Search Results (55)

In this work, the thermodynamics of molecular transport between two compartments connected by a nanochannel is investigated through an analysis of internal energy and entropy changes, with a focus on how these changes depend on intermolecular interaction strength. When interactions are weak, resembling gas-like behavior, entropy dominates and favors configurations in which molecules are evenly distributed between the two compartments, despite an increase in internal energy. In contrast, strong interactions, characteristic of liquid-like behavior, lead to dominant energetic contributions that favor configurations with molecules localized in a single compartment, despite entropy loss. Intermediate interaction strengths yield comparable entropic and energetic contributions that cancel each other out, resulting in oscillatory behavior between evenly distributed and localized configurations, as observed in previous work. This thermodynamic analysis reveals energy–entropy compensation, in which entropic and energetic contributions offset each other across different interaction strengths; notably, this compensatory relationship exhibits a linear trend. These findings provide insight into the thermodynamic origins of molecular transport behavior and highlight fundamental parallels between molecular transport and molecular binding, the latter being particularly relevant to molecular recognition and drug design. Full article

This article presents a mini-review of the available data on the thermodynamics of the complexation of amino acids and peptides with some nucleic bases in a buffer medium. Data on changes in thermodynamic parameters (binding constants, Gibbs energy, enthalpy, entropy) during the complexation of nucleic bases with amino acids and peptides as a function of physicochemical properties are given at T = 298.15 K. The effects of complexation on the volumetric properties of nucleic bases, including apparent molar volumes, standard molar volumes, and limiting molar expansibility, over a temperature range of 288.15 to 313.15 K are considered in detail. Differences in the behavior of amino acids and peptides caused by different modes of coordination with nucleic bases are noted. These manifest in the stoichiometry of the formed complexes, the relationship with the acid dissociation constants of carboxyl and amino groups, enthalpy–entropy compensation in the complexation process, the temperature dependence of the transfer volumes, and the effect of hydrophobicity on volumetric characteristics. Full article

The phenomenon of enthalpy–entropy compensation emerges as a ubiquitous feature of processes occurring in water, especially those involving biological macromolecules. In writing the present study, the aim was not to review most of the rationalizations proposed so far but to focus on a general theory of hydration, partly developed and applied by one of us. This theory poses a physical condition for the occurrence of enthalpy–entropy compensation: the energetic strength of the solute–water attraction must be weak compared to that of water–water H-bonds. This condition is largely fulfilled in water due to the cooperativity of its three-dimensional H-bonded network. Full article

The practical implementation of transition state theory (TST) commonly assumes equivalence between theoretical and experimentally determined rate constants, represented by Arrhenius parameters—the activation energy and pre-exponential factor. Here, we employed the General Rate Equation (GRE) to analyse solid–gas-phase thermolysis in two paradigms: mass loss (e.g., calcite decomposition) and mass gain (e.g., methane pyrolysis leading to solid carbon formation). By partitioning the Gibbs free energy of activation into forwards and reverse contributions, plus an additional term accounting for concurrent physical phenomena (notably nucleation and diffusion-viscosity effects), we derived an empirical universal expression relating both Arrhenius parameters and $∆G^{+}$ across 500–1500 K. We further demonstrate the utility of the isokinetic temperature for interpreting cases where only Kinetic Compensation or Enthalpy–Entropy Compensation effects are observed. This framework unifies kinetic and thermodynamic descriptions of complex thermolysis processes. Full article

The thermodynamic study of protein folding shows the generation of a narrow range of ΔG° values, as a net result of large changes in the ΔH° and TΔS° values of the folding process. The obvious consequence of this narrow range of values is that a linear enthalpy–entropy relationship, showing apparent enthalpy–entropy compensation (EEC), is clearly observed to be associated with the study of protein folding. Herein, we show the ΔH°, TΔS°, and ΔG° values for a set of 583 data from protein folding processes, at various temperatures, as calculated by using the Gibbs–Helmholtz equations. This set of thermodynamic data was calculated from the melting temperature (Tm), the melting enthalpy (ΔHm), and the change in heat capacity (ΔCp°) values, all of them associated with the heat-induced protein unfolding processes and included in the ProTherm Data Base. The average values of enthalpy (ΔH°av), entropy (TΔS°av), and free energy (ΔG°av) for the folding process were calculated within the range of temperature from 0 °C to the average value of Tm. The values and temperature dependency of TΔS°av within this temperature range are practically equal to those corresponding to ΔH°av, while ΔG°av remains small and displaying a curve with a minimum at about 10 °C and a value of ΔG° = −30.9 kJ/mol at the particular temperature of 25 °C. The large negative value of TΔS°av, together with the also large and negative value of ΔCp°av, suggests large conformational changes and important EEC, thus causing the small average value of ΔG° for protein folding, which is enough to guarantee both protein stability and molecular flexibility to allow for adaptation to the chemical potentials of the environment. Our analysis suggests that EEC may be the quantum-mechanical evolutive mechanism to make functional proteins adaptative to environmental temperature and metabolite concentrations. The analysis of protein folding data, compared with those of protein–ligand interaction, allows us to suggest strategies to overcome EEC in the design of new drugs. Full article

