Effects of concentration, relative permittivity, and temperature on the solution behavior of sodium carboxymethylcellulose as probed by electrical conductivity

Precise measurements on the electrical conductivity of solutions of sodium salt of carboxymethylcellulose in acetonitrile/water mixed-solvent media containing 10, 20, and 40 vol % of acetonitrile are reported as a function of temperature. The degree of substitution of carboxymethylcellulose used was 0.70, and the concentrations were varied from approximately 1 x 10(-4) to approximately 1 x 10(-2) equiv L(-1). The results showed a decrease in the equivalent conductivity with increasing polyelectrolyte concentration. The applicability of Manning's theory for salt-free polyelectrolyte solutions was examined, and a major discrepancy against the theory was observed. The calculated values of the equivalent conductivity deduced on the basis of this theory were found to be higher than the experimental ones. Possible reasons for this discrepancy have been discussed. The fractions of uncondensed counterions were evaluated, and these were found to depend on the polyelectrolyte concentration. The effects of the temperature and relative permittivity of the medium on the equivalent conductivity as well as on the fraction of uncondensed counterions were also investigated.     

The self-preserving size distribution theory. II. Comparison with experimental results for Si and Si3N4 aerosols

The gas to particle synthesis route is a relatively clean and efficient manner for the production of high-quality ceramic powders. These powders can be subsequently sintered in any wanted shape. The modeling of these production systems is difficult because several mechanisms occur in parallel. From theoretical considerations it can be determined, however, that coagulation and sintering are dominant mechanisms as far as shape and size of the particles are considered. In part I of this article an extensive theoretical analysis was given on the self-preserving size distribution theory for power law particles. In this second part, cumulative particle size distributions of silicon and silicon nitride agglomerates, produced in a laser reactor, were determined from TEM pictures and compared to the distributions calculated from this self-preserving theory for power law particles. The calculated distributions were in fair agreement with the measured results, especially at the high end of the distributions. Calculated and measured particle growth rates were also in fair agreement. Using the self-preserving theory an analysis was made on the distribution of annealed silicon agglomerates, of interest in applications to nanoparticle technology.     

What is the ‘Solvent’ effect on the electronic spectra of a solute in a polymer matrix?

The theory of solvent-induced shifts of the absorption and fluorescence band spectra of a solute is well known and has been tested for a multitude of systems. However, there are only few applications to polymers. By a direct comparison of the spectral shifts in liquid solvents with those in polymers it is possible to determine the microenvironment of the solutes in polymers within the frame of this theory. Polyethylene terephthalate as fabric and film was chosen as model polymer. The spectral shifts of 15 fluorescing solutes in this polymer as well as in 10 solvents with widely differing refractive indices n and permittivities ? were measured and fitted to the equations given by the theory of the solvent effect. It is found that interactions with the permanent dipoles of polyethylene terephthalate may be neglected within the limits of accuracy attainable for this polymer and the chosen solutes. Dispersion forces dominate the solvent effect. The refractive indices effective at the site of the solute molecules are n = 1.66 for the fabric and n = 1.70 for the film.     

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.     

固体分层取样方案的最优化设计

本文首次从理论上探讨了取得量对分层取样误差的影响,提出了总取样量一定时各层的最佳取样量和最小取样方差的计算公式,从而为分层取样的最佳取样方案设计提供了理论依据。     

Homogeneous nucleation in vapor-liquid phase transition of Lennard-Jones fluids: a density functional theory approach

Density functional theory (DFT) with square gradient approximation for the free energy functional and a model density profile are used to obtain an analytical expression for the size-dependent free energy of formation of a liquid drop from the vapor through the process of homogeneous nucleation, without invoking the approximations used in classical nucleation theory (CNT). The density of the liquid drop in this work is not the same as the bulk liquid density but it corresponds to minimum free energy of formation of the liquid drop. The theory is applied to study the nucleation phenomena from supersaturated vapor of Lennard-Jones fluid. The barrier height predicted by this theory is significantly lower than the same in CNT which is rather high. The density at the center of the small liquid drop as obtained through optimization is less than the bulk density which is in agreement with other earlier works. Also proposed is a sharp interface limit of the proposed DFT of nucleation, which is as simple as CNT but with a modified barrier height and this modified classical nucleation theory, as we call it, is shown to lead to improved results.     

