Molar Internal Energy Research Articles

Thermodynamic and kinetic approaches to lithium intercalation into a Li 1− δMn 2O 4 electrode using Monte Carlo simulation

The thermodynamics and kinetics of electrochemical intercalation of lithium into a Li 1− δ Mn 2O 4 electrode have been investigated theoretically by a statistical thermodynamics concept using a Monte Carlo simulation based upon the lattice gas model. From the fluctuations in the internal energy and the number of lithium ions in the grand canonical ensemble, the partial molar internal energy and entropy of lithium ions were obtained theoretically at a fixed chemical potential. Both theoretical and experimental partial molar quantities alike showed a negative deviation from those quantities of the ideal solution below (1− δ)=0.5 and a positive deviation above (1− δ)=0.5. The component diffusivity of lithium ions was calculated with the aid of a random walk algorithm in the canonical ensemble. From the combination of the thermodynamic enhancement factor and the component diffusivity of lithium ions calculated theoretically by introducing the irreversible lithium trap sites into the Li 1− δ Mn 2O 4 electrode, the chemical diffusivity of lithium ions was determined and compared with that measured using the galvanostatic intermittent titration technique. From the good coincidence between the chemical diffusivities calculated theoretically and determined experimentally, it was inferred that the lithium ions trapped irreversibly near structural defects disturb locally the ordering of lithium ions and hence the chemical diffusion of lithium ions in the ordered phase is strongly enhanced.

Properties of the liquid-vapour interface of fcc metals calculated using the tight-binding potential

The second-moment approximation (SMA) of the tight-binding (TB) scheme was used to calculate the molar volume, volume expansion, internal energy and pair correlation function for bulk liquids of the fee metals at several temperatures both above and below the melting point. The calculated values were found to be in generally good agreement with experiments, although the volume expansion upon melting does differ by 55% from the expected result for some of the elements studied. The total energy of a liquid system with surfaces was calculated, and the results were compared with the bulk liquid results to determine the enthalpy and width of the liquid-vapour interface. The TB SMA values for surface enthalpy were found to be lower than experimental values by by about 10-40%.

Design of experimental routes and data processing for the determination of the depth-distribution of energy in real solids

No adequate thermodynamic definition of non-equilibrated solids is available at present. In this paper a method is suggested for the energetic characterization of solids by estimation of the distribution of the differential molar internal energies — as they appear during the breakdown of sample e.g. by chemical reaction, i.e. the ‘depth distribution of differential energies’ (DDE) of samples. Thermodynamic considerations are presented for approximating this quantity — and experimental possibilities proposed to attain the needed input information by thermoanalytical methods. Application of the suggested procedure is supposed to contribute to the better understanding of structure — energy — reactivity relations in real solids.

Heat effects for toluene adsorption on activated carbon from supercritical carbon dioxide

The isochoric adsorption isotherms of toluene from supercritical carbon dioxide on activated carbon were provided in this study. The experimental data were obtained by a recycle technique. The activated carbon pellets were loaded in a spinning basket autoclave. After injection of a certain amount of toluene into autoclave, the equilibrium loadings of toluene on activated carbon at various temperatures were measured in a path of gradually decreasing or increasing temperatures. The equilibrium adsorption data for temperatures ranging from 308 to 338 K at CO 2 densities of 0.32, 0.45, and 0.69 g cm −3 were correlated accurately by the Toth isotherm expression. A thermodynamic model was proposed herein related the mole fraction of toluene in supercritical CO 2 phase with the changes in partial molar enthalpies, partial molar volumes, and partial molar internal energies of toluene. The experimental data obtained were analyzed by the proposed model revealing that the changes in partial molar enthalpies and partial molar volumes were always positive for the conditions studied and were significantly large near the CO 2 critical condition. This enthalpy change represents the energy transfer of one mole of toluene from the nonideal, supercritical solution onto the adsorbent surface at isobaric and isothermal operations. This quantity, however, is not the heat of adsorption as conventionally defined which represents the energy transfer of one mole of solute from an ideal gas solution onto the adsorbent surface. But on the other hand, the change in partial molar internal energies of toluene was found to be always negative. This indicated that the energy effects associated with an adsorption process at supercritical conditions should be clearly defined so as to elucidate the adsorption is endothermic or exothermic.

Measurements of (p,ϱ,T,x) for {x CS 2 + (1-x) Si(CH 3) 4}(1) from 198 to 298 K and pressures up to 104 MPa. Experimental results and derived thermodynamic properties

Molar densities have been measured by using an expansion technique at pressures up to 104 MPa and temperatures from 198 to 298 K for the mixture { x CS 2 + (1-x) Si(CH 3) 4}(1) over the whole composition range. Several thennodynamic properties (isothermal compressibility, thermal expansivity, and molar internal energy, enthalpy and entropy increments relative to liquid at saturation) have been directly obtained from the experimental densities. The isothermal compressibility and the thermal expansivity are both smooth functions of pressure, temperature and composition, although the isotherms of the thermal expansivity exhibit a characteristic crossover at high pressures. The intersection of isotherms of thermal expansivity seems to occur at a single point of the ( p,α p) diagram, showing a nearly linear dependence with the composition.

