A Comparative Analysis of the Rice-Allnatt and Square-Well Liquid Transport Theories

Abstract

The Yvon-Born-Green pair correlation function theory is discussed from the viewpoint of its role as theoretical data input for the Rice-Allnatt liquid transport theory. The general behavior of the Rice-Allnatt theory is shown to compare favorably with that of the square-well transport theory of Davis, Rice, and Sengers, although the former is not as quantitative. The predictive ability of the Rice-Allnatt theory is improved by a systematic adjustment of the Lennard-Jones parameters used in the YBG pair correlation functions, based on the critical point locus.     

Mean spherical approximation-mass action law theory of equilibrium and conductance in ionic solutions

An improved Bjerrum theory obtained by combining the mean spherical approximation with the mass action law (MSA&MAL) is used to calculate the fraction of ions unpaired over the full range of states of a primitive model electrolyte. It is combined with a new theory for the electrical conductance of the primitive model under the MSA to yield the conductance of an electrolyte over a wide range of concentrations and Bjerrum parameters with only two parameters A_o and R, the distance of closest approach, adjusted to fit the conductivity data. The theory fits the data for aqueous alkali halides over a wide concentration range with A_o values in good agreement with those deduced by more conventional theories and with reasonable small ion pairing constants deduced from the data. It fits the data for LiBr in octanol without the need for invoking triple ion formation. It leads to reasonable predictions for the conductance curves for 1:1 electrolytes even up to the molar region for solvents with dielectric constant from 10 to 80.     

Analysis of the hysteresis curve of ferroelectric polymers by a phenomenological relaxation theory

A simple relaxation theory for the displacement versus electric field hysteresis of ferroelectric polymers is developed in which the relaxation time is assumed to be a function of electric field, as has been experimentally evidenced by polarization-reversal switching. The theory gives an analytical expression for the hysteresis curve. The coercive field E_c predicted by the theory agrees well with data on E_c as a function of temperature for poly(vinylidene fluoride) from ?60 to 20°C and with data on E_c as a function of frequency for vinylidene fluoride/trifluoroethylene copolymer (73/27 molar ratio) at 20°C over the range 0.01–0.7 Hz.     

Solubility and diffusivity of methylmethacrylate and butylacrylate monomers in a MMA–BA copolymer

Mutual diffusion coefficients and sorption isotherms of methyl methacrylate (MMA) and butyl acrylate (BA) monomers in methyl methacrylate‐butyl acrylate copolymer (MMA‐BA) have been measured by gravimetric sorption. MMA is found to have higher solubility and diffusion rates in the copolymer than BA. Sorption data for MMA were interpreted using classical Flory‐Huggins thermodynamic theory with a constant interaction parameter (χ). A modified version of this theory has been applied to correlate the sorption data of BA, which exhibit a temperature and concentration‐dependent χ parameter. For MMA, the isotherm data reveal enhanced polymer‐solvent interactions with increasing temperature, while for BA the data indicate a drive toward phase separation with increasing temperature. Despite the difference in thermodynamic behavior, both monomers are found to exhibit Fickian diffusion and the diffusivity data are correlated reasonably well with the Vrentas‐Duda free volume theory. Some deviation between the free‐volume correlation and the experimental data is observed at the lowest temperature and BA concentration examined. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1996–2006, 2007     

Evaluation of the free‐volume theory of diffusion

General characteristics of the free‐volume theory of diffusion are discussed, and a recent data‐theory comparison involving free‐volume theory is critically evaluated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 501–507, 2003     

On the role of the reference system in perturbation theory: An augmented van der Waals theory of simple fluids

In this study, we show that the inclusion of a short-range part of the total attractive interaction into a reference system allows a natural extension of the traditional first-order perturbation theory of simple fluids to practically all thermodynamic states. This theory is applied to the thermodynamic functions and the liquid–vapor coexistence curve of the Lennard-Jones-like medium range Yukawa fluid and to the Sutherland fluid. Comparison with computer simulation data and the second-order Barker–Henderson perturbation theory is discussed.     

Application of Covington's nonstatistical distribution of solvate species theory to the preferential solvation of Tl+ in various binary solvent systems

Covington's nonstatistical distribution of solvate species theory of preferential solvation is used to analyze ²⁰⁵ Tl chemical shift data for 0.005M TlNO ₃ in nine binary solvent systems. The theory quite adequately fits the experimental data, and equilibrium constants and free energies of preferential solvation are obtained. The effect of choosing different values for the solvation number is investigated and found to be slight except for systems involving DMSO, ³ where decreasing the solvation number from 6 to 3 improves the fit to experimental data.     

