Free Energy Model Research Articles

Diversity of structural and magnetic instabilities in EuTiO3

The perovskite oxide EuTiO3 (ETO) has attracted increased scientific interest due to its potential multiferroic properties and magnetic activity above and below its structural phase transition at TS=282 K. Various experiments have indirectly evidenced that this transition is neither a cubic tetragonal nor the only one occurring in ETO. Here, we show results demonstrating two further instabilities below TS based on lattice dynamics and spin-phonon interactions combined with a Landau free energy model with coupled order parameters. The transition temperatures agree with available experimental data where further instabilities have been anticipated. Published by the American Physical Society 2024

Phase-field modeling of interdiffusion between dissimilar Fe-Cr-Ni alloys during non-isothermal hot isostatic pressing

Powder metallurgy hot isostatic pressing (PM-HIP) has emerged as a promising alternative to welding for joining dissimilar metals. During HIP, interfacial bonding is mediated by solid state diffusion. The interdiffusion zone across the interface depends on processing conditions, calling for the need for accurate numerical tools capable of simulating interdiffusion and possible phase transformation in order to optimize processing parameters. Here, a phase-field (PF) model based on CALPHAD-based free energy functionals is developed to simulate the interdiffusion and phase evolution between dissimilar Fe–Cr–Ni based steels undergoing HIP and is demonstrated using the interface between 316L and SA508 steels. To overcome the numerical challenges caused by the singular magnetic and entropy terms in the CALPHAD free energy models in the Fe–Cr-Ni system, polynomial functions are fitted with temperature dependent coefficients represented by Fourier series to accurately describe the phase stability of both fcc and bcc phases in the composition and temperature space. This enables simulations of non-isothermal HIP cycles. Diffusivity data from commercial software and literature are taken to parameterize the kinetic parameters. A discrete nucleation model is incorporated for possible phase transformation. The modified thermodynamic models are validated against previous experiments at 923 K and 1273 K. The interdiffusion kinetics are benchmarked against new HIP experiments joining powder and bulk 316L to bulk SA508 with three different HIP cycles. The good agreement between simulations and experiments on both phase stability and interdiffusion indicate that the model is suitable for simulating interdiffusion between Fe–Cr–Ni alloys during HIP cycles. It is also found that using powder and bulk 316L gives similar interdiffusion profiles at elevated temperature when a dense interface forms during HIP.

A free-energy based multiple-distribution-function lattice Boltzmann method for multi-component and multi-phase flows

This study presents the development of a multiple-distribution-function lattice Boltzmann model (MDF-LBM) for the accurate simulation of multi-component and multi-phase flow. The model is based on the diffuse interface theory and free energy model, which enable the derivation of hydrodynamic equations for the system. These equations comprise a Cahn-Hilliard (CH) type mass balance equation, which accounts for cross diffusion terms for each species, and a momentum balance equation. By establishing a relationship between the total chemical potential and the general pressure, the momentum balance equation is reformulated in a potential form. This potential form, together with the CH type mass balance equation, is then utilized to construct the MDF-LBM as a coupled convection–diffusion system. Numerical simulations demonstrate that the proposed MDF-LBM accurately captures phase behavior and ensures mass conservation. Additionally, the calculated interface tension exhibits good agreement with experimental data obtained from laboratory studies.

Solvent accessible surface area-assessed molecular basis of osmolyte-induced protein stability.

In solvent-modulated protein folding, under certain physiological conditions, an equilibrium exists between the unfolded and folded states of the protein without any need to break or make a covalent bond. In this process, interactions between various protein groups (peptides) and solvent molecules are known to play a major role in determining the directionality of the chemical reaction. However, an understanding of the mechanism of action of the co(solvent) by a generic theoretical underpinning is lacking. In this study, a generic solvation model is developed based on statistical mechanics and the thermodynamic transfer free energy model by considering the microenvironment polarity of the interacting co(solvent)-protein system. According to this model, polarity and the fractional solvent-accessible surface areas contribute to the interaction energies. The present model includes various orientations of participating interactant solvent surfaces of suitable areas. As model systems, besides the backbone we consider naturally occurring amino acid residues solvated in ten different osmolytes, small organic compounds known to modulate protein stability. The present model is able to predict the correct trend of the osmolyte-peptide interactions ranging from stabilizing to destabilizing not only for the backbone but also for side chains. Our model predicts Asn, Gln, Asp, Glu, Arg and Pro to be highly stable in most of the protecting osmolytes while Ala, Val, Ile, Leu, Thr, Met, Lys, Phe, Trp and Tyr are predicted to be moderately stable, and Ser, Cys and Histidine are predicted to be least stable. However, in denaturing solvents, both backbone and side chain models show similar stabilities in urea and guanidine. One of the important aspects of this model is that it is essentially parameter-free and consistent with the electrostatics of the interaction partners that make this model suitable for estimating any solute-solvent interaction energies.

