Van Der Waals Loop Research Articles

Influence of system size on the properties of a fluid adsorbed in a nanopore: Physical manifestations and methodological consequences.

Hysteresis and discontinuities in the isotherms of a fluid adsorbed in a nanopore in general hamper the determination of equilibrium thermodynamic properties, even in computer simulations. A way around this has been to consider both a reservoir of small size and a pore of small extent in order to restrict the fluctuations of density and approach a classical van der Waals loop. We assess this suggestion by thoroughly studying through Monte Carlo simulations and density functional theory the influence of system size on the equilibrium configurations of the adsorbed fluid and on the resulting isotherms. We stress the importance of pore-symmetry-breaking states that even for modest pore sizes lead to discontinuous isotherms and we discuss the physical relevance of these states and the methodological consequences for computing thermodynamic quantities.

Swim pressure: stress generation in active matter.

We discover a new contribution to the pressure (or stress) exerted by a suspension of self-propelled bodies. Through their self-motion, all active matter systems generate a unique swim pressure that is entirely athermal in origin. The origin of the swim pressure is based upon the notion that an active body would swim away in space unless confined by boundaries-this confinement pressure is precisely the swim pressure. Here we give the micromechanical basis for the swim stress and use this new perspective to study self-assembly and phase separation in active soft matter. The swim pressure gives rise to a nonequilibrium equation of state for active matter with pressure-volume phase diagrams that resemble a van der Waals loop from equilibrium gas-liquid coexistence. Theoretical predictions are corroborated by Brownian dynamics simulations. Our new swim stress perspective can help analyze and exploit a wide class of active soft matter, from swimming bacteria to catalytic nanobots to molecular motors that activate the cellular cytoskeleton.

On the existence of a hysteresis loop in open and closed end pores

We have studied the adsorption of argon at 87 K in slit pores of finite length with a smooth graphitic potential, open at both ends or closed at one end. Simulations were carried out using conventional GCMC (grand canonical Monte Carlo) or kMC (kinetic Monte Carlo) in the canonical ensemble with extremely long Markov chain, of at least 2 × 108 configurations; selected simulations with much longer Markov chains do not show any change in the results. When the pore width is in the micropore range (0.65 nm), type I isotherms are obtained for both pore models and for both simulation methods. However, wider pores (1, 2 and 3 nm in width) all exhibit hysteresis loops in the GCMC simulations, while in the canonical ensemble simulations, the isotherms pass through a sigmoid van der Waals type loop in the transition region. This loop locates the true equilibrium transition. For the pores with one closed end, this transition is close to, or coincides with, the adsorption branch of the GCMC hysteresis loop, but for the open-ended pores, it is more closely associated with the desorption branch. In a separate study of adsorption hysteresis in an infinitely long slit pore, using both simulation techniques, the van der Waals loop follows the adsorption branch of the GCMC isotherm to the transition, then reverts to a long vertical section that falls midway between the two hysteresis branches and finally moves to the desorption transition close to the evaporation pressure. An examination of molecular distributions inside the pores reveals two coexisting phases in the canonical simulations, whereas in the grand canonical simulations, the molecules are uniformly distributed along the length of the pores.

Influence of atomic size mismatch on binary alloy phase diagrams

The aim of this paper is to investigate the consequences of atomic size mismatch on the thermodynamics and the topology of binary phase diagrams of face centred cubic alloys. Simple pairwise interatomic potentials with few controlling parameters are used to identify general tendencies. Thermodynamic states are computed by Monte Carlo simulations on a non-rigid lattice. A special attention has been paid to the comparison between calculations in the canonical ensemble, where composition–temperature phase diagrams are determined through van der Waals loops, and in the grand canonical ensemble, where phase diagrams are computed using an interface migration technique. It is shown that these two procedures lead essentially to the same incoherent phase diagram. In the case of phase separating systems, we argue that the introduction of a size mismatch leads to a shrinkage of the solid solution domain and that the asymmetry of the miscibility gap is essentially controlled by the anharmonicity of the heteroatomic potential. Finally, in the case of ordering systems, we show that the asymmetry of the phase diagram may be due to the anharmonicity of the pair potentials or to the differences between their curvatures, the former effect being dominant if the atomic size mismatch is large.

