Phenomenological Thermodynamic Model Research Articles

Thermodynamics of protein unfolding-refolding transition

A phenomenological thermodynamic model is developed to investigate, in more detail than usual, the pressure-temperature phase diagram of proteins. Indeed, in the whole of previous studies the specific heat difference deltaCP is treated as pressure and temperature independent. This assumption is wrong, as confirmed by Yamaguchi et al (1995) which reported pressure dependence of deltaCP in the case of ribonuclease A. In this work, assuming that the chemical potential has a Taylor series expansion and having an additional thermodynamic piece of information, the analysis shows that it is possible to obtain a complete description of the unfolding-refolding transition of protein, to deduce the volumes, entropies, enthalpies versus transition temperatures and transition pressures and, for the first time, to deduce the specific heat changes versus transition temperatures and transition pressures. Special attention is given to the elliptical shape of the pressure-temperature phase diagram. A quantitative description of the phase transitions in the protein of Zn-Cytochrome c is given.

Thermodynamics of Protein Unfolding-Refolding Transition

A phenomenological thermodynamic model is developed to investigate, in more detail than usual, the pressure-temperature phase diagram of proteins. Indeed, in the whole of previous studies the specific heat difference deltaCP is treated as pressure and temperature independent. This assumption is wrong, as confirmed by Yamaguchi et al (1995) which reported pressure dependence of deltaCP in the case of ribonuclease A. In this work, assuming that the chemical potential has a Taylor series expansion and having an additional thermodynamic piece of information, the analysis shows that it is possible to obtain a complete description of the unfolding-refolding transition of protein, to deduce the volumes, entropies, enthalpies versus transition temperatures and transition pressures and, for the first time, to deduce the specific heat changes versus transition temperatures and transition pressures. Special attention is given to the elliptical shape of the pressure-temperature phase diagram. A quantitative description of the phase transitions in the protein of Zn-Cytochrome c is given.

Effect of Alkyl Chains Length on Ferroelectric Properties of Km/n and KLLm/n Homologous Series

In this work, a phenomenological thermodynamic model is used to describe the temperature variations of spontaneous polarization P0, tilt angle θ0, and helical pitch p of Sm C* phase near Sm A–Sm C* phase transition in two homologous series, Km/n and KLLm/n, of ferroelectric mesogens. The free-energy density of the system is written in terms of tensor orientational order parameter Qij, scalar smectic order parameter ψ, vector polarization order parameter P, and the resulting couplings between these order parameters. The tilt vector ξ is not considered an independent order parameter, as that Qij governs ξ. Adopting usual method, we evaluate the relative contribution of each individual term of the expansion series and the values of P0, θ0 and p as a function of temperature for the eleven ferroic mesogens, and found that the theoretical results agree very well with the experimental data of all the mesogens.

The Equation of State for Non-ideal Quark Gluon Plasma

The mass spectra of quarkonium systems at T= 0 are analyzed by solving the nonrelativistic radial wave equation using the internal energy potential. The QGP matter is studied through the dissociations of quarkonium states. A modified form of the internal energy potential function is used to determine the EoS at different number of quark flavors by using Mayer's cluster expansion theory and phenomenological thermodynamic model. The thermodynamic model gives a good agreement with the lattice results rather than Mayer’s cluster expansion theory. One can conclude that, the Mayer’s cluster expansion theory may be more suitable to study a weakly coupled plasma while, the QGP may be considered as a strongly interacting plasma.

A phenomenological thermodynamic model for the chemo-responsive shape memory effect in polymers based on Flory–Huggins solution theory

We present a phenomenological thermodynamic model to study the constitutive relations and working mechanism of the chemo-responsive shape memory effect (SME) in shape memory polymers (SMPs). On the origin of the Hildebrand solubility parameter, Flory–Huggins interaction parameter and relaxation theory, a phenomenological model is proposed to quantitatively identify the factors influencing the chemo-responsive SMPs. After this, a free-energy function is implemented to couple the constitutive relations of the chemical potential and stress as a function of the weight fraction of solvent and stretch, respectively. Furthermore, the simulation of the phenomenological thermodynamic model is compared with the available experimental results and the simulation results of a semi-empirical model reported in the literature for verification.

