The surface energy of kaolinite

The surface energy of kaolinite was determined from the water adsorption isotherm, the water/kaolinite contact angle, and the surface tension of water, using a formula obtained by combining the Young equation with the general equation of pair interaction. This formula could be represented by a polynomial function whose roots gave one real value of 252.57±2.75 mJ m^–2 for the surface energy of kaolinite. An important feature of the procedure for obtaining this energy is the use of the Young equation to determine the range in which the value of the surface energy lies.     

The surface energy of talc

The determination of an average value for the surface energy of talc (gammaS) via solid-water interfacial interactions is described. It is based on a formula obtained by the combination of the Young equation with a general equation of pair interaction. Important features of the method are (a) the use of the Young equation to determine the range where the value of the surface energy lies and (b) the determination of the mean value within this range using a probability function. The value found is 217.31 mJ m(-2) in the range 193.36-257.43 mJ m(-2).     

Thermodynamics of Chromium(VI) Anionic Species Sorption onto Surfactant-Modified Montmorillonite Clay

Batch sorption experiments performed on Cr(VI) species sorption showed a significantly enhanced removal of inorganic hexavalent chromium anionic species from aqueous solution by montmorillonite clays modified with quaternary amine, hexadecyltrimethylammonium (HDTMA) bromide. Unmodified clay had no affinity for chromium(VI) species. The sorption of Cr(VI) species has been carried out as a function of pH, contact time, adsorbate concentration (4.14x10(-5) to 8.62x10(-3) M), and temperature (5-45 degrees C). The surfactant-modified clay surface was stable when exposed to extremes in pH. The optimum pH for maximum sorption of Cr(VI) species was found to be at pH 1 and was constant between pH 2 and pH 6. The sorption data obtained was well described by DKR and Langmuir sorption isotherms. Sorption energy (E) for (i) surfactant sorption by montmorillonite clay and (ii) sorption of chromium(VI) species by surfactant modified clay have been computed from the DKR equation. Sorption energy evaluated for the sorption of both surfactant and Cr(VI) species showed that an ion-exchange mechanism was operative. The mechanism of retention appears to be replacement of counterion of the surfactant by Cr(VI) anionic species. Adsorbent capacity for the sorption of Cr(VI) species has been evaluated from the Langmuir sorption isotherm data. Thermodynamic parameters (Delta H degrees, Delta S degrees and Delta G degrees ) for surfactant sorption on montmorillonite clay and Cr(VI) sorption by modified clay have been evaluated. The specific rate constant for sorption of Cr(VI) species on modified montmorillonite was rapid during the first 10 min and equilibrium was found to be attained within 30 min. The sorption of Cr(VI) species onto modified montmorillonite clay followed first-order rate kinetics. Copyright 2000 Academic Press.     

Influence of the intercalated cations on the surface energy of montmorillonites: consequences for the morphology and gas barrier properties of polyethylene/montmorillonites nanocomposites

Organically modified montmorillonites obtained by cation exchange from the same natural layered silicate were studied. The surface properties of the pristine and a series of organically modified clays were determined by inverse gas chromatography and the water adsorption mechanisms were studied by a gravimetric technique coupled with a microcalorimeter. A significant increase of the specific surface area, a decrease of the water adsorption, and a decrease of the dispersive component of the surface energy were observed when the sodium cations of the natural montmorillonite were exchanged for a quaternary ammonium. Slighter differences in surface properties were observed, on the other hand, between the different types of organically modified montmorillonites. Indeed, similar dispersive components of the surface energy were determined on the organoclays. Nevertheless, the specific surface area increased in the range 48-80 m(2)/g with increasing d-spacing values and the presence of specific groups attached to the quaternary ammonium, such as phenyl rings or hydroxyl groups, led to some specific behaviors, i.e., a more pronounced base character and a higher water adsorption at high activity, respectively. Differences in interlayer cation chain organization, denoted as crystallinity, were also observed as a function of the nature of the chains borne by the quaternary ammonium. In a later step, polyethylene-based nanocomposites were prepared with those organically modified montmorillonites. The clay dispersion and the barrier properties of the nanocomposites were discussed as a function of the montmorillonite characteristics and of the matrix/montmorillonite interactions expected from surface energy characterization.     

