Basic Thermodynamic Quantities Research Articles

On Lewis acidity/basicity and hydrogen bonding in the equation-of-state approach

The central objective of this work is to revisit the development of the widely used Lewis acidity/basicity scales and seek possibilities for their eventual unification. The primary focus is on hydrogen bonding interactions which are dealt with the estimation of hydrogen-bond-donor (HBD) and hydrogen-bond-acceptor (HBA) capacity of the compounds. The developments are made by having in mind their implementation in a thermodynamic equation-of-state framework for the reliable estimation of all basic thermodynamic quantities of compounds over a broad range of external conditions. Gutmann’s donor and acceptor numbers, the Hard–Soft Acid and Base principle, Drago’s electrostatic and covalent interaction parameters E and C, the LFER/LSER acidity and basicity, α and β (A and B), parameters, the Hansen partial hydrogen – bonding solubility parameters and Klamt’s quantum-chemically derived hydrogen – bonding cosmoments are all combined with the recent partial solvation parameter (PSP) approach in an effort to develop a unified hydrogen bonding scale. The challenges and the perspectives of this unification are critically discussed.

Entangled quantum Otto and quantum Stirling heat engine based on two-spin systems with Dzyaloshinski-Moriya interaction

Recently, the influences of the Dzyaloshinski-Moriya (DM) interaction on the performances of the basic thermo-dynamical quantities have attracted a lot of attention. A large number of investigations on the quantum coupling systems with DM interaction have been carried out. However, the specific effects of spin-orbit coupling with the performance on the quantum heat engine have not been taken into account in previous studies. DM interaction is a special kind spin-orbit coupling. To enrich the research of the quantum heat engines, the investigation about the effect of DM interaction on its thermodynamic characteristics should be included. In this study, we construct two entangled quantum engines based on spin-1/2 systems with different DM interactions, with the spin exchange constant and magnetic field fixed. The quantum Otto engine and the quantum Stirling engine are discussed in this article. By numerical calculation, we obtain the expressions for several thermodynamic quantities and plot the isoline maps of the variation of the basic thermodynamic quantities such as heat transfer, work with D1 and D2 and their efficiency in the two engines. The results indicate that the DM interaction plays an important role in the thermodynamic quantities for the quantum Otto engine and the quantum Stirling engine. In addition, the positive work condition is discussed with different DM interactions, with the spin exchange constant and magnetic field. Furthermore fixed, it is found that the efficiency of quantum Otto engine cycle is smaller than the Carnot efficiency while the quantum Stirling cycle can exceed the Carnot efficiency by using the regenerator. Finally, the second law of thermodynamics is shown to be valid in the two entangled quantum systems.

Stochastic disks that roll.

We study a model of rolling particles subject to stochastic fluctuations, which may be relevant in systems of nano- or microscale particles where rolling is an approximation for strong static friction. We consider the simplest possible nontrivial system: a linear polymer of three disks constrained to remain in contact and immersed in an equilibrium heat bath so the internal angle of the polymer changes due to stochastic fluctuations. We compare two cases: one where the disks can slide relative to each other and the other where they are constrained to roll, like gears. Starting from the Langevin equations with arbitrary linear velocity constraints, we use formal homogenization theory to derive the overdamped equations that describe the process in configuration space only. The resulting dynamics have the formal structure of a Brownian motion on a Riemannian or sub-Riemannian manifold, depending on if the velocity constraints are holonomic or nonholonomic. We use this to compute the trimer's equilibrium distribution with and without the rolling constraints. Surprisingly, the two distributions are different. We suggest two possible interpretations of this result: either (i) dry friction (or other dissipative, nonequilibrium forces) changes basic thermodynamic quantities like the free energy of a system, a statement that could be tested experimentally, or (ii) as a lesson in modeling rolling or friction more generally as a velocity constraint when stochastic fluctuations are present. In the latter case, we speculate there could be a "roughness" entropy whose inclusion as an effective force could compensate the constraint and preserve classical Boltzmann statistics. Regardless of the interpretation, our calculation shows the word "rolling" must be used with care when stochastic fluctuations are present.

