Difference In Partial Molar Volume Research Articles

Understanding of Void Formation in Cu/Sn-Sn/Cu System During Transient Liquid Phase Bonding Process Through Diffusion Modeling

Transient Liquid Phase (TPL) bounding of Sn foil sandwiched between two Cu foils involves, in the temperature range above the melting point of Sn (232 °C) and below 350 °C, the formation and the growth of two intermetallic compounds (IMCs) Cu6Sn5 and Cu3Sn and mostly unintended micro-pores. The present study aims to analyze the mechanism of void development during the soldering process through an experimental and modeling approach of diffusion-controlled IMC transformation. This modeling couples the diffusion process and the interface motion with the volume shrinkage induced by the difference of partial molar volumes of atoms between each phase. We also consider two types of inter-diffusion transports: (i) inter-diffusion based on the exchange of Cu and Sn atoms and (ii) inter-diffusion of Sn atoms with vacancies allowing Kirkendall void formation. The simulations of IMC growth performed correspond to a sequence of planar phase layers, where the distinctive scallop morphology of the Cu6Sn5 layer is described through an analytical function allowing to quantify the grain boundary diffusion pathway. We take into account of the volume diffusion mechanism for Cu3Sn intermetallic. For Cu6Sn5 intermetallic two mechanisms are considered, volume diffusion and grain boundary diffusion, limited by grain growth. The simulations of IMC growth kinetics, for different transport scenarios, are compared to the experimental evolving morphologies to determine the most likely mechanism of micro-void formation.

Computer simulation of the interphase interaction in metal alloys

In this article we propose a mesoscopic model of the interphase interaction in binary metal alloys. The difference of partial molar volumes of the components of alloy was taken into account during the mathematical model building. The simulated sample is represented as a two-dimensional region, divided into square cells of nanometric size that are characterized by the value of concentration and belonging to the phase. Intermediate phase of alloy can include arbitrary forms. The proposed mesoscopic model provides a phase cells change and the implementation of the law of conservation of matter. Software implementation of the developed model is executed. The results of computer simulation are compared with the results of laboratory experiments interphase interaction in a binary metal alloy Mg-Al. The obtained computer model allows a numerical study of the evolution of the phase composition of alloy in the process of diffusion interaction.

Pressure effects on the structure, kinetic, and thermodynamic properties of heat-induced aggregation of protein studied by FT-IR spectroscopy

Pressure can retrain the heat-induced aggregation and dissociate the heat-induced aggregates. We observed the aggregation-preventing pressure effect and the aggregates-dissociating pressure effect to characterize the heat-induced aggregation of equine serum albumin (ESA) by FT-IR spectroscopy. The results suggest the α-helical structure collapses at the beginning of heat-induced aggregation through the swollen structure, and then the rearrangement of structure to the intermolecular β-sheet takes place through partially unfolded structure. We determined the activation volume for the heat-induced aggregation (ΔV# = +93 ml/mol) and the partial molar volume difference between native state and heat-induced aggregates (ΔV=+32 ml/mol). This positive partial molar volume difference suggests that the heat-induced aggregates have larger internal voids than the native structure. Moreover, the positive volume change implies that the formation of the intermolecular β-sheet is unfavorable under high pressure.

Temperature and Pressure Dependence of Alanine Dipeptide Studied by Multibaric−Multithermal Molecular Dynamics Simulations

We applied the multibaric-multithermal (MUBATH) molecular dynamics (MD) algorithm to an alanine dipeptide in explicit water. The MUBATH MD simulation covered a wide range of conformational space and sampled the states of PII, C5, alphaR, alphaP, alphaL, and C7(ax). On the other hand, the conventional isobaric-isothermal simulation was trapped in local-minimum free-energy states and sampled only a few of them. We calculated the partial molar enthalpy difference DeltaH and partial molar volume difference DeltaV among these states by the MUBATH simulation using the AMBER parm99 and AMBER parm96 force fields and two sets of initial conditions. We compared these results with those from Raman spectroscopy experiments. The Raman spectroscopy data of DeltaH for the C5 state against the PII state agreed with both MUBATH data with the AMBER parm96 and parm99 force fields. The partial molar enthalpy difference DeltaH for the alphaR state and the partial molar volume difference DeltaV for the C5 state by the Raman spectroscopy agreed with those for the AMBER parm96 force field. On the other hand, DeltaV for the alphaR state by the Raman spectroscopy was consistent with our AMBER-parm99 force-field result. All the experimental results fall between those of simulations using AMBER parm96 and parm99 force fields, suggesting that the ideal force-field parameters lie between those of AMBER parm96 and parm99.

