Local-composition models and prediction of binary liquid-liquid binodal curves from heats of mixing

The temperature dependence of several local-composition models has been studied in conjunction with the Gibbs-Helmholtz identity. Binary heat-of-mixing data at temperatures near but above the critical solution temperature have been used to fit parameters obtained from excess-free-energy models in conjunction with the Gibbs-Helmholtz equation. These models, if the temperature dependence is adequate, should allow prediction of liquid-liquid equilibria (LLE) from the fitted parameters. The NRTL, UNIQUAC, and modified NRTL and UNIQUAC models (modified by inclusion of temperature-dependent parameters) seldom provide even qualitatively correct LLE predictions. A new local-composition model due to Wang and Chao (1983) yields reasonably good predictions for some systems but incorrect results for others. Reasons for these model inadequacies are discussed in terms of a local-composition model for the excess enthalpy which can be used to predict binodal curves accurately, including reasonably accurate values for the critical solution temperature, if reference excess-free-energy data at higher temperatures are available from VLE maesurements.     

The use of Monte Carlo simulations to evaluate kinetic data and analytic approximations

Experimental kineticists are always faced with the problem of reducing kinetic data to extract physically meaningful information. A particularly vexing problem arises when different models reproduce the data but yield different values for the physical parameters. For over forty-five years Monte Carlo simulation techniques have been used to study the statistical behavior of parameters extracted from data. Not only do these simulations provide realistic uncertainties, correlation coefficients, and confidence envelopes, but they also provide insight into the nature of the model. These insights may be obtained by viewing two-dimensional scatter plots of the fractional changes of the parameters and one-dimensional histograms of the distributions of the changes in the parameters. Monte Carlo simulations are illustrated with examples from OH+CH₄ → CH₃+H₂O and the high-pressure rate coefficient for methyl-methyl association. A more complex problem involves models for pressure-dependent rate coefficients in the falloff region. We have modeled methyl-methyl association with five of the most current analytic approximations for behavior in the falloff region. All of these reproduce the data to within their uncertainties. However, when Monte Carlo techniques are applied the correlations between the parameters and the nonlinear nature of their behavior become evident. We postulate that the statistical behavior of the parameters of a model may be used to distinguish one model from another and, thereby, identify those analytic approximations that hold promise for further investigation and utilization. Finally, the recent advent of high-speed workstations implies that Monte Carlo simulations should become a routine part of the analysis of kinetic data. © 1997 John Wiley & Sons, Inc. Int J Chem Kinet 29: 803–817, 1997     

基于SAFT理论关联醇与DMF体系的1H NMR

混合物核磁共振化学位移可以用不同的化学缔合理论研究,但当形成的缔合体种类很多时,需要很多优化参数.作者从统计缔合流体理论（SAFT）出发,提出了一个能关联混合物核磁共振化学位移,但又不需要假设缔合平衡常数的模型.对于醇与N,N-二甲基甲酰胺（DMF）体系,关联的均方根偏差小于1.01％.讨论了醇与DMF体系和醇与正己烷体系核磁共振化学位移随醇的浓度变化趋势的差异,认为醇与DMF形成比醇的自缔更强的交叉缔合是造成这种变化趋势不同的主要原因.     

Interaction parameters for multi-component aromatic extraction with sulfolane

Aromatic extraction is an important operation in petrochemical processing. Design of an aromatic extractor requires the knowledge of multi-component liquid–liquid equilibrium (LLE) data. Such experimental LLE data are usually not available and therefore can be predicted using various activity coefficient models. These models require proper binary interaction parameters, which are not yet available for all aromatic extraction systems. Furthermore, the parameters available for most of the ternary systems are specific to that system only and cannot be used for other ternary or multi-component systems. An attempt has been made to obtain these parameters that are globally applicable. For this purpose, the parameter estimation procedure has been modified to estimate the parameters simultaneously for different systems involving common pairs. UINQUAC and UNIFAC models have been used for parameter estimation. The regressed parameters are shown to be applicable for the ternary as well as for the multi-component systems. It is observed that UNIQUAC parameters provide a better fit for ternary LLE data, whereas, as one moves towards the higher component systems (quaternary and quinary) the UNIFAC parameters, which are a measure of the group contributions, predict the LLE better. Effect of temperature on UNIQUAC binary interaction parameters has been studied and a linear dependence has been observed.     

