Entropy Term Research Articles

Additive single atom values for thermodynamics II: Enthalpies, entropies and Gibbs energies for formation of ionic solids

• Optimised atom terms are summed to generate inorganic formation enthalpies, formation entropies and formation Gibbs energies. • The number of atom terms is limited by the number of elements unlike group contribution methods which require numerous terms. • The atom terms for enthalpies closely follow Periodic Table trends while entropy values are roughly constant at 8 J K −1 mol −1 , but much more negative for the gaseous elements. In part I of this series we established optimised sum values, for each of the chemical elements, of formula volumes, of absolute entropies, and of constant pressure heat capacities, together with their temperature coefficients. These atom values, when summed for a chemical formula, provided zero-level estimates of the corresponding property of that chemical material. Atom sums have the particular advantage of being essentially complete because of the finite number of chemical elements and are of use in prediction and checking of values for chemical materials. However, this is at the expense of an inability to distinguish among isomers and phases with the same chemical formula nor do they allow for effects of atom interactions. In the present publication, we present optimised atom sums for formation entropies, formation enthalpies and their relation to formation Gibbs energies. In order to check the reliability of the results, comparison is made among methods of prediction using each of DFT calculations, a proprietary group contribution method, and the proposed single atom sum method. The single atom sum method is found to be most suitable as an initial estimate for large formation entropies and also for large values of formation enthalpies, which includes ionic hydrates. The energy contributions of the elements group into the Groups of the Periodic Table so that strict atom independence and thus additivity is not predominant while entropy terms are relatively constant (for the non-gaseous elements) implying that the atoms behave independently and thus additively in contributing to the entropy terms resulting from their vibrations within the ionic solids. This is possibly a unique demonstration resulting from this single atom sum collection. This now comprises a complete set for simple zero-order thermodynamic prediction and for checking, which should be complemented by whatever other resources are available to the researcher. Optimised single atom values for inorganic solids are summed to generate predictive values for formation enthalpies and formation entropies, supplementing the values for formula volumes, absolute entropies and heat capacities in our prior publication. This simple additive group contribution method requires no interaction terms, and applies best to materials with large formation enthalpies and large formation entropies, including hydrates. However, it does not distinguish among phases or structures with the same composition. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Solution-State Hydrostatic Pressure Chemistry: Application to Molecular, Supramolecular, Polymer, and Biological Systems

Pressure (P), as one of the most inherent state quantities, has become an academic subject of study and has attracted attention for a long time for the minute control of reaction equilibria and rates, not only in the gas phase, based on the gas state equation, but also in the solution state. In the latter case, the pressure applied to the solutions is classified as hydrostatic pressure, which is a type of isotropic mechanical force. For instance, deep-sea organisms are exposed to hydrostatic pressure environments of up to 100 MPa, implying that hydrostatic pressurization plays a role in homeostatic functions at physiological levels. The pressure control of such complicated biological behavior can be addressed by thermodynamics or kinetics. In fact, the spontaneity (ΔG) of a reaction that is governed by weak interactions (approximately 10 kcal/mol), such as electrostatic, van der Waals, hydrophobic, hydrogen bonding, and π-π stacking, is determined by the exquisite balance of enthalpy (ΔH) and entropy changes (ΔS), in accordance with the fundamental thermodynamic equation ΔG = ΔH - TΔS. The mutually correlated ΔH-ΔS relationship is known as the enthalpy-entropy compensation law, in which a more negative enthalpic change (more exothermic) causes further entropic loss based on a more negative entropy change. Namely, changing the temperature (T) as the state quantity, except for P, is highly likely to be equal to controlling the entropy term. The solution-state entropy term is relatively vague, mainly based on solvation, and thus unpredictable, even using high-cost quantum mechanical calculations because of the vast number of solvation molecules. Hence, such entropy control is not always feasible and must be demonstrated on a trial-and-error basis. Furthermore, the above-mentioned equation can be rearranged as ΔG = ΔF + PΔV, enabling us to control solution-state reactions by simply changing P as hydrostatic pressure based on the volume change (ΔV). The volume term is strongly relevant to conformational changes, solvation changes, and molecular recognition upon complexation and thus is relatively predictable, that is, volumetrically compact or not, compared to the complicated entropy term. These extrathermodynamic and kinetic observations prompted us to use hydrostatic pressure as a controlling factor over a long period. Hydrostatic pressure chemistry in the solution phase has developed over the past six decades and then converged and passed the fields of mechanochemistry and mechanobiology, which are new but challenging and current hot topics in multidisciplinary science. In this Account, we fully summarize our achievements in solution-state hydrostatic pressure chemistry for smart/functional molecular, supramolecular, polymer, and biological systems. We hope that the phenomena, mechanistic outcomes, and methodologies that we introduced herein for hydrostatic-pressure-controlling dynamics can provide guidance for both theoretical and experimental chemists working in supramolecular and (bio)macromolecular chemistry, mechanoscience, materials science, and technology.