Wetting of soap bubbles on topographic surfaces

HypothesisThere is a relationship between the static contact angle of droplets and soap bubbles on flat homogeneous surfaces, therefore, it should be possible to derive a relationship between the static contact angle of a soap bubble on a periodic topographic surface and a droplet on a flat homogeneous surface. ExperimentsA free energy model of the static contact angle of soap bubbles on a topographic surface in the Cassie-Baxter state was derived. Polydimethylsiloxane surfaces of varying area fraction (0.125, 0.250, 0.500, 0.750, and 1.00) and periodic topographies (lined and pillared) were fabricated using 3D printed moulds for pattern transfer. A bubble goniometer was developed to accommodate bubbles of 40,000 ± 5,000 mm3 and 50,000 ± 5,000 mm3 volumes. Then, the static contact angle of bubbles of both volumes were measured on the varying topographic surfaces. FindingsThe derived predictions imply that the relationship between the static contact angle for bubbles on a flat homogeneous surface and on a composite surface, has the same form as the Cassie-Baxter equation for a droplet. The experimental results for the measured static contact angle for both bubble volumes on the varying surfaces had good agreement with the predicted trends.

Bridging Machine Learning and Thermodynamics for Accurate pK a Prediction.

Integrating scientific principles into machine learning models to enhance their predictive performance and generalizability is a central challenge in the development of AI for Science. Herein, we introduce Uni-pK a, a novel framework that successfully incorporates thermodynamic principles into machine learning modeling, achieving high-precision predictions of acid dissociation constants (pK a), a crucial task in the rational design of drugs and catalysts, as well as a modeling challenge in computational physical chemistry for small organic molecules. Uni-pK a utilizes a comprehensive free energy model to represent molecular protonation equilibria accurately. It features a structure enumerator that reconstructs molecular configurations from pK a data, coupled with a neural network that functions as a free energy predictor, ensuring high-throughput, data-driven prediction while preserving thermodynamic consistency. Employing a pretraining-finetuning strategy with both predicted and experimental pK a data, Uni-pK a not only achieves state-of-the-art accuracy in chemoinformatics but also shows comparable precision to quantum mechanics-based methods.

A unified model for mechanical deformations of single stranded DNA-microbeam biosensors considering surface charge effects

A unified energy model for mechanical deformation of the microbeam included by single stranded DNA (ssDNA) adsorption considering the surface charge density on substrate is investigated. First, a free energy model is established to quantify the deflection and axial displacement of the microbeam, the ion concentration in the solution, as well as the electric potential distribution inside and outside the ssDNA film with a uniform surface charge density. Then, the governing equations and corresponding boundary conditions are obtained by minimizing the free energy with three types of variational variables. And, the relationship of the electric potential difference between the two sides of the ssDNA film and the deformation of microcantilever and simply support beam are determined in different solutions (1: 1, 1: 2, 1: 3). Moreover, the numerical solutions of the electric potential distribution inside and outside the ssDNA film are investigated by using the finite difference method and Newton's iteration method. The results suggest that the nonlinear model for electric potential distribution should be used under higher surface charge density. By fitting and comparing the present predictions with Arroyo-Hernandez's experimental data, the effectiveness of the model is verified. The study shows that the surface charge density can modulate the magnitude and direction of ssDNA-microbeam deformation, which also indicates that there exists a critical surface charge density, causing the failure of ssDNA-microbeam detection. These conclusions are helpful for designing the efficient biosensors based on DNA-microbeam.

