Molar Isothermal Compressibilities Research Articles

Two-dimensional core-softened model with water like properties. Study by thermodynamic perturbation theory

Thermodynamic properties of the particles interacting through smooth version of Stell-Hemmer interaction were studied using Wertheim's thermodynamic perturbation theory. The temperature dependence of molar volume, heat capacity, isothermal compressibility and thermal expansion coefficient at constant pressure for different number of bonding sites on particle were evaluated. The model showed water-like anomalies for all evaluated quantities, but thermodynamic perturbation theory does not properly predict the dependence of these properties at a fixed number of bonding points.

Liquid phase PVTx properties of (water + tert-butanol) binary mixtures at temperatures from 278.15 to 323.15 K and pressures from 0.1 to 100 MPa. II. Molar isothermal compressions, molar isobaric expansions, molar thermal pressure coefficients, and internal pressure

Molar isothermal compressions, molar isobaric expansions, molar coefficients of thermal pressure, and internal pressure were calculated over the whole concentration range of {water (1)+tert-butanol (2)} mixture at pressures from 0.1 to 100MPa and temperatures from 278.15 to 323.15K. It was revealed that the extremes, observed on concentration dependences of molar isothermal compression KT,m and molar isobaric expansion EP,m of the mixture, became more pronounced with pressure growth and temperature lowering. Values of molar thermal pressure coefficients of the mixture sharply rose at compositions with small TBA mole fraction and then decreased practically linearly with the alcohol content increasing. Temperature and pressure dependences of the mixture internal pressure were almost linear, and at low TBA concentrations changed significantly from the dependences of water, tert-butanol and their mixtures at large alcohol content.

Second-Order Derivatives of the Gibbs Energy for Liquid Mixtures of Alcohol + Heptane at Pressures up to 100 MPa

Second-order thermodynamic derivative properties, such as isobaric thermal molar expansions, isothermal and adiabatic molar compressibilities, and isochoric molar heat capacities of (ethanol, decan-1-ol, 2-methyl-2-butanol) + heptane mixtures at pressures up to 100 MPa and in the temperature range from 293.15 K to 318.15 K were derived from experimental speed-of-sound u(T, p), density ρ(T, p = 0.1 MPa), and isobaric heat-capacity Cp(T, p = 0.1 MPa) data using appropriate thermodynamic relations. Excess values for the given properties were calculated according to the criterion of thermodynamic ideality of a mixture (Douheret et al., Chem. Phys. Chem. 2, 148 (2001)), i.e., assuming that the chemical potential of component i in the ideal liquid mixture is equal to the chemical potential of component i in the mixture of perfect gases. The deviations from ideality for the mixtures under test have been explained in terms of the self-association of alcohols in solution which produces a strong departure from random mixing, the change in the non-specific interactions during mixing, and the packing effects.

Protein Conformational Intermediates Characterized with Novel High Pressure EPR and CD Techniques

Regulation of protein function is often linked to conformational intermediates that exist in equilibrium with the ground state. In many cases, these intermediate states exist as only a small fraction of the total protein conformational ensemble. It has been shown that high hydrostatic pressure is an invaluable tool for populating low-lying, excited states to levels amenable to spectroscopic detection. Here we demonstrate the usefulness of high pressure for populating such states as monitored by two novel techniques: High pressure electron paramagnetic resonance spectroscopy (EPR) and high pressure circular dichroism (CD). High pressure EPR was used in conjunction with site-directed spin labeling to monitor changes in local protein structure with applied pressure (up to 400 MPa). The relative partial molar volume and isothermal compressibility of each conformational substate was determined from the pressure dependence of the equilibrium constant determined from the continuous wave EPR spectra. High pressure CD was employed to detect global changes in secondary and tertiary structure at elevated pressure (up to 200 MPa). The combination of site-specific and global information provided by these techniques provides a more complete description of pressure excited intermediate states. Data from apomyoglobin and a cavity containing mutant (L99A) of T4 lysozyme are presented.