Grain boundary complexion transitions in WO3- and CuO-doped TiO2 bicrystals

Several grain boundary complexions (grain boundary interfacial phases) have been identified in TiO2 bicrystals by high-resolution transmission electron microscopy (TEM) and aberration-corrected scanning TEM (STEM). An intrinsic grain boundary with no apparent impurity segregation was observed in an undoped TiO2 bicrystal. In a WO3-doped TiO2 bicrystal, WO3 second-phase particles formed along the boundary, with a nominally clean, intrinsic-type grain boundary in between the particles. In a CuO-doped bicrystal, a remarkable series of three distinct grain boundary complexions with abrupt structural transitions was discovered coexisting at the grain boundary, and the existence of a fourth equilibrium complexion at the annealing temperature was implied. Thus, the WO3- and CuO-doped TiO2 bicrystals exhibit dramatically different solute partitioning behavior which can be understood in terms of the relative interphase boundary energies of these two systems. STEM–electron energy loss spectroscopy and energy-dispersive X-ray spectroscopy analysis of the nanoscale lens-shaped films of amorphous material in the CuO-doped TiO2 bicrystal demonstrated an excess of CuO, as expected, yet also revealed the unintentional presence of SiOx. The multiple grain boundary complexions in CuO-doped TiO2 offer an explanation for the CuO-enhanced grain growth and sintering of TiO2 that has been reported in the literature. Conversely, the intrinsic grain boundary complexion observed in WO3-doped TiO2 is consistent with previous work showing that WO3 has no effect on grain boundary mobility in TiO2. A phenomenological thermodynamic model is proposed to explain the physical origin of these observed grain boundary complexions and the abrupt, first-order complexion transitions that are believed to occur upon cooling of the CuO-doped TiO2 bicrystal.

A Free Energy Model of Boron Carbide

The assessed phase diagram of the boron-carbon system contains a single nonstoichiometric boron-carbide phase of rhombohedral symmetry with a broad, thermodynamically improbable, low temperature composition range. We combine first principles total energy calculations with phenomenological thermodynamic modeling to propose a revised low temperature phase diagram that contains two boron-carbide phases of differing symmetries and compositions. One structure has composition B4C and consists of B11C icosahedra and C-B-C chains, with the placement of carbon on the icosahedron breaking rhombohedral symmetry. This phase is destabilized above 600 K by the configurational entropy of alternate carbon substitutions. The other structure, of ideal composition B13C2, has a broad composition range at high temperature, with rhombohedral symmetry throughout, as observed experimentally.

Orientation dependence of the electrocaloric effect in [formula omitted] multilayers

A phenomenological thermodynamic model is presented to investigate the effects of the orientation and the relative thickness of SrTiO3 layer on the electrocaloric effect in PbTiO3/SrTiO3 multilayers. Theoretical calculations show that complete polarization suppression and a large electrocaloric effect take place at the critical relative thickness of SrTiO3 layer of 46%, 33%, and 30% for the (001), (110), and (111) oriented PbTiO3/SrTiO3 multilayers respectively, not occuring at the critical relative thickness of 63%, 50%, and 46% reported by Wu et al. [H.P. Wu, A.P. Liu, L.Z. Wu, S.Y. Du, Appl. Phys. Lett. 93 (2008) 242909]. Moreover, (111) oriented multilayers have the largest electrocaloric effect which is different from that of BaTiO3/SrTiO3 multilayers where (110) oriented multilayers have the largest electrocaloric effect. Consequently, the electrocaloric effect of PbTiO3/SrTiO3 multilayers can be adjusted by the orientation and the relative thickness of SrTiO3 layer.

First-principle study of strain-driven phase transition in incipient ferroelectric SrTiO 3

First-principle calculations were carried out to investigate the epitaxial strain dependence of the structural stability and related properties of SrTiO 3. The P4mm-to-P4/mmm-to-Amm2 phase transitions in SrTiO 3 with the epitaxial strain changing from compressive to expansive have been identified by analysis of the soft-mode eigendisplacement. The zero-temperature critical strains for the P4mm-to-P4/mmm and P4/mmm-to-Amm 2 phase transitions are −0.72% and 0.83%, respectively, which is consistent with the previous predictions based on the phenomenological thermodynamic model and the parameterized total-energy model. The influences of the epitaxial strain on the dielectric tensor and spontaneous polarization along the phase transition path are discussed in terms of charge transfer. Further investigations on the vibration modes show unusual softening behaviors of the A 1 and B 2 modes in the Amm2 phase, which may be associated with the soft phonon modes away from Γ point and possibly result in other phase transitions unreported by any previous studies.

Ordering in binary transition metal alloys

We present the phenomenological thermodynamic modeling of binary alloys which demonstrate solubility of the components at high temperatures, and form intermediate phase near equiatomic composition at lower ones (the so-called sigma-phase). Besides, the regular solution miscibility gap takes place also. The nonequilibrium thermodynamic potential is written out as a sum of the free energy of regular solution and polynomial term of scalar order parameter φ, which describes the σ-phase ordering. There are four parameters in the model: the energy of regular solution mixing, the energy of σ-phase formation at zero temperature, and the widths of temperature and concentration intervals of σ-phase existence in the alloy with frozen-in random distribution of components. Up to now, both phase transitions which take place in a number of transition metals binary alloys (the σ-phase formation and miscibility in the regular solution) have been treated separately. In present work, the standard technique of phase diagram calculation allows us to analyze all possible phase diagrams which may arise in the alloy.

