Search Results (41)

Temperature dependencies of the density, heat capacity at constant pressure, and isobaric thermal expansion coefficient are investigated for two liquid metal nuclear reactor coolants: pure sodium and sodium–potassium eutectic alloy (31.9 at. %Na). The variational method of the thermodynamic perturbation theory is used for the calculations. The calculations were carried out in temperature ranges of 373–1673 K for Na and 273–1573 K for 0.319Na-0.681K. The accuracy of two local pseudopotentials and three exchange–correlation functions is estimated. It is shown that two combinations between the pseudopotential and exchange–correlation function can be recommended for predicting the properties at high temperatures for which experimental information is absent. Full article

Markov chain perturbation theory is a rapidly developing subfield of the theory of stochastic processes. This review outlines emerging applications of this theory in the analysis of stochastic models of chemical reactions, with a particular focus on biochemistry and molecular biology. We begin by discussing the general problem of approximate modeling in stochastic chemical kinetics. We then briefly review some essential mathematical results pertaining to perturbation bounds for continuous-time Markov chains, emphasizing the relationship between robustness under perturbations and the rate of exponential convergence to the stationary distribution. We illustrate the use of these results to analyze stochastic models of biochemical reactions by providing concrete examples. Particular attention is given to fundamental problems related to approximation accuracy in model reduction. These include the partial thermodynamic limit, the irreversible-reaction limit, parametric uncertainty analysis, and model reduction for linear reaction networks. We conclude by discussing generalizations and future developments of these methodologies, such as the need for time-inhomogeneous Markov models. Full article

Using a Dyson–Schwinger approach, we perform an analysis of the non-trivial ground state of thermal $SU\left(N\right)$ Yang–Mills theory in the non-perturbative regime where chiral symmetry is dynamically broken by a mass gap. Basic thermodynamic observables such as energy density and pressure are derived analytically, using Jacobi elliptic functions. The results are compared with the lattice results. Good agreement is found at low temperatures, providing a viable scenario for a gas of massive glue states populating higher levels of the spectrum of the theory. At high temperatures, a scenario without glue states consistent with a massive scalar field is observed, showing an interesting agreement with lattice data. The possibility is discussed that the results derived in this analysis open up a novel pathway beyond lattice to precision studies of phase transitions with false vacuum and cosmological relics that depend on the equations of state in strong coupled gauge theories of the type of Quantum Chromodynamics (QCD). Full article

Background: During the dissolution of amorphous solid dispersion (ASD) formulations, the drug load (DL) often impacts the release mechanism and the occurrence of loss of release (LoR). The ASD/water interfacial gel layer and its specific phase behavior in connection with DL strongly dictate the release mechanism and LoR of ASDs, as reported in the literature. Thermodynamically driven liquid-liquid phase separation (LLPS) and/or drug crystallization at the interface are the key phase transformations that drive LoR. Methods: In this study, a combination of Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) thermodynamic modeling and in silico molecular simulation was applied to investigate the release mechanism and the occurrence LoR of an ASD formulation consisting of ritonavir as the active pharmaceutical ingredient (API) and the polymer, polyvinylpyrrolidone-co-vinyl acetate (PVPVA64). A thermodynamically modeled ternary phase diagram of ritonavir (PVPVA64) and water was applied to predict DL-dependent LLPS in the ASD/water interfacial gel layer. Microscopic Erosion Time Testing (METT) was used to experimentally validate the phase diagram predictions. Additionally, in silico molecular simulation was applied to provide further insights into the phase separation, the release mechanism, and aggregation behavior on a molecular level. Results: Thermodynamic modeling, molecular simulation, and experimental results were consistent and complementary, providing evidence that ASD/water interactions and phase separation are essential factors driving the dissolution behavior and LoR at 40 wt% DL of the investigated ritonavir/PVPVA64 ASD system, consistent with previous studies. Conclusions: This study provides insights into the potential of blending thermodynamic modeling, molecular simulation, and experimental research to comprehensively understand ASD formulations. Such a combined approach can be leveraged as a computational framework to gain insights into the ASD dissolution mechanism, thereby facilitating in silico screening, designing, and optimization of formulations with the benefit of significantly reducing the number of experimental tests. Full article

