Application of Continuous Thermodynamics to The Stability of Polymer Systems. IV

Abstract

A method for establishing in the framework of continuous thermodynamics the stability criteria for multiple critical states of increasing order is presented. The method applies to a relatively general class of Gibbs free energy relations for polymer solutions: The function replacing the χ-term in the classic Flory-Huggins theory is permitted to depend on a finite number of moments of the polymer distribution so as to embrace most Gibbs free energy relations used in practice. In this way, determinant criteria for multiple critical states are formulated that are analogous in structure to those in traditional (discrete) thermodynamics. However, the dimension of the determinants is reduced from N (number of polymer species) to n (number of moments taken into account).     

关于等温循环方法推导开尔文公式的讨论

等温循环方法是物理化学教材中推导开尔文公式的一个经典方法。本文从热力学基本原理出发,明确指出其中小液滴可逆相变为气体的吉布斯自由能变化值应由吉布斯自由能判据求解,并对温度恒定、两相压强分别恒定时的判据进行了重新推导。同时,本文还提出了一种对推导开尔文公式的等温循环法的新理解方式,该方式在建立的"箱管模型"辅助下,意义明确,便于理解,更适宜教学使用。     

醋酸离子液体[C2mim][OAc]水溶液的摩尔表面Gibbs自由能

在288.15-318.15 K温度范围内测定了不同浓度离子液体1-乙基-3-甲基咪唑醋酸盐([C₂mim][OAc])水溶液的表面张力和密度;在改进李以圭等人的溶液表面张力模型基础上,提出摩尔表面Gibbs自由能新概念,建立了摩尔表面Gibbs自由能随溶液浓度变化的线性经验方程,利用这个经验方程估算了[C₂mim][OAc]水溶液的摩尔表面Gibbs自由能,并进一步预测了该溶液的表面张力,其预测值与相应的表面张力实验值高度相关并非常相似。由此可见,摩尔表面Gibbs自由能与等张比容极其类似,可能成为预测离子液体及其溶液性质的一种新的半经验方法。在指定溶液浓度下,根据溶液的摩尔表面Gibbs自由能随温度呈线性变化的规律,得到了新的Eötvös方程,与传统的Eötvös方程相比,新Eötvös方程的每一个参数都有明确的物理意义:斜率的负值是摩尔表面熵,截距是摩尔表面焓,在指定浓度的溶液中摩尔表面焓几乎不随温度变化。     

Degenerate Critical States for Polydisperse Polymer Solutions

If, in a spinodal point, the rank of the stability matrix is less than the order of this matrix minus one, then Gibbs′ determinant criterion for the critical state loses its importance since it is fulfilled automatically by the spinodal condition. In this paper a generalized critical state criterion is established for such degenerate cases in polydisperse polymer solutions.     

A new method of semigrand canonical ensemble to calculate first-order phase transitions for binary mixtures

First-order phase transitions of binary mixtures at the given pressure (P) and temperature (T) are studied by taking into account the composition fluctuations. Isothermal-isobaric semigrand canonical ensemble is adopted to find the relations among the total number of molecules, the composition fluctuations and Gibbs free energy density. By combining two identical subsystems of mixtures successively, the free energy density is transformed until being stable and its linear segments represent phase transitions. A new method is developed to calculate the phase equilibriums of binary mixtures. The method handles multiple types and number of phase equilibriums at single time and its solutions are physically justified. One example is shown for calculating the phase diagram of binary Lennard-Jones mixture. It demonstrates that the fluctuations of the total number of molecules in mixtures are fundamental behind phase transitions and the van der Waals loops in Gibbs free energy are reasonable.     

含醇溶液的热力学研究IV.超额Gibbs自由能

利用先前提出的含醇溶液形成的热力学模型，以及释放和充入组分间引力势能 的方法，建立了超额Bibbs自由能方程，它可以避开计及化学作用对超额Gibbs自由 能的贡献，使方程的推导大为简化。这个模型能够联立地用来关联各种含醇溶液， 包括含醇水溶液的超额焓、超额Gibbs自由能和超额熵。对17个有代表性的含醇溶 液关联结果表明，与实验值的一致性是很令人满意的。     

基于吉布斯弯曲界面相平衡判据的开尔文方程推导

对两种界面热力学处理方法(古根海姆法与吉布斯法)进行了介绍。采用吉布斯界面热力学方法建立了存在界面相时两相平衡的热力学判据,并以此为基础提出了一种新的开尔文方程推导方法。     