Ho@C82 Metallofullerene: Calculated Isomeric Composition

Relative populations of the three energy-lowest IPR (isolated-pentagon-rule) isomers of Ho@C82 under the high-temperature synthetic conditions are computed using the Gibbs energy based on characteristics from the density functional theory calculations (B3LYP/3-21G ∼ SDD entropy term, B3LYP/6-31G* ∼ SDD energetics). Two major species are predicted, Ho@C 2v ; 9-C82 and Ho@C s (c); 6-C82, with rather comparable populations under supposed synthetic temperatures. Roles of the inter-isomeric thermodynamic equilibrium and solubility are discussed.

Distance-Based Knowledge Measure of Hesitant Fuzzy Linguistic Term Set With Its Application in Multi-Criteria Decision Making

Motivated by the structural aspect of the probabilistic entropy, the concept of fuzzy entropy enabled the researchers to investigate the uncertainty due to vague information. Fuzzy entropy measures the ambiguity/vagueness entailed in a fuzzy set. Hesitant fuzzy entropy and hesitant fuzzy linguistic term set based entropy presents a more comprehensive evaluation of vague information. In the vague situations of multiple-criteria decision-making, entropy measure is utilized to compute the objective weights of attributes. The weights obtained due to entropy measures are not reasonable in all the situations. To model such situation, a knowledge measure is very significant, which is a structural dual to entropy. A fuzzy knowledge measure determines the level of precision in a fuzzy set. This article introduces the concept of a knowledge measure for hesitant fuzzy linguistic term sets (HFLTS) and show how it may be derived from HFLTS distance measures. Authors also investigate its application in determining the weights of criteria in multi-criteria decision-making (MCDM).

Exploring the interaction between lactoferrin and CdTe quantum dots: Energetic and molecular dynamic study

• Quantum dots (QD) and lactoferrin (LF) formed a 1:1 [ L F - C d T e @ T G A ] ° stable complex. • [ L F - C d T e @ T G A ] ° formation was exothermic and entropically favorable at 298.15 K. • LF-QD binding is driven mainly by conformational and desolvation processes. • The [ L F - C d T e @ T G A ] ° formation passes by an [ L F - C d T e @ T G A ] ‡ intermediate state. • The [ L F - C d T e @ T G A ] ‡ formation occurred with iso -kinetic compensation. The kinetic and energetic characterization of interactions between quantum dots (QDs) and proteins is fundamental for understanding the toxicity and effectiveness of these nanoparticles in therapeutic applications. In this study, we combined kinetic and thermodynamic data from surface plasmon resonance (SPR) and isothermal titration microcalorimetry (ITC) to explore the complexation mechanism between thioglycolic acid-capped cadmium telluride QD (CdTe@TGA) and bovine lactoferrin (LF) under physiological conditions. The SPR results demonstrated that QD binds to LF forming a 1:1 [ L F - C d T e @ T G A ] ° thermodynamically stable complex, whose binding constant ( K b SPR ) ranged from 7.18 × 10 4 to 6.75 × 10 4 M −1 . The association rate constant ( k a ) values were in the order of 10 3 M −1 s −1 while the complex residence time ( t R ) was ∼70 s. The formation of both [ L F - C d T e @ T G A ] ° and [ L F - C d T e @ T G A ] ‡ activated complexes occurred with the compensation of the enthalpic and entropic terms with the increase in temperature, characterizing enthalpy–entropy compensation (EEC), and iso -kinetic (IC) compensation, respectively. Using ITC, we also found the formation of a 1:1 [ L F - C d T e @ T G A ] ° complex, but the calculated K b ITC values were on the order of 10 7 L mol −1 . Again, we found that the formation of [ L F - C d T e @ T G A ] °was exothermic and entropically favorable at 298.15 K, although Δ H ITC ° (−20.46 kJ mol −1 ) and T Δ S ITC ° (24.13 kJ mol −1 ) values were higher in magnitude than those found by SPR ( Δ H SPR ° =−17.35 kJ mol −1 and T Δ S SPR ° = 10.39 kJ mol −1 ). We believe that this fundamental study will provide new insights into the safe and effective application of QDs in biological and medical fields.

