Molecular thermodynamic model for equilibria in solution IV. Macroscopic partition functions

The molecular ensembles statistically distributed according to internal specific characteristics and distinguished for the different exchanges with the surroundings are represented on the macroscopic scale by appropriate partition functions. The partition function for osmotic non-reacting ensemble is a function of concentration or activity of the ligand and is suited to the definition of thermodynamic potential μ. The partition function for thermal non-reacting ensemble shows the dependence upon the temperature and that for thermo-osmotic non-reacting ensemble shows the dependence upon both concentration and temperature.

The reaction partition function is suited to show the distribution of the different species over the different enthalpy levels of the reacting ensemble. The dispersion of the distributions are represented by second derivatives of the partition function.

The information contained in the entropy axis of the thermodynamic space for reacting ensembles concerning the induced dilution of the bound ligand and final dilution of the free ligand can be spanned to a formation function diagram where free energy of reaction can be graphically represented.     

Molecular thermodynamic model for equilibria in solution: I. Reacting and non-reacting ensembles

The partition functions of solution thermodynamics are mathematical representations of the properties of molecular ensembles statistically distributed according to specific characteristics. The ensembles are classified as non-reacting or reacting. The non-reacting ensembles are characterized by one mean enthalpy level with dispersion around the mean. The reacting ensembles are characterized by two or more distinctly separated enthalpy levels over which the different species are variably distributed, depending on concentration and/or temperature.

The non-reacting ensembles can be distinguished into microcanonical, thermal, osmotic, thermo-osmotic ensembles, depending on the type of exchange with the surroundings which is connected to the fluctuations of the ensemble variables. The reacting ensembles can be distinguished into thermal, osmotic, thermo-osmotic, electrochemical, electro-osmotic, electro-thermal, electro-thermo-osmotic ensembles, depending on the type of reaction and of exchange with the surroundings.     

Molecular thermodynamic model for equilibria in solution II. Statistical microscopic properties of ensembles

A statistical thermodynamic model for the interpretation of the equilibria in solution is based on the principle that the representative statistical ensembles can be characterized by two types of molecular distribution, one for non-reacting systems and another for reacting ones, respectively. Non-reacting and reacting ensembles correspond at the molecular level to one or a couple of potential curves, respectively. The properties of the thermodynamic model for solutions can be set up following some rules. These concern the statistical extension of the microscopic model to the whole ensemble and the successive averaging to get a mean partition function. The mean partition function is linked to the experimental domain of concentrations, dilutions and equilibrium constants (probability space) and to that of calorimetry, chemical work, and potentiometry (thermodynamics space). The formal connection between probability and thermodynamic space and the conformity of thermal equivalent dilution with the formulations of statistical thermodynamics are also shown.     

Vibrational frequencies, force constants, mean amplitudes, shrinkage effects and thermodynamic functions for monohaloacetylenes

Harmonic force fields are developed for the monohaloacetylenes on the basis of recent vibrational spectra of H-CC-I and previously published spectra of H-CC-X (X = F, Cl, Br). Mean amplitudes of vibration and Bastiansen-Morino shrinkage effects are reported for monohaloacetylenes and their deuterated derivatives. Thermodynamic functions are listed for monoiodoacetylene.     

Interatomic interactions in momentum space. Momentum density and kinetic energy in chemical bonding

On the basis of the virial theorem for a uniform scaling process of a polyatomic system, the total energy and its gradient are quantitatively related with the behavior of the electron density in momentum space through the kinetic energy of the system. For attractive and repulsive interactions, the behavior of the momentum density distribution and its effect on the stabilization energy and the interatomic force are examined. Some guiding principles are deduced for their interrelation. The results are used to clarify the role of kinetic energy in chemical bonding. Possible energy partitioning in this approach is also mentioned.     

Effective potential approach to bulk thermodynamic properties and surface tension of molecular fluids I. Single component n-alkane systems

The aim of this work is to develop spherically symmetric effective potentials allowing bulk thermodynamic properties and surface tension of molecular fluids to be predicted semiempirically by the use of statistical mechanical methods. Application is made to the straight chain alkane fluids from methane to decane. An effective Lennard-Jones potential is generated with temperature-dependent parameters fitted to the critical temperature and pressure and to Pitzer's acentric factor. Insertion of this potential into the generalised van der Waals (GvdW) density functional theory yields bulk properties in good agreement with experiments. The surface tension is overestimated for the longer alkane chains. In order to account for the surface tension, an independently adjustable attractive range of interaction is required and obtained through the use of square-well potentials chosen so as to leave the bulk thermodynamics unaltered while the attractive range is fitted to the surface tension at a single temperature. The GvdW theory, which includes binding energy, entropic and profile shape contributions, then generates surface tension estimates that are of good accuracy over the full range of available experimental data. It appears that, given a sufficiently flexible form, effective potentials combined with simple statistical mechanical theory can reproduce both bulk and non-uniform fluid data of great variety in an insighful and practically useful way.     

