Total Free Energy Research Articles

The local topological free energy of proteins

Protein folding, the process by which proteins attain a 3-dimensional conformation necessary for their function, remains an important unsolved problem in biology. A major gap in our understanding is how local properties of proteins relate to their global properties. In this manuscript, we use the Writhe and Torsion to introduce a new local topological/geometrical free energy that can be associated to 4 consecutive amino acids along the protein backbone. By analyzing a culled protein dataset from the PDB, our results show that high local topological free energy conformations are independent of sequence and may be involved in the rate limiting step in protein folding. By analyzing a set of 2-state single domain proteins, we find that the total local topological free energy of these proteins correlates with the experimentally observed folding rates reported in Plaxco et al. (2000).

Magnetic Flux and Magnetic Nonpotentiality of Active Regions in Eruptive and Confined Solar Flares

Abstract With the aim of understanding how the magnetic properties of active regions (ARs) control the eruptive character of solar flares, we analyze 719 flares of Geostationary Operational Environmental Satellite (GOES) class ≥C5.0 during 2010–2019. We carry out the first statistical study that investigates the flare-coronal mass ejection (CME) association rate as a function of the flare intensity and the AR characteristics that produce the flare, in terms of its total unsigned magnetic flux (ΦAR). Our results show that the slope of the flare–CME association rate with flare intensity reveals a steep monotonic decrease with ΦAR. This means that flares of the same GOES class but originating from an AR of larger ΦAR, are much more likely to be confined. Based on an AR flux as high as 1.0 × 1024 Mx for solar-type stars, we estimate that the CME association rate in X100-class “superflares” is no more than 50%. For a sample of 132 flares ≥M2.0 class, we measure three nonpotential parameters including the length of steep gradient polarity-inversion line (L SGPIL), the total photospheric free magnetic energy (E free), and the area with large shear angle (A Ψ). We find that confined flares tend to have larger values of L SGPIL, E free, and A Ψ compared to eruptive flares. Each nonpotential parameter shows a moderate positive correlation with ΦAR. Our results imply that ΦAR is a decisive quantity describing the eruptive character of a flare, as it provides a global parameter relating to the strength of the background field confinement.

Bouncing drop impingement on heated hydrophobic surfaces

We extend a diffuse interface phase-field method for two-phase flow simulations so as to include interfacial heat transfer and the thermal Marangoni effect. The set of governing equations hold non-standard terms, which originally stem from the underlying variational consideration of the total free energy of the two-phase system. It consists of the coupled Cahn-Hilliard Navier-Stokes equations with a temperature-dependent mixing energy term and a temperature transport equation implemented in the OpenFOAM framework. The underlying solver phaseFieldFoam is validated for the test cases of thermocapillary convection in a two-fluid-layer and thermocapillary migration of a drop.In the main part of the paper, hydrodynamics and heat transfer of a droplet impinging on a heated hydrophobic surface with subsequent bouncing are studied in detail. By comprehensive simulations, the effects of impact velocity, droplet diameter (in mm range) and substrate wettability (contact angle) are investigated. The numerical results for spreading ratio, wall contact time and cooling effectiveness are found to compare well with experiments indicating that the developed code is well suited for heat transfer simulation in two-phase flow. For the maximum spreading ratio, a new generalizing correlation is proposed which models the kinetic energy and energy losses at maximum spreading by two coefficients, which are determined from simulation results. A new correlation is also proposed for the contact time, which takes into account surface wettability. For the time evolution of drop mean temperature, a crossover is observed when comparing simulations with constant and temperature-dependent surface tension, indicating that the inclusion of Marangoni effects increases both, the heat transfer between drop and wall during spreading and the heat transfer between drop and surrounding air after rebound.

A thermodynamically consistent model and its conservative numerical approximation for moving contact lines with soluble surfactants

We derive a continuum sharp-interface model for moving contact lines with soluble surfactants in a thermodynamically consistent framework. The model consists of the isothermal two-phase incompressible Navier–Stokes equations for the fluid dynamics and the bulk/surface convection–diffusion equations for the surfactant transportation. The interface condition, the slip boundary condition, the dynamic contact angle condition, and the adsorption/desorption condition are derived based on the principle of the total free energy dissipation. In particular, we recover classical adsorption isotherms from different forms of the surface free energy. The model is then numerically solved in two spatial dimensions. We present an Eulerian weak formulation for the Navier–Stokes equations together with an arbitrary Lagrangian–Eulerian weak formulation for the surfactant transport equations. Finite element approximations are proposed to discretize the two weak formulations on the moving mesh. The resulting numerical method is shown to conserve the total mass of the surfactants exactly. By using the proposed model and its numerical method, we investigate the droplet spreading and migration in the presence of surfactants and study their dependencies on various dimensionless adsorption parameters.

