Theory of time-resolved level anticrossing experiment

The purpose of the present paper is to present a general treatment of steady state and time-resolved level-anticrossing (LAC) experiments using the generalized master equation approach in which both radiate and nonradiative decays and dephasing processes have been considered. Several models are treated to demonstrate the theoretical method. The theory is applicable to both atoms and molecules. It is shown that under appropriate conditions, as derived in this paper, quantum beats can be observed in the time-resolved LAC experiment. Numerical calculations have been performed to show the time-dependent behavior (build-up and decay) of the time-resolved LAC experiment. These quantum beats are then a direct measurement of the microscopic coupling parameters in intersystem crossing, etc. It will be shown that combining the steady state and the time-resolved LAC experiments one can determine not only the microscopic coupling parameters but also the relaxation and/or the dephasing rate constants. Hence the particular virtues of time dependent LAC experiments are seen in these model calculations.     

Complete resolution of the ionization equilibria of 5-deoxypyridoxal in water-dioxane mixtures

We have used a potentiometric method to determine the thermodynamic equilibrium constants for the macroscopic ionization processes of 5-deoxypyridoxal (DPL) in water-dioxane mixtures (0-70% weight fraction in dioxane) at temperatures ranging from 10°C to 50°C. These data, together with previously published equilibrium constants for the tautomerism and hydration processes, have allowed us to resolve the complete microconstant system. We have also calculated the microscopic ionization equilibrium constants under all the experimental conditions. The changes of standard thermodynamic function for the macroscopic and microscopic ionization processes were obtained in various water-dioxane mixtures at 25°C. The values of a given microscopic pK with different solvents and temperatures fit very well to an equation which relates this magnitude with the thermodynamic parameters, the solvation of the components of the reaction, and a solvent parameter. We have obtained an interesting linear correlation between the thermodynamic parameters corresponding to all the microscopic ionizations of DPL and the net change of the solvation during the process: enthalpies correlate linearly for all the microscopic ionizations, while entropies do so for the phenols and pyridinium ions separately.     

多个时间常数线性体系暂态响应方程参数的代数求解法

从线性条件出发, 推导了含n个时间常数体系恒电位阶跃时暂态响应方程, 并提出一套解析形为ΔI=ΔI_∞+sum from i=1 to n k_iexp(-t/τ_i)暂态方程各未知参数的代数解法。该方法可对未知体系时间常数个数进行判定, 比起一般曲线拟合更加快速简便, 且抗干扰能力较强。     

Derivation of Martin-Hou Equation of State from Hard-particle Perturbation Theory

IntroductionIn the mid 1950's, an empirical equation of state was proposed by Martin and HouLI] abbreviated to the M--H equation. It is a more accurate equation of state applicable to real gasesincluding polar compounds, such as ammonia and water over a wide range of density and temperature. In 1981, the M--H equation was extended further to liquid domain by Hou et al. [2),and later, it was used to calculate the vapor--liquid equilibrium, liquid--liquid equilibrium andother thermodynamic p…     

A perturbed hard-sphere-chain equation of state for mixtures: Prediction from critical point constants

A modified perturbed hard-sphere-chain equation of state by Eslami [H. Eslami, Fluid Phase Equilibr. 216 (2004) 21-26], is extended to mixtures. The resulting equation of state for mixtures consists of two temperature-dependent parameters as well as an additional parameter, reflecting the segment size for pure components. The temperature-dependent parameters of the equation of state are correlated as universal functions of the reduced temperature. It is shown that knowing just the critical constants of pure components is sufficient to calculate the temperature-dependent parameters. The equation of state for mixtures is checked against the experimental pressure-volume-temperature data for a large number of mixtures, having varieties of molecular sizes and shapes. It is shown that no interaction parameter is needed to describe the behavior of fluid mixtures. Among about 3500 data points for mixtures, the average absolute deviation, compared to the experimental data, is about 0.93%.     

