenol pollutants were determined and used to derive the linear solvation free energy relationships (LSERs). The Abraham model was used to correlate retention time, retention index and correction coefficient of phenols with solute parameters. Linear solvation free energy relationship can be used for prediction and verification of experimental data. Although phenols are derivatized prior their determination, the Abraham parameters of underivatized phenols can be used for modelling, but the ∑ α 2 H parameter must be neglected as the derivatized phenols loose their ability to donate proton. Gas–liquid partition coefficient on hexadecane is the most important parameter when phenols are separated on non-polar phases. The effects of other parameters are not so well defined. The replacement of log L 16 term by the logarithm of octanol–water partitioning coefficient does not improve the relationships.

Adiabatic Limit for the Maxwell-Lorentz Equations

We consider the Abraham model of a rigid charge distribution coupled to the electromagnetic field and subject to, on the scale of the charge diameter, slowly varying external potentials. We prove that in the adiabatic limit the motion of the charged particle is governed by a effective Hamiltonian. To next order one has to add as a small correction the relativistically covariant radiation reaction. This third order equation has a repulsive center manifold and the true solution is well approximated by a trajectory on the center manifold.We also prove that in the adiabatic limit the fields are derived from the Liénard-Wiechert potentials of a moving point charge and that the radiated energy is given by Larmor's formula.

Estimation of Distribution Parameters of Organic Solutes in Cloud Point Extraction

Cloud point extraction of aromatic solutes in the system containing nonionic surfactant polyoxyethylene nonylphenyl ether (PONPE 10) was discussed in terms of their hydrogen-bond donating and accepting abilities and hydrophobicity. It was shown that the Abraham model could be used to estimate the distribution ratio and the effect of aromatic solutes on the cloud point.

Slow Motion of Charges¶Interacting Through the Maxwell Field

We study the Abraham model for $N$ charges interacting with the Maxwell field. On the scale of the charge diameter, $R_{\phi}$, the charges are a distance $\eps^{-1}R_{\phi}$ apart and have a velocity $\sqrt{\eps} c$ with $\eps$ a small dimensionless parameter. We follow the motion of the charges over times of the order $\eps^{-3/2}R_{\phi}/c$ and prove that on this time scale their motion is well approximated by the Darwin Lagrangian. The mass is renormalized. The interaction is dominated by the instantaneous Coulomb forces, which are of the order $\eps^{2}$. The magnetic fields and first order retardation generate the Darwin correction of the order $\eps^{3}$. Radiation damping would be of the order $\eps^{7/2}$.

On the dielectric continuum solvent model for theoretical estimates of the conformational equilibrium of molecules with an intramolecular hydrogen bond

Theoretical calculations of solvation energies for molecules with an intramolecular hydrogen bond have been performed using two types of continuum dielectric solvation models. One is the Onsager–Kirkwood–Abraham model (OKA) with a simple spherical cavity and the other is a polarized continuum (overlapping spheres) model (PCM) with a bubble-shaped solvent accessible surface. The solvation energies by the PCM model are several times larger than those by the OKA model. Nevertheless, the both models provide approximately consistent results with each other for differences in solvation energy, Δ E solv, between intramolecularly hydrogen bonded conformers and hydrogen-bond-free conformers. These results roughly reproduce the experimental values which were previously obtained by variable-temperature infrared spectroscopy. However, the agreement between the calculations and the experimental results is not satisfactory and not improved even by using the PCM model with the sophisticated solvent accessible surface instead of the simple OKA model. The problem might be attributed to a defect of the dielectric continuum approximation of solvent.

On the lack of invariance of some Bayesian outlier models

The property of non‐invariance to the scale of the data for the Abraham and Box (1978) Bayesian outlier model, and the model that generalizes the Guttman, Dutter and Freeman (1978) outlier analysis is discussed. This drawback is due to the non‐informative prior taken for the parameters. Freeman (1980) expected that most posterior weight would be put on the model with the most outliers if the improper prior is used. We show that this may not be correct. An illustrative example is given.

A study of 2-heptanone and 2-octanone as solvents for two-phase electrochemistry. Part 1. Simple ion transfers

Methyl n-pentyl ketone (2-heptanone) and methyl n-hexyl ketone (2-octanone) have been used as organic solvents in electrochemical studies of the water | organic solvent interfaces. The transfer of TBA +, TPrA +, ClO 4 − and I − ions across these interfaces has been observed when appropriate base electrolytes in both the aqueous and organic phases are chosen. The standard Gibbs energies of simple ion transfers from water to the solvents are calculated based on Abraham's model and a comparison has been made between theoretical and experimental results.

