Small Systems and Limitations on the Use of Chemical Thermodynamics

Limitations on using chemical thermodynamics to describe small systems are formulated. These limitations follow from statistical mechanics for equilibrium and nonequilibrium processes and reflect (1) differences between characteristic relaxation times in momentum, energy, and mass transfer in different aggregate states of investigated systems; (2) achievements of statistical mechanics that allow us to determine criteria for the size of smallest region in which thermodynamics can be applied and the scale of the emergence of a new phase, along with criteria for the conditions of violating a local equilibrium. Based on this analysis, the main thermodynamic results are clarified: the phase rule for distorted interfaces, the sense and area of applicability of Gibbs’s concept of passive forces, and the artificiality of Kelvin’s equation as a result of limitations on the thermodynamic approach to considering small bodies. The wrongness of introducing molecular parameters into thermodynamic derivations, and the activity coefficient for an activated complex into the expression for a reaction rate constant, is demonstrated.     

Molecular theory of irreversibility

A generalization of the Gibbs entropy postulate is proposed based on the Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy of equations as the nonequilibrium entropy for a system of N interacting particles. This entropy satisfies the basic principles of thermodynamics in the sense that it reaches its maximum at equilibrium and is coherent with the second law. By using a generalization of the Liouville equation describing the evolution of the distribution vector, it is demonstrated that the entropy production is a non-negative quantity. Moreover, following the procedure of nonequilibrium thermodynamics a transport matrix is introduced and a microscopic expression for this is derived. This framework allows one to perform the thermodynamic analysis of nonequilibrium steady states with smooth phase-space distribution functions which, as proven here, constitute the states of minimum entropy production when one considers small departures from stationarity.     

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.     

A differential fluctuation theorem

We derive a nonequilibrium thermodynamics identity (the "differential fluctuation theorem") that connects forward and reverse joint probabilities of nonequilibrium work and of arbitrary generalized coordinates corresponding to states of interest. This identity allows us to estimate the free energy difference between domains of these states. Our results follow from a general symmetry relation between averages over nonequilibrium forward and backward path functions derived by Crooks [Crooks, G. E. Phys. Rev. E 2000, 61, 2361-2366]. We show how several existing nonequilibrium thermodynamic identities can be obtained directly from the differential fluctuation theorem. We devise an approach for measuring conformational free energy differences, and we demonstrate its applicability to the analysis of molecular dynamics simulations by estimating the free energy difference between two conformers of the alanine dipeptide model system. We anticipate that these developments can be applied to the analysis of laboratory experiments.     

The line adsorption equation: the one-dimensional counterpart of the Gibbs adsorption equation

The thermodynamic development for multiphase contact lines is analogous to that for surfaces or interfaces. However, for one of the most important equations in surface thermodynamics, the Gibbs adsorption equation, the one-dimensional analogue is missing. This paper derives such an analogue, the line adsorption equation. Similarly to the Gibbs adsorption equation, the line adsorption equation is derived from Gibbsian thermodynamics. For a three-phase, three-component contact line system (e.g. an oil lens on the surface of an aqueous solution), the line concentrations (excesses) of two immiscible solvents can be made vanish by appropriately placing the dividing line. Consequently, the line concentration of the solute can be evaluated through the line tension change with the volume concentration of the solute. Such an evaluation provides information about molecular adsorption at the contact line, which is important in physical chemistry of lines, but difficult to obtain by any other means.     

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。     

Model hysteresis dimer molecule II: deductions from probability profile due to system coordinates

