Second-order Transition Temperature Research Articles

The Effect of Temperature on the London Dispersive and Lewis Acid-Base Surface Energies of Polymethyl Methacrylate Adsorbed on Silica by Inverse Gas Chromatography

Inverse gas chromatography at infinite dilution was used to determine the surface thermodynamic properties of silica particles and PMMA adsorbed on silica, and more particularly, to quantify the London dispersive energy γsd, the Lewis acid γs+, and base γs− polar surface energies of PMMA/silica composites as a function of the temperature and the recovery fraction θ of PMMA. The polar acid-base surface energy γsAB and the total surface energy of the different composites were then deduced as a function of the temperature. In this paper, the Hamieh thermal model was used to quantify the surface thermodynamic energy of polymethyl methacrylate (PMMA) adsorbed on silica particles at different recovery fractions. A comparison of the new results was carried out with those obtained by applying other molecular models of the surface areas of organic molecules adsorbed on the different solid substrates. An important deviation of these molecular models from the thermal model was proved. The determination of γsd, γs+, γs−, and γsAB of PMMA in both the bulk and adsorbed phases showed an important non-linearity variation of these surface parameters as a function of the temperature. The presence of maxima in the curves of γsd(T) highlighted the second-order transition temperatures in PMMA showing beta-relaxation, glass transition, and liquid–liquid temperatures. These three transition temperatures depended on the adsorption rate of PMMA on silica. The proposed method gave a new relation between the recovery fraction of PMMA and its London dispersive energy, showing an important effect of the temperature on the surface energy parameters of the adsorption of PMMA on silica. A universal equation relating γsd(T,θ) of the systems PMMA/silica to the recovery fraction and the temperature was proposed.

Effect of Al ions on the hyperthermia properties of oleic acid-coated Sr2-xAlxFeMoO6 nanoparticles

A self-regulating magnetic fluid with a suitable second-order phase transition temperature for achieving hyperthermia treatment temperatures is investigated for use as a possible mild cancer treatment. Current studies have focused on the optimization of magnetic fluids. In this work, magnetic fluids of Al-doped Sr2FeMoO6 nanoparticles are investigated based on their relatively high saturation magnetization. The nanoparticles are synthesized using a simple sol–gel method, successfully nanomized, and then coated by oleic acid through ball milling to prevent oxidation and improve biocompatibility. The crystal structure, morphology, basic magnetic properties and heating properties of the samples in a high-frequency magnetic field are investigated. It is found that oleic acid-coated Sr1.98Al0.02FeMoO6 nanoparticles with a particle diameter of ~ 140 nm and a maximum heating temperature of 47.8 °C at a concentration of 2 mg·ml−1 possess excellent induction heating properties. The saturation magnetization, coercive force, specific absorption rate and effective specific absorption rate are 18 emu/g, 5.14 mT, 41.8 W·g−1 and 0.0193 W·g−1·kHz·(kA·m−2), respectively.

The crystal-field dependency of sound attenuation in the spin-3/2 ising model

The effects of crystal-field (D) on sound attenuation are considered for the spin-3/2 Ising model by using Onsager theory of irreversible thermodynamics. It is assumed that the sound wave couples to the order-parameter fluctuations, therefore, it decays mainly via order-parameter relaxation process. The order-parameters, magnetization and quadrupole moment, are defined in terms of exact recursion relations (ERR) on Bethe lattice (BL). After our analysis, two relaxation times are obtained and they are used to calculate the sound attenuation coefficient (α). Consequently, the critical behaviors of sound attenuation coefficient are investigated in terms of frequency (w) and Onsager coefficient (γ) for the coordination numbers q=3, 4 ad 6 near the second-order (Tc) and first-order (Tt) phase transition temperatures in the ferromagnetic phase regions for the negative and positive D values and the results are presented on the (kBT/J, α) planes. It is found that the peaks about Tt’s are observed at the same temperature, but the peaks about Tc’s are observed shifted to lower and higher temperatures in increasing (w)’s and (γ)’s, respectively. In addition, the peaks are also obtained near the tricritical points for all q.

