Van Der Waals Loop Research Articles

Sensitivity of magnetohydrodynamic simulations of Joule-heated conductors to the vaporization curve in equations of state.

Magnetohydrodynamic (MHD) simulations of electrically exploded aluminum and copper rods demonstrate a technique to validate equationsof state (EOS) for rapidly Joule-heated conductors. The balance of internal and magnetic forces at the conductor-insulator interface drives the metal there along the vaporization phase boundary. Variations between critical points and vaporization curves in existing models predict differing densities and temperatures in MHD simulations for these models. The inclusion of Maxwell constructs in the liquid-vapor biphase region of the EOS caused the rod surface to vaporize earlier in time than unmodified tables with van der Waals loops. Velocimetry of recent experiments is used to validate the location of the vaporization curve in existing EOS models and differentiate between the vapor dome treatments. Dielectric coatings applied to the metal surface restricted the conductor's expansion and diverted the metal into the warm dense matter regime.

Computational investigation of hysteresis and phase equilibria of n-alkanes in a metal-organic framework with both micropores and mesopores

Adsorption hysteresis is a phenomenon related to phase transitions that can impact applications such as gas storage and separations in porous materials. Computational approaches can greatly facilitate the understanding of phase transitions and phase equilibria in porous materials. In this work, adsorption isotherms for methane, ethane, propane, and n-hexane were calculated from atomistic grand canonical Monte Carlo (GCMC) simulations in a metal-organic framework having both micropores and mesopores to better understand hysteresis and phase equilibria between connected pores of different size and the external bulk fluid. At low temperatures, the calculated isotherms exhibit sharp steps accompanied by hysteresis. As a complementary simulation method, canonical (NVT) ensemble simulations with Widom test particle insertions are demonstrated to provide additional information about these systems. The NVT+Widom simulations provide the full van der Waals loop associated with the sharp steps and hysteresis, including the locations of the spinodal points and points within the metastable and unstable regions that are inaccessible to GCMC simulations. The simulations provide molecular-level insight into pore filling and equilibria between high- and low-density states within individual pores. The effect of framework flexibility on adsorption hysteresis is also investigated for methane in IRMOF-1.

Phase behavior of metastable water based on fully ab initio simulations

Based on the strongly constrained and appropriately normed (SCAN) functional, phase behavior of metastable water is studied by ab initio molecular dynamics simulations. A clear van der Waals loop or two-phase coexistence line is observed in the simulated isotherms from 230 to 380 K, providing ab initio evidence for a first-order phase transition. The stability limit line formed by connecting the calculated spinodal points is observed to be a continuous reentrant curve, and the liquid-liquid critical point appears to be hidden at its minimum. The line of maximum density also tends to end at this minimum. These results suggest that the phase behavior of metastable water favors a critical-point-free scenario. Due to the potential limitations of the SCAN functional itself and the failure to take nuclear quantum effects into account, it remains to be further investigated whether the phase behavior of real water remains as predicted in the present work.

Unveiling the Molecular Origin of Vapor-Liquid Phase Transition of Bulk and Confined Fluids

At temperatures below the critical temperature, discontinuities in the isotherms are one critical issue in the design and construction of separation units, affecting the level of confidence for a prediction of vapor–liquid equilibriums and phase transitions. In this work, we study the molecular mechanisms of fluids that involve the vapor–liquid phase transition in bulk and confinement, utilizing grand canonical (GCE) and meso-canonical (MCE) ensembles of the Monte Carlo simulation. Different geometries of the mesopores, including slit, cylindrical, and spherical, were studied. During phase transitions, condensation/evaporation hysteretic isotherms can be detected by GCE simulation, whereas employing MCE simulation allows us to investigate van der Waals (vdW) loop with a vapor spinodal point, intermediate states, and a liquid spinodal point in the isotherms. Depending on the system, the size of the simulation box, and the MCE method, we are able to identify three distinct groups of vdW-type isotherms for the first time: (1) a smooth S-shaped loop, (2) a stepwise S-shaped loop, and (3) a stepwise S-shaped loop with just a vertical segment. The first isotherm type is noticed in the bulk and pores having small box sizes, in which vapor and liquid phases are close and not clearly identified. The second and the third types occurred in the bulk, cylindrical, and slit mesopores with sufficiently large spaces, where vapor and liquid phases are distinctly separated. Results from our studies provide an insight analysis into vapor–liquid phase transitions, elucidating the effect of the confinement of fluid behaviors in a visual manner.

