Free Energy Model Research Articles

DFT Investigation of Hydrogen Atom Abstraction from NHC-Boranes by Methyl, Ethyl and Cyanomethyl Radicals-Composition and Correlation Analysis of Kinetic Barriers.

Understanding the hydrogen atom abstraction (HAA) reactions of N-heterocyclic carbene (NHC)-boranes is essential for extending the practical applications of boron chemistry. In this study, density functional theory (DFT) computations were performed for the HAA reactions of a series of NHC-boranes attacked by •CH2CN, Me• and Et• radicals. Using the computed data, we investigated the correlations of the activation and free energy barriers with their components, including the intrinsic barrier, the thermal contribution of the thermodynamic reaction energy to the kinetic barriers, the activation Gibbs free energy correction and the activation zero-point vibrational energy correction. Furthermore, to describe the dependence of the activation and free energy barriers on the thermodynamic reaction energy or reaction Gibbs free energy, we used a three-variable linear model, which was demonstrated to be more precise than the two-variable Evans–Polanyi linear free energy model and more succinct than the three-variable Marcus-theory-based nonlinear HAA model. The present work provides not only a more thorough understanding of the compositions of the barriers to the HAA reactions of NHC-boranes and the HAA reactivities of the substrates but also fresh insights into the suitability of various models for describing the relationships between the kinetic and thermodynamic physical quantities.

A molecular parameter to scale the Gibbs free energies of adsorption and micellization for nonionic surfactants

A long standing goal in the interfacial thermodynamics community is free energies of adsorption and micellization in terms of molecular parameters. Historically, correlations for CiEj's, a common class of nonionic surfactants, have been proposed between the number of ethylene glycol groups and/or the number of carbons and thermodynamic parameters, such as the critical micelle concentration (CMC), the equilibrium constant (K), and the maximum surface concentration (Γ∞). However, no such correlations to date are capable of capturing a large dataset of CiEj thermodynamic parameters. In this paper we propose the functional form of the critical micelle concentration and adsorption isotherm parameters in terms of molecular parameters for nonionic, CiEj surfactant chemistry. An extensive review of the literature is performed to generate interfacial thermodynamic parameters for a wide-range of CiEj chemistries. The data are used to parameterize and validate the molecular models. More specifically, we combine the well known linear dependence of CMC and K on the number of carbons, NC, with the theorized dependence on hydrophilic-lipophilic balance (HLB), represented as yphob, which is capable of collapsing all experimental data onto mastercurves. The resulting free energy models represent the first successful phenomenological theory which is able to collapse a broad range of experimental data for CiEj surfactants. Furthermore, the proposed models for the free energies of micellization and adsorption are capable of predicting the maximum surface concentration of CiEj surfactants at the air–water interface, thus providing a link between the physics of adsorption and self-assembly. This theory is a step towards engineering interfacial thermodynamics by chemical design which enables prediction of interfacial properties of novel surfactants without extrapolation. In addition, this paper summarizes the many years of experimental and theoretical understanding of surfactant structure property relationships for CiEj's and the resulting theory quantitatively explains many hypotheses about their interfacial thermodynamics.

Predicting activity coefficients with the Debye–Hückel theory using concentration dependent static permittivity

AbstractIn order to investigate the impacts of a concentration dependent static permittivity in the Debye–Hückel theory, two electrostatic Helmholtz free energy models and four activity coefficient models, with the ion‐solvent interactions naturally included, are derived under different assumptions. The effects of static permittivity and model parameters are analyzed by predicting the mean ionic activity coefficients. It is found out that it is reasonable to assume a constant static permittivity in deriving the electrostatic Helmholtz free energy model but it is highly recommended to take the concentration dependence of static permittivity into account in subsequent calculations of thermodynamic properties. The activity coefficient model derived in this way accurately predicts the mean ionic activity coefficients of the investigated systems up to 0.1 mol/kg H2O, which indicates that the size parameters in the Debye–Hückel theory might be determined in advance before it is integrated into a more complete thermodynamic model.

Combining Molecular Dynamics and Machine Learning to Predict Self-Solvation Free Energies and Limiting Activity Coefficients.

