Solvation thermodynamics: theory and applications

Potential distribution and coupling parameter theories are combined to interrelate previous solvation thermodynamic results and derive several new expressions for the solvent reorganization energy at both constant volume and constant pressure. We further demonstrate that the usual decomposition of the chemical potential into noncompensating energetic and entropic contributions may be extended to obtain a Gaussian fluctuation approximation for the chemical potential plus an exact cumulant expansion for the remainder. These exact expressions are further related to approximate first-order thermodynamic perturbation theory predictions and used to obtain a coupling-parameter integral expression for the sum of all higher-order terms in the perturbation series. The results are compared with the experimental global solvation thermodynamic functions for xenon dissolved in n-hexane and water (under ambient conditions). These comparisons imply that the constant-volume solvent reorganization energy has a magnitude of at most approximately kT in both experimental solutions. The results are used to extract numerical values of the solute-solvent mean interaction energy and associated fluctuation entropy directly from experimental solvation thermodynamic measurements.     

Studies of the thermal degradation of acetaminophen using a conventional HPLC approach and electrospray ionization-mass spectrometry

The thermal degradation of acetaminophen is studied via conventional accelerated aging studies by initially thermally stressing the compound at temperatures between 160 degrees C and 190 degrees C and measuring the rate of decomposition by reversed-phase high-performance liquid chromatography. Rates of decomposition of the compound in the dry state and the activation energy for the process are determined and compared with previously published kinetic and thermodynamic data for the degradation of acetaminophen in solution. In addition, the thermal fragmentation of acetaminophen under electrospray ionization (ESI) conditions using an interface with a heated capillary inlet is studied and the apparent activation energy for this process also is characterized. A comparison of the data shows that acetaminophen is significantly more stable in the dry state than in solution. However, the gas-phase fragmentation of acetaminophen under ESI conditions occurs more readily than either dry- or solution-state degradation. Although the resulting electrospray fragmentation mimics the breakdown product that is formed when the compound undergoes either acid or base catalyzed hydrolysis in aqueous solutions, the mechanism that produces the fragment ion appears to involve a two-step process. Initially, the parent ion forms of the analyte are produced in the spray region of the interface followed by wall-catalyzed decomposition and re-ionization in the heated inlet capillary of the spectrometer.     

一种研究Aa型缩聚反应体系的新方法

应用统计力学基本原理, 从两种不同角度构造了Aa型缩聚反应的正则配分函数, 得到了体系的平衡自由能以及质量作用定律的解析表达式, 提出了获得数量分布函数的两种新方法. 进一步基于数量分布函数的不变性, 给出临界点后溶胶相和凝胶相的平衡自由能, 证明溶胶-凝胶相变是一类几何相变, 而非热力学相变.     

甲醇POSR制氢的反应网络热力学分析和有效因子的估算

在Cu/ZnO/Al2O3催化剂上对甲醇部分氧化蒸汽重整制备氢气反应的动力学过程进行了研究。在常压和473 K～1 073 K温度范围内对该反应网络中的甲醇部分氧化、甲醇蒸汽重整、甲醇分解和水煤气反应的化学平衡进行了分析。在对这些反应的催化剂Cu/ZnO/Al2O3动力学研究的基础上，根据有效因子的基本概念，考虑催化剂颗粒内的扩散限制，对每个反应沿反应器床层的有效因子进行了估算。     

Statistical mechanics of time independent nondissipative nonequilibrium states

We examine the question of whether the formal expressions of equilibrium statistical mechanics can be applied to time independent nondissipative systems that are not in true thermodynamic equilibrium and are nonergodic. By assuming that the phase space may be divided into time independent, locally ergodic domains, we argue that within such domains the relative probabilities of microstates are given by the standard Boltzmann weights. In contrast to previous energy landscape treatments that have been developed specifically for the glass transition, we do not impose an a priori knowledge of the interdomain population distribution. Assuming that these domains are robust with respect to small changes in thermodynamic state variables we derive a variety of fluctuation formulas for these systems. We verify our theoretical results using molecular dynamics simulations on a model glass forming system. Nonequilibrium transient fluctuation relations are derived for the fluctuations resulting from a sudden finite change to the system's temperature or pressure and these are shown to be consistent with the simulation results. The necessary and sufficient conditions for these relations to be valid are that the domains are internally populated by Boltzmann statistics and that the domains are robust. The transient fluctuation relations thus provide an independent quantitative justification for the assumptions used in our statistical mechanical treatment of these systems.     