On the existence of a third-order phase transition beyond the Andrews critical point: A molecular dynamics study

The possibility of the existence of a gas-liquid third order phase transition for fluids is becoming a subject of growing interest. Experimental work suggests its existence for specific systems while recent theoretical models claim its universality. In this work, we employ Molecular Dynamics and investigate the third-order phase transition beyond the Andrews critical point by treating a system of Lennard-Jones particles along three isotherms. Two partial derivatives of the Gibbs free energy are measured, namely the molar constant pressure heat capacity and isothermal compressibility. The convergence of these simulations with respect to the system size as well as the cut-off radius is carefully checked. The obtained results show that partial derivatives certainly do not present sharp cusp singularities at the maxima, and actually suggest that there are no singularities at all. On these basis we then conclude that a third-order phase transition in the considered temperature region: T∗ ≥ 1.36 may indeed not exist.

Compressed liquid densities for the ( n-heptane + n-decane) and ( n-octane + n-decane) systems from T = (313 to 363) K

Densities ( p, ρ, T, x 1) of two binary n-alkane systems are reported from T = (313 to 363) K in the compressed liquid phase up to 25 MPa over the whole range of composition. The binary mixtures { x 1 n-heptane + (1 − x 1) n-decane} and { x 1 n-octane + (1 − x 1) n-decane} were prepared at compositions of ( x 1 = 0.0531, 0.2594, 0.5219, 0.777, 0.952), and ( x 1 = 0.0616, 0.2801, 0.5314, 0.7736, 0.9623), respectively. A measuring system based on a vibrating tube densimeter, DMA HPM from Anton Paar with data acquisition system was developed in order to obtain experimental densities. Water and nitrogen were used as reference fluids to calibrate the densimeter. Experimental methodology was checked by comparing the n-heptane and n-decane densities against multi-parameter equations proposed in the literature. Differences between both sets of data show a maximum deviation of 0.07%. Excess molar volumes, isothermal compressibility and isobaric thermal expansivity were computed from experimental densities.

Amorphous Materials: Properties, Structure, and Durability: Compositional dependent compressibility of dissolved water in silicate glasses

The sound velocities and elastic properties of a series of hydrous rhyolite, andesite, and basalt glasses have been determined by Brillouin scattering spectroscopy at ambient conditions to elucidate the effect of glass composition on the compressibility of dissolved water. Both the adiabatic bulk (K S ) and shear modulus (μ) of the dry glasses decrease with increasing silica content (K S,basalt > K S,andesite > K S,rhyolite and μ basalt > μ andesite > μ rhyolite ). For each composition, the shear modulus systematically decreases with increasing water content. Although the addition of up to 14 mol% water decreases the K S of andesite and basalt glasses by up to 6%, there is no discernable effect of water on the K S of the rhyolite glasses. The partial molar KS of dissolved water (K S ) in rhyolite, andesite, and basalt glasses are 37 ± 5, 19 ± 7, and 40 ± 3 GPa, corresponding to partial molar isothermal compressibilities (β̅ T ) of 0.029 ± 0.005, 0.042 ± 0.004, and 0.026 ± 0.002 GPa −1 , respectively. These results indicate that the compressibility of dissolved water strongly depends on the bulk composition of the glass; hence, the partial molar volume of water cannot be independent of the bulk composition at elevated pressure. If the compressibility of dissolved water also depends on composition in the analog melts at high temperature and pressure, these observations will have important consequences for magmatic processes such as magma mixing/unmixing and fractional crystallization.

The partial molar heat capacity, expansion, isentropic, and isothermal compressions of thymidine in aqueous solution at T = 298.15 K

Solution densities have been determined for aqueous solutions of thymidine at T = (288.15, 298.15, 303.15, and 313.15) K. The partial molar volumes at infinite dilution, V 2 ∘ , obtained from the density data were used to derive the partial molar isobaric expansion at infinite dilution for thymidine at T = 298.15 K, E 2 ∘ { E 2 ∘ = ( ∂ V 2 ∘ / ∂ T ) p } . The partial molar heat capacity at infinite dilution for thymidine, C p , 2 ∘ , at T = 298.15 K has also been determined. Sound speeds have been measured for aqueous solutions of thymidine at T = 298.15 K. The partial molar isentropic compression at infinite dilution, K S , 2 ∘ , and the partial molar isothermal compression at infinite dilution, K T , 2 ∘ { K T , 2 ∘ = - ( ∂ V 2 ∘ / ∂ P ) T } , have been derived from the sound speed data. The V 2 ∘ , E 2 ∘ , C p , 2 ∘ , and K S , 2 ∘ results for thymidine are critically compared with those available from the literature.