Critical and multicritical behaviors of static and complex magnetic susceptibilities for the mean-field Blume-Capel model with a random crystal field

The static and dynamic linear response functions for the spin-1 mean-field Blume-Capel model with a random diluted single-ion anisotropy are derived using the thermodynamics of linear irreversible processes. Thermal dependence of the static susceptibility is studied in detail. In addition, by utilizing the stationary solution of the kinetic equation in existence of sinusoidal external magnetic field, the low frequency thermal behavior of the magnetic absorption and dispersion factors are investigated. Particularly, we have analyzed the behaviors of these quantities near both first- and second-order transition temperatures and multicritical points such as tricritical point, critical endpoint and double critical endpoint. The static and dynamical mean field critical exponents in hydrodynamic limit are also calculated in order to formulate the critical and multicritical behaviors of the magnetic susceptibility. Finally, a comparison of the findings of this study with previous theoretical and experimental studies is presented and it is shown that a good agreement is found with our results.

Ehrenfest equations for second-order phase transition under hydrostatic and uniaxial stresses

ABSTRACTFor 40 years, many research works have been confusing the linear part of the Ehrenfest equation for the shift of the second-order phase transition temperature in solids by the hydrostatic pressure with the equation for the shift caused by the uniaxial pressure . While the sum of the three slopes is trivially equal to the slope due to hydrostatic pressure , the sum of calculated from the exact Ehrenfest equation for the uniaxial pressure generally does not coincide with and may differ from by the sign and by the absolute value by more than three times.

Structural and magnetic properties with large reversible magnetocaloric effect in (La1-xPrx)0.85Ag0.15MnO3 (0.0 ≤ x ≤ 0.5) compounds

We report on the effect of Pr doping on structural, magnetic and magnetocaloric properties in (La1−xPrx)0.85Ag0.15MnO3 (0.0 ≤ x ≤ 0.5) compounds. The main crystal structure has been studied by performing X-ray diffraction method and structural analysis based on Rietveld method where it is found that although samples at low concentration level (x ≤ 0.2) have rhombohedral phase , others (x ≥ 0.3) have orthorhombic (Pbnm) phase. Scanning electron microscope images show that the average particle size decreases by increasing Pr amount in the main structure. It is observed that the second-order transition temperature from ferromagnetic to paramagnetic phase is dramatically decreased from 262 to 138 K by increasing Pr concentration in (La1−xPrx)0.85Ag0.15MnO3. On the other hand, all samples have also antiferromagnetic coupling observed below TN ~ 50 K. The maximum magnetic entropy change (−ΔSM)max and relative cooling power values were found in the range of 7.90–2.88 J/kg K and 213.32–153.50 J/kg, respectively, under 50 kOe field change in our samples. It can be argued that particularly the compounds LPAM with x = 0.0, 0.1 and 0.2 are expected to be promising candidate for magnetic refrigeration.

The thermodynamic functions of ferroelectric and paraelectric SbSI

A first-principle method is used to calculate phonon density of states, Helmholtz free energy, internal energy, and entropy for ferroelectric and paraelectric SbSI. Theoretical phase transition temperature was obtained using the difference of the Helmholtz free energy, internal energy, and entropy term between ferroelectric and paraelectric phases on temperature. The obtained value is in reasonable agreement with the experimental second-order phase transition temperature Tc2 = 233 K.

±J model on the Bethe lattice with crystal field interaction

±J model was exploited on the Bethe lattice for the spin-1 Blume–Capel model. Either ferromagnetic (J>0) or antiferromagnetic (J<0) interactions are assumed between the nearest-neighbor (NN) spins on the Bethe lattice for given probabilities p or 1−p, respectively. The phase diagrams of the model were calculated exactly on the temperature (T)–probability (p) or crystal field (D) planes for given coordination numbers q=3, 4 and 6. In addition to the first- and second-order phase transitions, another kind phase transition with zero magnetization and quadrupolar order-parameter presenting a jump was obtained above the second-order phase transition temperature which seems to be indicating the spin glass phase. When the lines of these three phases combine is a multicritical point and the first two combine is a tricritical point. In the (T,p) planes, the lower critical dimensions (the value of q) of obtaining any phase transition increase with increasing negative D values.

An effective field theory study of layering transitions in Blume–Capel thin films in the presence of quenched random crystal fields

In the presence of quenched random crystal fields, phase transitions in magnetic thin films described by the spin-1 Blume–Capel model have been investigated using effective field theory (EFT). Crystal field disorder has been sampled by introducing dilute and trimodal random crystal fields. For dilute crystal fields, in the highly anisotropic limit (D→∞), we have found that the critical value of the surface to bulk ratio of exchange interactions (Rc) at which the second-order transition temperature becomes independent of the film thickness is a spin-dependent property of thin magnetic films. Moreover, as a percolation problem, we have performed detailed calculations in the limit D→−∞, and it has been shown that a novel feature emerges in the presence of enhanced surfaces. Besides, for trimodal random crystal fields, the variation of the special point Rc as a function of the random field parameters has been elucidated. Finally, in the limit D→∞, based on the numerical data provided by EFT, we have introduced an analytical expression for the variation of Rc as a function of the randomness parameter p of the trimodal distribution.

