Free Energy Potential Research Articles

Computational simulation-driven discovery of novel zeolite-like carbon materials as seawater desalination membranes.

Freshwater is a scarce and vulnerable resource that has never encountered such an extensive focus on a nearly worldwide scale as it does today. Recently, it has been found that desalination powered by two-dimensional (2D) carbon materials as separation membranes has significantly reduced the operational costs and complexity but presents heavy requirements for the structural stability and separation properties of the membrane materials. Here, we combined carbon materials with promising adsorption properties and zeolites characterized by a regular pore structure to obtain a zeolite-like structured carbon membrane Zeo-C and investigated the suitability of the Zeo-C membrane for seawater desalination based on the computational-simulation-driven approach. The results of molecular dynamics (MD) simulations and density functional theory (DFT) calculations revealed that the periodic pore distribution conferred favorable structural stability and mechanical strength to the Zeo-C desalination membrane. The rejection rate of Na+ and Cl- is ensured at 100% under a pressure of 40-70 MPa, and that of Na+ could reach 97.85% even though the pressure increases to 80 MPa, exhibiting superior desalination properties. The porous nature of the zeolite-like structure and the low free energy potential barrier are conducive for reliable adsorption and homogeneous diffusion of salt ions, which facilitates the acquisition of desirable water molecule permeability and salt ion selectivity. In particular, the interlinked delocalized π-network imparts inherent metallicity to Zeo-C for self-cleaning in response to electrical stimulation, thereby extending the lifetime of the desalination membrane. These studies have greatly encouraged theoretical innovations and serve as a guiding reference for desalination materials.

A relaxation model for the non-isothermal Navier-Stokes-Korteweg equations in confined domains

The Navier-Stokes-Korteweg (NSK) system is a classical diffuse interface model which is based on van der Waals' theory of capillarity. Diffuse interface methods have gained much interest to model two-phase flow in porous media. However, for the numerical solution of the NSK equations two major challenges have to be faced. First, an extended numerical stencil is required due to a third-order term in the linear momentum and the total energy equations. In addition, the dispersive contribution in the linear momentum equations prevents the straightforward use of contact angle boundary conditions. Secondly, any real gas equation of state is based on a non-convex Helmholtz free energy potential which may cause the eigenvalues of the Jacobian of the first-order fluxes to become imaginary numbers inside the spinodal region.In this work, a thermodynamically consistent relaxation model is presented which is used to approximate the NSK equations. The model is complimented by thermodynamically consistent non-equilibrium boundary conditions which take contact angle effects into account. Due to the relaxation approach, the contribution of the Korteweg tensor in the linear momentum and total energy equations can be reduced to first-order terms which enables a straightforward implementation of contact angle boundary conditions in a numerical scheme. Moreover, the definition of a modified pressure function enables to formulate first-order fluxes which remain strictly hyperbolic in the entire spinodal region. The present work is a generalization of a previously presented parabolic relaxation model for the isothermal NSK equations.A high-order discontinuous Galerkin spectral element method which supports curved elements and hanging nodes is employed to discretize the system. The relaxation model and its corresponding boundary conditions are validated using solutions of the original NSK model and analytical results for one-, two- and three-dimensional test cases. The simulation of a spinodal decomposition in a three-dimensional porous structure underlines the capability of the presented approach.

Technology for the treatment of human diseases based on the use of simulated microwave radiation from the sun

Aim. Substantiation of the most probable reason for the increase in viral activity and disclosure of the main content of nature-like technology for the treatment of human diseases using simulated microwave radiation from the Sun reaching the Earth’s surface.Materials and methods. A description of the hardware and software tools for simulating solar microwave radiation is given, which makes it possible to simulate “bursts” of solar microwave radiation from several seconds to tens of minutes, both with linear and chaotic polarization in the frequency range of 4.0–4.3 GHz. In this case, the amplitude spectrum of such radiation can vary in width, shape, and intensity, which does not exceed 100 μW/cm2.Results and discussion. The mechanism of the corrective action of the above radiation on the human body is studied. It is associated with the conversion of electromagnetic energy absorbed by the body into the energy of lowintensity broadband elastic oscillations. This makes it possible to activate inactivated enzyme complexes under hypoxic conditions to restore the free energy potential in cellular structures.Conclusions. The evidence on the validity of the use of this radiation against inflammation at the clinical, preclinical, and microbiological levels gives grounds for predicting that it will also be effective in human viral diseases.

