Generalized Van Der Waals Research Articles

The hydrogen atom perturbed by a 1-dimensional Simple Harmonic Oscillator (1d-SHO) potential

Abstract The hydrogen atom perturbed by a constant 1-dimensional weak quadratic potential λz2 is solved at first-order perturbation theory using the eigenstates of the total angular momentum operator - the coupled basis. Physical applications of this result could be found, for example, in the study of a quadratic Zeeman effect weaker than fine-structure effects, or in a perturbation caused by instantaneous generalised van der Waals interactions.

Hierarchical Framework for Predicting Entropies in Bottom-Up Coarse-Grained Models.

The thermodynamic entropy of coarse-grained (CG) models stands as one of the most important properties for quantifying the missing information during the CG process and for establishing transferable (or extendible) CG interactions. However, performing additional CG simulations on top of model construction often leads to significant additional computational overhead. In this work, we propose a simple hierarchical framework for predicting the thermodynamic entropies of various molecular CG systems. Our approach employs a decomposition of the CG interactions, enabling the estimation of the CG partition function and thermodynamic properties a priori. Starting from the ideal gas description, we leverage classical perturbation theory to systematically incorporate simple yet essential interactions, ranging from the hard sphere model to the generalized van der Waals model. Additionally, we propose an alternative approach based on multiparticle correlation functions, allowing for systematic improvements through higher-order correlations. Numerical applications to molecular liquids validate the high fidelity of our approach, and our computational protocols demonstrate that a reduced model with simple energetics can reasonably estimate the thermodynamic entropy of CG models without performing any CG simulations. Overall, our findings present a systematic framework for estimating not only the entropy but also other thermodynamic properties of CG models, relying solely on information from the reference system.

Polymer free volume and its connection to the entanglement length and the plateau modulus via polymer mode-coupling theory and equation of state

Using a many-chain system of Gaussian chains interacting with each other through the Lennard-Jones (LJ) potential, we demonstrate that there exists a connection between polymer fractional free volume (f) and the entanglement chain length (Ne). Here, f is determined by the generic van der Waals (GvdW) equation of state using the intermolecular radial distribution function [g(r)] of the Gaussian chain generated by the polymer reference interaction sites model while Ne by the polymer mode-coupling theory (PMCT) for strongly coupled macromolecules. The key concept in PMCT is that intermolecular forces experienced by a bead in a chain surrounded by other chains are strongly coupled to the site specific intramolecular radial distribution function. The calculated Gp and η of polyethylene with chain lengths from 500 to 2000 interacting with one another through the LJ potential agree well with experiment and molecular dynamics simulation.

Toward Sustainable Ultrawide Bandgap van der Waals Materials: An ab initio Screening Effort

AbstractThe sustainable development of next‐generation device technology is paramount in the face of climate change and the looming energy crisis. Tremendous effort is made in the discovery and design of nanomaterials that achieve device‐level sustainability, where high performance and low operational energy cost are prioritized. However, many of such materials are composed of elements that are under threat of depletion and pose elevated risks to the environment and human health. The role of materials‐level sustainability in computational screening efforts is overlooked thus far. This work presents a general van der Waals materials screening framework imbued with sustainability‐motivated search criteria. Using ultrawide bandgap (UWBG) materials as a backdrop, 25 sustainable UWBG layered materials comprising only of low‐risks elements result from this screening effort, with several meeting the requirements for dielectric, power electronics, and ultraviolet device applications. These findings constitute a critical first‐step toward reinventing a more sustainable electronics landscape beyond silicon, with the framework established in this work serving as a harbinger of sustainable 2D materials discovery.

A four-parameter generalized van der Waals equation of state: theoretical determination of thermodynamic stability boundary and vapor–liquid equilibrium of vanadium, niobium and tantalum

ABSTRACT A new four-parameter generalized van der Waals equation of state is proposed. The criteria for the applicability of the proposed equation of state in describing the thermodynamic properties of substances have been formulated. The generalized van der Waals equation of state is found to be applicable to vanadium, niobium and tantalum. To validate the generalized van der Waals equation of state, the spinodal, ideal tensile strength, thermodynamic limit of superheat and binodal of vanadium, niobium and tantalum have been determined. The obtained results agree with that of Filippov correlation and other equations of state. Using the obtained spinodal, the binodal of vanadium, niobium and tantalum has been determined.

