Thermodynamic State Functions Research Articles

High efficiency simultaneous adsorption of rare earth elements from aqueous solutions using carbon xerogel-chitosan composite

ABSTRACT This study investigated the simultaneous sorption of rare earth elements (REEs) from acidic media using carbon xerogel functionalised with chitosan. The combined carbon xerogel with chitosan that was synthesised has a sphere-like structure and a larger BET surface area (275 m2 g−1) than pure carbon xerogel alone (228 m2 g−1). To determine the optimal conditions, adsorption of REEs was established under different variables, including pH, contact time, initial concentration, adsorbent wt. and temperature, as well as desorption experiments. The adsorption isotherms showed that both the Freundlich and Langmuir models were followed, in addition to a pseudo-second order kinetic model. The adsorption is likely exothermic, which confirms it is favourable at low temperatures, and a dissociative adsorption process is involved, according to analysis of thermodynamic state functions. Langmuir calculations revealed that the maximum amount of REEs that were adsorbed was 164 mg/g. Because of its superior adsorption capacity and simplicity in using a recycled material following several desorption cycles, carbon xerogel-chitosan is being employed as a novel adsorbent material to remove REEs from aqueous solutions.

Cognitive Improvement in Thermodynamic Functions With Calculus Chain Rule

This research was motivated by the low ability of students to apply mathematical solution methods to thermodynamic functions. Thermodynamic functions are functions that consist of pressure, temperature, volume and enthalpy functions where changes in one function can occur due to changes in other functions. The aim of this research was to show the implementation of chain rules in thermodynamic function problems by relying on a process technique to improve students' cognitive awareness of thermodynamic functions. The place of this research was at the TD Pardede Institute of Science and Technology. The process of understanding chain rules is very impactful for understanding thermodynamic state functions. Differential decomposition of functions within functions is also described in the chain rule method. Thermodynamic functions which consist of pressure, temperature, volume and enthalpy functions can depend on each other so that the chain rule analysis method can be clearly used. With this method students will also be given the opportunity to connect one concept with other thermodynamic concepts. Apart from that, this method can be used anywhere. This shows a cognitive increase in terms of cognitive elements, cognitive structure and cognitive function.

The Entropy of van der Waals Fluid.

Thermodynamic state functions are fundamental quantities in many fields. In this work, the van der Waals (vdW) equation of state and calculation formulas of state functions are derived with statistical thermodynamic method in three-dimensional (3D) and two-dimensional (2D) spaces. The heat capacity at constant volume (CV,m ) or area (CA,m ) is exactly the same as that of ideal gas, but the heat capacity at constant pressure (Cp,m ) and other state functions are different from those of ideal gas. The vdW equation of state is a cubic equation, which leads to the fact that the entropy and free energy changes of vdW fluid can be expressed as explicit expressions of volume rather than pressure. Therefore, the adsorbate entropy at constant area can still be theoretically proven to have a linear relationship with the gas-phase entropy at constant volume. However, the linear correlation between it and gas-phase entropy at constant pressure is no longer strictly true in theory. In addition, since the vdW equation of state is applicable to both gas and liquid, the linear correlation between adsorbate entropy and liquid-phase entropy can also be found. At last, the reference state for real gas or fluid at a constant molar volume is suggested.

Entropy and Energy Profiles of Chemical Reactions.

The description of chemical processes at the molecular level is often facilitated by the use of reaction coordinates or collective variables (CVs). The CV measures the progress of the reaction and allows the construction of profiles that track how specific properties evolve as the reaction progresses. Whereas CVs are routinely used, especially alongside enhanced sampling techniques, the links among reaction profiles, thermodynamic state functions, and reaction rate constants are not rigorously exploited. Here, we report a unified treatment of such reaction profiles. Tractable expressions are derived for the free-energy, internal-energy, and entropy profiles as functions of only the CV. We demonstrate the ability of this treatment to extract quantitative insight from the entropy and internal-energy profiles of various real-world physicochemical processes, including intramolecular organic reactions, ionic transport in superionic electrolytes, and molecular transport in nanoporous materials.

