Spinodal Point Research Articles

Rigidity-Controlled Crossover: From Spinodal to Critical Failure.

Failure in disordered solids is accompanied by intermittent fluctuations extending over a broad range of scales. The implied scaling has been previously associated with either spinodal or critical points. We use an analytically transparent mean-field model to show that both analogies are relevant near the brittle-to-ductile transition. Our study indicates that in addition to the strength of quenched disorder, an appropriately chosen global measure of rigidity (connectivity) can be also used to tune the system to criticality. By interpreting rigidity as a timelike variable we reveal an intriguing parallel between earthquake-type critical failure and Burgers turbulence.

Particle pinning suppresses spinodal criticality in the shear-banding instability.

Strained amorphous solids often fail mechanically by creating a shear band. It had been understood that the shear-banding instability is usefully described as crossing a spinodal point (with disorder) in an appropriate thermodynamic description. It remained contested, however, whether the spinodal is critical (with divergent correlation length) or not. Here we offer evidence for critical spinodal by using particle pinning. For a finite concentration of pinned particles the correlation length is bounded by the average distance between pinned particles, but without pinning it is bounded by the system size.

Prediction and Reasoning for the Occurrence of Lower Critical Solution Temperature in Aqueous Solution of Ionic Liquids

In this work, the combined COSMO-SAC and Pitzer–Debye–Huckel model is used for the prediction of the liquid–liquid equilibrium for 252 binary ionic liquid solutions, including 234 LCST (lower critical solution temperature)-negative mixtures and 18 LCST-positive mixtures. It is found that the combined model provides qualitative description of the mutual solubility of LCST-negative mixtures (AAD-x1 = 0.2451 and AAD-x2 = 0.04635) and LCST-positive mixtures (AAD-x1 = 0.3522 and AAD-x2 = 0.009418) when compared to experimental data. The model can also be used for the prediction of the LCST of such aqueous solutions. Though the ARD% of predicted lower critical solution temperatures is about 40%, the model usually provides correct relative LCST of different IL solutions. We found that the temperature derivative of the Gibbs free energy of mixing at the spinodal points provides very useful information regarding the occurrence of the critical solution behaviors. The fact that the model does not require any species...

On the canonical isotherms for bulk fluid, surface adsorption and adsorption in pores: A common thread

Kinetic Monte Carlo simulated isotherms calculated in the canonical ensemble, at temperatures below the critical temperature, for bulk fluid, surface adsorption and adsorption in a confined space, show a van der Waals (vdW) loop with a vertical phase transition between the rarefied and dense spinodal points at the co-existence chemical potential, µco. Microscopic examination of the state points on this loop reveals features that are common to these systems. At state points with chemical potentials greater than μco the microscopic configurations show clusters, which coalesce to form two co-existing phases along the vertical section of the loop (the coexistence line). As more molecules are added, the dense region expands at the expense of the rarefied region, to the point where the rarefied region becomes spherical (cylindrical for 2D-systems) with a curvature greater than that of the coexisting phases. This results in a decrease of chemical potential from µco to the liquid spinodal point where the rarefied region disappears. With a further increase in loading, the chemical potential and the density increase. The existence of a vdW loop is the microscopic reason for the hysteresis observed in the grand canonical isotherm, where the adsorption and desorption boundaries of the hysteresis loop are first-order transitions, enclosing the vertical section of the vdW loop of the canonical isotherm. However, a first-order transition is rarely observed in experiments where transitions are usually steep, but not vertical. From our extensive simulations, we provide two possible reasons: (1) the finite extent of the system and (2) the existence of high energy sites that localize the clusters. In the first case, the desorption branch, and in the second case the adsorption branch, either comes close to, or collapses onto the coexistence line. When both occur, the hysteresis loop disappears and the isotherm is reversible, as often observed experimentally.