从硬球微扰理论推导马丁-侯状态方程

从Ｂａｒｈｅｒ－Ｈｅｎｄｅｒｓｏｎ的硬球微扰理论出发，运用幂级数形式的径向分布函数和分段的势能函数导出马丁－侯状态方程，推导过程中导出了一种理论式，计算Ｐ－Ｖ－Ｔ性质的精确度与马丁－侯原式相当，理论式的常数与分子微观参数有确定的函数关系。     

Impact of carbon dioxide on the surface tension of 1-hexanol aqueous solutions

Effects of carbon dioxide presence on the surface tension and adsorption kinetics of 1-hexanol solutions were investigated. Experiments were performed at a range of carbon dioxide vapor pressures and varying concentrations of 1-hexanol aqueous solution. Both dynamic and steady-state surface tensions of 1-hexanol aqueous solution were found to decrease with carbon dioxide pressure, and a linear relationship was observed between the steady-state surface tension and carbon dioxide pressure. To explain the experiments, adsorption and desorption of the two species (1-hexanol and carbon dioxide) from two sides of the vapor-liquid interface were considered. A modified Langmuir isotherm, the modified Langmuir equation of state and the modified kinetic transfer equation were developed. The resulting steady-state and dynamic surface tension data were modeled using the modified Langmuir equation of state and the modified kinetic transfer equation, respectively. Equilibrium constants and adsorption rate constants of 1-hexanol and carbon dioxide were evaluated through a minimization procedure for CO₂ pressures ranging from 0 to 690 kPa. From the steady-state modeling, the equilibrium parameters for 1-hexanol and carbon dioxide adsorption from vapor phase and liquid phase were found unchanged at different pressures of carbon dioxide. From the dynamic modeling, the adsorption rate constants for 1-hexanol and carbon dioxide from vapor phase and liquid phase were found to decrease with carbon dioxide pressure. Some fluctuations in the fitting parameters of the dynamic modeling (adsorption rate constants) were observed. These fluctuations may be due to experimental errors, or more likely the limitations of the model used. A major limitation of the model is related to large differences in adsorption/desorption between initial and final stages of the process, and a single set of property parameters cannot describe both initial and final states of the system. Variations may occur depending on which set of data, of initial or final states, is used in the model predictions over the entire time range.     

Microscopic acid-base equilibria of arginine

Three and two protonation macroconstants as well as twelve and four microconstants have been determined for arginine and citrulline, respectively. These data include microscopic basicity values of the arginine guanidino group, for which no reliable constants have been reported earlier. The determinations were carried out by a combination of potentiometric and deductive methods. The guanidino basicity proved to be extremely high, and can be characterized by microconstants between 14.7 and 15.0 log k units. The interactivity parameters could also be determined from the microscopic protonation constants. These values for the guanidino—amino and the guanidino—carboxylate interactions are 0.2 and 0.1 log k units, respectively. The pH-dependent distribution of all eight arginine microspecies is made visual by a microspeciation diagram. The microspeciation diagram is the most useful tool to predict bidentate binding isomerism in metal complex formation and site-specific bioligand—bioligand associations.     

多个时间常数线性体系暂态响应方程参数的代数求解法

从线性条件出发,推导了含n个时间常数体系恒电位阶跃时暂态响应方程,并提出一套解析形为ΔI=ΔI_∞+sum from i=1 to n k_iexp(-t/τ_i)暂态方程各未知参数的代数解法。该方法可对未知体系时间常数个数进行判定,比起一般曲线拟合更加快速简便,且抗干扰能力较强。     

SRK equation of state: Predicting binary interaction parameters of hydrocarbons and related compounds

The parameter mixing rules of the Soave–Redlich–Kwong (SRK) equation of state are rewritten as Huron–Vidal mixing rules, where infinite-pressure activity coefficients are predicted by group contributions. Alkanes are treated as composed by one group type and aromatics by two types, aliphatic and aromatic. Hydrocarbon mixtures can be treated using one universal interaction parameter. Light compounds like methane, N₂, CO₂, H₂S, etc. are treated as separate groups; each one requires a pair of parameters for its interactions with aliphatic and aromatic groups. Group interaction parameters were determined from experimental VLE data. From them, binary interaction constants of the classical quadratic mixing rules can directly be derived.     