Fluctuation theory of molecular association and conformational equilibria

General expressions relating the effects of pressure, temperature, and composition on solute association and conformational equilibria using the fluctuation theory of solutions are provided. The expressions are exact and can be used to interpret experimental or computer simulation data for any multicomponent mixture involving molecules of any size and character at any composition. The relationships involve particle-particle, particle-energy, and energy-energy correlations within local regions in the vicinity of each species involved in the equilibrium. In particular, it is demonstrated that the results can be used to study peptide and protein association or aggregation, protein denaturation, and protein-ligand binding. Exactly how the relevant fluctuating properties may be obtained from experimental or computer simulation data are also outlined. It is shown that the enthalpy, heat capacity, and compressibility differences associated with the equilibrium process can, in principle, be obtained from a single simulation. Fluctuation based expressions for partial molar heat capacities, thermal expansions, and isothermal compressibilities are also provided.

Partial Molar Isentropic and Isothermal Compressions of the Nucleosides Adenosine, Cytidine, and Uridine in Aqueous Solution at 298.15 K

Sound speeds have been measured for aqueous solutions of the nucleosides adenosine, cytidine, and uridine at T = 298.15 K and at ambient pressure. For adenosine and uridine, the partial molar isentropic compressions at infinite dilution, KS,2o, were derived from the sound speed data using conventional methods. These KS,2o results were combined with the partial molar heat capacities and partial molar isobaric expansions at infinite dilution available from the literature to evaluate, for the first time, the partial molar isothermal compressions at infinite dilution, KT,2o {KT,2o = −(∂V2o/∂p)T, where V2o is the partial molar volume of the solute at infinite dilution}. An alternative method is described for the calculation of the KS,2o and KT,2o values for cytidine from the sound speed data. The KT,2o results for the nucleosides have been rationalized in terms of the likely solute−water interactions. For cytidine, an analysis of the molality dependence of the partial molar isothermal compression in terms of self-association has also been explored.

High-pressure EPR reveals conformational equilibria and volumetric properties of spin-labeled proteins.

Identifying equilibrium conformational exchange and characterizing conformational substates is essential for elucidating mechanisms of function in proteins. Site-directed spin labeling has previously been employed to detect conformational changes triggered by some event, but verifying conformational exchange at equilibrium is more challenging. Conformational exchange (microsecond-millisecond) is slow on the EPR time scale, and this proves to be an advantage in directly revealing the presence of multiple substates as distinguishable components in the EPR spectrum, allowing the direct determination of equilibrium constants and free energy differences. However, rotameric exchange of the spin label side chain can also give rise to multiple components in the EPR spectrum. Using spin-labeled mutants of T4 lysozyme, it is shown that high-pressure EPR can be used to: (i) demonstrate equilibrium between spectrally resolved states, (ii) aid in distinguishing conformational from rotameric exchange as the origin of the resolved states, and (iii) determine the relative partial molar volume (ΔV°) and isothermal compressibility (Δβ(T)) of conformational substates in two-component equilibria from the pressure dependence of the equilibrium constant. These volumetric properties provide insight into the structure of the substates. Finally, the pressure dependence of internal side-chain motion is interpreted in terms of volume fluctuations on the nanosecond time scale, the magnitude of which may reflect local backbone flexibility.

Densities, Excess Molar Volumes, Isothermal Compressibilities, and Isobaric Expansivities of Dimethyl Carbonate + Cyclohexane Systems at Temperatures from (293.15 to 313.15) K and Pressures from (0.1 to 40) MPa

The densities of dimethyl carbonate, cyclohexane, and their mixtures were measured for nine compositions at five different temperatures varying from (293.15 to 313.15) K and over the pressure range of (0.1 to 40) MPa. The densities of pure substances and their mixtures at atmospheric pressure were measured with a vibrating-tube densimeter. The densities at elevated pressures were measured with a high-pressure apparatus and a precise analytical balance. The molar volumes Vm, excess molar volumes VmE, isothermal compressibilities κ, and isobaric expansivities α were derived from the experimental densities.