Multiphysics approaches for modeling nanostructural evolution during physical vapor deposition of phase-separating alloy films

Physical vapor deposition of phase-separating alloy films yields a rich variety of distinct self-assembled nanostructures depending on the deposition rate and temperature. However, the role of grain boundaries, elastic imhomogeneity, and anisotropy, and surface tension, in the formation of such nanostructures is currently not well understood. Here, we employ a phase-field approach that couples the multiphysics of elemental diffusion, elastic misfit and anisotropy, surface tension, and grain boundaries with processing parameters, namely deposition rate and temperature, to investigate phase separation and grain boundary evolution in binary alloy films. We develop phase-field deposition models of increasing complexity to isolate and analyze the influence of processing parameters on nanostructural transitions in vapor co-deposited films. While it is found that such transitions are primarily guided by a minimization of total free energy, our simulation-based insights strongly indicate the phenomena of nanostructure selection at faster deposition rates. It is anticipated that the insights gained from this study will provide the much-required knowledgebase for establishing nanostructure-level control in the physical vapor deposition of alloy films.

Direct measurement of surface adhesion between thin films of nanocellulose and urea–formaldehyde resin adhesives

When applying an adhesive to wood, the chemical heterogeneity of the wood cell walls makes it difficult to understand the contribution they make to the interfacial adhesion between the adhesive and the wood as the adhesion is a very complex physical and chemical phenomenon. This study, for the first time, directly measured the surface adhesion between cellulose, a major component of wood, and urea–formaldehyde (UF) resin adhesives. The adhesion between thin, smooth nanocellulose films, such as cellulose nanofibrils (CNFs), carboxymethylated nanofibrils (CM)–CNFs, and carboxylated cellulose nanocrystals (C–CNCs), and UF resins with two formaldehyde to urea (F/U) molar ratios of 1.0 and 1.6 was measured using two approaches: (1) direct measurement of the adhesion force between nanocellulose films and liquid droplets of the UF resins, and (2) calculation of the work of adhesion between films of the nanocelluloses and UF resins using the contact angle and the van Oss–Chaudhury–Good method. The results show that the total surface free energies, either between the different nanocelluloses or between the two UF resins are somewhat similar, indicating the similarity in their surface properties. However, the adhesion force and work of adhesion of 1.6 UF resins with different types of nanocellulose are higher than those of 1.0 UF resins, which shows that van der Waals forces are dominant in their molecular interactions. These results suggest that the adhesion between 1.6 UF resins and nanocellulose is stronger than that when 1.0 UF resins are used because the 1.6 UF resins have a more branched structure, smoother surface, and higher surface free energy.

A discontinuous Galerkin method for a diffuse-interface model of immiscible two-phase flows with soluble surfactant

A numerical method using discontinuous polynomial approximations is formulated for solving a phase-field model of two immiscible fluids with a soluble surfactant. The proposed scheme is shown to decay the total free Helmholtz energy at the discrete level, which is consistent with the continuous model dynamics. The scheme recovers the Langmuir adsorption isotherms at equilibrium. Simulations of spinodal decomposition, flow through a cylinder and flow through a sequence of pore throats show the dynamics of the flow with and without surfactant. Finally the numerical method is used to simulate fluid flows in the pore space of Berea sandstone obtained by micro-CT imaging.

Electrochemistry from first-principles in the grand canonical ensemble.