Potential energy landscape and thermodynamic transitions of coarse-grained protein models revealed by the multicanonical generalized hybrid Monte Carlo method.

In the present study, thermodynamic properties of coarse-grained protein models have been studied by an extended ensemble method. Two types of protein model were analyzed; one is categorized into a fast folder and the other into a slow folder. Both models exhibit the following thermodynamic transitions: the collapse transition between random coil states and spatially compact, but non-native states and the folding transition between the collapsed states and the folded native states. Caloric curve for the fast folder shows strong statistical ensemble dependence, while almost no ensemble dependence is found for the slow folder. Microcanonical caloric curve for the fast folder exhibits S-shaped temperature dependence on the internal energy around the collapse transition which is reminiscent of the van der Waals loop observed for the first order transition; at the transition temperature, the collapsed and random coil states coexist dynamically. The corresponding microcanonical heat capacity is found to have negative region around the transition. This kind of exotic behaviors could be utilized to distinguish fast folding proteins.

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.

Plasma phase transition (by the fiftieth anniversary of the prediction)

At first, we present a brief review of the problem. Then, we consider plasma phase transition (PPT) as a mechanism of the first order fluid–fluid phase transition in warm dense hydrogen. The pros and cons are analysed. The properties of warm dense hydrogen are investigated by ab initio methods of molecular dynamics using the density functional theory. Strong ionization during the fluid–fluid phase transition in warm dense hydrogen makes this transition close to the prediction of the PPT. Finally, we present differences in the real phase transition from the prediction 1968–1969. Structures are observed with inter‐proton separations that are equal to the distances between protons in the and ions. The transition is not only ionization, but also structural. An analysis of the phase transition counterpart in solid hydrogen under high pressure allows us to reveal partially the character of the new structure. The ionized phase includes complex cluster ions. Van der Waals loops are of abnormal inverted form.

How to Force Polymer Gels to Show Volume Phase Transitions.

Relatively few polymer gels are known to show volume phase transition where the gels undergo an abrupt change in the degree of swelling by passing through a three-phase equilibrium. Characteristic for such transition is the existence of van der Waals (vdW) loop on the dependence of solvent chemical potential versus polymer concentration. For the χ-induced transition, the existence of vdW loop is determined by the concentration dependence of the interaction function. It is shown that expansive mechanical strains can assist in development of the vdW loop. Systems characterized by continuous change of the degree of swelling transform upon such strain into ones where the degree of swelling changes much and abruptly. Also, expansive modes of strain can make the transition wider and more robust in gels where transition is already observed under free swelling condition. The possibility to induce the volume phase transition by external stresses can be utilized for finding other stimuli sensitive gels, strengthening of gel response, and in modeling of properties of gel constructs by Finite Element Method.

Effective two-dimensional model for granular matter with phase separation.

Granular systems confined in vertically vibrated shallow horizontal boxes (quasi-two-dimensional geometry) present a liquid-to-solid phase transition when the frequency of the periodic forcing is increased. An effective model, where grains move and collide in two-dimensions is presented, which reproduces the aforementioned phase transition. The key element is that besides the two-dimensional degrees of freedom, each grain has an additional variable ɛ that accounts for the kinetic energy stored in the vertical motion in the real quasi-two-dimensional motion. This energy grows monotonically during free flight, mimicking the energy gained by collisions with the vibrating walls and, at collisions, this energy is instantaneously transferred to the horizontal degrees of freedom. As a result, the average values of ɛ and the kinetic temperature are decreasing functions of the local density, giving rise to an effective pressure that can present van der Waals loops. A kinetic theory approach predicts the conditions that must satisfy the energy growth function to obtain the phase separation, which are verified with molecular dynamics simulations. Notably, the effective equation of state and the critical points computed considering the velocity-time-of-flight correlations differ only slightly from those obtained by simple kinetic theory calculations that neglect those correlations.