Densities and Volumetric Properties of Ethylene Glycol + Dimethylsulfoxide Mixtures at Temperatures of (278.15 to 323.15) K and Pressures of (0.1 to 100) MPa

Densities, ρ, and compressibility coefficients, k = (vo − v)/vo, of ethylene glycol (1) + dimethylsulfoxide (2) mixtures were measured over the whole concentration range at pressures of (0.1 to 100) MPa and temperatures of (278.15 to 323.15) K. Excess molar volumes, isothermal compressibility, and thermal isobaric expansivity coefficients as well as thermal pressure coefficients were calculated. It was revealed that concentration dependences of specific volumes, v, at some state parameters passed a minimum. The shift of minimum position to molar fraction x2 = 0.5 was observed with increasing pressure and decreasing temperature. The negative excess molar volumes, VmE, indicated a compression of EG (1) + DMSO (2) systems when mixing. Composition dependences of isothermal compressibility, κT, and thermal isobaric expansivity coefficients, α, as well as thermal pressure coefficients, β, were near-linear. Both increasing and decreasing of κT and β values were observed with x2 increase depending on temperature ...

Densities, excess molar volume, isothermal compressibility, and isobaric expansivity of (dimethyl carbonate + n-hexane) systems at temperatures (293.15 to 313.15) K and pressures from 0.1 MPa up to 40 MPa

The densities of dimethyl carbonate, n-hexane and their mixtures were measured for 12 compositions at five different temperatures varying from (293.15 to 313.15) K and over the pressure range of (0.1 to 40) MPa. The densities of pure substances and their mixtures at atmospheric pressure were measured by a vibrating-tube densimeter. The densities at high pressures were measured by a variable-volume autoclave and precise analytical balance. The excess molar volume, isothermal compressibility, and isobaric expansivity were derived from the experimental densities.

Thermodynamic and transport properties of (1-Butanol + 1,4-Butanediol) at temperatures from (298.15 to 318.15) K

Densities and kinematic viscosities have been measured for (1-butanol + 1,4-butanediol) over the temperature range from (298.15 to 318.15) K. The speeds of sound within the temperature range from (293.15 to 318.15) K have been measured as well. Using these results and literature values of isobaric heat capacities, the molar volumes, isentropic and isothermal compressibility coefficients, molar isentropic and isothermal compressibilities, isochoric heat capacities as well as internal pressures were calculated. Also the corresponding excess and deviation values (excess molar volumes, excess isentropic and isothermal compressibility coefficients, excess molar isentropic and isothermal compressibilities, different defined deviation speed of sound and dynamic viscosity deviations) were calculated. The excess values are negative over the whole concentration and temperature range. The excess and deviation values are expressed by Redlich–Kister polynomials and discussed in terms of the variations of the structure of the system caused by the participation of the two different alcohol molecules in the dynamic intermolecular association process through hydrogen bonding at various temperatures. The predictive abilities of Grunberg–Nissan and McAllister equations for viscosities of mixtures have also been examined.

Thermodynamic properties of peptide solutions 19. Partial molar isothermal compressions at T = 298.15 K of some peptides of sequence gly-X-gly in aqueous solution

The partial molar isobaric expansions at infinite dilution and T = 298.15 K, E 2 ∘ { E 2 ∘ = ( ∂ V 2 ∘ / ∂ T ) p } were determined recently for some tripeptides of sequence glycyl-X-glycine, where X is one of the amino acids alanine, valine, leucine, isoleucine, phenylalanine, methionine, proline, serine, threonine, asparagine, glutamine, histidine, and tyrosine. These quantities, along with partial molar heat capacity data available from the literature, were used to convert the partial molar isentropic compressions at infinite dilution determined previously for these tripeptides into the partial molar isothermal compressions at infinite dilution and T = 298.15 K, K T , 2 ∘ { K T , 2 ∘ = - ( ∂ V 2 ∘ / ∂ p ) T } . These K T , 2 ∘ results, along with that for triglycine, were used to estimate the contributions of the amino acid side-chains to the partial molar isothermal compressions of peptides. The side-chain contributions have been rationalized in terms of the likely peptide–water interactions.

Application of the Kirkwood-Buff theory of solutions to acetonitrile + amide binary mixtures by using inversion procedure and regular solution theory

The Kirkwood-Buff (K-B) integrals play an important role in characterizing the intermolecular interactions in liquid mixtures. These are represented by the K-B parameters, G AA, G BB, and G AB, which reflect correlation between like-like and like-unlike species in the mixture. The K-B integrals of binary mixtures of acetonitrile (ACN) with formamide (FA), N,N-dimethylformamide (DMF), N-methylacetamide (NMA) and N,N-dimethylacetamide (DMA) at 298·15 K and at atmospheric pressure have been computed from the experimental data of ultrasonic speed and density. We have used the similar inverse procedure (as proposed by Ben-Naim) to compute the K-B Parameters of the mixtures, in which thermodynamic information on mixtures such as partial molar volumes, isothermal compressibility, and experimental data of partial vapour pressures are used. A new route has been incorporated by using regular solution theory in the computation of excess free energy for obtaining the partial vapour pressures of binary liquid mixtures. The low values of excess entropy (S E ≈ 0) obtained for these mixtures indicate the applicability of regular solution theory to these mixtures. The results obtained regarding intermolecular interaction in all the four mixtures under study from this new procedure are in good agreement with those obtained from the trends exhibited by the excess functions of these mixtures.