Comparison of selected retention models in reversed-phase liquid chromatography

Retention models are usually compared by how well the model equation fits retention data for one solute taken over a range of mobile phase compositions. Even when retention data for multiple solutes are used, the quality of the fit is often judged by the statistical goodness-of-fit alone. This study compared four different RPLC retention models, encompassing three distinct mathematical forms. Each model was fit to the retention data of multiple solutes and the sets of best-fit parameters were examined in terms of the underlying physico-chemical assumptions of the models. Next, for the linear and quadratic models, some of the model parameters were calculated a priori and the rest of the model parameters were then obtained in subsequent fittings. The sets of best-fit parameters obtained in this manner were more consistent with the underlying assumptions of these models than were the sets of parameters obtained entirely through regressions to the experimental data. Thus, the extraction of parameters by fitting a model to the retention data of a single solute may result in unreliable values for those parameters, even in the case of a fit that would be considered good when judged by conventional statistical criteria. That is, although parameters extracted in such a fashion may be suitable for optimization or similar uses, they may not be suitable for determining the appropriateness of the underlying assumptions of retention models.     

Excess volume of mixing and equation of state theories

Equation-of state theories of Flory and of Sanchez and Lacombe describe both enthalpy and volume of mixing of binary systems using single component properties and only one binary parameter X₁₂. We have evaluated this parameter from literature enthalpy data for numerous mixtures of two aromatic hydrocarbons, of alkanes with aromatic compounds, and of alkanes with carbonyl compounds. We have used this X₁₂ for calculation of excess volumes and compared the results with our previously measured experimental data. The agreement was fair for mixtures of two nonpolar components. Nevertheless, mixtures containing either cyclohexane or benzene displayed anomalies that could be traced to special packing of molecules in these compounds when pure. For mixtures of carbonyl compounds with alkanes, the theories predicted the qualitative trends correctly, but the quantitative agreement was rather poor. These results tend to support a model in which the enthalpy(cohesive energy) is inversely proportional to volume (as in the theories considered) only for dispersive interaction. When polar-polar interactions are involved, the dependence of excess volume on the excess enthalpy is much weaker.     

Statistical evaluation of linear solvation energy relationship models used to characterize chemical selectivity in micellar electrokinetic chromatography

Characterization of retention and selectivity differences between surfactants in micellar electrokinetic chromatography (MEKC) using linear solvation energy relationships (LSERs) has been given a significant amount of attention in the last four years. This report evaluates the validity of using the two LSER models that have been used to fit retention in MEKC in the literature. The results and the fit of the revised model and parameters developed by Abraham and coworkers are compared to the original model developed by Kamlet, Taft, and coworkers. LSERs can generally only be used as a comparative tool to describe the selectivity differences between surfactant systems used in MEKC. With this in mind, it was determined that the results of both models essentially provide the same information about these differences. However, the revised model and parameters have been found to yield a statistically better fit of the MEKC retention data as well as providing more chemically sound LSER coefficients.     

A Branched Pore Model Analysis for the Adsorption of Acid Dyes on Activated Carbon

A new branched-pore adsorption model has been developed using an external mass transfer coefficient, K _f, an effective diffusivity, D _eff, a lumped micropore diffusion rate parameter, K _b, and the fraction of macropores, f, to describe sorption kinetic data from initial adsorbent-adsorbate contact to the long-term adsorption phase. This model has been applied to an environmental pollution problem—the removal of two dyes, Acid Blue 80 (AB80) and Acid Red 114 (AR114), by sorption on activated carbon. A computer program has been used to generate theoretical concentration-time curves and the four mass transfer kinetic parameters adjusted so that the model achieves a close fit to the experimental data. The best fit values of the parameters have been determined for different initial dye concentrations and carbon masses. Since the model is specifically applicable to fixed constant values of these four parameters, a further and key application of this project is to see if single constant values of these parameters can be used to describe all the experimental concentration-time decay curves for one dye-carbon system.The error analysis and best fit approach to modeling the decay curves for both dye systems show that the correlation between experimental and theoretical data is good for the fixed values of the four fitted parameters. A significantly better fit of the model predictions is obtained when K _f, K _b and f are maintained constant but D _eff is varied. This indicates that the surface diffusivity may vary as a function of surface coverage.     

Using GEMANOVA to explore the pattern generating properties of the Delta‐Notch model

In the area of systems biology, increasingly complex models are developed to approximate biological processes. The complexity makes it difficult to derive the properties of such models analytically. An alternative to analytical considerations is to use multivariate statistical methods to reveal essential properties of the models. In this paper it is shown how the properties of a relatively complex mathematical model for describing cell‐pattern development, the Delta‐Notch model, can be explored by means of statistical analyses of data generated from the model. ANOVA is a well‐known and one of the most commonly used methods for analyzing data from designed experiments, but it turns out that it is not always appropriate for finding and exploring higher‐order interactions. For this purpose a multiplicative alternative—GEMANOVA—was used in the present paper for studying the Delta‐Notch model, for which the properties depend on higher order interactions between the model parameters. It is shown here how a forward selection strategy combined with bootstrapping can be used to identify GEMANOVA models with reasonable fit to the data, and it is demonstrated how new insight about the Delta‐Notch model can be gained from interpreting the GEMANOVA output. Copyright © 2010 John Wiley & Sons, Ltd.     