Phase diagram of ferroelectric nanowires and its mechanical force controllability

A phenomenological thermodynamic model of ferroelectric nanowires is developed to investigate the size-temperature phase diagrams. Considering existence of the surface tension, size, and external applied stress effects, the approximated expressions of the transition temperatures at which the paraelectric phase loses its stability with respect to the appearance of the spontaneous polarization are derived. At the same time, the size-temperature phase diagrams as functions of the ferroelectric nanowire radius are obtained, and also show its external mechanical stress controllability.

Evaluation of Residual Stress in a Multilayer Ceramic Capacitor and its Effect on Dielectric Behaviors Under Applied dc Bias Field

The residual stress in a multilayer ceramic capacitor (MLCC) has been evaluated by two‐dimensional finite element simulation in combination with X‐ray diffraction measurement. It is shown that there is a compressive in‐plane stress in the active layers of the MLCC, which increases with increases in the number of dielectric layers when both dielectric layer thickness and electrode thickness are kept constant. A good order of magnitude agreement between the residual stresses obtained from two approaches is found. The ɛ–V response of the MLCC with different number of dielectric layers demonstrates that under a given or no applied field, the dielectric permittivity increases with increasing compressive stress. Additionally, under dc bias field, the higher the compressive in‐plane stress existing in the MLCC, the more significant the decrease of the dielectric permittivity. These results can be explained through a phenomenological thermodynamic model, including both elastic and electrostatic energy, based on the Ginsburg–Landau–Devonshire theory.

Investigation of ferroelectric phase transition for modified barium titanate in multilayer ceramic capacitors by in situ Raman scattering and dielectric measurement

The ferroelectric phase behaviors of modified BaTiO3 in X7R multilayer ceramic capacitors (MLCCs) were investigated by dielectric measurements and in situ Raman scattering. The in situ thermo-Raman scattering shows that because of a residual stress existing in the MLCCs, the tetragonal to cubic phase transition for modified BaTiO3 in MLCCs takes place over a wide temperature range of 373 K to 473 K, suggesting a diffuse-like characteristic which can be well explained by a modified phenomenological thermodynamic model, while the dielectric measurement indicates that the tetragonal to cubic transition occurs at 393 K. A disagreement exists between the two experimental results. Furthermore, a dc field-induced paraelectric to ferroelectric transition was identified by the two measurement techniques, but their phase-transition mechanisms are different. The dielectric measurement reveals the polar-micro-region to macro-domain transformation in the shell part of the core–shell structure while the in situ Raman scattering shows the cubic to tetragonal transition under a dc bias field.

Phenomenological reconstructions of the solar signature in the Northern Hemisphere surface temperature records since 1600

A phenomenological thermodynamic model is adopted to estimate the relative contribution of the solar‐induced versus anthropogenic‐added climate forcing during the industrial era. We compare different preindustrial temperature and solar data reconstruction scenarios since 1610. We argue that a realistic climate scenario is the one described by a large preindustrial secular variability (as the one shown by the paleoclimate temperature reconstruction by Moberg et al. (2005)) with the total solar irradiance experiencing low secular variability (as the one shown by Wang et al. (2005)). Under this scenario the Sun might have contributed up to approximately 50% (or more if ACRIM total solar irradiance satellite composite (Willson and Mordvinov, 2003) is implemented) of the observed global warming since 1900.

Three-dimensional phenomenological thermodynamic model of pseudoelasticity of shape memory alloys at finite strains

The familiar small strain thermodynamic 3D theory of isotropic pseudoelasticity proposed by Raniecki and Lexcellent is generalized to account for geometrical effects. The Mandel concept of mobile isoclinic, natural reference configurations is used in order to accomplish multiplicative decomposition of total deformation gradient into elastic and phase transformation (p.t.) parts, and resulting from it the additive decomposition of Eulerian strain rate tensor. The hypoelastic rate relations of elasticity involving elastic strain rate \(\underline{{{\mathbf{d}}}}^{\rm e}\) are derived consistent with hyperelastic relations resulting from free energy potential. It is shown that use of Jaumann corotational rate of stress tensor in rate constitutive equations formulation proves to be convenient. The formal equation for p.t. strain rate \(\underline{{{\mathbf{d}}}}^{{\rm in}}\) , describing p.t. deformation effects is proposed, based on experimental evidence. Phase transformation kinetics relations are presented in objective form. The field, coupled problem of thermomechanics is specified in rate weak form (rate principle of virtual work, and rate principle of heat transport). It is shown how information on the material behavior and motion inseparably enters the rate virtual work principle through the familiar bridging equation involving Eulerian rate of nominal stress tensor.