Insight into anisotropic magnetocaloric effect of CrI[formula omitted

CrI3 is considered to be a promising candidate for spintronic devices and data storage. We derived the Heisenberg Hamiltonian for CrI3 from density functional calculations using the Liechtenstein formula. Moreover, the Monte–Carlo simulations with the Sucksmith–Thompson method were performed to analyze the effect of magnetic anisotropy energy on the thermodynamic properties. Our method successfully reproduced the negative sign of isothermal magnetic entropy changes when a magnetic field was applied along the hard plane. We found that the temperature dependence of the magnetocrystalline anisotropy energy is not negligible at temperatures slightly above the Curie temperature. We clarified that the origin of this phenomenon is attributed to anisotropic magnetic susceptibility and magnetization anisotropy. The difference between the entropy change of the easy axis and the hard plane is proportional to the temperature dependence of the magnetic anisotropy energy, implying that the anisotropic entropy term is the main source of the temperature dependence of the free energy difference when magnetizing in a specific direction other than the easy axis. We also investigated the magnetic susceptibility that can be used for the characterization of the negative sign of the entropy change in the case of a hard plane. The competition of the magnetocrystalline anisotropy energy and external magnetic field at a low temperature and low magnetic field causes a high magnetic susceptibility as the magnetization fluctuates. Meanwhile, the anisotropy energy is suppressed as a sufficient magnetic field is applied along the hard axis, and the magnetization is fully rotated to the direction of the external magnetic field.

A deep reinforcement learning-based approach for the residential appliances scheduling

This paper investigates the optimal real-time residential appliances scheduling of individual owner when participating in the demand response (DR) program. The proposed method is novel since we cast the optimization problem to an intelligent deep reinforcement learning (DRL) framework, which avoids solving a specific optimization model directly when facing dynamic operation conditions induced by the outdoor temperature, electricity price and resident’s behavior. We consider the scheduling of power-shiftable, time-shiftable and deferrable appliances for the optimization of profit and satisfaction rate of resident. The optimization problem is first modeled as a Markov decision process and then solved by a model-free entropy-based DRL algorithm. Unlike traditional model-based methods which rely on accurate knowledge of parameters and physical models that are difficult to obtain in practice, the proposed method can develop real-time near-optimal control behavior by interacting with the environment and learning from data, which avoids the error caused by the simplification and assumption when building physical model. The proposed scheduling algorithm also achieves better tradeoff between the profit and the satisfaction rate than deterministic DRL algorithm owing to the introduction of the entropy term. Simulation results using real-world data demonstrate the effectiveness of the proposed method.

