Positive Excess Volumes Research Articles

Excess mixing volume, microstrain, and stability of pyrope-grossular garnets

Synchrotron X-ray diffraction (XRD) was used to measure the unit-cell parameters of synthetic pyrope (Mg3Al2Si3O12), grossular (Ca3Al2Si3O12), and four intermediate garnet solid solutions. Garnets synthesized dry in multi-anvil (MA) apparatus at 6 GPa show irregular asymmetric positive quenchable excess volumes, with binary Margules parameters W V grossular = 2.04 ± 0.14 cm3/mol, and W V pyrope = 4.47 ± 0.15 cm3/mol. The two-parameter Margules equation is only an approximate description of the excess volumes in the pyrope-grossular garnets from this study and from the literature. The values for intermediate garnets in this report are roughly a factor of ~3 larger than previous literature reports of excess volumes of garnets grown at piston-cylinder (PC) pressures (2–4 GPa) with hydrothermal assistance. The discrepancy between our large dry excess volumes and the smaller hydrothermally assisted syntheses previously reported in the literature may be due in part to the hydrothermal assistance. When we do damp syntheses, we too get small excess volume. Although dampness produces smaller excess volumes, the mechanism by which this is achieved remains to be discovered. Does dampness relieve microstrains to relax excess volumes? Analysis of synchrotron X-ray diffraction profiles by using Williamson-Hall plots to test for microstrain shows that peak width does change with dampness and with garnet composition. Microstrain in the garnet structure, rather than grain size variation, is the principal reason for the observed XRD peak broadening. Damp garnets at Py60Gr40 have less microstrain and lower excess volume than dry Py60Gr40, in accord with the working hypothesis that dampness is responsible for diminished excess volume through strain relief. However garnets with compositions Py80Gr20 and Py20Gr80, close to the negligibly strained end-members pyrope (Py100) and grossular (Gr100), have large microstrains but relatively small excess volume. This is in contrast to Py40Gr60, which has the largest excess volume but almost no microstrain. (The end-members have no excess volume, by definition, and little microstrain.) This uncorrelated behavior demonstrates that microstrain in general is not directly related to the excess volumes, whatever else dampness may do to a specific composition, for instance introduce a small amount of clinopyroxene into the mode that partitions Ca preferentially away from garnet. Thus the mechanism responsible for the difference between our large excess volumes and the smaller ones in the literature may not be as complete or as simple as dampness relieves microstrain and relaxes excess volume. Our dry intermediate garnets have already been relieved of their microstrain by some other mechanism than dampness and still have large excess volume. The state of Ca-Mg ordering may also change, and we show that this may have a small effect on the excess volume through experiments using variable synthesis time and temperature. A potential test for whether our large, complex excess volumes, of whatever origin, are real (or not) is whether the rise of the solvus with pressure is better described by our large excess volumes or those smaller ones in the literature. We observe garnet phase exsolution at 8 GPa and show it to be reversible, at a temperature consistent with theoretical calculation using the large mixing volume presented in the current study.

Non-empirical phase equilibria in the Cr–Mo system: A combination of first-principles calculations, cluster expansion and Monte Carlo simulations

In this work, the low temperature part of the Cr–Mo phase diagram is calculated by a combination of first-principles calculations, cluster expansion, and Monte Carlo simulations without the use of empirical parameters. In brief, the miscibility gap in the bcc phase is computed through lattice Monte Carlo simulations with the energetics of the Cr–Mo system represented by cluster expansion Hamiltonians, wherein the Hamiltonians are firstly constructed using first-principles calculations of formation energies for supercells of various bulk compositions. It is demonstrated that the onset (critical) temperature of the miscibility gap is preliminarily computed to be Tc = 1720 K, and is significantly decreased to 1150 K once excess vibrational contribution to the free energy is considered. The resulting solid-state miscibility gap of the Cr–Mo binary system, largely improved by the contributions of atomic relaxation and positive excess volume of mixing in the Cr–Mo bcc alloys, also favors the approaches that extrapolate the Gibbs energy of the bcc phase retrieved at high temperatures, as in the CALPHAD method.