Progress in electrochemical technologies, such as automotive batteries, supercapacitors, and fuel cells, depends greatly on developing improved charged interfaces between electrodes and electrolytes. The rational development of such interfaces can benefit from the atomistic understanding of the materials involved by first-principles quantum mechanical simulations with Density Functional Theory (DFT). However, such simulations are typically performed on the electrode surface in the absence of its electrolyte environment and at constant charge. We have developed a new hybrid computational method combining DFT and the Poisson-Boltzmann equation (P-BE) capable of simulating experimental electrochemistry under potential control in the presence of a solvent and an electrolyte. The charged electrode is represented quantum-mechanically via linear-scaling DFT, which can model nanoscale systems with thousands of atoms and is neutralized by a counter electrolyte charge via the solution of a modified P-BE. Our approach works with the total free energy of the combined multiscale system in a grand canonical ensemble of electrons subject to a constant electrochemical potential. It is calibrated with respect to the reduction potential of common reference electrodes, such as the standard hydrogen electrode and the Li metal electrode, which is used as a reference electrode in Li-ion batteries. Our new method can be used to predict electrochemical properties under constant potential, and we demonstrate this in exemplar simulations of the differential capacitance of few-layer graphene electrodes and the charging of a graphene electrode coupled to a Li metal electrode at different voltages.

Spontaneous chiral self-assembly of CdSe@CdS nanorods

Spontaneous chiral self-assembly of CdSe@CdS nanorods

Accelerating finite-temperature Kohn-Sham density functional theory with deep neural networks

We present a numerical modeling workflow based on machine learning (ML) which reproduces the the total energies produced by Kohn-Sham density functional theory (DFT) at finite electronic temperature to within chemical accuracy at negligible computational cost. Based on deep neural networks, our workflow yields the local density of states (LDOS) for a given atomic configuration. From the LDOS, spatially-resolved, energy-resolved, and integrated quantities can be calculated, including the DFT total free energy, which serves as the Born-Oppenheimer potential energy surface for the atoms. We demonstrate the efficacy of this approach for both solid and liquid metals and compare results between independent and unified machine-learning models for solid and liquid aluminum. Our machine-learning density functional theory framework opens up the path towards multiscale materials modeling for matter under ambient and extreme conditions at a computational scale and cost that is unattainable with current algorithms.

Free energy and kinetics of cAMP permeation through connexin26 via applied voltage and milestoning

The connexin family is a diverse group of highly regulated wide-pore channels permeable to biological signaling molecules. Despite the critical roles of connexins in mediating selective molecular signaling in health and disease, the basis of molecular permeation through these pores remains unclear. Here, we report the thermodynamics and kinetics of binding and transport of a second messenger, adenosine-3′,5′-cyclophosphate (cAMP), through a connexin26 hemichannel (Cx26). First, inward and outward fluxes of cAMP molecules solvated in KCl solution were obtained from 4 μs of ± 200 mV simulations. These fluxes data yielded a single-channel permeability of cAMP and cAMP/K+ permeability ratio consistent with experimentally measured values. The results from voltage simulations were then compared with the potential of mean force (PMF) and the mean first passage times (MFPTs) of a single cAMP without voltage, obtained from a total of 16.5 μs of Voronoi-tessellated Markovian milestoning simulations. Both the voltage simulations and the milestoning simulations revealed two cAMP-binding sites, for which the binding constants KD and dissociation rates koff were computed from PMF and MFPTs. The protein dipole inside the pore produces an asymmetric PMF, reflected in unequal cAMP MFPTs in each direction once within the pore. The free energy profiles under opposite voltages were derived from the milestoning PMF and revealed the interplay between voltage and channel polarity on the total free energy. In addition, we show how these factors influence the cAMP dipole vector during permeation, and how cAMP affects the local and nonlocal pore diameter in a position-dependent manner.

Structural basis of different surface-modified fullerene derivatives as novel thrombin inhibitors: insight into the inhibitory mechanism through molecular modelling studies

Thrombin is the main target of antithrombotic and anticoagulant therapy. Although recent studies have shown that surface-modified fullerene derivatives can be used as novel nano-anticoagulants to effectively inhibit thrombin, the specific mechanism remains unclear. In this study, we investigated the binding mode and inhibition mechanism of fullerenes with thrombin by using various molecular modelling approaches. The results showed that owing to the hydrophobicity of the fullerene skeleton, the four existing fullerene inhibitors mainly combined with the active site of thrombin through van der Waals interaction and tended to make the surrounding environment hydrophobic. This made the inhibitors with hydrophobic side chains, especially those with large hydrophobic side chains containing benzene rings, have greater binding free energy with protein. However, as more hydrophilic groups can change the surrounding hydrophilic–hydrophobic environment and form more hydrogen bonds, the electrostatic contribution of the polyhydroxy side chain designed in this study was increased further. At the same time, the van der Waals interaction between the fullerene carbon skeleton and protein did not decrease significantly, resulting in a significantly increased total binding free energy and an enhanced inhibition effect. These findings provide a theoretical basis for the improvement of highly effective fullerene anticoagulants.

