Thermodynamic regularities for associating fluids from statistical associating fluid theory equation of state

In this work, we used a statistical associating fluid theory to analyze two important thermodynamic regularities for some associating fluids, including water, methanol and ethanol. The studied regularities included: (i) the common bulk modulus point on the isotherms of the reduced bulk modulus versus reduced density, (ii) near linearity of the reduced isothermal bulk modulus as a function of reduced pressure. In this work, we also reported the influence of the molecular size and interaction strength on the bulk modulus point.     

New regularities and an equation of state for liquids

Three regularities have been introduced for liquids (T < T_C and ρ > ρ_C) based on average potential energy. The experimental data have been used to show the validity of the regularities. First, there exists near-linearity relation between and ρ for all isotherms of a liquid, where P_i and ρ are internal pressure and density, respectively. Second, changes linearly with ρ for each isotherm of any liquid, where Z and V_m are compressibility factor and molar volume, respectively. Third, a new regularity using the definition of bulk modulus and our new equation of state between reduced bulk modulus and density has been introduced, that is versus ρ must be linear for all isotherms of a liquid where B_r is the reduced bulk modulus.

A new equation of state has been also derived. The density of some liquids in the extensive ranges of temperature and pressure has been calculated using the new equation of state. The densities calculated from this equation agree with experiment to better than 0.3%. The new equation of state can predict internal pressure, thermal expansion coefficient, and isothermal compressibility of liquids within experimental error.     

First‐principles calculations on thermodynamic properties of BaTiO3 rhombohedral phase

The calculations based on the linear combination of atomic orbitals have been performed for the low‐temperature phase of BaTiO₃ crystal. Structural and electronic properties, as well as phonon frequencies were obtained using hybrid PBE0 exchange–correlation functional. The calculated frequencies and total energies at different volumes have been used to determine the equation of state and thermal contribution to the Helmholtz free energy within the quasiharmonic approximation. For the first time, the bulk modulus, volume thermal expansion coefficient, heat capacity, and Grüneisen parameters in BaTiO₃ rhombohedral phase have been estimated at zero pressure and temperatures form 0 to 200 K, based on the results of first‐principles calculations. Empirical equation has been proposed to reproduce the temperature dependence of the calculated quantities. The agreement between the theoretical and experimental thermodynamic properties was found to be satisfactory. © 2012 Wiley Periodicals, Inc.     

Common Intersection Points of Bulk Modulus for Liquefied Natural Gas (LNG) Mixtures

During recent developments on the theories and experimental techniques of compressed liquids and liquid mixtures, it has been revealed that there exist some regularities. Among these, the regularity found by Huang and O'Connell is that the isotherms of reduced bulk modulus of compressed liquids as a function of molar volume intersect at a common point. This intersection is a useful tool for evaluating the reliability of an equation of state (EOS) for producing equilibrium properties of matter. This paper also deals with an extension of the above regularity to some liquefied natural gas (LNG) mixtures including: N₂+CH₄, N₂+C₂H₆, CH₄+C₂H₆, CH₄+C₃H₈, and CH₄+C₄H₁₀ at different temperatures. The present work gives a theoretical analysis for the common bulk modulus point in terms of a statistical‐mechanical equation of state for mixtures. In addition, we have calculated excess molar volume of N₂+CH₄ mixture in terms of temperature and compared it with experimental values.     

Volumetric profile of polymer melts from the ISM equation of state

Knowledge of the volumetric or pressure–volume–temperature (PVT) profile of molten polymers is important for both engineering and polymer physics. Ihm–Song–Mason (ISM) equation of state (EOS) has been employed to predict the volumetric properties of 12 molten polymers. The significance of the present paper is three temperature-dependent parameters of the ISM EOS to be determined using corresponding states correlations based on the molecular scaling constants, dispersive energy parameters between segments/monomers (ε) and segment diameter (σ) rather than bulk properties, e.g. the liquid density and temperature both at normal boiling point. The ability of the ISM EOS has been evaluated by comparing the results with 1390 literature datapoints for the specific volumes over the temperature range from 293 to 603.5 K and pressure range from 0.1 to 200 MPa. The average absolute deviation (AAD) of the calculated specific volumes from literature data was found to be 0.52%. The isothermal compressibility coefficients, κ_T values of molten polymers have also been predicted using the ISM EOS. From 684 datapoints examined, the AAD of estimated κ_T was equal to 7.55%. Our calculations on the volumetric and thermodynamic properties of studied polymers reproduce the literature data with reasonably good accuracy.     

