Methods Of Statistical Thermodynamics Research Articles

Swelling behavior of sodium lignosulfonate grafted polyacrylic acid highly absorbent hydrogels with two-phase structure

There exist two theories on the swelling behavior of cross-linked polymer networks treated by statistical thermodynamic and scalar methods, respectively. These two theories predict inconsistent network chain length dependence of the swelling ratio. The swelling of biopolymer gels is analysed with scaling laws from polymer physics, as an alternative for the classical Flory-Rehner theory. In this paper, the swelling data of sodium lignosulfonate grafted polyacrylic acid cross-linked networks in good solvents are reanalyzed, and it is pointed out that these networks are a typical model network conforming to the two-phase structural picture. For the swelling behavior of gels in the semi-dilute regime we derive the scaling theory based swelling equations, which make them compact and universal character.

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.

Study of the precipitation trend of asphaltenes and waxes in crude oil using computational chemistry and statistical thermodynamics methods

Asphaltenes aggregation and waxes in petroleum were simulated considering five molecular structures containing functional groups: asphaltenes, resins, and non-polar hydrocarbons in a heavy oil crude. The properties of molecules were calculated using the density functional theory. The van der Waals constants associated with the pairwise interactions and the Hamaker constants for the dispersed phase (formed by asphaltenes and waxes) and the dispersion medium (created by non-polar hydrocarbons) were estimated. Sparse pass size as a function of its composition is calculated using Qyle groups and the Young–Laplace equation. We also assessed the potential colloidal pair corresponding to the interactions between the asphaltene and resin aggregates for different dispersion media, the attractive energies between the asphaltene molecules (−60 10–20 J ≈ ) are more than twice as high as the attractive energies concerning the rest of the molecules present ( × -30–10] 10–20 ≈ × J). It is predicted that attraction energy between the aggregates decreases with the increase of the presence of resin in the dispersed phase, This is explained by the fact that the increase in the concentration n of resin can lead to a decrease in the relative size d of the aggregates by up to 90 % (for n = 0.1, d = 0.1 and for n = 0.9, d = 0.1). This decrease in aggregate size is manifested in a theoretically calculated effective viscosity reduction of up to 50 %.

On thermodynamics and relaxation properties of eukaryotic cells

Mechanical properties of eukaryotic cells play an important role in the development of pathological processes. Currently, there are no complete models reflecting the full phenomenology of the mechanical behavior of the cell. Statistical thermodynamics methods have the potential to provide a framework for understanding the influence of structural properties on the stress-strain state of cells under external loading. In this paper, we develop a statistically based thermodynamic description of the eukaryotic cell to simulate the processes of cell contraction or extension as well as stress relaxation. In addition, it is proposed to use an order parameter to describe the orientation properties of the cell cytoskeleton and obtained a form of free energy, depending on this parameter, temperature and external stress. An orientation-viscoelastic body as a model of a representative cell volume has been proposed in this paper. Following the linear thermodynamics, the evolution equations describing the mechanical behavior of the representative cell volume have been derived. It was shown that the power law for the relaxation times conventionally introduced by the usage of the fractional derivatives in generalized Maxwell-Kelvin viscoelasticity of the cell cytoskeleton mechanical behavior follows from the orientation kinetics of the ensemble of actin filaments revealing the orientation ordering with the signs of the first kind criticality. The introduction of a relaxation spectrum is discussed, allowing one to improve the consistency of simulation results with atomic force microscopy data of living cells.