The state of the art in methane pyrolysis does not yet provide a definitive answer as to whether the concept of an elementary reaction is universally applicable to the apparently simple process of methane dissociation. Similarly, the literature currently lacks a comprehensive and unambiguous description of the methane pyrolysis process and, in particular, a single model that would well represent its course at both the micro and macro scales. Given the wide range of conditions under which this reaction can occur—whether thermal or thermo-catalytic, in solid or fluidized bed reactors—it is crucial to evaluate the usefulness of different kinetic models and their compatibility with basic thermodynamic principles and design assumptions. To address these research gaps, the authors analysed the thermodynamic and kinetic dependencies involved in the thermal decomposition of methane, using the synthesis of methane from its elemental components and its reversibility as a basis for exploring suitable kinetic models. Using experimental data available in the literature, a wide range of kinetic models have been analysed to determine how they all relate to the reaction rate constant. It was found that regardless of whether the process is catalytic or purely thermal, for temperatures above 900 °C the reversibility of the reaction has a negligible effect on the hydrogen yield. This work shows how the determined kinetic parameters are consistent with the Kinetic Compensation Effect (KCE) and, by incorporating elements of Transition State Theory (TST), the possibility of the existence of Entropy–Enthalpy Compensation (EEC). The indicated correspondence between KCE and EEC is strengthened by the calculated average activation entropy at isokinetic temperature $({∆S}_B=-275.0 \mathrm{J}·(\mathrm{m}\mathrm{o}\mathrm{l}·\mathrm{K}{)}^{-1}).$ Based on these results, the authors also show that changes in the activation energy $(E=20–421 \mathrm{k}\mathrm{J}·{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1})$ can only serve as an estimate of the optimal process conditions, since the isoconversion temperature ($T_{iso}=1200-1450 \mathrm{K}>T_{eq}$) is shown to depend not only on thermodynamic principles but also on the way the reaction is carried out, with temperature (T) and pressure (P) locally compensating each other. Full article

In this work, an approach to the calculation of hydrogen bonding enthalpies is proposed. It employs the correlation proposed by M.H. Abraham, establishing the connection between the equilibrium constant (K_HB) and acidity (${\alpha }_2^{\mathrm{H}}$) and basicity (${\beta }_2^{\mathrm{H}}$) parameters: log K_HB = 7.354 · ${\alpha }_2^H$ · ${\beta }_2^H$ − 1.099. Hydrogen bonding enthalpy (Δ_HBH) is found using the compensation relationship with Gibbs energy (Δ_HBG): Δ_HBG = 0.66 · Δ_HBH + 2.5 kJ·mol⁻¹. This relationship enables the calculation of the enthalpy, Gibbs energy and entropy of hydrogen bonding. The validity of this approach was tested against 122 experimental hydrogen bonding enthalpies values available from the literature. The root mean square deviation and average deviation equaled 1.6 kJ·mol⁻¹ and 0.5 kJ·mol⁻¹, respectively. Full article