Mycelial pellets for alleviation of membrane fouling in membrane bioreactor

In this study, mycelial pellets (MPs) were employed as efficient and sustainable bio-carriers to alleviate membrane fouling in membrane bioreactor (MBR). The comparative study was performed in lab-scale MBR in the absence and presence of MPs addition under continuous operation for 80 days. The results demonstrated efficient removal of chemical oxygen demand (COD) and ammonia nitrogen (NH4+-N) for both systems, while MPs addition led to lower rate at which transmembrane-pressure was increased, lower filtration resistance, thinner bio-cakes and fewer contents of extracellular polymeric substances (EPS) and soluble microbial products (SMP) in bio-cakes of membrane surface. Adding MPs into MBR could enhance biomass retention and EPS content in suspended liquid, thus accelerating the granulation of activated sludge, which should be responsible for mitigation of membrane fouling. According to the extended Derjaguin-Landau-Verwey-Overbeek (XDLVO) theory, the total surface free energy between membrane and foulants was always attractive, but total interfacial interaction especially acid-based (AB) interaction in the presence of MPs was weaker than that in the absence, confirming lower adhesion force induced by MPs. Furthermore, high throughput sequencing analysis of bio-cakes illustrated that a smaller relative abundance of EPS producer including the classes Gammaproteobacteria, Alphaproteobacteria and Actinobacteria, and a higher abundance of SMP decomposer including the class Chloroflexia were observed. The relevant mechanisms were underlined schematically to explain the function of MPs in mitigating membrane fouling process, which could be attributed to formation of biofilm with MPs serving as bio-carriers followed by promoted sludge granulation. This study provides a proof-in-concept demonstration of using MPs as bio-carriers to mitigate membrane fouling, making wastewater treatment by MBR more efficient, more reliable and more sustainable.

Relative stabilities of Si polytypes under biaxial stress: A first-principles study

We explore the possibility of the production of Si polytypes via the total energies and free energies obtained in the density-functional theory and the density-functional perturbation theory. We first calculate the total energies of three polytypes of the tetrahedrally coordinated $s{p}^{3}$ Si atoms having the two-layer, three-layer, and four-layer stacking periods in the hexagonal unit cell (``$2H$'', ``$3H$'', and ``$4H$'') as a function of the in-plane lattice constant $a$ using the local-density approximation (LDA) and generalized gradient approximation (GGA) comparatively. In the LDA calculation, the $4H$ phase is energetically the most favorable among three phases in the range of 3.55 \AA{} $\ensuremath{\le}$ $a$ $\ensuremath{\le}$ 3.73 \AA{}. While the $4H$ phase is found to be more stable than the $2H$ phase at a relatively wide range of the $a$ value we studied, the $2H$ phase is found to be more stable than the $3H$ ($3C$) phase in the range of 3.57 \AA{} $\ensuremath{\le}a\ensuremath{\le}$ 3.61 \AA{}. In the GGA calculation, on the other hand, the $4H$ phase becomes the most favorable phase for almost the same range as the LDA case, 3.57 \AA{} $\ensuremath{\le}a\ensuremath{\le}$ 3.73 \AA{}. The $2H$ phase also becomes as stable as the $3H$ phase as in the case of the LDA around the small $a$ value of 3.62 \AA{}, although the $3H$ phase energy is always lower than that of the $2H$ phase in the GGA calculation. Considering the chemical vapor deposition (CVD) growth process, we calculate the biaxial stress values to reduce the lattice constant of the substrate Si crystal to realize the small $a$ values, which can lead to the homoepitaxial growth of the $4H$ phase. The values obtained are 4.69 GPa and 8.14 GPa for the LDA and GGA, respectively. Next, we study the thermal effect on the relative stabilities of the 3 phases. We calculate the phonon dispersion, bulk modulus and thermal expansion including the vibrational and thermal effect. From the comparison with experimental values of the $3C$ phase, it is found that the LDA results show much better agreement with experiment than the GGA, indicating that the LDA calculation is reliable to predict thermal properties of the real systems. Finally, we derive the free energy as a function of $a$ under several designated temperatures. The relative stabilities of the $2H$ and $4H$ phases with respect to the $3H$ phase are found to be enhanced. At around $a=3.65$ \AA{}, stabilities of $2H$ and $4H$ phases relative to the $3H$ phase become most prominent. Although stabilities of the $2H$ and $4H$ phases relative to the $3H$ phase are reduced with increasing temperature at around $a$ = 3.60 \AA{}, $2H$ phase is found to be as stable as $3H$ and $4H$ phases at higher temperatures, indicating the possibility of the production of the $2H$ phase via high-temperature CVD process with the biaxial stress.