Determination of Hydrogen’s Thermophysical Properties Using a Statistical Thermodynamic Method

Accurate determination of the thermophysical properties of hydrogen is a crucial issue in hydrogen system design. By developing computational programs, a statistical thermodynamic model based on fundamental equations of state was implemented to determine hydrogen’s thermophysical properties, including the ortho-hydrogen fraction in equilibrium hydrogen, para-ortho hydrogen conversion heat, isobaric heat capacities and enthalpies. The deviations of calculated para-hydrogen enthalpies from REFPROP data were within 2.22%, ranging from 20 K to 300K at 0.1 MPa, and within 2.32% between 100 K and 1500 K at pressures from 0.1 MPa to 20 MPa. To quantitatively assess the convenience of the statistical thermodynamic method, the running speeds of programs with different methods for determining hydrogen’s thermophysical properties were compared. The time required for statistical thermodynamic calculation was 7.95% that required for treading REFPROP data when the performance of the variable density multilayer insulation combined with a one vapor-cooled shield and para-ortho hydrogen conversion was calculated. The programs developed based on the statistical thermodynamic method can be used to determine the thermophysical properties of hydrogen or other fluids.

Vaporization thermodynamics of Leuco Dyes: Measurement and prediction

Leuco Dyes are colorless reduced forms of many organic dyes used in such fields as analytical chemistry, criminalistics, and organic synthesis. Due to the low volatility of these compounds, the determination of their vaporization parameters with conventional methods is a non-trivial task. In this work, the saturated vapor pressures of three Leuco Dyes over the liquid and supercooled liquid phases were measured using fast scanning calorimetry. The respective heat capacities were obtained with DSC, and the ideal gas phase heat capacities were calculated by the methods of quantum chemistry and statistical thermodynamics. The vaporization enthalpies at 298.15 K were estimated using the “molecule-additivity” approach and adjusted to the measurement temperatures in two different ways. The first is based on an approach employing a correlation between the heat capacity change on vaporization and the vaporization enthalpy at 298.15 K, recently proposed by our group. The second way is by using the values of liquid and ideal phase heat capacities obtained in this work. The predicted, measured, and adjusted values were compared and analyzed.

Anesthesia, Coming of Age in the World of Modern In Silico Drug Design.

Anesthesia, Coming of Age in the World of Modern In Silico Drug Design.

Computing the Differences between Asn-X and Gln-X Deamidation and Their Impact on Pharmaceutical and Physiological Proteins: A Theoretical Investigation Using Model Dipeptides

Protein deamidation is a degradation mechanism that significantly impacts both pharmaceutical and physiological proteins. Deamidation impacts two amino acids, Asn and Gln, where the net neutral residues are converted into their acidic forms. While there are multiple similarities between the reaction mechanisms of the two residues, the impact of Gln deamidation has been noted to be most significant on physiological proteins while Asn deamidation has been linked to both pharmaceutical and physiological proteins. For this purpose, we sought to analyze the thermochemical and kinetic properties of the different reactions of Gln deamidation relative to Asn deamidation. In this study, we mapped the deamidation of Gln-X dipeptides into Glu-X dipeptides using density functional theory (DFT). Full network mapping facilitated the prediction of reaction selectivity between the two primary pathways, as well as between the two products of Gln-X deamidation as a function of solvent dielectric. To achieve this analysis, we studied a total of 77 dipeptide reactions per solvent dielectric (308 total reactions). Modeled at a neutral pH and using quantum chemical and statistical thermodynamic methods, we computed the following values: enthalpy of reaction (ΔHRXN), entropy (ΔSRXN), Gibbs free energy of reaction (ΔGRXN), activation energy (EA), and the Arrhenius preexponential factor (log(A)) for each dipeptide. Additionally, using chemical reaction principles, we generated a database of computed rate coefficients for all possible N-terminus Gln-X deamidation reactions at a neutral pH, predicted the most likely deamidation reaction mechanism for each dipeptide reaction, analyzed our results against our prior study on Asn-X deamidation, and matched our results against qualitative trends previously noted by experimental literature.