Recent theories of gas sorption in polymers

Theories and models are presented for gas sorption in polymers above and below the glass transition temperature. With the exception of predictive theories that do not represent the data well, the models are fit to data for the carbon dioxide/silicone rubber and carbon dioxide/polycarbonate systems for the purposes of comparison. During the past decade, a number of new models and theories have been proposed specifically for gas sorption in glassy polymers. Each new model attempts to incorporate aspects of the gas sorption process that are unique to polymers below the glass transition temperature. This review discusses these recent advances, the assumptions used in their development and their advantages and disadvantages.     

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.     

Isopiestic determination of osmotic coefficients and evaluation of vapor pressures for solutions of calcium chloride and calcium nitrate in methanol at 298.15 K

The osmotic coefficients of calcium chloride and calcium nitrate in methanol have been measured by the isopiestic method at the temperature 298.15 K. Sodium iodide served as isopiestic standard for the calculation of osmotic coefficients. The Pitzer model and the self-consistent local composition (SCLC) model developed by Ananth and Ramachandran was used to fit each set of osmotic coefficients. The parameters from the fit were used to calculate the vapor pressures. The osmotic coefficient data are successfully correlated with these models, which provide reliable predictions of vapor pressures.     

Modeling the kinetics of step homopolymerization reactions--an assessment of different approaches

A critical analysis of two models used to describe the kinetics of step homopolymerization has been undertaken. The classical second-order kinetic model and the more widely adopted Mathew et al. oligomer precipitation model were tested against data published in the literature. The classical model, which predicts an identical molecular weight distribution to that obtained by Flory using a statistical approach, is based on a single rate constant and provided an excellent fit (R²>0.99) to the experimental data. Derived rate constants exhibited logical trends. The Mathew et al. oligomer precipitation model, on the other hand, requires three fitting parameters. This model also fitted the data well but in many cases yielded either negative rate constants for the purported termination step or illogical parametric trends. It was concluded that the classical model was superior to the precipitation model in describing the kinetics and reaction mechanisms of step homopolymerization.     

Investigate oxoazolidine-2,4-dione based eutectic mixture via DFT calculations and SAR

In this work, DFT calculations for the designed eutectic mixtures (EMs) using oxoazolidine 2,4-dione (OZD) and zinc chloride (ZnCl2) are done. The interaction between the hydrogen bond donor and hydrogen bond acceptor at atomic level to get EMs are studied using DFT calculations. At room temperature, the stability of these various systems have been investigated using thermodynamic values or parameters such as enthalpy, free energy and others. DFT calculations is used to investigate the possibility of forming the systems (EMs). Further, the impact of varying the temperature on each system was also investigated (323K, 348K). Various other thermodynamic parameters are studied like dipole moment, hardness, chemical potential of the systems (individual molecules and EMs) at different temperatures. The results of the calculations showed that O1Z4 and O4Z1 have maximum dipole moment having values 8.1291, 9.8801 respectively, indicating maximum polarizability. Change in free energy for O1Z4 is least and was found to be ?37.2496 kcal/ mol. Further on changing the temperature, the parameters do not show much variation. Additionally, we have analyzed structure activity relationship (SAR) method to understand the physico-chemical properties of designed EMs and predict their regression and correlation to optimized energy. From the calculated values of pOE model, the value of r² is 0.9995 confirms the validity of the equation obtained. The results of this study suggest a link between the structures that have been utilized to describe the intermolecular interaction between the hydrogen bond donor and acceptor, as well as the stability of the EMs.     

Estimation of first-order kinetic parameters by using the extended kalman filter

A model for first-order kinetics is derived for spectra obtained while a reaction is taking place. A technique for nonlinear-regression analysis known as the extended Kalman filter is used to estimate the initial concentrations of the reactants and the rate constant from the spectral data. The effects of the magnitude of the rate constant and the identity of the absorbing species are examined for synthetic spectra containing overlapped responses. The technique is used successfully to obtain the rate constant for the dissociation reaction of a praseodymium complex. The filter is also shown to be useful for the detection of erros in the kinetic model employed to fit the data. The extended Kalman filter can be used to fit kinetic models other than the one discussed here, and may prove to be a valuable technique for estimation of kinetic parameters.     

CF3CH3 --> HF + CF2CH2: a non-RRKM reaction?