SURFACE FREE ENERGY AND FLEXURAL PROPERTIES OF WOLLASTONITE FILLED POLYPROPYLENE COMPOSITES

Nowadays, appearance is an important factor in vehicles. For this reason, paint application is widely used in plastic parts. Surface energy is a key parameter for the adhesion of paint on the surface of polymers. Among thermoplastic polymers, polycarbonate and acrylonitrile butadiene styrene are commonly used materials due to their higher surface energies. For low surface energy materials, surface energies can be increased using streamer, plasma, corona, mechanical etching and chemical etching methods. The aim of this work is to eliminate the pre-treatments applied to parts produced with polypropylene (PP) polymer using wollastonite (CaSiO3) additive. For this purpose, CaSiO3 filled PP composites containing 40 wt.% wollastonite with different sizes and coatings were produced by extrusion process. Afterwards, plate samples were prepared from granules using a hot pressing device. Flexural properties and surface free energy measurements were performed on these composites produced in plate form. From the results, an increased surface free energy was observed for small particle size and aminosilane coated wollastonite added PP composite with an increase by 23% of the total surface free energy. Flexural strengths were well correlated with the surface free energy results and showed an increase by 1.2% for the same additive.

Nonreciprocality of a micromachine driven by a catalytic chemical reaction

We propose a model that describes cyclic state transitions of a micromachine driven by a catalytic chemical reaction. We consider a mechanochemical coupling of variables representing the degree of a chemical reaction and the internal state of a micromachine. The total free energy consists of a tilted periodic potential and a mechanochemical coupling energy. We assume that the reaction variable obeys a deterministic stepwise dynamics characterized by two typical timescales, i.e., the mean first passage time and the mean first transition path time. To estimate the functionality of a micromachine, we focus on the quantity called "nonreciprocality" and further discuss its dependence on the properties of catalytic reaction. For example, we show that the nonreciprocality is proportional to the square of the mean first transition path time. The explicit calculation of the two timescales within the decoupling approximation model reveals that the nonreciprocality is inversely proportional to the square of the energy barrier of catalytic reaction.

Synthesis of furfural from xylan in γ-valerolactone/molten salt hydrate biphasic system

Herein, we reported a facile and efficient process for synthesis of furfural (FAL) from xylan in biphasic system. The excellent performance of more than 99.9% conversion of xylan with 77.22 mol% yield of FAL was obtained at 140 °C for 2 h. Notably, γ-valerolactone (GVL) was selected as the organic phase which played a key role in extracting and preserving the product FAL. Furthermore, a self-prepared molten salt hydrate (LiCl·3H2O) was designed as the water phase which conducted as both the solvent and catalyst. Besides, a proposed mechanism for the process is also investigated, especially on the pathways for the isomerization of xylose catalyzed by Al2(SO4)3 and LiCl·3H2O, respectively. Moreover, density functional theory (DTF) calculations were implemented to get insights into the total activation free energy of xylose isomerization to xylulose under different solvent ratios. Both of the catalyst and biphasic system could be recycled by simple steps, accompanying with more than 73.0 mol% of FAL yield obtained after three retrievals, which sheds lights on facile and efficient industrial production of FAL from corncob and lignocellulosic biomass.

Energy Renewal: Isothermal Utilization of Environmental Heat Energy with Asymmetric Structures.

