Molecular thermodynamic model for equilibria in solution: I. Reacting and non-reacting ensembles

The partition functions of solution thermodynamics are mathematical representations of the properties of molecular ensembles statistically distributed according to specific characteristics. The ensembles are classified as non-reacting or reacting. The non-reacting ensembles are characterized by one mean enthalpy level with dispersion around the mean. The reacting ensembles are characterized by two or more distinctly separated enthalpy levels over which the different species are variably distributed, depending on concentration and/or temperature.

The non-reacting ensembles can be distinguished into microcanonical, thermal, osmotic, thermo-osmotic ensembles, depending on the type of exchange with the surroundings which is connected to the fluctuations of the ensemble variables. The reacting ensembles can be distinguished into thermal, osmotic, thermo-osmotic, electrochemical, electro-osmotic, electro-thermal, electro-thermo-osmotic ensembles, depending on the type of reaction and of exchange with the surroundings.     

Molecular thermodynamic model for equilibria in solution II. Statistical microscopic properties of ensembles

A statistical thermodynamic model for the interpretation of the equilibria in solution is based on the principle that the representative statistical ensembles can be characterized by two types of molecular distribution, one for non-reacting systems and another for reacting ones, respectively. Non-reacting and reacting ensembles correspond at the molecular level to one or a couple of potential curves, respectively. The properties of the thermodynamic model for solutions can be set up following some rules. These concern the statistical extension of the microscopic model to the whole ensemble and the successive averaging to get a mean partition function. The mean partition function is linked to the experimental domain of concentrations, dilutions and equilibrium constants (probability space) and to that of calorimetry, chemical work, and potentiometry (thermodynamics space). The formal connection between probability and thermodynamic space and the conformity of thermal equivalent dilution with the formulations of statistical thermodynamics are also shown.     

An effective calculation procedure for two-phase equilibria in multireaction systems

In this work, we present a method for the calculation of two-phase equilibria in multireaction systems. The procedure uses a transformed composition variable in the orthogonal derivatives of the Gibbs function and the tangent plane equation to form a system of non-linear equations. We solve this system with a Newton–Raphson method and our initialization procedure uses results from the reactive stability analysis and the reactive equal area rule. With this initialization strategy, convergence occurs with only a few iterations in the numerical method. Several examples with multiple chemical reactions demonstrate the performance of our approach.     

Effective potential approach to bulk thermodynamic properties and surface tension of molecular fluids I. Single component n-alkane systems

The aim of this work is to develop spherically symmetric effective potentials allowing bulk thermodynamic properties and surface tension of molecular fluids to be predicted semiempirically by the use of statistical mechanical methods. Application is made to the straight chain alkane fluids from methane to decane. An effective Lennard-Jones potential is generated with temperature-dependent parameters fitted to the critical temperature and pressure and to Pitzer's acentric factor. Insertion of this potential into the generalised van der Waals (GvdW) density functional theory yields bulk properties in good agreement with experiments. The surface tension is overestimated for the longer alkane chains. In order to account for the surface tension, an independently adjustable attractive range of interaction is required and obtained through the use of square-well potentials chosen so as to leave the bulk thermodynamics unaltered while the attractive range is fitted to the surface tension at a single temperature. The GvdW theory, which includes binding energy, entropic and profile shape contributions, then generates surface tension estimates that are of good accuracy over the full range of available experimental data. It appears that, given a sufficiently flexible form, effective potentials combined with simple statistical mechanical theory can reproduce both bulk and non-uniform fluid data of great variety in an insighful and practically useful way.     

Molecular thermodynamic model for associated polymers

A molecular thermodynamic model for homopolymer and copolymer systems with association segments was established by adopting the molecular thermodynamic model for hardsphere‐chain fluid as a reference, a perturbation term contributed by the square‐well potential and a contribution of association terms. The latter considers the multi‐associated‐segments in a chain‐like molecule based on the shield‐sticky model of chemical association. The model can be used to correlate the pVT of melten homopolymer and copolymer. Good agreements with experimental data have been obtained.     