The experimental shock tube data recently reported by Kiefer et al. [J. Phys. Chem. A 2004, 108, 2443-2450] for the title reaction at temperatures between 1600 and 2400 K have been compared to master equation simulations using three models: (a) standard RRKM theory, (b) RRKM theory modified by local random matrix theory, which introduces dynamical corrections arising from slow intramolecular vibrational energy randomization, and (c) an ad hoc empirical non-RRKM model. Only the third model provides a good fit of the Kiefer et al. unimolecular reaction rate data. In separate simulations, all three models accurately reproduce the experimental 300 K chemical activation data of Marcoux and Setser [J. Phys. Chem. 1978, 82, 97-108] when the energy transfer parameters are freely varied to fit the data. When experimental energy transfer parameters for a geometrical isomer (1,1,2-trifluoroethane) are used, the standard RRKM model fits the chemical activation data better than the other models, but if energy transfer in the 1,1,1-trifluoroethane is significantly reduced in comparison to the 1,1,2 isomer, then the empirical ad hoc non-RRKM model also gives a good fit. While the ad hoc empirical non-RRKM model can be made to fit the data, it is not based on theory, and we argue that it is physically unrealistic. We also show that the master equation simulations can mimic the Kiefer et al. vibrational relaxation data, which was the first shock tube observation of double-exponential relaxation. We conclude that, until more data on the trifluoroethanes become available, the current evidence is insufficient to decide with confidence whether non-RRKM effects are important in this reaction, or whether the Kiefer et al. data can be explained in some other way.     

Dynamics of mobile ions: fitting of CKN frequency response data without an excess wing

Ion dynamics effects and the resulting dispersed frequency response of conducting materials have often been explained in the past by a combination of the Moynihan original modulus formalism (OMF) and the Ngai coupling model (NCM). These incorrect approaches and their inappropriate conclusions are replaced by alternate, Kohlrausch-related physically reasonable conductive-system fitting and interpretation models that are then used for the analysis of both limited-range and wide-range data for the supercooled liquid 0.4Ca(NO3)2*0.6KNO3 (CKN). Detailed analysis of the limited-range 342 K data at the electric modulus immittance level shows that OMF fitting leads to an excess wing and that more appropriate models fit the data well without such a wing. Further, although such models allow estimation of the bulk dipolar dielectric constant of the material, as well as one associated only with mobile charges, they lead to implausibly small estimates of the important Kohlrausch K1 model shape parameter, beta1, and lead to an inadequate determination of its characteristic relaxation time. Therefore, wide-range CKN data sets extending to nearly 1012 Hz for the temperatures 342, 350, 356, and 361 K were very well-fitted with a more detailed composite model but one still involving K1 response. All model parameters were well-determined with no excess wings; beta1 estimates were all much closer to the universal value of 1/3; and the estimated model parameters led to a Boson peak beyond 1012 Hz, to very large thermal activation energies, and to evidence that the mobile charge concentration reached a saturation value at about 356 K. Such results do not support assumptions about variable ion-ion correlation, a mainstay of the OMF and NCM approaches. Finally, it is shown that although excess wings can sometimes be eliminated by using just an appropriate bulk fitting model and series blocking-electrode capacitor, as shown for the present narrow-range data, adequate fitting of the present wide-range data sets over their full spans of as much as 13 decades required the addition of an additional series dispersive-response model to the composite model. This addition seems likely to be required to take adequate account of the presence of more than one species of mobile charge in CKN.     

Optimized parameters for continuum solvation calculations with carbohydrates

Continuum solvent models have been shown to be an efficient method for the calculation of the energetics of biomolecules in solution. However, for these methods to produce accurate results, an appropriate set of atomic radii or volumes is needed. While these have been developed for proteins and nucleic acids, the same is not true of carbohydrates. Here, a set of optimized parameters for continuum solvation calculations of carbohydrates in conjunction with the Carbohydrate Solution Force Field are presented. Explicit solvent free-energy perturbation simulations were performed on a set of hexapyranose sugars and used to fit atomic radii for Poisson-Boltzmann and generalized-Born calculations, and to fit atomic volumes for use with the analytical continuum electrostatics model. The solvation energetics computed with the optimized radii and a Poisson-Boltzmann model show remarkable agreement with explicit solvent simulation, with a root-mean-square error of 1.19 kcal/mol over a large test set of sugars in many conformations. The generalized-Born model gives slightly poorer agreement, but still correlates very strongly, with an error of 1.69 kcal/mol. The analytical continuum electrostatics model correlates well with the explicit solvent results, but gives a larger error of 4.71 kcal/mol. The remarkable agreement between the solvation free energies computed in explicit and implicit solvent provides strong motivation for the use of implicit solvent models in the simulation of carbohydrate-containing systems.