Thermodynamics for single-molecule stretching experiments

We show how to construct nonequilibrium thermodynamics for systems too small to be considered thermodynamically in a traditional sense. Through the use of a nonequilibrium ensemble of many replicas of the system which can be viewed as a large thermodynamic system, we discuss the validity of nonequilibrium thermodynamics relations and analyze the nature of dissipation in small systems through the entropy production rate. We show in particular that the Gibbs equation, when formulated in terms of average values of the extensive quantities, is still valid, whereas the Gibbs-Duhem equation differs from the equation obtained for large systems due to the lack of the thermodynamic limit. Single-molecule stretching experiments are interpreted under the prism of this theory. The potentials of mean force and mean position, now introduced in these experiments in substitution of the thermodynamic potentials, correspond respectively to our Helmholtz and Gibbs energies. These results show that a thermodynamic formalism can indeed be applied at the single-molecule level.     

Modelling the Vapor–Liquid Equilibrium of Polymer Solutions Using a Cubic Equation of State

This work presents the vapor–liquid equilibrium calculations in an isothermal flash, applied to polymer solutions, using the Peng–Robinson cubic equation of state modified by Stryjek–Vera, and the mixing rule introduced by Wong–Sandler. This rule allows combining the rigid lattice thermodynamic model of Flory–Huggins to the Peng–Robinson–Stryjek–Vera equation of state. As the Gibbs free energy must be minimum in the equilibrium state, a stochastic optimization method, the simulated annealing algorithm, was used to find out the extreme of this thermodynamic potential.     

Ionic strength dependence of heavy metal tartrate complex stabilities

Summary Ion chromatography and potentiometry were used for the determination of the stability constants Pb, Zn, Co, Ni, Mn tartrate complexes at different ionic strengths. An extrapolation function based on the Debye-Hückel equation was applied to obtain the thermodynamic stability constants.     

Thermodynamic consistency of high pressure ternary mixtures containing a compressed gas and solid solutes of different complexity

A thermodynamic consistency test applicable to high pressure binary gas–solid mixtures is extended to ternary mixtures containing a compressed gas and two solid solutes. A high pressure mixture containing carbon dioxide as solvent and two chemically similar solutes (2,3 dimethylnaphthalene and 2,6 dimethylnaphthalene) and a high pressure mixture containing carbon dioxide as solvent and two chemically different solutes (capsaicin and β-carotene), are considered in the study. Several sets of isothermal solubility data for binary and ternary mixtures are considered in the study. The Peng–Robinson equation of state with the mixing rules of Wong and Sandler have been employed for modeling the solubility of the solid in the case of binary mixtures, while the classical van der Waals mixing rules were used for modeling the ternary mixtures containing two solid solutes. Then the proposed thermodynamic consistency test has been applied. The results show that the thermodynamic test for ternary mixtures can be applied with confidence determining consistency or inconsistency of the experimental data used.     

Relative Boltzmann entropy, evolution equations for fluctuations of thermodynamic intensive variables, and a statistical mechanical representation of the zeroth law of thermodynamics

Generalized thermodynamics or extended irreversible thermodynamics presumes the existence of thermodynamic intensive variables (e.g., temperature, pressure, chemical potentials, generalized potentials) even if the system is removed from equilibrium. It is necessary to properly understand the nature of such intensive variables and, in particular, of their fluctuations, that is, their deviations from those defined in the extended irreversible thermodynamic sense. The meaning of temperature is examined by means of a kinetic theory of macroscopic irreversible processes to assess the validity of the generalized (or extended) thermodynamic method applied to nonequilibrium phenomena. The Boltzmann equation is used for the purpose. Since the relative Boltzmann entropy has been known to be intimately related to the evolution of the aforementioned fluctuations in the intensive thermodynamic variables, we derive the evolution equations for such fluctuations of intensive variables to lay the foundation for investigating the physical implications and evolution of the relative Boltzmann entropy, so that the range of validity of the thermodynamic theory of irreversible processes can be elucidated. Within the framework of this work, we examine a special case of the evolution equations for the aforementioned fluctuations of intensive variables, which also facilitate investigation of the molecular theory meaning of the zeroth law of thermodynamics. We derive an evolution equation describing the relaxation of temperature fluctuations from its local value and present a formula for the temperature relaxation time.     

Vapor-liquid equilibrium of hexadecapolar fluids from a perturbation-based equation of state

In this work a numerically tractable expression for the interaction potential between two point hexadecapoles with octahedral symmetry and a molecular-based equation of state derived by perturbation theory for hexadecapolar fluids are presented. The polar system is modeled by square-well particles with a point hexadecapole with octahedral symmetry at their centers. This equation of state is analytical in the state variables and in the potential parameters and allows us to study the effects of the hexadecapolar moment strength on the thermodynamic properties and liquid-vapor phase diagram. The equation presented here is applied to the thermodynamics of sulfur hexafluoride and gives very good predictions for the saturation pressures and the vapor-liquid phase diagram.     