Enthalpies of formation and decomposition of nickel hydride and nickel deuteride derived from (p,c,T) relationships

Measurements of equilibrium hydrogen pressure as a function of hydrogen content and of temperature are a convenient way to determine the thermodynamic properties of metal–hydrogen systems. To date such studies have only been carried out for the systems at relatively low hydrogen pressure. We have developed a high-pressure apparatus capable of pressures up to 1.2 GPa and temperatures up to T =  450 K for the studies of equilibrium conditions in the Ni–H systems and the Ni–D systems in order to derive corresponding enthalpies of formation and decomposition. The results show that although the pressures at given temperatures are always higher for (Ni  +  D₂) than for (Ni  +  H₂), the values of enthalpies are almost identical within the experimental error. The enthalpies of the formation and decomposition of both systems derived from these studies are compared with calorimetric measurements carried out at high pressure. The difference between enthalpies of formation and decomposition for both systems reflect hysteresis, a common phenomenon in transition metal hydrides.     

Simulation of thermobaric conditions of the formation,composition, and structure of mixed hydrates containing xenon and nitrous oxide

Structural, dynamic, and thermodynamic features of double hydrates of xenon and nitrous oxide are calculated. Thermodynamic stability regions of these hydrates are found. At the atmospheric pressure the xenon hydrate is in the equilibrium with the gas phase at temperatures up to 263 K, whereas at these pressures the nitrous oxide hydrate decomposes already at 218 K. A strong dependence of the equilibrium temperatures and pressures of the formation/decomposition of double nitrous oxide and xenon hydrates on the composition of their mixture in the gas phase is shown.     

Extrathermodynamic Study of Retention Equilibrium in RP-LC Using a C18-Silica Monolithic Stationary Phase

This study is concerned with the explanation of some thermodynamic properties of the retention equilibrium on a C₁₈-silica monolithic column. Pulse response experiments were carried out in a reversed-phase liquid chromatography system using a methanol/water mixture (70/30, v/v) and n-alkylbenzene homologs as the mobile phase and sample compounds, respectively, in the temperature range between 278 and 318 K. The retention equilibrium constant (K _a) was calculated from the first absolute moment of elution peaks. The dependence of K _a on the column temperature was analyzed using the modified van??t Hoff plot proposed by Krug et al. to derive the changes of the Gibbs free energy, the enthalpy and the entropy concerning the retention behavior. First, the presence of a real enthalpy?Centropy compensation (EEC) for the retention equilibrium was demonstrated. Then, a thermodynamic model based on the real EEC was developed to explain the temperature dependence of the linear free energy relationship (LFER) of the retention equilibrium. The model indicates how the slope and intercept of the LFER are correlated with the compensation temperatures and several molecular thermodynamic parameters. The model was effective for explaining the thermodynamic properties of the retention equilibrium of the C₁₈-silica monolithic stationary phase.     

Representability problems for coarse-grained water potentials

The use of an effective intermolecular potential often involves a compromise between more accurate, complex functional forms and more tractable simple representations. To study this choice in detail, we systematically derive coarse-grained isotropic pair potentials that accurately reproduce the oxygen-oxygen radial distribution function of the TIP4P-Ew water model at state points over density ranges from 0.88 to 1.30 g/cm3 and temperature ranges from 235 to 310 K. Although by construction these effective potentials correctly represent the isothermal compressibility of TIP4P-Ew water, they do not accurately resolve other thermodynamic properties such as the virial pressure, the internal energy, or thermodynamic anomalies. Because at a given state point the pair potential that reproduces the pair structure is unique, we have therefore explicitly demonstrated that it is impossible to simultaneously represent the pair structure and several key equilibrium thermodynamic properties of water with state-point dependent radially symmetric pair potentials. We argue that such representability problems are related to, but different from, more widely acknowledged transferability problems and discuss in detail the implications this has for the modeling of water and other liquids by coarse-grained potentials. Nevertheless, regardless of thermodynamic inconsistencies, the state-point dependent effective potentials for water do generate structural and dynamical anomalies.     