Influence of glycerol and water activity on the properties of compressed egg white-based bioplastics

In this paper, the effects of glycerol (35%, 40% and 45%) and water activity (0.34 and 0.48) on the physical, mechanical and morphological properties of compressed egg white-based bioplastics are investigated. Lighter, more reddish and less yellowish sheets with a decreased thickness and second-order transition temperature, improved mechanical properties (increased flexibility and decreased rigidity and stiffness) and constant moisture content can be obtained by increasing water activity. Increasing the GLY content results in the same type of changes but to a lesser extent and increased moisture content. Increasing both, water activity and GLY, leads to a more pronounced effect for some properties. This study demonstrates that compressed egg white-based bioplastics with desired properties can be obtained by adjusting water activity and GLY content during their synthesis.

Relaxation and Miscibility of the Blends of a Poly (Ether Imide) (Ultem™) and a Phenol-A-Based Copolyester (Ardel™) by Inverse Gas Chromatography

Inverse gas chromatography (IGC) was used to analyze the secondary transition temperatures and the miscibility of binary mixtures of poly (ether imide) (Ultem™) and a copolyester of bisphenol-A with terephthalic and isophthalic acids (50/50) (Ardel™) in three compositions (25/50, 50/50 and 75/25). Retention diagrams of the mixtures of Ultem™ and Ardel™ for n-nonane, n-decane, n-butyl acetate and isoamyl acetate were obtained at temperatures between 60 and 285 °C. Second-order transition temperatures of the mixtures were determined according to the slope change in retention diagrams of the solvents. The glass transition temperatures of the mixtures suggested the miscibility of the polymers. Polymer–polymer interaction parameters of binary mixtures of the polymers were determined at temperatures between 260 and 285 °C by Flory–Huggins theory. The polymer–polymer interaction parameters were dependent on the solvent used. The small values of polymer–polymer interaction parameters close to zero suggest some weak interactions between the polymers in the mixture. It was concluded that it was possible to obtain more meaningful information related to the interactions of polymers in a mixture from IGC measurements, if binary polymer–solvent interaction parameters of the used solvent probes were around 0.5.

The Bethe lattice treatment of sound attenuation for a spin- 3/2 Ising model

The sound attenuation phenomena is investigated for a spin- 3/2 Ising model on the Bethe lattice in terms of the recursion relations by using the Onsager theory of irreversible thermodynamics. The dependencies of sound attenuation on the temperature (T), frequency (w), Onsager coefficient (γ) and external magnetic field (H) near the second-order (Tc) and first-order (Tt) phase transition temperatures are examined for given coordination numbers q on the Bethe lattice. It is assumed that the sound wave couples to the order-parameter fluctuations which decay mainly via the order-parameter relaxation process, thus two relaxation times are obtained and which are used to obtain an expression for the sound attenuation coefficient (α). Our investigations revealed that only one peak is obtained near Tt and three peaks are found near Tc when the Onsager coefficient is varied at a given constant frequency for q=3. Fixing the Onsager coefficient and varying the frequency always leads to two peaks for q=3,4 and 6 near Tc. The sound attenuation peaks are observed near Tt at lower values of external magnetic field, but as it increases the sound attenuation peaks decrease and eventually disappear.

Topologically correct phase boundaries and transition temperatures for Ising Hamiltonians via self-consistent coarse-grained cluster-lattice models

We derive a cluster mean-field theory for an Ising Hamiltonian using a cluster-lattice Fourier transform with a cluster of size ${N}_{\mathrm{c}}$ and a coarse-grained (CG) lattice into cells of size ${N}_{\mathrm{cell}}$. We explore forms with ${N}_{\mathrm{cell}}\ensuremath{\geqslant}{N}_{\mathrm{c}}$, including a non-CG (NCG) version with ${N}_{\mathrm{cell}}\ensuremath{\rightarrow}\ensuremath{\infty}$. For ${N}_{\text{c}}={N}_{\mathrm{cell}}$, the set of static, self-consistent equations relating cluster and CG lattice correlations is analogous to that in dynamical cluster approximation and cellular dynamical mean-field theory used in correlated electron physics. A variational ${N}_{\mathrm{c}}$-site cluster grand potential based on ${N}_{\mathrm{c}}={N}_{\mathrm{cell}}$ CG lattice maintains thermodynamic consistency and improves predictions, recovering Monte Carlo and series expansion results upon finite-size scaling; notably, the ${N}_{\mathrm{c}}=1$ CG results already predict well the first- and second-order phase boundary topology and transition temperatures for frustrated lattices. The NCG version is significantly faster computationally than the CG case and more accurate at fixed ${N}_{\mathrm{c}}$ for ferromagnetism, which is potentially useful for cluster expansion and quantum cluster applications.