Comparative study of galaxy clustering using halo approximation and mean-field theory in the light of modified theories of gravity

In this manuscript, we have explored the large-scale structure (LSS) of the Universe using the halo approximation of galaxies and the mean-field (mean-field approximation) theory of galaxy clusters. Employing the modified gravitational potential, which relies on Boltzmann’s statistics, we have analyzed the effect of galaxy clusters on the large-scale structure of the Universe. With both of these approximations, we have observed the significance of the modified potential. Also, the gravitational partition function obtained from the applied approximations has been used to determine the thermodynamic properties of these galaxy clusters. Besides this, the impact of these approximations on the derived quantities, such as Helmholtz free energy, entropy, internal energy, pressure, and chemical potential, was observed and is also evident from their respective plots along with their distribution functions. Importantly, the divergence of configurational integrals has been removed through the said approach.

Optimal rate convergence analysis of a numerical scheme for the ternary Cahn–Hilliard system with a Flory–Huggins–deGennes energy potential

We present an error analysis for a fully discrete finite difference scheme for the three-component Macromolecular Microsphere Composite (MMC) hydrogels system, a ternary Cahn–Hilliard system with a Flory–Huggins–deGennes free energy potential. The numerical scheme was recently proposed, and the positivity-preserving property and unconditional energy stability were theoretically established. In this paper, we rigorously prove first order convergence in time and second order convergence in space for the numerical scheme, in the LΔt∞(0,T;Hh−1)∩LΔt2(0,T;Hh1) norm. Many highly non-standard estimates have to be involved, due to the nonlinear and singular nature of the surface diffusion coefficients. The combination of (i) a higher order asymptotic expansion of the numerical solution (up to second order temporal accuracy); (ii) a rough error estimate (to establish the LΔt∞ bound for the phase variables); (iii) and a refined error estimate have to be carried out to conclude such a convergence result. To our knowledge, it will be the first work to provide an optimal rate convergence estimate for a ternary phase field system with singular energy coefficients.

A gradient micromorphic modeling for plasticity softening

Localization of internal quantities, which induce material softening, potentially leads to an ill-posed global partial differential equation. Along with further developments of singularity issues in the simulations, an unwanted divergent numerical solution may occur. The work at hand attempts to formulate a ductile softening model by considering a size reduction of the plastic yield surface. An internal variable to reduce the size of the plastic yield surface is constituted by a gradient micromorphic approach. In detail, a degradation function induced by an internal softening quantity is employed to multiply the thermodynamic force of plastic hardening in the yield function. In this regard, a gradually shrinking plastic yield surface is constituted to model the overall softening response. The evolution of the internal softening variable is governed by a Kuhn–Tucker condition together with its non-local extension. The present constitutive model of the coupled softening problem is derived based on a thermodynamically consistent algorithm from a well-defined Helmholtz free energy potential, which is implemented into the context of a conventional Finite Element Method. A representative and meaningful numerical example is studied to demonstrate the capability of the present model.

Kinetics of Hawking-Page phase transition with the non-Markovian effects

Based on the free energy landscape description of Hawking-Page phase transition, the transition process from the Schwarzschild-anti-de Sitter black hole to the thermal anti-de Sitter space are considered to be stochastic under the thermal fluctuations. If the correlation time of the effective thermal bath is comparable or even longer than the oscillating time of the spacetime state in the potential well on the free energy landscape, the non-Markovian model of the black hole phase transition is required to study the kinetics of the transition processes. The non-Markovian or memory effect is represented by the time dependent friction kernel and the kinetics is then governed by the generalized Langevin equation complemented by the free energy potential. As the concrete examples, we study the effects of the exponentially decay friction kernel and the oscillatory friction kernel on the kinetics of Hawking-Page phase transition. For the exponentially decayed friction, the non-Markovian effects promote the transition process, and for the oscillatory friction, increasing the oscillating frequency also speeds up the transition process.