First principle calculations of thermodynamic properties of pure graphene sheet and graphene sheets with Si, Ge, Fe, and Co impurities

The thermal properties of pure graphene and graphene–impurity (impurity = Fe, Co, Si, and Ge) sheets have been investigated at various pressures (0–7 GPa) and temperatures (0–900 K). Some basic thermodynamic quantities such as bulk modulus, coefficient of volume thermal expansion, heat capacities at constant pressure and constant volume of these sheets as a function of temperature and pressure are discussed. Furthermore, the effect of the impurity density and tensile strain on the thermodynamic properties of these sheets are investigated. All of these calculations are performed based on the density functional theory and full quasi harmonic approximation.

Soft mean spherical approximation for dusty plasma liquids: Level of accuracy and analytic expressions

The soft mean spherical approximation is employed for the study of the thermodynamics of dusty plasma liquids, the latter treated as Yukawa one-component plasmas. Within this integral theory method, the only input necessary for the calculation of the reduced excess energy stems from the solution of a single non-linear algebraic equation. Consequently, thermodynamic quantities can be routinely computed without the need to determine the pair correlation function or the structure factor. The level of accuracy of the approach is quantified after an extensive comparison with numerical simulation results. The approach is solved over a million times with input spanning the whole parameter space and reliable analytic expressions are obtained for the basic thermodynamic quantities.

Vigorous thermal excitations in a double-tetrahedral chain of localized Ising spins and mobile electrons mimic a temperature-driven first-order phase transition.

A hybrid spin-electron system defined on a one-dimensional double-tetrahedral chain, in which the localized Ising spin regularly alternates with two mobile electrons delocalized over a triangular plaquette, is exactly solved with the help of generalized decoration-iteration transformation. It is shown that a macroscopic degeneracy of ferromagnetic and ferrimagnetic ground states arising from chiral degrees of freedom of the mobile electrons cannot be lifted by a magnetic field in contrast to a macroscopic degeneracy of the frustrated ground state, which appears due to a kinetically driven frustration of the localized Ising spins. An anomalous behavior of all basic thermodynamic quantities can be observed on account of massive thermal excitations, which mimic a temperature-driven first-order phase transition from the nondegenerate frustrated state to the highly degenerate ferrimagnetic state at nonzero magnetic fields. A substantial difference in the respective degeneracies is responsible for an immense low-temperature peak of the specific heat and very abrupt (almost discontinuous) thermal variations of the entropy and sublattice magnetizations.

A kinetic model for anisotropic reactions in amorphous solids

When mechanical constraints are present, solid-state reactions often induce deviatoric inelastic strains in addition to volume change. Existing models either attribute such deformation to the plastic flow driven by the stress exceeding a non-measurable kinetic-dependent yield strength, or need to introduce a deviatoric-stress-dependent chemical potential. By employing the transformation strain to characterize the state of reaction, this letter formulates a kinetic model via averaging the reaction rate at all possible orientations. The model is illustrated through the constrained lithiation–delithiation process of silicon as an example. With just one fitting parameter, the model can quantitatively capture the experimental results. The model only hypothesizes linear kinetics, and does not need to introduce kinetic-dependent plasticity or modify basic thermodynamic quantities. This approach can also be applied to other material systems, as well as extended to the nonlinear kinetics of far-from-equilibrium reactions.