Recent Developments in Kramers’ Theory of Reaction Rates

In this short review, we provide an update of recent developments in Kramers’ theory of reaction rates. After a brief introduction stressing the importance of this theory initially developed for chemical reactions, we briefly present the main theoretical formalism starting from the generalized Langevin equation and continue by showing the main points of the modern Pollak, Grabert and Hänggi theory. Kramers’ theory is then sketched for quantum and classical surface diffusion. As an illustration the surface diffusion of Na atoms on a Cu(110) surface is discussed showing escape rates, jump distributions and diffusion coefficients as a function of reduced friction. Finally, some very recent applications of turnover theory to different fields such as nanoparticle levitation, microcavity polariton dynamics and simulation of reaction in liquids are presented. We end with several open problems and future challenges faced up by Kramers turnover theory.     

应用于聚合物中的正电子湮没寿命谱技术

正电子湮没寿命谱技术是一种新型聚合物结构探测与表征技术,针对此技术在聚合物自由体积研究中的应用,首先介绍了该技术的基本原理和应用理论,接着针对寿命谱数据的处理手段和计算方法,对国内外的研究进展进行了概述和总结,最后展示了该技术在聚合物材料研究中用于基本理论,实际运用和结构理论等三个方面的情况。     

Molecular rearrangements through thermal [1,3] carbon shifts

Molecular rearrangements through thermal [1,3] carbon shifts, such as vinylcyclopropane-to-cyclopentene and vinylcyclobutane-to-cyclohexene isomerizations, were recognized and exemplified repeatedly from 1960-1964. Serious mechanistic studies of these and related rearrangements over the past 40 years have provided ample grounds for interpreting them as processes taking place by way of conformationally flexible but not statistically equilibrated diradical intermediates. Orbital symmetry theory fails to account for the stereochemical characteristics of [1,3] carbon shifts. For sigmatropic reactions of this class the theory can no longer be retained as a valid basis for mechanistic interpretations, or even as a serious contender for consideration as a mechanistic possibility.     

SurfKin: An ab initio kinetic code for modeling surface reactions

In this article, we describe a C/C++ program called SurfKin (Surface Kinetics) to construct microkinetic mechanisms for modeling gas–surface reactions. Thermodynamic properties of reaction species are estimated based on density functional theory calculations and statistical mechanics. Rate constants for elementary steps (including adsorption, desorption, and chemical reactions on surfaces) are calculated using the classical collision theory and transition state theory. Methane decomposition and water–gas shift reaction on Ni(111) surface were chosen as test cases to validate the code implementations. The good agreement with literature data suggests this is a powerful tool to facilitate the analysis of complex reactions on surfaces, and thus it helps to effectively construct detailed microkinetic mechanisms for such surface reactions. SurfKin also opens a possibility for designing nanoscale model catalysts. © 2014 Wiley Periodicals, Inc.     

Slater-type geminals in explicitly-correlated perturbation theory: application to n-alkanols and analysis of errors and basis-set requirements

In the recent years, Slater-type geminals (STGs) have been used with great success to expand the first-order wave function in an explicitly-correlated perturbation theory. The present work reports on this theory's implementation in the framework of the Turbomole suite of programs. A formalism is presented for evaluating all of the necessary molecular two-electron integrals by means of the Obara-Saika recurrence relations, which can be applied when the STG is expressed as a linear combination of a small number (n) of Gaussians (STG-nG geminal basis). In the Turbomole implementation of the theory, density fitting is employed and a complementary auxiliary basis set (CABS) is used for the resolution-of-the-identity (RI) approximation of explicitly-correlated theory. By virtue of this RI approximation, the calculation of molecular three- and four-electron integrals is avoided. An approximation is invoked to avoid the two-electron integrals over the commutator between the operators of kinetic energy and the STG. This approximation consists of computing commutators between matrices in place of operators. Integrals over commutators between operators would have occurred if the theory had been formulated and implemented as proposed originally. The new implementation in Turbomole was tested by performing a series of calculations on rotational conformers of the alkanols n-propanol through n-pentanol. Basis-set requirements concerning the orbital basis, the auxiliary basis set for density fitting and the CABS were investigated. Furthermore, various (constrained) optimizations of the amplitudes of the explicitly-correlated double excitations were studied. These amplitudes can be optimized in orbital-variant and orbital-invariant manners, or they can be kept fixed at the values governed by the rational generator approach, that is, by the electron cusp conditions. Electron-correlation effects beyond the level of second-order perturbation theory were accounted for by conventional coupled-cluster calculations with single, double and perturbative triple excitations [CCSD(T)]. The explicitly-correlated perturbation theory results were combined with CCSD(T) results and compared with literature data obtained by basis-set extrapolation.     