Computational prediction of limiting activity coefficients is of great relevance for process design. For highly nonideal mixtures including molecules with directed interactions, methods that maintain the molecular character of the solvent are most promising. Computational expense and force-field deficiencies are the main limiting factors that prevent the use of high-throughput molecular dynamics (MD) simulations in a predictive setup. The combination of MD simulations and machine learning used in this work accounts for both issues. Comparison to published data including free-energy simulations, COSMO-RS and UNIFAC models, reveals competitive prediction accuracy.

Scaling dynamics of globule-to-coil phase transition in double-network hydrogel with ultra-high stretchable strength

Temperature-induced globule-to-coil transition in polymers has well been studied, and it is dependent strongly on temperature in their solutions due to significantly conformational changes of polymer molecules. In this study, a scaling framework is firstly developed to investigate stress-induced globule-to-coil transition in double-network (DN) hydrogels with an ultra-high stretchable strength. Free energy and globule radius functions are introduced to formulate the constitutive relationship of the DN hydrogels, in which stress-induced swelling and globule-to-coil transition are described for the hydrotropic and relatively hydrophobic networks, respectively. A cooperative free energy model based on the Flory-Huggins solution theory is then proposed for the DN hydrogels. The effectiveness of model is demonstrated by applying it to predict stress-induced globule-to-coil transitions in DN hydrogels and elastomers, where the theoretical results show good agreements with the experimental ones. We expect this study explores the scaling dynamics and provides an effective guidance on designing advanced ultra-high mechanical performance in DN hydrogel and elastomer.

Hydrogen Atom Transfer Reaction Free Energy as a Predictor of Abiotic Nitroaromatic Reduction Rate Constants: A Comprehensive Analysis.

A linear free energy model is presented that predicts the second-order rate constant for the abiotic reduction of nitroaromatic compounds (NACs). Previously presented models use the one-electron reduction potential of the NAC reaction . If is not available, it has been proposed that be computed directly or estimated from the gas-phase electron affinity (EA). The model proposed uses the Gibbs free energy of the hydrogen atom transfer (HAT) reaction as the parameter in the linear free energy model. Both models employ quantum chemical computations for the required thermodynamic energies. The available and proposed models are compared using experimentally determined second-order rate constants from 5 investigations from the literature in which a variety of NACs were exposed to a variety of reductants. A comprehensive analysis utilizing all the NACs and reductants demonstrate that the HAT energy model and the experimental one-electron reduction potential model have similar root mean square errors and residual error probability distributions. In contrast, the model using the computed EA has a more variable residual error distribution with a significant number of outliers. The results suggest that a linear free energy model utilizing computed HAT reaction free energy produces a more reliable prediction of the NAC abiotic reduction second-order rate constant than previously available methods. The advantages of the proposed HAT energy model and its mechanistic implications are discussed as well. Environ Toxicol Chem 2020;39:1678-1684. © 2020 SETAC.

Evolution of Multiphase Lattice Boltzmann Method: A Review

With the simplicity and robustness of the lattice Boltzmann method (LBM), it is getting more attention nowadays in the multiphase flow applications. Different models of multiphase flow studies are available in LBM. Theory and applications of lattice Boltzmann multiphase models R–K color gradient, Shan–Chen (SC), Free energy (FE) and He–Chen–Zhang (HCZ) approaches have been discussed in this review. The methodologies of these methods have been explained in details. Besides, the advantages and limitations of these models have been explained by considering the application field. Based on the applications in the multiphase flows, recent developments in these models have been explained. The major applications of LBM in multiphase flows are flow through porous media, cavitation phenomenon, bubble rise or droplet fall, Rayleigh–Taylor instabilities, coalescence of bubbles or droplets, wettability and contact angles. An effort has been made to explain the methodologies for the multiphase LBM. Modified R–K color gradient model is more accurate and less efficient. SC model is more efficient and less accurate. FE model is numerically more accurate and less efficient. HCZ model more efficient and more accurate. The efficiency of modified R–K color gradient and free energy models almost similar.

Novel phosphatidylinositol 4-kinases III beta (PI4KIIIβ) inhibitors discovered by virtual screening using free energy models.