Visualizing Invisible Phase Transitions in Blue Phase Liquid Crystals Using Early Warning Indicators.

Changes in the statistical properties of data as a system approaches a critical transition is studied intensively as early warning signals, but their application to materials science, where phase transitions-a type of critical transition-are of fundamental importance, are limited. Here, a critical transition analysis is applied to time-series data from a microscopic 3D ordered soft material-blue phase liquid crystals (BPLC)-and demonstrates that phase transitions that are invisible under ambient conditions can be visualized through the choice of appropriate early warning indicators. After discussing how a phase transition affects the statistical properties in a system with a Landau-de Gennes type free energy potential, the predicted changes are experimentally observed at the two types of phase transitions that occur in a BPLC: the isotropic to simple cubic, and simple cubic to body-centered cubic transitions. In particular, it is shown that the skewness of the intensity distribution inverts its sign at the phase transition, enabling temporally and spatially resolved mapping of phase transitions. This approach can be easily adapted to a wide variety of material systems and microscopy techniques, providing a powerful tool for studying complex critical transition phenomena.

SPICA Force Field for Proteins and Peptides.

A coarse-grained (CG) model for peptides and proteins was developed as an extension of the Surface Property fItting Coarse grAined (SPICA) force field (FF). The model was designed to examine membrane proteins that are fully compatible with the lipid membranes of the SPICA FF. A preliminary version of this protein model was created using thermodynamic properties, including the surface tension and density in the SPICA (formerly called SDK) FF. In this study, we improved the CG protein model to facilitate molecular dynamics (MD) simulations with a reproduction of multiple properties from both experiments and all-atom (AA) simulations. An elastic network model was adopted to maintain the secondary structure within a single chain. The side-chain analogues reproduced the transfer free energy profiles across the lipid membrane and demonstrated reasonable association free energy (potential of mean force) in water compared to those from AA MD. A series of peptides/proteins adsorbed onto or penetrated into the membrane simulated by the CG MD correctly predicted the penetration depths and tilt angles of peripheral and transmembrane peptides/proteins as comparable to those in the orientations of proteins in membranes (OPM) database. In addition, the dimerization free energies of several transmembrane helices within a lipid bilayer were comparable to those from experimental estimation. Application studies on a series of membrane protein assemblies, scramblases, and poliovirus capsids demonstrated the good performance of the SPICA FF.

Rate-type models of dissipative compressible fluids

Two models of dissipative compressible fluids are established within the general setting of Rational Thermodynamics. It is a common feature underlying the analysis of the thermodynamic consistency that the entropy production and the free energy potential are viewed as constitutive functions of the same set of physical variables and no internal variable is involved. Also in light of late experimental observations, hysteretic models are established for the dependence of pressure on the mass density. Next relaxation properties are modelled via rate equations with an objective derivative which combines the corotational rate with the divergence of the velocity.

Variational Onsager Neural Networks (VONNs): A thermodynamics-based variational learning strategy for non-equilibrium PDEs

We propose a thermodynamics-based learning strategy for non-equilibrium evolution equations based on Onsager’s variational principle, which allows us to write such PDEs in terms of two potentials: the free energy and the dissipation potential. Specifically, these two potentials are learned from spatio-temporal measurements of macroscopic observables via proposed neural network architectures that strongly enforce the satisfaction of the second law of thermodynamics. The method is applied to three distinct physical processes aimed at highlighting the robustness and versatility of the proposed approach. These include (i) the phase transformation of a coiled-coil protein, characterized by a non-convex free-energy density; (ii) the one-dimensional dynamic response of a three-dimensional viscoelastic solid, which leverages the variational formulation as a tool for obtaining reduced order models; and (iii) linear and nonlinear diffusion models, characterized by a lack of uniqueness of the free energy and dissipation potentials. These illustrative examples showcase the possibility of learning partial differential equations through their variational action density (i.e., a function instead), by leveraging the thermodynamic structure intrinsic to mechanical and multiphysics problems.

