Variation Of Free Energy Research Articles

Development of a kinetic model for low temperature Fischer-Tropsch synthesis

A challenge to the simulation of the Fischer–Tropsch reaction system is the lack of reliable kinetic models which correctly account for the deviations from ideal polymerisation behaviour. The current trend in literature is to attribute these deviations to kinetic effects only. This ignores that the reactions in Fischer–Tropsch synthesis contain many aspects of an equilibrium-controlled process. This arises since the rate of chain growth is much faster than the rate of monomer formation from CO. Consequently, the production distribution and the observed trends in reaction behaviour can be described by thermodynamics. A model has been developed to describe the reaction kinetics wherein each rate expression for n-paraffin and 1-olefin formation is expressed as equilibrium-limited. This arises because of the linear variation of the ideal gas Gibbs free energy of formation with carbon number. It was therefore shown that the high methane yield, low ethene yield and the decrease in olefin-to-paraffin ratio with carbon number could effectively be captured in a light weight and tractable manner. The model preserves the polymerisation character of reaction and has been extended to include products of carbon number up to C81. The equilibrium basis of the model also successfully describes the dominant trends in the product distribution as a function of CO conversion, temperature and pressure.

First Steps towards Understanding the Non-Linear Impact of Mg on Calcite Solubility: A Molecular Dynamics Study

Magnesium (Mg2+) is one of the most common impurities in calcite and is known to have a non-linear impact on the solubility of magnesian calcites. Using molecular dynamics (MD), we observed that Mg2+ impacts overall surface energies, local free energy profiles, interfacial water density, structure and dynamics and, at higher concentrations, it also causes crystal surface deformation. Low Mg concentrations did not alter the overall crystal structure, but stabilised Ca2+ locally and tended to increase the etch pit nucleation energy. As a result, Ca-extraction energies over a wide range of 39 kJ/mol were observed. Calcite surfaces with an island were less stable compared to flat surfaces, and the incorporation of Mg2+ destabilised the island surface further, increasing the surface energy and the calcium extraction energies. In general, Ca2+ is less stable in islands of high Mg2+ concentrations. The local variation in free energies depends on the amount and distance to nearest Mg in addition to local disruption of interfacial water and the flexibility of surface carbonate ions to rotate. The result is a complex interplay of these characteristics that cause variability in local dissolution energies. Taken together, these results illustrate molecular scale processes behind the non-linear impact of Mg2+ concentration on the solubility of magnesium-bearing calcites.

Local detailed balance across scales: From diffusions to jump processes and beyond.

Diffusive dynamics in presence of deep energy minima and weak nongradient forces can be coarse grained into a mesoscopic jump process over the various basins of attraction. Combining standard weak-noise results with a path integral expansion around equilibrium, we show that the emerging transition rates satisfy local detailed balance (LDB). Namely, the log ratio of the transition rates between nearby basins of attractions equals the free-energy variation appearing at equilibrium, supplemented by the work done by the nonconservative forces along the typical transition path. When the mesoscopic dynamics possesses a large-size deterministic limit, it can be further reduced to a jump process over macroscopic states satisfying LDB. The persistence of LDB under coarse graining of weakly nonequilibrium states is a generic consequence of the fact that only dissipative effects matter close to equilibrium.

Phase-field crystal simulation of evolution of liquid pools in grain boundary pre-melting regions

Abstract Pre-melting is a phenomenon that below the melting point the liquid-like structure appears at the grain- boundary while the grain interior remains a crystal structure. The phase-field crystal method was employed to investigate the early evolution of the liquid pools in pre-melting regions, mainly involving four structural transformations: solid−solid state → small droplet → large liquid pool → homogeneous liquid melting. The microscopic morphology and free energy variation with different average atomic densities demonstrate that the average atomic density is sensitive to the morphological characteristics of liquid pools. Both two-dimensional and three-dimensional simulation results show that the amplitude reduction of order parameters can promote the order−disorder transition of grain boundaries, causing pre-melting in the edge dislocation aggregation. The relationship between the average atomic density and the width of the liquid pools is verified from thermodynamics, which provides a prerequisite for the application of high-temperature strain in the later stage to some extent.