Densities and Viscosities of Binary Mixtures Containing Ethyl Formate and 2-Alkanols: Friction Theory and Free Volume Theory

The present study reports the densities and viscosities of mixing at various temperatures [(293.15 to 323.15) K] for mixtures composed of ethyl formate and 2-alkanols (from 2-propanol to 2-pentanol). From these measurements, excess molar volumes VmE and viscosity deviations Δη were calculated. These results were fitted to Redlich–Kister type polynomials. Positive excess molar volumes and negative viscosity deviations for studied mixtures indicate that no strong specific interactions occur in the mixtures. The data of viscosities have been used to study the performance of two viscosity models. The evaluated models are friction theory and free volume theory. Overall two models can describe the fluid viscosity with good accuracy. Results show that the performance of friction theory for correlating the viscosities is more satisfactory.

Thermo-compression of pyrope-grossular garnet solid solutions: Non-linear compositional dependence

Unit-cell parameters of a series of synthetic garnets with the pyrope, grossular, and four intermediate compositions were measured up to about 900 K and to 10 GPa using synchrotron X-ray powder diffraction. Coefficients of thermal expansion of pyrope-grossular garnets are in the range 2.10–2.74 × 10−5 K−1 and uniformly increase with temperature. Values for the two end-members pyrope and grossular are identical within experimental error 2.74 ± 0.05 × 10−5 K−1 and 2.73 ± 0.01 × 10−5 K−1, respectively. Coefficients of thermal expansion for intermediate compositions are smaller than those of end-members and are not linearly dependent on composition. Bulk modulus of grossular is K = 164.3(1) GPa (with K ′ the pressure derivative of the bulk modulus fixed to 5.92) and bulk modulus of pyrope is K = 169.2(2) GPa (with K ′ fixed to 4.4) using a third-order Birch-Murnaghan equation of state, which are consistent with previously reported values. The bulk moduli of garnets of intermediate composition are between ~155 and ~160 GPa, smaller than those of the end-members no matter which K ′ is chosen. The compositional dependence of bulk modulus resembles the compositional dependence of thermal expansion. Intermediate garnets on this binary have large positive excess volume, which makes them more compressible. We find that excess volumes in the pyrope-grossular series remain relatively large even at high pressure (~6 GPa) and temperature (~800 K), supporting the observation of crystal exsolution on this garnet join. The curiously “W”-shaped compositional variation of thermal expansion and bulk modulus is anti-correlated with the compositional dependence of microstrain documented in our companion paper (Du et al. in preparation) on the excess volumes in this series of garnets. Minimum thermal expansions and bulk moduli go with maximum microstrains.

First-principles study of energy and atomic solubility of twinning-associated boundaries in hexagonal metals

Twinning-associated boundaries (TB), {101¯n} coherent twin boundaries (CTB) and the coherent basal–prismatic (CBP) boundary in six hexagonal metals (Cd, Zn, Mg, Zr, Ti and Be) are studied using first-principles density function theory, with the focus on the structural character of TB and the solute’s solubility at TB. Regarding the structure and energy of TB, the formation of TB is associated with the creation of an excess volume. All six metals show positive excess volume associated with (101¯1) and (101¯3) CTB, but the excess volume associated with (101¯2) CTB and CBP can be positive or negative, depending on the metal. The (101¯2) CTB has higher excess energy than (101¯1) and (101¯3) CTB for metals with c/a<8/3 , but lower for metals with c/a>8/3. More interestingly, CBP has lower excess energy than (101¯2) CTB for all metals. This is consistent with the recent finding concerning the pure-shuffle nucleation mechanism of (101¯2) twins. To understand solubility at TB, the solubility of solute atoms in Mg, Ti and Zr is calculated for solute positions in bulk, (101¯2) CTB and CBP boundaries. In general, solute atoms have better solubility at CTB and CBP than in bulk. Interestingly, the solubility of solute atoms changes linearly with normal strain at CBP, increasing with normal strain for solute atoms with a greater metallic radius than the matrix, and decreasing with normal strain for solute atoms with a smaller metallic radius than the matrix. This suggests that the distribution of solute atoms in bulk, CTB and CPB boundaries varies with stress state and, in turn, affects the mobility of TB.

