True reactivity ratios for styrene-methyl methacrylate copolymerization in bulk

The local composition concept has been adopted to account for the monomer partitioning effect in the vicinity of the growing macroradical in radical copolymerization. Local compositions were calculated in a two step procedure. In the first step the activity coefficients were calculated in the assumed model systems using the UNIFAC group contribution method

1 UNIFAC means UNIQUAC Functional Group Activity Coefficients, where UNIQUAC stands for Universal Quasichemical Activity Coefficients.

. Subsequently, the modified Wilson equation was applied for estimation of the Boltzmann factor in the derived formulae. Terminal and penultimate models for the bulk copolymerization were investigated. For both models corresponding formulae were derived relating copolymer composition with local mole fractions and the true reactivity ratios. Test calculations have been performed for the bulk styrene-methyl methacrylate system at 313.15 K.     

Theoretical prediction of the coordination number, local composition, and pressure-volume-temperature properties of square-well and square-shoulder fluids

By assuming a Boltzmann distribution for the molecular equilibrium between local and bulk environments, a general model is derived for the prediction of coordination numbers and local compositions of square-well and square-shoulder fluids. The model has no empirical parameter fitted from the data of square-well and square-shoulder fluids, but is valid from the low-density limit to the high-density limit. The applicable width of well or shoulder covers the commonly used range varying from 1.0 to 2.0. The model can accurately predict the coordination numbers of pure square-well and square-shoulder fluids, so the equation of state derived from it is superior to other equations of state based on the existing coordination number models. The model also accurately predicts the local compositions of mixtures in wide ranges of density and size ratio (1.0-8.0), as well as the configuration energy of lattice gases and highly nonideal lattice mixtures. It is remarkable that the model correctly predicts temperature-dependent coordination numbers and local compositions for both equal- and unequal-sized mixtures at close packing, which cannot be predicted by the existing coordination number models. Our derivation demonstrates that the energy parameters in local composition models should represent the potential difference of a molecule between the local and bulk environments, not the pair-interaction potential, and depend on the system conditions and different kinds of pair-interaction parameters. This result is very useful for the development of local composition and activity coefficient models and the mixing rules of equations of state.     

A note on excess Gibbs energy models,equations of state and the local composition concept

A density-dependent local composition expression for the residual energy is derived from a generalized NRTL expression for the excess energy and the van der Waals fluid theory. Integration of this expression yields a volume-dependent expression for the Helmholtz energy from which equations of state utilizing the local composition concept are derived and which in the high-density limit contain the well-known activity coefficient models.The local composition versions of the Carnahan—Starling—van der Waals, the Redlich—Kwong—Soave and the Peng—Robinson equations of state are derived. It is further shown that the group contribution versions of the NRTL, the Wilson and the UNIQUAC excess models may be derived from the generalized NRTL expression for the residual energy when applied to groups instead of molecules.It is thus demonstrated that all current local composition activity-coefficient models can be derived from a local composition version of the van der Waals equation of state using different sets of assumptions. In the same way the van Laar, the Scatchard—Hildebrand and the Flory—Huggins activity coefficient models are obtained from the van der Waals equation of state using the original mixing rules.     

Phase equilibria for liquid mixtures of (butanenitrile + a carboxylic acid + water) at 298.15 K

Liquid–liquid equilibrium data are presented for mixtures of (butanenitrile (1)+acetic acid or propanoic acid or butanoic acid or 2-methylpropanoic acid or pentanoic acid or 3-methylbutanoic acid (2)+water (3)) at 298.15 K. The relative mutual solubility of all the carboxylic acids is higher in the butanenitrile layer than in the aqueous layer. The influence of acetic acid and propanoic acid on the solubility of water in butanenitrile is greater than that of the other acids. Three parameter equations have been fitted to the binodal curve data. These equations are compared and discussed in terms of statistical consistency. Selectivity values for solvent separation efficiency were derived from the tie-line data. The NRTL and UNIQUAC models were used to correlate the experimental results and to calculate the phase compositions of the ternary systems. The NRTL equation fitted the experimental data far better than the UNIQUAC equation.     