High-field metamagnetism in the antiferromagnetCeRh2Si2

A study of the antiferromagnet CeRh$_2$Si$_2$ by torque, magnetostriction, and transport in pulsed magnetic fields up to 50 Tesla and by thermal expansion in static fields up to 13 Tesla is presented. The magnetic field-temperature phase diagram of CeRh$_2$Si$_2$, where the magnetic field is applied along the easy axis $\mathbf{c}$, is deduced from these measurements. The second-order phase transition temperature $T_{N}$ and the first-order phase transition temperature $T_{1,2}$ (=~36 K and 26 K at zero-field, respectively) decrease with increasing field. The field-induced antiferromagnetic-to-paramagnetic borderline $H_c$, which equals 26 T at 1.5 K, goes from first-order at low temperature to second-order at high temperature. The magnetic field-temperature phase diagram is found to be composed of (at least) three different antiferromagnetic phases. These are separated by the first-order lines $H_{1,2}$, corresponding to $T_{1,2}$ at H=0, and $H_{2,3}$, which equals 25.5 T at 1.5 K. A maximum of the $T^2$-coefficient $A$ of the resistivity is observed at the onset of the high-field polarized regime, which is interpreted as the signature of an enhanced effective mass at the field-induced quantum instability. The magnetic field dependence of the $A$ coefficient in CeRh$_2$Si$_2$ is compared with its pressure dependence, and also with the field dependence of $A$ in the prototypal heavy-fermion system CeRu$_2$Si$_2$.

Thermal Analytical Investigation of Biopolymers and Humic- and Carbonaceous-Based Soil and Sediment Organic Matter

Improved understanding of the physical, chemical, and thermodynamic properties of soil and sediment organic matter (SOM) is crucial in elucidating sorption mechanisms of hydrophobic organic compounds (HOCs) in soils and sediments. In this study, several thermoanalytical techniques, including thermal gravimetric analysis (TGA), differential scanning calorimetry (DSC), temperature-modulated differential scanning calorimetry (TMDSC), and thermal mechanical analysis (TMA) were applied to 13 different organic materials (three woods, two humic acids, three kerogens, and five black carbons) representing a spectrum of diagenetic and/or thermal histories. Second-order thermal transition temperatures (T(t)) were identified in most materials, where the highest observed T(t) values (typically characterized as glass transition temperatures (T(g were shown to closely relate to chemical characteristics of the organic samples as influenced by diagenetic or thermal alteration. Results further suggest a positive correlation between glass transition temperature and a defined diagenetic/thermal index, where humic-based SOM (e.g., humic and fulvic acids) possess lowertransition temperatures than more "mature" carbonaceous-based SOM (i.e., kerogens and black carbons). The observed higher thermal transition temperature of aliphatic-rich Green River shale kerogen (approximately 120 degrees C) relative to that of aromatic-rich humic acids suggests that a sole correlation of aromaticity to thermal transition temperature may be inappropriate.

DC electric field effects on Ehrenfest-like relations at the glass transition

There have been numerous studies on the effects of dc and alternating electric fields on phase transitions in small-molecule mixtures and high-molecular weight polymers. Furthermore, textbook examples discuss modifications in the melting temperature of pure materials that are subjected to uniform dc fields. This thermodynamic analysis extends some of these predictions to second-order phase transitions. Upon invoking both volume and entropy continuity via the integral approach to phase equilibrium at second-order transitions, electric field effects on the glass transition are developed that parallel the Ehrenfest equations for the pressure dependence of Tg. Both Tg-field equations predict small changes in the glass transition temperature that scale as the square of the electric field strength. If one equates the dependence of Tg on the magnitude of the electric field via (i) volume continuity and (ii) entropy continuity, it is possible to obtain the electric-field analog of the Prigogine–Defay equality, in which thermophysical properties and discontinuous observables at the zero-field and field-dependent second-order phase transition temperatures are related. When the temperature and pressure dependencies of the relative electric permittivity (i.e., dielectric constant) are neglected in the absence of external fields, one recovers the classic Prigogine–Defay equality (i.e., the lower limit of the Prigogine–Defay ratio) that was developed from a consideration of volume and entropy continuity for the pressure dependence of Tg, by invoking the differential approach to phase equilibrium.

