Metastable System Research Articles

Controlled perturbation of the thermodynamic equilibrium by microfluidic separation of porphyrin-based aggregates in a multi-component self-assembling system

In a microfluidic H-cell, a multi-component self-assembled system is brought out-of-equilibrium by changing the bimodal composition of porphyrin stacks and pyridine-capped dimers. Driven by their different diffusivities, diffusion-controlled separation in methylcyclohexane reveals different compositions when detected in-line and off-line, which demonstrates the kinetic behaviour of this metastable system. The microfluidic technique also proves to be highly equipped to determine diffusion constants of the different assemblies.

METASTABLE SYSTEMS AS RANDOM MAPS

Metastable dynamical systems were recently studied [González-Tokman et al., 2011] in the framework of one-dimensional piecewise expanding maps on two disjoint invariant sets, each possessing its own ergodic absolutely continuous invariant measure (acim). Under small deterministic perturbations, holes between the two disjoint systems are created, and the two ergodic systems merge into one. The long term dynamics of the newly formed metastable system is defined by the unique acim on the combined ergodic sets. The main result of [González-Tokman et al., 2011] proves that this combined acim can be approximated by a convex combination of the disjoint acims with weights depending on the ratio of the respective measures of the holes. In this note we present an entirely different approach to metastable systems. We consider two piecewise expanding maps: one is the original map, τ1, defined on two disjoint invariant sets of ℝN and the other is a deterministically perturbed version of τ1, τ2, which allows passage between the two disjoint invariant sets of τ1. We model this system by a position dependent random map based on τ1 and τ2, to which we associate position dependent probabilities that reflect the switching between the maps. A typical orbit spends a long time in one of the ergodic sets but eventually switches to the other. Such behavior can be attributed to physical holes as between adjoining billiard tables or more abstract situations where balls can "leap" from one table to the other. Using results for random maps, a result similar to the one-dimensional main result of [González-Tokman et al., 2011] is proved in N dimensions. We also consider holes in more than two invariant sets. A number of examples are presented.

Calculating the Lifetimes of Metastable States with Complex Density Functional Theory.

Among other applications, complex absorbing potentials (CAPs) have proven to be useful tools in the theory of metastable states. They facilitate the conversion of unbound states of a finite lifetime into normalized bound states with a complex energy. Adding CAPs to a conventional Hamiltonian turns it into a non-Hermitian operator. Recently, we introduced a complex density functional theory (CODFT) that extends the Kohn-Sham method to the realm of non-Hermitian systems. Here, we combine CAPs with CODFT and present the first application of CODFT to metastable systems. In particular, we consider the negative ions of the beryllium atom and the nitrogen molecule. Using conventional exchange-correlation functionals as functionals of a complex density, the resonance positions and the resonance lifetimes are obtained, and they are in line with the findings of other studies.

Controlling the noise enhanced stability effect via noise recycling in a metastable system

We analyze the role of the delay time τ d and the fraction e of recycled noise on the enhancement of the mean first-passage time (MFPT) in a metastable system with recycled noise, generated by the superposition of a primary Gaussian noise source with a second component of constant delay. The results indicate that MFPT as a function of the noise intensity D shows either a non-monotonic behavior with a maximum or a divergent behavior, which is the identifying characteristic of the noise enhanced stability (NES) phenomenon. The increasing of τ d or e strengthens the NES effect for e > 0. However, for e < 0, there is a critical value of τ d , below which we observe an increase of MFPT whose maximum goes to infinity, and above which the divergent behavior tends to disappear and MFPT versus D shows a transition from one peak to two peaks and eventually one peak as τ d or |e| increases. Moreover, we also discuss the effect of different initial conditions. These observations illustrate that the noise recycling may be used as an effective scheme for controlling the NES effect.

Pointwise estimates and exponential laws in metastable systems via coupling methods

We show how coupling techniques can be used in some metastable systems to prove that mean metastable exit times are almost constant as functions of the starting microscopic configuration within a “meta-stable set.” In the example of the Random Field Curie Weiss model, we show that these ideas can also be used to prove asymptotic exponentiallity of normalized metastable escape times.

RELAXATION PHENOMENA IN CLASSICAL AND QUANTUM SYSTEMS

classical and quantum systems are investigated. First, the role of multiplicative and additive noise in a classical metastable system is analyzed. The mean lifetime of the metastable state shows a nonmonotonic behavior with a maximum as a function of both the additive and multiplicative noise intensities. In the second system, the simultaneous action of thermal and non-Gaussian noise on the dynamics of an overdamped point Josephson junction is studied. The eect of a Levy noise generated by a Cauchy‐Lorentz distribution on the mean lifetime of the superconductive metastable state, in the presence of a periodic driving, is investigated. We find resonant activation and noise enhanced stability in the presence of Levy noise. Finally, the time evolution of a quantum particle moving in a metastable potential and interacting with a thermal reservoir is analyzed. Within the Caldeira‐Legget model and the Feynman‐Vernon functional approach, we obtain the time evolution of the population distributions in the position eigenstates of the particle, for dierent values of the thermal bath coupling strength.