Column chromatographic boron isotope separation at 5 and 17 MPa with diluted boric acid solution

Boron isotopic fractionation factor ( S) between boron taken up in strongly basic anion exchange resin and boron in aqueous solution was determined by breakthrough column chromatography at 5 and 17 MPa at 25 °C, using 0.1 mM boric acid solution as feed solution. The S values obtained were 1.018 and 1.012, respectively, which were smaller than the value reported by using the same chromatographic method at the atmospheric pressure at 25 °C with the boron concentration of 10 mM, but were larger than the values under the same condition with much higher concentration of 100 and 501 mM. Calculations based on the theory of isotope distribution between two phases estimated that 21% (5 MPa) and 47% (17 MPa) of boron taken up in the resin phase was in the three-coordinated B(OH) 3-form, instead of in the four-coordinated B(OH) 4-form, at high pressures even with a very diluted boric acid solution. We discussed the present results by introducing (1) hydration and (2) a partial molar volume difference between isotopic molecules. Borate may have been partially dehydrated upon transfer from the solution phase to the resin phase at high pressures, which resulted in smaller S values compared with those at the atmospheric pressure. Instead, it may be possible that the difference in the isotopic partial molar volume difference between B(OH) 3 and B(OH) 4 − caused the S value to decrease with increasing pressure.

Pressure effects on the heat-induced aggregation of equine serum albumin by FT-IR spectroscopic study: Secondary structure, kinetic and thermodynamic properties

Pressure can restrain the heat-induced aggregation and dissociate the heat-induced aggregates. We investigated the aggregation-preventing pressure effect and the aggregates-dissociating pressure effect to characterize the heat-induced aggregation of equine serum albumin (ESA) by Fourier transform infrared spectroscopy. The results suggest that the α-helical structure collapses at the beginning of heat-induced aggregation, then the rearrangement of structure from partially unfolded structure to the intermolecular β-sheet takes place through the activated state. We determined the activation volume for the heat-induced aggregation (Δ V ≠ = + 92 ± 8 ml mol − 1 ) and the partial molar volume difference between native state and heat-induced aggregates (Δ V N → HA = + 32 ml mol − 1 ). This positive partial molar volume difference suggests that the heat-induced aggregates have larger internal voids than the native structure. Moreover, the positive volume change implies that the formation of the intermolecular β-sheet is unfavorable under high pressure. We also determined the free energy profile of ESA. This energy profile explains the restriction of the formation of heat-induced aggregates by pressure. These results explain the structural differences between heat-induced aggregates with intermolecular β-sheet and pressure-induced aggregates without intermolecular β-sheet.

Diels-Alder reaction volumes in the solid state and solution

The densities of anthracene, tetracyanoethylene, maleic anhydride, N-phenylmaleineimide, trans, trans-1,4-diphenylbuta-1,3-diene, and their Diels-Alder adducts were measured in the solid state and in solution at 25 °C. The reaction volumes in the solid state were calculated from the difference in molar volumes. They turned out to be low, close to each other (−4 to −11 cm3 mol−1), and slightly different from the reaction volumes (−8±1 cm3 mol−1) calculated from the van der Waals radii. The reaction volumes in solutions (−15 to −32 cm3 mol−1) were found from the difference in partial molar volumes of the reactants in dioxane, acetonitrile, and 1,2-dichloroethane, The experimental Diels-Alder reaction volumes in solution are determined not only by the formation of new bonds in an adduct: a considerably higher contribution (to 75%) is made by a change in the volume of intermolecular empty spaces in solution on going from reactants to adducts.

High-sensitivity sapphire cells for high pressure NMR spectroscopy on proteins

High pressure NMR spectroscopy is a most exciting method for studying the structural anisotropy and conformational dynamics of proteins. The restricted volume of the high pressure glass cells causes a poor signal to noise ratio which up to now renders the application of most of the multidimensional NMR experiments impossible. The method presented here using high strength single crystal sapphire cells doubles the signal-to-noise ratio and allows to perform high pressure NMR measurements more easily. As a first application the difference of partial molar volumes caused by cis–trans-isomerisation of a prolyl peptide bond in the tetrapeptide Gly-Gly-Pro-Ala could be determined as 0.25 ml mol −1 at 305 K.