Liquid State of One-Dimensional Bose Mixtures: A Quantum Monte Carlo Study

By using exact quantum MonteCarlo methods we calculate the ground-state properties of the liquid phase in one-dimensional Bose mixtures with contact interactions. We find that the liquid state can be formed if the ratio of coupling strengths between interspecies attractive and intraspecies repulsive interactions exceeds a critical value. As a function of this ratio we determine the density where the energy per particle has a minimum and the one where the compressibility diverges, thereby identifying the equilibrium density and the spinodal point in the phase diagram of the homogeneous liquid. Furthermore, in the stable liquid state, we calculate the chemical potential, the speed of sound, as well as structural and coherence properties, such as the pair correlation function, the static structure factor, and the one-body density matrix, thus providing a detailed description of the bulk region in self-bound droplets.

Three-dimensional simulation of dual-scale deposition structures from evaporative self-assembly of nanofluid films

Self-assembly of nanomaterials from the drying of nanofluid films has aroused great interest due to its applications in micro/nano fabrication, ink-jet printing, and thin film coatings. Numerical models are developed to investigate the single-scale deposition structures from the drying of nanofluid films, including network structures, continuous labyrinthine, branched structures and micro-sized rings. In the case of the actual drying of nanofluid films, dual-scale cellular networks and nano-rings are also discovered. In order to study the formation mechanism of dual-scale deposition structures, a three-dimensional kinetic Monte Carlo model is developed based on two-dimensional lattice gas model, and the dynamic chemical potential which couples solvent evaporation rate is implemented. Different dynamic chemical potentials are defined for each layer of the thin-film in the model to mimic the real evaporation situation. Considering the Brownian motion and the interaction between particles, the formation of dual-scale cellular networks and nano-rings coexisting with small scale patternis achieved via coupling the chemical potential to the solvent evaporation rate. The simulation results accord well with the results from many experimentally studied de-wetting systems. The effects of the chemical potential sharpness and critical evaporation rate of fluids on the dual-scale deposition structures are discussed. It can be found that the evaporation mode of thin-film is dominated by nucleation and growth at the initial stage. If the spinodal point is passed, the residual solvent will evaporate suddenly, and the nanoparticles do not accumulate further but directly deposit into small-scale structures, thus forming a dual-scale deposition structures at the final stage of the evaporation. The simulation results also show that the chemical potential sharpness will affect the deposition structure after the mutation in a certain range. When the chemical potential sharpness equals zero, the sedimentary structure is the same as the single-scale sedimentary structure when the constant chemical potential is applied. When the chemical potential sharpness is small, the large-scale network structure interacts closely with the small-scale network structure. With the increase of chemical potential sharpness, the large-scale deposition structure remains unchanged, while the dense small-scale network structure becomes small-scale point structure. When the chemical potential sharpness exceeds a certain large value, the effect of chemical potential sharpness on the deposition structure will gradually decrease, and finally the dual-scale deposition structure will remain unchanged. The critical evaporation rate of fluids determines the area ratio of the two kind of structures in the dual-scale deposition. With the increase of the critical evaporation rate of fluids, the area ratio of small-scale structures decreases while that of the large-scale structure increases. When critical evaporation rate increases to a certain value, the final deposition structure will evolve into a single-scale deposition structure.

Size-dependent phase morphologies in LiFePO4 battery particles

Lithium iron phosphate (LiFePO4) is the prototypical two-phase battery material whose complex patterns of lithium ion intercalation provide a testing ground for theories of electrochemical thermodynamics. Using a depth-averaged (a-b plane) phase-field model of coherent phase separation driven by Faradaic reactions, we reconcile conflicting experimental observations of diamond-like phase patterns in micron-sized platelets with observations of surface-controlled patterns in nanoparticles. Elastic analysis predicts this morphological transition for particles whose a-axis dimension exceeds twice the bulk elastic stripe period. We also simulate a rich variety of non-equilibrium patterns, influenced by size-dependent spinodal points and electro-autocatalytic control of thermodynamic stability.