New viscosity method for estimating unperturbed chain dimensions of macromolecules when draining effect and/or non-gaussian nature in the unperturbed state are not negligible

An attempt has been made to establish a new method for estimating the unperturbed chain dimensions of macromolecules when the partially free draining effect and/or the non-gaussian nature in the unperturbed state are not negligible, using the Mark-Houwink-Sakurada (MHS) equation. For this purpose, a previous treatment was generalized and an equation was derived. This method was applied to cellulose and amylose derivatives; the results agreed well with those estimated by thermodynamic and other hydrodynamic approaches.     

Crossover Peng-Robinson equation of state with introduction of a new expression for the crossover function

In this research, we use the original Peng-Robinson (PR) equation of state (EOS) for pure fluids and develop a crossover cubic equation of state which incorporates the scaling laws asymptotically close to the critical point and it is transformed into the original cubic equation of state far away from the critical point. The modified EOS is transformed to ideal gas EOS in the limit of zero density. A new formulation for the crossover function is introduced in this work. The new crossover function ensures more accurate change from the singular behavior of fluids inside the regular classical behavior outside the critical region. The crossover PR (CPR) EOS is applied to describe thermodynamic properties of pure fluids (normal alkanes from methane to n-hexane, carbon dioxide, hydrogen sulfide and R125). It is shown that over wide ranges of state, the CPR EOS yields the thermodynamic properties of fluids with much more accuracy than the original PR EOS. The CPR EOS is then used for mixtures by introducing mixing rules for the pure component parameters. Higher accuracy is observed in comparison with the classical PR EOS in the mixture critical region.     

Thermodynamic Properties of Liquid Alkali Metals

Abstract

Modified form of the pressure equation appropriate to liquid alkali metals is applied to the calculations of the thermal pressure coefficient and the thermal expansion coefficient. Comparison is made with the hard sphere reference system to understand the role of softness in the pair potential on the thermodynamic properties of alkali metals.     

Viscosity,refractive index,and surface tension of multicomponent systems: Mathematical representation and estimation from data for binary systems

An equation previously developed for estimation of the excess thermodynamic properties of multicomponent systems from binary mixing data has been applied to other physical properties through extrathermodynamic properties such as the excess Gibbs free energy of activation for viscous flow, molar refractivity, and exess surface free energy. This equation provides reasonably accurate predictions for viscosity, refractive index and surface tension of ternary and quaternary systems, given the properties of the various binary combinations of the components. The equation also serves quite well as a point-of-departure for mathematical representation of experimental data, in that all of the data considered could be represented within experimental uncertainty with the aid of no more than one adjustable parameter for each multicomponent system.     

由成核率数据拟合饱和蒸汽压力

Saturated vapor pressure was calculated from the nucleation experimental data using the thermodynamically consistent nucleation theory in which the effect of real gas is considered. The cubic polynomial fit equations of saturation pressure for several substances were obtained based on the calculation. The results of the calculations were compared to those of thermodynamic equilibrium equation and the empirical equation and applied to the predictions of the classical nucleation theory. The results show that the saturation pressures estimated from the nucleation data agree fairly well with those of empirical equations for the substances investigated, and this indicates that the predictions from the classical nucleation theory are close to the experimental data.     

Revision of a multiparameter equation of state to improve the representation in the critical region: application to water

We have developed a crossover formalism for the thermodynamic surface of pure fluids, which can be applied to any multiparameter equation of state. This procedure has been used to incorporate scaling law behavior into a representation of the thermodynamic properties of water and steam developed by Pruss and Wagner (PW EOS) and adopted recently by the International Association for the Properties of Water and Steam. Our revision to this equation retains most of the functional form and coefficients of the PW EOS, but replaces two of the terms with a crossover representation of scaling law behavior. In order to develop this model, we first developed a new crossover formulation for steam in the critical region, and second, we have incorporated universal crossover functions into the original PW EOS. In the modified form, the PW equation of state reproduces the scaling laws down to dimensionless temperatures τ=10⁻⁷. Far from the critical point the equations practically coincide.     

Thermodynamic Consistency Test of Vapor–liquid Equilibrium Data of Binary Systems Including Carbon Dioxide (CO 2 ) and Ionic Liquids Using the Generic Redlich–Kwong Equation of State

The thermodynamic consistency test of solubility P–T–x data for binary mixtures including carbon dioxide (CO2) + a room temperature ionic liquid has been investigated. Experimental solubility data taken from the open literature for 32 binary mixtures of CO2/RTILs contains 80 isotherms. The applied consistency test is based on the fundamental Gibbs–Duhem equation with use of the generic Redlich–Kwong (GRK) equation of state (EoS) coupled with the van der Waals–Berthelot (GRK/vdWB) mixing rule. The optimum parameters were obtained by minimizing the summation of per cent relative deviations between modeled and experimental data, based on the bubble pressure algorithm. Modeling was found acceptable for all isotherms, which demonstrated the usability of the GRK equation of state. Results of the thermodynamic consistency test showed that 36 of the isothermal data sets were thermodynamically consistent, 37 were not fully consistent, 6 were thermodynamically inconsistent and only one data set was found to need another model.     