Hydrogen accommodation in the TiZrNbHfTa high entropy alloy

The equiatomic TiZrNbHfTa high entropy alloy (HEA) and its hydrides (TiZrNbHfTaH0.4- 2.0) have been modelled at the atomic scale and the phase transformations that occur during hydrogen absorption have been simulated. The thermodynamics of vacancy formation, hydrogen accommodation and hydride decomposition have been examined using density functional theory, linking results to experimental investigations. A model predicting the decomposition of the TiZrNbHfTaH system is proposed based on the temperature dependence of configurational and vibrational entropy terms and the hydrogen solution energies of individual interstitials. The presence of hydrogen in the HEA structure was shown to promote the formation of vacancies due to a 0.21 eV reduction of the energy barrier for vacancy formation. Interstitials placed around vacancies were observed to relax onto octahedral sites from initial tetrahedral positions, while interstitials placed in the same environment, without the vacancy present, were observed to relax onto tetrahedral sites from initial octahedral positions. This provides a mechanistic basis for experimentally observed behaviour. The phase stabilities of each arrangement of the TiZrNbHfTaH structure were explored, identifying that the FCC arrangement of the dihydride at the hydrogen to metal atom ratio (H/M) = 2.0, is more stable than the BCT arrangement at 550 K. The spontaneous BCC to BCT transformation, observed in the H/M range 1.2 – 1.6, and the thermodynamically favourable BCT to FCC phase transformation at H/M = 2.0, provides a comprehensive depiction of the mechanistic behaviour of the TiZrNbHfTa HEA during hydrogen absorption.

MR brain tissue classification based on the spatial information enhanced Gaussian mixture model

BACKGROUND: Classifying T1-weighted Magnetic Resonance brain scans into cerebrospinal fluid, gray matter and white matter is one of the most critical tasks in neurodegenerative disease analysis. Since manual delineation is a labor-intensive and time-consuming process, automated methods have been widely adopted for this purpose. One group of commonly used method by biomedical researchers are based on Gaussian mixture model. The main drawbacks of this model include complex computational cost and parameter selection with the presence of imaging defects such as intensity inhomogeneity and noise.OBJECTIVE: To alleviate these aspects, an improved Gaussian mixture model-based method is proposed in this work.METHODS: Standard mixture model was used to formulate individual voxel intensity. A set of spatial weightings were created to represent local tissue characteristics. The emphasis of this method is its “lite” and robust implementation mode highlighted by a dedicated entropy term. The Expectation-Maximization algorithm was then iteratively executed to estimate model parameters. The Maximum a Posteriori criterion was employed to determine for each voxel if it belongs to a certain tissue.RESULTS: The proposed method was validated on both simulated and real MR scans. The averaged Dice coefficient of segmented brain tissues on each dataset ranged between [66.41, 87.42] for cerebrospinal fluid, [80.57, 85.35] for gray matter, and [83.17, 85.63] for white matter.CONCLUSIONS: Experiments illustrated the effectiveness and reliability in tissue classification against imaging defects compared with manually constructed reference standard.

Phase diagram and mechanical properties of fifteen quaternary high-entropy metal diborides: First-principles calculations and thermodynamics

First-principles calculations and thermodynamic theory of mixing entropy and enthalpy are employed to study the phase stability, mechanical properties, and melting points of 15 existing and hypothetical quaternary high-entropy metal diborides (HEMB2s) composed of boron and six group IVB and VB refractory transition metals. A phase diagram in terms of a structural parameter, δ (the lattice size difference), and two thermodynamic parameters, ΔHmix (the mixing enthalpy) and Ω (the ratio of the entropy and enthalpy terms) is constructed. The phase diagram shows that all the 15 metal diborides satisfy the established Ω-δ criterion (i.e. Ω>1 and δ<6.6%), suggesting that they can be formed as single-phase HEMB2s. While five of these equiatomic four-metal diborides were experimentally synthesized already, the remaining ten single-phase HEMB2s are predicted by this work. Each of the 15 quaternary HEMB2s is found to have high Vickers hardness and high fracture toughness, together with an ultrahigh melting point.