Bulk-boundary thermodynamic equivalence: a topology viewpoint

Setting the cosmological constant to be dynamical, we study the bulk and boundary thermodynamics of charged Anti-de Sitter black holes. We develop mass/energy formulas in terms of thermodynamic state functions for the extended thermodynamics, mixed thermodynamics, and boundary conformal field theory thermodynamics. We employ the residue method to study the topological properties of the phase transitions. Our analysis reveals that the bulk and boundary thermodynamics are topologically equivalent for both criticalities and first-order phase transitions in the canonical ensembles, as well as for the Hawking-Page(-like) phase transitions in the grand canonical ensembles. Additionally, those three kinds of phase transitions are shown to be distinguished by their unique topological charges. Our results exemplify the gravity-gauge duality in terms of topology.

Electron gases in toroidal shells: Mode coupling and state functions

Eigenvalues and wave functions describing free electron gases in toroidal shells are determined using a basis set expansion natural to the system geometry. Couplings between azimuthal and poloidal modes are found to be appreciable at lower values of ${m_\phi}$, modifying single particle density distributions within the shells. Thermodynamic state functions are calculated and contrasted with those of a solid toroidal volume.

The prediction method for standard enthalpies of apatites using the molar volume, lattice energy, and linear correlations from existing experimental data

Experimental data of thermodynamic state functions and molar volume for phosphate, arsenate, and vanadate apatites containing Ca, Sr, Ba, Pb, end Cd at the cationic positions Me2+ and F, OH, Cl, Br, and I at the halide position X were collected. The apatite supergroup splits into distinct subgroups (populations) constituted by Me10(AO4)6X2 with the same Me2+ cations and tetrahedral AO43− anions but with different anions at the X position. Linear relationships between various parameters within apatite subgroups are observed. The prediction method for standard enthalpies of apatites (ΔHºf,el) is based on regression analysis of the linear correlations within the subgroups between ΔH°f,el of apatites and their molar volume Vm, lattice energy UPOT, and ΔH°f,el of their anions AO43− or X−. This allowed to predict 22 new ΔH°f,el values for apatites and materials with an apatite structure. The prediction precision is comparable to the experimental uncertainty obtained when reproducing experimental data using calorimetric measurements or dissolution experiments and can be applied to a wider range of apatites than other methods.

Особенности дисмутации арилдихлорфосфитов

The paper considers the spontaneous rearrangement, i.e., dismutation, of phosphorous acid dichlorides (aryl dichlorophosphites) into acid chlorides (diaryl chlorophosphites) with separation of phosphorus trichloride. The starting materials contained phenyl, 1- and 2-naphthols as aromatic radicals. The main patterns of dismutation of aryldichlorophosphites were revealed and the basic factors influencing the process time were determined. The dismutation parameters of aryldichlorophosphites were compared with the regularities revealed earlier for a similar process with the participation of diamidoesters of phosphorous acid containing phenyl and naphthyl substituents as an ether component. Calculations of thermodynamic functions of state, i.e., standard enthalpies of ΔfH0298 formation and S0298 entropies, for the dismutation participants, standard values of the Gibbs energy of ΔrG0298 reactions, were calculated. Calculations were carried out without taking into account the influence of the solvent and for the case of standard conditions, as well as for similar systems --- diamidoesters of phosphorous acid. The calculations allowed us to show the thermodynamic possibility of implementing dismutation of aryl dichlorophosphites at relatively low temperatures. The semi-empirical calculation method (RM1) made it possible to establish the lowest-energy conformations of diaryl chlorophosphites formed as a result of dismutation and show their fundamental difference

From Darcy Equation to Darcy Paradox

This theoretical paper focuses on the single-phase fluid flow through a granular porous medium. The emphasis is on the Darcy flow regime (without free boundary) of a linear viscous fluid in a saturated, deformable, homogeneous porous medium. The approach is developed at the Darcy scale (also referred to as macroscale or phenomenological scale). Within this framework, some discrete aspects of the flow model are highlighted, the governing equations are revisited, the thermodynamic state functions are reconsidered, and the Darcy paradox is presented. The Darcy paradox is illustrated for the isoshoric-isothermal flow of a viscous fluid in the liquid state, in a homogenous porous medium. After some remarks about the intrinsic assumption of this kind of flow, the governing equations are reduced to a well-known parabolic equation. According to this equation, infinitesimal pressure disturbances diffuse at an infinite speed. To remove this paradox, a mathematical model, based on the elementary scales method, is employed.