Molecular dynamics simulation of the thermodynamic properties of mercury at pressures below 2.5 GPa and temperatures below 10000 K

Models of mercury were constructed by molecular dynamics using the interparticle potential of the embedded atom model (EAM) at temperatures below 10 000 K and pressures below 2.5 GPa. The thermodynamic properties of the models were presented on the isobars of 0.5, 1.0, 1.5, 2.0, and 2.5 GPa. The compressibility factors Z = pV/(RT) were calculated; the coordinates of the inversion points of the Joule–Thomson coefficient below 5600 K were found from the positions of minima on the Z(p, T) isobars. At densities above 8–9 g/cm3, the results of simulation agreed well with experiment; at lower densities there were discrepancies associated with a loss of metal properties by real mercury. The behavior of the models was analyzed in the region of the van der Waals loop. The calculated critical temperature of mercury was found to be significantly overestimated relative to the experiment. Modeling the “meta-mercury” with the EAM potential with excluded embedded potential contribution gave better agreement with the equation of state of mercury at lower densities. The states with Z = 1 can be observed below 1.0 GPa. The calculated temperature of the inversion of the Joule–Thomson coefficient increased monotonically to 5600 K as the pressure increased to 2.5 GPa.

Coexistence of low and high overlap phases in a supercooled liquid: An integral equation investigation.

The pair structure, free energy, and configurational overlap order parameter Q of an annealed system of two weakly coupled replicas of a supercooled "soft sphere" fluid are determined by solving the hypernetted-chain (HNC) and self-consistent Rogers-Young (RY) integral equations over a wide range of thermodynamic conditions ρ (number-density), T (temperature), and inter-replicas couplings ε12. Analysis of the resulting effective (or Landau) potential W(ρ,T; Q) and of its derivative with respect to Q confirms the existence of a "precursor transition" between weak and strong overlap phases below a critical temperature Tc well above the temperature To of the "ideal glass" transition observed in the limit ε12→0. The precursor transition is signalled by a loss of convexity of the potential W(Q) and by a concomitant discontinuity of the order parameter Q just below Tc, which crosses over to a mean-field-like van der Waals loop at lower temperatures. The HNC and RY equations lead to the same phase transition scenario, with quantitative differences in the predicted temperatures Tc and To.

Topological approach to microcanonical thermodynamics and phase transition of interacting classical spins

We propose a topological approach suitable to establish a connection between thermodynamics and topology in the microcanonical ensemble. Indeed, we report on results that point to the possibility of describing interacting classical spin systems in the thermodynamic limit, including the occurrence of a phase transition, using topological arguments only. Our approach relies on Morse theory, through the determination of the critical points of the potential energy, which is the proper Morse function. Our main finding is that, in the context of the classical models studied, the Euler characteristic embeds the necessary features for a correct description of several magnetic thermodynamic quantities of the systems, such as the magnetization, correlation function, susceptibility, and critical temperature. Despite the classical nature of the models, such quantities are those that do not violate the laws of thermodynamics (with the proviso that van der Waals loop states are mean field (MF) artifacts). We also discuss the subtle connection between our approach using the Euler entropy, defined by the logarithm of the modulus of per site, and that using the Boltzmann microcanonical entropy. Moreover, the results suggest that the loss of regularity in the Morse function is associated with the occurrence of unstable and metastable thermodynamic solutions in the MF case. The reliability of our approach is tested in two exactly soluble systems: the infinite-range and the one-dimensional short-range XY models in the presence of a magnetic field. In particular, we confirm that the topological hypothesis holds for both the infinite-range () and the short-range (Tc = 0) XY models. Further studies are very desirable in order to clarify the extension of the validity of our proposal.

A van der Waals-like Transition Between Normal and Cancerous Phases in Cell Populations Dynamics of Colorectal Cancer.

Based on a deterministic continuous model of cell populations dynamics in the colonic crypt and in colorectal cancer, we propose four combinations of feedback mechanisms in the differentiations from stem cells (SCs) to transit cells (TCs) and then to differentiated cells (DCs), the four combinations include the double linear (LL), the linear and saturating (LS), the saturating and linear (SL), and the double saturating (SS) feedbacks, respectively. The relative fluctuations of the population of SCs, TCs, and DCs around equilibrium states with four feedback mechanisms are studied by using the Langevin method. With the increasing of net growth rate of TCs, it is found that the Fano factors of TCs and DCs go to a peak in a transient phase, and then increase again to infinity in the cases of LS and SS feedbacks. The “up-down-up” characteristic on the Fano factor (like the van der Waals loop) demonstrates that there exists a transient phase between the normal and cancerous phases, our novel findings suggest that the mathematical model with LS or SS feedback might be better to elucidate the dynamics of a normal and abnormal (cancerous) phases.