The thermal properties of Al–Mg–TM (TM = Sc,Zr): Ab initio study

Ab initio density functional theory (DFT) and density function perturbation theory (DFPT) have been used to investigate the thermal properties of the Al–Mg–Sc, Al–Mg–Zr and Al–Mg–Sc–Zr alloys over a wide range of temperature and pressure. Phonon dispersions are obtained at equilibrium and strained configurations by DFPT. Using the quasiharmonic approximation (QHA) for the free energy, several physical quantities of interest such as thermal Grüneisen parameter, heat capacity at constant pressure and at constant volume, thermal expansion coefficient, entropy, adiabatic bulk modulus and isothermal bulk modulus as a function of temperature and pressure are calculated and discussed. The present results show that the thermal expansion coefficient of the Al–Mg–Sc–Zr is far lower than that of Al–Mg–Sc and Al–Mg–Zr, and the variation features in the adiabatic bulk modulus and isothermal bulk modulus for the Al–Mg–Sc–Zr are also very different from that of Al–Mg–Sc and Al–Mg–Zr.     

Bulk modulus and density of polyethylene to 30 kbar

The results of bulk modulus and density measurements on low-density polyethylene to 30 kbar are presented. From these data the pressure coefficient dT_t/dp of the glass transition temperature is obtained, and a comparison is made with data calculated from Pastine's theoretical equation of state for polyethylene.     

Pressure and volume dependence of thermal conductivity and isothermal bulk modulus up to 1 GPa for poly(isobutylene)

The thermal conductivity λ and heat capacity per unit volume ρc_p of poly(isobutylene)s, one 2.8 in weight average molecular weight and one 85 kg mol⁻¹ in viscosity average molecular weight (PIB-2800 and PIB-85000), have been measured in the temperature range 170–450 K at pressures up to 2 GPa using the transient hot-wire method. At 297 K and atmospheric pressure, λ = 0.115 W m⁻¹ K⁻¹ for PIB-2800 and λ = 0.120 W m⁻¹ K⁻¹ for PIB-85000. The bulk modulus B_T has been measured in the temperature range 170–297 K up to 1 GPa. At atmospheric pressure, the room temperature bulk moduli B_T are 2.0 GPa for PIB-2800 and 2.5 GPa for PIB-85000 with dB_T/dp = 10 for both. These data were used to calculate the volume dependence of λ, At room temperature and atmospheric pressure (liquid phase) we find g = 3.4 for PIB-2800 and g = 3.9 for PIB-85000, but g depends strongly on temperature for both molecular weights. The difference in g between the glassy state and liquid phase is small and just outside the inaccuracy of g of about 8%. The best predictions for g are given by the theoretical model of Horrocks and McLaughlin. We have found that PIB exhibits two relaxations, where one is associated with the glass transition. The value for dT_g/dp at atmospheric pressure (for the main glass transition) is about 0.21 K MPa⁻¹ for both molecular weights. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1781–1792, 1998     

Rheo-optical studies of high polymers. XIV. Study of the deformation mechanism in polymer blends of polypropylene with ethylene–propylene rubber

To clarify the deformation mechanism in polyblends of polypropylene with ethylene–propylene rubber having different compositions, simultaneous measurements of the infrared dichroism with stress and strain under a constant rate of strain of 1.64%/min have been carried out. The orientation function of the crystallographic c axis of polypropylene in the blends has been obtained as a function of strain ranging from 0 to 20% and of polypropylene content ranging from 0.3 to 1.0. These results have been compared with the temperature dependences of the dynamic Young's modulus and of the loss modulus, as well as of stress–strain curves for the same blends. The modulus data analyzed by Kerner's equation reveal the occurrence of phase inversion at polypropylene contents higher than about 0.5, and this is supported by the infrared dichroism data. The strong effect of quenching on crystalline structure and mechanical properties of pure polypropylene has also been elucidated.     