Defect-induced melting in nematic liquid crystals

In this paper we employ a relatively simple theory to show how a nematic disclination line can act as a nucleation site for the growth of the isotropic phase. With this theory we are able to find analytical expressions for the critical temperature of nucleation and the behaviour of the core radius as a function of temperature. We are then able to compare these results with a previous numerical model of this effect.     

甲醇钠引发的环氧乙烷开环聚合反应过程

运用密度泛函理论(DFT)的Dmol3方法, 计算了甲醇钠引发的环氧乙烷开环聚合的反应过程. 并运用前线轨道理论对该聚合反应的各步反应历程进行了分析. 计算结果表明, 链引发为无能垒的放热反应, 放出的能量达到92.560 kJ·mol-1, 而链增长过程则需越过100.951 kJ·mol-1的反应能垒, 链增长物种与环氧乙烷的前线轨道相对称, 可以使开环聚合反应继续进行下去. 当向反应体系中加入草酸、磷酸等质子酸时, 会立即发生链终止反应. 此外, 还对链增长过渡态的合理性进行了确认, 绘出了相应的反应势能曲线.     

Revisiting the foundations of the quantum theory of atoms in molecules: Some open problems

In a series of papers in the last 10 years, various aspects of the mathematical foundations of the quantum theory of atoms in molecules have been considered by this author and his coworkers in some details. Although these considerations answered part of the questions raised by some critics on the mathematical foundations of the quantum theory of atoms in molecules, however, new mathematical problems also emerged during these studies that were reviewed elsewhere [Sh. Shahbazian Int. J. Quantum Chem. 2011 , 111, 4497.]. Beyond mathematical subtleties of the formalism that were the original motivation for initial exchanges and disputes, the questions raised by critics had a constructive effect and prompted the author to propose a novel extension of the theory, now called the multi‐component quantum theory of atoms in molecules [M. Goli, Sh. Shahbazian Theor. Chem. Acc. 2013 , 132, 1365.]. Taking this background into account, in this paper a new set of open problems is put forward that the author believes proper answers to these questions, may open new doors for future theoretical developments of the quantum theory of atoms in molecules. Accordingly, rather than emphasizing on the rigorous mathematical formulation, the practical motivations behind proposing these questions are discussed in detail and the relevant literature are reviewed while when possible, evidence and routes to answers are also provided. The author hopes that proposing these open questions as a compact package may motivate more mathematically oriented people to participate in future developments of the quantum theory of atoms in molecules and its multi‐component version.     

A molecular Debye-Hückel theory and its applications to electrolyte solutions

In this report, a molecular Debye-Hu?ckel theory for ionic fluids is developed. Starting from the macroscopic Maxwell equations for bulk systems, the dispersion relation leads to a generalized Debye-Hu?ckel theory which is related to the dressed ion theory in the static case. Due to the multi-pole structure of dielectric function of ionic fluids, the electric potential around a single ion has a multi-Yukawa form. Given the dielectric function, the multi-Yukawa potential can be determined from our molecular Debye-Hu?ckel theory, hence, the electrostatic contributions to thermodynamic properties of ionic fluids can be obtained. Applications to binary as well as multi-component primitive models of electrolyte solutions demonstrated the accuracy of our approach. More importantly, for electrolyte solution models with soft short-ranged interactions, it is shown that the traditional perturbation theory can be extended to ionic fluids successfully just as the perturbation theory has been successfully used for short-ranged systems.     