Sliding dynamics of ring on a fixed rod-like block copolymer in rotaxane: Molecular dynamics simulations vs Lifson-Jackson formula

Rotaxane is a mechanically interlocked molecule in which ring chains are threaded onto a linear axial polymer chain, and a typical feature of rotaxane is that the ring chains can slide along the axial chain. In this study, molecular dynamics simulations and Lifson-Jackson formula are performed to examine the sliding dynamics of ring chain threaded on a fixed rod-like AB block copolymer consisting of A and B blocks in which the A-block composed of NA monomers is attractive to the ring chain, while the B-block with NB monomers is repelled from the ring chain. From a series of studies on ring sliding along the AB block copolymer with the repeat unit of ANABNB, we find that the sliding dynamics of ring relies strongly on the block length of (NA+NB), the volume fraction fa of A-block as well as the block-ring interaction ε. First, the sliding diffusion coefficient D of ring decreases sharply by several orders magnitude with an increase in block length or block-ring interaction strength. Next, the sliding dynamics has a strongly non-monotonic dependence on fa, and the slowest diffusion motion occurs for ring threaded onto the symmetric block copolymer with fa=0.5. From the view of free energy potential, both the width of free energy potential well and the height of free energy potential barrier govern the sliding diffusion behavior of ring chain. According to potential of mean force (PMF) of ring sliding along the fixed rod-like block copolymer, we find that our results are good agreement with the theoretical analysis using the Lifson-Jackson formula. Our investigation can provide a simple as well as practical model to study the diffusion of particle in a periodic medium, which is one of the interesting problems in many different fields of sciences, such as physics, chemistry and biology.

A time–energy uncertainty relation in chemical thermodynamics

An analogy between the thermodynamic inequalities presented by Nicholson et al. [Nat. Phys. 16, 1211 (2020)] and by Yoshimura and Ito [Phys. Rev. Res. 3, 013175 (2021)] is discussed. As a result, a time–energy uncertainty relation in chemical thermodynamics in terms of Gibbs free energy and chemical potential is derived. It is numerically demonstrated that the uncertainly relation holds in a model system of oscillatory Brusselator reactions. Our result bridges the thermodynamic time–information uncertainty relation and free energy evolution in chemical reactions.

Free-Energy Model of Emotion Potential: Modeling Arousal Potential as Information Content Induced by Complexity and Novelty.

Appropriate levels of arousal potential induce hedonic responses (i.e., emotional valence). However, the relationship between arousal potential and its factors (e.g., novelty, complexity, and uncertainty) have not been formalized. This paper proposes a mathematical model that explains emotional arousal using minimized free energy to represent information content processed in the brain after sensory stimuli are perceived and recognized (i.e., sensory surprisal). This work mathematically demonstrates that sensory surprisal represents the summation of information from novelty and uncertainty, and that the uncertainty converges to perceived complexity with sufficient sampling from a stimulus source. Novelty, uncertainty, and complexity all act as collative properties that form arousal potential. Analysis using a Gaussian generative model shows that the free energy is formed as a quadratic function of prediction errors based on the difference between prior expectation and peak of likelihood. The model predicts two interaction effects on free energy: that between prediction error and prior uncertainty (i.e., prior variance) and that between prediction error and sensory variance. A discussion on the potential of free energy as a mathematical principle is presented to explain emotion initiators. The model provides a general mathematical framework for understanding and predicting the emotions caused by novelty, uncertainty, and complexity. The mathematical model of arousal can help predict acceptable novelty and complexity based on a target population under different uncertainty levels mitigated by prior knowledge and experience.