Highly effective photocatalyst of TiO2 nanoparticles dispersed on carbon nanotubes for methylene blue degradation in aqueous solution

AbstractIn the present study, titania nanoparticles are highly dispersed on carbon nanotubes via hydrolysis process of tetra‐isopropyl‐orthotitanate Ti[OCH(CH3)2]4 (TPOT). The obtained composite (TiO2/CNTs) is characterized by modern methods. The anatase‐TiO2 phase is realized based on X‐ray diffraction spectrum at different pHs of hydrolysis solution. The band gap of TiO2/CNTs (Eg) is calculated by Tauc method using diffuse reflectance spectroscopy (DRS). The TiO2/CNTs composite plays as an active photocatalyst for methylene blue (MB) decomposition in aqueous solution. The effect of time to photocatalytic ability of TiO2/CNTs composite is described using Langmuir‐Hinshelwood kinetic model. The values of enthalpy variation (ΔH), entropy change (ΔS) and Gibbs free energy variation (ΔG) of the decomposition of MB are determined from thermodynamic study. In the range temperature from 283 K to 323 K, the positive values of ΔH and negative value of ΔG confirms endothermic and spontaneous nature of MB degradation. With the increase of temperature, the reaction occurs more easily, which is proved by more negative values of Gibbs free energy calculated from Van't Hoff equation.

Surface Free Energy and Bacterial Attachment on Microtextured Ti6Al4V Alloy

The present study investigated the variation in surface free energy, adhesion strength, and bacterial attachment during early colonization. Two different sizes of micro dimple textured surface MDS 400 and MDS 200 on Ti6Al4V were fabricated using mechanical micro-milling and studied with an un-textured surface. One polar (water) and dispersive liquid (diiodomethane) were used to study the work of adhesion and surface free energy of both surfaces. The Neumann method and Owen & Wendt approach were used to calculate the SFE. EDS analysis was carried out to check the surface composition. E. coli bacterial strain was used to study the early colonization responses using FESEM and optical microscope. Results indicate that the formed textures are uniform with good quality and as per the design of experiment. Area surface roughness values of the textured surface have been increased from UTS. Besides, no tool wear debris has been found on textured surfaces. SFE and adhesion strength of water and diiodomethane increase due to surface texturing and initial colonization of bacteria on textured surfaces is in the form of E. coli cellular chains has been observed. The current study offers insights into the surface free energy, adhesion strength of water and diiodomethane, and bacterial attachment during the early stage of colonization.

Numerical simulation of three-dimensional multicomponent Cahn–Hilliard systems

Complex dynamics of phase changes occur when the alloy solution's temperature suddenly drops below a critical value. The well-known Cahn-Hilliard model shows that a system of fourth-order parabolic partial equations controls this intricate process. However, the Cahn-Hilliard equation with more than four component phases in three dimensions has not been solved to our best knowledge. In this work, the negative chemical potential, namely the first variation of free energy, was convoluted with a sixth-order accurate Laplacian kernel and used as the gradient flow in a projected gradient method. Also, we calculated the Lagrangian multiplies of Gibbs n-simplex phase constraint in a nested loop. Numerical examples illustrate that the proposed method can reveal the nucleation, separation, and growth of grains for alloys with up to 16 component phases in three dimensions. When the number of component phases is large than four, we found small grains are usually dissolved and redeposited onto larger ones. However, the separated phases twist into a highly interconnected structure in the binary and ternary alloys.