Determination of the Molecular Area on a Liquid Surface from Thermodynamic Functions: Application to Alkanes

A method is proposed to calculate the molecular area on the surface of a liquid from thermodynamic parameters such as the molar internal energy, the surface free energy, and the surface entropy. When the method is applied to the series of normal alkanes, it allows calculation of the area of the molecules on these liquid surfaces and to deduce the orientation of these molecules. Moreover, the molecular areas of the first terms of the alkane series and of hydrogen are also obtained by extrapolation.

Thermodynamic study on phase transition in mixed monolayers of cholesterol, lecithin and lithocholic acid

For mixed monolayers of cholesterol, lecithin and lithocholic acid the surface pressure has been measured as a function of molecular area at various compositions and temperatures. The liquid-expanded (LE)/liquid-condensed (LC) phase transition takes place over a wide range of monolayer compositions. The cholesterol monolayers are of the condensed type, but they become gradually expanded as the composition of lecithin or lithocholic acid increases. As expected the transition surface pressure increases as temperature increases. From the temperature dependence of the transition surface pressure, the apparent molar entropy, enthalpy and internal energy associated with the phase transition have been calculated. The contribution of lecithin and lithocholic acid molecules to the phase transition are not equivalent. The condensing effect of cholesterol on lithocholic acid is more pronounced than that of lecithin on this bile acid.

Towards molecular-thermodynamic aspects of postulated Pd/D low-temperature nuclear fusion: a useful example of a failure of the conventional translational partition function

The partition function of translation in a cubical box of very small volume has been studied. Decreasing dimensions of the cube have been found to cause gradually larger deviations from the conventionally used partition function. This is manifested in the corresponding values of thermodynamic quantities. Special attention was paid to the molar internal energy of translation, and marked differences from the conventional term of 3 RT/2 were observed for very small dimensions of the cube, this energy term being increased without limitation in the limiting case. These results were applied to the hydrogen isotopes occluded in elementary cubic cells of Pd. The results are interpreted as a possible auxiliary contribution to the overall mechanism of the low-temperature nuclear fusion presumed to take place in a Pd electrode fed with deuterium.

Calculation of infinite‐dilution partial molar properties by computer simulation

AbstractPartial molar properties at infinite dilution for binary Lennard‐Jones mixtures are calculated using Monte Carlo simulation methods. The variation of these properties with density, temperature, and intermolecular force parameters is systematically studied. Simulation pair correlation functions are used to examine the structure of the mixtures at the molecular level. Results are also compared to predictions of the van der Waals I conformal solution theory.Partial molar volume and internal energy are found to be strongly dependent on the isothermal compressibility of the mixture and on the proximity of the mixture state condition to phase boundaries. The van der Waals I conformal solution theory gave good results for the infinite‐dilution chemical potential μ and reasonable results for the partial molar internal energies and volumes. However, it is suspected that this is limited to the infinite‐dilution case, where the isothermal compressibility of the mixture is well represented by the pure‐fluid equation of state.

Multilayer isotherms of neon adsorbed on exfoliated graphite

Isotherms of neon adsorbed on compressed exfoliated graphite were measured, using a standard volumetric method, in the temperature interval of 12–24 K for the four first layers. The critical temperatures for the first three layers were determined to be 16.0±1.0, 19.0±1.0 K, and 18.0±1.0 K, respectively. From the isotherms, the isosteric heats of adsorption were calculated as a function of coverage, indicating some interesting features, which may be attributed to possible phase transitions. The isosteric heat of adsorption for the fourth layer on,Q st/R=.275 K, is comparable to the three-dimensional latent heat of sublimation 256 K at the triple point. The binding energies for the first, second, and third layers were obtained from the isosteric heats as V → 0, yielding 302.5, 237.5, and 227.5 K, respectively. The differential molar entropies and internal molar energies were also calculated as a function of coverage. The possibility of a coexistence region with two solids having different structures in the phase diagram for the first layer is discussed. Whenever possible, the results are compared with theoretical evaluations and previous experimental data.

Stefan's rule as a consequence of cohesive forces

This work is concerned with the derivation of Stefan's rule. The treatment is based on the thermodynamic definition of internal pressure and it leads to an expression correlating internal pressure, molar volume and total molar surface energy of pure liquids. Further, the molar internal energy of vaporization is introduced with the help of the definition equation of the solubility parameter and the equation of Stefan results. All the liquid properties that appear in this derivation are closely related to the cohesive forces acting in fluids. The numerical value of the geometric factor k in the final equation is for simple liquids closely equal to three. This is in agreement with the theory, whilst the speculative value suggested by Stefan is equal to two. In liquids in which the intermolecular forces depart greatly from spherical symmetry and in interacting systems k becomes considerably higher.