Gibbs free-energy estimates from direct path-sampling computations

We have implemented a path-sampling scheme enabling a direct estimation of Gibbs free energy. This scheme consists of a Monte Carlo sampling of constant-pressure Langevin paths, followed by an ensemble averaging carried out over the Markov chain of paths. In practice, we sample an umbrella path ensemble, which requires to rigorously define a statistical weight for the paths, equivalent of the Boltzmann weight. This statistical weight is a function of an effective work related to the path. The umbrella ensemble is chosen so that its work histogram overlaps with the histograms corresponding to the ensembles of forward and backward paths. We have finally investigated the relations between numerical efficiency and overlapping properties of the various work histograms. This analysis yields a built-in criterion for diagnosing the convergence during a single-run simulation.     

关于弯曲界面气液两相相平衡化学势相等热力学判据的讨论

Thermodynamic criterion of equal chemical potential for phase equilibrium between gas and liquid in curved interface has been introduced in many textbooks and papers. In this paper, the process of the derivation of the criterion is proved to be wrong with analysis. In order to solve the problem, a proof procedure for the thermodynamic criterion of equal chemical potential is provided based on the definition of chemical potential. At the same time, a new thermodynamic criterion of two-phase equilibrium in curved interface is established using Gibbs interface thermodynamics and a new method for derivation of Kelvin equation is put forward based on the thermodynamic criterion of two-phase equilibrium. The new criterion which is derived directly from the second law of thermodynamics has a specific thermodynamic significance and clear physical model.     

Invariance of free energy against a shift of the dividing surface of arbitrary geometry

This paper demonstrates that within the context of the generalized theory of capillarity, the free energy remains invariant against an arbitrary shift of the dividing surface for a general surface geometry. The Gibbs adsorption equation is used to illustrate the importance of being able to shift the dividing surface. The mathematical proof makes use of an equation describing the change of free energy for a shift of the dividing surface, derived in an independent development of a hydrostatic approach to capillarity.     

Systematic study of the tautomerism of uracil induced by proton transfer. Exploration of water stabilization and mutagenicity

To systematically investigate all the possible tautomerisms from uracil (U) and its enol form (U) induced by proton transfer, we describe a study of structural tautomer interconversion in the gas phase, in a continuum solvent, and in a microhydrated environment with 1 or 2 explicit water molecules, using density functional theory (DFT) calculations by means of the B3LYP exchange and correlation functions. A total of 62 geometries including 25 transition states were optimized, and the geometrical parameters have been discussed. Some rules of the configuration variation in tautomerization were summarized. The relative stabilities of all the tautomers were established. When a proton transfers from the di-keto form to the keto-enol form, water molecules in different regions show absolutely opposite effects: some assist, whereas others hinder the tautomerization. However, when a proton transfers from the keto-enol form to the di-enol form, water molecules in different regions show similar effects: the Gibbs free energy always increases and the activation energy always decreases. Additionally, some important factors that obviously affect the activation energy and Gibbs free energy were found and discussed in detail. The reasons that water molecules can assist or prevent the proton transfer were given. Furthermore, on the basis of our calculated results, we explain why it is hard to detect the di-enol form of uracil in general experiments.     

Melting temperature of Pb nanostructural materials from free energy calculation

The thermodynamic properties of lead, including the entropy, heat capacity, Gibbs free energy, and surface free energy have been studied. Based on bulk thermodynamic properties of lead, Gibbs free energy for nanostructural materials is obtained and used to calculate the size-dependent melting point depression for lead nanostructural materials. The studies indicate that the surface free energy difference between solid phase and liquid phase is a decisive factor for the size-dependent melting of nanostructural materials. The calculated results are in agreement with recent experimental values and the available molecular dynamics simulation data.     

Development of the theory of strong electrolytes considering the concentration dependence of hydration numbers

An expression for the Gibbs free energy is obtained that takes into account the contribution of interactions in the hydrate shells of ions and is compared with experimental data on the concentration dependence of hydration numbers. The activity coefficient derived from this expression is consistent with experiment up to the concentrations corresponding to the total solvation boundary (TSB). The relations describing the thermodynamics of solutions in the region of concentrations exceeding TSB are proposed. The analysis of the obtained expressions confirms their adequacy to experiments.     