Phase separation in a binary mixture confined between symmetric parallel plates: Capillary condensation transition near the bulk critical point

We investigate phase separation of near-critical binary mixtures between parallel symmetric walls in the strong adsorption regime. We take into account the renormalization effect due to the critical fluctuations using the recent local functional theory [J. Chem. Phys. 136, 114704 (2012)]. In statics, a van der Waals loop is obtained in the relation between the average order parameter $<psi>$ in the film and the chemical potential when the temperature $T$ is lower than the film critical temperature $T_c^{ca}$ (in the case of an upper critical solution temperature). In dynamics, we lower $T$ below the capillary condensation line from above $T_c^{ca}$. We calculate the subsequent time-development assuming no mass exchange between the film and the reservoir. In the early stage, the order parameter $psi$ changes only in the direction perpendicular to the walls. For sufficiently deep quenching, such one-dimensional profiles become unstable with respect to the fluctuations varying in the lateral directions. The late-stage coarsening is then accelerated by the hydrodynamic interaction. A pancake domain of the phase disfavored by the walls finally appears in the middle of the film.

A non-classical van der Waals loop: Collective variables method

The equation of state is investigated for an Ising-like model in the framework of collective variables method. The peculiar feature of the theory is that a non-classical van der Waals loop is extracted. The results are compared with the ones of a trigonometric parametric model in terms of normalized magnetization, \tilde{M}, and field, \tilde{H}.

Beyond the Van Der Waals loop: What can be learned from simulating Lennard-Jones fluids inside the region of phase coexistence

As a rule, mean-field theories applied to a fluid that can undergo a transition from saturated vapor at density ρυ to a liquid at density ρℓ yield a van der Waals loop. For example, isotherms of the chemical potential μ(T,ρ) as a function of the density ρ at a fixed temperature T less than the critical temperature Tc exhibit a maximum and a minimum. Metastable and unstable parts of the van der Waals loop can be eliminated by the Maxwell construction. Van der Waals loops and the corresponding double minimum potentials are mean-field artifacts. Simulations at fixed μ=μcoex for ρυ&amp;lt;ρ&amp;lt;ρℓ yield a loop, but for sufficiently large systems this loop does not resemble the van der Waals loop and reflects interfacial effects on phase coexistence due to finite size effects. In contrast to the van der Waals loop, all parts of the loop found in simulations are thermodynamically stable. The successive umbrella sampling algorithm is described as a convenient tool for seeing these effects. It is shown that the maximum of the loop is not the stability limit of a metastable vapor but signifies the droplet evaporation-condensation transition. The descending part of the loop contains information on Tolman-like corrections to the surface tension, rather than describing unstable states.

A new method of semigrand canonical ensemble to calculate first-order phase transitions for binary mixtures

First-order phase transitions of binary mixtures at the given pressure (P) and temperature (T) are studied by taking into account the composition fluctuations. Isothermal-isobaric semigrand canonical ensemble is adopted to find the relations among the total number of molecules, the composition fluctuations and Gibbs free energy density. By combining two identical subsystems of mixtures successively, the free energy density is transformed until being stable and its linear segments represent phase transitions. A new method is developed to calculate the phase equilibriums of binary mixtures. The method handles multiple types and number of phase equilibriums at single time and its solutions are physically justified. One example is shown for calculating the phase diagram of binary Lennard-Jones mixture. It demonstrates that the fluctuations of the total number of molecules in mixtures are fundamental behind phase transitions and the van der Waals loops in Gibbs free energy are reasonable.

Monte Carlo simulations of a clay inspired model suspension: the role of rim charge

We present a theoretical investigation of a model clay dispersion in 1-1 salt solutions by varying the particle volume fraction and ionic strength as well as the charge distribution on the clay platelets. The platelets are modeled as discs with charged sites distributed on a hexagonal lattice. The edge sites can be positively charged while the remaining sites are negative giving rise to a strong charge anisotropy. Simulations are carried out using a Monte Carlo method in the canonical ensemble. The interactions between the platelet sites are described with a screened Coulomb potential plus a short range repulsive potential. Simulations show a complex phase behavior. When the charge anisotropy is strong, i.e. all edge sites are positively charged, a fluid phase dominated by repulsion is found at low volume fraction and ionic strength. When increasing the latter an attractive liquid phase forms. At these volume fractions the platelets aggregate in an “Overlapping Coins” configuration. With increasing volume fraction the dispersion becomes unstable and the pressure goes through a van der Waals loop. A liquid crystalline phase, Smectic B, forms in the thermodynamically unstable region. On the other side of the van der Waals loop a stable gel phase is found. A phase separation between a fluid and a gel is thus predicted. The threshold value of the volume fraction at which the phase separation occurs is found to increase with the salt concentration. The gel structure is a mixture of “Overlapping Coins” and “House of Cards” configurations. When the charge anisotropy is intermediate, no phase separation occurs. Instead, a gel forms from a sol of clusters of individual particles randomly oriented that progressively grow with the volume fraction. These results are discussed in light of experimental observations on clay suspensions.