Three approaches for determining the thermodynamic stability of irreversible processes are described in generalized formulations. The simplest is the Gibbs–Duhem theory, specialized to irreversible trajectories, which uses the concept of virtual displacement in the reverse direction. Its only drawback is that even a trajectory leading to an explosion is identified as a thermodynamically stable motion. In the second approach, we use a thermodynamic Lyapunov function and its time rate from the Lyapunov thermodynamic stability theory (LTS, previously known as CTTSIP). In doing so, we demonstrate that the second differential of entropy, a frequently used Lyapunov function, is useful only for investigating the stability of equilibrium states. Nonequilibrium steady states do not qualify. Without using explicit perturbation coordinates, we further identify asymptotic thermodynamic stability and thermodynamic stability under constantly acting disturbances of unperturbed trajectories as well as of nonequilibrium steady states. The third approach is also based on the Lyapunov function from LTS, but here we additionally use the rates of perturbation coordinates, based on the Gibbs relations and without using their explicit expressions, to identify not only asymptotic thermodynamic stability but also thermodynamic stability under constantly acting disturbances. Only those trajectories leading to an infinite rate of entropy production (unstable states) are excluded from this conclusion. Finally, we use these findings to formulate the Fourth Law of thermodynamics based on the thermodynamic stability. It is a comprehensive statement covering all nonequilibrium trajectories, close to as well as far from equilibrium. Unlike previous suggested “fourth laws”, this one meets the same level of generality that is associated with the original zeroth to third laws. The above is illustrated using the Schlögl reaction with its multiple steady states in certain regions of operation. Full article

We propose a thermodynamic model describing the thermoelastic behavior of composition graded materials. The compatibility of the model with the second law of thermodynamics is explored by applying a generalized Coleman–Noll procedure. For the material at hand, the specific entropy and the stress tensor may depend on the gradient of the unknown fields, resulting in a very general theory. We calculate the speeds of coupled first- and second-sound pulses, propagating either trough nonequilibrium or equilibrium states. We characterize several different types of perturbations depending on the value of the material coefficients. Under the assumption that the deformation of the body can produce changes in its stoichiometry, altering locally the material composition, the possibility of propagation of pure stoichiometric waves is pointed out. Thermoelastic perturbations generated by the coupling of stoichiometric and thermal effects are analyzed as well. Full article

During the dissolution of amorphous solid dispersion (ASD) formulations, the gel layer that forms at the ASD/water interface strongly dictates the release of the active pharmaceutical ingredient (API) and, hence, the dissolution performance. Several studies have demonstrated that the switch of the gel layer from eroding to non-eroding behavior is API-specific and drug-load (DL)-dependent. This study systematically classifies the ASD release mechanisms and relates them to the phenomenon of the loss of release (LoR). The latter is thermodynamically explained and predicted via a modeled ternary phase diagram of API, polymer, and water, and is then used to describe the ASD/water interfacial layers (below and above the glass transition). To this end, the ternary phase behavior of the APIs, naproxen, and venetoclax with the polymer poly(vinylpyrrolidone-co-vinyl acetate) (PVPVA64) and water was modeled using the perturbed-chain statistical associating fluid theory (PC-SAFT). The glass transition was modeled using the Gordon–Taylor equation. The DL-dependent LoR was found to be caused by API crystallization or liquid-liquid phase separation (LLPS) at the ASD/water interface. If crystallization occurs, it was found that API and polymer release was impeded above a threshold DL at which the APIs crystallized directly at the ASD interface. If LLPS occurs, an API-rich phase and a polymer-rich phase are formed. Above a threshold DL, the less mobile and hydrophobic API-rich phase accumulates at the interface which prevents API release. LLPS is further influenced by the composition and glass transition temperature of the evolving phases and was investigated at 37 °C and 50 °C regarding impact of temperature of. The modeling results and LoR predictions were experimentally validated by means of dissolution experiments, microscopy, Raman spectroscopy, and size exclusion chromatography. The experimental results were found to be in very good agreement with the predicted release mechanisms deduced from the phase diagrams. Thus, this thermodynamic modeling approach represents a powerful mechanistic tool that can be applied to classify and quantitatively predict the DL-dependent LoR release mechanism of PVPVA64-based ASDs in water. Full article

The aim of this paper is to present a model for the rheological behavior of simple liquids as a function of the amplitude of the imposed shear stress or strain. The elastic mode theory is first generalized to take into account the fact that, during a flow experiment, mechanical energy is injected in a system initially at thermodynamic equilibrium. This generalized theory can be seen as a particular aspect of the general problem of perturbation by the measurement, associated with that of the coupling between fluctuation and dissipation. This generalization leads to a “finitary” character of the model. It is then combined with the inertial mode theory. The formalism thus obtained allows us to model the rheological behavior of liquids over a wide range of velocity gradients, including the intermediate narrow range corresponding to the Newtonian regime. As experimental tests, viscosity measurements with two kinds of moving rotor rheometers were performed. Only data obtained with liquid water at room temperature are presented and quantitatively analyzed here. It is also shown that liquid n-octane exhibits the same qualitative behaviors as those of liquid water. In the appendices, connection of this theory with quantum mechanics and turbulence phenomena are discussed, and the notion of viscous mass is introduced. Full article