剩余函数量子Monte Carlo方法

为量子Ｍｏｎｔｅ Ｃａｒｌｏ方法提出一条新途径－剩余函数法,引入了Ｓｃｈｒｏｅｄｉｎｇｅｒ方程剩余函数的概念,利用剩余函数将一种新的有明显物理意义的试探函数应用到量子Ｍｏｎｔｅ Ｃａｒｌｏ过程中,这种试探函数是通过一种迭进式的方式确定的,它不需要在Ｍｏｎｔｅ Ｃａｒｌｏ过程中优化参数。文中我们将给出这种试探函数的具体形式,证明由这种试探函数求出的能量期望值收敛于体系真实的能量值;文中还给出这种试探     

Characterization and adsorption properties of tetrabutylammonium montmorillonite (TBAM) clay: thermodynamic and kinetic calculations

The montmorillonite has been subjected to modification through ion-exchange reaction by tetrabutylammonium bromide (TBAB). The modified sample was studied by X-ray diffraction (XRD) technique, Fourier transform infrared (FTIR) spectroscopy, and thermogravimetric analysis (TGA) methods. The basal spacing of modified montmorillonite was determined as 14.40 A. The IR spectra of modified montmorillonite showed CH vibrations. The characterization of tetrabutylammonium montmorillonite (TBAM) and the adsorption of p-chlorophenol (p-CP) on organomontmorillonite was studied as a function of the solution concentration and temperature. The observed adsorption rates were found to fit to the pseudo-second-order kinetics. The rate constants were calculated for temperatures ranging between 25.0-35.0 degrees C at constant concentration. The adsorption energy, E, and adsorption capacity, (q(m)), for phenolic compounds adsorbing on organomontmorillonite were estimated using the Dubinin-Radushkevich (D-R) equation. Thermodynamic parameters (delta g(a) = -11.063 and -11.802 kJ/mol, delta h(a) = -30.032 and -30.789 kJ/mol, delta s(a) = -0.0636 and -0.0637 kJ/mol K for 298 and 308 K, respectively) were calculated by a new approximation from the adsorption isotherms of p-CP on organomontmorillonite. These isotherms were modeled according to Freundlich and Dubinin-Radushkevich adsorption isotherms, through which the first-order and second-order coefficients (K(1ads) = 0.0152 and 0.0127 micromol/g min, K(2ads) = 0.0130 and 0.0108 L/min micromol, respectively) were obtained at 298 and 308 K.     

Evaluation of surface tension and Tolman length as a function of droplet radius from experimental nucleation rate and supersaturation ratio: metal vapor homogeneous nucleation

Zinc and silver vapor homogeneous nucleations are studied experimentally at the temperature from 600 to 725 and 870 K, respectively, in a laminar flow diffusion chamber with Ar as a carrier gas at atmospheric pressure. The size, shape, and concentration of aerosol particles outcoming the diffusion chamber are analyzed by a transmission electron microscope and an automatic diffusion battery. The wall deposit is studied by a scanning electron microscope (SEM). Using SEM data the nucleation rate for both Zn and Ag is estimated as 10(10) cm(-3) s(-1). The dependence of critical supersaturation on temperature for Zn and Ag measured in this paper as well as Li, Na, Cs, Ag, Mg, and Hg measured elsewhere is analyzed. To this aim the classical nucleation theory is extended by the dependence of surface tension on the nucleus radius. The preexponent in the formula for the vapor nucleation rate is derived using the formula for the work of formation of noncritical embryo [obtained by Nishioka and Kusaka [J. Chem. Phys. 96, 5370 (1992)] and later by Debenedetti and Reiss [J. Chem. Phys. 108, 5498 (1998)]] and Reiss replacement factor. Using this preexponent and the Gibbs formula for the work of formation of critical nucleus the dependence of surface tension on the radius R(S) of the surface of tension is evaluated from the nucleation data for above-mentioned metals. For the alkali metals and Ag the surface tension was determined to be a strong function of R(S). For the bivalent metals (Zn, Hg, and Mg) the surface tension was independent of radius in the experimental range. A new formula for the Tolman length delta as a function of surface tension and radius R(S) is derived by integration of Gibbs-Tolman-Koenig equation assuming that delta is a monotonic function of radius. The formula derived is more correct than the Tolman formula and convenient for the elaboration of experimental data. Using this formula the values of delta are determined as a function of R(S) from the experimental nucleation data. It is determined that all the metals considered are characterized by strong dependence of delta on radius; for the bivalent metals delta changes sign.     