The Relationship between Symmetry and Specific Properties of Supramolecular Systems

Released agent is a supramolecular system formed around nanobubbles in highly diluted solutions of substances subjected to technological processing. Released agent retains the structure and symmetry of the supramolecular system of the dissolved substance. It has two specific properties: (1) when combined with the original substance, it modifies its effect on an organism; (2) and it could cause an atypical pathological reaction in some individuals. These properties could be due to the transmission of symmetry from released agent to the receptor in the molecular recognition reaction by deforming the receptor structure. A theoretical analysis of these properties was carried out using methods of statistical thermodynamics of complex systems, chemical thermodynamics of supramolecular systems, and analytical mechanics. The released agent’s modifying effect is a phenomenon of the receptor pre-organization in the molecular recognition reaction. The selective ability and free energy of complex formation of released agent (from highly diluted antibodies to the beta-subunit of the insulin receptor) with the insulin receptor was evaluated. The atypical pathological reaction of some individuals to released agents resembles a resonance phenomenon that occurs when the symmetries (structures) of released agent and the receptor coincide. The obtained results show a possibility to investigate released agents’ properties not only empirically, but also using the methods of theoretical physics.

Calculation of Entropy for a Two-Dimensional (2D) Ideal Gas with a Statistical Thermodynamic Method

Calculation of Entropy for a Two-Dimensional (2D) Ideal Gas with a Statistical Thermodynamic Method

Entropy characteristics in an electric double layer with off-centre charge ions. A statistical thermodynamics approach

Statistical thermodynamics methods are utilised to characterise aspects of the entropy of formation of a planar electric double layer. The model system consists of a primitive model electrolyte but with off-centre charge cations and centro-symmetric anions, next to a planar, uniformly charged electrode. An expression is developed for the entropy of off-centre charge ions. The theoretically predicted results of this entropy as a function of the electrode surface charge are compared with those from the corresponding Monte Carlo simulations. The entropy change with respect to the absolute value of the surface charge density is seen to be negative (or normal) if the displacement of the cation charge centre is zero or is independent of temperature. However, if the displacement is temperature dependent, the entropy can be positive (or anomalous). In each situation, the simulation data are well reproduced by the predicted results.

The Ionic Product of Water in the Eye of the Quantum Cluster Equilibrium.

The theoretical description of water properties continues to be a challenge. Using quantum cluster equilibrium (QCE) theory, we combine state-of-the-art quantum chemistry and statistical thermodynamic methods with the almost historical Clausius–Clapeyron relation to study water self-dissociation and the thermodynamics of vaporization. We pay particular attention to the treatment of internal rotations and their impact on the investigated properties by employing the modified rigid-rotor–harmonic-oscillator (mRRHO) approach. We also study a novel QCE parameter-optimization procedure. Both the ionic product and the vaporization enthalpy yield an astonishing agreement with experimental reference data. A significant influence of the mRRHO approach is observed for cluster populations and, consequently, for the ionic product. Thermodynamic properties are less affected by the treatment of these low-frequency modes.

Theoretical study on the kinetics and thermodynamics of H‐atom abstractions from tetramethylsilane‐related species

AbstractTheoretical kinetics and thermochemistry investigations on the H‐atom abstraction reactions by H and O atoms and OH and HO2 radicals from Si−C−O‐containing species such as Si(CH3)4, Si(CH3)3(OH), Si(CH3)2(OH)2, and Si(CH3)(OH)3 have been carried out in this work. The geometry, vibrational frequencies, and hindrance potential for each species are calculated at the B3LYP/6‐31G(2df,p) level of theory with the single‐point energies calculated at the G4 level of theory. The composite methods G3 and G4 are utilized to derive enthalpies of formation at 0 K by the atomization reaction methodology. ΔHf(298 K), S(298 K), and Cp(T) are calculated by using the statistical thermodynamics method. Conventional transition state theory is used over a wide temperature range (298.15−2000 K) for H‐atom abstraction reactions by H, O, and HO2 radicals from the species mentioned above, and variational transition state theory is used for H‐atom abstraction reactions by the OH radical. The kinetic and thermodynamic parameters based on high‐level theoretical calculations are compared with the literature data. Reactivity comparison between the similar hydrocarbons and silicon‐organic compounds for H‐atom abstractions is explored. A large difference exists between these two different systems when H‐atom abstractions are on hydroxyl sites.

