Nucleation Free Energy Research Articles

Evaluation of the energetics of copper-vacancy clusters in Fe

A theoretical study is conducted to evaluate the nucleation free energy of copper-vacancy clusters in Fe as a function of the numbers of copper atoms and of vacancies in a cluster. Using this free energy value, cluster nucleation processes during irradiation are investigated. The results clearly show that there are two different types of cluster nucleation paths on the free energy surface; one is the formation of empty voids by jumping over the ridge of the free energy surface, and the other corresponds to a path for the formation of copper clusters by going around the ridge. The dependence of easy nucleation paths on the damage rate is discussed.

Self-Assembly Dynamics of Linear Virus-Like Particles: Theory and Experiment.

We experimentally and theoretically studied the self-assembly kinetics of linear virus-like particles (VLPs) consisting of double-stranded DNA and virus-like coat proteins. The polynucleotide acts as a self-assembly template for our proteins with engineered attractive protein-DNA and protein-protein interactions that imitate the physicochemical functionality of virus coat proteins. Inspired by our experimental observations, where we found that VLPs grow from one point onward, our model presumes a nucleation step before subsequent sequential cooperative binding from one of the ends of the polynucleotide. By numerically solving the pertinent reaction rate equations, we investigated the assembly dynamics as a function of the ratio between the number of available binding sites and proteins in the solution, i.e., the stoichiometry of the molecular building blocks. Depending on the stoichiometry, we found monotonic or nonmonotonic assembly kinetics. If the proteins in the solution vastly outnumber the binding sites on all of the polynucleotides, then the assembly kinetics were strictly monotonic and the assembled fraction increases steadily with time. However, if the concentration of proteins and binding sites is equal, then we found an overshoot in the concentration of fully covered polynucleotides. We compared our model with length distributions of two types of VLPs measured by atomic force microscopy imaging and found satisfactory agreement, suggesting that a relatively simple model may be useful in describing the assembly kinetics of chemically complex systems. We furthermore re-evaluated data by Hernandez-Garcia et al. (Nat. Nanotechnol. 2014, 9, 698-702) to include the effect of a finite protein concentration previously ignored. By fitting our model to the experimental data, we were able to pinpoint the sum of the protein-protein and protein-DNA interaction free energies, the binding rate of a protein to the DNA, and the nucleation free energy associated with switching a protein from the solution to the bound conformation. The values that we found for the VLPs are comparable to virus capsid binding energies of linear and spherical viruses.

Effect of ions on sulfuric acid‐water binary particle formation: 1. Theory for kinetic‐ and nucleation‐type particle formation and atmospheric implications

AbstractWe derive a version of Classical Nucleation Theory normalized by quantum chemical results on sulfuric acid‐water hydration to describe neutral and ion‐induced particle formation in the binary sulfuric acid‐water system. The theory is extended to treat the kinetic regime where the nucleation free energy barrier vanishes at high sulfuric acid concentrations or low temperatures. In the kinetic regime particle formation rates become proportional to sulfuric acid concentration to second power in the neutral system or first power in the ion‐induced system. We derive simple general expressions for the prefactors in kinetic‐type and activation‐type particle formation calculations applicable also to more complex systems stabilized by other species. The theory predicts that the binary water‐sulfuric acid system can produce strong new particle formation in the free troposphere both through barrier crossing and through kinetic pathways. At cold stratospheric and upper free tropospheric temperatures neutral formation dominates the binary particle formation rates. At midtropospheric temperatures the ion‐induced pathway becomes the dominant mechanism. However, even the ion‐induced binary mechanism does not produce significant particle formation in warm boundary layer conditions, as it requires temperatures below 0°C to take place at atmospheric concentrations. The theory successfully reproduces the characteristics of measured charged and neutral binary particle formation in CERN CLOUD3 and CLOUD5 experiments, as discussed in a companion paper.

A superrepellent coating with dynamic fluorine chains for frosting suppression: effects of polarity, coalescence and ice nucleation free energy barrier

We designed 3 types oleophobic smooth surface (DTMS, FAS13, FAS17) with dynamic molecular chains and investigated their anti-frosting property under freezing conditions.

Understanding the sensitivity of nucleation free energies: The role of supersaturation and temperature.