Equation of state from the Potts-percolation model of a solid

We expand the Potts-percolation model of a solid to include stress and strain. Neighboring atoms are connected by bonds. We set the energy of a bond to be given by the Lennard-Jones potential. If the energy is larger than a threshold the bond is more likely to fail, whereas if the energy is lower than the threshold, the bond is more likely to be alive. In two dimensions we compute the equation of state: stress as a function of interatomic distance and temperature by using renormalization-group and Monte Carlo simulations. The phase diagram, the equation of state, and the isothermal modulus are determined. When the Potts heat capacity is divergent the continuous transition is replaced by a weak first-order transition through the van der Waals loop mechanism. When the Potts transition is first order the stress exhibits a large discontinuity as a function of the interatomic distance.

A new grand canonical ensemble method to calculate first-order phase transitions

A theory about first-order phase transition of pure fluids is proposed. The theory is developed by combining grand canonical ensemble with density functional for homogeneous fluids. It is based on the fact that the grand partition function of one macroscopic volume is the product of the grand partition functions of its subvolumes. Density fluctuations of molecules determine the relation between the grand partition function and the free energy density. By combining pairs of subvolumes successively, the free energy density is transformed and rapidly becomes stationary. The stationary curve versus molecule density is convex and its linear segments represent phase transitions. The transform leads to the new grand canonical method to calculate phase equilibrium, which is more robust than classic ones. The transform suggests that classical van der Waals loop is physical and essential to phase transition.

Asymmetry of the vapor–liquid coexistence curve: The asymptotic behavior of the "diameter"

We analyze, without resort to any model field-mixing scheme, the leading temperature-dependent term in the "diameter" of the coexistence curve asymptotically close to the vapor–liquid critical point. For this purpose, we use a simple non-parametric equation of state which we develop by meeting several general requirements. Namely, we require that the desired equation (1) lead to correct asymptotic behavior for a limited number of the fluid's parameters along selected thermodynamic paths, (2) reveal a Van der Waals loop below the critical point, and (3) be consistent with a rigorous definition of the isothermal compressibility in the critical region. For the temperature interval in question, the proposed equation approximates experimental data with an accuracy comparable to those given by Schofield's parametric equation and by other authors' equations. The desired term is obtained by applying the Maxwell rule to the equation and can be represented as D 2 β | τ| 2 β , where | τ| = | T − T c |/ T c and β is the critical exponent for the order parameter. The amplitude D 2 β is determined explicitly for the volume–temperature and entropy–temperature planes. The results obtained are contrasted with experiment to estimate the values of the amplitude coefficients of the nonanalytic terms in the "diameters" for the volume–temperature and density–temperature planes.

Hydrogen embrittlement under load as a first-order phase transition

The stress-strain equation of state for a material with dissolved hydrogen is derived within a two-component continuum model. It is demonstrated that, for the parameters corresponding to conventional metals, it has the shape of a loop similar to the van der Waals loop. On this basis, it is concluded that hydrogen embrittlement of materials under load is a typical first-order phase transition and, therefore, occurs through nucleation of a new phase. Thermodynamic and kinetic theories of this transition are developed, and time dependences of all the main characteristics of this process are calculated.

Analysis of van der Waals loops in the adsorption isotherms of porous systems

The properties of the van der Waals loops for isotherms of the adsorbate located in the slit-shaped and cylindrical pores of different width were analyzed. The adsorbate molecules are modeled by spherical Lennard-Jones type particles. The calculation was based on the latticegas model in the quasichemical approximation for intermolecular interactions. The accuracy of calculations of the adsorption hysteresis loops increases due to the use of distributed models, which reflect the spatial inhomogeneity of the distribution of molecules along the normal to the pore wall. The effect of the adsorbate-adsorbent interaction potential and pore width on the pattern of adsorption isotherms is considered. Taking into account the inhomogeneity of the spatial distribution of molecules changes the course of the spinodal sections of the adsorption isotherms.