Merger Speculation in Financial Media: The Valuation of Investigative Reporting

We study abnormal returns and volume in the days surrounding takeover speculation by financial media. Significantly positive price and volume responses two days after publication are observed. While most of this effect dissipates shortly thereafter, some excess returns remain impounded into the stock price. A study of the ex-post takeover probabilities suggests that a positive response is justified, as takeover probabilities for such firms subsequently increase. This evidence is consistent with the idea that financial media speculation can facilitate the release of useful private information to shareholders. However, significantly positive excess returns and volume in the few days prior to publication also suggests that certain shareholders may benefit disproportionately.

Enhanced CO2 Capture in Binary Mixtures of 1-Alkyl-3-methylimidazolium Tricyanomethanide Ionic Liquids with Water

Absorption of carbon dioxide and water in 1-butyl-3-methylimidazoliun tricyanomethanide ([C4C1im][TCM]) and 1-octyl-3-methylimidazolium tricyanomethanide ([C8C1im][TCM]) ionic liquids (ILs) was systematically investigated for the first time as a function of the H2O content by means of a gravimetric system together with in-situ Raman spectroscopy, excess molar volume (V(E)), and viscosity deviation measurements. Although CO2 absorption was marginally affected by water at low H2O molar fractions for both ILs, an increase of the H2O content resulted in a marked enhancement of both the CO2 solubility (ca. 4-fold) and diffusivity (ca. 10-fold) in the binary [C(n)C1im][TCM]/H2O systems, in contrast to the weak and/or detrimental influence of water in most physically and chemically CO2-absorbing ILs. In-situ Raman spectroscopy on the IL/CO2 systems verified that CO2 is physically absorbed in the dry ILs with no significant effect on their structural organization. A pronounced variation of distinct tricyanomethanide Raman modes was disclosed in the [C(n)C1im][TCM]/H2O mixtures, attesting to the gradual disruption of the anion-cation coupling by the hydrogen-bonded water molecules to the [TCM](-) anions, in accordance with the positive excess molar volumes and negative viscosity deviations for the binary systems. Most importantly, CO2 absorption in the ILs/H2O mixtures at high water concentrations revealed that the [TCM](-) Raman modes tend to restore their original state for the heavily hydrated ILs, in qualitative agreement with the intriguing nonmonotonous transients of CO2 absorption kinetics unveiled by the gravimetric measurements for the hybrid solvents. A molecular exchange mechanism between CO2 in the gas phase and H2O in the liquid phase was thereby proposed to explain the enhanced CO2 absorption in the hybrid [C(n)C1im][TCM]//H2O solvents based on the subtle competition between the TCM-H2O and TCM-CO2 interactions, which renders these ILs very promising for CO2 separation applications.

Carbon dioxide absorption in the ionic liquid 1-ethylpyridinium ethylsulfate and in its mixtures with another ionic liquid

Ionic liquids are a potential alternative of interest for the replacement of volatile organic compounds in the technologies currently used for the capture of carbon dioxide from gaseous streams. Most studies carried out to date on the absorption of CO2 by ionic liquids focus on imidazolium ionic liquids. Pyridinium ionic liquids can exhibit a similar CO2 absorption capacity, while optionally possessing some advantages over the imidazolium ones. In this work, we have investigated the ability of the ionic liquid 1-ethylpyridinium ethylsulfate ([C2py][EtSO4]) to absorb CO2 at 298.2K, up to a pressure of ca. 1.6MPa. In a strategy for optimisation of the solvent to be used in a CO2 absorption process, mixtures of [C2py][EtSO4] with the ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)amide ([C2mim][NTf2]), have been studied. For the mixtures [C2py][EtSO4]+[C2mim][NTf2], the variation of the CO2 solubility and of the thermal and physical properties have been analysed as a function of the composition of the mixture. Higher absorption capacity than that corresponding to the weighted average of the capacity of the pure ionic liquids is observed for these mixtures. This synergistic effect might be in connection, at least in part, with the positive excess molar volumes observed for the mixture.