Sideways dynamics of ferroelectric domain walls

Characteristic features of the sideways motion of domain walls in ferroelectrics are considered. The proposed model for calculating the mobility of domain walls for this type of motion is based on the approaches developed by D. G. Sannikov and M. A. Collins et al. We examine the dynamics of domain walls in the vicinity of second-order phase transitions. The calculated domain wall mobility is in agreement with experiment in Pb 5Ge 3O 11, Pb 5− x Ba x Ge 3O 11, Rochelle salt, gadolinium molybdate, terbium molybdate, triglycine sulphate, and barium titanate. It is shown that the velocity of domain walls is proportional to the difference between the applied field and a threshold field. Good agreement with experiments in a number of ferromagnets and ferroelectrics is obtained in this aspect. The coupling of the spontaneous polarization to the strain is shown to induce propagation of solitary stress waves during the domain wall motion in ferroelectrics. We analyse some properties of stress wave propagation within the framework of the suggested model as well the elastic, electrostrictive and piezoelectric effects on the domain wall motion. The contribution of inertia to the velocity of domain walls is calculated. The domain wall mass for 180° walls in barium titanate estimated in the framework of the model is in accordance with its known value. Magnetic-field-induced motion of ferroelectric domain walls is considered. The finite-size effect on the mobility of domain walls is calculated. The mobility exhibits a critical increase when the sample thickness decreases. This behaviour is similar to the temperature growth of the mobility in the vicinity of the second-order phase transition temperature obtained in this model.

Structural and Magnetic Transition Temperatures of Full Heusler Ni-Mn-Sn Alloys Determined by Van der Pauw Method

We have measured the electrical resistivity of full Heusler Ni2Mn2–xSnx (0.52 ≤ x ≤ 0.6) by a Van der Pauw method to determine a first-order structural transition temperature, MS, and a second-order magnetic transition temperature, TC. MS and TC are respectively decreasing and increasing linearly with the increasing Sn content x. Although the MS and TC become closer, two phase transitions, i.e., the magnetic and martensitic phase transitions, do not undergo simultaneously in the range of 0.52 ≤ x ≤ 0.6.

On the glassy state of multiphase and pure polymer materials

In this work we formulate a new glass theory and investigate its suitability for describing the mechanical response of thermoplastic elastomers composed of styrenic-block copolymers. These materials are composed of glassy domains of polystyrene, which physically link soft rubbery chain segments made of either polybutadiene or polyisoprene. We demonstrate that the crossover in the shift factors, observed experimentally to change from Williams–Landel–Ferry to Arrhenius behavior passing through a characteristic crossover temperature T∗ from below, coincides with the crossover from power-law to stretched-exponential behavior of the stress relaxation found in recent tensile experiments. Moreover, we show that the characteristic crossover temperature T∗ is identical with the underlying true equilibrium second-order phase transition temperature T2 of the polystyrene crosslinks, predicted by the thermodynamic theory of Gibbs and Di Marzio for pure glassy polystyrene in the infinite-time limit. By combining the recently introduced theory of Di Marzio and Yang with the significant-structure theory of Eyring and Ree, we develop a new glass theory, which is capable of explaining the mechanical response of multiphase as well as pure glassy materials. Moreover, we show a clear evidence for the existence of T2 postulated in 1950s for pure glasses and hotly debated since then.

Theory of relaxation phenomena in a spin- [formula omitted] Ising system near the second-order phase transition temperature

The relaxation behavior of the spin- 3 / 2 Ising model Hamiltonian with bilinear and biquadratic interactions near the second-order phase transition temperature or critical temperature is studied by means of the Onsager's theory of irreversible thermodynamics or the Onsager reciprocity theorem (ORT). First, we give the equilibrium case briefly within the molecular-field approximation in order to study the relaxation behavior by using the ORT. Then, the ORT is applied to the model and the kinetic equations are obtained. By solving these equations, three relaxation times are calculated and examined for temperatures near the second-order phase transition temperature. It is found that one of the relaxation times goes to infinity near the critical temperature on either side, the second relaxation time makes a cusp at the critical temperature and third one behaves very differently in which it terminates at the critical temperature while approaching it, then showing a “flatness” property and then decreases. We also study the influences of the Onsager rate coefficients on the relaxation times. The behavior of these relaxation times is discussed and compared with the spin- 1 / 2 and spin-1 Ising systems.