The hysteresis dimer reaction of the first sequel is applied to test the Gibbs density-in-phase hypothesis for a canonical distribution at equilibrium. The probability distribution of variously defined internal and external variables is probed using the algorithms described, in particular the novel probing of the energy states of a labeled particle where it is found that there is compliance with the Gibbs’ hypothesis for the stated equilibrium condition and where the probability data strongly suggests that an extended equipartition principle may be formulated for some specific molecular coordinates, whose equipartition temperature does not equal the mean system temperature and a conjecture concerning which coordinates may be suitable is provided. Evidence of violations to the mesoscopic nonequilibrium thermodynamics (MNET) assumptions used without clear qualifications for a canonical distribution for internal variables are described, and possible reasons outlined, where it is found that the free dimer and atom particle kinetic energy distributions agree fully with Maxwell–Boltzmann statistics but the distribution for the relative kinetic energy of bonded atoms does not. The principle of local equilibrium (PLE) commonly used in nonequilibrium theories to model irreversible systems is investigated through NEMD simulation at extreme conditions of bond formation and breakup at the reservoir ends in the presence of a temperature gradient, where for this study a simple and novel difference equation algorithm to test the divergence theorem for mass conservation is utilized, where mass is found to be conserved from the algorithm in the presence of flux currents, in contradiction to at least one aspect of PLE in the linear domain. It is concluded therefore that this principle can be a good approximation at best, corroborating previous purely theoretical results derived from the generalized Clausius Inequality, which proved that the PLE cannot be an exact principle for nonequilibrium systems.      

On the nonequilibrium thermodynamics of large departures from Butler-Volmer behavior

Large deviations from the behavior predicted by the Butler-Volmer equation of electrochemistry are accounted for using mesoscopic nonequilibrium thermodynamics. The nonequilibrium thermodynamic hypotheses are extended to include velocity space and cope with imperfect reactant transport leading to departures from Butler-Volmer behavior. This results in a modified Butler-Volmer equation in good agreement with experimental data. The distinct advantages of the method and its applicability to analyze other systems are briefly discussed.     

Calculating potentials of mean force from steered molecular dynamics simulations

Steered molecular dynamics (SMD) permits efficient investigations of molecular processes by focusing on selected degrees of freedom. We explain how one can, in the framework of SMD, employ Jarzynski's equality (also known as the nonequilibrium work relation) to calculate potentials of mean force (PMF). We outline the theory that serves this purpose and connects nonequilibrium processes (such as SMD simulations) with equilibrium properties (such as the PMF). We review the derivation of Jarzynski's equality, generalize it to isobaric--isothermal processes, and discuss its implications in relation to the second law of thermodynamics and computer simulations. In the relevant regime of steering by means of stiff springs, we demonstrate that the work on the system is Gaussian-distributed regardless of the speed of the process simulated. In this case, the cumulant expansion of Jarzynski's equality can be safely terminated at second order. We illustrate the PMF calculation method for an exemplary simulation and demonstrate the Gaussian nature of the resulting work distribution.     

丙烷甲醇制烯烃共反应的热力学和动力学分析

通过计算和实验研究相结合的方法研究丙烷甲醇共进料制烯烃反应热力学及动力学过程.热力学过程采用Gibbs最小自由能法模拟丙烷甲醇制烯烃反应体系的平衡组成,同时结合响应面分析法建立了温度、压力、丙烷甲醇进料摩尔比对产物中丙烯的摩尔分数的函数关系,通过回归方程分析最佳工艺范围.热力学分析了反应条件对平衡产物的影响,随着反应温度升高,平衡产物丙烯的质量分数先增高后降低;平衡产物中丙烯的质量分数随着丙烷甲醇进料中丙烷摩尔比增高而增高,但是实际的反应状态和催化剂也是相关的,因此研究了存在催化剂情况下,丙烷脱氢和丙烷甲醇共进料反应的活化能.反应活化能动力学实验表明,通过添加少量甲醇可以降低耦合过程中丙烷脱氢表观活化能.     

Some remarks to the derivation of the “generalized Lippmann equation”

In the present communication, an attempt is made to demonstrate (once again) some of the problems with the derivation of the “generalized Lippmann equation” considered to be valid by many researchers for solid electrodes and to address the problems in the framework of the Gibbs model of the interface by using only the basic principles of thermodynamics. By surveying the relevant literature, it has been shown that during the derivation of the equation, it was completely ignored that the Gibbs-Duhem equation (i.e., the electrocapillary equation) is a mathematical consequence which follows directly from the homogeneous degree one property of the corresponding thermodynamic potential function; consequently, the resulting expression cannot be correct. Some alternative approaches have also been considered. The adequacy of the open system and the partly closed system approach has been critically discussed, together with the possibility of introducing new thermodynamic potential functions.

     

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。