Douglas–Kroll–Hess Theory: a relativistic electrons-only theory for chemistry

A unitary transformation allows to separate (block-diagonalize) the Dirac Hamiltonian into two parts one part: solely describes electrons, while the other gives rise to negative-energy states, which are the so-called positronic states. The block-diagonal form of the Hamiltonian no longer accounts for the coupling of both kinds of states. The positive-energy (‘electrons-only’) part can serve as a ‘fully’ relativistic electrons-only theory, which can be understood as a rigorous basis for chemistry. Recent developments of the Douglas–Kroll–Hess (DKH) method allowed to derive a sequence of expressions, which approximate this electrons-only Hamiltonian up to arbitrary-order. While all previous work focused on the numerical stability and accuracy of these arbitrary-order DKH Hamiltonians, conceptual issues and paradoxa of the method were mostly left aside. In this work, the conceptual side of DKH theory is revisited in order to identify essential aspects of the theory to be distinguished from purely computational consideration.     

Defect-induced melting in nematic liquid crystals

In this paper we employ a relatively simple theory to show how a nematic disclination line can act as a nucleation site for the growth of the isotropic phase. With this theory we are able to find analytical expressions for the critical temperature of nucleation and the behaviour of the core radius as a function of temperature. We are then able to compare these results with a previous numerical model of this effect.     

A simple calculational model for predicting the site for nucleophilic substitution in aromatic perfluorocarbons

We present a simple model for predicting the principal site for nucleophilic substitution in aromatic perfluorocarbons. Our model is based on the relative stabilities of the Meisenheimer complexes as calculated using density functional theory with a modest basis set. (Hartree-Fock theory will do just as well.) Although such calculations were essentially impossible to carry out when early theoretical work on this topic was undertaken in the mid-1960s and early 1970s, they are now routine and full geometry optimization for any of the systems studied in this work can be completed in a matter of minutes with modern quantum chemistry programs and computational hardware. Predictions from our model agree with experimental observations for 16 aromatic perfluorocarbons, and together with additional NMR calculations, lead us to conclude that the earlier prediction that perfluoroanthracene undergoes nucleophilic substitution in the 2-position is incorrect, and is based on a misinterpretation of the experimental ¹⁹F NMR spectrum.     

Design of CuCs-doped Ag-based Catalyst for Ethylene Epoxidation

Our recent theoretical studies have screened out CuCs-doped Ag-based promising catalysts for ethylene epoxidation [ACS Catal. 11 , 3371 (2021)]. The theoretical results were based on surface modeling, while in the actual reaction process Ag catalysts are particle shaped. In this work, we combine density functional theory (DFT), Wulff construction theory, and micro kinetic analysis to study the catalytic performance of Ag catalysts at the particle model. It demonstrates that the CuCs-doped Ag catalysts are superior to pure Ag catalysts in terms of selectivity and activity, which is further proved by experimental validation. The characterization analysis finds that both Cu and Cs dopant promote particle growth as well as particle dispersion, resulting in a grain boundary-rich Ag particle. Besides, CuCs also facilitate electrophilic atomic oxygen formation on catalyst surface, which is benefitial for ethylene oxide formation and desorption. Our work provides a case study for catalyst design by combining theory and experiment.     

Emulsion polymerization. VII. Effects of instantaneous chain termination during the interval of particle nucleation

In the Smith-Ewart treatment of particle nucleation all particles were assumed to grow as if they contained exactly one radical. Modification of particle growth rate by chain termination in growing particles and reinitiation of nongrowing particles by radicals entering them was neglected in this interval although such effects were taken into account after the particle number became constant. The present theory eliminates this inconsistency for the case where chain termination is instantaneous. This refinement does not change previous predictions for the final number of particles, the steady state rate or the particle radius. Unlike the old theory, the present theory predicts continuous decay of the average number of radicals per particle from the initial value of unity to the steady-state value of one half. It also provides new theoretical predictions for the shape of the conversion-time curve at the initial stages of the reaction. Experimental data are reviewed in the context of the theory. Experimental particle sizes, steady-state conversion rates, and conversions at completion of particle nucleation were often in good quantitative agreement with the theoretical predictions. The predicted maximum in the conversion rate at the time when particle nucleation became completed was observed in a few instances. The theoretically predicted initial shape of the conversion-time curve may not be always observable due to experimental difficulties mainly associated with induction effects.