Excess volume and heat of mixing in Cu-Ti liquid mixture

Molar excess volume of Cu-Ti liquid mixture has been investigated to elucidate how the excess volume in binary alloys is related to mixing enthalpy and microscopic interactions. Cu-Ti is used as a key example for systems showing positive excess volume and negative mixing enthalpy. For this purpose, the density of several Cu-Ti binary mixtures has been measured over the whole composition range by the containerless technique of electromagnetic levitation as a function of temperature. A linear temperature dependence of the density has been found for all investigated alloys. In addition, the density decreases with increasing Ti content in the alloys, showing a negative deviation from the ideal solution model. As mentioned, a positive excess volume was found whereas the enthalpy of mixing is negative. This behavior has been discussed in relation with chemical ordering and the role played by attractive and repulsive interactions in the system, according to previous results obtained by means of molecular dynamics simulation on binary dense fluids.

Volumetric behaviour of the (2,2,4-trimethylpentane + methylbenzene + butan-1-ol) ternary system and its binary sub-systems within the temperature range (298.15–328.15) K

Densities and speeds of sound of the (2,2,4-trimethylpentane+methylbenzene+butan-1-ol) ternary system as well as all its binary sub-systems were measured at four temperatures, namely 298.15K, 308.15K, 318.15K, and 328.15K at atmospheric pressure by a vibrating-tube densimeter DSA5000. The binary (isooctane+toluene) system was studied previously. Excess quantities (molar volume, adiabatic compressibility, and isobaric thermal expansivity) of the mixtures studied were calculated from the experimental densities and speed of sounds. The excess molar volume data were correlated using the Redlich–Kister equation. Both the positive and S-shaped excess molar volume curves were found for the systems studied. The excess molar volumes versus concentration of binary systems differed in the shape and temperature dependence. The experimental binary data were compared with literature data. The experimental excess molar volumes were analyzed by means of the Extended Real Associated Solution (ERAS) model. The experimental data and the ERAS model can help to estimate real behaviour of the systems studied.

Density and thermal expansion of Cr–Fe, Fe–Ni, and Cr–Ni binary liquid alloys

Densities and their temperature coefficients of liquid Cr–Fe, Fe–Ni, and Cr–Ni binary alloys have been measured containerless using the technique of electromagnetic levitation. Data have been obtained in a wide temperature range including the supercooled region. The density measurements indicate that these binary systems have a small and positive excess volume, whereas the excess free energies are negative. The temperature coefficients of these alloys can be estimated from those of the pure components. Hence, possible contributions from the temperature dependence of the excess volume can be ignored to calculate the temperature coefficient of density.

The thermodynamic link between excess ultrasound speed, excess molar volume and excess molar isentropic compression of liquid mixtures

A thermodynamic relationship among excess ultrasound speed, excess molar volume and excess molar isentropic compression of liquid mixtures is revisited. The consequences of this relationship, which stems from the Newton–Laplace equation, are discussed. The constraints for possible values taken by Balankina's relative excess properties, that is, ratios between excess and ideal quantities, are further developed. It is demonstrated that, besides the requirement for, if two of these properties attain extreme values at a common exact composition, then the remaining one also takes an extreme value at that composition, further constraints apply to the signs of their rate of change with composition. Using accurate literature data for a binary liquid mixture possessing small positive relative excess molar volumes over the entire composition range, coupled with large positive relative excess ultrasound speeds and large negative relative excess molar isentropic compressions, it is shown that the thermodynamic equations under scrutiny are numerically verified. It is concluded that present theoretical developments can confidently be used for testing the thermodynamic consistency of experimentally determined excess properties of liquid mixtures.

Volumetric Properties of Glycerol Formal + Propylene Glycol Mixtures at Several Temperatures and Correlation with the Jouyban–Acree Model

Molar volumes, excess molar volumes, and partial molar volumes were investigated for glycerol formal + propylene glycol mixtures from density measurements at temperatures from (278.15 to 313.15) K. Mixture compositions were varied in 0.05 in mass fraction of both components. Excess molar volumes were fitted to the Redlich–Kister equation and compared with literature values for other systems. The system exhibits positive excess volumes probably due to increased non-specific interactions. The effect of temperature on the different volumetric properties studied was also analyzed. In addition, the volumetric thermal expansion coefficients were calculated. The Jouyban–Acree model was used for density and molar volume correlations of the mixtures at the different experimental temperatures. The mean relative deviations between experimental and calculated data are 0.04±0.03 and 0.04 ±0.05, respectively, for the density and molar volumes, using the minimum number of data points, the Jouyban–Acree model can predict density and molar volume with acceptable accuracies (0.06±0.04 and 0.08±0.05, respectively).

