Partial Enthalpies Research Articles

Contribution to the description of the absorber rod behavior in severe accident conditions: An experimental investigation of the Ag–Zr phase diagram

Most pressurized water reactor (PWR) absorber rods are composed of an Ag–In–Cd (SIC) alloy inside a stainless steel (SS) cladding, themselves inserted into a Zircaloy tube. During a severe accident, the SIC alloy which melts at 800 °C does not practically interact with SS. However, the cladding failure results from its internal pressurization and its eutectic interaction with Zircaloy and occurs at temperatures greater than 1200 °C. The subsequent interaction between the SIC melt and the Zircaloy has a strong impact on the quantities of aerosols released into the primary circuit and finally on the iodine chemistry. Accurate knowledge of the Ag–Zr system is a prerequisite to address this issue. Within this concern, our experimental work is focused both on the investigation of the Ag–Zr phase diagram and on the determination of the thermodynamic properties of the intermetallic compounds in the system. Two intermetallic compounds (AgZr and AgZr2) were identified. Ag–Zr cast alloys with a Ag/Zr ratio of 1:1 elaborated using an arc-melting furnace, once annealed, contained only a single phase AgZr. From metallographic observations, it appears that AgZr2 likely forms by the peritectic reaction from liquid and the bcc (βZr) phase. The partial enthalpies of solution of silver and zirconium in aluminum were experimentally determined at 723 °C in order to determine the enthalpies of formation of the intermetallic compounds. For silver solution calorimetry in aluminum bath, our measurements were successful and in agreement with the previous data. Yet, this study shows that liquid aluminum should not be used as a solvent for zirconium below 1000 °C.

Enthalpy of Mixing of Liquid Cu-Fe-Zr Alloys at 1873 K (1600 °C)

The enthalpies of mixing of liquid Cu-Fe-Zr alloys were determined at 1873 K (1600 °C) by using a high-temperature isoperibolic calorimeter. The measurements were performed along sections xCu/xFe = 3/1, 1/1, 1/3 in the composition range xZr = 0 to 0.55. The limiting partial enthalpies of mixing of undercooled liquid zirconium in liquid Cu-Fe alloys are (–91.8 ± 8.4) kJ mol−1 (section xCu/xFe = 3/1), (–94.1 ± 12.8) kJ mol−1 (section xCu/xFe = 1/1), and (–107.3 ± 15.6) kJ mol−1 (section xCu/xFe = 1/3). The integral mixing enthalpies are sign changing over the investigated composition range. The Redlich–Kister–Muggianu polynomial was used for the least square fit of the experimental results in order to obtain an analytical expression for the integral mixing enthalpy.

Prediction of the thermodynamic functions of mixing of binary oxide melts in the PbO–SiO2, Al2O3–SiO2 and CaO–Al2O3 systems by structure-based modification of the quasi-chemical model

A structure-based modification of the Guggenheim's quasi-chemical model for the prediction of the thermodynamic functions of mixing in binary silicate and aluminate melts is presented and the extension of this approach to ternary systems is discussed. Based on the “anionic” point of view on the oxide melts structure, the novel method for determination of the interchange energy (a principal parameter of the quasi-chemical theory) was proposed along with a simple and general set of the equations. The activity calculations of the end-member components and integral and partial enthalpies and Gibbs free of mixing along with the whole range of compositions for PbO–SiO2 and Al2O3–SiO2 systems as well as the model calculations of components in CaO–Al2O3 melts were made. The reasonable agreement between results of model calculations and experimental data showed the reliability of this approach in predicting of the thermodynamic functions of mixing in binary and aluminate systems. This approach has the advantage that prior knowledge of the experimental mixing properties of liquid oxide systems is not required.

Calorimetric investigation of mixing enthalpy of liquid (Co + Cu + Zr) alloys at T = 1873 K

The enthalpies of mixing of liquid (Co+Cu+Zr) alloys have been determined using the high-temperature isoperibolic calorimeter. The measurements have been performed along three sections (xCo/xCu=3/1, 1/1, 1/3) with xZr=0 to 0.55 at T=1873K. Over the investigated composition range, the partial mixing enthalpies of zirconium are negative. The limiting partial enthalpies of mixing of undercooled liquid zirconium in liquid (Co+Cu) alloys are (−138±18)kJ·mol−1 (the section xCo/xCu=3/1), (−155±10)kJ·mol−1 (the section xCo/xCu=1/1), and (−130±22)kJ·mol−1 (the section xCo/xCu=1/3). The integral mixing enthalpies are sign-changing. The isenthalpic curves have been plotted on the Gibbs triangle. The main features of the composition dependence of the integral mixing enthalpy of liquid ternary alloys are defined by the pair (Co+Zr) and (Cu+Zr) interactions.