Observation of magnetoelectric effect in epitaxial ferroelectric film/manganite crystal heterostructures

A multiferroic heterostructure is constructed by growing an epitaxial piezoelectric $\mathrm{Pb}({\mathrm{Zr}}_{0.3},{\mathrm{Ti}}_{0.7}){\mathrm{O}}_{3}$ film on a magnetostrictive layered manganite single crystal of composition ${\mathrm{La}}_{1.2}{\mathrm{Sr}}_{1.8}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$. The efficient mechanical coupling at the interface results in a remarkable magnetoelectric (ME) effect. The ME voltage is $\ensuremath{\sim}87%$ of the theoretical value predicted by a phenomenological thermodynamic model. The ME effect peaks at the ferromagnetic transition temperature of the manganite, a consequence of its magnetostrictive characteristics.

Dissolution Kinetics of Titanium Dioxide Nanoparticles: The Observation of an Unusual Kinetic Size Effect

Different types of industrially produced titanium dioxide nanoparticles and a precipitated titanium dioxide have been dissolved in aqueous NaCl solutions at temperatures of 25 and 37 degrees C. The titanium concentration in solution with regard to dependence on time has been determined up to 3000 h after starting the dissolution experiment. The effect of particle size, pH value, temperature, background electrolyte concentration, and mass concentration of titanium dioxide exposed to the liquid phase has been studied. The nanoparticles have been characterized by N2 physisorption measurements and XRD. The total dissolved titanium in solution has been determined by adsorptive stripping voltammetry (AdSV) and inductively coupled plasma mass spectrometry (ICP-MS). A new kinetic size effect has been observed. It turns out that this effect can be explained by applying an already existing phenomenological thermodynamic and kinetic model. The model describes all possible phenomena in a colloidal dispersion, nucleation, growth of particles, Ostwald ripening, and dissolution of particles using a uniform concept.

Thermodynamic theory of stress distribution in epitaxial Pb(Zr, Ti)O3 thin films

A phenomenological thermodynamic model has been developed to account for the effects of the film thickness on various properties of ferroelectric thin films. To this end, we have suitably incorporated a position-dependent stress distribution function into the elastic Gibbs function. Various physical properties can be predicted as a function of the film thickness using this modified thermodynamic formalism. A comparison of the theoretical predictions with experimental values of the average strain and the para-ferro transition temperature indicates that the tensile stress caused by the cubic-tetragonal displacive phase transition dominates over the compressive thermal stress in the epitaxially oriented tetragonal Pb(Zr, Ti)O3 thin films.

Transport between an aqueous phase and a CTAB/hexanol-octane reversed micellar phase

Using bovine serum albumin (BSA) as a model protein, protein transport between an aqueous phase and a reversed micellar organic phase was examined. From near-infrared spectra and UV absorption spectra, it was confirmed that CTAB (cetyl trimethyl ammonium bromide)/hexanol octane reversed micellar solution is a suitable medium for BSA solubilization. It seems that the forward transfer efficiency depends not only on the parameters of the two phases (for example: the pH value, the concentration and species of ions in the aqueous phase, the content of surfactant and co-solvent in reversed micellar solution), but also the titration behaviour and the concentration of the protein in aqueous phase. The experimental results lead to the conclusion that the major driving force in the protein extraction is electrostatic interaction. A modified phenomenological thermodynamic model for reversed micellar extraction was presented, and shown to correlate the data on extraction efficiency of BSA with both pH value and surfactant concentration. The effects of various factors, such as pH, and the type and concentration of salt in stripping solution, on BSA back transfer were also studied. It was found that the backward transfer efficiency of BSA is strongly influenced by the type of ions in stripping solution. When the operation runs under optimized conditions and with suitable phase ratio, the recovery and concentration of protein were successfully obtained. In addition, the problems how long the reversed micellar solutions can be recycled and how much of the surfactant will be lost to the aqueous phase have been examined.

Aqueous and nonaqueous microemulsions with high molecular weight alkanes

This study extends the existing phenomenological thermodynamic model of aqueous microemulsions to nonaqueous microemulsions and examines the phase patterns when the melting temperature of the alkane oil is in the range of other liquid-liquid transition temperatures. The liquid paraffins studied are the alkane oils of greater than 17 carbons and are solid at room temperature. Water, water and ethylene glycol (4∶1 by wt.), propylene glycol and water (4∶1 by wt.), and propylene glycol are the four non-oleic components examined. Homogeneous polyoxyethylene nonionic surfactants and the commercial surfactants of the Brij series, Neodol series, and the LP series were used. Small-angle x-ray scattering gives evidence for the presence of microstructures in these solutions and, thus these systems are true microemulsions at temperatures above the melting point of the alkane. Systematic paths to move from aqueous to nonaqueous microemulsions are outlined. These results are utilized in optimizing the performance requirements of an inkjet printing application.