ZrBDC-Based Functional Adsorbents for Small-Scale Methane Storage Systems

Metal-organic frameworks (MOF), potentially porous coordination structures, are envisioned for adsorption-based natural gas (ANG) storage, including mobile applications. The factors affecting the performance of the ANG system with a zirconium-based MOF with benzene dicarboxylic acid as a linker (ZrBDC) as an adsorbent were considered: textural properties of the adsorbent and thermal effect arising upon adsorption. The high-density ZrBDC-based pellets were prepared by mechanical compaction of the as-synthesized MOF powder at different pressures from 30 to 240 MPa at 298 K without a binder and mixed with polymer binders: polyvinyl alcohol (PVA) and carboxyl methylcellulose (CMC). The structural investigations revealed that the compaction of ZrBDC with PVA under 30 MPa was optimal to produce the ZrBDC-PVA adsorbent with more than a twofold increase in the packing density and the lowest degradation of the porous structure. The specific total and deliverable volumetric methane storage capacities of the ZrBDC-based adsorbents were evaluated from the experimental data on methane adsorption measured up to 10 MPa and within a temperature range from 253 to 333 K. It was measured experimentally that at 253 K, an 100 mL adsorption tank loaded with the ZrBDC-PVA pellets exhibited the deliverable methane storage capacity of 172 m3(NTP)/m3 when the pressure dropped from 10 to 0.1 MPa. The methane adsorption data for the ZrBDC powder and ZrBDC-PVA pellets were used to calculate the important thermodynamic characteristic of the ZrBDC/CH4 adsorption system—the differential molar isosteric heat of adsorption, which was used to evaluate the state thermodynamic functions: entropy, enthalpy, and heat capacity. The initial heats of methane adsorption in powdered ZrBDC evaluated from the experimental adsorption isosteres were found to be ~19.3 kJ/mol, and then these values in the ZrBDC/CH4 system decreased at different rates during adsorption. In contrast, the heat of methane adsorption onto the ZrBDC-PVA pellets increased from 19.4 kJ/mol to a maximum with a magnitude, width, and position depended on temperature, and then it fell. The behaviors of the thermodynamic state functions of the ZrBDC/CH4 adsorption system were interpreted as a variation in the state of adsorbed molecules determined by a ratio of CH4-CH4 and CH4-ZrBDC interactions. The heat of adsorption was used to calculate the temperature changes of the ANG systems loaded with ZrBDC powder and ZrBDC pellets during methane adsorption under adiabatic conditions; the maximum integrated heat of adsorption was found at 273 K. The maximum temperature changes of the ANG system with the ZrBDC materials during the adsorption (charging) process did not exceed 14 K that are much lower than those reported for the systems loaded with activated carbons. The results obtained are of direct relevance for designing the adsorption-based methane storage systems for the automotive industry, developing new gas-power robotics systems and uncrewed aerial vehicles.

Strength, deformability and toughness of uncrosslinked fibrin fibers from theoretical reconstruction of stress-strain curves