Self-consistent theory for systems with mesoscopic fluctuations

We have developed a theory for inhomogeneous systems that allows for the incorporation of the effects of mesoscopic fluctuations. A hierarchy of equations relating the correlation and direct correlation functions for the local excess of the volume fraction of particles ζ has been obtained, and an approximation leading to a closed set of equations for the two-point functions has been introduced for the disordered inhomogeneous phase. We have numerically solved the self-consistent equations for one-dimensional (1D) and three-dimensional (3D) models with short-range attraction and long-range repulsion. Predictions for all of the qualitative properties of the 1D model agree with the exact results, but only semi-quantitative agreement is obtained in the simplest version of the theory. The effects of fluctuations in the two 3D models considered are significantly different, despite the very similar properties of these models in the mean-field approximation. In both cases we obtain the sequence of large–small–large compressibility for increasing ζ. The very small compressibility is accompanied by the oscillatory decay of correlations with correlation lengths that are orders of magnitude larger than the size of particles. In one of the two models considered, the small compressibility becomes very small and the large compressibility becomes very large with decreasing temperature, and eventually van der Waals loops appear. Further studies are necessary in order to determine the nature of the strongly inhomogeneous phase present for intermediate volume fractions in 3D.

Molecular dynamics simulation of the structure and thermodynamic properties of liquid rubidium at pressures of up to 10 GPa and temperatures of up to 3500 K

The models of rubidium at temperatures of up to 3500 K, degrees of compression of up to Y = V/V 0 = 0.3, and pressures of up to 32 GPa were constructed by molecular dynamics (MD) using the interparticle potential ЕАМ. The thermodynamic properties of the MD models agree satisfactorily with experiment in the range of parameters under study at rubidium densities higher than 0.86 g/cm3. The behavior of the models in the range of the van der Waals loop was analyzed; the calculated critical temperature of rubidium T c is ∼2250 ± 25 K, density ∼0.41 g/cm3, pressure ∼0.019 GPa, and compressibility factor Z = pV/RT ≈ 0.137. The states with the unity factor Z = 1 were observed at pressures of up to 0.30 GPa (at ∼3000 K); the temperature dependence of the density of the models with Z = 1 is nearly linear, and the Boyle temperature is T B ≈ 10160 K. The ratio T c/T B = 0.221 is close to this value for cesium (0.23) and mercury (0.276). In the temperature and pressure ranges under study, the inversion of the Joule–Thomson coefficient did not take place, but should be observed at pressures of ⩽0.3 GPa and elevated temperatures. It was found that the diffusion coefficient D(T) dependences do not straighten in the usually used coordinates within wide temperature ranges. It was concluded that the structure of the liquid smoothly changes when the rubidium models are compressed and this reveals in the change of the degree of asymmetry of the first peak of the radial distribution function.

Structure and thermodynamic properties of liquid cesium at pressures below 10 GPa and temperatures below 4000 K according to the molecular dynamics data

The models of cesium at temperatures of up to 4000 K, compressions of up to Y = V/V0 = 0.3, and pressures of up to 24 GPa were constructed by the molecular dynamics (MD) method using the ЕАМ interparticle potential. The thermodynamic properties of the models are presented in the tables. The compressibility factors were calculated: Z = pV/RT. The thermodynamic properties of the MD models were in satisfactory agreement with experiment in the range of parameters under study at a cesium density of higher than 1.2 g/cm3. The behavior of the models in the region of the van der Waals loop was analyzed. The calculated critical temperature of cesium Tc was shown to be ~1950 ± 25 K, approximating the real temperature, the density was ~0.53 g/cm3, the pressure ~0.015 GPa, and the compressibility factor Z = pV/RT ≈ 0.23. The states with a unity factor Z = 1 were observed at pressures below 0.20 GPa (at 2800 K); the temperature dependence of the density of the models with Z = 1 was almost linear, and the Boyle temperature TB was 7160 K; the ratio Tc/TB = 0.269 was very close to that for mercury (0.276). In the pressure and temperature ranges under study, the inversion of the Joule–Thomson coefficient was not observed, but took place at densities below 1.2 g/cm3. The structure of the liquid changed when the degree of compression of the cesium models changed from 0.54 to 0.52. This was reflected by a change in the degree of asymmetry of the first peak of the radial distribution function. An analysis of the structural data of the models of liquid sodium, potassium, and rubidium showed that the structure of these metals also experienced similar changes near the degree of compression 0.5; these changes in alkali metals are not related to the 6s → 5d electron transition.