Calculating thermodynamic properties from perturbation theory: Part III. The mixtures of square-well chain fluid

A completely analytic perturbation theory has been developed to calculate the Helmholtz energy, compressibility factor, internal energy and constant-volume heat capacity for square-well chain fluid mixtures. This theory is based on the improved Barker–Henderson macroscopic compressibility (mc) approximation proposed by Zhang, the first-order perturbation theory of Wertheim in which Zhang’s analytic monomer radial distribution function as the function of temperature and monomer density is used, and a simple mixing rule similar to that of Hino–Prausnitz. The validity of the perturbation theory is evaluated by comparing the calculated compressibility factor, internal energy and constant-volume heat capacity for the freely jointed square-well chain mixtures from the theory to MC simulation data. The results show that the theory predicts results in good agreement with simulation results.     

Comparison of Stress-Strain Relations of Polybutadiene Vulcanizates in Compression and in Extension

Abstract

According to elementary statistical theory of rubber elasticity, the modulus of rigidity τ/(λ - λ^?2) is constant. The phenomenological theory predicts that this modulus is in first approximation equal to the sum of a constant (2C₁) and a deformation-dependent term, 2C₂. The dependence on elongation of experimental modulus data of many elastomers agrees more or less with the C₂ term. Several attempts have been made to explain this dependence on the basis of molecular phenomena or by refinements of the statistical theory of elasticity. At present there is no consensus of opinion on the origin or interpretation of the deformation-dependent term. Almost all of the data on this dependence have been generated in extension experiments.     

Analysis of concentration polarization phenomenon in ultrafiltration under turbulent flow conditions

An ultrafiltration data set previously reported by Gekas and Olund is used to test three concentration polarization models. The data consist of testing eight ultrafiltration membranes representing different polymer materials and molecular weight cut-offs with 0.5 wt% Dextran T10 at 25°C and 0.5 MPa under turbulent flow conditions. The tested concentration polarization models include the modified film theory model, the original film theory model and the Sherwood correlation model. The Chilton-Colburn analogy is the common foundation of the these models.     

On the use of the variational method for interpreting the solubilities of gases in liquids

The Variational theory of mixtures due to Mansoori and Leland is modified to account for translational quantum effects in solution, and this modified form of the theory is applied to the problem of gas solubilities in liquids. The theory is used to derive expressions for the Henry's law constant, the molar heat of solution at infinite dilution, and the partial molar volume at infinite dilution for a solute in a liquid solution. These expressions are applied, over a range of temperatures, to the following systems; H₂ in each of Ar, N₂, and CH₄; He in each of Ar, N₂, and CH₄; and Ne in each of Ar and N₂. Lennard-Jones 6–12 pair potentials are used for these calculations. The Lennard-Jones parameters are taken from gas-phase second virial coefficient data. The results obtained are compared with experimental data and with previous calculations on these systems based on the Leonard-Henderson-Barker theory. The variational results appear to be in better agreement with experiment for the He-containing systems, while the Leonard-Henderson-Barker theory seems better for the other systems. An explanation for this is suggested.     

Glass transition in polyacrylonitrile: Analysis of dielectric relaxation data

Dielectric relaxation of polyacrylonitrile (PAN) samples, in which the presence of an amorphous phase is evidenced by x-ray diffraction, has been studied over the temperature range 30–150°C and frequency range 10²–10⁵ Hz. These data as well as those reported by other authors, reveal several points useful to the understanding of the dielectric relaxations of PAN in relation to its structure. A glass transition in PAN is evidenced by at least two of the four data sets investigated; the third shows combined effect of two relaxations, whereas the fourth clearly shows a relaxation process different from the glass transition. The glass-transition behavior of the dielectric relaxation data is confirmed by Williams-Landel-Ferry theory and a recent theory of Phillips, both of which lead to consistent conclusions.     

Optimal structure and energetical relations on the catalyst surface: Evolution of concepts

Principles of the multiplet theory in heterogeneous catalysis are discussed in connection with studies of Professor Tétényi, new data and assumptions. It is desirable to put some correctives into the principles of structure and energetic correspondence proposed in this theory. Dedicated to Professor Pál Tétényi on the occasion of his 70th birthday     