Surface tension correlation for pure polar fluids by a new molecular model and SRK equation of state

In this work, a new model based on molecular thermodynamic was presented to correlate the surface tension of pure polar liquids. This model was developed based on the Davis theory. According to this theory, the surface tension is defined as a function of radial distribution function (RDF) and potential function (PF) as well. The proposed model includes three additive terms; hard sphere, dispersion and polar interactions. The RDF of Kolafa equation of state and Dirac delta function as a PF were used for hard sphere interaction. The RDF expression of Xu and Hu was considered for both dispersion and polar interactions. The presented model has two adjustable parameters, size and energy, which were obtained by optimization of an objective function for each pure fluid. This proposed approach was used for 19 pure polar fluids divided into 6 groups; organic acids, alcohols, ketones, ethers, aldehydes, and water. The average absolute deviation percent (AAD%) obtained for 19 fluids are 0.74. Also the surface tension of these 19 fluids was calculated by the use of SRK EOS and Sugden empirical formula in two cases. In case 1, Sugden's Parachor was calculated from Hugill and van Welsenes correlation and in case 2, it was obtained by optimization of an objective function for each component. The values of AAD% are 43.544 and 2.281 for cases 1 and 2, respectively. These results show the new model, which includes two adjustable parameters, can correlate the surface tension of the pure polar liquids with a high accuracy.     

Study of the influence of location of substitutions on the surface energy of dioctahedral smectites

The surface energy of some clays belonging to the smectite group has been calculated starting from crystal structures and combining a partial charge model with the computation of the lattice energy. The dioctahedral smectites studied here include montmorillonite; beidellites; and nontronite. One of the differences between these clays is the location of the substitution in the octahedral sheet or in the tetrahedral one. Another is the possibility of vacancies in cis- or trans-octahedral positions. These locations and vacancies have an effect on the distortion of the crystal framework and therefore on the surface energy. Calculated surface energies of the solid samples increase in the order beidellites > montmorillonite > nontronite. The bond energy between the interlayer cation and the layer appears to follow the same order and to depend both on the nature of the most electropositive elements of the layer and on their location. The trends obtained provide elements for an analysis of data related to interlayer enlargement.     

Nuclear quantum effects on the nonadiabatic decay mechanism of an excited hydrated electron

We present a kinetic analysis of the nonadiabatic decay mechanism of an excited state hydrated electron to the ground state. The theoretical treatment is based on a quantized, gap dependent golden rule rate constant formula which describes the nonadiabatic transition rate between two quantum states. The rate formula is expressed in terms of quantum time correlation functions of the energy gap and of the nonadiabatic coupling. These gap dependent quantities are evaluated from three different sets of mixed quantum-classical molecular dynamics simulations of a hydrated electron equilibrated (a) in its ground state, (b) in its first excited state, and (c) on a hypothetical mixed potential energy surface which is the average of the ground and the first excited electronic states. The quantized, gap dependent rate results are applied in a phenomenological kinetic equation which provides the survival probability function of the excited state electron. Although the lifetime of the equilibrated excited state electron is computed to be very short (well under 100 fs), the survival probability function for the nonequilibrium process in pump-probe experiments yields an effective excited state lifetime of around 300 fs, a value that is consistent with the findings of several experimental groups and previous theoretical estimates.     