Fluctuation-induced non-equilibrium transition in a liquid-crystal metastable system

The research herein studies the Langevin dynamics that allows for an exchange of energy between liquid crystals and the thermal environment. This dynamics leads to fluctuation and dissipation behaviors in the motions of liquid crystals, and therefore drives the system toward non-equilibrium evolutional processes. In particular, for the operations of liquid-crystal metastable systems, the fluctuation could allow an excitation (non-equilibrium) transition against energy barriers to the globally-stable state. Implemented with an actual case of liquid crystal π configuration, this work statistically studies the non-equilibrium metastable transitions and shows the dependence of the transition-time on the correlations (of fluctuations).

Interplay of formulation and process methodology on the extent of nifedipine molecular dispersion in polymers

The aim of this study is to evaluate effects of formulation and process technology on drug molecular dispersibility in solid dispersions (SDs). Nifedipine solid dispersions with ethylcellulose (EC) and/or Eudragit RL (RL) prepared by co-precipitation, co-evaporation, and fusion methods were characterized with FTIR, DSC, and XRPD for the content of nifedipine as molecular dispersion, amorphous and/or crystalline suspensions. A method was developed based on regular solution and Flory–Huggins theories to calculate drug–polymer interaction parameter in solid dispersion systems. A synergic effect of RL and EC on nifedipine molecular dispersibility in solid dispersions was observed. Increasing RL/EC ratio resulted in a higher degree of drug–polymer interaction that thermodynamically favored molecular dispersion, which, however, was counteracted by a corresponding decrease in the matrix glass transition point that kinetically favored phase-separation. Process methodology was found to play an important role in the formation of amorphous SD. The ranking of technologies with respect to the extent of molecular dispersion from high to low is fusion > co-evaporation > co-precipitation, wherein the solidification rate of polymeric solution and non-solvent effects were linked to kinetic entrapment of drug molecules in polymeric networks. Since nifedipine molecular dispersibility in EC/RL polymer(s) is a result of interplay between thermodynamic and kinetic factors, nifedipine molecular dispersions prepared for this study are thermodynamically metastable systems. To explore those supersaturation systems for use in drug delivery of poorly water soluble drugs, it is critical to balance drug–polymer interactions and matrix glass transition point and to consider a process technology with a fast solidification rate during formulation and process development of amorphous SD.

The effect of surface tension on liquid–gas equilibria in isochoric systems and its application to fluid inclusions

We present a thermodynamic model to analyse the effect of surface tension on the size evolution and disappearance of a vapour bubble in an isochoric pure water system. The model relies on the minimisation of the Helmholtz energy of the system, derived from the iapws-95 formulation, and predicts the thermodynamic state, the vapour bubble radius, and the densities and pressures of the liquid and the vapour phase at a given temperature, volume, and mean density. The model reveals a transition from the stable to the metastable two-phase system, representing a bubble binodal, where both the liquid–vapour and the homogeneous liquid state can be stable. Furthermore, the transition from the metastable to the unstable two-phase system denotes the bubble spinodal, where the vapour bubble collapses from a non-zero radius upon homogenisation to the stable liquid state that extends to negative pressures. The model can be applied to the analysis of fluid inclusions in minerals of relevance for paleoclimatology, where the surface tension significantly influences the temperature of liquid–vapour homogenisation. It allows to calculate the formation density and the volume of a fluid inclusion from the observed homogenisation temperature and the measured bubble radius.

Metastable Phase Equilibrium in the Aqueous Ternary System Li2SO4 + MgSO4 + H2O at 323.15 K

The metastable solubilities and physicochemical properties (densities and refractive index) of the aqueous ternary system (Li2SO4 + MgSO4 + H2O) at 323.15 K were determined by the isothermal evaporation method. According to the experimental results, the metastable phase diagram and the diagram of physicochemical properties versus composition were plotted. It was found that there are one eutectic point (Li2SO4·H2O + MgSO4·6H2O), two univariant curves, and two crystallization regions corresponding to lithium sulfate monohydrate (Li2SO4·H2O) and hexahydrite (MgSO4·6H2O) in the metastable ternary system. The system belongs to a simple eutectic type, and neither double salts nor solid solutions were found. It can be found that the solution density and refractive index of the metastable ternary system changed regularly with the content change of lithium sulfate, and all reach the maximum value at eutectic point. The calculated values of densities and refractive index with empirical equations are in good agreement with the experimental data.