Scale translation yields insights into gas adsorption under nanoconfinement

This work describes a scale-translating simulation framework to investigate gas adsorption behavior in nanoconfined pores. The framework combines molecular simulations (MSs), equation of state (EoS), and lattice Boltzmann (LB) simulations. MSs reveal the physics of methane adsorption in nano-sized pores, where input values of fugacity coefficients are optimized based on EoS predictions. Then, an LB free-energy model, which incorporates a viral EoS, upscales intermolecular forces and estimates adsorption behavior via a proposed fluid–wall interaction model. Armed with the values of the LB interaction parameter as a function of pressure, the LB model is used to predict fluid behavior in irregular nanopores, and the results are validated against reference MS data. The LB model is then used to study adsorption behavior at a continuum scale in representative organic shale nanopores based on finely characterized Vaca Muerta shale samples. The results show that methane adsorption could significantly increase contained fluids by 10%–25% in pores smaller than 20 nm. However, in larger pores (40 nm to 90 nm), adsorption's impact diminishes to 2%–3%, suggesting sorption's negligible role beyond a 40 nm pore size.

Structural-functional integrated TiBw/Ti–V–Al lightweight shape memory alloy composites

Driven by the increasing demands in advanced aerospace engineering, the integrated structural and functional materials are explored. In present study, we fabricate the TiBw/Ti–V–Al lightweight shape memory alloy composites with large recoverable strain (>5 %), high specific strength (>200 MPa cm3/g) and good elongation (>20 %). The satisfied structural and functional performances are attributed to the unique gradient microstructure, including TiB whiskers, short-range martensitic nanodomains and long-range martensitic microdomains. TiBw with the optimized orientation exhibits high load-bearing capacity. The transition area between TiBw and matrix is composed of short-range martensitic nanodomains. Nanodomains are affected by the diffused interstitial B atoms and local internal stress field regulated by TiBw. The elastic interaction energy between nanodomains and TiBw are calculated according to the Eshelby method. Upon deformation, nanodomains grow to long-range martensitic laths. The long-range martensitic laths keep stable after unloading. The microstructure evolution ties well with the Landau free energy model. It achieves effective loading transfer from matrix to reinforcement phase, resulting in less irreversible defects and better shape memory effect. In addition, grain refinement strengthening, loading transfer strengthening and solution strengthening are utilized to achieve the improvement of the strength and plasticity. The finding offers a promising inspiration for the development of new type shape memory alloy composites with integrated structural and functional properties.

Atomic-scale visualization of a cascade of magnetic orders in the layered antiferromagnet GdTe3

GdTe3 is a layered antiferromagnet which has attracted attention due to its exceptionally high mobility, distinctive unidirectional incommensurate charge density wave (CDW), superconductivity under pressure, and a cascade of magnetic transitions between 7 and 12 K, with as yet unknown order parameters. Here, we use spin-polarized scanning tunneling microscopy to directly image the charge and magnetic orders in GdTe3. Below 7 K, we find a striped antiferromagnetic phase with twice the periodicity of the Gd lattice and perpendicular to the CDW. As we heat the sample, we discover a spin density wave with the same periodicity as the CDW between 7 and 12 K; the viability of this phase is supported by our Landau free energy model. Our work reveals the order parameters of the magnetic phases in GdTe3 and shows how the interplay between charge and spin can generate a cascade of magnetic orders.

Self-Assembly of Ionic Superdiscs in Nanopores.

Discotic ionic liquid crystals (DILCs) consist of self-assembled superdiscs of cations and anions that spontaneously stack in linear columns with high one-dimensional ionic and electronic charge mobility, making them prominent model systems for functional soft matter. Compared to classical nonionic discotic liquid crystals, many liquid crystalline structures with a combination of electronic and ionic conductivity have been reported, which are of interest for separation membranes, artificial ion/proton conducting membranes, and optoelectronics. Unfortunately, a homogeneous alignment of the DILCs on the macroscale is often not achievable, which significantly limits the applicability of DILCs. Infiltration into nanoporous solid scaffolds can, in principle, overcome this drawback. However, due to the experimental challenges to scrutinize liquid crystalline order in extreme spatial confinement, little is known about the structures of DILCs in nanopores. Here, we present temperature-dependent high-resolution optical birefringence measurement and 3D reciprocal space mapping based on synchrotron X-ray scattering to investigate the thermotropic phase behavior of dopamine-based ionic liquid crystals confined in cylindrical channels of 180 nm diameter in macroscopic anodic aluminum oxide membranes. As a function of the membranes' hydrophilicity and thus the molecular anchoring to the pore walls (edge-on or face-on) and the variation of the hydrophilic-hydrophobic balance between the aromatic cores and the alkyl side chain motifs of the superdiscs by tailored chemical synthesis, we find a particularly rich phase behavior, which is not present in the bulk state. It is governed by a complex interplay of liquid crystalline elastic energies (bending and splay deformations), polar interactions, and pure geometric confinement and includes textural transitions between radial and axial alignment of the columns with respect to the long nanochannel axis. Furthermore, confinement-induced continuous order formation is observed in contrast to discontinuous first-order phase transitions, which can be quantitatively described by Landau-de Gennes free energy models for liquid crystalline order transitions in confinement. Our observations suggest that the infiltration of DILCs into nanoporous solids allows tailoring their nanoscale texture and ion channel formation and thus their electrical and optical functionalities over an even wider range than in the bulk state in a homogeneous manner on the centimeter scale as controlled by the monolithic nanoporous scaffolds.

