On some variational approximations in two-dimensional classical lattice systems

A new derivation is presented of some variational approximations for classical lattice systems that belong to the class of cluster-variation methods, among them the well-known Bethe-Peierls and Kramers-Wannier approximations. The limiting behavior of a hierarchical sequence of cluster-variation approximations, the so-calledC hierarchy, is discussed. It is shown that this hierarchy provides a monotonically decreasing sequence of upper boundsf _n on the free energy per lattice sitef and thatf _n f asn . Our results are based on extension theorems for states given on subsets of the lattice, which might be of some independent interest, and on an application of transfer matrix concepts to the variational characterization of translation-invariant equilibrium states.     

A Robust and Efficient Method for the Computation of Equilibrium Composition in Gaseous Mixtures

This paper presents in detail a robust, efficient and accurate methodology for the computation of equilibrium composition in gaseous mixtures. The methodology is founded on the concept of the chemical basis, which is defined and formalized using a powerful matricial approach. The method is specially designed to be general, thus providing basic thermodynamic data in several areas, such as combustion, plasma chemistry and, more generally speaking, computational fluid dynamics. The performance of the method is given in terms of CPU usage and the computed results are compared with those in the published literature. The method is shown to yield results of very high quality in terms of accuracy and smoothness.     

LiCl—HOAc和LiCl—HOAc—H2O体系（25℃）相图

测定了LiCl-HOAc和LiCl-HOAc-H_2O体系25℃时的溶度,绘制了溶度图.在LiCl-HOAc体系的相图中有LiCl及LiCl·1/2HOAc2种固相,后者是固液异成分化合物,体系中未发现LiCl·5HOAc或LiCL·HOAc的生成.LiCl-HOAc-H_2O体系25℃时的相图中有3种固相,即LiCl·H_2O、LiCl和LiCl·(1/2)HOAc.相变LiCl·H_2O→LiCl→LiCl·(1/2)HOAc表明HOAc在该三元体系中具有盐溶、脱水和溶剂合3种作用.此结果提供了一种制备无水LiCl的新方法.     

Vapor pressure of R227ea + ethanol at 343.13 K by molecular simulation

A new molecular model for 1,1,1,2,3,3,3-heptafluoropropane (R227ea) was developed on the basis of quantum chemical calculations and optimized using experimental vapor pressure and bubble density data. In combination with an existing model for ethanol, a molecular model for the binary mixture R227ea + ethanol was defined, using the Lorentz–Berthelot combining rule. It was validated at 283.17 K, where, considering the statistical uncertainties, it agrees to the experimental vapor pressure. The vapor–liquid equilibrium, comprising both bubble line and dew line data, was predicted at 343.13 K by molecular simulation. The Peng–Robinson equation of state fails for this system.     

Thermochemistry of thermal plasma chemical reactions. Part I. General rules for the prediction of products

Equilibrium calculations based on the standard technique of minimization of the Gibbs free energy, with consideration of both gas and condensed phases, are shown to be inadequate for predicting the yield or even the proper composition of the products from thermal plasma reaction systems. This is due to the dominating influence of nucleation kinetics, a nonequilibrium effect.In this paper a modification of the equilibrium approach is proposed, whereby the supersaturation of a phase which may condense is calculated, and species with low supersaturation pressures which are unlikely to precipitate are subsequently removed from consideration.A comparison is made between the former equilibrium predictions and these quasi-equilibrium predictions. When compared with experimental data taken from the extant literature and from the authors' own research, the quasi-equilibrium modification is seen to provide excellent agreement with respect to product composition and yield. Examples are discussed including the thermal plasma production of hydrogen cyanide, ammonia, acetylene, silicon carbide, silicon nitride, and titanium carbide.     

Determining PPARγ-ligand binding affinity using fluorescent assay with cis-parinaric acid as a probe

Upon the study of small-molecules binding to proteins, the traditional methods for calculating dissociation constants (Kd and Ki) have shortcomings in dealing with the single binding site models. In this paper, two equations have been derived to solve this problem. These two equations are independent of the total concentration or initial degree of saturation of receptor and the activity of the competitive molecule. Through nonlinear fitting against these two equations, Kd value of a probe can be obtained by binding assay, and Ki value of a ligand can be obtained by competitive assay. Moreover, only the total concentrations of receptor([R]t), ligand([L]t) and probe([P]t) are required for the data fitting. In this work, Ki values of some typical ligands of PPARγ were successfully determined by use of our equations, among which the Ki value of PPARγ-LY171883 was reported for the first time.     