Bulk and shear rheology of a symmetric three‐arm star polystyrene

The bulk and shear rheological properties of a symmetric three‐arm star polystyrene were measured using a self‐built pressurizable dilatometer and a commercial rheometer, respectively. The bulk properties investigated include the pressure–volume–temperature behavior, the pressure‐dependent glass transition temperature (T_g), and the viscoelastic bulk modulus and Poisson's ratio. Comparison with data for a linear polystyrene indicates that the star behaves similarly but with slightly higher T_gs at elevated pressures and slightly higher limiting bulk moduli in glass and rubbery states. The Poisson's ratio shows a minimum at short times similar to what is observed for the linear chain. The horizontal shift factors above T_g obtained from reducing the bulk and shear viscoelastic responses are found to have similar temperature dependence when plotted using T ? T_g scaling; in addition, the shift factors also exhibit a similar temperature dependence to linear polystyrene. The retardation spectra for the bulk and shear responses are compared and show that the long time molecular mechanisms available to the shear response are unavailable to the bulk. At short times, the two spectra have similar slopes, but the short‐time retardation spectrum for the shear response is significantly higher than that for the bulk, a finding that is, as yet, unexplained. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Common compression factor and bulk modulus quiescence points of liquid cesium

In this paper, a recently developed analytical equation of state (EOS) is used to investigate the bulk modulus of compressed liquid cesium and to locate common compression factor and the bulk modulus quiescence point(s). This EOS is applied quick well to Na and Rb far from T_c. Bulk modulus of liquid cesium have two quiescence points, a sharp one in the range 1100–1500 K and a diffused one in the range 1600–1900 K. Therefore, two types of liquid cesium metal may be identified with characteristic structure and interaction potential energy. It is a constant independent of temperature, however, some residual change is seen due to the change in the values of integral of pair correlation function as temperature is increased. Furthermore, it is related to the shape of the unit cell and the atomic size at equilibrium. Observation of distinct liquid in the metal–nonmetal transition range is compared with NMR studies and molecular dynamic results.     

Volume dependence of thermal conductivity and isothermal bulk modulus up to 1 GPa for poly(vinyl acetate)

The thermal conductivity λ and heat capacity per unit volume of poly(vinyl acetate) (260 kg mol⁻¹ in weight average molecular weight) have been measured in the temperature range 150–450 K at pressures up to 1 GPa using the transient hot-wire method, which yielded λ = 0.19 W m⁻¹ K⁻¹ at atmospheric pressure and room temperature. The bulk modulus K has been measured in the temperature range 150–353 K up to 1 GPa. At atmospheric pressure and room temperature, K = 4.0 GPa and (∂K/∂p)_T = 8.3. The volume data were used to calculate the volume dependence of λ, $g = - \left( {\frac{{\partial \lambda /\lambda }}{{\partial V/V}}} \right)_T .$ The values for g of the liquid and glassy states were 3.0 and 2.7, respectively, and g of the latter was almost independent of volume and temperature. Theoretical models can predict the value for g of the glassy state to within 25%. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1451–1463, 1998     

Pressure-induced metallization in the absence of a structural transition in the layered transition-metal dichalcogenide ZrSe2