Stefan's rule as a consequence of cohesive forces

This work is concerned with the derivation of Stefan's rule. The treatment is based on the thermodynamic definition of internal pressure and it leads to an expression correlating internal pressure, molar volume and total molar surface energy of pure liquids. Further, the molar internal energy of vaporization is introduced with the help of the definition equation of the solubility parameter and the equation of Stefan results. All the liquid properties that appear in this derivation are closely related to the cohesive forces acting in fluids. The numerical value of the geometric factor k in the final equation is for simple liquids closely equal to three. This is in agreement with the theory, whilst the speculative value suggested by Stefan is equal to two. In liquids in which the intermolecular forces depart greatly from spherical symmetry and in interacting systems k becomes considerably higher.

Monte Carlo calculations of solvent effect in the reaction F- + CH3F = F...CH3....F-

A new approach is suggested and tested to calculation of solvent effect on chemical reactivity based on the statistical-thermodynamic Monte Carlo simulation of models of aqueous solutions devised by Metropolis. The results of computer experiments are presented for the following systems: F-.26H2O, CH3F.26H2O, FCH3F-.52H2O, 26 H2O, 52 H2O at a temperature of 300 K at the conditions of canonical ensemble. The pair potentials MCY-CI (for water-water interactions) and 4-31G (for solute-water interactions) have been used. The 4-31G potentials have been derived from the SCF calculations of the interaction energies of the systems: F-.H2O, CH3F.H2O, and FCH3F-.H2O. Internal energies, radial distribution functions, and snapshots of the configurations have been calculated. The calculated partial molar internal energies depend strongly on quality of the solute-water pair potentials and are overestimated with respect to experiment. On the basis of the results obtained, further possibilities of the suggested approach are discussed.

Methane in aqueous solution at 300 K

A Monte Carlo simulation for a methane molecule within a cluster of 202 water molecules is presented and compared with previous studies by Scheraga and Beveridge. Whereas the structural information obtained agrees with previous findings, the energy points to the need for a very large number of Monte Carlo steps and for a different algorithm to compute the partial molar internal energy.

Transition temperatures, entropies, internal energies, and heats of desorption of 4He films adsorbed on graphite from vapor pressure measurements

Vapor pressure measurements of 4He adsorbed on Grafoil for coverages x = 0.94 and 1.00 were made as a function of temperature in the temperature range of 5–10 K. The data are presented as plots of ln p vs. 1/T and from these dp/dT vs. T curves are presented. For both coverages there is an indication of a phase transition, which agrees with the conclusions from specific heat data on the same system obtained by other authors. Molar entropies and internal energies, as well as isosteric heats of adsorption, were obtained as a function of coverage, and from the data the contribution to the total specific heat of the adsorbed films due to desorption was found to be considerable.

Vapor pressure measurements of adsorbed neon on exfoliated graphite between 15 and 30 K

Vapor pressure measurements of neon adsorbed on bare Grafoil for coverages of 0.5, 0.75, 1.00, 1.25, 1.50, and 1.75 were made as a function of temperature in the range 15–30 K using a standard volumetric method. Data plots of ln p vs. (1/T) were obtained for the coverages x of 1.25, 1.50, and 1.75 monolayers and there is an indication of a phase transition at about 19 K, which agrees with the results of specific heat data on the same system. The molar entropy and internal energy were computed as a function of coverage. Isosteric heats of adsorption as a function of coverage were also computed from the data and are in good agreement with the results given by other authors on graphite surfaces. The binding energy of Ne on Grafoil was calculated from the isosteric heat for x → 0, yielding a value of 323 K.

Constitutive equations for ideal gas mixtures and ideal solutions as consequences of simple postulates

It is shown that all features one normally associates with ideal gas mixtures (Boyle's law, Charles' law, the existence of a universal gas constant common to all species in the mixture, etc.) follow easily from standard equations of classical thermodynamics taken together with three postulates which state nothing more than the variables upon which chemical potentials, partial molar volumes, and partial molar internal energies depend. The standard equations for ideal solutions comprised of three or more species can be derived in a similar fashion from slightly weaker postulates; these postulates do not suffice to yield the ideal solution equations for binary mixtures, as is shown by counterexample.

On the determination of interaction energy functions II. Crystalline formic acid

A procedure for deriving molecular interaction energy functions from known equilibrium properties of crystals is described. Formic acid is successfully used as a model test system. The known equilibrium properties of formic acid which were employed are: the average molar internal energy, the minimum nature of the internal energy, and the lack of rotatory motion of each of the molecules in the crystal. The molecular interaction energy functions are represented as pairwise sums of atom-atom terms, which in turn are expressed as 1-4-6-12 inverse power expansions of atom-atom distances.