Ab initio metadynamics calculations reveal complex interfacial effects in acetic acid deprotonation dynamics

Acid-base reactions play a central role in solution chemistry, with carboxylic acids being particularly important in atmospheric chemical processes. In this work, we harness metadynamics calculations with Born-Oppenheimer molecular dynamics (BOMD) simulations to understand deprotonation dynamics of acetic acid (CH3COOH) in both bulk and air-water interfacial environments. Collective variables are carefully chosen in our well-tempered metadynamics simulations to capture the deprotonation process in various aqueous configurations. Our findings show that the free energy barrier for deprotonation of acetic acid at the air-water interface is lower than in the bulk, in accordance with the available experimental data. Furthermore, our well-tempered metadynamics calculations suggest that the variations in free energy are primarily due to intricate solvation shell effects.

Comparing the effects of polymer binders on Li+ transport near the liquid electrolyte/LiFePO4 interfaces: A molecular dynamics simulation study

Various functional polymers as electrode binders with enhanced lithium ion conductivity have been proposed recently to improve the overall performance of high-power lithium ion battery (LIB). To identify the critical features of polymer binders, we utilized molecular dynamics (MD) simulations to systematically examine and compare the molecular effects of poly(vinylidene fluoride) (PVDF), poly(ethylene oxide) (PEO), polyacrylonitrile (PAN), poly(N-vinylformamide) (PNVF), and poly(styrene sulfonate) (PSS) binders on lithium ion transports at liquid electrolyte/LiFePO4 (LFP) cathode interface. Compared with conventional PVDF, all tested functional polymers have higher Li+ affinity and can disrupt the electric double layer structure. As a binder, PEO can form stable coordination complex with Li+ to effectively lower the free energy of Li+ at interface, resulting in a significantly reduction of interfacial impedance Rint. Both PAN and PNVF have polar side-chains where the PNVF formamide groups has higher Li+ affinity than PAN nitrile. PNVF can further enhance the Li+ mobility near the LFP surface and lower the total Rint. In contrast, rigid PAN has minor effects on Li+ free energy at interface, giving little impacts toward the total Rint. Finally, the negatively charged PSS can significantly reduce the surface electric potential and lower the Li+ free energy over a wide range near the interface, which greatly reduces the total Rint. The combined results suggest that improving the Li+ affinity and the local mobility at interface are important factors for a good binder, where the free energy variations play more dominant effects. The presented molecular mechanisms of various functional polymer binders provide valuable insights for novel binder design.

Free energy and segregation dynamics of two channel-confined polymers of different lengths.

Polymers confined to a narrow channel are subject to strong entropic forces that tend to drive the molecules apart. In this study, we use Monte Carlo computer simulations to study the segregation behavior of two flexible hard-sphere polymers under confinement in a cylindrical channel. We focus on the effects of using polymers of different lengths. We measure the variation of the conformational free energy, F, with the center-of-mass separation distance, λ. The simulations reveal four different separation regimes, characterized by different scaling properties of the free energy with respect to the polymer lengths and the channel diameter, D. We propose a regime map in which the state of the system is determined by the values of the quantities N_{2}/N_{1} and λ/(N_{1}+N_{2})D^{-β}, where N_{1} and N_{2} are the polymer lengths, and where β≈0.64. The observed scaling behavior of F(λ) in each regime is in reasonable agreement with predictions using a simple theoretical model. In addition, we use MC dynamics simulations to study the segregation dynamics of initially overlapping polymers by measurement of the incremental mean first-passage time with respect to λ. For systems characterized by a wide range of λ in which a short polymer is nested within a longer one, the segregation dynamics are close to that expected for two noninteracting one-dimensional random walkers undergoing unbiased diffusion. When the free-energy gradient is large, segregation is rapid and characterized by out-of-equilibrium effects.

Wettability of cellulose surfaces under the influence of an external electric field

HypothesisInterfacial tensions play an important role in dewatering of hydrophilic materials like nanofibrillated cellulose, and are affected by the molecular organization of water at the interface. Application of an electric field influences the orientation of water molecules along the field direction. Hence, it should be possible to alter the interfacial free energies to tune the wettability of cellulose surface through application of an external electric field thus, aiding the dewatering process. SimulationsMolecular dynamics simulations of cellulose surface in contact with water under the influence of an external electric field have been conducted with GLYCAM-06 forcefield. The effect of variation in electric field intensity and directions on the spreading coefficient has been addressed via orientational preference of water molecules and interfacial free energy analyses. FindingsThe application of electric field influences the interfacial free energy difference at the cellulose-water interface. The spreading coefficient increases with the electric field directed parallel to the cellulose-water interface while it decreases in the perpendicular electric field. Variation in interfacial free energies seems to explain the change in contact angle adequately in presence of an electric field. The wettability of cellulose surface can be tuned by the application of an external electric field.