According to second law of thermodynamics, the local entropy production must be nonnegative for arbitrary thermodynamic processes. In 1996, Muschik and Ehrentraut observed that such a constraint can be fulfilled in two different ways: either by postulating a suitable form of the constitutive equations, or by selecting among the solutions of the systems of balance laws those which represent physically realizable thermodynamic processes. Hence, they proposed an amendment to the second law which assumes that reversible process directions in state space exist only in correspondence with equilibrium states. Such an amendment allowed them to prove that the restriction of the constitutive equations is the sole possible consequence of non-negative entropy production. Recently, Cimmelli and Rogolino revisited the classical result by Muschik and Ehrentraut from a geometric perspective and included the amendment in a more general formulation of the second law. Herein, we extend this result to nonregular processes, i.e., to solutions of balance laws which admit jump discontinuities across a given surface. Two applications of these results are presented: the thermodynamics of an interface separating two different phases of a Korteweg fluid, and the derivation of the thermodynamic conditions necessary for shockwave formation. Commonly, for shockwaves the second law is regarded as a restriction on the thermodynamic processes rather than on the constitutive equations, as only perturbations for which the entropy continues to grow across the shock can propagate. We prove that this is indeed a consequence of the general property of the second law of thermodynamics that restricts the constitutive equations for nonregular processes. An analysis of shockwave propagation in different thermodynamic theories is developped as well. Full article

We establish a direct route for the accurate determination of the solvent effect on the Krichevskii parameter of a solute, based solely on the contrasting solvation behavior of the solute in the desired solvent relative to that of the reference solvent, i.e., in terms of the distinct solvation Gibbs free energies of the solute and the corresponding Krichevskii parameters of an ideal gas solute in the pair of solvents. First, we illustrate the proposed approach in the determination of the $H/D-$solvent effect on the Krichevskii parameter of gaseous solutes in aqueous solutions, when the solvents are different isotopic forms (isotopomers) of water, and then, by generalizing the approach to any pair of solvents. For that purpose, we (a) identify the links between the standard solvation Gibbs free energy of the $i-$solute in the two involved solvent environments and the resulting Krichevskii parameters, (b) discuss the fundamentally based linear behavior between the Krichevskii parameter and the standard solvation Gibbs free energy of the $i-$solute in an $\alpha -$solvent, and interpret two emblematic cases of solutions involving either an ideal gas solute or an $i-$solute behaving identically as the solvating species, as well as (c) provide a novel microstructural interpretation of the solvent effect on the Krichevskii parameter according to a rigorous characterization of the critical solvation as described by a finite unambiguous structure making/breaking parameter ${\mathcal{S}}_{i\alpha }^{\infty }\left(SR\right)$ of the $i-$solute in the pair of $\alpha -$solvents. Full article

In this study, the correlated resolution-of-identity Møller–Plesset perturbation theory of second order (RIMP2) ab initio level of theory has been combined with the newly parameterised, flexible SPC-mTR2 water model to formulate an advanced QM/MM MD simulation protocol to study the solvation properties of the solutes F${}^{-}$, Cl${}^{-}$ and Br${}^{-}$ in aqueous solution. After the identification of suitable ion–water Lennard–Jones parameters for the QM/MM coupling, a total simulation period of 10 ps (equilibration) plus 25 ps (sampling) could be achieved for each target system at QM/MM conditions. The resulting simulation data enable an in-depth analysis of the respective hydration structure, the first shell ligand exchange characteristics and the impact of solute–solvent hydrogen bonding on the structural properties of first shell water molecules. While a rather unexpected tailing of the first shell ion–oxygen peak renders the identification of a suitable QM boundary region challenging, the presented simulation results provide a valuable primer for more advanced simulation approaches focused on the determination of single-ion thermodynamical properties. Full article