The bubble effect on the thermal expansion coefficient of few-layer MoS2

The thermal expansion coefficient of van der Waals layered structures plays an important role in governing the thermal stability of high-performance electronic devices. Meanwhile, bubbles are frequently observed in the van der Waals layered structures due to the weak inter-layer interaction and the extremely small bending stiffness of the layered structure, but the effect of bubbles on the thermal expansion coefficient for layered structures remains unclear. We derive an analytic formula for the bubble effect on the length variation of the MoS2 layer. In the analytic derivation, the MoS2 layer is described by three mechanics models, including the elastic membrane theory, the nonlinear plate theory, and the linear plate theory. The gas inside the bubble is described by two types of state equations, including the ideal gas law and the generalized van der Waals equation. It is found that the nonlinear plate theory with the generalized van der Waals equation gives the most accurate description for the bubble effect, since MoS2 has a moderate bending stiffness. The analytic formula shows that the bubble can cause strong thermal contraction for few-layer MoS2 with increasing temperature. The analytic predictions are verified by comprehensive molecular dynamic simulations for few-layer MoS2 with different layer numbers and different gas molecule numbers. These results shall be valuable for understanding the thermal stability of functional devices based on the van der Waals layered structure.

Room-Temperature Intrinsic Ferromagnetic Chromium Tellurium Compounds with Thickness-Tunable Magnetic Texture.

2D ferromagnetic chromium tellurides exhibit intriguing spin configurations and high-temperature intrinsic ferromagnetism, providing unprecedented opportunities to explore the fundamental spin physics and build spintronic devices. Here, a generic van der Waals epitaxial approach is developed to synthesize the 2D ternary chromium tellurium compounds with thicknesses down to mono-, bi-, tri-, and few-unit cells(UC). The Mn0.14 Cr0.86 Te evolves from intrinsic ferromagnetic behavior in bi-UC, tri-UC, and few-UC to temperature-induced ferrimagnetic behavior as the thickness increases, resulting in a sign reversal of the anomalous Hall resistance. Temperature- and thickness-tunable labyrinthine-domain ferromagnetic behaviors are derived from the dipolar interactions in Fe0.26 Cr0.74 Te and Co0.40 Cr0.60 Te. Furthermore, the dipolar-interaction-induced stripe domain and field-induced domain wall (DW) motion velocity are studied, and multibit data storage is realized through an abundant DW state. The magnetic storage can function in neuromorphic computing tasks, and the pattern recognition accuracy can reach up to 97.93%, which is similar to the recognition accuracy of ideal software-based training (98.28%). Room-temperature ferromagnetic chromium tellurium compounds with intriguing spin configurations can significantly promote the exploration of the processing, sensing, and storage based on 2D magnetic systems.

Generation IV Nuclear Reactor: Coolant Materials in the Supercritical State

On the basis of the generalized van der Waals equations of state, the quasispinodal and the supercritical-point parameters of the Generation IV nuclear reactor coolant materials, namely, sodium, lead and bismuth, have been determined. To improve accuracy, the known van der Waals equation of state has been generalized in three different ways. That is, the attractive term in the van der Waals equation of state has been modified by introducing new substance-specific parameters. The parameters of the generalized van der Waals equations of state have been determined through vapor-liquid critical-point parameters. The mean percentage error in the determined quasispinodal for sodium, lead, and bismuth is less than 3% in comparison with the Semenchenko correlation. T he temperature correlation of the quasispinodal pressure for sodium, lead, and bismuth, formulated in this work, is statistically excellent with the mean correlation coefficient of 0.99995 and the coefficient of determination of 0.999895. The mean supercritical-point parameters of sodium, lead, and bismuth, based on the three-parameter generalized van der Waals equations of state, are found to be (28.80 MPa, 15.1563 10−5 m3/mol, and 2563 K), (207.2275 MPa, 8.876 10−5 m3/mol, and 5278 K) and (155.338 MPa, 10.5923 10−5 m3/mol, and 4788 K) respectively. The generalized van der Waals equations of state are presented in the reduced form from which follows the law of corresponding states.