Physicochemical characterization and activity coefficients at infinite dilution of molecular compound in poly(ethylene glycol)dimethyl ether and the eutectic mixture composed of poly(ethylene glycol) with cyclic carbonate

• The poly(ethylene glycol) and its eutectic with cyclic carbonate are tested as separating agents. • The activity coefficients at infinite dilution of different molecular compounds are presented. • The selectivity and capacity values are presented and discussed. • The physicochemical characterization of proposed extractants are presented. This work is focused on determining the effectiveness of using hitherto unexplored extractants in separation processes. It is proposed to use poly(ethylene glycol) and the eutectic mixture composed of poly(ethylene glycol) with cyclic carbonate as separating agents in desulphurization of model fuel (heptane/thiophene) and alkanes from aromatic hydrocarbons (heptane/toluene) processes. The selected glycol was poly(ethylene glycol)dimethyl ether with an average molecular weight of M = 250 g·mol −1 (abbreviated as PEG250DME). The second component of the mixture was ethylene cyclic carbonate (abbreviated as EC). These components create a non-crystallizing mixture at a temperature below T = 203 K in the range of 25–40% ethylene carbonate, thus a mixture with the following composition 30% of EC and 70% of PEG250DME ( w EC = 0.331) was investigated. For this purpose, the extensive research on the infinite dilution activity coefficients for 45 molecular compounds including alkanes, alkenes, alkynes, aromatic hydrocarbons, alcohols, water, ethers, pyridine, thiophene, acetone, acetonitrile, and 1-nitropropane in both PEG250DME and {[PEG250DME] + [EC], w EC = 0.331} were determined. The experiment was performed at a temperature range from T = (308.15 to 338.15) K with an increment of 10 K using gas–liquid chromatography (GLC). Based on the experimental data, the infinite dilution capacity and selectivity of the PEG250DME and DES: {[PEG250DME] + [EC], w EC = 0.331} are presented to evaluate the effectiveness of using them as an extractant in the separation of aliphatic from aromatic hydrocarbons and sulfur compounds from alkanes. Obtained selectivity and capacity values for different separation processes are compared with the literature data for other separating agents presented in the available literature reports. From the temperature - dependence of the infinite dilution activity coefficient, the partial molar excess Gibbs energy, Δ G 1 E , ∞ , enthalpy Δ H 1 E , ∞ and entropy term T ref Δ S 1 E , ∞ at infinite dilution were calculated and discussed. Additionally, the liquid density and dynamic viscosity of pure PEG250DME and it’s eutectic mixture with EC as a function of temperature were determined. Both of the physicochemical parameters are important from a technological point of view.

Classical Thermodynamic Analysis of Deuterium-Based Fusion Reactions

The fusion reactions involving deuterium are of great interest for the exploitation of the fusion energy via magnetic-confinement devices. In classical thermodynamics, the spontaneity of a process is established through the assessment of the change in Gibbs free energy. So far, the feasibility of nuclear reactions has been characterized in terms of cross section and Q-value while the entropic term (T ΔS) has been neglected. Such an assumption is always justified for fission reactions where the term ΔS is positive. In the case of fusion reactions that operate at very high temperatures (106–107 K) and where ΔS is negative, the change in Gibbs free energy may be positive, making the reaction non-spontaneous. This paper proposes a classical thermodynamic analysis of D-based reactions of interest for the magnetic-confinement fusion applications. The entropy contribution was evaluated via the Sackur–Tetrode equation while the change in enthalpy was considered constant and as corresponding to the Q-value of the fusion reaction. The results of the thermodynamic analysis are compared with nuclear reaction feasibility criteria based on the reaction reactivity. The DT and D3He reactions show a high degree of spontaneity although the second one presents a lower reactivity. An increase in temperature could enhance the reactivity of the D3He reaction at the cost of decreasing its thermodynamic spontaneity. Both branches of the DD reaction are characterized by a much lower thermodynamic spontaneity than that of the DT and D3He reactions. Furthermore, at the temperature of their maximum cross section, the DD reactions exhibit a largely positive change in Gibbs free energy and, therefore, are not spontaneous. At the temperature of magnetic-confinement fusion machines (1.5 × 108 K), among the D-based reactions studied, the DT one exhibits the highest degrees of spontaneity and reactivity.