Thermodynamic derivations of conditions for chemical equilibrium and of Onsager reciprocal relations for chemical reactors

For an isolated chemical reactor, we derive the conditions for chemical equilibrium in terms of either energy, volume, and amounts of constituents or temperature, pressure, and composition, with special emphasis on what is meant by temperature and chemical potentials as the system proceeds through nonequilibrium states towards stable chemical equilibrium. For nonequilibrium states, we give both analytical expressions and pictorial representations of the assumptions and implications underlying chemical dynamics models. In the vicinity of the chemical equilibrium state, we express the affinities of the chemical reactions, the reaction rates, and the rate of entropy generation as functions of the reaction coordinates and derive Onsager reciprocal relations without recourse to statistical fluctuations, time reversal, and the principle of microscopic reversibility.     

Thermodynamic characterization of weak association equilibria accompanied with spectral overlapping by a SVD-based chemometric method

A singular value decomposition (SVD)-based chemometric method is used for deconvolution of spectral information obtained from a single sample containing an equilibrium system with spectral overlapping at different temperatures. The output of analysis is the association constants at each temperature, thermodynamic parameters and the component spectral profiles. Thermodynamic characterization of charge-transfer complex formation between chloranil and some aromatic hydrocarbons are used as a model system for weak association equilibria and strong component spectral overlapping. The approach can be successfully applied for studying equilibrium systems, which cannot be treated with classical methods like Benesi-Hildebrand method due to the presence of systematic errors.     

Metastable extension of the liquid-vapor phase equilibrium curve and surface tension

The method of molecular dynamics has been used to calculate the parameters of liquid-vapor phase equilibrium and the surface tension in a two-phase system of 4096 Lennard-Jones particles. Calculations have been made in a range from the triple point to near-critical temperature and also at temperatures below the triple point corresponding to the metastable equilibrium of a supercooled liquid and supersaturated vapor. To determine the surface tension, along with a mechanical approach a thermodynamic one has been used as well. The latter was based on calculation of the excess internal energy of an interfacial layer. It has been shown that in accuracy the thermodynamic approach is as good as the more sophisticated mechanical one. Low-temperature asymptotics of the phase-equilibrium curve and also of liquid and vapor spinodals have been considered in the Lennard-Jones and the van der Waals models. The behavior of the surface tension and the excess internal energy of an interfacial layer at T-->0 is discussed.     

Molecular cluster decay viewed as escape from a potential of mean force

We show that evaporation from a quasistable molecular cluster may be treated as a kinetic problem involving the stochastically driven escape of a molecule from a potential of mean force. We derive expressions for the decay rate, and a relationship between the depth of the potential and the change in system free energy upon loss of a molecule from the cluster. This establishes a connection between kinetic and thermodynamic treatments of evaporation, but also reveals differences in the prefactor in the rate expression. We perform constant energy molecular dynamics simulations of cluster dynamics to calculate potentials of mean force, friction coefficients and effective temperatures for use in the kinetic analysis, and to compare the results with the directly observed escape rates. We also use the simulations to estimate the escape rates by a probabilistic analysis. It is much more efficient to calculate the decay rate by the methods we have developed than it is to monitor escape directly, making these approaches potentially useful for the assessment of molecular cluster stability.     

Thermal decomposition temperatures of metal sulfates

The thermal decomposition of sixteen metal sulfates was studied by thermogravimetry at heating rates of 2 and 5°C min^?1 in flowing air and high-purity nitrogen. Their decomposition behaviors, especially the initial decomposition temperatures, were examined with relation to the thermodynamic functions for decomposition. Of the factors possibly influencing the decomposition temperature, the equilibrium SO₃ pressures over the sulfates were evaluated: the equilibrium pressures at the initial temperatures for sulfates of metals, of which the oxidation state was unchanged during decomposition, were nearly equal to 1×10^?4 atm at 2°C min^?1 in flowing nitrogen.     