Vacuum structure of Yang-Mills theory as a function of \u03b8

It is believed that in SU(N) Yang-Mills theory observables are N -branched functions of the topological θ angle. This is supposed to be due to the existence of a set of locally-stable candidate vacua, which compete for global stability as a function of θ. We study the number of θ vacua, their interpretation, and their stability properties using systematic semiclassical analysis in the context of adiabatic circle compactification on ℝ3 × S1. We find that while observables are indeed N-branched functions of θ, there are only ≈ N/2 locally-stable candidate vacua for any given θ. We point out that the different θ vacua are distinguished by the expectation values of certain magnetic line operators that carry non-zero GNO charge but zero ’t Hooft charge. Finally, we show that in the regime of validity of our analysis YM theory has spinodal points as a function of θ, and gather evidence for the conjecture that these spinodal points are present even in the ℝ4 limit.

On spinodal points and Lee-Yang edge singularities

We address a number of outstanding questions associated with the analytic properties of the universal equation of state of the theory, which describes the critical behavior of the Ising model and ubiquitous critical points of the liquid–gas type. We focus on the relation between spinodal points that limit the domain of metastability for temperatures below the critical temperature, i.e. , and Lee-Yang edge singularities that restrict the domain of analyticity around the point of zero magnetic field for . The extended analyticity conjecture (due to Fonseca and Zamolodchikov) posits that, for , the Lee-Yang edge singularities are the closest singularities to the real axis. This has interesting implications, in particular, that the spinodal singularities must lie off the real axis for , in contrast to the commonly known result of the mean-field approximation. We find that the parametric representation of the Ising equation of state obtained in the expansion, as well as the equation of state of the -symmetric theory at large , are both nontrivially consistent with the conjecture. We analyze the reason for the difficulty of addressing this issue using the ε expansion. It is related to the long-standing paradox associated with the fact that the vicinity of the Lee-Yang edge singularity is described by Fisher’s theory, which remains nonperturbative even for , where the equation of state of the theory is expected to approach the mean-field result. We resolve this paradox by deriving the Ginzburg criterion that determines the size of the region around the Lee-Yang edge singularity where mean-field theory no longer applies.

Stability limits and consolute critical conditions for liquid mixtures

ABSTRACTThis work addresses the determination of stability limits and consolute critical conditions for multicomponent liquid mixtures. Using the NRTL model, thermodynamic stability and criticality criteria are implemented for ternary liquid mixtures to predict stability limit loci and critical composition at its specified temperature and pressure. The method is general and applicable for the prediction of spinodal curves and critical points for liquid–liquid-phase transitions in multicomponent liquid mixture using liquid–liquid equilibrium data even over a limited range of composition. Stability limits’ loci for 18 aqueous and 3 nonaqueous ternary liquid mixtures were used in validating the method. For ternary systems that were studied over the whole composition range including the critical zone, where experimental compositions at the critical point were available, the predicted results agree with the experimental measurements within 0.7 mol%.

Mechanical failure in amorphous solids: Scale-free spinodal criticality.

The mechanical failure of amorphous media is a ubiquitous phenomenon from material engineering to geology. It has been noticed for a long time that the phenomenon is "scale-free," indicating some type of criticality. In spite of attempts to invoke "Self-Organized Criticality," the physical origin of this criticality, and also its universal nature, being quite insensitive to the nature of microscopic interactions, remained elusive. Recently we proposed that the precise nature of this critical behavior is manifested by a spinodal point of a thermodynamic phase transition. Demonstrating this requires the introduction of an "order parameter" that is suitable for distinguishing between disordered amorphous systems. At the spinodal point there exists a divergent correlation length which is associated with the system-spanning instabilities (known also as shear bands) which are typical to the mechanical yield. The theory, the order parameter used and the correlation functions which exhibit the divergent correlation length are universal in nature and can be applied to any amorphous solid that undergoes mechanical yield. The phenomenon is seen at its sharpest in athermal systems, as is explained below; in this paper we extend the discussion also to thermal systems, showing that at sufficiently high temperatures the spinodal phenomenon is destroyed by thermal fluctuations.