The thermodynamic phase behavior of charged polymers is a crucial property underlying their role in biology and various industrial applications. A complete understanding of the phase behaviors of such polymer solutions remains challenging due to the multi-component nature of the system and the delicate interplay among various factors, including the translational entropy of each component, excluded volume interactions, chain connectivity, electrostatic interactions, and other specific interactions. In this work, the phase behavior of partially charged ion-containing polymers in polar solvents is studied by further developing a liquid-state (LS) theory with local shortrange interactions. This work is based on the LS theory developed for fully-charged polyelectrolyte solutions. Specific interactions between charged groups of the polymer and counterions, between neutral segments of the polymer, and between charged segments of the polymer are incorporated into the LS theory by an extra Helmholtz free energy from the perturbed-chain statistical associating fluid theory (PC-SAFT). The influence of the sequence structure of the partially charged polymer is modeled by the number of connections between bonded segments. The effects of chain length, charge fraction, counterion valency, and specific short-range interactions are explored. A computational App for salt-free polymer solutions is developed and presented, which allows easy computation of the binodal curve and critical point by specifying values for the relevant model parameters. Full article

The efficacy of pure and aluminum (Al)-doped boron nitride nanocarriers (B₁₂N₁₂ and AlB₁₁N₁₂) in adsorbing Chlormethine (CM), an anti-cancer drug, was comparatively dissected by means of the density functional theory method. The CM∙∙∙B₁₂N₁₂ and ∙∙∙AlB₁₁N₁₂ complexes were studied within two configurations, A and B, in which the adsorption process occurred via N∙∙∙ and Cl∙∙∙B/Al interactions, respectively. The electrostatic potential affirmations confirmed the opulent ability of the studied nanocarriers to engage in delivering CM via two prominent electrophilic sites (B and Al). Furthermore, the adsorption process within the CM∙∙∙AlB₁₁N₁₂ complexes was noticed to be more favorable compared to that within the CM∙∙∙B₁₂N₁₂ analog and showed interaction and adsorption energy values up to –59.68 and −52.40 kcal/mol, respectively, for configuration A. Symmetry-adapted perturbation theory results indicated that electrostatic forces were dominant in the adsorption process. Notably, the adsorption of CM over B₁₂N₁₂ and AlB₁₁N₁₂ nanocarriers exhibited predominant changes in their electronic properties. An elemental alteration was also revealed for the softness and hardness of B₁₂N₁₂ and AlB₁₁N₁₂ nanocarriers before and following the CM adsorption. Spontaneity and exothermic nature were obviously observed for the studied complexes and confirmed by the negative values of thermodynamic parameters. In line with energetic manifestation, Gibbs free energy and enthalpy change were drastically increased by the Al doping process, with values raised to –37.15 and –50.14 kcal/mol, respectively, for configuration A of the CM∙∙∙AlB₁₁N₁₂ complex. Conspicuous enhancement was noticed for the adsorption process in the water phase more than that in the gas phase and confirmed by the negative values of the solvation energy up to −53.50 kcal/mol for configuration A of the CM∙∙∙AlB₁₁N₁₂ complex. The obtained outcomes would be the linchpin for the future utilization of boron nitride as a nanocarrier. Full article

This article aims to review the application of various quantum chemical methods (semi-empirical, density functional theory (DFT), second order Møller–Plesset perturbation theory (MP2)) in the studies of cyclodextrin host–guest complexes. The details of applied approaches such as functionals, basis sets, dispersion corrections or solvent treatment methods are analyzed, pointing to the best possible options for such theoretical studies. Apart from reviewing the ways that the computations are usually performed, the reasons for such studies are presented and discussed. The successful applications of theoretical calculations are not limited to the determination of stable conformations but also include the prediction of thermodynamic properties as well as UV–Vis, IR, and NMR spectra. It has been shown that quantum chemical calculations, when applied to the studies of CD complexes, can provide results unobtainable by any other methods, both experimental and computational. Full article

Water decreases the stability of amorphous solid dispersions (ASDs) and water sorption is, therefore, unwanted during ASD storage. This work suggests a methodology to predict the water-sorption isotherms and the water-sorption kinetics in amorphous pharmaceutical formulations like ASDs. We verified the validity of the proposed methodology by measuring and predicting the water-sorption curves in ASD films of polyvinylpyrrolidone-based polymers and of indomethacin. This way, the extent and the rate of water sorption in ASDs were predicted for drug loads of 0.2 and 0.5 as well as in the humidity range from 0 to 0.9 RH at 25 °C. The water-sorption isotherms and the water-sorption kinetics in the ASDs were predicted only based on the water-sorption isotherms and water-sorption kinetics in the neat polymer on the one hand and in the neat active pharmaceutical ingredient (API) on the other hand. The accurate prediction of water-sorption isotherms was ensured by combining the Perturbed-Chain Statistical Association Theory (PC-SAFT) with the Non-Equilibrium Thermodynamics of Glassy Polymers (NET-GP) approach. Water-sorption kinetics were predicted using Maxwell–Stefan diffusion coefficients of water in the ASDs. Full article