Density of Multicomponent Melts Measured by Electromagnetic Levitation

A significant amount of time and costs could be saved on the development of new materials through numerical modeling, if there was an understanding on how their thermophysical properties change with a change of composition. Here, we report on systematic measurements of the density for a number of liquid metallic alloys. These measurements were carried out containerlessly using the technique of electromagnetic levitation. Systems were investigated from mono-atomic liquid metals, to binary and ternary alloys. The results are discussed using the excess volume as the key mixing parameter. We found that there is no strict rule for liquid alloys, whether or not the excess volume should be positive, negative, or zero. However, a clear tendency was observed: immiscible systems tend to exhibit a positive excess volume, strongly mixing systems show a negative excess volume, and alloys of which the components are chemically similar, exhibit an excess volume of almost zero.

Effect of mixing rule boundary conditions on high pressure (liquid + liquid) equilibrium prediction

We examine the prediction of high pressure (liquid + liquid) equilibrium (LLE) from the Peng–Robinson equation with three excess Gibbs free energy ( G ex)-based mixing rules (MR): the first order modified Huron–Vidal (MHV1), the Wong–Sandler (WS), and a hybrid of these two (referred to as G ex B 2). These mixing rules differ by the boundary conditions used for determination of the temperature and composition dependence of parameters a and b in the PR EOS. The condition of matching the excess Gibbs free energy from the EOS at zero pressure to that from the G ex model, used in MHV1 and G ex B 2 MR, leads to a similar miscibility gap from PR EOS and the G ex model used. On the other hand, the condition of matching excess Helmholtz energy from the EOS at infinite pressure to that from the G ex model, used in the WS MR, shows remarkable deviations. The condition of quadratic composition dependence in the second virial coefficient ( B 2), used in WS and G ex B 2 MR, allows for both positive and negative values in the molar excess volume. Depending on the mixture, either the increase or decrease of the miscibility gap with pressure can be observed when the WS or the G ex B 2 MR is used. The condition of linear combination of molecular sizes of each component used in the MHV1 MR, however, often leads to small, positive molar excess volumes. As a consequence, the predicted LLE from using the MHV1 MR are insensitive to pressure. Therefore, we find that the G ex B 2 mixing rule provides the best predictive power for the LLE over a wide range of temperature and pressure.

Positive excess volume of liquid Fe–Cu alloys resulting from liquid structure change

The densities of liquid Fe–Cu alloy system were investigated in the temperature range of 1200–2000 K, covering both a superheating range and a large metastable undercooled regime. For all the Fe x Cu 100 − x ( x = 0 , 10, 20, 30, 40, 50, 60, 70, 80, 90, 100) alloys, the density is a linear function of temperature. In all the cases, the densities of Fe–Cu alloys with different compositions are smaller than those of ideal solution. This indicates that Fe–Cu alloys deviate from ideal solution and have positive excess volumes. Furthermore, the liquid structure change is described by the pair distribution function and the coordinate number for different liquid Fe–Cu alloys. It is revealed that the atomic packing degree is responsible for the positive excess volume. Moreover, the thermal expansion coefficients are also derived and display a rise with the increase of Cu content.

Glass transitions in binary drug + polymer systems

To evaluate miscibility, glass transition temperatures T g have been determined for two binary polymer (Plasdone S-630 copovidone or Eudragit® E) + drug systems as a function of composition. Each polymer serves for encapsulation of the anti-HIV drug Efavirenz. In both systems the T g vs. drug concentration diagrams are s-shaped. T gs of Efavirenz + Plasdone mixtures with drug mass fraction below φ drug = 0.6 are above linear values. This implies enhanced thermal and mechanical stability—an advantage for the drug encapsulation. In the other system, a strong negative deviation of T gs is observed over the entire compositional range and explained by positive excess mixing volumes. Several equations are used to represent T g vs. composition diagrams, but only one (Brostow et al. Mater Lett 2008; 62:3152) provides reliable results.