An algebraic method that includes Gibbs minimization for performing phase equilibrium calculations for any number of components or phases

The most widely used technique for performing phase equilibria calculations is the K-value method (equality of chemical potentials). This paper proposes a more efficient algorithm to achieve the results that includes Gibbs minimization when we know the number of phases. Using the orthogonal derivatives, the tangent plane equation and mass balances, it is possible to reduce the Gibbs minimization procedure to the task of finding the solution of a system of non-linear equations. Such an operation is easier and faster than finding tangents or areas, and appears to converge as fast as the K-value method. Examples illustrate application of the new technique to two and three phases in equilibrium for binary and ternary mixtures.     

Isobaric vapor–liquid equilibria for the quaternary reactive system: Ethanol + water + ethyl lactate + lactic acid at 101.33 kPa

Isobaric vapor–liquid equilibrium (VLE) data of the reactive quaternary system ethanol (1) + water (2) + ethyl lactate (3) + lactic acid (4) have been determined experimentally. Additionally, the reaction equilibrium constant was calculated for each VLE experimental data. The experimental VLE data were correlated using the UNIQUAC equation to describe the chemical and phase equilibria simultaneously. For some of the non-reactive binary systems, UNIQUAC binary interaction parameters were obtained from the literature. The rest of the binary UNIQUAC parameters were obtained by correlating the experimental quaternary VLE data obtained in this work. A maximum pressure azeotrope at high water concentration for the binary reactive system ethyl lactate + water has been calculated.     

An equilibrium and calorimetric investigation of the hydrolysis of L-tryptophan to (indole + pyruvate + ammonia)

Apparent equilibrium constants and calorimetric enthalpies of reaction have been measured for the reaction L-tryptophan(aq) + H₂O(l) = indole(aq) + pyruvate(aq) + ammonia(aq) which is catalyzed by L-tryptophanase. High-pressure liquid-chromatography and microcalorimetery were used to perform these measurements. The equilibrium measurements were performed as a function of pH, temperature, and ionic strength. The results have been interpreted with a chemical equilibrium model to obtain thermodynamic quantities for the reference reaction: L-tryptophan(aq) + H₂O(l) = indole(aq) + pyruvate^–(aq) + NH ₄ ⁺ (aq). At T=25°C and I_m=O the results for this reaction are: K^o=(1.05±0.13)×10^–4, G°=(22.71±0.33) kJ-mol^–1, H°=(62.0±2.3) kJ-mol^–1, and S°=(132±8) J-K^–1-mol^–1. These results have been used together with thermodynamic results from the literature to calculate standard Gibbs energies of formation, standard enthalpies of formation, standard molar entropies, standard molar heat capacities, and standard transformed formation properties for the substances participating in this reaction.Presented at the Symposium, 76^th CSC Congress, Sherbrooke, Quebec, May 30–June 3, 1993, honoring Professor Donald Patterson on the occasion of his 65^th birthday.     

On the conformational stability and dimerization of phosphotransferase enzyme I from Escherichia coli

The activity of enzyme I (EI), the first protein in the bacterial PEP:sugar phosphotransferase system, is regulated by a monomer–dimer equilibrium where a Mg²⁺-dependent autophosphorylation by PEP requires the homodimer. Using inactive EI(H189A), in which alanine is substituted for the active-site His189, substrate binding effects can be separated from those of phosphorylation. Whereas 1 mM PEP (with 2 mM Mg²⁺) strongly promotes dimerization of EI(H189A) at pH 7.5 and 20 °C, 5 mM pyruvate (with 2 mM Mg²⁺) has the opposite effect. A correlation between the coupling of N- and C-terminal domain unfolding, measured by differential scanning calorimetry, and the dimerization constant for EI, determined by sedimentation equilibrium, is observed. That is, when the coupling between N- and C-terminal domain unfolding produced by 0.2 or 1.0 mM PEP and 2 mM Mg²⁺ is inhibited by 5 mM pyruvate, the dimerization constant for EI(H189A) decreases from >10⁸ to <5 × 10⁵ or 3 × 10⁷ M⁻¹, respectively. With 2 mM Mg²⁺ at 15–25 °C and pH 7.5, PEP has been found to bind to one site/monomer of EI(H189A) with K_A′10⁶ M⁻¹ (ΔG′=−33.7±0.2 kJ mol⁻¹ and ΔH=+16.3 kJ mol⁻¹ at 20 °C with ΔC_p=−1.4 kJ K⁻¹ mol⁻¹). The binding of PEP to EI(H189A) is synergistic with that of Mg²⁺. Thus, physiological concentrations of PEP and Mg²⁺ increase, whereas pyruvate and Mg²⁺ decrease the amount of dimeric, active, dephospho-enzyme I.