Prediction of tautomer ratios by embedded-cluster integral equation theory

The “embedded cluster reference interaction site model” (EC-RISM) approach combines statistical-mechanical integral equation theory and quantum-chemical calculations for predicting thermodynamic data for chemical reactions in solution. The electronic structure of the solute is determined self-consistently with the structure of the solvent that is described by 3D RISM integral equation theory. The continuous solvent-site distribution is mapped onto a set of discrete background charges (“embedded cluster”) that represent an additional contribution to the molecular Hamiltonian. The EC-RISM analysis of the SAMPL2 challenge set of tautomers proceeds in three stages. Firstly, the group of compounds for which quantitative experimental free energy data was provided was taken to determine appropriate levels of quantum-chemical theory for geometry optimization and free energy prediction. Secondly, the resulting workflow was applied to the full set, allowing for chemical interpretations of the results. Thirdly, disclosure of experimental data for parts of the compounds facilitated a detailed analysis of methodical issues and suggestions for future improvements of the model. Without specifically adjusting parameters, the EC-RISM model yields the smallest value of the root mean square error for the first set (0.6 kcal mol⁻¹) as well as for the full set of quantitative reaction data (2.0 kcal mol⁻¹) among the SAMPL2 participants.     

Generalized van Vleck perturbation theory (GVVPT2) study of the excited states of benzene and the azabenzenes

Generalized van Vleck perturbation theory (GVVPT2) for molecular electronic structures is applied to examine the azabenzene series: benzene, pyridine, pyrazine, symmetric triazine and symmetric tetrazine. The spectra of azabenzenes are complex with large numbers of excited states at low energies comprising n --> pi* and pi --> pi* excited states and also doubly excited states of the n,n --> pi*,pi* type. The calculations are complicated due to strong correlation effects in the nitrogen lone-pair orbitals and the pi electrons. This study is the first to use GVVPT2 on conjugated systems. Comparison is made with experimental data and complete active space second-order perturbation theory, equation of motion coupled cluster and similarity transformed equation of motion coupled cluster theory data. Using polarized valence double split basis sets for benzene and pyrazine (cc-pVDZ) and pyridine (ANO-S) and polarized triple split basis sets (ANO-L) for triazine and tetrazine, the n --> pi* and pi --> pi* states are computed with an average error of 0.28 eV in comparison with available experimental data.     

Comparison of theories of ion-induced nucleation

A theory of nucleation on ions and a theory of nucleation in the presence of ions are presented. The calculated data obtained within these theories are compared to the experimental data for the nucleation of vapors of different compounds. It is shown that the theory of nucleation in the presence of ions is in better agreement with the experimental data than the theory of nucleation on ions. It is assumed within the theory of nucleation in the presence of ions that each ion in the vapor phase forms a stable ion associate with vapor molecules.     

Biocontrol of water quality: Multifunctional role of biota in water self-purification

The experimental data analysis, concepts, and generalizations in this article provide the fundamental elements of the qualitative theory of biocontrol of water quality in a systematized form. The theory covers water self-purification in freshwater and marine ecosystems. The theory is supported by the results of the author’s experimental studies of the effects exerted by some chemical pollutants including synthetic surfactants, detergents, and other xenobiotics onaquatic organisms. The theory provides a basis for remediation of polluted aquatic ecosystems including purification of water bodies and streams, and briefly present the qualitative theory of the self-purification mechanism of aquatic ecosystems, phytoremediation and other types of technologies.     

The effect of pressure on the mechanical properties of polymers. IV. Measurements in torsion

Stress relaxation was studied in torsion under superposed hydrostatic pressure using a newly constructed device. Two materials, a styrene–butadiene rubber and a butadiene rubber, were studied in the range from ?60 to 30°C at pressures up to 500 MPa. The time–temperature–pressure superposition of the data can be described by the FMT form of the free-volume theory which uses input from relaxation experiments at high pressure. The applicability of the Havlí?ek–Ilavský–Hrouz form of the Adam–Gibbs theory was also examined. This theory, which does not require information from high-pressure relaxation experiments, offers less flexibility than the FMT theory and is less successful in predicting superposition. The data are also examined in light of an adaptation of the Simha–Somcynsky equation of state to the free-volume theory. Prediction of the effect of pressure by the theory requires a single adjustable parameter. It was possible to calculate the free-volume parameters of several polymers without use of information from high-pressure experiments.     

The viscoelasticity of polymer solutions: Comparison of theory and experiment

The theory of the preceding paper is compared with previously unpublished experimental results on the viscoelastic properties of two polystyrene fractions of molecular weight 1.9 × 10⁶ and 1.2 × 10⁶ in nitropropane, which is very nearly a theta solvent, and in toluene, a good solvent. At the concentrations used, around 1%, the theory predicts extensive departures from non-draining toward free-draining behavior; these effects are observed. The theory similarly fits experimental data of Johnson on a sample of polystyrene of molecular weight 860,000 in decalin and dioctyl phthalate in the same concentration range.