Thermodynamic Properties for Carbon Dioxide

Sustainable Copolymer Synthesis from Carbon Dioxide and Butadiene

Carbon dioxide (CO2) has long been recognized as an ideal C1 feedstock comonomer for producing sustainable materials because it is renewable, abundant, and cost-effective. However, activating CO2 presents a significant challenge because it is highly oxidized and stable. A CO2/butadiene-derived δ-valerolactone (EVP), generated via palladium-catalyzed telomerization between CO2 and butadiene, has emerged as an attractive intermediate for producing sustainable copolymers from CO2 and butadiene. Owing to the presence of two active carbon-carbon double bonds and a lactone unit, EVP serves as a versatile intermediate for creating sustainable copolymers with a CO2 content of up to 29 wt % (33 mol %). In this Review, advances in the synthesis of copolymers from CO2 and butadiene with divergent structures through various polymerization protocols have been summarized. Achievements made in homo- and copolymerization of EVP or its derivatives are comprehensively reviewed, while the postmodification of the obtained copolymers to access new polymers are also discussed. Meanwhile, potential applications of the obtained copolymers are also discussed. The literature references were sorted into sections based on polymerization strategies and mechanisms, facilitating readers in gaining a comprehensive view of the present chemistry landscape and inspiring innovative approaches to synthesizing novel CO2-derived copolymers.

Prediction of vibrational spectrum and thermodynamic properties for phosphorus mononitride

In this work, an accurate potential energy curve (PEC) for the ground electronic state of phosphorus mononitride (PN) molecule has been determined from a variationally improved Hulburt-Hirschfelder (VIHH) oscillator model in conjunction with the experimental spectral constants (De,ωe,ωexe,Be,αe,re). We have numerically solved the Schrödinger equation for the VIHH potential using the LEVEL program, obtaining the pure vibrational spectrum that converges to the dissociation limit. In addition, the partition functions of PN molecule are calculated using the full rovibrational energies. Ultimately, thermodynamic properties like molar heat capacity, entropy, enthalpy, and Gibbs free energy were calculated for the PN molecule and show good agreement with those data from the NIST (National Institute of Standards and Technology) database.

Bound-state energy spectrum and thermochemical functions of the deformed Schiöberg oscillator

In this study, a diatomic molecule interacting potential such as the deformed Schiöberg oscillator (DSO) have been applied to diatomic systems. By solving the Schrödinger equation with the DSO, analytical equations for energy eigenvalues, molar entropy, molar enthalpy, molar Gibbs free energy and constant pressure molar heat capacity are obtained. The obtained equations were used to analyze the physical properties of diatomic molecules. With the aid of the DSO, the percentage average absolute deviation (PAAD) of computed data from the experimental data of the 7Li2 (2 3Πg), NaBr (X 1Σ+), KBr (X 1Σ+) and KRb (B 1Π) molecules are 1.3319%, 0.2108%, 0.2359% and 0.8841%, respectively. The PAAD values obtained by employing the equations of molar entropy, scaled molar enthalpy, scaled molar Gibbs free energy and isobaric molar heat capacity are 1.2919%, 1.5639%, 1.5957% and 2.4041%, respectively, from the experimental data of the KBr (X 1Σ+) molecule. The results for the potential energies, bound-state energy spectra, and thermodynamic functions are in good agreement with the literature on diatomic molecules.

Visible-light-induced bifunctionalisation of (homo)propargylic amines with CO2 and arylsulfinates

An unprecedented carboxylative sulfonylation of (homo)propargyl amines with CO2 and sodium arylsulfinates under visible light irradiation has been developed with high efficiency. This ruthenium-catalysed photochemical protocol offers broad substrate scope giving 2-oxazolidinones and 2-oxazinones bearing alkyl sulfones in good yields under ambient reaction conditions. An in situ double bond isomerisation occurs in tandem. A mechanistic rationale for these radical-initiated carboxylative cyclisations involving sulfinyl radicals is presented, supported by control and quenching experiments.

Information theory and thermodynamic properties of diatomic molecules using molecular potential

Owing to the devise applications of molecules in industries, the bound state solution of the non-relativistic wave equation with a molecular potential function has been obtained in a closed-form using the Nikiforov-Uvarov method. The solutions of the bound state are then applied to study the information-theoretic measures such as the one-dimensional Shannon and Renyi entropic densities. The expectation values for the position and momentum spaces were obtained to verify the Heisenberg's uncertainty principle. Utilizing the energy spectrum equation, the thermodynamic vibrational partition function is obtained via the Poisson summation. Other thermodynamic function variations with absolute temperature have been obtained numerically for four diatomic molecules (H2, N2, O2, and HF) using Maple 18 software. The Shannon global entropic sum inequality has also been verified. The Renyi sum for constrained index parameters satisfies the global entropic inequality. The thermodynamic properties of the four molecules are similar and conform to works reported in the existing literature. The obtained vibrational energies are in fair agreement with the ones obtained using other forms of potential energy. The result further indicates that the lowest bounds for the Shannon, Renyi, and Heisenberg inequalities are ground states phenomena.