Nuclear matter at finite temperature and static properties of proto-neutron star

With the effective chiral model, the finite temperature properties of nuclear matter have been studied at different temperatures. For symmetric nuclear matter, I particularly focused on the possibility of liquid–gas phase transition at low temperature and density. The critical temperature obtained in this context, is consistent with the experimental and empirical findings. The free energy and entropy variation are also studied for different values of temperature. A few asymmetric nuclear matter properties like the equation of state and the speed of sound with respect to temperature are also examined. The work is also extended to obtain the equation of state β stable nuclear matter at finite temperature. For the neutrino free case, the various static proto-neutron star properties are computed for a wide range of temperature, relevant to proto-neutron stars. For all the values of temperature, the obtained estimates of maximum gravitational mass are found to be in good agreement with the observational constraints specified from massive pulsars like PSR J0348 + 0432 and PSR J0740 + 6620. The results of surface redshift for all the temperature also satisfy the maximum surface redshift constraints from EXO 07482-676, 1E 1207.4-5209 and RX J0720.4-3125.

Revealing Thermodynamics and Kinetics of Lipid Self-Assembly by Markov State Model Analysis.

Self-assembly is ubiquitous in the realm of biology and has become an elegant bottom-up approach to fabricate new materials. Although molecular dynamics (MD) simulations can complement experiments by providing the missing atomic details, it still remains a grand challenge to reveal the thermodynamic and kinetic information on a self-assembly system. In this work, we demonstrate for the first time that the Markov state model analysis can be used to delineate the variation of free energy during the self-assembly process of a typical amphiphilic lipid dipalmitoyl-phosphatidylcholine (DPPC). Free energy profiles against the solvent-accessible surface area and the root-mean-square deviation have been derived from extensive MD results of more than five hundred trajectories, which identified a metastable crossing-cylinder (CC) state and a transition state of the distorted bilayer with a free energy barrier of ∼0.02 kJ mol-1 per DPPC lipid, clarifying a long-standing speculation for 20 years that there exists a free energy barrier during lipid self-assembly. Our simulations also unearth two mesophase structures at the early stage of self-assembly, discovering two assembling pathways to the CC state that have never been reported before. Further thermodynamic analysis derives the contributions from the enthalpy and the entropy terms to the free energy, demonstrating the critical role played by the enthalpy-entropy compensation. Our strategy opens the door to quantitatively understand the self-assembly processes in general and provides new opportunities for identifying common thermodynamic and kinetic patterns in different self-assembly systems and inspiring new ideas for experiments. It may also contribute to the refinement of force field parameters of various self-assembly systems.

Analysis of the Liquid–Cluster State of Melts near the Melting Point

We have analyzed the available data on the transition from equilibrium crystallization of melts of various substances to nonequilibrium explosive crystallization depending on preliminary heating of the liquid phase to temperature $$T_{C}^{ + }$$ . Analogously to the liquid-crystal state, superheating interval Δ $$T_{L}^{ + }$$ = $$T_{C}^{ + }$$ – TL relative to melting temperature TL is ascribed to the region of existence of a mesophase described by order parameter Q. A comparative analysis has been performed for the dependence of the free energy variation on the order parameter for clusters in the mesophase and on the sizes of crystalline nuclei in the metastable region below the melting point.