Molecular theory of phase equilibria in model and real associated mixtures III. Binary solutions of inert gases and n-alkanes in ammonia and methanol

Using new molecular models of ammonia and methanol and thermodynamic perturbation theory, the global phase diagrams of model mixtures of these compounds with a van der Waals fluid, representing a simple nonpolar fluid, have been calculated. The global phase diagram of these mixtures is much richer than that of corresponding aqueous mixtures. More types of critical line behavior are found, including the presence of van Laar points and a small region where the mixtures exhibit a closed liquid-liquid immiscibility loop (Type VI phase behavior). The individual mixture components are characterized by two molecular parameters, which can be adjusted to their critical temperature and critical volume; the mixture model itself contains no adjustable parameters. It is shown that the theory gives qualitatively correct predietions of mixtures with n-alkanes. This includes the prediction of Type III critical line behavior for small and large values of the ratio of the critical temperatures of the components, and Type II over a large range of conditions, including the presence or absence of absolute or limited azeotropy, and temperature and pressure extrema of critical lines and their dependence on the number of carbon atoms.     

Coherent thermodynamic model for solid,liquid and gas phases of elements and simple compounds in wide ranges of pressure and temperature

Thermodynamic modeling of fluids (liquids and gases) uses mostly series expansions which diverge at low temperatures and do not fit to the behavior of metastable quenched fluids (amorphous, glass like solids). These divergences are removed in the present approach by the use of reasonable forms for the “cold” potential energy and for the thermal pressure of the fluid system. Both terms are related to the potential energy and to the thermal pressure of the crystalline phase in a coherent way, which leads to simpler and non diverging series expansions for the thermal pressure and thermal energy of the fluid system. Data for solid and fluid argon are used to illustrate the potential of the present approach.     

Computation in kinetics, III. A new method for kinetic model search based on simultaneous regression estimation of rate constants, stoichiometry and/or reaction order

Modified samples of natural mordenites have been found to catalyze the oxidative condensation of methane to yield ethane and ethylene. The selectivity towards C₂ hydrocarbons increases, whereas the acidity of zeolites falls.

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Energy transfer between polyatomic molecules. 1. Gateway modes, energy transfer quantities and energy transfer probability density functions in benzene-benzene and Ar-benzene collisions

We report collisional energy transfer, CET, quantities for polyatomic-polyatomic collisions and use excited benzene collisions with cold benzene bath, B-B, as our sample system and compare our results with the CET of excited benzene with Ar bath. We find that the gateway mode for both systems is the out-of-plane modes and that in B-B CET, vibration to vibration, V-V, is the dominant channel. Rotations play a mechanistic role in the CET but the net rotational energy transfer is small compared to V-V. The shape of the down side of the energy transfer probability density function, P(E,E'), is convex for B-B collisions and it becomes less so as the temperature increases. In Ar-B collisions, P(E,E') is concave and it becomes less so as the temperature decreases. We report average vibrational, rotational, and translational energy transferred, , as function of temperature for various initial conditions.     

Lewis-Randall to McMillan-Mayer conversion for the thermodynamic excess functions of solutions. Part II. Excess energy and volume

Derivations are given for the equations expressing the McMillan-Mayer functions in terms of Lewis-Randall functions.     

Searching for Stable,Five‐Coordinate Aquated Al(III) Species. Water Exchange Mechanism and Effect of pH.

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract, please click on HTML or PDF.     

Equilibrium solubility of 6-propyl-2-thiouracil in nine pure solvents: Determination,correlation, Hansen solubility parameter and thermodynamic properties

Investigation upon the solid–liquid equilibrium on solubility data of 6-propyl-2-thiouracil (PLT) in pure organic solvents is essential for separation and purifying in industry process. In this work, PLT solubility in nine neat solvents was experimentally determined at 278.15 K–323.15 K under P = 0.1 MPa. These selected solvents were tetrahydrofuran(THF), acetone, acetonitrile,1-butanol,1-pentanol, 2-butanol, methyl acetate, ethyl acetate,1-propyl acetate, respectively. Experiment results showed that solubility was consistent with temperature and decreased according to the order: THF > acetone>1-butanol≈1-pentanol> 2-butanol > methyl acetate > ethyl acetate>1-propyl acetate > acetonitrile. Solvent effect and Hansen solubility parameter (HSP) were incited to explain dissolution rule on solute. Four thermodynamic models (modi?ed Apelblat model, Van't model, λh model and NRTL model) were adopted to correlate PLT solubility and provide good correlations on basis of RD, ARD and RMSD. In addition, thermodynamic properties (ΔH°, ΔS° and ΔG°) of PLT dissolution process in pure solvents were discussed and proved to be endothermic, entropically driven and non-spontaneous process.     