Consistent look-up table interpolation method for real-gas flow simulations

Nowadays the reliable modeling of real fluid flows is of paramount importance in many industrial applications, especially in the energy field with the growing diffusion of Organic Rankine Cycles, supercritical CO2 compressors, and advanced refrigeration systems. In these applications the assumption of flow ideality is profoundly inaccurate and may lead to erroneous physical interpretations. As a consequence thereof, various thermodynamic models have been recently developed for real gases and a number of tools are by now available to accurately predict the thermodynamic properties of fluids in presence of relevant non-ideal effects. However, these thermodynamic libraries are frequently computationally inefficient when coupled with existing simulation codes, such as in process modeling and computational fluid-dynamics (CFD).An effective alternative is proposed in this paper. The equations of state embedded in the thermodynamic programs are used, at preliminary level, to construct a grid of nodes storing a subset of thermo-physical properties, i.e. v,s,e,k,μ, required by the method for a given region of interest. Then, an interpolation-based method is conceived for determining the remaining properties in any other point. A key feature is as follows: the nodal values of the basic thermodynamic quantities are used to locally construct, i.e., within each cell of the table, a model of the fundamental relation, assuming a differentiable functional form of at least C2 class.The presented Look-up Table (LuT) approach is intrinsically consistent and guarantees thermodynamic stability, with inherent high accuracy and very limited computational costs, as demonstrated by the quantitative examples reported in the paper. As a final step, the LuT method is coupled with two in-house flow solvers and applied to simulate real gas transonic flow in Organic Rankine Cycle turbines; a comprehensive assessment of the approach is provided by comparison with direct equations of state implementation.

Soft mean spherical approximation for dusty plasma liquids: One-component Yukawa systems with plasma shielding.

The structure and thermodynamics of strongly coupled dusty plasmas are investigated with the soft mean spherical approximation. This integral theory approach is analytically solvable for Yukawa pair interactions yielding a closed-form solution for the direct correlation function. The pair correlation function, the structure factor, and basic thermodynamic quantities are calculated for a wide range of parameters. Exact consistency between the "energy"-"virial" thermodynamic routes and approximate consistency between the "energy"-"compressibility" paths is demonstrated. Comparison with extensive molecular dynamics results is carried out and a remarkable agreement from the Coulomb limit to the strongly screened limit is revealed. The soft mean spherical approximation is concluded to be particularly well suited for the study of dusty plasma liquids, uniquely combining simplicity and accuracy.

Interaction of Mn with GaAs and InSb: incorporation, surface reconstruction and nano-cluster formation

The deposition of Mn on to reconstructed InSb and GaAs surfaces, without coincident As or Sb flux, has been studied by reflection high energy electron diffraction, atomic force microscopy and scanning tunnelling microscopy. On both Ga- and As-terminated GaAs(0 0 1), (2 × n) Mn-induced reconstruction domains arise with n = 2 for the most well ordered reconstructions. On the Ga-terminated (4 × 6), the Mn-induced (2 × 2) persists up to around 0.5 ML Mn followed by Mn nano-cluster formation. For deposition on initially β2(2 × 4)-reconstructed GaAs(0 0 1), the characteristic trench structure of the reconstruction is partially preserved even beyond 1 monolayer Mn coverage. On both the β2(2 × 4) and c(4 × 4) surfaces, MnAs-like nano-clusters form alongside the reconstruction changes. In contrast, there are no new Mn-induced surface reconstructions on InSb. Instead, the Sb-terminated surfaces of InSb (0 0 1), (1 1 1)A and (1 1 1)B revert to reconstructions characteristic of clean In-rich surfaces after well defined coverages of Mn proportional to the Sb content of the starting reconstruction. These surfaces are decorated with self-assembled MnSb nanoclusters. These results are discussed in terms of basic thermodynamic quantities and the generalized electron counting rule.

Magnetization and Susceptibility of a Diluted Triangular Ising Antiferromagnet in a Field

Within the framework of the e ectiveeld theory with correlations we investigate e ects of an external magnetic eld and random site dilution on basic thermodynamic quantities, such as the magnetization and the magnetic susceptibility, on the geometrically frustrated triangular lattice Ising antiferromagnet. Behavior of these quantities is presented in the temperatureeld parameter space for selected mild degrees of dilution. It is found that, besides the anomalies associated with phase transitions from the ferrimagnetic to the paramagnetic state, in certain regions of the parameter space these functions display some more anomalies and peculiarities, as a result of joint e ects of the geometrical frustration, magnetic dilution, thermal uctuations and the applied magnetic eld.

Magnetization process, bipartite entanglement, and enhanced magnetocaloric effect of the exactly solved spin-1/2 Ising-Heisenberg tetrahedral chain.