Shear bands as manifestation of a criticality in yielding amorphous solids

Amorphous solids increase their stress as a function of an applied strain until a mechanical yield point whereupon the stress cannot increase anymore, afterward exhibiting a steady state with a constant mean stress. In stress-controlled experiments, the system simply breaks when pushed beyond this mean stress. The ubiquity of this phenomenon over a huge variety of amorphous solids calls for a generic theory that is free of microscopic details. Here, we offer such a theory: The mechanical yield is a thermodynamic phase transition, where yield occurs as a spinodal phenomenon. At the spinodal point, there exists a divergent correlation length that is associated with the system-spanning instabilities (also known as shear bands), which are typical to the mechanical yield. The theory, the order parameter used, and the correlation functions that exhibit the divergent correlation length are universal in nature and can be applied to any amorphous solids that undergo mechanical yield.

Comparison of predictions of the PC-SAFT equation of state and molecular simulations for the metastable region of binary mixtures

The metastable region of binary mixtures is examined with the PC-SAFT equation of state (EOS) and compared to molecular simulations. The studied mixtures are Methane + Ethane, Methanol + Ethanol, Carbon Dioxide + Toluene, Carbon Dioxide + Hydrogen Chloride and Hydrogen Chloride + Toluene. In order to calculate the spinodal, the second partial derivatives with respect to the components molarities are analytically determined for the PC-SAFT EOS. Thermal properties as well as the spinodal points determined using PC-SAFT and molecular simulation are compared. For the studied metastable gas phases the results obtained with PC-SAFT and the molecular simulations agree well. For liquid phases the metastable region calculated with the PC-SAFT EOS is typically broader than that obtained from the molecular simulations. No unphysical results were obtained with PC-SAFT for metastable states. Hence, PC-SAFT EOS is found to be principally suitable for predicting metastable states and spinodals of mixtures.

Shear Yielding and Shear Jamming of Dense Hard Sphere Glasses.

We investigate the response of dense hard sphere glasses to a shear strain in a wide range of pressures ranging from the glass transition to the infinite-pressure jamming point. The phase diagram in the density-shear strain plane is calculated analytically using the mean-field infinite-dimensional solution. We find that just above the glass transition, the glass generically yields at a finite shear strain. The yielding transition in the mean-field picture is a spinodal point in presence of disorder. At higher densities, instead, we find that the glass generically jams at a finite shear strain: the jamming transition prevents yielding. The shear yielding and shear jamming lines merge in a critical point, close to which the system yields at extremely large shear stress. Around this point, highly nontrivial yielding dynamics, characterized by system-spanning disordered fractures, is expected.

Confinement effects on phase separation of a polyelectrolyte solution

Formulating an analytical theory, we study phase separation of a polyelectrolyte solution under poor solvent condition confined in three types of finite geometric spaces: slab, cylinder, and sphere. Divided by a Lifshitz line, bulk polyelectrolyte solution undergoes either micro- or macro-phase separation. Confinement effects for both scenarios are studied. Composition fluctuations inducing phase separation are classified in terms of eigenmodes of the inverse structure factor operator in the corresponding geometric spaces. Tracking each eigenmode, the instability lines under confinement effects are derived in closed forms. For the confined microphase separation, we find a decaying oscillatory dependence of the spinodal point on the confinement size, which represents the commensurability between the finite period of the soft mode and the confining boundary size. For the confined macrophase separation, a typical mean-field finite size scaling of the Ising universality class is observed under the strong screening condition.

Direction and pressure response of osmotic pressure in binary polymer solutions

Using a molecular equation-of-state (EOS) theory, I discuss the direction and pressure response of osmotic pressure П for a composite system with a pure solvent and its non-ideal solution of a polymeric component separated by a semi-permeable membrane. A perturbed hard sphere chain model is chosen here for the EOS to estimate П in a general way while pressure is applied. It is shown that П is a phase behavior in connection with the phase stability of the solution. In case of an incompatible pair upon forcing a single phase, there exists a region inside the binodal line for negative П possessing a spinodal point as the threshold of П=0. It is the potential energy term that contributes to the negative П and drives solvent molecules away from polymers. Those actions are reversed when phase separation occurs on the solution side. In addition, it is revealed that the solution responds to pressure with either increase or decrease in П upon pressurization, which depends on the pressure coefficients of spinodals and solvent compressibility.