Escape of Brownian particles and stochastic resonance with low-temperature quantum fluctuations

In this paper, we investigate the escape of Brownian particles and stochastic resonance (SR) with low-temperatures quantum fluctuations by using the quantum Smoluchowski equations at low-temperature. Two specific examples have been considered: one is the example of bistable system, and the other is the example of metastable system. The explicit expressions of the mean-first passage time (MFPT) and signal-to-noise ratio (SNR) for both specific examples are obtained, respectively. Based on the numerical computations, we compare the quantum case with its classical counterpart. Our research results show that: (i) the quantum effect accelerates the escape of the Brownian particle in comparison with the classical result and (ii) the quantum effect enhances the SR in the SNR as a function of β for a bistable system (i.e., β = 1/k B T, k B is the Boltzmann constant and T is the temperature), while for a metastable system, the β amplifies the quantum effects, and the quantum effect weakens the SNR as a function of β.

Metastable Phase Equilibrium in the Aqueous Ternary System (MgCl2+ MgSO4+ H2O) at 308.15 K

The metastable solubilities and the refractive indices in the aqueous ternary system (MgCl2 + MgSO4 + H2O) at 308.15 K were determined with the method of isothermal evaporation, and the metastable phase diagram and the diagram of refractive index versus composition were plotted. Four two-salt cosaturated points of epsomite (MgSO4·7H2O, Eps) + hexahydrite (MgSO4·6H2O, Hex), Hex + pentahydrite (MgSO4·5H2O, Pen), Pen + tetrahydrite (MgSO4·4H2O, Tet), and Tet + bischofite (MgCl2·6H2O, Bis), five isothermal univariant curves, and five metastable crystallization fields corresponding to Eps, Hex, Pen, Tet, and Bis were formed in the metastable ternary system. A comparison of the stable and metastable phase diagrams of the ternary system at 308.15 K shows that one more metastable crystallization field is formed. Neither a solid solution nor double salts are found. The solubility predictions of the metastable ternary system at 308.15 K based on Pitzer’s ion-interaction model and its extended Harvie−Weare (HW) model are presented, and the calculated results were in good agreement with the experimental results.

Structural memory of natively unfolded tau protein detected by small‐angle X‐ray scattering

Small-angle X-ray scattering (SAXS) is a universal low-resolution method to study size and shape of globular proteins in solution but recent developments facilitate the quantitative characterization of the structure and structural transitions of metastable systems like partially or completely unfolded proteins. We present here a study of temperature induced transitions in tau, a natively unfolded protein involved in Alzheimer's disease. Previous studies on full length tau and several disease-related mutants provided information about the residual structure in different domains revealing a specific role and extended conformations of the so-called repeat domains, which are considered to be responsible for the formation of amyloid-like fibrils ("paired helical filaments"). Here, we employ SAXS to investigate the temperature dependent properties of tau. Slow heating/cooling of the full length protein from 10°C to 50°C did not lead to detectable changes in the overall size. Surprisingly, quick heating/cooling caused tau to adopt a significantly more compact conformation, which was stable over up to 3 h and represents a structural "memory" effect. This compaction is not observed for the shorter tau constructs containing largely the repeat domains. The structural and functional implications of the observed unusual behavior of tau under nonequilibrium conditions are discussed.

Additional Comments on “An Essay on Contact Angle Measurements” by M. Strobel and C. S. Lyons

After the impact of the great review of M. Strobel and C. S. Lyons on contact angle measurements, we discuss some claims of the authors. The Wilhelmy method is not generally “the best technique for measuring the contact angle hysteresis” as the authors claimed. Otherwise, we think that, even though equilibrium contact angle is an “unattainable” angle, the most-stable contact angle obtained from the system relaxation is experimentally accessible. The most-stable contact angle is energetically significant for evaluating quantitatively the surface energy value of rough, chemically homogeneous surfaces from the Wenzel equation, and the average surface energy of smooth, chemically heterogeneous surfaces from the Cassie equation. The most-stable contact angle, the advancing contact angle and the receding contact angles enable the thermodynamic description of the range of contact angle hysteresis and the distribution of metastable system configurations.

On two approaches to determination of the nucleation rate of a new phase in computer experiments

The present paper gives a comparative evaluation of two approaches to the determination of the homogeneous nucleation rate in molecular dynamics computer experiments, viz. the methods of the mean lifetime of a metastable system and the mean time of the first passage to a cluster of a prescribed size. The crystal nucleation rate in a supercooled Lennard–Jones liquid has been determined in molecular dynamics simulation as a function of pressure at a reduced temperature T* = 0.55. The results of simulation have been compared with classical homogeneous nucleation theory. Good agreement between theory and the results of computer simulation has been found.