Fluid-fluid phase behaviour in the explicit hard spherocylinder solvent ionic model confined in a disordered porous medium

We propose a theoretical approach that takes into account the effects of a disordered porous confinement on the liquid–liquid phase behavior of the ionic solution modelled by the restricted primitive model with an explicit consideration of the neutral hard spherocylinder solvent. The theory is based on a combination of two approaches: the scale particle theory for the description of the reference system represented by a mixture of hard spheres and hard spherocylinders confined in a disordered hard-sphere matrix and the associative mean-spherical approximation for taking into account Coulomb interactions between ions. Alternatively, the mean spherical approximation is applied for the description of the ionic subsystem for comparison. For the considered solvent explicit model in a matrix, analytical expressions for pressure, free energy and partial chemical potentials are derived for the first time. Using these expressions, the liquid–liquid phase transition is studied, where one phase is enriched with ions and another one – with solvent particles. In the solvent-rich phase, the isotropic-nematic phase transition is observed due to the orientational ordering of the spherocylinder solvent particles at different porosities of a matrix. The effects of the matrix confinement and of the solvent particle elongation on the liquid–liquid and isotropic-nematric phase transitions are studied at different pressures. The role of association phenomena appearing between positively and negatively charged ions in phase behavior of the considered ionic solutions under confinement is discussed.

Modeling stress–strain response of shape memory alloys during reorientation of self-accommodated martensites with different morphologies

The shape memory effect observed in many alloys arises due to stress induced transformation between variants of the martensitic phase. It is difficult to study this process in detail using continuum approaches and particle based methods are eminently more suitable. In this work, we study detwinning, which is the transformation between martensite variants due to applied stress using a novel discrete particle model. The approach uses a novel multibody interparticle interaction defined directly using a non-convex free energy potential pertinent to such material behavior. This model is able to describe simultaneously occurring multiple microscale events during the detwinning process: nucleation and propagation of ledges along twin boundary. Due to these underlying microscale events the plateau region of stress–strain response shows a jerky nature. The effect of temperature and morphology on the stress–strain behavior of the self-accommodated martensite microstructure is studied in detail. From the simulations, we identify the morphological features affecting the transformation stress for detwinning. The critical parameters are found to be the length and number of twin and macro-twin boundaries and the number of mobile ledges.

Unconditionally energy stable second-order numerical scheme for the Allen\u2013Cahn equation with a high-order polynomial free energy

In this article, we consider a temporally second-order unconditionally energy stable computational method for the Allen–Cahn (AC) equation with a high-order polynomial free energy potential. By modifying the nonlinear parts in the governing equation, we have a linear convex splitting scheme of the energy for the high-order AC equation. In addition, by combining the linear convex splitting with a strong-stability-preserving implicit–explicit Runge–Kutta (RK) method, the proposed method is linear, temporally second-order accurate, and unconditionally energy stable. Computational tests are performed to demonstrate that the proposed method is accurate, efficient, and energy stable.

A highly efficient and accurate exponential semi-implicit scalar auxiliary variable (ESI-SAV) approach for dissipative system

The scalar auxiliary variable (SAV) approach [42] is a very popular and efficient method to simulate various phase field models. To save the computational cost, a new SAV approach is given in [25] by introducing a new variable θ. The new SAV approach can be proved to save nearly half CPU time of the original SAV approach while keeping all its other advantages. In this paper, we propose a novel technique to construct an exponential semi-implicit scalar auxiliary variable (ESI-SAV) approach without introducing any extra variables. The new proposed method also only needs to solve one linear equation with constant coefficients at each time step. Furthermore, the constructed ESI-SAV method does not need the bounded below restriction of nonlinear free energy potential which is more reasonable and effective for various phase field models. Meanwhile it is easy to construct first-order, second-order and higher-order unconditionally energy stable time-stepping schemes. Other than that, the ESI-SAV approach can be proved to be effective to solve the non-gradient but dissipative system such as Navier-Stokes equations. Several numerical examples are provided to demonstrate the improved efficiency and accuracy of the proposed method.