Electronic and Electrochemical Characteristics of Metal-Graphene Hybrid System: DFT Approach

Epitaxially grown Pt thin film on a graphene template is found to have a few monolayer thickness with structural stability comparable to Pt(111) surface and promising electrochemical activity. The newly synthesized thin film shows a quadrilateral-polygon structure of Pt in monolayer on graphene surface. In this study, we present a computational research on the unique architecture of the graphene-templated epitaxial Pt monolayer. Recently proposed strongly constrained and appropriately normed (SCAN) density function study (DFT) is employed to investigate the characteristics of the system. Electrochemical activities of the system are evaluated in terms of the free energy variation in oxygen reduction reaction (ORR). In architectures, Pt exhibits registry with the C-C bridge sites along the armchair and zigzag directions forming strong covalent bonds. Here, the details of the atomistic/electronic structures and binding energies are discussed. Interestingly, the ORR can occur on both Pt and graphene surfaces. This would provide a good strategy to protect metallic catalyst and to tune electronic structure of catalyst.

Investigation on Phase-Induced Surface Energy Change of HfO2 Thin Films Prepared By Plasma Enhanced Atomic Layer Deposition

Wettability of nanomaterials has been researched for the scientific physics based on solid/liquid interfaces. In particular, wettability of ceramic materials which is directly relevant to the surface free energy has been researched for its nature continuously in terms of thin film coatings.1 The development of such materials with finely tunable surface free energy and adequate stability under harsh conditions has been attracted enormous interests involving various applications.2,3 Among them, Hafnium oxide (HfO2), one of the representative transition metal oxides, has been recently studied for robust coating materials with investigation of its surface free energy. However, due to the complexity derived from environmental factors in a stack and differences between variety of deposition parameters, the surface free energy of HfO2 films has not been fully understood. Apart from the fact that the previously reported water contact angle (WCA) of HfO2 thin or bulk films highly vary between literatures, the interpretation of surface free energy of HfO2 and its intrinsic wettability still lacks of systematic approaches. In this study, we comprehensively investigated the surface free energy variation in HfO2 films prepared by plasma enhanced atomic layer deposition (PE-ALD). Upon precise control of film thickness with the aid of PE-ALD technique, we analyzed the surface free energy changes depending on the various properties of HfO2 films including film thickness, chemical composition, surface roughness, film crystallinity. We focused on a dependency of surface free energy of HfO2 films on film crystallinity as a determining factor for wettability changes. For in-depth studies, we performed thermal annealing treatment on PE-ALD HfO2 films and observed apparent correlation between wettability and film crystallinity. Based on the control of film crystallinity, PE-ALD HfO2 thin films show versatile wetting behaviors as to exposure of liquids with different surface energies. The experimental results from our work will contribute to the fundamental understanding of surface free energy of thin film HfO2 and its scientific backgrounds, and can also lead to feasible applications including liquid separation and purifications using HfO2 as robust coating film.

Effect of Presence of Aliphatic Glycine in the Anti-cancer Platinum Complex Structure on Human Serum Albumin Binding

In this work, a new water-soluble Pt(II) complex was synthesized with aliphatic glycine ligand with a formula of cis-[Pt(NH3)2(isopentylgly)]NO3, as an anti-cancer drug, and characterized. To determine the binding constant of the human serum albumin (HSA, the most abundant carrier proteins in the human circulatory system) to this complex and the binding site of the complex on HSA, the melting point of HSA and the kinetics of this interaction were investigated to introduce an anti-breast cancer drug with fewer side effects. HSA interaction with the complex was studied via a spectroscopic method at 27 and 37 °C and physiological situation (I = 10 mM, pH = 7.4) and molecular docking. The toxicity value of this complex was obtained against the human cancer breast cell line of MCF-7. The thermodynamic parameters of enthalpy and entropy were also achieved in the empirical procedure. Due to the spontaneity of the interaction, Gibbs free energy variation was obtained negative. The binding constant of this complex to HSA was 3.9 × 105 (M−1). Empirical results showed that the quenching mechanism was static. Hill coefficients, Hill constant, complex aggregation number around protein, number of binding sites, and protein melting temperature with complex were obtained. The kinetics of this interaction was also investigated, which showed that this interaction follows a second-order kinetic. The molecular docking data indicated that the position of the interaction of complex on the protein was the site I in the sub-second IIA. Also, the hydrogen bonding and the hydrophobic interaction as the dominant binding forces were seen in complex–HSA formation. This interaction with positive cooperativity was recognized via a superior hydrogen bond. The reasonable binding constant was also obtained, which could ultimately be a good option as an anti–breast cancer drug.