Experimental determination of the NH4NO3/(NH4)2SO4/H2O phase diagram

We have studied the thermodynamic properties of the ammonium nitrate/ammonium sulfate/water system using differential scanning calorimetry and infrared spectroscopy of thin films at low temperatures. This is the first study focused on low temperatures, as previous experimental work on this system has been at 273 K and above. We have combined our experimental results with melting point data from the literature at high temperatures to create a solid/liquid phase diagram of the ammonium nitrate/ammonium sulfate/water system for temperatures below 343 K. Using phase diagram theory and Alkemade lines, we predict which solids are stable at equilibrium for all concentrations within the studied region. We also observed the decomposition of a solid at low temperatures which has not previously been reported. Finally, we have compared our predicted solids and final melting temperatures to the Aerosol Inorganics Model (AIM).     

On the fluctuation theorem for the dissipation function and its connection with response theory

Recently, there has been considerable interest in the fluctuation theorem (FT). The Evans-Searles FT shows how time reversible microscopic dynamics leads to irreversible macroscopic behavior as the system size or observation time increases. We show that the argument of this FT, the dissipation function, plays a central role in nonlinear response theory and derive the dissipation theorem, giving exact relations for nonlinear response of classical N-body systems that are more widely applicable than previous expressions. These expressions should be verifiable experimentally. When linearized they reduce to the well-known Green-Kubo expressions for linear response.     

Density-dependent analysis of nonequilibrium paths improves free energy estimates II. A Feynman-Kac formalism

The nonequilibrium fluctuation theorems have paved the way for estimating equilibrium thermodynamic properties, such as free energy differences, using trajectories from driven nonequilibrium processes. While many statistical estimators may be derived from these identities, some are more efficient than others. It has recently been suggested that trajectories sampled using a particular time-dependent protocol for perturbing the Hamiltonian may be analyzed with another one. Choosing an analysis protocol based on the nonequilibrium density was empirically demonstrated to reduce the variance and bias of free energy estimates. Here, we present an alternate mathematical formalism for protocol postprocessing based on the Feynmac-Kac theorem. The estimator that results from this formalism is demonstrated on a few low-dimensional model systems. It is found to have reduced bias compared to both the standard form of Jarzynski's equality and the previous protocol postprocessing formalism.     

Geometric description of chemical reactions

We use the formalism of Geometrothermodynamics to describe chemical reactions in the context of equilibrium thermodynamics. Any chemical reaction in a closed system is shown to be described by a geodesic in a 2-dimensional manifold that can be interpreted as the equilibrium space of the reaction. We first show this in the particular cases of a reaction with only two species corresponding to either two ideal gases or two van der Waals gases. We then consider the case of a reaction with an arbitrary number of species. The initial equilibrium state of the geodesic is determined by the initial conditions of the reaction. The final equilibrium state, which follows from a thermodynamic analysis of the reaction, is shown to correspond to a coordinate singularity of the thermodynamic metric which describes the equilibrium manifold.     

Thermodynamic perturbation theory of simple liquids. A hierarchy of equations for expansion coefficients

The properties of an expansion of the statistical sum of a simple liquid with respect to the potential in thermodynamic perturbation theory are analyzed. The coefficients of this expansion are determined by the unperturbed potential, depend on temperature and density, and can be calculated by means of mathematical modeling. It is shown here that the derivatives of these coefficients with respect to temperature and density are expressed through the higher expansion coefficient (these relations are usually called a hierarchy of equations). These coefficients determine the expansion of the Helmholtz free energy and RDF with respect to the perturbation potential. The thermodynamic characteristics of the system (entropy, internal energy, pressure) are expressed through both the differential relations for the Helmholtz free energy and the integral expressions containing RDF. It is found that the hierarchy of equations obtained in this work makes these different methods equivalent. This is important for the application of thermodynamic perturbation theory because it becomes unnecessary to model any other equilibrium properties of the system apart from the expansion coefficients.