Herein, the LASSBio Chemical Library is presented as a valuable source of compounds for screening to identify hits suitable for subsequent hit-to-lead optimization stages. A feature of the LASSBio Chemical Library worth highlighting is the fact that it is a smart library designed by medicinal chemists with pharmacological activity as the main priority. The great majority of the compounds part of this library have shown in vivo activity in animal models, which is an indication that they possess overall favorable bioavailability properties and, hence, adequate pharmacokinetic profiles. This, in turn, is supported by the fact that approximately 85% of the compounds are compliant with Lipinski’s rule of five and ca. 95% are compliant with Veber’s rules, two important guidelines for oral bioavailability. In this work it is presented a virtual screening methodology combining a pharmacophore-based model and an empirical Gibbs free energy-based model for the ligand–protein interaction to explore the LASSBio Chemical Library as a source of new hits for the inhibition of the phosphatidylinositol 4-kinase IIIβ (PI4KIIIβ) enzyme, which is related to the development of viral infections (including enteroviruses, SARS coronavirus, and hepatitis C virus), cancers and neurological diseases. The approach resulted in the identification of two hits, LASSBio-1799 (7) and LASSBio-1814 (10), which inhibited the target enzyme with IC50 values of 3.66 μM and IC50 and 6.09 μM, respectively. This study also enabled the determination of the structural requirements for interactions with the active site of PI4KIIIβ, demonstrating the importance of both acceptor and donor hydrogen bonding groups for forming interactions with binding site residues Val598 and Lys549.Electronic supplementary materialThe online version of this article (10.1007/s10822-020-00327-9) contains supplementary material, which is available to authorized users.

Dynamic wetting of solid-liquid-liquid system by molecular kinetic theory

HypothesisThe mechanisms of dynamic wetting of solid–liquid-liquid (SLL) system, especially the viscosity effects of two liquids, can be investigated by the molecular kinetic theory (MKT). MethodsThe molecular kinetic theory combined with published data was used to study the roles of a fluid viscosity and a solid surface in dynamic wetting. FindingsFirst, the MKT on dynamic wetting was introduced and its limitation was analyzed. Second, a viscosity effect and a solid surface effect were considered. The viscosity effect was divided into three parts for the first time, including two pure liquid zones and a mixing zone. Third, a coefficient activation free energy model was proposed, considering the effects of mixing liquids and a solid surface. Finally, the key parameters in the MKT and the application and validation of the coefficient activation free energy model were discussed in detail. This model can explain the energy dissipation in a vicinity of a three-phase contact-line successfully in a SLL wetting system. This work sheds light on the physical mechanisms of fluid and solid surface properties on the dynamic wetting in a SLL system.

Large non-saturating shift of the torsional resonance in a doubly clamped magnetoelastic resonator

The magnetic field dependence of the resonance frequencies of Co1−xFex thin film microfabricated resonators was examined for fields applied in the plane of the film. Remarkably, the observed resonance frequency shift with an applied magnetic field did not saturate even up to fields of nearly 2 T. A minimized mechanical and magnetic free energy model of clamped–clamped resonators revealed that for a two-dimensional structure, both bending and torsional modes are allowed, but would have have very different resonance shift behavior with the applied field. A post-anneal of the structure confirms this case by increasing the stress-induced anisotropy of CoFe, which selectively enhances the contribution of the torsional mode and creates the non-saturating field-induced frequency shift. By using the resonance shift in this device in a potential magnetic field sensing paradigm, such a non-saturating torsional mode may be useful for applications such as nuclear magnetic resonance or MRI, which specifically requires sensitive detection of small fluctuations in high magnetic fields.