Analysis of Micro Arc Plasma Characteristics of the Mixed Metal Vapor in Vacuum Circuit Breaker

For the mechanical vacuum circuit breaker, the particle composition group of the metal vapor arc varies with different operating conditions, which will lead to the discontinuous variation of the electrical conductivity between electrodes. The change of mixed metal vapor arc macroscopic electrical characteristics results from the space-time change of microscopic arc plasma characteristics. For the vacuum circuit breaker, the interruption performance is directly influenced by the composition of the metal vapor arc plasma and the characteristic parameters. For evaluating the electrode characteristics and establishing a database of mixed metal vapor arc characteristic parameters for the vacuum interrupter, this paper presents a study of the copper chromium (CuCr) alloy contacts used in vacuum circuit breakers. The Eindhoven model was used to derive a Local Thermodynamic Equilibrium (LTE) vacuum arc plasma particle composition model. The thermodynamic parameter variation of metal vapor arc plasma is calculated by statistical thermodynamic method, and the electrical conductivity was calculated by Chapman-Enskog method. The mass density, enthalpy, specific heat and electrical conductivity for different alloy proportion (CuCr25, CuCr40, CuCr50, CuCr60 and CuCr75) were compared and quantitatively characterized.

Study on Hydrate Phase Equilibrium Diagram of Methane Containing System Based on Thermodynamic Model

Natural gas hydrate is a potential energy source in the future, which widely occurs in nature and industrial activities, and its formation and decomposition are identified by phase equilibrium. The calculation of multicomponent gas phase equilibrium is more complex than that of single component gas, which depends on the accurate model characterized by enthalpy and free energy. Based on the Kvamme-Tanaka statistical thermodynamic model, theoretical and experimental methods were used to predict and verify the phase equilibrium of pure methane hydrate and carbon dioxide hydrate in the temperature range of 273.17–289.05 K. The phase equilibrium curves of methane-containing gases such as CH4+CO2,CH4+C2H6,CH4+H2S and CH4+CO2+H2S under different mole fractions were drawn and analyzed, and the decomposition or formation enthalpy and free energy of hydrate were calculated. The results show that, the phase equilibrium curves of the methane containing systems is mainly related to the guest molecule type and the composition of gas. The evolution law of phase equilibrium pressure of different gases varies with composition and temperature, and the phase splitting of CO2at the quadruple point affects the phase equilibrium conditions. Due to the consideration of the interaction between the motion of guest molecules and the vibration of crystal lattice, the model exhibits a good performance, which is quantified in terms of mean square error (MSE) with respect to the experimental data. The magnitudes of MSE percent are respectively 1.2, 4.8, 15.12 and 9.20 MPa2for CH4+CO2, CH4+C2H6, CH4+H2S and CH4+CO2+H2S systems, and the values are as low as 3.57 and 1.32 MPa2for pure methane and carbon dioxide, respectively. This study provides engineers and researchers who want to consult the diagrams at any time with some new and accurate experimental data, calculated results and phase equilibrium curves. The research results are of great significance to the development and utilization of gas hydrate and the flow safety prediction of gas gathering and transportation.

Equilibrium state thermodynamic properties of rare gas dimers and trimers obtained from equations of state and statistical thermodynamics: Application to neon, argon, krypton and xenon

The equilibrium thermodynamic properties of gas phase dimerization and trimerization of Ne, Ar, Kr, and Xe are calculated from equations of state (EOS). The equilibrium constants, changes in enthalpy, Gibbs energy, entropy and heat capacity are determined over 10-kelvin ranges are reported. These quantities are calculated from accurate and precise equations of state available from the NIST Thermophysical Tables. In addition, the molar entropies and heat capacities are calculated for the dimers, and molar entropies for the trimers. Statistical thermodynamic (ST) methods are used to complement these calculations and employ dimer partition functions obtained from a sum-over-state approach that includes both bound and metastable rovibrational states. For the trimers, such calculations are carried out only for neon, for which the rovibrational energies of the bound states are available. The results of the EOS and ST calculations for the Ne – Xe dimers are in good agreement with each other, while those for the neon trimer are less so. The effect of excluding the metastable states from the dimer partition functions is demonstrated. The results indicate that the thermodynamic properties of dimerization/trimerization for polyatomic molecules may be obtained if accurate EOS data is available, suggesting that the method may be applied to polyatomic molecules. Relationships between the enthalpies of dissociation of the dimers and trimers and the enthalpies of vaporization of the respective liquids are demonstrated.