A quasi lattice-local composition model for the excess Gibbs free energy of liquid mixtures

Two new expressions for the excess Gibbs energy of liquid mixtures are derived from Guggenheim's quasi-lattice model and Wilson's local composition concept. These are called the Local Surface Guggenheim equation (LSG) and the Local Composition Guggenheim equation (LCG). The LSG equation is similar, but not identical to UNIQUAC. The new equations require only two adjustable parameters per binary, and no higher-order parameters for extension to multicomponent systems.A critical discussion is given of Guggenheim's quasi-lattice expression for the excess Gibbs energy of athermal mixtures. This expression gives the combinatorial contribution to the new equations.A new method is proposed in the evaluation of the pure component structural parameters, independent of particular assumptions about the lattice parameters.The application of the LSG and the LCG equations to practical problems of phase-equilibria is considered in detail.     

Thermodynamics of the Laminar Donnan System

Thermodynamic quantities of a polyelectroyte immersed in salt solution are derived modeling the polyelectrolyte by a sequence of charged parallel flat plates. The starting point for the analysis is the derivation of the Gibbs free enthalpy in its canonic variables pressure (p) and temperature (T), i.e., as a thermodynamic potential. From this, further thermodynamic quantities such as Helmoltz free energy, entropy, internal energy, compressibility, isobar and isochor heat capacities, and expansive force are derived in analytical expressions by differentiation. All these formulas contain the parameter plate surface charge density (sigma) that provides a measure of the discontinuity of the polymer charge distribution that can be used to fit the theory to experimental data. Thermodynamic quantities are also known from the classical Donnan equilibrium that treats the polyelectroyte charge network as a charge continuum. A limiting process is used to perform the transition from the laminar Poisson- Boltzmann model to the continuous Donnan equilibrium. In general, the expressions of the Donnan system are recovered for plate charge density sigma-->0, number of plates Z-->infinity, and sigma Z=constant. Copyright 2000 Academic Press.     

Activity coefficients in mixed solvent electrolyte solutions

A brief, rigorous derivation is given for activity coefficients used in phase equilibruim calculations of multicomponents salts and solvents where an extended Debye—Hückel theory for long-range interactions is combined with short-range interaction effects using an excess Gibbs energy model, such as UNIQUAC. Calculations indicate only minor differences from approximate forms previously used for the salt effect on azeotropes.     

A Statistical Mechanical View of the Determination of the Composition of Multi‐Temperature Plasmas

It is important that plasma composition is calculated in a manner consistent with statistical mechanics, particularly since the Boltzmann equation is the basis from which transport coefficients and the fluiddynamic equations are derived. It is shown from statistical mechanical considerations based on the Boltzmann equation and the Htheorem that it is (i) not possible for a plasma to have more than one temperature in equilibrium in the absence of external forces and gradients, and (ii) not possible to draw conclusions about the change in entropy of a plasma in the presence of external forces and gradients. Derivations of the twotemperature Saha equation, and more generally calculations of the composition of a multitemperature plasma, that are based on entropy maximization are therefore invalid. A thermodynamic derivation of the composition of a multitemperature plasma that is consistent with the statistical mechanical results is presented. The derivation shows that the equilibrium composition of a plasma can be correctly calculated by minimization of the internal or free energy.     

Derivation of Copolymer Composition Equation Through Kinetic Theory in Binary Copolymerization Systems with Antepenultimate Effect

A new treatment to characterize copolymer composition in binary copolymerization systems was developed by using a steady-state assumption for free radicals. It gives a copolymer composition equation solely through classical kinetic theory with the antepenultimate effect taken into account. This equation and its derivation procedure are compared with those previously published.     

Equilibrium of multi-phase systems in gravitational fields

Four necessary conditions for equilibrium of an isolated solid-liquid-vapor system in a gravitational field were derived by Ward and Sasges (1998) in a unified setting, by using an entropy maximization approach, and under the assumption that the liquid-vapor surface tension does not depend on elevation. These are thermal equilibrium, the Laplace and Young equations, and a condition on the chemical potentials of the components present in the system. Gibbs (1876) had obtained the Young equation in a derivation separate from the derivation of the other three conditions and by using an energy minimization approach. However, Gibbs had derived a more general form of the Laplace equation than Ward and Sasges's. Gibbs's equation contained a term expressing the contribution of the variation of surface tension with elevation. This equation has since been neglected by most of the scientific community. In the present paper, the same approach as Ward and Sasges's is used to derive, in an unified setting, the conditions for equilibrium of an isolated solid-liquid-vapor system in a gravitational field but under the assumption that the liquid-vapor surface tension may depend on elevation. The four well-known conditions for equilibrium are obtained, with Gibbs's generalized Laplace equation instead of the classical Laplace equation. The derivations in this paper were carried out for two different system geometries, namely, for a sessile drop and for a conical capillary tube, and similar conditions for equilibrium were obtained.     