Assessment of the SM12, SM8, and SMD Solvation Models for Predicting Limiting Activity Coefficients at 298.15 K

The SMx (x = 12, 8, or D) universal solvent models are implicit solvent models which using electronic structure calculations can compute solvation free energies at 298.15 K. While solvation free energy is an important thermophysical property, within the thermodynamic modeling of phase equilibrium, limiting (or infinite dilution) activity coefficients are preferred since they may be used to parameterize excess Gibbs free energy models to model phase equilibrium. Conveniently, the two quantities are related. Therefore the present study was performed to assess the ability to use the SMx universal solvent models to predict limiting activity coefficients. Two methods of calculating the limiting activity coefficient where compared: (1) the solvation free energy and self-solvation free energy were both predicted and (2) the self-solvation free energy was computed using readily available vapor pressure data. Overall the first method is preferred as it results in a cancellation of errors, specifically for the case in which water is a solute. The SM12 model was compared to both the Universal Quasichemical Functional-group Activity Coefficients (UNIFAC) and modified separation of cohesive energy density (MOSCED) models. MOSCED was the highest performer, yet had the smallest available compound inventory. UNIFAC and SM12 exhibited comparable performance. Therefore further exploration and research should be conducted into the viability of using the SMx models for phase equilibrium calculations.

Modelling double emulsion formation in planar flow-focusing microchannels

Double emulsion formation in a hierarchical flow-focusing channel is systematically investigated using a free energy ternary lattice Boltzmann model. A three dimensional formation regime diagram is constructed based on the capillary numbers of the inner ($Ca_i$), middle ($Ca_m$) and outer ($Ca_o$) phase fluids. The results show that the formation diagram can be classified into periodic two-step region, periodic one-step region, and non-periodic region. By varying $Ca_i$ and $Ca_m$ in the two-step formation region, different morphologies are obtained, including the regular double emulsions, decussate regimes with one or two alternate empty droplets, and structures with multiple inner droplets contained in the continuous middle phase thread. Bidisperse behaviors are also frequently encountered in the two-step formation region. In the periodic one-step formation region, scaling laws are proposed for the double emulsion size and for the size ratio between the inner droplet and the overall double emulsion. Furthermore, we show that the interfacial tension ratio can greatly change the morphologies of the obtained emulsion droplets, and the channel geometry plays an important role in changing the formation regimes and the double emulsion sizes. In particular, narrowing the side inlets or the distance between the two side inlets promotes the conversion from the two-step formation regime to the one-step formation regime.

First and second order rotational transitions of skyrmion crystal in multiferroic Cu2OSeO3 under electric field

We investigate the electric-field-induced rotations of a skyrmion crystal (SkX) in multiferroic Cu2OSeO3. We perform our analysis within a free energy model that incorporates both the exchange anisotropy and the fourth order magnetocrystalline anisotropy, and both the deformation and rotation of SkX are taken into account. We find that for a background magnetic field along the direction [110], (i) electric fields out of the (11¯0) plane lead to continuous rotations of SkX, which explains the experiments [White et al., Phys. Rev. Lett. 113, 107203 (2014)] and (ii) electric fields in the (11¯0) plane may lead to 30° rotations of SkX. Our results provide an understanding of manipulation of SkX by the electric field, which may contribute to the applications of skyrmion-based spintronic devices without Joule heating energy losses.

Steady-State Dynamic Phase Diagram Calculation of U-Ti and U-V Binary System under Irradiation

In this paper, by considering the irradiation-enhanced diffusion, a combination of effective free energy model and the thermodynamic model was used for studying the phase relationships in the U-Ti and U-V binary system under irradiation. The steady-state dynamical phase diagrams of U-Ti and U-V binary alloys under different irradiation intensities were calculated and compared with the conventional thermodynamic equilibrium phase diagram. The calculated results show that under irradiation the high-temperature stable (βTi, γU) and (γU,V) phases were stabilized at relatively low temperature resulting in invariant reactions at relatively low temperature. In addition, with the increase of the irradiation intensity, the temperature of the invariant reactions increased, and the phase regions of the (βTi, γU) and (γU,V) also increased.