Through the research presented herein, it is quite clear that there are two thermodynamically distinct types (A and B) of energetic processes naturally occurring on Earth. Type A, such as glycolysis and the tricarboxylic acid cycle, apparently follows the second law well; Type B, as exemplified by the thermotrophic function with transmembrane electrostatically localized protons presented here, does not necessarily have to be constrained by the second law, owing to its special asymmetric function. This study now, for the first time, numerically shows that transmembrane electrostatic proton localization (Type-B process) represents a negative entropy event with a local protonic entropy change () in a range from −95 to −110 J/K∙mol. This explains the relationship between both the local protonic entropy change () and the mitochondrial environmental temperature (T) and the local protonic Gibbs free energy () in isothermal environmental heat utilization. The energy efficiency for the utilization of total protonic Gibbs free energy ( including ) in driving the synthesis of ATP is estimated to be about 60%, indicating that a significant fraction of the environmental heat energy associated with the thermal motion kinetic energy (kBT) of transmembrane electrostatically localized protons is locked into the chemical form of energy in ATP molecules. Fundamentally, it is the combination of water as a protonic conductor, and thus the formation of protonic membrane capacitor, with asymmetric structures of mitochondrial membrane and cristae that makes this amazing thermotrophic feature possible. The discovery of energy Type-B processes has inspired an invention (WO 2019/136037 A1) for energy renewal through isothermal environmental heat energy utilization with an asymmetric electron-gated function to generate electricity, which has the potential to power electronic devices forever, including mobile phones and laptops. This invention, as an innovative Type-B mimic, may have many possible industrial applications and is likely to be transformative in energy science and technologies for sustainability on Earth.

Toward a theory of machine learning

We define a neural network as a septuple consisting of (1) a state vector, (2) an input projection, (3) an output projection, (4) a weight matrix, (5) a bias vector, (6) an activation map and (7) a loss function. We argue that the loss function can be imposed either on the boundary (i.e. input and/or output neurons) or in the bulk (i.e. hidden neurons) for both supervised and unsupervised systems. We apply the principle of maximum entropy to derive a canonical ensemble of the state vectors subject to a constraint imposed on the bulk loss function by a Lagrange multiplier (or an inverse temperature parameter). We show that in an equilibrium the canonical partition function must be a product of two factors: a function of the temperature, and a function of the bias vector and weight matrix. Consequently, the total Shannon entropy consists of two terms which represent, respectively, a thermodynamic entropy and a complexity of the neural network. We derive the first and second laws of learning: during learning the total entropy must decrease until the system reaches an equilibrium (i.e. the second law), and the increment in the loss function must be proportional to the increment in the thermodynamic entropy plus the increment in the complexity (i.e. the first law). We calculate the entropy destruction to show that the efficiency of learning is given by the Laplacian of the total free energy, which is to be maximized in an optimal neural architecture, and explain why the optimization condition is better satisfied in a deep network with a large number of hidden layers. The key properties of the model are verified numerically by training a supervised feedforward neural network using the stochastic gradient descent method. We also discuss a possibility that the entire Universe at its most fundamental level is a neural network.

Molecular-level understanding of gibbsite particle aggregation in water

Using molecular dynamics simulations, we investigate the molecular scale origin of crystal face selectivity when one gibbsite particle attaches to another in water. A comparison of the free energy per unit surface area of particle–particle attachment indicates that particle attachment through edge surfaces, where the edge surfaces are either (1 0 0) or (1 1 0) crystal faces, is more energetically favorable compared to attachment between two basal surfaces (i.e., (0 0 1) crystal faces) or between the basal surface of one particle and the edge surface of another. This result suggests that gibbsite crystals with low basal/edge surface area ratio will preferentially attach through edge surfaces, potentially helping the crystals grow laterally. However, for larger gibbsite particles (high basal/edge surface area ratio) the total free energy, not normalized by surface area, of particle attachment through the basal surfaces is lower (more negative) than attachment through the edge surfaces, indicating that larger gibbsite particles will preferentially aggregate through basal surface attachments. The short-range electrostatic interactions including the interparticle hydrogen bonds from surface –OH groups drive particle attachment, and the dominant contribution to the free energy minimum is enthalpic rather than entropic. However, the enthalpy of basal-edge attachment is significantly offset by the entropy leading to a higher free energy (less negative) compared to that of basal-basal attachment. Study of the free energy for a few imperfect attachments of two particles indicates a higher free energy (i.e., less negative, less stable), compared to a perfect attachment