Sense of agency in operations with delays: A free-energy model and application to interface design

Action-feedback delay during operation reduces sense of agency (SoA). In this study, using information-theoretic free energy, we formalized a novel mathematical model for explaining the influence of delay on SoA in continuous operations. Based on the mathematical model, we propose that visualization of predicted future outcomes prevents SoA degradation resulting from response delays. Model-based simulations and operational experiments with participants confirmed that operational delay considerably reduces SoA. Furthermore, the proposed visualization mitigates these problems. Our findings support the model-based interface design for continuous operations with delay to prevent SoA degradation.

Kirkwood-Buff Analysis of Binary and Ternary Systems Consisting of Alcohols (Methanol, Ethanol, 1-Propanol, and 2-Propanol), Water, and n-Hexane to Understand the Formation of Surfactant-Free Microemulsions.

Surfactant-free microemulsion (SFME) represents a class of fluid mixtures that can form microheterogeneous structures without detergents, offering an environmentally benign alternative to traditional microemulsions. However, the formation mechanism is still elusive. This work applies the Kirkwood-Buff theory to mixtures of alcohols, water, and n-hexane to elucidate the SFME formation mechanism. To ensure robust calculation of the Kirkwood-Buff integrals (KBIs), we construct a data set of densities and excess free energies of binary and ternary systems. Multiple excess Gibbs free energy models are assessed against this data set to select the most suitable model reproducing the experimental results. In addition, we introduce statistical methods to determine the optimal polynomial order of the Redlich-Kister correlation for the excess volume data. We first validate our methodology in binary systems. Then, we extend the calculation method to ternary mixtures. The KBI calculation results reveal that the alcohol-hexane and water-hexane interactions do not significantly affect SFME formation. In contrast, the interplay among water-water, water-alcohol, and alcohol-alcohol interactions critically influences the ability of a liquid mixture to form SFME structures. SFME systems exhibit the facile formation of water aggregates enveloped by alcohols, whereas non-SFME systems demonstrate homogeneous alcohol/water droplets dispersed in an oil continuous medium.

Thermodynamics and kinetics of interconversion between platinum nanoparticles and cations in zeolites

In metal-containing zeolites, sintering and redispersion processes exercise control over the identity of metal site structures, but the thermodynamic and kinetic factors that influence these molecular-level processes are not completely understood. Here, we assess the ability of first principles informed free energy models (for supported and unsupported nanoparticles) and kinetic models integrating Ostwald ripening with atom trapping to describe the interconversion between Pt cations and nanoparticles encapsulated in chabazite (CHA) zeolites. Density functional theory-derived thermodynamic phase diagrams show that the interconversion between cations, favored in oxidizing environments, and particles, favored in reducing environments, is fully reversible within a wide range of their respective conditions (temperatures and pressures) for CHA and several other zeolite topologies. Kinetic Monte Carlo simulations of Pt redispersion are consistent with experimentally observed redispersion kinetics of encapsulated Pt nanoparticles in CHA zeolites, and model results suggest the zeolite host imparts additional stability for Pt nanoparticles. We envision our thermodynamic and kinetic models for Pt-CHA are also capable of describing nanoparticle and cation interconversions for other zeolite frameworks under similar conditions.

Exotic self-assembly of hard spheres in a morphometric solvent

The self-assembly of spheres into geometric structures, under various theoretical conditions, offers valuable insights into complex self-assembly processes in soft systems. Previous studies have utilized pair potentials between spheres to assemble maximum contact clusters in simulations and experiments. The morphometric approach to solvation free energy that we utilize here goes beyond pair potentials; it is a geometry-based theory that incorporates a weighted combination of geometric measures over the solvent accessible surface for solute configurations in a solvent. In this paper, we demonstrate that employing the morphometric model of solvation free energy in simulating the self-assembly of sphere clusters results, under most conditions, in the previously observed maximum contact clusters. Under other conditions, it unveils an assortment of extraordinary sphere configurations, such as double helices and rhombohedra. These exotic structures arise specifically under conditions where the interactions take multibody potentials into account. This investigation establishes a foundation for comprehending the diverse range of geometric forms in self-assembled structures, emphasizing the significance of the morphometric approach in this context.