Adapting gaze-transition entropy analysis to compare participants’ problem solving approaches for chemistry word problems

A method is adapted for calculating two measures of entropy for gaze transitions to summarize and statistically compare eye-tracking data. A review of related eye-tracking studies sets the context for this approach. We argue that entropy analysis captures rich data that allows for robust statistical comparisons and can be used for more subtle distinctions between groups of individuals, expanding the scope and potential for eye-tracking applications and complementing other analysis methods. Results from two chemistry education studies help to illuminate this argument and areas for further research. The first experiment compared the viewing patterns of twenty-five undergraduate students and seven instructors across word problems of general chemistry topics. The second experiment compared viewing patterns for eighteen undergraduate students divided into three intervention groups with a pre- and post-test of five problems involving periodic trends. Entropy analysis of the data from these two experiments revealed significant differences between types of questions and groups of participants that complement both visualization techniques like heat maps and quantitative analysis methods like fixation counts. Finally, we suggest several considerations for other science education researchers to standardize entropy analyses including normalizing entropy terms, choosing between collapsed sequences or transitions within areas of interest, and noting if fixations in blank spaces are included in the analysis. These results and discussion help to make this powerful analysis technique more accessible and valuable for eye-tracking work in the field of science education research.

Extending defect models for Si processing: The role of energy barriers for defect transformation, entropy and coalescence mechanism

Emergent alternative Si processes and devices have promoted applications outside the usual processing temperature window and the failure of traditional defect kinetics models. These models are based on Ostwald ripening mechanisms, assume pre-established defect configurations and neglect entropic contributions. We performed molecular dynamics simulations of self-interstitial clustering in Si with no assumptions on preferential defect configurations. Relevant identified defects were characterized by their formation enthalpy and vibrational entropy calculated from their local vibrational modes. Our calculations show that entropic terms are key to understand defect kinetics at high temperature. We also show that for each cluster size, defect configurations may appear in different crystallographic orientations and transformations among these configurations are often hampered by energy barriers. This induces the presence of non-expected small-size defect cluster configurations that could be associated to optical signals in low temperature processes. At high temperatures, defect dynamics entails mobility and ripening through a coalescence mechanism.

Investigation of hybrid nanomaterial application in melting process of paraffin enhanced with nanoparticles

Current study is about the charging process of paraffin within a tank with spiral duct. The paraffin has been enhanced with adding CuO nanoparticles. The hot fluid within the spiral pipes is hybrid nanomaterial. The fraction of nano-sized material is poorer than 0.04 and selecting single phase methodology is acceptable. Finite volume approach with including implicit method was applied to solve these transient equations. Grids with structural configurations were utilized for two suggested styles of containers. Verification with empirical data reveals that nice agreement exist for utilized mathematical model. Entropy generation components were measured and reported in contours forms. Also, important role of buoyancy force were reported in streamline contours. Increase of time leads to increase in liquid fraction in both cases and first configuration reach to maximum value in lower time. The amount of liquid fraction (LF) for first style is higher than second style which means better performance of first configuration. When time increase up to 80 min, the amount of LF for second and first configuration are 5.77 and 4.9 times bigger than those of t = 300 s. With rise of time, frictional irreversibility augments owing to augmentation of velocity of liquid paraffin. Also, with rise of volume of liquid paraffin, the temperature gradient (∇T) reduces which provides lower value of thermal irreversibility. The first configuration has greater frictional entropy term while its thermal irreversibility is lower than second approach. With reduce of solid paraffin, temperature decreases and reaches to uniform value about 368 K. The first configuration has greater temperature and maximum difference occurs at t = 45 min.

Accelerating Causal Inference and Feature Selection Methods through G-Test Computation Reuse.