Theoretic measure and thermal properties of a standard Morse potential model

Since the proposition of the standard form of Morse potential [Formula: see text] model over the years, there has not been much attention on the potential. Its application to different studies such as the thermodynamic properties and information theory are yet to be reported to the best of our understanding. In this study, the solutions of the radial Schrödinger equation for the standard Morse potential is obtained using supersymmetric approach. The effect of the quantum number on the energy eigenvalue for the standard Morse potential is examined numerically for the hydrogen molecule (H₂), lithium molecule (Li₂), and potassium molecule (K₂). Using the energy equation and the wave function obtained, the theoretic measures and thermodynamic properties of hydrogen, lithium, and potassium molecules are calculated via maple program. It has been shown that the energy of the standard Morse potential is fully bounded for the three molecules studied. A higher concentration of electron density corresponds to a strongly localized distribution in the position configuration. The Beckner, Bialynicki-Birula, and Mycieslki (BBM) inequality is satisfied for both the ground state and the first excited state. Finally, the product of uncertainty obtained obeyed the Heisenberg uncertainty relation.

Magneto-transport and Thermal properties of TiH diatomic molecule under the influence of magnetic and Aharonov-Bohm (AB) fields

In this study, the effects of Aharonov-Bohm (AB) and magnetic fields on the thermodynamic and magneto-transport properties of TiH diatomic molecule using the Deng-Fan potential as a model are investigated. The functional analysis approach (FAA) is used to solve the Schrodinger equation in the presence of magnetic and AB fields with Deng-Fan potential. The energy equation, as well as the wave function, have been derived. The analytic expressions for the thermo-magnetic and transport properties of the Deng-Fan potential are derived using the energy equation and the partition function. These properties obtained are thoroughly analysed utilising graphical representations. Our analysis shows that the magnetic susceptibility of the TiH exhibits a diamagnetic behaviour, and the specific heat capacity behaviour agrees with the famous Dulong-Petit law when the system is subjected to AB field variations and a fixed magnetic field. Albeit, a slight anomaly is observed in the behaviour of the specific heat capacity. Our findings will be valuable in various fields of physics, including chemical and molecular physics and condensed matter physics, where the derived models could be applied to study other diatomic molecules and quantum dots, respectively.

Morse oscillator equation of state: An integral equation theory based with virial expansion and compressibility terms

A number of interaction energy types are employed in the vibrations studies, especially in the spectroscopic analysis, such as the harmonic oscillator and Morse oscillator. In this research, a derivation of an analytical formula of equation of state of Morse oscillator is considered by employing the approximations used in the simple fluids theory. The compressibility formula of the pressure and the virial expansion formula of the pressure using the solutions of the main equation of the simple fluids theory with one of the approximations of the theory are employed for the purpose of the derivation. The virial coefficients of the total Morse oscillator pressure (the first order one, and the second order one) are found for Morse oscillator with respect to the fractional volume of the components, where we conclude that the first order term is proportional to the absolute temperature directly and depends on the diameter of the particles, while we concluded that the second order coefficient term is more complicated than the first order one with temperature, and also, depends on the three Morse oscillator parameters and the diameter of the particles. Besides, we conclude that the total pressure of Morse oscillator, generally, depends on the minimum energy of the well of Morse oscillator, the width parameter of Morse oscillator, and the equilibrium bond distance of the oscillator, in addition to their dependence on the absolute temperature of the components, and the diameter of the particles. The formula of the Morse oscillator equation of state which is found in this research can be applied to multiple materials described using Morse oscillator such as lots of dimers in the vibrations spectroscopy.

Multi-dimensional designer catalysts for negative emissions science (NES): bridging the gap between synthesis, simulations, and analysis

Negative emissions technologies will play a critical role in limiting global warming to sustainable levels. Electrocatalytic and/or photocatalytic CO2 reduction will likely play an important role in this field moving forward, but efficient, selective catalyst materials are needed to enable the widespread adoption of these processes. The rational design of such materials is highly challenging, however, due to the complexity of the reactions involved as well as the large number of structural variables which can influence behavior at heterogeneous interfaces. Currently, there is a significant disconnect between the complexity of materials systems that can be handled experimentally and those that can be modeled theoretically with appropriate rigor and bridging these gaps would greatly accelerate advancements in the field of Negative Emissions Science (NES). Here, we present a perspective on how these gaps between materials design/synthesis, characterization, and theory can be resolved, enabling the rational development of improved materials for CO2 conversion and other NES applications.

