Modified interfacial statistical associating fluid theory: a perturbation density functional theory for inhomogeneous complex fluids

A density functional theory based on Wertheim's first order perturbation theory is developed for inhomogeneous complex fluids. The theory is derived along similar lines as interfacial statistical associating fluid theory [S. Tripathi and W. G. Chapman, J. Chem. Phys. 122, 094506 (2005)]. However, the derivation is more general and applies broadly to a range of systems, retaining the simplicity of a segment density based theory. Furthermore, the theory gives the exact density profile for ideal chains in an external field. The general avail of the theory has been demonstrated by applying the theory to lipids near surfaces, lipid bilayers, and copolymer thin films. The theoretical results show excellent agreement with the results from molecular simulations.     

Integral equation theory of random copolymer melts: self-consistent treatment of intramolecular and intermolecular correlations

A self-consistent integral equation theory is presented for the conformational properties and spinodal lines of random copolymer melts. The theory combines field-theoretic methods with the polymer reference interaction site model (PRISM) theory. The many-chain problem is replaced by a single chain where the sites interact via a bare plus a self-consistently determined medium-induced potential, and the conformational properties are obtained using a variational method. The theoretical prediction for the spinodal line is qualitatively similar to that of non-self-consistent PRISM theory. The theory predicts macroscopic phase separation for all values of the monomer correlation strength, lambda. The inverse spinodal temperature is a nonmonotonic function of lambda with a maximum at lambda(max). For large values of lambda( approximately 1), the values of spinodal temperatures are almost identical to those of non-self-consistent PRISM theory. For low values of lambda, however, the theory predicts higher values for spinodal temperatures than non-self-consistent PRISM theory. The theory predicts significant changes in the mean-square end-to-end distance as the temperature is decreased.     

Density functional theory for Yukawa fluids

We develop an approximate field theory for particles interacting with a generalized Yukawa potential. This theory improves and extends a previous splitting field theory, originally developed for counterions around a fixed charge distribution. The resulting theory bridges between the second virial approximation, which is accurate at low particle densities, and the mean-field approximation, accurate at high densities. We apply this theory to charged, screened ions in bulk solution, modeled to interact with a Yukawa potential; the theory is able to accurately reproduce the thermodynamic properties of the system over a broad range of conditions. The theory is also applied to "dressed counterions," interacting with a screened electrostatic potential, contained between charged plates. It is found to work well from the weak coupling to the strong coupling limits. The theory is able to reproduce the counterion profiles and force curves for closed and open systems obtained from Monte Carlo simulations.     

柔性高分子/小分子液晶混合物的自洽场理论

发展了柔性高分子/小分子液晶混合物连续自洽场理论，将小分子液晶模型化 为取向与位置无关的单体分子，小分子液晶间存在各向异性的Maier-Saupe相互作 用，该理论可还原成高分子和各向同性小分子组成的Flory-Huggins溶液理论和纯 液晶的Maier-Squpe液晶理论，通过数值解自洽场方程组，还将理论用于研究柔性 高分子/小分子液晶混合物相分离开界面性质，得到的结果与用Helfand格子界面理 论和MOnte Carlo模拟的结果一致。     

Analysis of micropore volume size distributions of activated carbon fibers

The microporous structure of activated carbon fibers is studied in terms of the BET theory, the theory of volume filling of micropores, the Horvath-Kawazoe theory, and the nonlocal density functional theory. It is shown that effective micropore sizes, as calculated within the framework of the theory of volume filling of micropores, lie in the region of the maximum of the pore volume distribution function calculated by the density functional theory, whereas the distributions found via the Horvath-Kawazoe theory are shifted to the region of fine pores.     