First-principles calculations were carried out on the ZrSe₂ compound, which has been of interest owing to its technologically important physical properties. The structural, electronic and optical properties of this compound were investigated under pressure through the plane wave pseudopotential approach within the framework of density functional theory. A comparison between the computed crystal structure parameters and the corresponding experimental counterparts shows a very good agreement between them. Fitting the pressure–volume data using the third-order Birch–Murnaghan equation of state yielded a bulk modulus B₀ = 38.17 GPa and a pressure derivative of bulk modulus  = 8.2 for hexagonal ZrSe₂. The relationship between the band structure and pressure is revealed. We calculated the total density of state (TDOS) under different pressures and partial density of state (PDOS) from 0 to 10 GPa. According to our calculations, metallization of hexagonal ZrSe₂ is predicted to occur at around 10 GPa and pressure-induced band-gap engineering reveals the transformation of the indirect to direct band gap with increasing pressure. Furthermore, optical properties, such as the complex dielectric function, refractive index and reflectivity spectra of this compound, were studied for incident electromagnetic waves in an energy range up to 45 eV. The contributions to various transition peaks in the optical spectra are analyzed and discussed with the help of the energy-dependent imaginary part of the dielectric function.     

Model for phase coexistence in phase transitions

We propose a general model for describing the phenomena of phase coexistence in relation to pressure induced phase transformations by means of the T–P distribution in statistical thermodynamics. Using the well‐known B1–B2 transition in NaCl as a prototype, we demonstrate how phase coexistence gives rise to the changes in the bulk modulus and the equation‐of‐state across the transition. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Relation between the network structure and dynamic mechanical properties of a typical amine-cured epoxy polymer

The dynamic mechanical properties of a series of epoxy polymers of known network structure have been investigated. It was shown that the distance between crosslinks could be predicted from either the shift in the glass transition temperature T_g or by use of the dynamic modulus above T_g. The front factor in the equation of state for rubber elasticity was near unity for stoichiometric equivalence of epoxy and amine and increased slowly with excess of either component.     

Molecular modeling study on surface,thermal, mechanical and gas diffusion properties of chitosan

The motivation of this work is to provide reliable and accurate modeling studies of the physical (surface, thermal, mechanical and gas diffusion) properties of chitosan (CS) polymer. Our computational efforts have been devoted to make a comparison of the structural bulk properties of CS with similar type of polymers such as chitin and cellulose through cohesive energy density, solubility parameter, hydrogen bonding, and free volume distribution calculations. Atomistic modeling on CS polymer using molecular mechanics (MM) and molecular dynamics (MD) simulations has been carried out in three dimensionally periodic and effective two dimensionally periodic condensed phases. From the equilibrated structures, surface energies were computed. The equilibrium structure of the films shows an interior region of mass density close to the value in the bulk state. Various components of energetic interactions have been examined in detail to acquire a better insight into the interactions between bulk structure and the film surface. MD simulation (NPT ensemble) has also been used to obtain polymer specific volume as a function of temperature. It is demonstrated that these V–T curves can be used to locate the volumetric glass transition temperature (T_g) reliably. The mechanical properties of CS have been obtained using the strain deformation method. Diffusion coefficients of O₂, N₂, and CO₂ gas molecules at 300 K in CS have been estimated. The calculated properties of CS are comparable with the experimental values reported in the literature. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1260–1270, 2007     

Dilational Rheological Properties of Non-Ionic Surfactants at the Water–Decane Interface: Effect of Unsaturated Hydrophobic Group