Characterization of ester hydrolysis in terms of microscopic rate constants

Hydroxide-catalyzed ester hydrolysis for molecules of coexisting species is quantitated in terms of microscopic rate constants, a new, species-specific physicochemical parameter. Relationships between the overall and component reactions, as well as the macroscopic and microscopic rate constants are deduced. Experimental techniques, evaluation methods, and feasibility are discussed. Species-specific, pH-independent rate constants of four coexisting, differently hydrolyzing microspecies are determined for the first time. Protonation of an alpha-amino and beta-imidazolyl site in amino acid esters has been found to accelerate the hydroxide-catalyzed hydrolysis by factors of 120 and 7.5, respectively, whereas they jointly exert a nearly 3000-fold acceleration. A total of 20 microscopic protonation equilibrium constants, as component parameters in the rate equations, have also been determined. The species-specific rate constants have been found to correlate with the site- and species-specific basicity of the leaving group and the NMR chemical shift of an adjacent proton. Individual contributions of the various microforms to the overall hydrolysis rate are depicted in microscopic reaction fraction diagrams.     

Analytical solutions to mathematical models of the surface and bulk erosion of solid polymers

The process by which polymeric materials hydrolyze and disappear into their environments is often called erosion. Two types of erosion have been defined according to how the hydrolysis takes place. If hydrolysis occurs throughout the entire specimen at the same time, it is called bulk erosion. If the hydrolysis is mainly confined to a region near the surface of the specimen and the surface continuously degrades by moving inward, it is termed surface erosion. In this article, a kinetic relationship for bulk erosion is developed. This relationship provides a method for estimating the hydrolysis kinetic constants for bulk‐eroding polymers. This same relationship is also applicable to surface erosion at a microscopic level. Through its combination with a diffusion–reaction equation and the provision of moving boundary conditions, an analytical solution to the steady‐state surface‐erosion problem is obtained. The erosion rate, erosion front width, and induction time can all be expressed as simple functions of the rate of polymer bond hydrolysis, water diffusivity, and solubility, plus other parameters that can be experimentally determined. The erosion front width is the product of the induction time and the erosion rate. The ratio of the erosion front width to the polymer specimen thickness is a parameter that determines whether the specimen undergoes surface or bulk erosion. Theoretical results are compared with experimental observations from the literature, and agreement is found. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 383–397, 2005     

跨接VTSRK方程计算烃类的pVT性质

烃类pVT性质的精细表征对能源动力、化工等领域应用有重要价值,临界区热力性质描述是难点之一.本文建立了烷烃（C1-C20）的跨接比容平移Soave-Redlich-Kwong（SRK）（跨接VTSRK）状态方程,在SRK状态方程的基础上引入了比容平移和跨接方法,以改善饱和液相密度和近临界区域热力学性质的计算精度,方程参数被表达为物质临界参数和偏心因子的函数. 比较结果表明,跨接方程对烷烃（C1-C20）饱和蒸气压、饱和气相密度、饱和液相密度的计算平均偏差分别为1.01%、1.83%和0.93%,显著优于原方程,单相区和近临界区的pVT性质计算精度也比原状态方程有较大改善. 进一步将方程推广到环烷烃（环丙烷、环戊烷和环己烷）和苯、甲苯的计算,也获得了较好效果,验证了方程的预测能力.     

跨接VTSRK方程计算烃类的pVT性质

烃类pVT性质的精细表征对能源动力、化工等领域应用有重要价值,临界区热力性质描述是难点之一.本文建立了烷烃(C1-C20)的跨接比容平移Soave-Redlich-Kwong(SRK)(跨接VTSRK)状态方程,在SRK状态方程的基础上引入了比容平移和跨接方法,以改善饱和液相密度和近临界区域热力学性质的计算精度,方程参数被表达为物质临界参数和偏心因子的函数.比较结果表明,跨接方程对烷烃(C1-C20)饱和蒸气压、饱和气相密度、饱和液相密度的计算平均偏差分别为1.01%、1.83%和0.93%,显著优于原方程,单相区和近临界区的pVT性质计算精度也比原状态方程有较大改善.进一步将方程推广到环烷烃(环丙烷、环戊烷和环己烷)和苯、甲苯的计算,也获得了较好效果,验证了方程的预测能力.     