最大泡压法测表面张力等温线的数据处理方法比较*

对乙酸、丙酸、正丁酸、2-甲基丁酸、3-甲基丁酸、正戊酸、正己酸、乙醇、丙醇、异丙醇、正丁醇、异丁醇、1,2-丙二醇等13种常用试剂在25 ℃下的表面张力数据拟合方法进行了比较,分析了图解法处理数据及多项式、一阶指数函数、幂函数、Shishkovsky经验公式拟合数据的优缺点。指出Shishkovsky经验公式拟合结果准确,受数据样本量影响小,是理想的表面张力数据拟合方法。     

Energy of a polynomial and the Coulson integral formula

The energy of an arbitrary polynomial is defined in analogy to the energy of a graph, so that the Coulson integral formula remains valid. In particular, we extend the Coulson integral formula to the case when the zeros of the underlying polynomial are not real and simple. Some related proofs from a recent paper by Peña and Rada are corrected and their results generalized.     

Making More Extensive Use of the Coupled-cluster Wave Function: from the Standard Energy Expression to the Energy Expectation Value

The standard coupled-cluster (CC) scheme with single and double excitations in the cluster operator (CCSD) includes only up to quadruple excitations in the equations. The CCSD exponential expansion generates, however, all possible excitations out of the reference function through products of the cluster operators. Clearly, in all standard approximate CC approaches only a part of the CC wave function is used in the equations. If the standard CCSD wave function is inserted into the energy expectation value expression then the complete CCSD wave function contributes to the energy. Such an energy expectation value expression can be presented as a sum of the standard CCSD energy formula plus correction terms. The correction terms provide an information about the quality of the total CC function. Contributions associated with the presence of higher than double excitations in the bra CCSD wave function supplement the CCSD energy obtained within the standard scheme. These contributions can be generated in a sequential way by considering intermediate excitation levels for the bra CCSD wave function in the expectation value expression before reaching the highest excitation level. In this way the importance of particular components differing in the standard and expectation value CCSD energies can be investigated. Some of the contributions can be recognized as close to or identical with the so-called renormalized noniterative corrections to the CC methods. We try to see to what an extent the nonstandard energy expressions, like the energy expectation value or the asymmetric energy formula, can be used to extend the applicability of the CCSD method illustrating our considerations with some numerical examples.Dedicated to Professor Jean-Paul Malrieu to honor his contribution to quantum chemistry and physics     

A multichannel electron energy loss spectrometer for low-temperature condensed films

We describe a wide-gap multichannel cylindrical deflection electron energy analyzer suitable for measuring the weak signals characteristic of electronically inelastic electron energy loss spectra. The analyzer has nearly ideal fringing field termination, and its resolution and energy dispersion were characterized as a function of energy by solving numerically the equation of motion of electrons in an ideal cylindrical electric field. The numerical results for the radial location of the electrons at the detector as a function of the entrance location, angle, and energy are closely approximated by a second order polynomial, and match closely with those observed. The detection efficiency of the analyzer is 100-150 times better than that of an equivalent single-channel instrument, but limited energy transmission of the zoom lens system used in our case reduced it by a factor of about 2. The performance of the new instrument was demonstrated by measuring the (3)E(1u) electronic spectrum of benzene in only 2 min and the spectrum of endo-benzotricyclo[4.2.1.0(2.5)]nonane.     

2-吡嗪羧酸银的合成、晶体结构及热化学性质

以二次蒸馏水为溶剂,合成了2-吡嗪羧酸银(Ag(pyza)(s)),并利用X-射线单晶衍射法表征了其晶体结构.根据晶体结构数据计算得到2-吡嗪羧酸银的晶格能为554.10 kJ/mol.利用TG/DSC热分析技术研究了该化合物的热分解过程;用精密自动绝热热量计测量了其在78~378 K温区的低温热容;通过最小二乘法拟合得到了摩尔热容随折合温度变化的多项式方程,利用此方程计算出该化合物的舒平热容和各种热力学函数.通过设计合理的热化学循环,利用等温环境溶解-反应热量计分别测定了所设计热化学反应的反应物和产物在选定溶剂中的溶解焓,通过计算得到反应的反应焓为:?(31.919±0.526)kJ/mol.利用Hess定律计算出2-吡嗪羧酸银的标准摩尔生成焓为:?(243.659±1.298)kJ/mol.利用紫外-可见光谱仪对反应物和产物溶解所得溶液分别进行测量,从而证实了所设计热化学循环的可靠性.     