The frustrated spin-1/2 Ising-Heisenberg ladder with Heisenberg intra-rung and Ising inter-rung interactions is exactly solved in a longitudinal magnetic field by taking advantage of the local conservation of the total spin on each rung and the transfer-matrix method. We have rigorously calculated the ground-state phase diagram, magnetization process, magnetocaloric effect, and basic thermodynamic quantities for the model, which can be alternatively viewed as an Ising-Heisenberg tetrahedral chain. It is demonstrated that a stepwise magnetization curve with an intermediate plateau at half of the saturation magnetization is also reflected in respective stepwise changes of the concurrence serving as a measure of bipartite entanglement. The ground-state phase diagram and zero-temperature magnetization curves of the Ising-Heisenberg tetrahedral chain are contrasted with the analogous results of the purely quantum Heisenberg tetrahedral chain, which have been obtained through density-matrix renormalization group (DMRG) calculations. While both ground-state phase diagrams fully coincide in the regime of weak inter-rung interaction, the purely quantum Heisenberg tetrahedral chain develops Luttinger spin-liquid and Haldane phases for strongly coupled rungs, which are absent in the Ising-Heisenberg counterpart model.

A special entangled quantum heat engine based on the two-qubit Heisenberg XX model

We construct a special four-level entangled quantum Otto heat engine based on the two-qubit Heisenberg XX model, in which we assume that all the energy gaps are changed in the same ratio in the two quantum adiabatic processes. Hence during the whole cycle, the relative coupling constant κ = J/B is fixed, where J and B are the coupling constant and the external magnetic field, respectively. The dependence of the basic thermodynamical quantities on the two entanglements at the end of two quantum isochoric processes with different relative coupling constants κ is studied. Our results show that in the weak coupling region, i.e. κ < 1, the heat engine can be operated in both areas where c1 < c2 and c1 > c2, whereas when κ ⩾ 1, it only operates under the condition c1 < c2. Here c1 and c2 are entanglements of the working substance when it comes into contact with hot and cold baths, respectively. Moreover, we find that the maximal work output for fixed κ increases with the relative coupling constant.

Bulk viscosity of quark-gluon matter in a magnetic field

On the basis of low-energy QCD theorems, the bulk viscosity ζ(T, µ, H) is expressed in terms of basic thermodynamic quantities that characterizes quark-gluon matter at finite temperature and a finite baryon density in a magnetic field. Various limiting cases are considered.

MAGNETIC IMPURITY IN THE VICINITY OF A VACANCY IN BILAYER GRAPHENE

We use quantum Monte Carlo method to study a magnetic impurity located next to a vacancy in Bernal stacked bilayer graphene. Due to the broken symmetry between two sublattices in bilayer system, there exist two different types of vacancy induced localized state. We find that the magnetic property of the adatom located on the adjacent site of the vacancy depends on whether the vacancy belongs to A or B sublattice. In general, local moment is more strongly suppressed if the vacancy belongs to the sublattice A near the zero-energy. We switch the values of the chemical potential and study the basic thermodynamic quantities and the correlation functions between the magnetic adatom and carbon sites.

A thermal entangled quantum refrigerator based on a two-qubit Heisenberg model with Dzyaloshinskii—Moriya interaction in an external magnetic field

Based on an isotropic two spin-1/2 qubits Heisenberg model with the Dzyaloshinskii—Moriya interaction in an external magnetic field, we have constructed an entangled quantum refrigerator. Expressions for the basic thermodynamic quantities, i.e., the heat exchanged, the net work input, and the coefficient of performance, are derived. Some intriguing features and their qualitative explanations in zero and non zero magnetic fields are given. The influence of the thermal entanglement on the refrigerator is investigated. The results obtained here have general significance and will be helpful to understand the performance of an entangled quantum refrigerator.