Inversion of the Kirkwood–Buff Theory of Solutions: Application to Tetrahydrofuran + Aromatic Hydrocarbon Binary Liquid Mixtures

The Kirkwood–Buff (K-B) integrals play an important role in characterizing the intermolecular interactions in liquid mixtures. The interaction is represented by the K-B parameters, GAA,GBB, and GAB, which reflect correlation between like-like and like-unlike species in the mixture. The K-B integrals of binary mixtures of tetrahydrofuran with benzene, toluene, o-xylene, m-xylene, p-xylene and mesitylene at 298.15 K and atmospheric pressure have been computed from the experimental data of ultrasonic speed and density. We have used the similar inverse procedure (as proposed by Ben-Naim) to compute the K-B parameters of the mixture, in which thermodynamic information on mixtures, such as partial molar volumes, isothermal compressibility and experimental data of partial vapor pressures were used. A new route has been incorporated by using regular solution theory in the computation of excess Gibbs energy for obtaining the partial vapor pressures of binary liquid mixtures. The low values of excess entropy, SE≈0, obtained for these mixtures indicate the applicability of regular solution theory to the mixtures. The values of the K-B parameter, GAB, obtained using this procedure indicate that the correlation/affinity between THF and aromatic hydrocarbon molecules follows the order: benzene > toluene > o-xylene > m-xylene > p-xylene > mesitylene, which is in good agreement with the results obtained from the trends exhibited by the excess functions of these mixtures.

New acoustic velocity measurements on CaO‐MgO‐Al2O3‐SiO2 liquids: Reevaluation of the volume and compressibility of CaMgSi2O6‐CaAl2Si2O8 liquids to 25 GPa

Relaxed sound speed measurements on 12 liquids in the CaO‐MgO‐Al2O3‐SiO2 (CMAS) system have been performed from 1410 to 1620°C at 1 bar with a frequency sweep acoustic interferometer. In all liquids, the sound speeds either decrease or remain constant with increasing temperature. These data are combined with those in the literature to calibrate models for βT and (∂V/∂P)T as a function of composition and temperature for CMAS liquids. CaO is the only oxide component that contributes to the temperature dependence of compressibility. The new compressibility models permit the bulk modulus (KT,0) of CaMgSi2O6 (Di), CaAl2Si2O8 (An), and the Di64‐An36 eutectic liquid to be directly obtained. These results are used to uniquely constrain values for the pressure dependence of the bulk modulus (K0′ = dK0/dP) in a third‐order Birch‐Murnaghan equation of state (EOS) for these three liquids from shock wave data in the literature. The revised K0′ value is 6.8 (versus 6.9) for CaMgSi2O6 liquid, 4.7 (versus 5.3) for CaAl2Si2O8 liquid, and 5.6 (versus 4.85) for Di64‐An36 liquid. Information on both KT,0 and K0′ allows the density and compressibility for each of these three liquids to be calculated as a function of pressure to 25 GPa. Both the molar volume and isothermal compressibility of CaMgSi2O6‐CaAl2Si2O8 liquids mix ideally between 0 and 25 GPa. The dominant mechanism of compression at low pressure (0–5 GPa) for all three liquids (CaMgSi2O6, CaAl2Si2O8, and the Di64‐An36 eutectic) is topological, whereas gradual Al/Si coordination change plays an increasingly important role at higher pressure as topological mechanisms of compression are diminished.

Isothermal compressibility and internal pressure of 1-butanol + 1,3-butanediol at the temperature 298.15 K determined by an acoustic method

Excess molar isothermal compressibilities and internal pressures for 1-butanol + 1,3-butanediol at the temperature 298.15 K were estimated basing on an acoustic method. The results are expressed by Redlich-Kister polynomials and discussed in terms of intermolecular interactions. The estimation by neglecting the excess isobaric expansibility, often used in practice, is discussed too.