Layering transitions in the Abraham model

We show by means of a low-temperature series expansion that a large, possibly infinite number of interface layering transitions are observed for the Abraham model in dimensions d>or=3.

Interpretation of the influence of temperature on the solvation properties of gas chromatographic stationary phases using Abraham's solvation parameter model

Abraham's solvation parameter model is used to interpret the influence of temperature on the contribution of cavity formation and solute—solvent intermolecular interactions to the solvation of a varied group of 62 solutes on ten representative stationary phases used in gas chromatography. It was observed that the magnitude of polar interactions increased at lower temperatures and that the change in the characteristic phase constants deduced from Abraham's model as a function of temperature could be described by a second-order polynomial function. Since the susceptibility of a solvent for a particular intermolecular interaction changes in a phase-specific manner as a function of temperature the observed ranking of phases for a particular intermolecular interaction at one temperature cannot be used to predict phase rankings at another temperature for the same interaction. A comparison of Abraham's model with an alternative cavity model proposed by Poole for the sum of the cavity and dispersion contributions to solvation shows similar trends as a function of temperature but differences in the magnitude of the contribution of the cavity—dispersion term to the overall free energy change for the solvation process. Agreement for the contribution of polar interactions to the solvation process is only qualitative for the two models unless a correction is made for the difference in magnitude for the cavity—dispersion contribution. A correction can be made by dividing the c term in Abraham's model into two contributions; a constant term independent of temperature which is assigned to the cavity-dispersion contribution to solvation and a temperature dependent term which is assigned to the polar interaction contribution to solvation. With this construct the two solvation models agree within experimental error for the relative contribution made by the cavity—dispersion term and solute—solvent polar interaction forces to the solvation process.

First-order depinning transition in two-dimensional abraham model: RG approach

Using a position-space renormalization group (RG) we analyse the competition for an interface between the boundary defect and an additional line of defect bonds in the two-dimensional Abraham model. The RG phase diagram, obtained over the whole range of temperatures and pinning parameters, indicate that beside the continuous wetting transition this model exhibits a finite-temperature interface depinning transition of the first order in agreement with recently obtained exact results.

First-order unbinding transition of an interface in two dimensions.

A two-dimensional model describing the unbinding of an interface from an attracting substrate, induced by a defect line in the bulk, is proposed. It contains Abraham's model as a special case. Although only short-range interactions are present, a sharp first-order unbinding transition is shown to take place. The model is formulated in terms of both the solid-on-solid model and Ising spins. Thermodynamic properties are evaluated exactly in both cases. The average interface distance from the substrate and the full magnetization profile are calculated in the solid-on-solid version. The first-order transition is discussed in light of Cahn's wetting criterion.

Depinning from the defect located at a finite distance from the surface in the planar Abraham model

A recently developed renormalisation group approach to interface pinning problems is generalised to deal with the depinning from the defect at a finite distance z removed from the surface in the planar Abraham model. The phase diagrams and the incremental defect free energies over the whole range of temperatures and distances z are obtained. The agreement with exact results, when available, is quite satisfactory.

A series approach to wetting and layering transitions. II. Solid-on-solid models

For pt.I see ibid., vol.20, p.5635, (1987). This is the second of three papers in which the authors discuss the applicability of series methods to interface wetting and layering transitions. Here they study the behaviour of a solid-on-solid interface, which is attracted to a surface by a local pinning potential. They find that, both for the standard and the restricted solid-on-solid models, the interface depins from the surface through an infinite sequence of layering transitions as the potential tends to zero. The applicability of the results to previous work on the Abraham model in three dimensions is discussed.

Low-temperature series analysis of multilayer adsorption at surfaces

It is shown that a low-temperature series analysis, taken to all orders by selecting important graphs at each stage, can be used to demonstrate that an Ising system with an interface forced upon it exhibits an infinite sequence of first-order layering transitions as a function of applied magnetic field. A model with a short-range surface potential, the Abraham model (1980), is also discussed and it is shown that it exhibits at least one layering transition at low temperatures.

Computation of periods of acoustical oscillations of the Sun

DISCOVERY of the regular pulsations of the Sun was reported in 1975–1976 by three groups of investigators1–3. It has been difficult to identify these oscillations, particularly the very stable 2 h 40 min one1,2,4. Having had experience in calculations of the free oscillations of gaseous–liquid Jupiter and Saturn5, we decided to compute the periods of some acoustical modes for one of the complete solar models. We chose the Abraham and Ibem6 Model I as a model of the interior, and a model of the convective zone from Spruit7 which had a depth of 198,00 km; an empirical model HRSA8 was taken as a model of the solar atmosphere.