On the influence of clustering processes in the liquid structure on Raman scattering

A mathematical relation has been obtained that makes it possible to calculate the polarizability of a polyatomic molecule in the structure of a cluster. It is shown that the scattered frequencies in the Raman effect are proportional to the square root of the number of particles in the most probable (or average) cluster in the liquid structure. The appearance of frequencies in the far part of the Raman spectrum region is caused by the processes of intermolecular interactions in clusters and the processes of disintegration or formation of cluster systems in the structure of disordered condensed media. According to the proposed model and experimental data in the frequency range 20–1300 cm-1, it has been carried out the comparison of the values of the calculated frequencies of the Raman spectrum and their mutual position, which has shown the adequacy of the proposed model. The cluster model of liquid structure and the methods of mathematical statistics and statistical thermodynamics make it possible to expand the capabilities of the classical theory of Raman scattering in liquids and to predict the position of spectral bands in Raman spectra in the far long-wavelength region of the spectrum. It is revealed that the formation and breakdown of the most probable clusters is associated with the correlations of the most stable clusters (in terms of the number of particles) in a condensed medium with the Fibonacci numbers.

Prediction of the Solubilities of Water in Hydrocarbons with COSMO-RS and Interpretation of the Solubility Characteristics

The solubilities of water in various hydrocarbons are usually needed to assess the water content in oil products. Because the solubilities of water in hydrocarbons are very small, which usually leads to large deviations in experiments, and because we have trouble carrying out experiments on bulk hydrocarbons, it is necessary to develop a more convenient molecular simulation approach to predict the solubility. In this paper, COSMO-RS, a statistical thermodynamic method based on quantum chemistry, has been employed to obtain the solubilities of water in n-alkanes, alkylcyclohexanes, alkylbenzenes and 1-alkenes by calculating the difference of the thermodynamic properties during the dissolution process. The predictions of COSMO-RS were compared with the experimental data, as well as those of API correlations and the Tsonopoulos correlation. The results indicate that COSMO-RS can better predict the trends of the solubility with high accuracy, where the deviations are within ± 29.41%. The characteristics of the solubilities of water in various hydrocarbons are interpreted systemically, especially for the influence of carbon number, CN. It particularly focuses on the non-monotonicity of the solubility curves of water in n-alkanes with the increase of CN. In addition, the effect of temperature on the characteristic of solubility is simultaneously investigated.

Hydrophobic Hydration Processes: Intensity Entropy and Null Thermal Free Energy and Density Entropy and Motive Free Energy.