The Hofmeister series categorizes ions based on their effects on protein stability, yet the microscopic mechanism remains a mystery. In this series, NaCl is neutral, Na₂SO₄ and Na₂HPO₄ are kosmotropic, while GdmCl and NaSCN are chaotropic. This study employs CD and NMR to investigate the effects of NaCl, Na₂SO₄, and Na₂HPO₄ on the conformation, stability, binding, and backbone dynamics (ps-ns and µs-ms time scales) of the WW4 domain with a high stability and accessible side chains at concentrations ≤ 200 mM. The results indicated that none of the three salts altered the conformation of WW4 or showed significant binding to the four aliphatic hydrophobic side chains. NaCl had no effect on its thermal stability, while Na₂SO₄ and Na₂HPO₄ enhanced the stability by ~5 °C. Interestingly, NaCl only weakly interacted with the Arg27 amide proton, whereas Na₂SO₄ bound to Arg27 and Phe31 amide protons with Kd of 32.7 and 41.6 mM, respectively. Na₂HPO₄, however, bound in a non-saturable manner to Trp9, His24, and Asn36 amide protons. While the three salts had negligible effects on ps-ns backbone dynamics, NaCl and Na₂SO₄ displayed no effect while Na₂HPO₄ significantly increased the µs-ms backbone dynamics. These findings, combined with our recent results with GdmCl and NaSCN, suggest a microscopic mechanism for the Hofmeister series. Additionally, the data revealed a lack of simple correlation between thermodynamic stability and backbone dynamics, most likely due to enthalpy–entropy compensation. Our study rationalizes the selection of chloride and phosphate as the primary anions in extracellular and intracellular spaces, as well as polyphosphate as a primitive chaperone in certain single-cell organisms. Full article

Equilibrium density fluctuations at the molecular level produce cavities in a liquid and can be analyzed to shed light on the statistics of the number of molecules occupying observation volumes of increasing radius. An information theory approach led to the conclusion that these probabilities should follow a Gaussian distribution. Computer simulations confirmed this prediction across various liquid models if the size of the observation volume is not large. The reversible work required to create a cavity and the chance of finding no molecules in a fixed observation volume are directly correlated. The Gaussian formula for the latter probability is scrutinized to derive the changes in enthalpy and entropy, which arise from the cavity creation. The reversible work of cavity creation has a purely entropic origin as a consequence of the solvent-excluded volume effect produced by the inaccessibility of a region of the configurational space. The consequent structural reorganization leads to a perfect compensation of enthalpy and entropy changes. Such results are coherent with those obtained from Lee in his direct statistical mechanical study. Full article

The thermodynamics of protein–ligand interactions seems to be associated with a narrow range of Gibbs free energy. As a consequence, a linear enthalpy–entropy relationship showing an apparent enthalpy–entropy compensation (EEC) is frequently associated with protein–ligand interactions. When looking for the most negative values of ∆H to gain affinity, the entropy compensation gives rise to a barely noticeable increase in affinity, therefore negatively affecting the design and discovery of new and more efficient drugs capable of binding protein targets with a higher affinity. Originally attributed to experimental errors, compensation between ∆H and T∆S values is an observable fact, although its molecular origin has remained obscure and controversial. The thermodynamic parameters of a protein–ligand interaction can be interpreted in terms of the changes in molecular weak interactions as well as in vibrational, rotational, and translational energy levels. However, a molecular explanation to an EEC rendering a linear enthalpy–entropy relationship is still lacking. Herein, we show the results of a data search of ∆G values of 3025 protein–ligand interactions and 2558 “in vivo” ligand concentrations from the Protein Data Bank database and the Metabolome Database (2020). These results suggest that the EEC may be plausibly explained as a consequence of the narrow range of ∆G associated with protein–ligand interactions. The Gaussian distribution of the ∆G values matches very well with that of ligands. These results suggest the hypothesis that the set of ∆G values for the protein–ligand interactions is the result of the evolution of proteins. The conformation versatility of present proteins and the exchange of thousands (even millions) of minute amounts of energy with the environment may have functioned as a homeostatic mechanism to make the ∆G of proteins adaptive to changes in the availability of ligands and therefore achieve the maximum regulatory capacity of the protein function. Finally, plausible strategies to avoid the EEC consequences are suggested. Full article