Simulations are used to investigate the vapor-to-liquid nucleation of water for several different force fields at various sets of physical conditions. The nucleation free energy barrier is found to be extremely sensitive to the force field at the same absolute conditions. However, when the results are compared at the same supersaturation and reduced temperature or the same metastability parameter and reduced temperature, then the differences in the nucleation free energies of the different models are dramatically reduced. This finding suggests that comparisons of experimental data and computational predictions are most meaningful at the same relative conditions and emphasizes the importance of knowing the phase diagram of a given computational model, but such information is usually not available for models where the interaction energy is determined directly from electronic structure calculations.

Communication: Activation energy of tension-induced pore formation in lipid membranes.

Tension plays a vital role in pore formation in biomembranes, but the mechanism of pore formation remains unclear. We investigated the temperature dependence of the rate constant of constant tension (σ)-induced pore formation in giant unilamellar vesicles of lipid membranes using an experimental method we developed. By analyzing this result, we determined the activation energy (Ua) of tension-induced pore formation as a function of tension. A constant (U0) that does not depend on tension was found to contribute significantly to Ua. Analysis of the activation energy clearly indicated that the dependence of Ua on σ in the classical theory is correct, but that the classical theory of pore formation is not entirely correct due to the presence of U0. We can reasonably consider that U0 is a nucleation free energy to form a hydrophilic pre-pore from a hydrophobic pre-pore or a region with lower lateral lipid density. After obtaining U0, the evolution of a pre-pore follows a classical theory. Our data provide valuable information that help explain the mechanism of tension-induced pore formation in biomembranes and lipid membranes.

The crystal-fluid interfacial free energy and nucleation rate of NaCl from different simulation methods.

In this work, we calculate the crystal-fluid interfacial free energy, γ(cf), for the Tosi-Fumi model of NaCl using three different simulation techniques: seeding, umbrella sampling, and mold integration. The three techniques give an orientationaly averaged γ(cf) of about 100 mJ/m(2). Moreover, we observe that the shape of crystalline clusters embedded in the supercooled fluid is spherical. Using the mold integration technique, we compute γ(cf) for four different crystal orientations. The obtained interfacial free energies range from 100 to 114 mJ/m(2), being (100) and (111) the crystal planes with the lowest and highest γ(cf), respectively. Within the accuracy of our calculations, the interfacial free energy either does not depend on temperature or changes very smoothly with it. Combining the seeding technique with classical nucleation theory, we also estimate nucleation free energy barriers and nucleation rates for a wide temperature range (800-1040 K). The obtained results compare quite well with brute force calculations and with previous results obtained with umbrella sampling [Valeriani et al., J. Chem. Phys, 122, 194501 (2005)].

Bubble nucleation in simple and molecular liquids via the largest spherical cavity method.

In this work, we propose a methodology to compute bubble nucleation free energy barriers using trajectories generated via molecular dynamics simulations. We follow the bubble nucleation process by means of a local order parameter, defined by the volume of the largest spherical cavity (LSC) formed in the nucleating trajectories. This order parameter simplifies considerably the monitoring of the nucleation events, as compared with the previous approaches which require ad hoc criteria to classify the atoms and molecules as liquid or vapor. The combination of the LSC and the mean first passage time technique can then be used to obtain the free energy curves. Upon computation of the cavity distribution function the nucleation rate and free-energy barrier can then be computed. We test our method against recent computations of bubble nucleation in simple liquids and water at negative pressures. We obtain free-energy barriers in good agreement with the previous works. The LSC method provides a versatile and computationally efficient route to estimate the volume of critical bubbles the nucleation rate and to compute bubble nucleation free-energies in both simple and molecular liquids.

Nanoconfined Solid–Solid Transitions: Attempt To Separate the Size and Surface Effects

The solid–solid phase transitions in ammonium nitrate, ammonium perchlorate, and sodium nitrite confined to native and organically modified silica nanopores are analyzed by differential scanning calorimetry. The study reveals the effect of nanoconfinement on the transition temperature and links it to the kinetic parameters of the process. It is suggested that the effect of nanoconfinement is primarily the surface interaction effect in the native pores and the size effect in organically modified pores. It has been found that in organically modified pores the transition temperature is always depressed relative to the bulk, whereas in the native pores its behavior is generally unpredictable. Kinetic analysis of the transitions in terms of a nucleation model indicates that the experimentally observed shifts in temperature can be explained by a combination of changes in the free energy of nucleation and preexponential factor of the respective processes.