Understanding rich oxygen vacant hollow CeO2@MoSe2 heterojunction for accelerating photocatalytic CO2 reduction

Solar-driven CO₂ reduction into gas fuels is desirable for a sustainable carbon cycle. To improve the photocatalytic activity of CO₂RR, the unique rich oxygen (Vo) vacant hollow CeO₂@MoSe₂ is designed. The introduction of Vo is conducive to the capture of electrons by CO₂ and promotes the process of photocatalytic CO₂RR. The heterojunction formed by introducing the narrow band gap semiconductor MoSe₂ increases the absorption range of visible light and improves the separation efficiency of photogenerated carriers. The hollow structure improves the CO₂ adsorption capacity and improves the use of light effect. Therefore, the prepared H-Vo-CeO₂@49.7 wt% MoSe₂ exhibits enhanced photocatalytic activity for CO₂RR. The yield of CH₄ and CO is 10.2 µmol and 33.2 µmol in 4 h. Moreover, the photocatalytic mechanism is discussed through DFT and in-situ DRIFTS. This work provides new insights to the role of Vo in active CO₂ photoconversion and exploits an important application of CO₂ reduction.

Challenges and recent advancements in the transformation of CO2 into carboxylic acids: straightforward assembly with homogeneous 3d metals

Transformation of carbon dioxide (CO2) into valuable organic carboxylic acids is essential for maintaining sustainability. In this review, such CO2 thermo-, photo- and electrochemical transformations under 3d-transition metal catalysis are described from 2017 until 2022.

Vibrational energies of some diatomic molecules for a modified and deformed potential

A molecular potential model is proposed and the solutions of the radial Schrӧdinger equation in the presence of the proposed potential is obtained. The energy equation and its corresponding radial wave function are calculated using the powerful parametric Nikiforov–Uvarov method. The energies of cesium dimer for different quantum states were numerically obtained for both negative and positive values of the deformed and adjustable parameters. The results for sodium dimer and lithium dimer were calculated numerically using their respective spectroscopic parameters. The calculated values for the three molecules are in excellent agreement with the observed values. Finally, we calculated different expectation values and examined the effects of the deformed and adjustable parameters on the expectation values.

Joule-Thomson Effect on a CCS-Relevant (CO2 + N2) System

The Joule-Thomson effect is a key chemical thermodynamic property that is encountered in several industrial applications for CO₂ capture and storage (CCS). An apparatus was designed and built for determining the Joule-Thomson effect. The accuracy of the device was verified by comparing the experimental data with the literature on nitrogen and carbon dioxide. New Joule-Thomson coefficient (μ_JT) measurements for three binary mixtures of (CO₂ + N₂) with molar compositions x _N2 = (0.05, 0.10, 0.50) were performed in the temperature range between 298.15 and 423.15 K and at pressures up to 14 MPa. Three equations of state (GERG-2008 equation, AGA8-92DC, and the Peng-Robinson) were used to calculate the μ_JT compared with the corresponding experimental data. All of the equations studied here except PR have shown good prediction of μ_JT for (CO₂ + N₂) mixtures. The relative deviations with respect to experimental data for all (CO₂ + N₂) mixtures from the GERG-2008 were within the ±2.5% band, and the AGA8-DC92 EoSs were within ±3%. The Joule-Thomson inversion curve (JTIC) has also been modeled by the aforementioned EoSs, and a comparison was made between the calculated JTICs and the available literature data. The GERG-2008 and AGA8-92DC EoSs show good agreement in predicting the JTIC for pure CO₂ and N₂. The PR equation only matches well with the JTIC for pure N₂, while it gives a poor prediction for pure CO₂. For the (CO₂ + N₂) mixtures, the three equations all give similar results throughout the full span of JTICs. The temperature and pressure of the transportation and compression conditions in CCS are far lower than the corresponding predicted P _inv,max and T _inv,max for (CO₂ + N₂) mixtures.

Tunable Metallogels Based on Bifunctional Ligands: Precursor Metallogels, Spinel Oxides, Dye and CO2 Adsorption

A semisolid gel material is a gift of serendipity via various chemical interactions, and metal incorporation (metallogels) imparts diverse functional properties. In this work, we have synthesized four metallogels from tetrapodal and hexapodal carboxylic acid/amide-based low-molecular-weight gelators with Ni(II) and Cu(II) salts. These metallogels can be tuned to be a low-temperature precursor of porous spinel oxides. These xerogels exhibit impressive water soluble dye and carbon dioxide adsorption, which coupled with the tunability and facile synthesis of porous spinel oxides underscores their potential in environmental remediation and energy applications.

Predictions of Entropy and Gibbs Energy for Carbonyl Sulfide

Many chemical and physical equilibrium conditions can be determined from minimizing the Gibbs free energies of the system. Efficient analytical representations of the entropy and Gibbs free energy of carbonyl sulfide remain elusive in the communality of science and engineering. Here, we report two analytical representations of the entropy and Gibbs free energy for carbonyl sulfide, and the prediction procedures only involve six molecular constants of the carbonyl sulfide molecule. In the temperature range from 300 to 6000 K, the average relative deviations of the predicted molar entropy and reduced Gibbs free energy values of carbonyl sulfide from the National Institute of Standards and Technology database are arrived at 0.150 and 0.189%, respectively.