A microscopic theory for solution chemical reactions: Introduction of reactant and medium structures into generalized langevin equation formalism

A microscopic formulation of solution chemical reactions, taking reactants and medium structures into consideration, is presented on the basis of microscopic understandings obtained by recent quantum chemical methods (i.e., ab initio molecular orbital theory, etc.). Assuming thermal equilibrium of the medium bath, an effective internal Hamiltonian is derived, and, further, its derivative with respect to internal normal coordinates is proved explicitly to give the same force field as is provided by the free-energy surface or potential of mean force. The free-energy surface can be expressed in the composite normal coordinate system (CNCS ) consisting of some normal coordinate systems of isolated reactants and surrounding solvent molecules (i.e., medium solvent molecules). In CNCS , in use of diagonal elements obtained in the Hessian matrix of the free-energy surface, effective normal-mode frequencies, which reflect the equilibrium solvent effect, are estimated. Furthermore, on the generalized Langevin equation (GLE ) treatment, a closed expression of the time-dependent frictional coefficient is derived on a microscopic basis, reflecting the reactant and solvent structures. The nonequilibrium effect is estimated by an analytical expression similar to that in the Grote–Hynes theory. The rate constant is evaluated for a typical model system and it is shown that the equilibrium rate constants should be reduced by a factor 0.997. Finally, it is concluded that the present microscopic theory is reasonably applicable to the estimation of chemical reaction rate constants in solution. © 1994 John Wiley & Sons, Inc.     

Structure-ionization relationship of tyrosine-containing peptides

The arid-base chemistry of tyrosine-containing peptides such as enkephalin, tyrosylglycylglycine, tyrosylglycine and analogous peptides is described. For each peptide and tyrosine derivative, microscopic and macroscopic acid dissociation constants and the thermodynamic parameters for proton dissociations were determined from pH-titrations and ultraviolet absorption spectra. The relative concentrations of various ionic forms for the peptides were calculated from the microscopic constants. The concentration ratio, represented by the tautomeric equilibrium constant (K(t)), showed a definite relationship to structure.     

The rate of reaction of methyl radicals with ozone

The absolute rate constant for the reaction of methyl radicals with ozone has been measured as a function of temperature. Small concentrations of CH₃ were generated by flash photolyzing CH₃NO₂ at 193 nm with an ArF laser. A photoionization mass spectrometer was used to follow the rate of decay of CH₃ at various ozone concentrations. The resulting rate constants could be fit by the expressions over the temperature range of 243–384 K. These rate constants can be modeled by simple transition state theory using reasonable parameters for the activated complex. Use of this rate constant shows that less than 1% of the methyl radicals formed in the stratosphere react with ozone.     

Thermodynamic modeling of solute adsorption equilibrium from near-critical carbon dioxide

Modeling of adsorption equilibrium for supercritical fluid mixtures, with as few parameters as possible, is important in applications of the technology of supercritical fluid adsorption. In this paper, a correlative model has been developed to represent the adsorption equilibria of solutes from the near-critical CO(2) fluid. A two-dimensional van der Waals equation of state and the three-dimensional P - R equation of state were used to describe the adsorbed and bulk phases, respectively. This model contains five parameters for adsorption equilibrium isotherms at finite concentrations and two parameters for adsorption equilibrium constants at infinite dilution. All the parameters are independent of temperature and pressure. By applying the model to the experimental data from the literature, it was shown that this model is capable of describing the adsorption behavior of solutes from supercritical carbon dioxide over relatively wide temperature and pressure ranges. In addition, the adsorption behavior of supercritical fluid mixtures was investigated at finite and infinite dilution conditions.     

On finding the rate constants of linear and nonlinear systems

In lowest approximation, a certain chemical reaction is described by a system of first-order linear differential equations with unknown constant coefficients. One can therefore write down an expression for the state of the system at time t, and from this find the endpoint of the reaction in terms of the initial state and the rate constants. The relative values of some rate constants can then be estimated from experimental data. A better approximation in which the differential equations are nonlinear is also considered, and it turns out that because of symmetry in the reaction, the relationship between the final state and the ratios of the rate constants is unchanged. Although the differential equations now appear much less tractable, the problem of relating the rate constants to the endpoint of the reaction can be formulated and solved in terms of probabilities. The results illustrate an important property of reaction schemes in which some of the steps are reversible. More generally, this is a property of differential equations: provided that they continue to satisfy certain linear constraints, the parameters of a linear system of ordinary differential equations can vary without affecting the asymptotic solution.