Statistical thermodynamics of irreversible aggregation: the sol-gel transition.

Binary aggregation is known to lead, under certain kinetic rules, to the coexistence of two populations, one consisting of finite-size clusters (sol), and one that contains a single cluster that carries a finite fraction of the total mass (giant component or gel). The sol-gel transition is commonly discussed as a phase transition by qualitative analogy to vapor condensation. Here we show that the connection to thermodynamic phase transition is rigorous. We develop the statistical thermodynamics of irreversible binary aggregation in discrete finite systems, obtain the partition function for arbitrary kernel, and show that the emergence of the gel cluster has all the hallmarks of a phase transition, including an unstable van der Waals loop. We demonstrate the theory by presenting the complete pre- and post-gel solution for aggregation with the product kernel.

On the phase transition of argon adsorption in an open end slit pore—Effects of temperature and pore size

The phase evolution of argon adsorbed in open ended graphitic slit pores at temperatures below the 2D-critical temperature of the first layer was simulated using the grand canonical Monte Carlo (GCMC) and meso-canonical ensembles (MCE). In the latter the adsorption system is connected to a finite reservoir and the combined system is a canonical ensemble. Hysteresis loops and sigmoid van der Waals loops were found for the GCMC and MCE simulations respectively, corresponding to the observed 2D-transitions, which comprised vapor–solid, vapor–liquid and liquid–solid changes of state depending on the temperature. The MCE isotherms in large open end pores exhibited a sequential adsorption, not previously noted in the literature, where the monolayer filling on one wall is followed by monolayer filling on the opposite wall, giving rise to a double van der Waals loop. When the spacing between the pore walls is decreased, this double-vdW loop evolves to form a fused single loop, and the transition shifts from being predominantly a surface adsorption to pore volume filling.

On the phase transition in a monolayer adsorbed on graphite at temperatures below the 2D-critical temperature

Monte Carlo simulations in the grand ensemble and meso-canonical ensemble in which the adsorbent is connected to a finite reservoir have been used to study adsorption isotherms for monolayer argon adsorption on graphite at temperatures below the 2D-critical temperature in order to elucidate the microscopic details of the 2D-transitions: vapour–solid, vapour–liquid and liquid–solid. An S-shaped van der Waals (vdW) loop was found when a small square surface was used; however, for large square surfaces and rectangular surfaces the isotherms exhibit a vdW-type loop with a vertical segment which indicates the coexistence of two phases separated by a boundary that changes its shape with the loading. This coexistence occurs at the same chemical potential as determined by the mid-density scheme, developed by Do and co-workers (Z. Liu, L. Herrera, V.T. Nguyen, D.D. Do, and D. Nicholson, A Monte Carlo scheme based on mid-density in a hysteresis loop to determine equilibrium phase transition. Mol Simul. 37(11):932–939, 2011; Z. Liu, D.D. Do, and D. Nicholson, A thermodynamic study of the mid-density scheme to determine the equilibrium phase transition in cylindrical pores. Mol Simul. 38(3):189–199, 2011).

Communication: Phase diagram of C₃₆ by atomistic molecular dynamics and thermodynamic integration through coexistence regions.

We report an atomistic molecular dynamics determination of the phase diagram of a rigid-cage model of C36. We first show that free energies obtained via thermodynamic integrations along isotherms displaying "van der Waals loops," are fully reproduced by those obtained via isothermal-isochoric integration encompassing only stable states. We find that a similar result also holds for isochoric paths crossing van der Waals regions of the isotherms, and for integrations extending to rather high densities where liquid-solid coexistence can be expected to occur. On such a basis we are able to map the whole phase diagram of C36, with resulting triple point and critical temperatures about 1770K and 2370K, respectively. We thus predict a 600K window of existence of a stable liquid phase. Also, at the triple point density, we find that the structural functions and the diffusion coefficient maintain a liquid-like character down to 1400-1300K, this indicating a wide region of possible supercooling. We discuss why all these features might render possible the observation of the melting of C36 fullerite and of its liquid state, at variance with what previously experienced for C60.