A new form of the equation of state for pure substances and its application to oxygen

Schmidt, R. and Wagner, W., 1985. A new form of the equation of state for pure substances and its application to oxygen. Fluid Phase Equilibria, 19: 175–200.A new wide range equation of state is presented and expressed analytically in the form of the free energy as a function of density and temperature. This fundamental equation contains, in addition to pure polynomial and “BWR”-terms, new exponential functions especially convenient for the critical region. To guarantee an effective structure, the combination of the terms of the equation was found by using an optimization method recently developed. As a result, the optimized function for the free energy is capable of representing the thermodynamic surface of oxygen in the range 54 ≤ T ≤ 300 K, 0 < p ≤ 818 bar and 0 < ρ ≤ 41 mol dm^?3 within the experimental uncertainty of the data available. With the exception of very few items of data, this statement is also valid for the whole coexistence curve and the critical region. Extrapolations of this new equation beyond the range of data yield physically meaningful results.     

Asymptotic series for the quantum quartic anharmonic oscillator

We propose a numerical method to find solutions of the one-dimensional Schrödinger equation when the potential is symmetric and can be expanded in a polynomial form. We used a non-perturbative method, in which we include explicitly the correct asymptotic behavior of the wave function computed by the WKB method. The numerical convergence is very fast and allows to compute the energy eigenvalues and eigenfunctions simultaneously. The method is applied to the quartic anharmonic oscillator with one and two wells, we compute the energy eigenvalues for the ground state and for the first six excited states, the results obtained are in agreement with those reported previously in the literature.     

Influence de la Structure de Diverses Fonctions sur l'Evaluation de l'Energie de Correlation

The influence of various correlation functions, multiplying the monoelectronic space function, is studied and applied to the Helium atom and its isoelectronic series. We used Slater-type basis orbitals and the ground and first excited states have been studied, taking into account the virial and cusp conditions. In the ground state, a very good value for the correlation energy is obtained, using a function of the type For the excited states, this type of function overestimates the assumed value of the correlation energy.     

New approach to the correlation problem: Electron interaction potential as a variable in solving the many-particle Schrödinger equation

The many-electron wave function is represented as the product of the wave function of the independent particles and the function that depends only on the value of the interelectron interaction potential. The function defines the electron correlation effects; a standard linear differential equation was derived to define the function. The equation depends on the functions of independent particles; a generalization of the Hartree-Fock equations including electron correlation was obtained for these functions. The total energy calculation of two-electron ions shows that even solving an ordinary differential equation for the function of independent particles represented by the functions of noninteracting electrons leads to higher accuracy than the one achieved in the Hartree-Fock theory.     

The equation of state for an interface during the adsorption of organic substances on an electrode

The state of the interface between a metal and a solution of an electrolyte containing a neutral surfactant was investigated using a method alternative to the traditional thermodynamic approach. The method was based on the concept that there was a stability limit of a surfactant on an electrode, and the corresponding state could be described in terms of the catastrophe theory. The surface pressure was approximated by the Whitney polynomial in powers of the de Donder parameter (completeness of adsorption) with the coefficients depending on the chemical potential and polarization of the interface. The equation of state and the equation for the stability limit were obtained from the condition of zero first and second derivatives. These equations correctly described the results of electrocapillary measurements in the spirit of the law of corresponding states. The correlation between surface pressure maxima and critical stability potentials predicted by the theory was substantiated by the electrocapillary measurements data provided that the inflexions of surface pressure curves calculated from the electrocapillary data were related to the limiting stability at which the competing forces are balanced during the adsorption of surfactants. A simple equation for surface pressure was suggested in the form of a function of the state of thermodynamic parameters and completeness of adsorption. This function described the state of a surfactant at the interface. Equilibrium equations were derived for the state of a surfactant and the spinodal.