Hydrogen bonding in supercritical methanol studied by infrared spectroscopy

We report the first Fourier transform infrared spectroscopic studies of the hydrogen-bonding interactions in supercritical methanol and methanol/methanol-d1 mixtures. At 523 K and below ∼0.3 mol/l, methanol chiefly existed in a monomeric form. However, at 523 K and between ∼0.3 and 2 mol/l, in the regions of O–H, C–O, and C–H stretching vibrations, there were clear indications of methanol monomer–dimer equilibrium. The effect of temperature on the equilibrium constant was also investigated. As a result, the partial molar volume difference and enthalpy of the dimerization were estimated and correlated with the behavior of the methanol isothermal compressibility. It was also concluded that at 523 K and density higher than ∼15 mol/l, the hydrogen-bonding equilibrium started to shift toward larger aggregates.

Pressure effect on the rate and equilibrium constants of the Diels-Alder reaction 9-chloroanthracene with tetracyanoethylene

The pressure effect on the forward and backward rate constants and equilibrium constants of the Diels-Alder reaction of 9-chloroanthracene with tetracyanoethylene has been investigated in 1,2-dichloroethane up to 1000 kgcm −2 at 298.15 K. The reaction volume obtained from the pressure effect on equilibrium (−20.6 ±1.5 cm 3mol −1) and as difference of activation volumes of forward (−28.5±1.5) and backward (−6.5 ± 0.5) reaction (−22.0±1.5 cm 3mol −1) are in agreement with partial molar volume difference of adduct (255.5±1.5) diene (170.7±0.5) and dienophile (107.8±0.2) giving −23.0 ±2 cm 3mol −1.

The effect of pressure on the equilibrium in the Diels–Alder reaction between 9-chloroanthracene and tetracyanoethylene

Equilibrium constants for the Diels-Alder reaction of 9-chloroanthracene with tetracyanoethylene have been determined in the pressure range 0-970 kg cm-2 in 1,2-dichloroethane at 298 K and the value of the reaction volume (-20.6 ±1.5 cm3mol-1) has been compared with the difference in partial molar volume of the dienophile (107.8±0.2), diene (170.7±0.5) and adduct (255.5±1.5 cm3mol-1).

Pressure-Induced Isomerization of 2-(2‘-Hydroxyphenyl)benzoxazole in Solid Media

2-(2‘-Hydroxyphenyl)benzoxazole (HBO) has three isomers: a ketone (Kt), an enol (1) which is intramolecularly hydrogen bonded, and a second enol (2) which is not. Enol 1 does not emit but transforms in the excited state to the ketone Kt which can emit fluorescence or return by various paths to the ground state of enol 1. Enol 2 fluoresces but at atmospheric pressure is present, in general, in very low concentration except in hydrogen-bonding media. The fluorescence of HBO was measured as a function of pressure to 60 kbar in five media: poly(methyl methacrylate) (PMMA), poly(ethyl methacrylate) (PEMA), poly(butyl methacrylate) (PBMA), poly(2-hydroxyethyl methacrylate), (PHEMA), and poly(vinyl chloride) (PVCl). In all cases enol 2 is stabilized relative to enol 1 by pressure. With reasonable assumptions it was possible to extract ΔV̄, the difference in partial molar volume of enol 1 − enol 2, as a function of pressure. For the methacrylates ΔV̄ decreases strongly with increasing pressure. The indications are that enol 2, which hydrogen bonds to the methacrylate, has initially a smaller ΔV̄ but also the configuration has a smaller compressibility. In PVCl ΔV̄ is relatively small but independent of pressure.

Effects of hydrostatic pressure on the kinetics of electron transfer in an isolated system of chloroplast cytochrome bf complex, plastocyanin and P700