Structural mechanisms underlying the mechanical properties of fibrin fibers are elusive. We combined tensile testing of uncrosslinked fibrin polymers in vitro and in silico to explore their material properties. The experimental stress (σ) – strain (ε) curves for fibrin fibers are characterized by elastic deformations with a weaker elastic response for ε<160% due to unraveling of αC tethers and straightening of fibrin protofibrils, and a stronger response for ε>160% owing to unfolding of the coiled coils and γ nodules in fibrin monomers. Fiber rupture for strains ε>212% is due to dissociation of the knob-hole bonds and rupture of D:D interfaces. We developed the Fluctuating Bilinear Spring model to interpret the σ−ε profiles in terms of the free energy for protofibril alignment ΔG0 = 10.1–11.5 kBT, Young's moduli for protofibril alignment Yu = 1.9-3.2 MPa and stretching Ya = 5.7–9.7 MPa, strain scale ε˜≈ 12–40% for fiber rupture, and protofibril cooperativity m= 3.6–8. We applied the model to characterize the fiber strength σcr≈ 12-13 MPa, deformability εcr≈ 222%, and rupture toughness U≈ 9 MJ/m3, and to resolve thermodynamic state functions, 96.9 GJ/mol entropy change for protofibril alignment (at room temperature) and 113.6 GJ/mol enthalpy change for protofibril stretching, which add up to 210.5 GJ/mol free-energy change. Fiber elongation is associated with protofibril dehydration and sliding mechanism to create an ordered protofibril array. Fibrin fibers behave like a hydrogel; protofibril dehydration and water expulsion account for ∼94-98% of the total free-energy changes for fiber elongation and rupture. Statement of significanceStructural mechanisms underlying the mechanical properties of fibrin fibers, major components of blood clots and obstructive thrombi, are elusive. We performed tensile testing of uncrosslinked fibrin polymers in vitro and in silico to explore their material properties. Fluctuating Bilinear Spring theory was developed to interpret the stress-strain profiles in terms of the energy for protofibril alignment, elastic moduli for protofibril alignment and stretching, and strain scale for fiber rupture, and to probe the limits of fiber strength, extensibility and toughness. Fibrin fibers behave like a hydrogel. Fiber elongation is defined by the protofibril dehydration and sliding. Structural rearrangements in water matrix control fiber elasticity. These results contribute to fundamental understanding of blood clot breakage that underlies thrombotic embolization.

Experimental Study on the Liquid‐Phase Adsorption Equilibrium of n‐Butanol over Amberlyst™15 and Contribution of Diffusion Resistances

AbstractThis work investigates the liquid‐phase adsorption of n‐butanol on Amberlyst™15 in the temperature range 295–323 K at different initial adsorbate concentrations. The adsorbent was characterized by N2 physisorption, Fourier transform infrared adsorption of pyridine, scanning electron microscopy, and powder X‐ray diffraction. The data obtained confirmed an adsorbent structure with two porosity levels and amorphous polymer structure. The active sites in Amberlyst™15 are of Brønsted or Brønsted‐Lewis type. The liquid‐phase adsorption equilibrium constants were determined at different temperatures from slurry adsorber experiments. The thermodynamic state functions were estimated and are consistent thermodynamically with physical adsorption. The macropore diffusion coefficients of n‐butanol on Amberlyst™15 were estimated by using the moment technique, and the contribution of surface diffusion to the macropore diffusion coefficients was evaluated.

Efficient removal of direct yellow dye using chitosan crosslinked isovanillin derivative biopolymer utilizing triboelectric energy produced from homogeneous catalysis

A tailored chitosan crosslinked isovanillin (CCIV) polymeric adsorbent generated using homogeneous catalysis was applied for the extraction and removal of direct yellow dye 50 (DY 50), through rapid adsorption due to an electrostatic attraction between the dye molecules and CCIV frameworks. The removal efficiency of DY 50 was systematically investigated to determine the effect of contact time, incubation temperature, pH of the solution, initial dye concentration, and adsorbent mass. The adsorbent also appeared to exert a novel tribocatalytic energy effect for dye decompositions, which is confirmed through comparison of removal from agitation (friction) which is thought to promote the generation of reactive oxygen species. The DY 50 adsorption was almost instantaneous, where up to 83.3% of the initial DY 50 load was removed within and up to 10 min, and then to 90–97.9% by physicochemical adsorption after 45–180 min using 0.05 g of CCIV bio sorbents under ambient temperature. The variations of DY 50 initial concentrations, contact time, and temperatures allowed us to implement three isotherm models, kinetics, and thermal dynamic studies. The comparison of adsorption equilibrium data of DY 50 on the CCIV surfaces was obtained from Langmuir, Freundlich, and Temkin isotherms models, indicating the “monomer to bilayer” is favorable through van der Waals interaction. Validation of the kinetic models was obtained through the ratio of 95% and 5% extraction time (t95/t5=19.42) and residual sum of squares (RSS<0.01). These statistical tolerance analyses confirmed the kinetics was consistent with a pseudo-second-order adsorption kinetic profile. The thermodynamic state functions and operational parameters (ΔH, ΔS, and ΔG) were calculated, suggesting DY 50 adsorption underwent a spontaneous and exothermic process.