局域平衡假设和反应-扩散过程

局域平衡假设作为不可逆过程热力学理论的基础通常被认为适用于一般条件下的物理化学过程。本文从玻耳兹曼方程和涨落的随机理论出发重新研究了局域平衡假设对反应—扩散过程的适用性。表明对于涉及非线性化学动力学的反应—扩散过程, 从随机理论得到的结果和局域平衡假设是不一致的。     

Prediction and experimental determination of the binary and ternary phase diagrams of (±)medetomidine hydrochloride

The binary phase diagram of medetomidine hydrochloride was determined based on thermogravimetric differential thermal (TGA/DTA) measurements. The binary phase diagram presented a eutectic point in the 19:81 [(R)/(S)] composition and the ternary phase diagram in the presence of 2-propanol showed a eutectic point in the 75:25 [(S)/(R)] composition, both characterizing the product as a racemic compound forming system. The solubility of enantiomeric mixtures in 2-propanol was measured at 10, 20 and 30 °C. The ideal solubility curves of the mixtures were calculated and the activity coefficients derived. A semi-empirical thermodynamic model UNIversal QUAsi-Chemical (UNIQUAC) was used to predict the solubility of various compositions of enantiomers at different temperatures. There was good agreement between the experimental solubility data of medetomidine hydrochloride and the results obtained from the UNIQUAC equation.     

Liquid—liquid equilibrium data: Their retrieval,correlation and prediction Part II: Correlation

The correlation of liquid—liquid equilibrium data using models for the liquid phase activity coefficients — for example NRTL and UNIQUAC — is reviewed. Different numerical procedures used in the computation of liquid—liquid equilibrium compositions on the basis of these models are evaluated. Methods for obtaining parameters from liquid—liquid equilibrium data are described, and a method leading to improved representation of tie lines using relatively few parameters is recommended. The NRTL and UNIQUAC equations are compared with respect to their ability of representing binary and ternary liquid—liquid equilibrium data. The UNIQUAC equation appears to be more convenient to use and to correlate the data slightly better than does NRTL with the same number of parameters.     

Thermodynamics of associated mixtures of the Mecke—Kempter type

A chain-forming associated solution theory based on the UNIQUAC equation is presented for alcohol-unassociated active component liquid mixtures of the Mecke—Kempter type. The capability of the theory in reproducing the excess Gibbs free energy and excess enthalpy data for many binary mixtures is successfully shown. Ternary extension of the theory is presented in the calculations of vapor—liquid and liquid—liquid equilibria and excess enthalpy data from binary data.     

Breaking the polar‐nonpolar division in solvation free energy prediction

Implicit solvent models divide solvation free energies into polar and nonpolar additive contributions, whereas polar and nonpolar interactions are inseparable and nonadditive. We present a feature functional theory (FFT) framework to break this ad hoc division. The essential ideas of FFT are as follows: (i) representability assumption: there exists a microscopic feature vector that can uniquely characterize and distinguish one molecule from another; (ii) feature‐function relationship assumption: the macroscopic features, including solvation free energy, of a molecule is a functional of microscopic feature vectors; and (iii) similarity assumption: molecules with similar microscopic features have similar macroscopic properties, such as solvation free energies. Based on these assumptions, solvation free energy prediction is carried out in the following protocol. First, we construct a molecular microscopic feature vector that is efficient in characterizing the solvation process using quantum mechanics and Poisson–Boltzmann theory. Microscopic feature vectors are combined with macroscopic features, that is, physical observable, to form extended feature vectors. Additionally, we partition a solvation dataset into queries according to molecular compositions. Moreover, for each target molecule, we adopt a machine learning algorithm for its nearest neighbor search, based on the selected microscopic feature vectors. Finally, from the extended feature vectors of obtained nearest neighbors, we construct a functional of solvation free energy, which is employed to predict the solvation free energy of the target molecule. The proposed FFT model has been extensively validated via a large dataset of 668 molecules. The leave‐one‐out test gives an optimal root‐mean‐square error (RMSE) of 1.05 kcal/mol. FFT predictions of SAMPL0, SAMPL1, SAMPL2, SAMPL3, and SAMPL4 challenge sets deliver the RMSEs of 0.61, 1.86, 1.64, 0.86, and 1.14 kcal/mol, respectively. Using a test set of 94 molecules and its associated training set, the present approach was carefully compared with a classic solvation model based on weighted solvent accessible surface area. © 2017 Wiley Periodicals, Inc.     