Conformational, concomitant polymorphs of 4,4-diphenyl-2,5-cyclohexadienone: conformation and lattice energy compensation in the kinetic and thermodynamic forms

4,4-Diphenyl-2,5-cyclohexadienone (1) crystallized as four conformational polymorphs and a record number of 19 crystallographically independent molecules have been characterized by low-temperature X-ray diffraction: form A (P2(1), Z'=1), form B (P1, Z'=4), form C (P1, Z'=12), and form D (Pbca, Z'=2). We have now confirmed by variable-temperature powder X-ray diffraction that form A is the thermodynamic polymorph and B is the kinetic form of the enantiotropic system A-D. Differences in the packing of the molecules in these polymorphs result from different acidic C-H donors approaching the C=O acceptor in C-H...O chains and in synthons I-III, depending on the molecular conformation. The strength of the C-HO interaction in a particular structure correlates with the number of symmetry-independent conformations (Z') in that polymorph, that is, a short C-HO interaction leads to a high Z' value. Molecular conformation (Econf) and lattice energy (Ulatt) contributions compensate each other in crystal structures A, B, and D resulting in very similar total energies: Etotal of the stable form A=1.22 kcal mol(-1), the metastable form B=1.49 kcal mol(-1), and form D=1.98 kcal mol(-1). Disappeared polymorph C is postulated as a high-Z', high-energy precursor of kinetic form B. Thermodynamic form A matches with the third lowest energy frame based on the value of Ulatt determined in the crystal structure prediction (Cerius2, COMPASS) by full-body minimization. Re-ranking the calculated frames on consideration of both Econf (Spartan 04) and Ulatt energies gives a perfect match of frame #1 with stable structure A. Diphenylquinone 1 is an experimental benchmark used to validate accurate crystal structure energies of the kinetic and thermodynamic polymorphs separated by <0.3 kcal mol(-1) (approximately 1.3 kJ mol(-1)).     

Fundamental studies of grafting reactions in free radical copolymerization. I. A detailed kinetic model for solution polymerization

Graft site initiation occurs by primary radical and/ or polymeric radical attack on the back-bone polymer. The controlling mechanism is determined by the structure of the backbone and the activity of the free radicals. The efficiency of incorporating monomer into the graft chains depends upon the graft site initiation mechanism and the mode of polymer chain termination (recombination or disproportionation). A kinetic analysis results a series of uniquely different expressions describing the graft efficiency, ? corresponding to different combinations of graft site initiation and chain termination mechanisms. The dependency of ? upon monomer, initiator, and backbone concentrations is different from case to case. The complete kinetic model is capable of predicting reaction rate, graft efficiency, graft frequency, graft ratio, and molecular weight averages and distributions. Simulations are provided to compare predicted results with experimental data for two different systems which show contrasting mechanisms of graft site initiation and mode of termination. © 1995 John Wiley & Sons, Inc.     

Determination and correlation of liquid–liquid equilibria for four binary N,N-dimethylformamide + hydrocarbon systems

Liquid–liquid equilibrium measurements for four binary N,N-dimethylformamide + hydrocarbon (hexane, heptane, octane, and cyclohexane) systems were performed using a laser scattering technique. The experimentally determined cloud points were satisfactorily correlated with two local composition models (NRTL, and Tsuboka–Katayama's modification of the Wilson equation). In addition, the prediction of LLE by means of the modified UNIFAC (Dortmund) model was also tested.     

Rate constants for the bimolecular self-reactions of ethyl,isopropyl, and tert-butyl radicals in solution. A direct comparison

A competitive method involving the direct measurement of radical concentrations by EPR spectroscopy has been used to show that in solution at 25°C the rate constants for the bimolecular self-reactions of ethyl, isopropyl, tert-butyl, cyclopentyl, and trichloromethyl are all approximately equal, as had been indicated previously by direct measurement of the rate constants for decay of these radicals.     

Coupled‐cluster theory for the polarizable continuum model. III. A response theory for molecules in solution

A coupled‐cluster (CC) response functions theory for molecular solutes described with the framework of the polarizable continuum model (PCM) is presented. The theory is an extension to the dynamical molecular properties of the PCM‐CC analytic derivatives recently proposed for the calculation of static molecular properties (Cammi, Jr Chem Phys 2009, 131, 164104). The theory is presented for linear and quadratic response functions, and the operative expressions of these response functions can accurately account for the nonequilibrium solvation effects. The excitation energies and transition moments of the solvated chromophores have been determined from the linear response functions. Accurate expressions for gradients of excitation energies for the evaluation of the excited state properties have been also discussed. © 2012 Wiley Periodicals, Inc. Int J Quantum Chem, 2012