Interfacial free energy of the NaCl crystal-melt interface from capillary wave fluctuations.

In this work we study, by means of molecular dynamics simulations, the solid-liquid interface of NaCl under coexistence conditions. By analysing capillary waves, we obtain the stiffness for different orientations of the solid and calculate the interfacial free energy by expanding the dependency of the interfacial free energy with the solid orientation in terms of cubic harmonics. We obtain an average value for the solid-fluid interfacial free energy of 89 ± 6 mN m(-1) that is consistent with previous results based on the measure of nucleation free energy barriers [Valeriani et al., J. Chem. Phys. 122, 194501 (2005)]. We analyse the influence of the simulation setup on interfacial properties and find that facets prepared as an elongated rectangular stripe give the same results as those prepared as squares for all cases but the 111 face. For some crystal orientations, we observe at small wave-vectors a behaviour not consistent with capillary wave theory and show that this behavior does not depend on the simulation setup.

Isothermal Crystallization Kinetics of Palm Oil with Additives

This study investigates the isothermal crystallization kinetics of palm oil with additives by Differential Scanning Calorimetry (DSC). The induction time of nucleation and crystallization are obtained by simulating the crystal process using the Gompertz model. The equilibrium melting temperature is obtained via the Hoffman-Weeks methods. The Gibbs free energy of nucleation was calculated by using the Fisher-Turnbull equation and the equilibrium melting temperature. The results indicate that the span 85 has an inhibition effect on nucleation and crystallization kinetics of palm oil. The span 85 can raise the equilibrium melting temperature of palm oil. The span 85 can obviously delay the induction time of nucleation and crystallization at 0.01 and 0.1% level. Although span 85 at 0.05% concentration level also can delay the induction time, it exhibits an effect of promoting nucleation. However, the crystal is uncomplicated in the system containing additives compared to the pure palm oil.

제4암모늄기의 곁가지를 가지는 폴리프로필렌에서 등온결정화속도

In this paper, the isothermal crystallization kinetics of a functional PP (FPP) with different grafting yields (GY)-methacryloxyethyltrimethyl ammonium chloride (DMC) grafted PP were investigated by differential scanning calorimetry (DSC). The results showed that the crystallization rate of FPP (GY=4.83%) was the highest for all of the studied samples. Furthermore, for the FPP with different GY, the value of <TEX>$t_{1/2}$</TEX> became longer with increasing the grafting yield (GY). The possible explanation was that the quaternary ammonium groups introduced affected the crystallization process of the FPP in two opposite directions, i.e. promoting the nucleation and hindering the transport of the chain molecules towards the growing nuclei. Polarized optical micrographs showed that the DMC chains acted as nucleating agents, which accelerated the nucleation. In addition, the results showed the FPP had lower nucleation free energy than the PP. This study would be useful for designing the processing parameters of the grafted samples.

Nicotinamide–Indole Binary Drug System: Thermodynamic and Interfacial Studies

Crystal engineering, which can potentially be applied to a wide range of crystalline materials, offer an alternative and potentially fruitful method for improving pharmaceutical properties of drugs. The molecular mobility inherent to amorphous/crystalline phases can lead to molecular associations between different components, such that a single crystalline phase of multiple components is formed. The present investigation measures the solid–liquid equilibria (SLE) of nicotinamide (NA)-indole (IN) binary drug system. The solid–liquid equilibrium phase diagram of NA-IN system was determined by the thaw-melt method in the form of a temperature-composition curve. It shows the formation of a simple eutectic at a 0.953 mole fraction of indole, at 48°C. The excess thermodynamic quantities (gE, hE, and sE) have been estimated by computing heat of fusion data and activity coefficient of the component in a binary mix. These values highlight the ordering, stability, and structure of eutectic and non-eutectic alloys. The thermodynamic mixing functions provide information about the nature of mixing of the components during alloying. The negative value of the integral mixing function, ΔGM for eutectic and some non-eutectic alloys indicates spontaneous mixing. The driving force of nucleation during solidification (ΔGv) and the critical free energy of nucleation (ΔG*) obtained at different undercoolings have also been highlighted. The values of radius of critical nucleus (r*) of alloys lies within the nm scale, which suggests new dimensions of solidification processes for nano solid drug dispersions. The solid–liquid interfacial energy (σ), the grain boundary energy (σgb), and the Gibbs–Thomson coefficient (τ) of the drug alloys have been discussed. Interface morphology of the alloys follows the Jackson's surface roughness (α) theory and predicts that faceted growth (α > 2) proceeds in all cases.Supplemental data for this article can be accessed at www.tandfonline.com/gmcl