Multiphase lattice Boltzmann method and its applications in phase-change heat transfer

<p indent=0mm>In the past three decades, the lattice Boltzmann (LB) method has been developed into an efficient numerical method for simulating fluid flow and heat transfer. It is a mesoscopic numerical approach, sitting in the middle between the molecular dynamic method and conventional numerical methods based on the continuum assumption. Unlike conventional numerical methods, the LB method is built on the mesoscopic kinetic equation. It tracks the evolution of a particle distribution function and then accumulates the particle distribution function to obtain the macroscopic properties. Owing to its kinetic nature, the LB method has exhibited many advantages over conventional numerical methods. For example, in the LB equation the convective operator is linear, whereas the convective terms of the Navier-Stokes equations are nonlinear. Moreover, in the LB simulations the complex boundary conditions can be formulated with the elementary mechanical rules such as the bounce-back rule according to the interaction of the “LB particles” with the solid walls. Furthermore, the LB method is ideal for parallel computing because of its explicit scheme and local interactions. Particularly, the intermolecular interactions of fluids can be easily incorporated into the LB method. As a result, the interface between different phases can arise, deform, and migrate naturally in the LB modeling without using any techniques to track or capture the interface, which is often required in the VOF or Level Set method. The existing multiphase LB models can be generally classified into four categories, i.e., the color-gradient model, the pseudopotential model, the free-energy model, and the phase-field model. In the color-gradient LB model, two distribution functions are introduced to represent two different fluids and a color-gradient-based perturbation operator is employed to generate surface tension. Moreover, a recoloring step is used in the color-gradient model so as to separate different phases. The pseudopotential LB model is the simplest and the most popular multiphase LB model. In this model, the fluid interactions are mimicked by an interparticle potential, through which the separation of different phases or components can be achieved naturally. Accordingly, the interface between different phases can arise, deform and migrate naturally. The free-energy LB model was developed based on thermodynamics considerations, which modifies the second-order moment of the particle equilibrium distribution function so as to include a non-ideal thermodynamic pressure tensor. The phase-field LB model is based on the phase-field theory, in which the interface dynamics is described by an order parameter that obeys the Cahn-Hilliard equation or a Cahn-Hilliard-like equation. In this paper we briefly review some recent advances in these multiphase LB models. Particularly, recent progress in the pseudopotential LB model is highlighted. It is shown that the thermodynamic consistency of the pseudopotential model can be achieved by adjusting the mechanical stability condition via an improved forcing scheme. Furthermore, an alternative approach is presented to tune the surface tension of the pseudopotential model and an improved contact angle scheme is introduced, which retains the advantages of the original virtual-density scheme but does not suffer from an unphysical thick mass-transfer layer near the solid boundary. Moreover, the applications of the pseudopotential LB model to boiling and condensation heat transfer are outlined.

Axial-torsion behavior of superelastic tubes: Part I, proportional isothermal experiments

The tensile response of superelastic shape memory alloys (SMAs) has been widely studied, but detailed experimental studies under multi-axial loading are relatively rare. In Part I, we present the isothermal responses of commercially-available superelastic NiTi tubes for a series of proportional stretch-twist controlled histories, spanning pure tension to simple torsion to pure compression. These axial-shear responses are used to quantify the onset and saturation during forward (loading) and reverse (unloading) stress-induced transformations for the first time. Each of the four transformation surfaces is well-captured by a smooth (three-parameter) ellipse in both strain and stress space. A simple Gibbs free energy model is presented to show how the driving force for phase transformation is approximately constant across all proportional strain paths and how the stress and strain transformation surfaces are conjugate to one another. In addition, transformation kinetics and surface strain morphologies are characterized by stereo digital image correlation (DIC). Under extension at low amounts of twist, stress-induced transformation involves strain localization in helical bands that evolve into axial propagation of ring-like transformation fronts with fine criss-crossing fingers (similar to those seen by Q. P. Sun and co-workers in pure extension). However, at large amounts of twist, including simple torsion and pure torsion, we report a new transformation morphology, involving strain localization along nearly longitudinal bands in the tube. The sequel (Part II) will address the response to non-proportional stretch-twist paths. Together, these detailed multi-axial results advance the scientific understanding of superelasticity and inform efforts to develop high-fidelity SMA constitutive models and simulation tools.