Criticality points on the phase diagram of substances as scaling parameters in the law of corresponding states: alkali metals

The law of corresponding states (LCS), based on a generalized van der Waals equation of state (gvdWEoS) has been formulated by rescaling its thermodynamic variables with liquid- vapour critical—point parameters, the spinodal, the thermodynamic limit of superheat (TLS) and the supercritical (SC) point. This gvdWEoS differs from the known van der Waals equation of state (vdWEoS) by the modified attractive term. The scaling properties have been derived on the basis of the gvdWEoS. The expressions for the isothermal compressibility, a derivate of Gibbs free energy, have been derived. In all the cases of rescaling, the gvdWEoS has the similar functional form and the expression for isothermal compressibility has a similar functional form. This shows that the parameters of any spinodal-point on the phase diagram, including the TLS as a particular case, and the SC point, characteristic point on the quasispinodal, provide the alternate scales of parameterizing the thermodynamic properties of substances other than the liquid-vapour critical point. Moreover, an isothermal compressibility regularity is formulated on the basis of the gvdWEoS and it is found to satisfactorily trace the literature data for saturated liquid alkali metals.

Two‐phase states of the generalized van der Waals gas: Conditions of absolute and neutral shock wave stability

AbstractIn this work we discuss an approach to the construction of the areas of two‐phase states for real gases, state equations for which are from the article by Fogelson and Likhachev in 2004 and formulate conditions that define absolute and neutral stability of the shock waves.

Extension of a square-well equation of state for chain-like molecules using perturbed hard chain theory

The Square-Well equation of state developed by Haghtalab and Mazloumi [A. Haghtalab, S.H. Mazloumi, Fluid Phase Equilib., 280 (2009) 1–8.] is extended for chain like molecules using a generalized van der Waals partition function for polyatomic fluids suggested by Donohue and Prausnitz [M.D. Donohue, J.M. Prausnitz AICHE J., 24 (1978) 849-860.]. The proposed EOS has three physical parameters per each pure fluid that are close-packed volume, characteristic temperature and one-third of external degree of freedom of the molecule. Here in, the parameters of the new EOS for a selection of pure fluids containing normal alkanes from C1 up to C20 are reported that are obtained by correlating saturated vapor pressure and liquid density of the fluids. Then, using proper mixing rules, vapor-liquid equilibrium calculation of a number of binaries are successfully carried out. The comparisons of the results with SPHCT EOS demonstrate the good accuracy of the new EOS.

Further Results on a Generalized van der Waals Model

A generalized van der waals model is considered to study the thermodynamic properties of pure fluids. Analytical solution of the equivalent cubic equation of state is presented and the critical properties in the general form are derived. The fluctuations of number of particles are calculated in the grand canonical ensemble by using three quantities (scaled variance omega (N), skewness Ssigma, and kurtosis ksigma ^2). The critical behavior of these quantities is investigated in terms of the dimensionless particle number density and temperature for different models. It is found that the fluctuations have a singular behavior close to the critical point.

An inertial number regulated stress model for gas-particle flows with particle friction and volume fraction gradient

In this study, a solid stress model that can be used in both dilute and dense regimes for simulation of gas-particle flows with comprehensive considerations of friction and the effect of local solid volume fraction gradient is proposed. In the dilute regime, solid stress is closed by a modified kinetic theory that accounts for the effect of particle friction and volume fraction gradient. In the dense regime, solid stress is closed by the inertial number model. The transition from dilute to dense regimes is realized by using a dimensionless parameter χ , which is a function of the inertial number I s . This new model is validated with experimental data and discrete particle simulation from spout-fluid bed and bubbling fluidized bed. When compared with the traditional kinetic-frictional stress model, this new model improves the transition from dilute to dense regimes and the particle velocity predictions in both beds. • A solid stress model is proposed in both dilute and dense regimes for gas-solid flow. • The model comprehensively considers the effect of friction and volume fraction gradient. • The expression of excluded volume is derived from the generalized van der Waals theory. • The model gives a better prediction of spout-fluid bed and bubbling fluidized bed.

Janus van der waals equations for real molecules with two-sided phase transitions

We obtained families of generalized van der Waals equations characterized by an even number n = 2, 4, 6 and a continuous free parameter, which is tunable for a critical compressibility factor. Each equation features two adjacent critical points which have a common critical temperature Tc and arbitrarily two close critical densities. The critical phase transitions are naturally two-sided: the critical exponents are αP=γP=23 and βP=δ−1=13 for T > Tc and αP=γP=nn+1 and βP=δ−1=1n+1 for T < Tc. In contrast with the original van der Waals equation, our novel equations all reduce consistently to the classical ideal gas law in the low-density limit. We tested our formulas against the NIST data for 11 major molecules and showed agreements better than the original van der Waals equation, not only near to the critical points but also in low-density regions.