Molecular dynamics study of phonon-mediated thermal transport in a Ni50Al50 melt: case analysis of the influence of the process on the kinetics of solidification

The phonon-mediated contribution to the thermal transport properties of liquid NiAl alloy is investigated in detail over a wide temperature range. The calculations are performed in the framework of equilibrium molecular dynamics making use of the Green–Kubo formalism and one of the most reliable embedded-atom method potentials for the intermetallic alloy. The phonon-mediated contribution to the thermal conductivity of the liquid alloy is calculated at equilibrium as well as for the steady state. The relative magnitude of the thermal conductivity decrease induced by the transition to the steady state is estimated to be less than 2% below 2000 K and less than 1% at 3000 and 4000 K. It is also found that the phonon-mediated contribution to the thermal conductivity of the liquid alloy can be accurately estimated (well within 1%) on the basis of an approximation which invokes the straightforwardly accessible microscopic expression for the total heat flux without demanding calculations of the partial enthalpies needed for the precise evolution of the reduced heat flux (pure heat conduction). On the basis of these calculations, the correspondence between the experimentally observed and modelled kinetics of solidification due to a difference in thermal conductivity is discussed.

Isothermal Titration Calorimetry: Application of the Gibbs–Duhem Equation to the Study of the Relationship Between Forward and Reverse Titrations

In this work we rigorously demonstrate that, in dilute solutions, the partial enthalpy of interaction of the ligand can be measured by a forward titration and that the partial enthalpy of interaction of the macromolecule with the ligand can be calculated from the Gibbs–Duhem equation. Using a reverse titration, it is possible to experimentally obtain the partial enthalpy of interaction of the macromolecule and to calculate that of the ligand. Based on this fact, we propose a thermodynamic criterion to experimentally discern when the forward process is equal to or different from the reverse process: they are equal (or different) if the interaction partial enthalpies obtained experimentally are equal to (or different from) those calculated from the Gibbs–Duhem equation. The above criterion is applied to four systems taken from the literature. The first system features the interaction between a bilayer and a surfactant. The second system features a binding interaction with two binding sites that are equivalent and independent. The final two systems feature binding interactions with two non-equivalent binding sites.

A Thermodynamic Method to Study the Interaction Between NaOH and Highly Carboxylated Polymeric Particles in Solution

One of the most important challenges facing nanotechnology is to identify methods that relate the synthesis of nanomaterials with their final applications. This work proposes a thermodynamic method to understand the stimuli–response of functionalized polymeric particles with NaOH using the partial volumes of interaction, partial compressibilities of interaction, partial enthalpies of interaction and the average hydrodynamic diameter. These properties have been calculated from experimental measurements made by mechanical oscillation densimetry, the sound speed technique, isothermal titration calorimetry, dynamic light scattering and zeta potential. The thermodynamic method allows determination of how and where the interactions take place on the polymeric particles. From the methodological point of view, the thermodynamic fundamentals of the method were tested by simulating the partial properties calculated from volumetric data of a ternary liquid mixture taken from the literature.

The calorimetric investigation of the mixing enthalpy of liquid Co–Ni–Zr alloys at 1873 K

The partial mixing enthalpies of zirconium in liquid Co–Ni–Zr alloys have been determined by means of high-temperature isoperibolic calorimeter. The measurements have been performed along the sections x Co/x Ni = 3/1, 1/1, 1/3 in the composition range x Zr = 0–0.50 at 1,873 K. The values of the partial function are negative over the investigated composition range. The limiting partial enthalpies of mixing of undercooled liquid zirconium in liquid Co–Ni alloys are (−140 ± 10) kJ mol−1 (the section x Co/x Ni = 3/1), (−199 ± 11) kJ mol−1 (the section x Co/x Ni = 1/1), and (−193 ± 16) kJ mol−1 (the section x Co/x Ni = 1/3). The integral mixing enthalpies have been calculated by Gibbs–Duhem integration. The calculated values are mainly negative. The obtained experimental results together with literature calorimetric data have been described by a least square fit using the Redlich–Kister–Muggianu polynomial. The integral mixing enthalpy has been calculated over the entire composition range.