Multi-component chemo-mechanics based on transport relations for the chemical potential

A chemo-mechanical model for a finite-strain elasto-viscoplastic material containing multiple chemical components is formulated and an efficient numerical implementation is developed to solve the resulting transport relations. The numerical solution relies on inverting the constitutive model for the chemical potential. In this work, a semi-analytical inversion for a general family of multi-component regular-solution chemical free energy models is derived. This is based on splitting the chemical free energy into a convex contribution, treated implicitly, and a non-convex contribution, treated explicitly. This results in a reformulation of the system transport equations in terms of the chemical potential rather than the composition as the independent field variable. The numerical conditioning of the reformulated system, discretised by finite elements, is shown to be significantly improved, and convergence to the Cahn–Hilliard solution is demonstrated for the case of binary spinodal decomposition. Chemo-mechanically coupled binary and ternary spinodal decomposition systems are then investigated to illustrate the effect of anisotropic elastic deformation and plastic relaxation of the resulting spinodal morphologies in more complex material systems.

A phase-field approach for modeling equilibrium solute segregation at the interphase boundary in binary alloys

A number of experimental and theoretical findings in age hardening alloys suggest that specific solute elements preferentially segregate to and reduce the energy of the interphase boundary (IB). This segregation mechanism can stabilize the precipitation microstructure against coarsening, allowing higher operating temperatures in structural applications. Herein, we present a phase field model of solute segregation to IBs that separate matrix and precipitate phases in binary alloys. The proposed modeling framework is capable of capturing bulk thermodynamics and interfacial free energies, while also accounting for various mass transport mechanisms. Analytical equilibrium solutions of one-dimensional systems are presented, and excess IB quantities are evaluated independent of the Gibbs dividing surface convention. With the aid of the parallel tangent construction, IB segregation isotherms are established in terms of the alloy composition and the model parameters describing the free energy functions. Under the regular solution approximation, computational studies elucidating the dependence of the IB energy and segregation levels on temperature and free energy model parameters are presented. We show that the model is consistent with the Gibbs adsorption equation; therefore, it is possible to compare the adsorption behavior predicted by the model parameters with experiments and atomistic simulations. Future work on extending the model to ternary alloys, and incorporating the effect of elastic interactions on IB segregation is expected.

An improved equation of state of binary CO2–N2 fluid mixture and its application in the studies of fluid inclusions

An equation of state (EOS) in the form of Helmholtz free energy for fluid mixtures was improved by using four mixing parameters. It can calculate the pressure-volume-temperature-composition (PVTx) and vapor-liquid equilibrium (VLE) properties of the CO2–N2 fluid mixture. This EOS is based on highly accurate EOSs of pure CO2 and N2 fluids and contains a simple generalized departure function of Lemmon and Jacobsen (1999). This EOS can reproduce experimental PVTx and VLE data available up to 673 K and 1000 bar, with an accuracy within or close to experimental uncertainties. The EOS of CO2–N2 fluid mixture and an updated Gibbs free energy model of solid CO2, can be combined to determine the compositions and molar volumes of CO2–N2 fluid inclusions with the melting temperature of solid CO2 and the vapor-liquid homogenization temperature which can be directly obtained from experimental microthermometric analysis. Isochores of CO2–N2 inclusions can be easily calculated from this EOS.

Large negative magnetoelectric coupling in Fe substituted ferroelectric Bi0.5Na0.5TiO3: An experimental study supported by Landau-Devonshire free-energy model based calculations

This work presents an experimental and analytical study of a negative magnetoelectric (ME) effect observed in Fe substituted Bi0.5Na0.5TiO3 (BNT). Experiments are performed on solid solutions of Bi0.5Na0.5(FexTi(1 − 3x/4))O3 (BNFT), for x = 0 to 0.2, synthesized using the conventional solid state reaction route. X-ray diffraction studies confirm that Fe ions are completely soluble in a BNT matrix, up to the highest solubility of x = 0.2, thus forming a single-phase perovskite structure. As expected, partial substitution of Fe ions at Ti4+ sites diminishes the ferroelectric behavior of BNFT. For the optimal composition of x = 0.05, electrical poling of the sample results in an ∼19% decrease in magnetization, i.e., a large negative ME coupling is observed. Experimental results are supported by the Landau–Devonshire thermodynamic model based calculations for single-phase multiferroics. The model is utilized to obtain a theoretical estimate of the ME coupling coefficient of approximately −430 kV/cm Oe.