Solid-solute phase equilibria in aqueous solution. IV. Calculation of Phase Diagrams

The thermodynamic principles of conventional (T-x, P-T) phase diagrams and solubility (log ΣK-x) diagrams depicting solid-solute phase equilibria in aqueous solution are derived from a unifying point of view. It is shown that thermodynamic quantities necessary for the construction of conventional phase diagrams can be obtained from solubility measurements. The unary system calcite-aragonite and the binary system aragonite-strontianite, where solubility data are available over the whole compositional range, have been selected as examples. In the latter case, the constraint of constant composition of the solid phase leading to a metastable equilibrium with the respective solute species is an essential point in the thermodynamic derivation and was observed experimentally as well.     

Enthalpy changes in protolytic equilibria of glycyl-β-alanine in an aqueous solution

Reaction enthalpy changes were measured with the use of calorimetric method for the protonation and neutralization of glycyl-β-alanine at 298.15 K and ionic strengths 0.5, 1.0, 1.5 mol L⁻¹ (KNO₃), and the corresponding standard thermodynamic parameters were evaluated. The results obtained were compared with the literature data on related compounds.     

Molecular mechanics of organic halides. V. Conformational equilibria in solution

With a view of using data on solutions and liquids for parameter fitting in molecular mechanical force fields, Abraham's theory of solvation is incorporated in the force field procedure. Geometries and bond moments are estimated internally, partial account being taken of bond–bond induction, and used to calculate the intramolecular electrostatic energy, dipole moment, and the dipole and quadrupole terms in the solvation energy. Three dielectric constants are used, one for the solute in the vapor, one for the solution, and one for the intramolecular space through which dipole–dipole interactions take place. Examples are given, including such where computation differs with measurement, to illustrate the performance of the scheme.     

A molecular thermodynamic model for random copolymer solutions

A new Helmholtz energy model of mixing for random copolymer solutions based on a close-packed lattice has been developed. The model contains three terms: the contribution of the athermal mixing of polymer chain and solvent, the Helmoltz energy of mixing in a multi-component Ising lattice where the interactions between segments is accounted for, and the contribution of the dissociation of the polymer and the association of monomers. The Guggenheim model, Yang et al.'s model and the sticky-point model of Cummings, Zhou and Stell are used respectively, for the above three contributions. Comparisons between Monte Carlo simulated coexistence curves with those predicted by various theories for random copolymer solutions with various chain lengths, chain compositions and inter-segment interaction parameters show that the agreement between simulations and the predictions of this work is nearly perfect. The model can be used satisfactorily to correlate the liquid–liquid equilibria of practical random copolymer solutions.     

Calculating thermodynamic properties from perturbation theory: II. An analytic representation for the square-well chain fluid

An analytic representation of thermodynamic properties of the freely jointed square-well chain fluid is developed based on the thermodynamic perturbation theory of Barker–Henderson, Zhang and Weitheim. By using a real function expression for the radial distribution function and incorporating structural information for square-well monomer of TPT1 model, an analytic expression for the Helmholtz energy of square-well chain fluid is expanded from Zhang’s analytic expressions for thermodynamic properties of square-well monomer. The expression leads to good predictions of the compressibility factor, residual internal energy and constant-volume heat capacity for 4-mer, 8-mer and 16-mer square-well fluids when compared with the Monte Carlo (MC) simulation results. The incorporating structural information for square-well dimer of TPT-D model is also calculated. To obtain the constant-volume heat capacity needed, NVT MC simulations were performed.     

反胶束系统及萃取蛋白质的分子热力学模型1: 反胶束系统的分 子热力学模型

以反胶束系统稳定性的热力学分析为基础,综合分析了反胶束系统的三大效应,即低界面张力效应、界面弯矩效应、混合熵效应,提出了一个分子热力学模型,模型所预言的反胶束水分含量随无机盐种类、浓度、表面活性剂浓度以及助表面活性剂含量的变化与所获实验规律定量相符,还能预言反胶束内表面处电势值、表面活性剂解离度。     

Coherent thermodynamic model for solid,liquid and gas phases of elements and simple compounds in wide ranges of pressure and temperature

Thermodynamic modeling of fluids (liquids and gases) uses mostly series expansions which diverge at low temperatures and do not fit to the behavior of metastable quenched fluids (amorphous, glass like solids). These divergences are removed in the present approach by the use of reasonable forms for the “cold” potential energy and for the thermal pressure of the fluid system. Both terms are related to the potential energy and to the thermal pressure of the crystalline phase in a coherent way, which leads to simpler and non diverging series expansions for the thermal pressure and thermal energy of the fluid system. Data for solid and fluid argon are used to illustrate the potential of the present approach.     