Regulating the coordination environment through doping N atoms for single-atom Mn electrocatalyst of N2 reduction with high catalytic activity and selectivity: A theoretical study

Electrochemical N2 reduction reaction (NRR) is a promising way for ammonia synthesis, and developing novel electrocatalyst with high catalytic activity and selectivity is an urgent matter. Herein, the catalytic performances of single-atom Mn catalysts supported with nitrogen-doped graphene substrates (MnSA@Vx-Ny, x = s, d. y = 0, 1, 2, 3, 4.) for NRR have systematically investigated through density functional theory (DFT) calculations. The catalytic activity and selectivity of MnSA@Vx-Ny were discussed through reaction path, Gibbs free energy variation, hydrogen evolution reaction (HER), electron transfer and projected density of states. The result reveals the adsorption energy of N2 and catalytic activity of MnSA@Vx-Ny were effectively regulated through modulating the coordination environment of Mn atom. MnSA@Vs-N1 has the highest catalytic activity and selectivity among all studied catalysts for NRR at room temperature. MnSA@Vs-N1 can facilitate NRR by the distal mechanism, and the potential determining step is *N2 + H++ e− → *NNH with a free energy variation of 0.77 eV. Simultaneously, HER is suppressed by the high selectivity of N2 adsorption on MnSA@Vs-N1. This adjusting method can provide a guideline for developing robust electrocatalyst for NRR.

Manipulating electronic delocalization of Mn3O4 by manganese defects for oxygen reduction reaction

Manganese-based oxides are promising in electrocatalytic oxygen reduction reaction, but the activity and conductivity need further improvement. Herein manganese defected Mn3O4 was fabricated by solvothermal synthesis of manganese glycerate and then thermal calcination. The experimental and computational results reveal that manganese defects in Mn3O4 modify the electronic structure to improve conductivity and electronic delocalization, which helps to expose more surface Mn3+ as major active site, thereby facilitating O2 activation and OH* desorption, and reducing the Gibbs free energy variation in the rate-limiting step of ORR. Accordingly, the onset potential, half-wave potential and limiting current density of manganese defected Mn3O4 are 0.87 V, 0.65 V and 5.0 mA cm-2, better than that of normal Mn3O4 (0.77 V, 0.62 V and 2.6 mA cm-2). This work provides an effective approach to tune the defects and electronic structures of Mn3O4 for better electrochemical activity.

Ligand-protein interactions in lysozyme investigated through a dual-resolution model.

A fully atomistic (AT) modeling of biological macromolecules at relevant length‐ and time‐scales is often cumbersome or not even desirable, both in terms of computational effort required and a posteriori analysis. This difficulty can be overcome with the use of multiresolution models, in which different regions of the same system are concurrently described at different levels of detail. In enzymes, computationally expensive AT detail is crucial in the modeling of the active site in order to capture, for example, the chemically subtle process of ligand binding. In contrast, important yet more collective properties of the remainder of the protein can be reproduced with a coarser description. In the present work, we demonstrate the effectiveness of this approach through the calculation of the binding free energy of hen egg white lysozyme with the inhibitor di‐N‐acetylchitotriose. Particular attention is payed to the impact of the mapping, that is, the selection of AT and coarse‐grained residues, on the binding free energy. It is shown that, in spite of small variations of the binding free energy with respect to the active site resolution, the separate contributions coming from different energetic terms (such as electrostatic and van der Waals interactions) manifest a stronger dependence on the mapping, thus pointing to the existence of an optimal level of intermediate resolution.