Van der Waals model for phase transitions in thermoresponsive surface films

Phase transitions in polymeric surface films are studied with a simple model based on the van der Waals equation of state. Each chain is modeled by a single bead attached to the surface by an entropic-Hooke's law spring. The surface coverage is controlled by adjusting the chemical potential, and the equilibrium density profile is calculated with density functional theory. The interesting feature of this model is the multivalued nature of the density profile seen at low temperature. This van der Waals loop behavior is resolved with a Maxwell construction between a high-density phase near the wall and a low-density phase in a "vertical" phase transition. Signatures of the phase transition in experimentally measurable quantities are then found. Numerical calculations are presented for isotherms of surface pressure, for the Poisson ratio, and for the swelling ratio.

The Relation of Interface Properties and Bulk Phase Stability: Molecular Dynamics Simulations of Carbon Dioxide

The limit of metastability, the so-called spinodal, is calculated for pure carbon dioxide by molecular dynamics simulation. The determination of the spinodal is based on properties of the liquid vapor interface using a recently developed method. This method relates the tangential pressure component through the vapor-liquid interface to the van der Waals loop in the two-phase region of the phase diagram. By application of the thermodynamic stability criteria, the location of the spinodal can be determined. The spinodal determined in this way is called interface spinodal here. Furthermore, the simulation provides equation of state properties in the complete metastable region of the phase diagram. The performance of different correlation equations for the density and the pressure tensor profiles with respect to the estimation of the spinodal is compared. It has been found that the interface spinodal coincides with the thermodynamic mean field spinodal within some reasonable deviation. Finally the influence of the size of the simulation box on the spinodal properties is investigated showing that the temperature-density spinodal data are independent of the interface thickness. Additional simulations using a Lennard-Jones fluid confirm these results over a range of 1.5 orders of magnitude for the systems size. A further result is that interface systems require a very long simulation time in order to obtain reliable results.

Liquid-Liquid Transition in Supercooled Silicon Determined by First-Principles Simulation

First-principles molecular dynamics simulations reveal a liquid-liquid phase transition in supercooled elemental silicon. Two phases coexist below Tc approximately 1232 K and above pc approximately -12 kB. The low-density phase is nearly tetracoordinated, with a pseudogap at the Fermi surface, while the high-density phase is more highly coordinated and metallic in nature. The transition is observed through the formation of van der Waals loops in pressure-volume isotherms below Tc.

STATE EQUATION FOR THE THREE-DIMENSIONAL SYSTEM OF "COLLAPSING" HARD SPHERES

By the Wertheim method, the exact solution of the Percus–Yevick integral equation for a system of particles with the "repulsive step potential" interacting ("collapsing" hard spheres) is obtained. On the basis of this solution, the state equation for the "repulsive step potential" is built and determined, that the Percus–Yevick equation does not show the Van der Waals loop for "collapsing" hard spheres.

Influence of Go-Like Interactions on Global Shapes of Energy Landscapes in β-Barrel Forming Model Proteins: Inherent Structure Analysis and Statistical Temperature Molecular Dynamics Simulation

Recently, the native-centric, coarse-grained "Go-like" protein model has gained a renewed popularity because of its computational simplicity and successful description of some key aspects of folding thermodynamics and kinetics. In the present paper, the properties of Go-like models are investigated in terms of the potential energy landscape (PEL). The non-native attractions of the beta-barrel forming BLN model 46-mer are scaled with a parameter 0 < or = lambda < or = 1, to make a continuous tuning of the PEL from multi-funneled and energetically frustrated at lambda = 1 to a perfect funnel including only topological frustration at lambda = 0. The combination of the enhanced sampling of "statistical temperature molecular dynamics", STMD (Kim, J.; Straub, J. E.; Keyes, T. Phys. Rev. Lett. 2006, 97, 050601), and extensive inherent structure (IS) analysis, clearly demonstrates the evolution of the topography of the PEL. It is shown that a small amount of Go-like interactions brings about a significant modification in the occupation of low-lying IS by destabilizing the misfolding funnel into a higher energy region, strongly influencing the folding thermodynamics. The alteration of the PEL also induces a dramatic change in the folding mechanism, from a second-order-like collapse transition into a cooperative, first-order-like folding transition, occurring through a transient, intermediate state ensemble characterized by partially structured IS. The appearance of multiple van der Waals loops in the statistical temperature of the Go-like model is associated with the development of the intermediate states.

Freezing kinetics in overcompressed water

We report high-pressure dynamic compression experiments of liquid water along a quasiadiabatic path leading to the ice-VII region of the phase diagram. We observe dynamic features resembling van der Waals loops and find that liquid water is compacted to a metastable state close to the ice density before the onset of crystallization. By analyzing the characteristic kinetic time scale involved we estimate the nucleation barrier and conclude that liquid water has been compressed to a high-pressure state close to its thermodynamic stability limit.