A comparative study of statistical models for nuclear equation of state of stellar matter

We compare three different statistical models for the equation of state (EOS) of stellar matter at subnuclear densities and temperatures (0.5–10 MeV) expected to occur during the collapse of massive stars and supernova explosions. The models introduce the distributions of various nuclear species in nuclear statistical equilibrium, but use somewhat different nuclear physics inputs. It is demonstrated that the basic thermodynamical quantities of stellar matter under these conditions are similar, except in the region of high densities and low temperatures. We demonstrate that mass and isotopic distributions have considerable differences related to the different assumptions of the models on properties of nuclei at these stellar conditions. Overall, the three models give similar trends, but the details reflect the uncertainties related to the modeling of medium effects, such as the temperature and density dependence of surface and bulk energies of heavy nuclei, and the nuclear shell structure effects. We discuss importance of new physics inputs for astrophysical calculations from experimental data obtained in intermediate energy heavy-ion collisions, in particular, the similarities of the conditions reached during supernova explosions and multifragmentation reactions.

Unconventional quantum ordered and disordered states in the highly frustrated spin-12Ising-Heisenberg model on triangles-in-triangles lattices

The spin-$\frac{1}{2}$ Ising-Heisenberg model on two geometrically related triangles-in-triangles lattices is exactly solved through the generalized star-triangle transformation, which establishes a rigorous mapping correspondence with the effective spin-$\frac{1}{2}$ Ising model on a triangular lattice. Basic thermodynamic quantities were exactly calculated within this rigorous mapping method along with the ground-state and finite-temperature phase diagrams. Apart from the classical ferromagnetic phase, both investigated models exhibit several unconventional quantum ordered and disordered ground states. A mutual competition between two ferromagnetic interactions of basically different character generically leads to the emergence of a quantum ferromagnetic phase, in which a symmetric quantum superposition of three up-up-down states of the Heisenberg trimers accompanies a perfect alignment of all Ising spins. In the highly frustrated regime, we have either found the disordered quantum paramagnetic phase with a substantial residual entropy or a similar but spontaneously ordered phase with a nontrivial criticality at finite temperatures. The latter quantum ground state exhibits a striking coexistence of imperfect spontaneous order with partial disorder, which is evidenced by a quantum reduction of the spontaneous magnetization of Heisenberg spins that indirectly causes a small reduction of the spontaneous magnetization of otherwise classical Ising spins.

Polymer–polymer miscibility and partial solvation parameters

The novel predictive approach of Partial Solvation Parameters (PSP) is extended and applied to polymer mixtures. Quantum mechanics and statistical thermodynamics are used in order to extract information on the molecular descriptors of each compound and develop simple analytical expressions for all basic thermodynamic quantities of mixtures. Emphasis is given on hydrogen-bonded polymer mixtures. Apart from polymer–polymer miscibility, the PSP approach is used for the prediction of melting point depression, fraction of hydrogen-bonded groups, critical composition of a copolymer for miscibility with another polymer, and the Flory–Huggins χ1,23 interaction parameter of a solute-probe (1) at infinite dilution in a mixture of polymers (2,3) which is obtained from inverse gas chromatography (IGC) experiments. The predictions are compared with experimental data and the agreement is critically discussed. The predictions of polymer–polymer miscibility on the basis of spinodal lines are compared with the corresponding predictions on the basis of χ interaction parameters. The strength and weakness of the approach are also critically discussed in relation with its capacity and reliability to act as a designing tool of new compatible polymer blends. The perspectives of this unified approach to solution thermodynamics are discussed.

Thermal entangled quantum Otto engine based on the two qubits Heisenberg model with Dzyaloshinskii–Moriya interaction in an external magnetic field

Based on the isotropic two spin-1/2 qubits Heisenberg model with Dzyaloshinskii–Moriya interaction in a constant external magnetic field, we have constructed the entangled quantum Otto engine. Expressions for the basic thermodynamic quantities, i.e. the amount of heat exchange, the net work output and the efficiency, are derived. The influence of thermal entanglement on these basic thermodynamic quantities is investigated. Moreover, some intriguing features and their qualitative explanations in zero and finite magnetic field are given. The validity of the second law of thermodynamics is confirmed in the system. The results obtained here have general significance and will be useful in increasing understanding of the performance of an entangled quantum engine.