The interfacial tensions and dilational properties of adsorbed films of two non-ionic surfactants with different hydrophobic groups, polyoxy-ethylene sorbitan stearate (Tween 60) and polyoxy-ethylene sorbitan monooleate (Tween 80), at the water–decane interface have been investigated by the drop-shape analysis method. The effects of dilational frequency and bulk concentration on the interfacial properties were expounded. The influence of low temperature on the interfacial tensions and dilational properties have also been researched. The experiment results show that the interfacial activity of Tween 80 is rather large compared with Tween 60. The minimum area per molecule at the water–decane interface (A_min) value of Tween 80 is little large than that of Tween 60, which is due to the steric effect of unsaturated double bond in Tween 80 molecule. The dilational data show that the ethylene oxide groups of non-ionic surfactant form a stable sub-layer, which results in the increase of modulus and the decrease of phase angle for both Tween 60 and Tween 80 than those of common ionic surfactants. Moreover, the unsaturated hydrophobic group of Tween 80 is much flexible, which is easily crosslinked and entangled. Therefore, dilational modulus of Tween 80 is higher and phase angle is lower than that of Tween 60. Low temperature decreases the flexibility of unsaturated hydrophobic group and lessens the influence on the interaction of saturated hydrophobic group. Saturated surfactant molecules of Tween 60 almost lose temperature response.     

Time–temperature-dependent behavior of a substituted poly(paraphenylene): Tensile,creep, and dynamic mechanical properties in the glassy state

The linear viscoelastic behavior of a poly(paraphenylene) with a benzoyl substituent has been examined using tensile, dynamic mechanical, and creep experiments. This amorphous polymer was shown to have a tensile modulus of 1–1.5 Msi, nearly twice that of most common engineering thermoplastics. The relaxation behavior, which is similar to that of common thermoplastics, can be described by the WLF equation. Outstanding creep resistance was observed at low temperatures, with rubbery-like behavior being exhibited as the temperature approached T_g. Physical aging was shown to interact with long-term creep, rendering time–temperature superposition invalid for predicting the long-term properties. The effect of physical aging on the creep behavior was characterized by the shift rate μ. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 70: 2971–2979, 1998     

Bulk rigid-rod molecular composites of articulated rod copolymers with thermoplastic pendants

Bulk rigid-rod molecular composites were successfully obtained by powder consolidation of a copolymer containing both the reinforcing rigid-rod segments and the thermoplastic matrix. By chemically linking the reinforcing segments and the matrix molecule, the copolymer was designed to minimize phase separation in the molecular composite. The copolymer was an articulated rigid-rod poly(p-phenylenebenzobisthiazole), aPBT, with an aromatic poly(ether ketone), mPEK, thermoplastic pendant grafted at the points of articulation. The copolymer powder was pre-formed and compression molded at an elevated temperature, which resulted in bulk rigid-rod molecular composites with three-dimensionally isotropic properties. Compared to the neat mPEK homopolymer, significant increases in glass transition temperature T_g and tensile properties have been realized for the aPBT-g(mPEK) copolymers with low rod content. Taking into account the aspect ratio of the aPBT, the bulk rigid-rod molecular composite showed a tensile modulus as predicted by the Halpin-Tsai equation. In addition, x-ray scattering revealed minimal rod aggregation. However, for the copolymer of higher rod content, significant phase separation was observed in the copolymer powder, which resulted in a decrease in T_g as well as reinforcement efficiency of the bulk rigid-rod molecular composite as compared to those derived from the copolymers of low rod content. © 1992 John Wiley & Sons, Inc.     

The structural,electronic, elastic,vibration and thermodynamic properties of GdMg

We have investigated the structural, elastic, electronic, vibration and thermodynamic properties of GdMg alloy using the methods of density functional theory within the generalized gradient approximation (GGA) for the exchange-correlation functional. We have presented the results on the basic physical parameters, such as the lattice constant, bulk modulus, pressure derivative of bulk modulus with and without spin-polarization (SP), second-order elastic constants, Zener anisotropy factor, Poisson's ratio, Young's modulus, and isotropic shear modulus. The thermodynamic properties of the considered compound are obtained through the quasi-harmonic Debye model. In order to obtain further information, we have also studied the pressure and temperature-dependent behavior of the volume, bulk modulus, thermal expansion coefficient, heat capacity, and Debye temperature in a wide temperature range of 0–1200 K. We have also calculated phonon frequencies and one-phonon density of states for B2 structure of GdMg compound. The temperature-dependent behavior of heat capacity and entropy obtained from phonon density of states for GdMg compound in B2 phase is also presented.