灌浆理论浅析

详细分析了两种灌浆液体的类型牛顿体和宾汉姆体的力学特征以及二者之间异同和联系,介绍了岩土体结构的基本理论、灌浆的基本理论、渗透灌浆理论机制及内容、劈裂灌浆理论机制及内容、压密灌浆理论机制及内容。     

Specific interactions and single-lon activity coefficients in mixed electrolyte solutions

A reexamination of Guggenheim's theory of specific interactions for dilute aqueous electrolyte solutions shows that the parameters of the theory should include terms for interactions between like-charged ions. The equations developed are analogous to those in Pitzer's treatment of concentrated solutions, and the inclusion of ion-solvent interaction parameters allows comparison with the Stokes and Robinson hydration theory treatment. As with hydration theory, specific-interaction theory predicts differences in single-ion activity coefficients.     

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.     

Extended multi-configuration quasi-degenerate perturbation theory: the new approach to multi-state multi-reference perturbation theory

The distinctive desirable features, both mathematically and physically meaningful, for all partially contracted multi-state multi-reference perturbation theories (MS-MR-PT) are explicitly formulated. The original approach to MS-MR-PT theory, called extended multi-configuration quasi-degenerate perturbation theory (XMCQDPT), having most, if not all, of the desirable properties is introduced. The new method is applied at the second order of perturbation theory (XMCQDPT2) to the 1(1)A(')-2(1)A(') conical intersection in allene molecule, the avoided crossing in LiF molecule, and the 1(1)A(1) to 2(1)A(1) electronic transition in cis-1,3-butadiene. The new theory has several advantages compared to those of well-established approaches, such as second order multi-configuration quasi-degenerate perturbation theory and multi-state-second order complete active space perturbation theory. The analysis of the prevalent approaches to the MS-MR-PT theory performed within the framework of the XMCQDPT theory unveils the origin of their common inherent problems. We describe the efficient implementation strategy that makes XMCQDPT2 an especially useful general-purpose tool in the high-level modeling of small to large molecular systems.     

Voids, generic van der Waals equation of state, and transport coefficients of liquids

In this Perspective, we discuss the role of voids in transport processes in liquids and the manner in which the concept of voids enters the generic van der Waals equation of state and the modified free volume theory. The density fluctuation theory is then discussed and we show how the density fluctuation theory can be made a molecular theory with the help of the modified free volume theory and the generic van der Waals equation of state. The confluence of the aforementioned three theories makes it possible to calculate the transport coefficients of liquids by using the information on the equilibrium pair correlation function, which can be calculated either by an integral equation theory or Monte Carlo simulations. A number of relations between transport coefficients are also presented, which are derived on the basis of the density fluctuation theory. Since they can be used to obtain one transport coefficient from another they can be very useful in handling experimental and theoretical data. An application of the modified free volume theory to polymer melts is discussed as an example for a theory of transport properties of complex liquids.     

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.     

Assessing the performance of density functional theory for the electronic structure of metal-salens: the 3d(0)-metals

A series of metal-salen complexes of the 3d(0) metals Sc(III), Ti(IV), V(V), Cr(VI), and Mn(VII) have been explored using high-level electronic structure methods including coupled-cluster theory with singles, doubles, and perturbative triples as well as complete active-space third-order perturbation theory. The performance of three common density functional theory approaches has been assessed for both the geometries and the relative energies of the low-lying electronic states. The nondynamical correlation effects are demonstrated to be extremely large in all of the systems examined. Although density functional theory provides reasonable results for some of the systems, the overall agreement is quite poor. This said, the density functional theory approaches are shown to outperform the single-reference perturbation theory and coupled-cluster theory approaches for cases of strong nondynamical correlation.     

Three-dimensional distribution function theory for the prediction of protein-ligand binding sites and affinities: application to the binding of noble gases to hen egg-white lysozyme in aqueous solution

The three-dimensional distribution function theory of molecular liquids is applied to lysozyme in mixtures of water and noble gases. The results indicate that the theory has the capability of predicting the protein-ligand binding sites and affinities. First, it is shown that the theory successfully reproduces the binding sites of xenon found by X-ray crystallography. Then, the ability of the theory to predict the size selectivity of noble gases is demonstrated. The effect of water on the selectivity is clarified by a theoretical analysis. Finally, it is demonstrated that the dose-response curve, which is employed in experiments for examining the binding affinity, is realized by the theory.     