This article presents a novel and remarkably efficient method of computing the statistical G-test made possible by exploiting a connection with the fundamental elements of information theory: by writing the G statistic as a sum of joint entropy terms, its computation is decomposed into easily reusable partial results with no change in the resulting value. This method greatly improves the efficiency of applications that perform a series of G-tests on permutations of the same features, such as feature selection and causal inference applications because this decomposition allows for an intensive reuse of these partial results. The efficiency of this method is demonstrated by implementing it as part of an experiment involving IPC–MB, an efficient Markov blanket discovery algorithm, applicable both as a feature selection algorithm and as a causal inference method. The results show outstanding efficiency gains for IPC–MB when the G-test is computed with the proposed method, compared to the unoptimized G-test, but also when compared to IPC–MB++, a variant of IPC–MB which is enhanced with an AD–tree, both static and dynamic. Even if this proposed method of computing the G-test is presented here in the context of IPC–MB, it is in fact bound neither to IPC–MB in particular, nor to feature selection or causal inference applications in general, because this method targets the information-theoretic concept that underlies the G-test, namely conditional mutual information. This aspect grants it wide applicability in data sciences.

Residue-Specific Kinetic Insights into the Transition State in Slow Polypeptide Topological Isomerization by NMR Exchange Spectroscopy.

The characterization of the transition state is a central issue in biophysical studies of protein folding. NMR is a multiprobe measurement technique that provides residue-specific information. Here, we used exchange spectroscopy to characterize the transition state of the two-state slow topological isomerization of a 27-residue lantibiotic peptide. The exchange kinetic rates varied on a per-residue basis, indicating the reduced kinetic cooperativity of the two-state exchange, as well as the previously observed reduced thermodynamic cooperativity. Furthermore, temperature-dependent measurements revealed large variations in the activation enthalpy and entropy terms among residues. Interestingly, we found a linear relationship between the logarithm of the equilibrium constants and that of the exchange rates. Because the data points are derived from amino acid residues in one polypeptide chain, we refer to the linear relationship as the residue-based linear free energy relationship (rbLFER). The rbLFER offers information about the transition state of the two-state exchange.

High entropy alloys and thermodynamically derived high stability alloys; a compositional comparative study of all 3–7 element systems composed of ten 3d metals at 1273 K

Studies of high entropy or multi-principal element alloys are focused mainly on equimolar or near-equimolar compositions for which configurational entropy is maximized. Negligence of interactions between elements forming such alloys, namely enthalpy of mixing, may detract these studies from a desirable target, which is a stabilization of single-phases instead of intermetallic compounds. In this work, both entropy and enthalpy terms are taken into account for the determination of the high stability compositions, for which the Gibbs free energy of mixing is minimized. For the ten 3d metals (Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn and Al) all possible combinations forming 3- (120 compositions), 4- (210), 5- (252), 6- (210) and 7-component systems (120) are analyzed. Two numerical methods: a genetic algorithm (GA) and a hybrid one (a combination of GA with the gradient method) give convergent results regarding the high stability compositions at 1273 K (a typical temperature used on HEAs synthesis). It is found surprisingly that such compositions are dominated by the Ti and Al or Ni contents with minor ones of the seven remaining elements, especially for 6 and 7-component systems. These numbers can be related to average parameters of interaction (of a given element with the remaining ones) giving almost monotonic dependence; the lower the average value of the interaction parameter of a given element − the higher its content in the alloys of the high stability. Such selective preferences in compositions are reflected by high deviations between the high stability compositions and equimolar ones, with an average reaching 48% for ternary systems to 105% for 7-component alloys (expressed as normalized root mean square errors).