H2O-NH4Cl system: Is there a thermodynamic response to the nucleation point?

According to literature data (J. Phys. Chem. A, 115, 3393–3460 (2011)), NH4Cl concentrations in nanoobjects such as aerosol droplets can be as high as 28m, which corresponds to a 60 % solution (nucleation concentration). At this concentration, the heat of dissolution of the salt is shown to be temperature independent (the heat capacity of dissolution is zero). This means that the entropy of dissolution is also temperature independent. Relative partial enthalpies are determined for the components of the H2O-NH4Cl system over the entire range of compositions at 248–373 K. The excess enthalpy of the 60 % solution has extreme values of 810 J/mol, 261 J/mol, −184 J/mol, and −553 J/mol at 273 K, 298 K, 323 K, and 348 K, respectively. At 312 K, HE ≈ 0. At 298 K, the excess heat capacity and volume show negative nonidealities with a minimum at 60 % for CPE (−19.7 J/(mol·K)) and 57% for VE (−0.44 cm3/mol). The composition dependence of the specific heat capacity (in relation to a unit of weight) has a minimum at an equimolar salt:water ratio.

Partial and integral enthalpies of mixing in the liquid Ag–In–Sn–Zn quaternary alloys

The partial and integral enthalpies of mixing of liquid quaternary Ag–In–Sn–Zn alloys have been measured at 500 °C along seven ternary sections: In0.450Sn0.450Zn0.100, In0.375Sn0.375Zn0.250, In0.333Sn0.333Zn0.334, In0.225Sn0.550Zn0.225, In0.100Sn0.800Zn0.100, In0.550Sn0.225Zn0.225 and In0.800Sn0.100Zn0.100. The measurements were carried out using a Calvet-type microcalorimeter and drop calorimetric technique. Additionally, the enthalpies of mixing of the liquid Ag–In–Sn–Zn have been calculated using the traditional Kohler, Muggianu, Toop and Hillert geometric models and compared to the experimental one.

The reaction enthalpy of hydrogen dissociation calculated with the Small System Method from simulation of molecular fluctuations.

We show how we can find the enthalpy of a chemical reaction under non-ideal conditions using the Small System Method to sample molecular dynamics simulation data for fluctuating variables. This method, created with Hill's thermodynamic analysis, is used to find properties in the thermodynamic limit, such as thermodynamic correction factors, partial enthalpies, volumes, heat capacities and compressibility. The values in the thermodynamic limit at (T,V, μj) are then easily transformed into other ensembles, (T,V,Nj) and (T,P,Nj), where the last ensemble gives the partial molar properties which are of interest to chemists. The dissociation of hydrogen from molecules to atoms was used as a convenient model system. Molecular dynamics simulations were performed with three densities; ρ = 0.0052 g cm(-3) (gas), ρ = 0.0191 g cm(-3) (compressed gas) and ρ = 0.0695 g cm(-3) (liquid), and temperatures in the range; T = 3640-20,800 K. The enthalpy of reaction was observed to follow a quadratic trend as a function of temperature for all densities. The enthalpy of reaction was observed to only have a small pressure dependence. With a reference point close to an ideal state (T = 3640 K and ρ = 0.0052 g cm(-3)), we were able to calculate the thermodynamic equilibrium constant, and thus the deviation from ideal conditions for the lowest density. We found the thermodynamic equilibrium constant to increase with increasing temperature, and to have a negligible pressure dependence. Taking the enthalpy variation into account in the calculation of the thermodynamic equilibrium constant, we found the ratio of activity coefficients to be in the order of 0.7-1.0 for the lowest density, indicating repulsive forces between H and H2. This study shows that the compressed gas- and liquid density values at higher temperatures are far from those calculated under ideal conditions. It is important to have a method that can give access to partial molar properties, independent of the ideality of the reacting mixture. Our results show how this can be achieved with the use of the Small System Method.