Phase behaviour of globular protein and flexible polymer in an aqueous medium

A simple model for the phase behaviour of a globular protein and a flexible polymer in an aqueous medium is described, in which both the compact feature of the protein and the flexble feature of the polymer have been included. The phase diagrams calculated by using the model suggest that for a given protein, the behaviour depends strongly on the polymer molecular weight. Fluid-fluid-solid three-phase and fluid-fluid two-phase equilibria can be found only when the polymer molecular weight is sufficiently high; otherwise, the only two-phase region in the phase diagram is a fluid-solid two-phase region.     

Applicability of a modified double lattice model for liquid-liquid equilibria of mixed-solvent polymer systems

Expanding upon a previous study, the modified double lattice model for mixed-solvent polymer systems was developed by employing new universal constants. The calculated results of the proposed model showed good agreement with Monte Carlo simulation results and hypothetically predicted Types 0 and 3 phase separations of the Treybal classification. To describe real systems, the chain length of the polymer and energy parameters were adjusted to fit experimental data. The proposed model correlated well with experimental data from real systems incorporating low to high molecular weight polymers (PEO 200, dextran 40 350, PS 300 000) using reasonable model parameters.     

A critique of a thermodynamic description of hydrophobic aggregation in aqueous solution

The conclusions recently summarised by A. Marmur [J. Am. Chem. Soc. 122 (2000) 2120] concerning hydrophobic aggregation of solutes in aqueous solution are examined. The thermodynamic analysis is critically reviewed and the impact of implicit extrathermodynamic assumptions discussed. These assumptions are questioned and shown to lead to a model for hydrophobic aggregation which is flawed.     

Molecular mechanics calculations on carbonyl compounds. IV. Heats of formation

Molecular mechanics (MM4) calculations on the heats of formation of aldehydes and ketones were carried out for a total of 59 compounds (10 aldehydes and 49 ketones). Optimization of the heat of formation parameters was obtained by a least squares fit to the experimentally known heats of formation. With the optimized MM4 heat of formation parameters, the MM4 calculated heats of formation showed significant improvement over those of MM3. The standard and weighted root mean square deviations for the MM4 values were 0.35 and 0.31 kcal mol^?1, respectively, whereas for the MM3 values they were 0.42 and 0.39 kcal mol^?1, respectively. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1476–1483, 2001     

Regression of binary interaction parameters for thermodynamic models using an inside-variance estimation method (IVEM)

An inside-variance estimation method (IVEM) for binary interaction parameter regression in thermodynamic models is proposed. This maximum likelihood method involves the re-computation of the variance for each iteration of the optimization procedure, automatically re-weighting the objective function. Most of the maximum likelihood approaches currently used to regress the parameters of thermodynamic models fix the variances, converting the problem into a traditional weighted least squares minimization. However, such approaches lead to residual variances (between measured and calculated values) that are inconsistent with the fixed variances and, thus, do not necessarily produce optimum parameters for prediction purposes. The new method (IVEM) substantially improves fluid phase equilibria predictions (as shown by the examples presented) by maintaining consistency between the residual variances and the variance used in the objective function. This results in better parameter estimation and to a direct measure of the uncertainty in the model prediction.     

Dependence of the distribution constant in liquid–liquid partition equilibria on the van der Waals molecular surface area

The direct calculation of free energy of interactions between a solute j and two immiscible liquids shows a linear dependence between the (logarithm of) the distribution constant in liquid–liquid partition equilibrium log K_j and the van der Waals surface area of the solute. The study provides a thermodynamic proof for the formula log K_BA,j = c₁ log K_BC,j + c₂ that describes the linear dependence between (the logarithm of) the distribution constant for a solute j in a solvent system (B/A) and (the logarithm of) the distribution constant for the same solute in a different solvent system (B/C). This relation has been well proven by various experimental studies and it is frequently used in liquid chromatographic separations as well as in liquid–liquid extractions, but was not explained previously based on thermodynamic results. The theory was verified using the prediction of octanol/water distribution constants log K_ow for a wide range of molecules, including hydrocarbons and compounds with a variety of functional groups. The results have also been verified for the distribution constants in other solvent systems. The expression for the distribution constant obtained in this study also gives a theoretical base for the additive fragment methodology used for the prediction of log K_ow.