Experimental measurements and correlation of vapor–liquid equilibrium data for the difluoromethane (R32) + 1,3,3,3-tetrafluoropropene (R1234ze(E)) binary system from 254 to 348 K

In this study, we present new experimental data of vapor–liquid equilibrium for the binary system difluoromethane (R32) + 1,3,3,3-tetrafluoropropene (R1234ze(E)), measured at 273.14 and 363.32 K and at pressure ranging from 0.1568 to 4.3553 MPa. A “static-analytic”-type apparatus is used to do the measurements, with sampling of the equilibrium phases via capillary sampler (ROLSI®). We used three different models to correlate the data: 1) the Peng–Robinson cubic equation of state combined with the NRTL excess free energy model and Wong-Sandler mixing rules, 2) Helmholtz energy model like the one incorporated in REFPROP 10.0 software and 3) Predictive PPR78 model for which the new group parameter of R32 was adjusted. All of the three models show a very good agreement with the experimental data except for temperature higher that R32 critical temperature.

Influence of Ionic Conductivity in Polymer Dispersed Antiferroelectric Liquid Crystals (PDAFLC): A Comparison of Critical Fields

Theoretically critical unwinding field was studied using Landau free energy model of three different geometrical configuration of antiferroelectric liquid crystals. In this study, we considered the influence of ionic conductivity both in pure antiferroelectric liquid crystals and polymer dispersed antiferroelectric liquid crystals. We observed that the modified elastic constant which accounted for the interaction of ionic conductivity and polymer cross-linked chains is very much responsible for the variation of critical field.

Modeling of rigidly-constrained pure shear dielectric elastomer actuators: electromechanical coupling network method

The rigidly-constrained pure shear dielectric elastomer actuator (PS-DEA) has become one of the critical configurations in linear soft actuator design due to its excellent uni-directional actuation performance and convenient preparation process. However, the theoretical analyses are primarily conducted by employing ideal models and lack consideration of the lateral necking deformation of PS-DEA, which has an essential impact on the performance evaluation and optimal design of PS-DEA. Therefore, in this paper, a user subroutine that describing the behavior of the electromechanical behavior of DE in terms of the Gent free-energy model is developed, and then a parametric model of the PS-DEA is established. Different combinations of actuator parameters are obtained by Latin hypercube sampling, and the actuator’s performance under the parameters is simulated by the finite element method. The finite element results are taken as a sample set, and a BP neural network with three hidden layers is employed to train the samples and obtain a PS-DEA network prediction model, which is experimentally analyzed to validate its accuracy and effectiveness. The prediction model explores the influence of geometric and pre-stretching parameters on the actuator’s performance and obtains the difference between the ideal theoretical and the network prediction model under various parameters. The method in this paper provides a new design methodology and theoretical basis for developing high-performance DE actuators.

Uncertainty driven active learning of coarse grained free energy models

Coarse graining techniques play an essential role in accelerating molecular simulations of systems with large length and time scales. Theoretically grounded bottom-up models are appealing due to their thermodynamic consistency with the underlying all-atom models. In this direction, machine learning approaches hold great promise to fitting complex many-body data. However, training models may require collection of large amounts of expensive data. Moreover, quantifying trained model accuracy is challenging, especially in cases of non-trivial free energy configurations, where training data may be sparse. We demonstrate a path towards uncertainty-aware models of coarse grained free energy surfaces. Specifically, we show that principled Bayesian model uncertainty allows for efficient data collection through an on-the-fly active learning framework and opens the possibility of adaptive transfer of models across different chemical systems. Uncertainties also characterize models’ accuracy of free energy predictions, even when training is performed only on forces. This work helps pave the way towards efficient autonomous training of reliable and uncertainty aware many-body machine learned coarse grain models.

Sense of Agency as a Function of Prediction Errors and Uncertainties: Free Energy Model and Experimental Evidence

Sense of Agency as a Function of Prediction Errors and Uncertainties: Free Energy Model and Experimental Evidence