The effects of pressure on the kinetics of redox reactions in and around the chloroplast cytochrome bf complex were studied using a reconstituted system consisting of Photosystem I (PS I) particles, cytochrome bf complex and plastocyanin (PC), all derived from pea chloroplasts. There were no significant permanent effects of pressure in the range 0.1-191 MPa on the reaction kinetics, or on the shape of the absorption spectra of components studied. Discernable effects on rate-coefficients of increasing pressure were observed on the reduction of P700(+) by PC(I), on the reduction of PC(II) by ascorbate, and on the oxidation of decyl plastoquinol by the bf complex. The volumes of activation ΔV(#) were determined from the dependence of the rate-coefficient on pressure using: [Formula: see text] The volume of activation is the difference in partial molar volume between the activated state and the reactants for the redox reaction. Such data was sought to help define in detail those redox reactions and the corresponding activated states. For the reduction of P700(+) by PC(I) and the oxidation of decyl plastoquinol by the bf complex, the rate coefficient decreased with increase in pressure, whilst for the reduction of PC(II) by ascorbate it increased. The corresponding volumes of activation were 9.6±0.6×10(-6) m(3) mol(-1), 18±2×10(-6) m(3) mol(-1) and -14±1×10(-6) m(3) mol(-1), respectively. Much of the pressure-dependence of PC(II) reduction by ascorbate was ascribed to an increase in ascorbate ionisation with increase in pressure. There was little effect of pressure on the kinetics of oxidation of ferrocytochrome f by PC(II), or on the equilibrium constant of the redox pair ferrocytochrome f/ferricytochrome f: PC(II)/PC(I). Possible physical bases for these activation volumes are discussed, and they are compared with literature values.

Experimental study in the system albite-andalusite-quartz-NaCl-HCl-H 2O at 600°C and 400 to 2000 bars

The composition of aqueous fluid equilibrated with a mineral assemblage of quartz, albite, and andalusite was experimentally obtained at 600°C, with pressure ranging from 400 to 2000 bars and NaCl concentrations ranging from 0.05 to almost 100 m. This allowed us to determine 1. (1) the pressure dependence of the apparent equilibrium constant (Ka) of the following reaction under critical and subcritical conditions, 1 2 Al 2SiO 5 + 5 2 SiO 2 + 1 2 H 2O + NaCl = NaAlSi 3O 8 + HCl 2. (2) the composition of coexisting vapor and liquid phases in the NaCl-HCl-H 2O system. The Ka was obtained as the HCl NaCl concentration ratio in dilute fluid (〈 2 m). The equilibrium constant ( K) of the reaction, which is equivalent to the Ka with an assumption of a unit activity coefficient ratio of HCl and NaCl, varies from 0.013 at 2000 bars to 1.7 at 400 bars with ( ∂ lnK/ ∂P) being greater at lower pressure. The large pressure dependence of the equilibrium constant is attributed to the large difference in partial molar volumes of HCl and NaCl in the aqueous phase at high temperature and low pressure. The compositions of the coexisting vapor and liquid phases are graphically estimated on a diagram showing concentrations of NaCl and HCl by regarding the above reaction as a buffer reaction. The concentration ratio of HCl in vapor to liquid phase ( m HCl vapor m HCl liquid ) ranges from 1.5 at 1000 bars to 7 at 400 bars. The addition of HCl into the NaCl-H 2O system increases the critical pressure and also increases the concentration of NaCl in the vapor phase at low pressure. These results indicate that the effects of pressure are comparable but inverse to temperature effects and must be considered in modeling the geochemical structure of hydrothermal systems.

Interdiffusion and Kirkendall Effect in Cu–Sn Alloys

Interdiffusion coefficients in copper-rich copper-tin solid solutions containing up to 6 at% of Sn have been determined by Matano’s analysis in the temperature range between 973 and 1101 K using semi-infinite couples with Kirkendall markers consisting of pure copper and Cu–Sn alloys. An anomalously large Kirkendall effect reported by several authors has been shown to be an overestimation resulting from the disregard for the large difference in partial molar volumes between Cu and Sn in the alloy. Using the data on the interdiffusion coefficient, the marker shift, the partial molar volumes and Darken’s relation, the intrinsic diffusion coefficients, DSn, and DCu, in the Cu-alloys containing 0.9, 1.7, 3.1 and 4.9 at% of Sn have been determined, and the ratio of DSn⁄DCu has been found to be about three. In addition to the above experiments with semi-infinite couples, the intrinsic diffusion coefficients in the Cu-alloys containing 0.6, 1.4, 2.6 and 3.5 at% of Sn at 1089 K have been determined by Heumann’s method using finite thin plate couples. Using the tracer diffusion data in pure Cu and the value of DCu in the infinite dilution of Sn evaluated from the detailed concentration dependence of DCu thus obtained, the vacancy flow factor which is expressed by the ratio of the phenomenological coefficients of flux equations in the infinite dilution of Sn, (LCuSn⁄LSnSn)NSn=0, at 1014 and 1089 K, has been estimated to be −1.06−0.24+0.18 and −0.84−0.13+0.12, respectively. Such a negative large ratio suggests that the jump between a tin atom and a vacancy in copper is strongly correlated.