The processes at the molecule level, which are the source of the ergodic properties of thermodynamic systems, are analyzed with special reference to entropy. The entropy change produced by increasing the temperature T depends on the increase of velocity of the particles with a decrease of the squared mean sojourn time (τm2) and gradual loss of instant energy intensity. The diminution, which is due to dilution, of the number of terms in the summation of cumulative sojourn time (τi2)Σ produces loss of energy density, thus generating a gradual increase of density entropy, dSDens. The ergodic property of thermodynamic systems consists of the equivalence of density entropy (dependent on dilution) with intensity entropy (dependent on temperature). This equivalence has been experimentally verified in every hydrophobic hydration process as thermal equivalent dilution. An ergodic dual-structure partition function {DS-PF} represents the state probability of every hydrophobic hydration process, corresponding to the biphasic composition of these systems. The dual-structure partition function {DS-PF} (Kmot·ζth) is the product of a motive partition function {M-PF} (Kmot) multiplied by a thermal partition function {T-PF} (ζth = 1). {M-PF} gives rise to changes of density entropy, whereas {T-PF} gives rise to changes of intensity entropy. {M-PF} is referred to a reacting mole ensemble (reacting solute) composed of few elements (moles), ruled by binomial distribution, whereas {T-PF} is referred to a nonreacting molecule ensemble (NoremE) (nonreacting solvent), which is composed of a very large population of elements (molecules), ruled by Boltzmann statistics. Statistical thermodynamic methods cannot be applied to {M-PF} that can be calculated by numerical methods from the experimental titration data. By development of the dual-structure partition function {DS-PF}, parabolic convoluted binding functions are obtained. The tangents to the binding functions represent the dual enthalpy, −ΔHdual = (−ΔHmot – ΔHth), and the dual entropy, ΔSdual = (ΔSmot + ΔSth). The connections between canonical and grand-canonical partition functions of statistical thermodynamics with thermal and motive partition functions of chemical thermodynamics, respectively, are discussed. Special attention has been devoted to the equality ΔHth/T + ΔSth = 0, typical of NoremEs, as an entropy–enthalpy compensation with ΔGth/T = 0. The thermodynamic potential change Δμ, as proposed by potential distribution theorem (PDT) for iceberg formation from {T-PF} of the solvent, is nonexistent because the excess solvent is at a constant potential (Δμsolv = 0). The information level offered by the ergodic algorithmic model (EAM) is more complete and correct than that offered by the potential distribution theorem (PDT): the stoichiometry of the water reaction in hydrophobic hydration processes is determined by the EAM as the function of the number ±ξw. Quasi-chemical approximation, renamed the chemical molecule/mole scaling function (Che. m/M. sF), is a fundamental breakthrough in the application of statistical thermodynamics to chemical reactions. Boltzmann statistical molecule distribution of the thermal partition function {T-PF} is scaled with binomial mole distribution of the motive partition function {M-PF}. For computer-assisted drug design, the alternative calculation procedure of Talhout, based on the previous experimental determination of binding functions, is recommended. The ergodic algorithmic model (EAM), applied to the experimental convoluted binding functions, can recover the distinct terms of intensity entropy (ΔHmot/T) and density entropy (ΔSmot), together with other essential information elements, lost by computer simulations.

Theoretical explanation for the pharmaceutical incompatibility through the cooperativity effect of the drug-drug intermolecular interactions in the phenobarbital∙∙∙paracetamol∙∙∙H2O complex.

In order to reveal the essence of the pharmaceutical incompatibility, the cooperativity effects of the drug-drug intermolecular π∙∙∙π and H∙∙∙O H-bonding interactions involving hydration were evaluated in the phenobarbital∙∙∙paracetamol∙∙∙H2O complex at the M06-2X/6-311++G** and MP2/6-311++G** levels. The thermodynamic cooperativity effects were also investigated by the statistical thermodynamic method. The results show that the π∙∙∙π stacking ternary complexes with the moderate anti-cooperativity effects are dominant in controling the aggregation process of phenobarbital, paracetamol, and H2O, as is confirmed by the atoms-in-molecules (AIM) and reduced density gradient (RDG) analyses. Therefore, it can be inferred that the anti-cooperativity effect plays an important role in forming the pharmaceutical incompatibility, and thus a deduction on the formation process of the pharmaceutical incompatibility between phenobarbital and paracetamol, with the hydration effect, is given. Several valuable models that relate the features of molecular surface electrostatic potentials or their statistical parameters, such as the surface areas, average values ([Formula: see text]), variances ([Formula: see text], [Formula: see text] and [Formula: see text]), and product of [Formula: see text] and electrostatic balance parameter (ν) ([Formula: see text]ν), to the values of the cooperativity effects were predicted. The formation of the pharmaceutical incompatibility is a thermodynamic cooperativity process driven by the enthalpy change. Graphical abstract Anti-cooperativity effect plays an important role in forming the pharmaceutical incompatibility.