Noise enhanced stability effect in a metastable system with two different kinds of time delays and cross-correlated noises

We numerically investigate the influences of the time delay τ simultaneously existing in both the deterministic and fluctuating forces, the time delay τr existing only in the fluctuating force and the cross-correlation strength λ on the enhancement of the mean first-passage time (MFPT) as a function of the additive D and the multiplicative α noise intensities in a metastable system. The results indicate that both the multiplicative and additive noises can induce the noise-enhanced stability (NES) effect. An increase of λ can enhance or weaken the NES effect induced by the additive noise, depending on the value of τ. However, it weakens the NES effect induced by the multiplicative noise with a suppression of the effect of λ caused by increasing τ. The τ-induced critical behavior on both NES effects can be observed, i.e. an increase of τ can enhance or restrain the NES effects induced by the two kinds of noises. With an increase of λ and τ, MFPT versus D shows a transition from one peak to two peaks and finally one peak, implying the multiple NES effect caused by λ and τ. An increase of τr can enhance the NES effect induced by the additive noise and weaken the NES effect induced by the multiplicative noise.

Adjusting framework ionicity to favour crystallisation of zeolites with strained structural units. Periodic quantum chemical studies

Porosity in silicates is reached against the thermodynamic trend that favours the formation of the most dense phases. Porous silica materials, like Si-zeolites, are, therefore, metastable systems that take and keep their shape upon crystallisation and further calcination owing to a compromise between rigidity and flexibility of the various structural units. It is shown that, in the synthesis of porous silicates, one of the key effects that drive crystallisation is the framework ionicity in the as-made phase. This favours the formation of structural units which in the pure silica form are remarkably strained and barely stable. In this Perspective article, we employ ab initio quantum chemical results to analyse the influence of the polarisation of T–O bonds and, therefore, framework ionicity, in the synthesis of two types of zeolites: frameworks with cations more electropositive than Si and pure silica materials crystallised in the fluoride medium. It is shown that the enhancement of the structural flexibility driven by electronic effects in these cases favours the formation of structures with strained sub-units that in other synthesis conditions could not be reached.

The Dominant Role of the Crack-tip Mechanical Environment into the Cyclic Response

The process-zone characterization provides an essential pillar in forming the crack stability equation. Thus both, the driving force and the material resistance require comprehensive local exploration in the framework of a global mechanical response envelope. The present study consisted on iron-based single crystals and polycrystalline metastable austenitic stainless steel systems. In both, by following micro-structural and mechanical characterization, fatigue tests have been conducted including load and hydrogen interactions. Assisted by novel techniques, the investigation procedure have been supplemented by ultra fine scale visualization and acoustic emission tracking. Considering the sub-critical crack regime retardation the line profiles of two defined but different process zones have been compared. The single crystal activities provided experimental/theoretical insight into the basic aspects of deformation/hydrogen interaction supported by computational mechanics and simulations. Particularly in interactive cases the combined contribution of mechanical and material science to conceptual issues becomes highly promising.

Novel Micro- and Nano-particles Cellulose Based Pickering Emulsions.

AbstractEmulsions are usually metastable systems of two non-miscible phases stabilized by surface active species like surfactant molecules. Emulsions stabilized by solid colloidal particles adsorbed at the interface (Pickering emulsions) offer some competitive advantages with respect to classical emulsions. Most studies published up to now concern emulsions stabilized by inorganic (metallic oxides, exfoliated clays, carbonates and phosphates) or polymeric particles while biomass derived alternatives have only been explored to a limited extent. For the first time, we report the stabilization of emulsions by unmodified cellulose nanocrystals [1, 2] . Cellulose nanocrystals were produced from bacterial cellulose and used to form Pickering emulsions. We demonstrate by SEM that the nanocrystals are adsorbed at the oil/water interface. We also study the size distribution of the droplets that was found to range around 4μm in diameter with very narrow dispersity. The stability of the emulsions was also investigated. The fabrication of new armored microparticles exposing cellulose acicular nanocrystals from cellulose nanocrystals opens opportunities to build materials from low cost and environmental friendly resource.

Lecithin-based nanoemulsions

Lipid-based emulsions with particle sizes in the submicron range have been extensively investigated as vehicles for various active agents during the last decades. This review summarizes the current knowledge about nanoemulsions with a special focus on nanoemulsions comprising lecithin as the main emulsifier. A short introduction is given on the origin of lecithin-based nanoscale emulsions and the properties of these metastable systems. The differences between nanoemulsions and microemulsion phases are highlighted and recent discrepancies in terminology are discussed. Furthermore, the peculiarities of lecithin as emulsifying agent are presented. The production and optimization of nanoemulsions as well as the controversy concerning the different proposed production methods is another important aspect that is covered in detail. Moreover, general information about the stability and characterization of lecithin-based nanoemulsions is included. The last part of the review deals with current applications and research focuses with emphasis on the application of lecithin-based nanoemulsions on skin.