An analysis was carried out on the thermal dissociation of selected inorganic salts according to Transition-State Theory (TST). For this purpose, two possibilities were compared in the context of rate constants: in the first case using the Arrhenius constant directly from TST, and in the second, using the thermodynamic equilibrium constant of the reaction/process of active state formation. The determined relationships are presented in the form of temperature profiles. It was established that TST applies to reactions for which there is a formally and experimentally reversible reaction, in the literal sense or catalytic process. The importance of the isoequilibrium temperature, which results from the intersection of the thermodynamic temperature profile and the Gibbs free energy of activation, was demonstrated. Its values close to the equilibrium temperature are indicative of more dynamic kinetic qualities. As part of the discussion, the Kinetic Compensation Effect (KCE) was used to observe changes in the entropy of activation by comparing two kinetic characteristics of the same reaction. Enthalpy–Entropy Compensation (EEC) was shown to be the same law as KCE, just expressed differently. This was made possible by TST, specifically the entropy of activation at isokinetic temperature, by which the perspective of the relationship of energy effects changes. Full article

The interactions of metal ions with fulvic acids were investigated from the point of view of the thermodynamic aspects of complexation as well as the size and charge of the formed complexes. Thermodynamic aspects were studied by means of isothermal titration calorimetry. Particle size distribution was determined by the method of dynamic light scattering and charge by the measurement of zeta potential. Complexation resulted in changes in particle size and charge. The particle size distribution was trimodal for fulvic acids and bimodal for fulvic complexes with calcium and magnesium, while copper–fulvic complexes had only one size fraction. The compensation of the negative charge of carboxylic and phenolic functional groups by positively charged metal ions resulted in an increase in zeta potential which became closer to zero in the case of copper–fulvic complexes. However, all metal–humic complexes behaved as colloidally unstable, which resulted in visually observable sedimentation. Calorimetric measurements provided positive values for changes in enthalpy, which indicated endothermic processes. In contrast, quantum chemical calculations as well as experiments with model compounds provided negative values indicating exothermic processes. Changes in Gibbs energy were determined as negative and changes in entropy as positive. Full article

The effect of the partial substitution of Cr with Fe on the thermodynamic parameters of vanadium-rich Ti₁₆V₆₀Cr_24-xFe_x alloys (x = 0, 4, 8, 12, 16, 20, 24) was investigated. For each composition, a pressure–concentration isotherm (PCI) was registered at 298, 308, and 323 K. The PCI curves revealed a reduction in plateau pressure and a decrease in desorbed hydrogen capacity with an increasing amount of Fe. For all alloys, about 50% or less of the initial hydrogen capacity was desorbed for all chosen temperatures. Entropy (ΔS) and enthalpy (ΔH) values were deducted from corresponding Van’t Hoff plots of the PCI curves: the entropy values ranged from −150 to −57 J/K·mol H₂, while the enthalpy values ranged from −44 to −21 kJ/mol H₂. They both decreased with an increasing amount of Fe. Plotting ΔS as function of ΔH showed a linear variation that seems to indicate an enthalpy–entropy compensation. Moreover, a quality factor analysis demonstrated that the present relationship between entropy and enthalpy is not of a statistical origin at the 99% confidence level. Full article

Moisture adsorption and desorption isotherms of gelatin extracted from whitefish skin powder (FSGP) at different temperatures across a wide range of water activity were determined along with their thermodynamic properties. Nine mathematical models were utilized for fitting the experimental data and simulating the adsorption and desorption behavior. The thermodynamic properties were determined and fitted to the experimental data. The results showed that Peleg and GAB models were the best fit for FSGP. The energies involved in the adsorption and desorption process of FSGP indicated a stronger dependence on equilibrium moisture content (X_e). When X_e decreased, there was a consistent trend of increasing thermodynamic properties. Both the moisture adsorption and desorption behaviors of FSGP were, therefore, non-spontaneous processes. Linear correlations between the changes in enthalpy and entropy for adsorption and desorption were observed, indicating the presence of enthalpy–entropy compensation for FSGP. For preserving FSGP quality, it should be stored with X_w ≤ 8 (g_w/g_dm, d.b.) at temperatures below 53 °C and an RH of 50% to avoid it becoming rubbery. These findings are crucial for providing insight into the optimal drying and storage conditions. Full article

In this paper, we report the effect of the Cr/Mn ratio on the thermodynamic properties of Ti₃₀V₆₀Mn_(10−x)Cr_x (x = 0, 3.3, 6.6 and 10) + 4 wt.% Zr alloys. It was found that the enthalpy and entropy change with the Cr/MN ratio and that the entropy and entropy variation is coupled in an enthalpy-entropy compensation fashion. Using a compensation quality factor, it was established that the enthalpy-entropy compensation is not due to a statistical origin, with a confidence of more than 95%. Full article