Solubility and dissolution mechanisms of vanadinite Pb5(VO4)3Cl: Effects of temperature and PO4 substitutions

The effects of temperature and PO4 substitutions on the solubility of a series of vanadinite (Van) Pb5(VO4)3Cl–pyromorphite (Py) Pb5(PO4)3Cl solid solutions were experimentally investigated to determine differences in dissolution mechanisms and to estimate the Ksp and thermodynamic state functions ΔH°f, ΔG°f, S°, and ΔC°p. Dissolution of Van and the selected phases from the Van–Py series at pH 2.0 was congruent at 5 °C, but it became noncongruent with precipitation of a secondary phase - chervetite Pb2V2O7 in the temperature range of 25–65 °C. The isomorphic substitution of VO4 with PO4 reduced the level of Pb released during dissolution into the equilibrium solution from approximately 207.2 mg Pb L−1 for Van to 131 mg Pb L−1 for Py (at 5 °C). This substitution, however, simultaneously caused a very strong increase in the thermodynamic solubility constant Ksp, which showed a large difference (over 14 orders of magnitude) for the end members of the series. The experimentally determined Ksp at 5 °C varied from 10−96.89±0.53 for Van to 10−80.91±0.70 for Py. The variation in Ksp was linear with substitution of VO4 with PO4 and curvilinear with change in temperature. The more the amount of vanadium in the structure, the stronger was the temperature effect. Because of the noncongruent dissolution followed by far from equilibrium state for V-reach samples at higher temperatures, the experimental determination of thermodynamic state functions was possible only for pyromorphite and some P-reach members of Py–Van solid solution series. For Py, ΔH°f = −4098 ± 5 (kJ mol−1), ΔG°f = −3763 ± 4 (kJ mol−1), S° = 667 ± 313.4 (kJ mol−1 K−1), and ΔC°p = −930.9 ± 345.2 (kJ mol−1 K−1). For Van, ΔH°f = −3796 ± 10 (kJ mol−1), ΔG°f = −3486 ± 4 (kJ mol−1), S° = 719 ± 694 (kJ mol−1 K−1), and ΔC°p = −1037 ± 605 (kJ mol−1 K−1) were estimated.

Influence of Moringa Leaves Extract on Hb Response to Radiation Dose Rates’ Changes: I. Permittivity and Its Thermodynamic Driven State Functions

The harm caused by ionizing radiation is well known and is performed by depositing energy from the radiation source into the irradiated material. Biosystems fight back to maintain their integrity and functions. Doing so requires external help where important supplements are provided to enable the biosystem to challenge destruction done by irradiation in the form of ionization and free radicals. This work investigates the effect of Moringa oleifera leaves extract, MOLE, on two different gamma radiation dose rates’ damages on the biosystem. This is done by estimating physical parameters that belong to dielectric factors, static permittivity, or based upon them as thermodynamic state functions; changes in Helmholtz free energy, internal energy, and entropy of the sample under assessment. Good sensitivity to factors causing changes in the studied system's net dipole moment is noticed, especially within the 1st week. The help of MOLE, a natural supplement, to the biosystem repairing the damage caused by irradiation was tested. Data indicated that MOLE has a powerful influence that could help the biosystem, based on its vast nutrients, trace elements, and antioxidants to fight radiation damage.

Peculiarities of Thermodynamic Behaviors of Xenon Adsorption on the Activated Carbon Prepared from Silicon Carbide.

An activated carbon prepared from silicon carbide by thermochemical synthesis and designated as SiC-AC was studied as an adsorbent for xenon. The examination of textural properties of the SiC-AC adsorbent by nitrogen vapor adsorption measurements at 77 K, powder X-ray diffraction, and scanning electron microscopy revealed a relatively homogeneous microporous structure, a low content of heteroatoms, and an absence of evident transport macropores. The study of xenon adsorption and adsorption-induced deformation of the Si-AC adsorbent over the temperature range of 178 to 393 K and pressures up to 6 MPa disclosed the contraction of the material up to −0.01%, followed by its expansion up to 0.49%. The data on temperature-induced deformation of Si-AC measured within the 260 to 575 K range was approximated by a linear function with a thermal expansion factor of (3 ± 0.15) × 10−6 K−1. These findings of the SiC-AC non-inertness taken together with the non-ideality of an equilibrium xenon gaseous phase allowed us to make accurate calculations of the differential isosteric heats of adsorption, entropy, enthalpy, and heat capacity of the Xe/SiC-AC adsorption system from the experimental adsorption data over the temperature range from 178 to 393 K and pressures up to 6 MPa. The variations in the thermodynamic state functions of the Xe/SiC-AC adsorption system with temperature and amount of adsorbed Xe were attributed to the transitions in the state of the adsorbate in the micropores of SiC-AC from the bound state near the high-energy adsorption sites to the molecular associates.