Thermodynamic properties and equilibrium constant of chemical reaction in nanosystem: An theoretical and experimental study

The theoretical relations of thermodynamic properties, the equilibrium constant and reactant size in nanosystem are described. The effects of size on thermodynamic properties and the equilibrium constant were studied using nanosize zinc oxide and sodium bisulfate solution as a reaction system. The experimental results indicated that the molar Gibbs free energy, the molar enthalpy and the molar entropy of the reaction decrease, but the equilibrium constant increases with decreasing reactant size. Linear trends were observed between the reciprocal of size for nano-reactant and thermodynamic variable, which are consistent with the theoretical relations.     

Optimal diabatic bases via thermodynamic bounds

Describing kinetic processes within a perturbation theory approach such as Fermi's golden rule requires an understanding of the initial and final states of the system. A number of different methods have been proposed for obtaining these diabatic-like states, but a robust criterion for evaluating their accuracy has not been established. Here, we approach the problem of determining the most appropriate set of diabatic states for use in incoherent rate expressions. We develop a method that rotates an initial set of diabats into an optimized set beginning with a zeroth-order diabatic Hamiltonian and choosing the rotation that minimizes the effect of non-diabatic terms on the thermodynamic free energy. The Gibbs-Bogoliubov (GB) bound on the Helmholtz free energy is thus used as the diabatic criterion. We first derive the GB free energy for a two site system and then find an expression general for any electronic system Hamiltonian. Efficient numerical methods are used to perform the minimization subject to orthogonality constraints, and we examine the resulting diabats for system Hamiltonians in various parameter regimes. The transition from localized to delocalized states is clearly seen in these calculations, and some interesting features are discussed.     

Dependence of Thermal Decomposition Rate Constant on Temperature of Reaction

On the basis of results of kinetic investigates of many compounds general temperature dependence of Gibbs free energy of activated complexes created in thermal decomposition processes and the reaction rate constant were calculated. This revised version was published online in July 2006 with corrections to the Cover Date.     

反相高效液相色谱中溶质保留过程的热力学研究Ⅰ: 柱相比, 吉氏自由能变及其分量, 吸附和解吸附自由能变

从热力学观点给反相高效液相色谱(RP-HPLC)中的相比以新的定义, 提出了测定该相比的方法并准确测定了RP-HPLC中溶质计量置换过程中的吉氏自由能变△G~(Pα)。发现在RP-HPLC中相比对保留过程中溶质总自由能变的贡献值几乎可与溶质本身的保留值相当。依据液相色谱中溶质计量置换保留模型。将溶质的△G~(Pα)分成与溶质吸附及解吸有关的两项独立的自由能变分量。△G~(Ⅰ,α)和△G~(Z,D)。对不同流动相组成条件下的△G~(Pα)和△G~(Z,D)进行了估算, 并与实验结果进行了比较, 偏差一般小于±2%。     

不同标态下标准电极电势间关系的热力学解释

利用标准吉布斯自由能变化ΔrGm与标准电极电势和标准反应平衡常数间的联系,分析不同标态下电极标准电极电势间的关系。根据这一思想,以水解离平衡为例,讨论了设计原电池求化学反应平衡常数的一般方法。     

STUDY OF GRAFT SITES IN EPOXY GRAFT COPOLYMERS BY QUANTUM CHEMISTRY CALCULATIONS

Exploration and characterization of grafting productions by experimental methods are often cumbersome or sometimes impossible. Therefore, quantum chemistry calculations were performed to characterize the graft sites of epoxy resin. According to the Gibbs free energy criterion of the second law of thermodynamic, the reported graft sites were confirmed, and more important, some unreported graft sites were found. In addition, method of increasing the number of graft sites was studied in this article.     

Solvophobic effects: Qualitative determination and quantitative description

Solvophobic effects strongly influence the thermodynamic properties of solutions and are one of the driving forces of self-assembly processes of supramolecular structures. However, the generally accepted definition and a quantitative measure of these effects have so far been absent. Based on the analysis of a large set of experimental data on the thermodynamic functions of solvation in various systems, we propose a qualitative criterion allowing us to judge about whether the solvophobic effects are manifested in the solution or not, and also a method to determine their contributions to the thermodynamic functions of solvation. A feature of the solvophobic effect is a violation of the linear relationship between the Gibbs free energy and the enthalpy of solvation, which is fulfilled for the solutions of different compounds in many non-associated solvents. It is shown that in self-associated solvents the solvophobic effect is observed for any dissolved compounds, including well soluble ones, resulting in an increase in the Gibbs energy of solvation. Previously proposed solvophobicity parameters are considered and compared with our results.