A refinement of the terpolymer equation and its simple extension to two- and four-component systems

Terpolymer composition estimation with an established equation has been found to give results that vary with the feed monomer ratio substitution pattern used. A new copolymer equation has been derived that overcomes this difficulty to give the same composition results regardless of the order of monomer substitution. The new equation also gives comparable or better agreement with experimentally determined copolymer compositions than obtained by use of the established Alfrey-Goldfinger terpolymer equation. In addition, this new terpolymer equation demonstrates a versatility not shown by the present terpolymer equations in that it can be readily adapted by inspection to enable estimation of copolymer compositions for two- or for four-component polymer systems. It is also readily adaptable for copolymers with more than four components, and may also be valid for composition estimation of these because of the derivation method used, although it has not as yet been possible to test this possibility. © 1996 John Wiley & Sons, Inc.     

(Liquid + liquid) equilibria of {heptane + xylene + N-formylmorpholine} ternary system

(Liquid + liquid) equilibrium (LLE) data for ternary system {heptane (1) + m-xylene (2) + N-formylmorpholine (3)} have been determined experimentally at temperatures ranging from 298.15 K to 353.15 K. Complete phase diagrams were obtained by determining solubility and tie-line data. Tie-line compositions were correlated by Othmer-Tobias and Bachman methods. The universal quasichemical activity coefficient (UNIQUAC) and The non-random two liquids equation (NRTL) were used to correlate the phase equilibrium in the system using the interaction parameters determined from experimental data. It is found that UNIQUAC and NRTL used for LLE could provide a good correlation. Distribution coefficients, separation factors, and selectivity were evaluated for the immiscibility region.     

On evaluate of the integral methods for the determination of the activation energy

Recently, Órfão obtained two simple equations for the estimation of the relative error in the activation energy calculated by the integral methods [2]. In this short communication, the validity of the equations has been evaluated by comparing the results calculated by the equations with the results calculated by the equation from theoretical derivation without introducing any assumption.     

Approximate expression for the potential energy of double-layer interaction between two parallel similar plates with constant surface potential

An approximate equation for the electric potential distribution is obtained by linearizing the Poisson–Boltzmann with respect to the deviation of the electric potential from the surface potential. On the basis of the solution to this linearized Poisson–Boltzmann equation, an approximate expression is derived for the potential energy of the double layer interaction per unit area between two parallel similar plates at constant surface potential. It is found that this linearization approximation works quite well for small plate separations for all values of the surface potentials.     

A Comparative Study of Calibration Free Methods for the Elemental Analysis by Laser Induced Breakdown Spectroscopy

We have used two calibration free laser induced breakdown spectroscopy (CF-LIBS) methods for the quantitative analysis of Pb–Sn alloys with different compositions. The first method is based on Boltzmann plots where the elemental concentration is determined from the intercept along the y-axis whereas the second method is the electron density conservation method, in which elemental compositions are determined by comparing the experimentally measured number density with the theoretical results obtained by CF-LIBS. The neutral spectral lines of lead and tin have been used for the estimation of plasma temperature by the Boltzmann plot method whereas the Saha–Boltzmann equation has been used to calculate the electron number density. By comparing the results of both CF-LIBS methods, it is concluded that the CF-LIBS (electron number density conservation) method is more appropriate than the CF-LIBS (Boltzmann plot method) for the quantitative elemental analysis.