Liquid–liquid miscibility and volumetric properties of aqueous solutions of ionic liquids as a function of temperature

The volumetric properties of seven {water + ionic liquid} binary mixtures have been studied as a function of temperature from (293 to 343) K. The phase behaviour of the systems was first investigated using a nephelometric method and excess molar volumes were calculated from densities measured using an Anton Paar densimeter and fitted using a Redlich–Kister type equation. Two ionic liquids fully miscible with water (1-butyl-3-methylimidazolium tetrafluoroborate ([C 1C 4Im][BF 4]) and 1-ethyl-3-methylimidazolium ethylsulfate ([C 1C 2Im][EtSO 4])) and five ionic liquids only partially miscible with water (1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C 1C 2Im][NTf 2]), 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C 1C 4Im][NTf 2]), 1-butyl-3-methylimidazolium hexafluorophosphate ([C 1C 4Im][PF 6]), 1-butyl-3-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide ([C 1C 4Pyrro][NTf 2]), and butyltrimethylammonium bis(trifluoromethylsulfonyl)imide ([N 4111][NTf 2])) were chosen. Small excess volumes (less than 0.5 cm 3 · mol −1 at 298 K) are obtained compared with the molar volumes of the pure components (less than 0.3% of the molar volume of the pure ionic liquid). For all the considered systems, except for {[C 1C 2Im][EtSO 4] + water}, positive excess molar volumes were calculated. Finally, an increase of the non-ideality character is observed for all the systems as temperature increases.

Insights into the Coal Extractive Solvent N-Methyl-2-pyrrolidone + Carbon Disulfide

A wide set of experimental and computational tools were used to characterize the N-methyl-2-pyrrolidone (NMP) + carbon disulfide mixed solvent in the full composition range. The interest in this solvent rose from its very efficient use for coal extraction through a mechanism still not fully understood. Thermophysical properties at ambient pressure together with pressure-volume-temperature (PVT) behavior were measured with the objective of providing the required data for the industrial use of the mixed fluid and to get insight into the fluid structure at the molecular level. NMR, FTIR, and solvatochromic studies were performed together with microwave dielectric relaxation spectroscopy (DRS) measurements, thus providing more information on the fluid's structure and allowing one to relate the molecular level behavior with the measured macroscopic properties. Moreover, density functional theory (DFT) and classical molecular dynamics simulations (MD) were used to obtain a detailed picture of the intermolecular interactions within the fluid, at short and long ranges, and of other relevant features leading to the structure of the studied system. The whole study leads to a fluid's picture in which carbon disulfide hinders the development of NMP/NMP intermolecular dipolar interactions, thus increasing the monomer population. We should remark that some properties reported in thismore » work are in remarkable disagreement with previously reported studies, the most important one being the positive excess molar volume in the whole pressure-temperature range studied, which contrasts with the negative values reported in the literature. Previously reported properties are hardly justified with a coherent molecular level picture, whereas the whole collection of properties reported in this work leads to a more reasonable fluid's structure. 56 refs., 17 figs., 2 tabs.« less

Effects of Fatty Acid Inclusion in a DMPC Bilayer Membrane

Free fatty acids in biomembranes have been proposed to be a central component in several cellular control and regulatory mechanisms. To elucidate some fundamental elements underlying this, we have applied molecular dynamics simulations and experimental density measurements to study the molecular packing and structure of oleic acid (HOA) and stearic acid (HSA) in fluid bilayers of dimyristoylphosphatidylcholine (DMPC). The experimental data show a small but consistent positive excess volume for fatty acid concentrations below 10 mol %. At higher concentrations the fatty acids mix ideally with fluid DMPC. The simulations, which were benchmarked against the densitometric data, revealed interesting differences in the structure and location of the fatty acids depending on their protonation status. Thus, the protonated (uncharged) acid is located rather deeply in the membrane with an average position of the carboxy group near the second carbon segment of the lipid chains with a typical end-to-end distance of 16-18 A. This structure of the fatty acid brings about a rather tight lateral packing in the mixed membrane and a moderate ordering and hence stretching of the lipid chains. Deprotonation of the fatty acids is associated with a pronounced movement of their carboxy group to a more hydrated position at the membrane interface and a lateral expansion driven by the mutual repulsion of the anions. These changes increase both the disorder and the degree of interdigitation of the lipid chains, and they make the membrane thinner by 2-3 A.