Thermodynamic properties of alloys of the Ni-Sc and Ni-Y systems

Partial and integral enthalpies of mixing for Ni-Y melts at 1775 K (0 < xY < 0.34), 1850 K (0.72 < xY < 1) and Ni-Sc at 1880 K (0 < xSc < 0.35, 0.51 < xSc < 1) are determined by means of calorimetry. Thermodynamic properties of liquid and solid alloys and phase diagrams of Ni-Sc(Y) systems in wide ranges of concentration and temperature are modeled using the ideal associated solution theory. It is found that the activities of components exhibit strong negative deviations from the Raoult’s law.

Simulation of supercritical water–hydrocarbon mixing in a cylindrical tee at intermediate Reynolds number: Formulation, numerical method and laminar mixing

The objective of this work is to study the flow dynamics and mixing of supercritical water and a model hydrocarbon (n-decane), under fully miscible conditions, in a small scale cylindrical tee mixer (pipe ID=2.4mm), at an intermediate inlet Reynolds number of 500 using 3-D CFD simulations. A Peng–Robinson EoS with standard van der Waals mixing rules is employed to model the near-critical thermodynamics with the mixture binary interaction parameter obtained from a Predictive Peng–Robinson EoS using group contribution theory (PPR78). The n-decane stream is introduced at the colder temperature of 700K to ensure operation above the Upper Critical Solution Temperature (UCST, 632K) of the water n-decane system while the water stream enters at a higher temperature of 800K. Under these conditions, the flow in the tee mixer remains laminar and steady-state is reached. Mixing occurs predominantly due to the circulating action of a counter-rotating vortex pair (CVP) in the body of the hydrocarbon jet entering from the top. This CVP is formed due to the reorientation of the streamwise vorticity pre-existing within the hydrocarbon jet as it flows down the vertical pipe of the tee junction. The advective transport is further assisted by a secondary flow of water from the bottom stream, around the hydrocarbon jet, toward the space vacated near the top of the downstream pipe section by the downward motion of the HC jet. The CVP becomes progressively weaker due to vorticity diffusion as it is advected downstream and beyond 10–12 diameter lengths downstream of the mixing joint, transport is mainly controlled by molecular diffusion. It was found that the variations of density and transport properties with temperature do not have a significant impact on the flow and mixing dynamics for a ΔT=100K between the two streams. Local cooling of the fluid mixture was also observed in the mixing of water and n-decane streams entering at the same temperature (initially isothermal). This cooling effect is due to the diffusion of species along a gradient in their partial enthalpy in the mixture. Such gradients in species partial enthalpies are non-zero under near-critical conditions even for initially isothermal flows due to the non-ideality of the fluid mixture under these conditions. This local heating/cooling effect at near-critical conditions could give rise to unexpected formation of phases when operating close to critical points.

A study of the hydration of ribonuclease A using isothermal calorimetry

This work is part of a systematic study undertaken to find the excess thermodynamic functions of binary protein–water systems. Isothermal calorimetry and water sorption measurements were applied to characterize the hydration dependencies of the excess thermodynamic functions. The advantages of our methodology are (i) we are able to simultaneously determine the excess partial quantities of water and proteins; (ii) these thermodynamic quantities can be determined in the entire range of water content. Here, in particular, the excess partial enthalpies of water and bovine pancreatic ribonuclease A (RNase A) have been determined. The excess partial enthalpies for RNase A are compared with the published data for several unrelated globular proteins (lysozyme, chymotrypsinogen A, serum albumin, lactoglobulin). These biomacromolecules represent a series of proteins in which the hydrophobicity of proteins is gradually changed in a wide range. It was found that the excess partial quantities for the studied proteins are determined by the hydration of the hydrophilic and hydrophobic protein groups. The more hydrophilic a protein, the more significant a hydrophilic hydration contribution is and vice versa. RNase A is the most hydrophilic protein under the study. This protein has the most significant hydrophilic hydration contribution. Lactoglobulin is the most hydrophobic protein under the study. This protein has the most significant hydrophobic hydration contribution.

The Enthalpies of Mixing of Liquid Ni-Sn-Zn Alloys.