Application of a synthesized ionic liquid for possible use in industrial separation problems: A useful tool for solvent selection

A novel ionic liquid (2′,3′-epoxypropyl-N-methyl-2-oxopyrrolidinium salicylate) was assessed for possible use in industrial separation problems. This was conducted using a gas liquid chromatography technique at different temperatures, T = (313.15 – 343.15) K and at atmospheric pressure. The molecular interactions within the ionic liquid were determined for 34 solutes (alkanes, alkenes, alkynes, alcohols, ketones, aromatic compounds, sulphur compound, THF, acetonitrile) and water. Excess thermodynamic properties (enthalpies, ΔH1E,∞, Gibbs free energy, ΔG1E,∞ as well as the entropy term, Tref ΔS1E,∞) at infinite dilution were calculated to further elucidate the intermolecular interactions occurring within the ionic liquid and solutes. The separation parameters (selectivity and capacity) values were computed from the activity coefficients at infinite dilution using the retention data obtained utilizing g.l.c to determine the feasibility of the ionic liquid for industrial separation processes. From the calculated selectivities and capacities, the presented ionic liquid can be suitable for the separation of industrial close boiling points mixtures. For the petrochemical separation problems, the investigated ionic liquids showed that large quantities would be required. The influence of cation and anion in the ionic liquid has been discussed. The investigated ionic liquid may be proposed for the separation of azeotropic mixtures such as alkane/alcohols, THF or acetone/alcohols.

Cell’s Thermochemistry and I²R Formula

All electrochemical power sources of practical use emit heat during discharge. This heat primarily warms the battery itself. The amount of heat, as well as the heat flow, depend on the discharging rate. In case of the lithium-ion battery, high-rate (fast) process can overheat the battery up to unsafe conditions, causing sometimes fire and explosion. Thus, understanding and quantifying the character of heat releasing processes is important for batteries’ usage, maintenance, modeling, and developing.All of the following reasoning relates to the situation when the battery operates under projected use conditions.Direct calorimetric measurements that provide immediate answer need special equipment, such as, for example, the ARC instrument. However, both entities, that is, total heat and heat flow, can be derived relatively easily employing the general ideas of thermochemistry and thermodynamics. The approach is based on comparing the enthalpy of the redox reaction of the cell and the useful energy produced by the cell during discharge at a certain rate. The latter is measured in a typical battery test; the enthalpy ΔH being the sum of Gibbs’ (free) energy ΔG and the entropy component T ΔS (T is absolute temperature, and ΔS is entropy change, ΔH = ΔG + T ΔS) can be easily determined through additional though simple experiment. Electrochemical objects give a unique opportunity of obtaining both enthalpy components directly by measuring the open circuit voltage (OCV) of the cell at various temperatures and state of charge. Indeed, by definition, the cells’ OCV is in fact the free energy expressed in electric units U = -ΔG/zF, where U is the OCV, F is the Faraday constant, and z is the number of electrons involved in the redox reaction. Further, since dG = -SdT + Vdp (V and p are volume and pressure, respectively), the temperature coefficient of the OCV (∂U/∂ T)p = -ΔS/zF. The talk presents the results of examining of three lithium-ion batteries of extensively used chemistries: lithium cobalt oxide-graphite, lithium iron phosphate-graphite, and lithium nickel cobalt aluminum oxide-graphite. For performing the comparison and analyzing the results, uncomplicated but special computational procedures were developed. Particular attention is given to the effect of the entropy of the reactions on batteries’ thermal behavior. As it was mentioned above, the enthalpy is comprised of Gibbs energy and the entropy member. Since there is a solid-state reaction in the batteries, a good assumption is that entropy should not change much, and the entropy term might be neglected. Of course, such an assumption needs verification. Our investigation showed in which cases this hypothesis is correct, and if it is incorrect – to what degree.Total heat and heat flow depend upon the current of discharge I. In battery engineering practice, it is commonly assumed that this dependence can be expressed in terms of the Joule-Lenz law where the voltage is substituted with resistance and current according to Ohm’s equation. However, the electrochemical electrodes are essentially non-Ohmic elements meaning that there is a non-linear connection between voltage and current. In the present work, empirical relationships have been suggested: Total Heat is proportional to I1/2 , and Heat Flow – to I3/2 . The proportionality factor evidently cannot be interpreted as resistance – first of all, because its unit of measure is different. The explanation of the phenomenon is based on the non-Ohmic nature of the battery behavior.In some experimental series, we measured the temperature of the cells during cycling. The experiments revealed impressive matching of the temperature and entropy profiles.