Kinetics and thermodynamics of the adsorption of some dyestuffs and p-nitrophenol by chitosan and MCM-chitosan from aqueous solution

The effect of initial concentration, temperature, and shaking rate on the adsorption of three dyestuffs [orange II (O-II), crystal violet (CV), and reactive blue 5 (RB5)] and an ideal adsorbate, p-nitrophenol (PNP), by chitosan (Sigma C-3646) and the effect of temperature on the adsorption of O-II and CV by monocarboxymethylated chitosan (MCM-chitosan) were investigated. Kinetic data obtained for the adsorption of each dyestuff and PNP by chitosan and of O-II and CV by MCM-chitosan at different temperatures were applied to the Lagergren equation, and adsorption rate constants (k(ads)) at these temperatures were determined. These rate constants related to the adsorption of O-II and RB5 by chitosan and of O-II by MCM-chitosan were applied to the Arrhenius equation, and activation energies (E(a)) were determined. In addition, the isotherms for adsorption, at different temperatures, of each dyestuff and PNP by chitosan and of O-II and CV by MCM-chitosan were also determined. These isothermal data were applied to linear forms of isotherm equations that they fit, and isotherm constants were calculated. Because the isotherm curves obtained for the adsorption of O-II and CV by chitosan and of CV by MCM-chitosan fit the Langmuir adsorption isotherm, b constants were applied to thermodynamic equations, and thermodynamic parameters (delta G, delta H, and delta S) were calculated. Lastly, chitosan and MCM-chitosan were compared with respect to the ability to take up the dyestuffs and PNP.     

粘土矿物对低浓度镧、钕的吸附性研究

采用振荡平衡法,对高岭土、膨润土、凹凸棒石等3种不同类型的粘土矿物进行低浓度稀土元素镧、钕的吸附试验;通过ICP测定培养溶液的平衡浓度和吸附量,绘制各自的等温吸附曲线并拟合吸附热力学方程.得出 Langmuir方程能较好地描述低浓度条件下3种粘土矿物对稀土元素(La,Nd)的等温吸附过程;发现3种粘土矿物对稀土元素(La,Nd)的吸附性能大小排序为:膨润土＞凹凸棒石＞高岭土,吸附性能表现的差异性主要由粘土矿物自身的晶层结构决定.     

Multi-element Saha–Boltzmann and Boltzmann plots in laser-induced plasmas

A multi-element Saha–Boltzmann plot method is proposed for the determination of the temperature and the relative number density in laser-induced plasmas, assuming local thermodynamic equilibrium and stoichiometry conservation. The method has been applied to the characterization of a plasma generated with a Cu–Fe–Ni–Mn alloy, using a Nd:YAG laser in air at atmospheric pressure. Spectra of the local emissivity have been obtained by spatial deconvolution of the intensity spectra, obtained with spatial resolution. Saha–Boltzmann plots obtained from the emissivities of 58 spectral lines of Fe I, Fe II, Ni I, Ni II, Mn I and Mn II have been fitted to linear behavior with high correlation, which shows the validity of the equation proposed. Radial distributions of the temperature and number densities of neutral atoms and ions have been determined. The results obtained reinforce the initial considerations of local thermodynamic equilibrium and conservation of stoichiometry. The proposed equation can also be applied to only one ionization species (multi-element Boltzmann plot). Spatially-integrated measurements of the plasma emission have also been performed to show that, in this case, the application of the method to the line intensities provides the two different apparent temperatures for neutral atoms and ions.     

利用两种模型预测多孔介质中气体水合物平衡分解条件

分别利用两种热力学方法(基于逸度相等的方法与基于活度相等的方法)预测了不同多孔介质中气体水合物的平衡分解条件, 对于非水合物相, 逸度方法采用Trebble-Bishnoi (TB)方程, 而活度方法则使用Soave-Redlich-Kwong (SRK)方程, 对于水合物相, 两种方法都利用了van der Waals-Platteeuw模型结合Llamedo等关于毛细管力作用模型来模拟. 两种方法的预测结果与实验结果吻合, 逸度方法的预测效果要好于活度方法.     

The reduced equation of state and related properties of molten high polymers

The significant-structure theory of liquids has been applied to molten amorphous polymers. Expressions of reduced states for these systems are derived for the equation of state and thermodynamic properties such as expansion coefficient, compressibility, internal pressure, and cohesive energy density, and the surface tension. The calculated values are in good agreement with experimental results in comparison with those from other models. In particular, our model predicts the corresponding dependence of the internal pressure better than other models.     

A new equation for correlation of vapour-liquid equilibrium data of strongly non-ideal mixtures

A new equation for correlation of the thermodynamic excess functions of mixing, based on considerations of geometrical shape is proposed. Use of this equation for the correlation of heat of mixing data and vapour-liquid equilibrium data is proposed. The possibility of predicting multicomponent vapour-liquid equilibrium from binary data by using the proposed equation is shown. The equation is especially useful for correlating the excess functions of strongly non-ideal systems and for checking thermodynamic consistency of vapour-liquid equilibrium data.