Thermodynamics of Denaturation Transition of DNA Duplex Oligomers in the Context of Nearest Neighbor Models: A Short Review

In this article, it is shown how additive physical properties of DNA double strand polymers can be expanded in terms of 8 irreducible parameters. This provides self-consistency relations among the corresponding 10 duplex dimer contributions. To allow for oligomer analysis, initiation parameters must be added, and, this adds extra degrees of freedom to the fore mentioned parameters. This modelling permits that nucleation free energies could be calculated as a function of the mean global composition of the chain.

Nucleation free-energy barriers with Hybrid Monte-Carlo/Umbrella Sampling.

The aim of this work is to evaluate nucleation free-energy barriers using molecular dynamics (MD). More specifically, we use a combination of Hybrid Monte Carlo (HMC) and an Umbrella Sampling scheme, and compute the crystallisation barrier of NaCl from its melt. Firstly the convergence and performance of HMC for different time-steps and the number of MD steps within a HMC cycle are assessed. The calculated potential energies and densities converge regardless of the chosen time-step. However the acceptance ratio of the Metropolis step within the HMC scheme strongly depends on the time-step and affects the performance. It is shown that the acceptance ratio is close to 100% for time-steps of the order of those commonly used in molecular dynamics runs. We then explore the results obtained with a "non-Metropolised" version of HMC where the MD trajectories are always accepted (omitting the Metropolis criteria) and conclude that they are satisfactory for time-steps below 5 fs. Next, HMC is combined with Umbrella Sampling (HMC/US) to compute the nucleation free-energy for both the standard and the "non-Metropolised" HMC (using a small time-step) and in both cases find excellent agreement with the reported values. To conclude, we explore approximations to the HMC/US technique implementing HMC with isothermal-isobaric MD trajectories. The computed nucleation free-energy curve is coincident, within the statistical error, with previous calculations.

Sorption Isotherms of Water in Nanopores: Relationship Between Hydropohobicity, Adsorption Pressure, and Hysteresis

The motivation of this study is to elucidate how the condensation and desorption pressures in water sorption isotherms depend on the contact angle. This question is investigated for cylindrical pores of 2.8 nm diameter by means of molecular dynamics simulations in the grand canonical ensemble, in combination with the mW coarse-grained model for water. The contact angle is characterized for different sets of water–surface interactions. First, we show that desorption in open-ended pores with moderate or low water affinity, with contact angles greater or equal than 24°, is a nonactivated process in which pressure is accurately described by the Kelvin equation. Then, we explore the influence of hydrophobicity on the capillary condensation and on the width of the hysteresis loop. We find that a small increase in the contact angle may have a significant impact on the surface density and consequently on the nucleation free energy barrier. This produces a separation of the adsorption and desorption branches, exacerbating the emerging hysteresis. These results suggest that the contact angle is not as relevant as the adsorption energy in determining condensation pressure and hysteresis. Finally, we consider nonequilibrium desorption in pores with no open ends and describe how homogeneous and heterogeneous cavitation mechanisms depend on hydrophilicity.