Structural instability of transition metals upon ultrafast laser irradiation

Precision in laser material structuring is critically defined by the energy flow during the irradiation process, particularly in ultrafast regimes. Alternative to thermal evolutions, nonequilibrium electronic excitation can exercise a direct influence on the atomic bonding delivering a potentially rapid destructuring process. In this context, the atomic disordering of transition metals (Cr, Ni, and Ti) induced by nonequilibrium electronic excitation typical for ultrafast laser processing is studied with an emphasis on the role of the $d$-band filling and crystalline structure. The density functional theory is used to obtain, from first principles, structural stability criteria and nonthermal disordering pathways on timescales shorter than picosecond electron-phonon dynamics. We show that the hot electrons distort charge distribution in the cold crystalline arrangement and increase the entropy of the system, thus driving the mechanical expansion. The calculated nonequilibrium free-energy potentials indicate that a solid destabilization is possible when electron temperature reaches a universal value of around 2 eV for all considered metals. Under a uniaxial lattice relaxation expected in the laser ablation of surface layers, the charge redistribution and loss of lattice stability is shown to be oriented along specific crystal directions. Moreover, we show that the interatomic potential destabilization is energetically more favorable for Ni than for Cr and Ti. Lattice dynamics is affected by space-charge redistribution induced by Fermi smearing associated with anisotropic expansion due to electron pressure gradients. This ultrafast destructuring mechanism is shown to be a general feature of partially filled $d$-band transition metals.

Bottom-up coarse-grain modeling of plasticity and nanoscale shear bands in α-RDX.

Computationally inexpensive particle-based coarse-grained (CG) models are essential for use in molecular dynamics (MD) simulations of mesoscopically slow cooperative phenomena, such as plastic deformations in solids. Molecular crystals possessing complex symmetry present enormous practical challenges for particle-based coarse-graining at molecularly resolved scales, when each molecule is in a single-site representation, and beyond. Presently, there is no published pairwise non-bonded single-site CG potential that is able to predict the space group and structure of a molecular crystal. In this paper, we present a successful coarse-graining at a molecular level from first principles of an energetic crystal, hexahydro-1,3,5-trinitro-s-triazine (RDX) in the alpha phase, using the force-matching-based multiscale coarse-graining (MSCG/FM) approach. The new MSCG/FM model, which implements an optimal pair decomposition of the crystal Helmholtz free energy potential in molecular center-of-mass coordinates, was obtained by force-matching atomistic MD simulations of liquid, amorphous, and crystalline states and in a wide range of pressures (up to 20GPa). The MSCG/FM potentials for different pressures underwent top-down optimization to fine-tune the mechanical and thermodynamic properties, followed by consolidation into a transferable density-dependent model referred to as RDX-TC-DD (RDX True-Crystal Density-Dependent). The RDX-TC-DD model predicts accurately the crystal structure of α-RDX at room conditions and reproduces the atomistic reference system under isothermal (300K) hydrostatic compression up to 20GPa, in particular, the Pbca symmetry of α-RDX in the elastic regime. The RDX-TC-DD model was then used to simulate the plastic response of uniaxially ([100]) compressed α-RDX resulting in nanoscale shear banding, a key mechanism for plastic deformation and defect-free detonation initiation proposed for many molecular crystalline explosives. Additionally, a comparative analysis of the effect of core-softening of the RDX-TC-DD potential and the degree of molecular rigidity in the all-atom treatment suggests a stress-induced short-range softening of the effective intermolecular interaction as a fundamental cause of plastic instability in α-RDX. The reported RDX-TC-DD model and overall workflow to develop it open up possibilities to perform high quality simulation studies of molecular energetic materials under thermal and mechanical stimuli, including extreme conditions.