The freeon theory of magnetism. I. The Heisenberg interaction

The freeon theory of magnetism is a viable alternative to the well-known Heisenberg theory. In particular, the freeon-exchange theory provides a deeper insight into the nature of the magnetic interaction than does the spin-exchange theory. In addition, it avoids the superfluous M_S quantum number in zero-field splitting, the overcounting of spin states, the spin frustration, and the spin paradigm. The freeon-exchange theory employs the algebra of the symmetric group and/or the unitary group in place of the spin algebra. The basis vectors of freeon theory are the Gel'fand states which are uniquely labeled by Gel'fand diagrams; the latter provide both the electron configuration and the spin quantum number. Both the spin and the freeon formulations support the Landé interval rule. In this article, we apply freeon theory to transition-metal dimers, trimers, and tetramers; these are examples of molecular magnets which have applications to microcircuitry. The freeon theory follows the permutation-group principle laid down by Herman Weyl over one-half a century ago. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 287–297, 1997     

A new theory for polymer/solvent mixtures based on hard-sphere limit

Based on hard-sphere limit of binary mixtures with different molecular size of components a theory has been developed for calculating activities of solvents in polymer/solvent mixtures. The theory considers various chain configurations for polymer molecules, varying from extended chain to the coiled chain. According to this theory the activity of solvent can be calculated from molecular weights (MWs) and densities as the only input data. The only adjustable parameter in the calculations, is the hard-sphere diameter of polymer, which provides useful criteria for the judgement on the chain configuration of polymer.The activity calculations have been performed for seven binary mixtures of polymer/solvent and compared with experimental data at various temperatures and for a varying range of MWs of polymers.The solvents in the mixtures were both of polar and nonpolar natures. The activity calculations for the same systems were performed by the well-known Flory-Huggins theory. Comparing the results of calculations with those of Flory-Huggins theory indicates that, the proposed theory is able to predict the activities of the solvent with good accuracy.The radius of gyration, excluded volume and interaction parameter for polymer chain have been calculated using the parameter obtained in the new theory. The calculated interaction parameter in the new theory, is interpreted in terms of attraction, repulsion and interchange energy of polymer and solvent in the mixture.     

Integral equation theory for two-dimensional polymer melts

The polymer reference interaction site model theory is investigated for two-dimensional polymer melts composed of freely-jointed hard disk chains and tangent-disk rods. Exact results for the intramolecular pair correlation functions are input into the theory, and predictions of the theory for the intermolecular pair correlation functions are tested via comparison with simulation. The theory is not as accurate for this system as it is for three-dimensional polymer melts, and the quantitative predictions are not good except at the highest area fractions. Possible reasons for the deficiency in the theory are discussed.     

Modified interfacial statistical associating fluid theory: application to tethered polymer chains

Modified interfacial statistical associating fluid theory density functional theory is extended to tethered polymer chains in the absence or presence of free polymer chains. The structures of the "dry" and "wet" polymer brushes have been calculated and compared with simulation results available in the literature. The comparisons show that the theory accurately predicts the structure of the tethered polymer brush. The average brush heights calculated from the theory agree with well-established scaling theories for tethered polymers. However, these scaling theories cannot predict the detailed structure, accurately. The effects of the segment-segment interactions of the tethered polymer and the free polymer have been effectively captured by the theory.     

Scattering in view of the Titchmarsh–Weyl theory

The Titchmarsh–Weyl theory for a singular second-order differential equation is presented. The equations, however, are arranged such that the theory is immediately applicable to the multichannel formulation. The mathematical basis of the Titchmarsh–Weyl theory (TWT) is outlined and the Titchmarsh–Weyl m function is presented. Relations to the associated Green's function and the spectral function are given. It is shown how some quantities common in scattering theory can be expressed in terms of the TWT. The method of complex rotation is then applied to the TWT to create a complex rotated analog of the Titchmarsh–Weyl theory. This is then extended as exterior complex scaling is introduced. An outline of a proof for the method of exterior complex scaling is presented and some numerical results of the complete theory are given.