The partial and integral enthalpies of mixing of liquid ternary Ni-Sn-Zn alloys were determined. The system was investigated along two sections x Ni/x Sn ≈ 1:9, x Ni/x Sn ≈ 1:6 at 1073 K and along two sections x Sn/x Zn ≈ 9:1, x Sn/x Zn ≈ 4:1 at 873 K. The integral enthalpy of mixing at each temperature is described using the Redlich-Kister-Muggianu model for substitutional ternary solutions. In addition, the experimental results were compared with data calculated according to the Toop extrapolation model. The minimum integral enthalpy of approx. −20000 J mol-1 corresponds to the minimum in the constituent binary Ni-Sn system, the maximum of approx. 3000 J mol-1 is equal to the maximum in the binary Sn-Zn system.

Thermodynamic properties of Eu-Pt and Al-Eu-Pt melts

The partial and integral enthalpies of mixing of Eu-Pt melts were determined by calorimetry at 1300 K in the composition range 0 < xPt < 0.36. The first partial enthalpy of mixing of Pt was found to be −171 ± 2 kJ/mol. The thermodynamic properties of the Eu-Pt melts were modeled in terms of ideal associated solution theory in wide composition and temperature ranges. The results indicate that the activities of the components have large negative deviations from Raoult’s law and that the integral Gibbs energy and enthalpy of mixing have a minimum near xPt = 0.7. The enthalpy and excess Gibbs energy of mixing of Al-Eu-Pt ternary melts were modeled using our and others’ data and Kohler’s equation.

The impact of oxygen nonstoichiometry upon partial molar thermodynamic quantities in PrBaCo2O5+δ

The coulometric titration data are utilized in order to calculate changes of oxygen partial entropy and enthalpy in PrBaCo2O5+δ with variations of oxygen content and temperature. The thermodynamic equilibrium of the cobaltite with the ambient gas phase is analyzed based on the interface of oxygen exchange and oxidation, and the intrinsic reaction of thermal excitation of Co3+ cations. The partial thermodynamic functions of the movable oxygen in PrBaCo2O5+δ are shown to be interrelated with the thermodynamic parameters of the defect formation reactions. The existence of a band gap of about 0.4eV in the electronic spectrum of the cobaltite follows from a favorable comparison of the calculated and experimental dependencies of the partial thermodynamic functions of the movable oxygen.

Thermodynamic properties of melts of the binary Ag(Au)-Sm systems

The enthalpies of mixing for liquid alloys of the Ag-Sm system are determined by isoperibolic calorimetry at 1450–1506 K in the 0.46 < x Sm < 1 range of concentrations. The partial and integral enthalpies of mixing for melts of the Ag-Sm system are obtained over the whole range of concentrations. The activities of components and the entropy of mixing in melts of the Ag-Sm system at 1506 K are calculated using a model of ideal associated solutions (IAS). The partial and integral enthalpies of mixing for melts of the Ag-Sm system, the activities of the components, and the molar fractions of associates in them are calculated using the IAS model. It is concluded that the thermodynamic activities of components in melts of the Ag (Au)-Sm system at 1506 K exhibit great negative deviation from the ideal behavior, and the enthalpies of mixing indicate there are considerable exothermal effects.

Thermodiffusion in binary liquids: the role of irreversibility

We study thermal diffusion in binary mixtures in the framework of non-equilibrium thermodynamics. Our formal result displays the role of partial enthalpies hi and Onsager’s generalized mobilities Ai. The ratio A1/A2 provides a measure for the irreversible character of thermal diffusion. Comparison with experimental data on benzene, cyclohexane, toluene and n-alkanes shows that irreversibility is essential for thermal diffusion, and in particular for the isotope effect.

Enthalpy of mixing of liquid Ag–Bi–Cu alloys at 1073 K

The Ag–Bi–Cu system is among those ternary systems which have not been fully studied yet, in particular the thermodynamic description of the liquid phase is missing. Partial and integral enthalpies of mixing of liquid ternary Ag–Bi–Cu alloys were determined over a broad composition range along six sections: x(Ag)/x(Bi)=0.25, 1, 4; x(Ag)/x(Cu)=1.5; x(Bi)/x(Cu)=1.86, 4. Measurements were carried out at 1073K using two Calvet type microcalorimeters and drop calorimetric technique. It was found that integral enthalpies of mixing are small and endothermic, similarly to limiting binary alloys. The ternary data were fitted on the basis of an extended Redlich–Kister–Muggianu model for substitutional solutions. There are no significant additional ternary interactions.