Van der Waals shock polars with multiple or supersonic critical points

It is shown that the γ-van der Waals equation of state (eos) permits shock polars with supersonic critical points, corresponding to critical or strong-type shock reflections that are supersonic, which is not possible for ideal gas. It is also shown that general van der Waals eos permits polars with multiple critical points, corresponding to four or more reflected shocks for the same deflection angle. Of these reflected shocks, at least two are weak-type, i.e., deflection angle increasing with increasing shock strength, so that standard literature has no criteria to select one of the two. Both phenomena can be found with Hugoniot curves entirely in the region of convex and thermodynamically stable eos, avoiding the coexistence region and satisfying various shock stability criteria.

Phase Transition and Criticality of Methane Confined in Nanopores.

For the first time, the phase transition and criticality of methane confined in nanoporous media are measured. The measurement is performed by establishing an experimental setup utilizing a differential scanning calorimeter capable of operating under very low temperatures as well as high pressures to detect the capillary phase transition of methane inside nanopores. By performing experiments along isochoric cooling paths, both the capillary condensation and the bulk condensation of methane are detected. The pore critical point of nanoconfined methane is also determined and then used to derive the parameters of a previously developed self-consistent equation of state based on the generalized van der Waals partition function. Using these parameters, the equation of state can predict the capillary-condensation curves that agree well with the experimental data.

Scalable Van der Waals Encapsulation by Inorganic Molecular Crystals.

Encapsulation is critical for devices to guarantee their stability and reliability. It becomes an even more essential requirement for devices based on 2D materials with atomic thinness and far inferior stability compared to their bulk counterparts. Here a general van der Waals (vdW) encapsulation method for 2D materials using Sb2 O3 layer of inorganic molecular crystal fabricated via thermal evaporation deposition is reported. It is demonstrated that such a scalable encapsulation method not only maintains the intrinsic properties of typical air-susceptible 2D materials due to their vdW interactions but also remarkably improves their environmental stability. Specifically, the encapsulated black phosphorus (BP) exhibits greatly enhanced structural stability of over 80 days and more sustaining-electrical properties of 19 days, while the bare BP undergoes degradation within hours. Moreover, the encapsulation layer can be facilely removed by sublimation in vacuum without damaging the underlying materials. This scalable encapsulation method shows a promising pathway to effectively enhance the environmental stability of 2D materials, which may further boost their practical application in novel (opto)electronic devices.

Effects of porous media on the phase behaviour of polypeptide solutions

The generalized van der Waals equation for anisotropic fluids in porous media, proposed by the authors in previous works, is used to describe the effect of porous media on the phase behavior of polypeptide solutions. By introducing the temperature dependence for the depth of the potential well and the geometric parameters of the spherocylinder, the main features of phase behavior of the polypeptide poly (γ-benzyl-L-glutamate) (PBLG) in a solution of dimethylformamide, including the existence of two nematic phases, is reproduced. It is shown that the presence of a porous medium shifts the phase diagram to the region of lower densities and lower temperatures.

Van der Waals anomaly: Analog of dark energy with ultracold atoms

In inhomogeneous dielectric media the divergence of the electromagnetic stress is related to the gradients of \varepsilon and \mu, which is a consequence of Maxwell's equations. Investigating spherically symmetric media we show that this seemingly universal relationship is violated for electromagnetic vacuum forces such as the generalized van der Waals and Casimir forces. The stress needs to acquire an additional anomalous pressure. The anomaly is a result of renormalization, the need to subtract infinities in the stress for getting a finite, physical force. The anomalous pressure appears in the stress in media like dark energy appears in the energy-momentum tensor in general relativity. We propose and analyse an experiment to probe the van der Waals anomaly with ultracold atoms. The experiment may not only test an unusual phenomenon of quantum forces, but also an analogue of dark energy, shedding light where nothing is known empirically.

Symmetries and criticality of generalised van der Waals models

We consider a family of thermodynamic models such that the energy density can be expressed as an asymptotic expansion in the scale formal parameter and whose terms are suitable functions of the volume density. We examine the possibility to construct solutions for the Maxwell thermodynamic relations relying on their symmetry properties and deduce the critical properties implied in terms of the dynamics of coexistence curves in the space of thermodynamic variables.