Alternative method to characterize continuous and discontinuous phase transitions in surface reaction models

In this paper we revisited the Ziff-Gulari-Barshad model to study its phase transitions and critical exponents through time-dependent Monte Carlo simulations. We use a method proposed recently to locate the nonequilibrium second-order phase transitions and that has been successfully used in systems with defined Hamiltonians and with absorbing states. This method, which is based on optimization of the coefficient of determination of the order parameter, was able to characterize the continuous phase transition of the model, as well as its upper spinodal point, a pseudocritical point located near the discontinuous phase transition. The static critical exponents β,ν_{∥}, and ν_{⊥}, as well as the dynamic critical exponents θ and z for the continuous transition point, were also estimated and are in excellent agreement with results found in literature.

Fluctuation effects in metastable states near first-order phase transitions

Fluctuation effects at first-order phase transitions driven by changes of other-than-temperature factors like pressure, concentration or external fields are investigated by perturbation theory. The results for the fluctuation contributions to the order parameter, the internal energy and the free energy at pre-transitional states near spinodal points of first-order phase transitions are presented to the first-nonvanishing order of the expansion parameters of the theory.

Critical phenomena at a first-order phase transition in a lattice of glow lamps: Experimental findings and analogy to neural activity.

Networks of non-linear electronic oscillators have shown potential as physical models of neural dynamics. However, two properties of brain activity, namely, criticality and metastability, remain under-investigated with this approach. Here, we present a simple circuit that exhibits both phenomena. The apparatus consists of a two-dimensional square lattice of capacitively coupled glow (neon) lamps. The dynamics of lamp breakdown (flash) events are controlled by a DC voltage globally connected to all nodes via fixed resistors. Depending on this parameter, two phases having distinct event rate and degree of spatiotemporal order are observed. The transition between them is hysteretic, thus a first-order one, and it is possible to enter a metastability region, wherein, approaching a spinodal point, critical phenomena emerge. Avalanches of events occur according to power-law distributions having exponents ≈3/2 for size and ≈2 for duration, and fractal structure is evident as power-law scaling of the Fano factor. These critical exponents overlap observations in biological neural networks; hence, this circuit may have value as building block to realize corresponding physical models.

ChemInform Abstract: Entropic Phase Transitions and Accompanying Anomalous Thermodynamics of Matter

Thermodynamic consequences of subdivision for all first-order phase transitions (PT) into enthalpy- and entropy-driven ones (H-PT and S-PT), proposed previously [arXiv:1403.8053], are under discussions. Key-value for proposed discrimination is main benefit (decreasing) in enthalpy or (nega)entropy in spontaneous phase decomposition, i.e. the sign of latent heat of PT and consequent slope of its P(T)-dependence. The main driving mechanism for many isostructural S-PT is the decay (delocalization) of some kind of bound complexes, e.g. atoms, molecules etc. Thermodynamic features of H-PT and S-PT differ significantly. Entropic PT are always the part of more general thermodynamic anomaly—domain where great number of usually positive second cross derivatives (e.g. Gruneisen parameter, thermal pressure coefficient etc.) became negative simultaneously. This domain is restricted (in the case of isostructural S-PT) by remarkable bound, where all mentioned second derivatives are equal to zero. Isostructural S-PT has more complicated topology of stable, metastable and unstable states and their boundaries—binodals and spinodals in comparison with ordinary enthalpic PTs. Two new thermodynamic objects accompany isostructural S-PT: (i) appearance of third (additional) region of metastable states with positive compressibility, isolated from the regions of stable states; (ii) appearance of new additional spinodal, topped with a new singular point, separating metastable and unstable states. These additional spinodal and singular point obey to relation (∂P/∂V)T = ∞. All thermodynamic anomalies of entropic PTs correspond to conclusive and transparent geometrical feature of such PTs: multilayered structure of thermodynamic surfaces for temperature, entropy and internal energy as pressure- density functions U(P, V), S(P, V) and T(P, V).