Relativistic State Functions from a Time Dilation Perspective

To embrace the special theory of relativity with classical thermodynamics correct Lorentz transformations of thermodynamic state functions are formulated. All of these Lorentz transformations of state functions equally support the time dilation phenomenon which is an experimentally verified fact. Relativistic Boltzmann constant proves entropy to be the Lorentz variant. Twin paradox thought experiments for heat engines prove heat flux to be Lorentz variant. Lorentz transformation of entropy and heat flux proves temperature Lorentz invariant. All thermodynamic state functions are proved to be Lorentz variant which is shown in accord with Lorentz transformation of thermodynamic work.

Thermodynamic analysis of hydrate-based refrigeration cycle

Clathrate hydrates (hydrates) have a larger dissociation heat than an evaporation heat of the working fluid of conventional refrigeration systems. This property can be applied to a novel refrigeration system. In this study, theoretical performance analysis of the refrigeration system utilizing hydrates as its working medium was conducted. We modeled the thermodynamic cycle of the hydrate-based refrigeration system composed of following processes: adiabatic compression, hydrate formation at high temperature, adiabatic expansion, and hydrate dissociation at low temperature. Based on the thermodynamic cycle, the coefficient of performance (COP) of the hydrate cycle was theoretically formulated with thermodynamic state functions of the working medium. Using the formula, COP was calculated on the three hydrate forming systems including HFC-32 + cyclopentane (CP) + water, Kr + CP + water, and HFC-41 + CP + water. The analysis based on the calculated results revealed that the dissociation heat of hydrates and the enthalpy change of guest gas were dominant factors to COP and polyatomic molecules would be appropriate for guest gas of hydrates. The maximum COP values on the hydrate cycle were comparable to those of the reversed Rankine cycle. The hydrate-based refrigeration system outperformed conventional refrigeration systems in terms of safety and environmental-friendliness.

Adsorption of Lead and Cadmium Ions onto Soils: Isotherm Models, and Thermodynamic Studies

The source of pollution of both underground-water and water is the existence of heavy metals in such an environment. constitutes. This research sheds light on the lead (Pb) reactivity with Cadmium (Cd) throughout their transferal in the different soils. The batch technique was used in order to demonstrate the influence of temperature, initiate concentration, adsorption-isotherm. The consequences reveal that the Freundlich model, Langmuir model, Harkin-Jura model, and Halsey model are able to adequately describe the adsorption-isotherm parameter. The adsorption ability of the heavy metals decreased once temperatures increased. On the bases of the highest ability of adsorption (Qm), the order of affinity of Lead and Cadmium for the investigated soil occurred at Pb &amp;gt; Cd, and the maximum capacities of adsorption of competition of two cations are decreased for the same effective sites. The change in the thermodynamic state functions such as standard free-energy (ΔGo), standard entropy (ΔSo), and standard enthalpy (ΔHo) were investigated. The interaction of adsorption is revealed to be exothermic in nature

State function‐based flash specifications for open systems in the absence or presence of chemical reactions

AbstractDiverse engineering fields require flash calculations like isothermal flash, isenthalpic flash, and isentropic flash. They can be cast as minimization of a thermodynamic state function and solved by Michelsen's Q‐function approach. Flash calculations for open systems, that is, systems where chemical potentials are specified instead of the mole numbers for some components, also belong to this scope. By analyzing the construction of Q‐functions through Legendre transforms, we extend this approach to the flash for open systems in the absence or presence of chemical reactions, resulting in general formulations for various specifications. For systems without reactions, the classical framework using mole numbers as independent variables is employed; for those with reactions, the modified‐RAND framework is employed. We present examples for open systems at constant temperature and pressure. Using the Q‐function minimization, we can solve multicomponent nonreactive or reactive systems at a specified chemical potential with quadratic convergence over a wide range of conditions.