Phase-Field Modeling of Nucleation in Solid-State Phase Transformations

Nucleation is a critically important process as the rate of nucleation determines the number density of new phase particles and thus microstructures of a material during phase transformations. Predicting and controlling nucleation rates in solids is one of the grand challenges in materials science because the spatial scale involved in nucleation is at the atomic/nanoscale, the rate of nucleation process is extremely temperature sensitive, and the morphology of a critical nucleus can be highly nonspherical and complex. In this article, we briefly review the recent advances in modeling and predicting nucleation during solid-phase transformations based on the diffuse-interface or nonclassical description of critical nucleus profiles. The focus is on predicting the critical nucleus morphology and nucleation free energy barrier under the influence of anisotropic interfacial energy and elastic interactions. Incorporation of nucleation events in phase-field modeling of solid-to-solid phase transformations and microstructure evolution is also discussed.

Correlation between thermodynamic anomalies and pathways of ice nucleation in supercooled water.

The well-known classical nucleation theory (CNT) for the free energy barrier towards formation of a nucleus of critical size of the new stable phase within the parent metastable phase fails to take into account the influence of other metastable phases having density/order intermediate between the parent metastable phase and the final stable phase. This lacuna can be more serious than capillary approximation or spherical shape assumption made in CNT. This issue is particularly significant in ice nucleation because liquid water shows rich phase diagram consisting of two (high and low density) liquid phases in supercooled state. The explanations of thermodynamic and dynamic anomalies of supercooled water often invoke the possible influence of a liquid-liquid transition between two metastable liquid phases. To investigate both the role of thermodynamic anomalies and presence of distinct metastable liquid phases in supercooled water on ice nucleation, we employ density functional theoretical approach to find nucleation free energy barrier in different regions of phase diagram. The theory makes a number of striking predictions, such as a dramatic lowering of nucleation barrier due to presence of a metastable intermediate phase and crossover in the dependence of free energy barrier on temperature near liquid-liquid critical point. These predictions can be tested by computer simulations as well as by controlled experiments.

On the entropic nucleation barrier in a martensitic transformation

The nucleation of martensite in alloys is hindered by a free energy nucleation barrier, hence comprising contributions of the potential energy and the entropy. The leading effect is commonly attributed to the potential energy barrier due to strain fields. In this contribution, we investigate the nature of the entropic barrier by means of molecular dynamics (MD) simulations. We study a transformation process of an undercooled single crystal and examine two nucleation events observed under adiabatic conditions using vibrational mode analysis of the atomic trajectories. Our analysis shows that martensitic nucleations are indicated by transit from a state of uncorrelated into a state of correlated atomic motions. This correlation process is built up locally by a small group of atoms even before the product lattice can be recognized morphologically and it produces vibrational ‘soft’ modes along transformation paths. Phase space analyses unveil that the correlation process is characterized by narrow domains – ‘nucleation channels’ – the atomic trajectories have to pass, connecting the phase space domains of the parent and the product lattice. For a successful nucleation event, the nucleus atoms have to pass this channel collectively, which stochastically represents a rare event. Thermal fluctuations prevent finding the channel at elevated temperature and give rise for entropic stabilization of the parent phase. This ‘entropic nucleation barrier’ is reduced in the undercooled state but still effective, thus preventing the parent phase from collapsing into the product. The entropic barrier may be interpreted as the probability of a group of atoms to simultaneously pass the nucleation channel. Such group then represents a nucleus.

Surface induced nucleation of a Lennard-Jones system on an implicit surface at sub-freezing temperatures: A comparison with the classical nucleation theory

The aggregation-volume-bias Monte Carlo method was employed to study surface-induced nucleation of Lennard-Jonesium on an implicit surface below the melting point. It was found that surfaces catalyze not only the formation of the droplets (where the nucleation free energy barriers were shown to decrease with increasing surface interaction strength), but also the transition of these droplets into crystal structures due to the surface-induced layering effects. However, this only occurs under suitable interaction strength. When surface attraction is too strong, crystallization is actually inhibited due to the spread of the particles across the surface and corresponding formation of two-dimensional clusters. The simulation results were also used to examine the bulk-droplet based classical nucleation theory for surface-induced nucleation, particularly the additional contact angle term used to describe both the nucleation free energy barrier heights and the critical cluster sizes compared to its homogeneous nucleation formalism. Similar to what has been found previously for homogeneous nucleation, the theory does poorly toward the high-supersaturation region when the critical clusters are small and fractal, but the theoretical predictions on both barrier heights and critical cluster sizes improve rapidly with the decrease of the supersaturation.