A general local composition and coordination number model for square-well fluids with variable well width and diameter ratio

A radial distribution function for attractive hard-core systems is obtained from the equilibrium of a molecular pair between local and bulk environments. With this function, a general model is established for the coordination number (CN) and local composition (LC) of square-well fluids. It meets the low-density, high-density and high-temperature limit conditions, as well as the unlike pair conservation and quasi-chemical equilibrium conditions. It also has some other features that many other models do not have: (1) its CN and LC expressions contain all pair potentials; (2) it yields temperature-dependent CN and LC for closely packed mixtures with different pair potentials; (3) its energy parameter is the difference of the total potentials of one pair in local and bulk environments, not the difference of two pair potentials. This model can accurately predict the CN, LC and compressibility factors of square-well fluids from computer simulation over a wide range of density, well width (λ?=?1–2) and diameter ratio. For the case λ?=?1.5, this model is better than or comparable with semi-empirical models; in other cases, it is far better than semi-empirical models. It does not need any empirical parameter for LC prediction. For the prediction of CN and compressibility factors, it only needs the smoothed radial distribution function of pure hard-sphere fluids. It also gives excellent results for lattice gases and highly nonideal lattice mixtures.     

Quasi-2D and prewetting transitions of square-well fluids on a square-well substrate

Molecular simulation methodologies are employed to study the first-order transition of variable square-well (SW) fluids on a wide range of weak attractive surfaces. Surface phase diagram of SW fluids of attractive well diameter λ _ff = 1.5, 1.75, 2.0 on a smooth, structureless surface modelled by a SW potential is reported via grand-canonical transition-matrix Monte Carlo (GC-TMMC) and histogram reweighting techniques. Fluids with λ _ff = 1.5 and 1.75 show quasi-2D vapour–liquid phase transition; on the other hand, prewetting transition is visible for a SW fluid with larger well-extent λ _ff = 2.0. The prewetting line, its length, and closeness to the bulk saturation curve are found to depend strongly on the nature of the fluid–fluid and fluid–wall interaction potentials. Boundary tension of surface coexistence films is calculated by two methods. First, the finite size scaling approach of Binder is used to evaluate the boundary tension via GC-TMMC. Second, the results of the boundary tension are verified by virtue of its relation to the pressure tensor components, which are calculated using a NVT-Monte Carlo approach. The results from the two methods are in good agreement. Boundary tension is found to increase with the increase in the wall–fluid interaction range for the quasi-2D system; conversely, boundary tension for thin–thick film, at prewetting transition, decreases with the increase in the wall–fluid interaction range.     

Thermodynamic properties of square-well fluids from a new coordination number model

A new coordination number model is proposed for square-well fluids at λ?=?1.5. The model modifies the theory previously developed for the coordination number of square-well fluids derived on the basis of the generalized Van der Waals theory by Largo and Solana. The present work proposes a new formula for the maximum reduced density and a new method to solve the integral corresponding to coordination number of hard sphere fluids. Thermodynamic quantities such as pair correlation function at contact, excess internal energy and constant volume excess heat capacity are determined employing the model. Good agreement is achieved between theoretical results and Monte Carlo (M.C.) data. As expected, the results of the excess heat capacity are poor at low temperatures.     

An equation of state contribution for dipolar and quadrupolar square-well fluids

A dipolar–quadrupolar contribution to the residual Helmholtz energy for a polar square well (a square well plus either a point dipole or a point quadrupole) fluid is developed based on the Padé approximation. Taking the square well system as reference, the contribution is formulated using an expansion for radial distribution function of the reference system. In addition to square well potential parameters the contribution depends only on dipole and quadrupole moments. This term is added as perturbation to a generalized equation of state for square well fluids. The results are then compared with the available simulation data in the literature. With the new equation obtained, it was possible to predict liquid–vapour equilibrium properties and critical properties of polar square well fluids more accurately than with available perturbation theories for multipolar square well systems. Application of the equation of state to a real dipolar (water) and a real quadrupolar (carbon dioxide) fluid indicated that the polar contribution greatly improved the predictions of saturation properties. Accurate prediction of critical properties for polar square well fluids remains as a challenge. This work can be useful in the development of better equations of state.     

Heat transfer over a stretching surface with variable heat flux in micropolar fluids

Heat transfer over a stretching surface with uniform or variable heat flux in micropolar fluids is investigated in this Letter. The boundary layer equations are transformed into ordinary differential equations, and then they are solved numerically by a finite-difference method. The effects of the material parameter K, Prandtl number Pr, velocity exponent parameter m, and heat flux exponent parameter n on the heat transfer characteristics are studied. It is found that the local Nusselt number is higher for micropolar fluids compared to Newtonian fluids.     

An accurate theory for the square-well potential: from long to short well width

Density function theory (DFT) is combined with the first-order mean spherical approximation (FMSA) to study the radial distribution function (RDF) of the square-well (SW) potential. The combination (DFT + FMSA) is based on the direct correlation function (DCF) of the FMSA. Upon comparison with computer simulation data, DFT + FMSA is shown to give better performance than FMSA for mid- and long-range attractions. For short-range and very short-range attractions, the theory successfully corrects the deficiencies of the original FMSA. Comparisons include the evaluation of contact values, gap height at a discontinuity and profiles of the RDF. This work provides an accurate and consistent way to handle the SW potential.     

An integral equation and Monte Carlo study of homo- and hetero- nuclear square-well diatomic fluids

Square-well homo-nuclear and hetero-nuclear diatomic fluids are studied using the Ornstein-Zernike equation and the recently proposed RHNC-VM closure. Monte Carlo canonical simulations have been performed to complete recent literature simulation data. The integral equation thermodynamic and structural results are compared with these and literature simulation data at three elongations over a large range of densities and temperatures. The RHNC-VM theory agrees excellently with the simulation thermodynamic and structural results. Its accuracy revealed slight errors in simulation data in work by Lisal and Nezbeda [1999, Molec. Phys., 96, 335]. The data have been re-simulated.     

Classical fluids of negative heat capacity

It is shown that new parametersX can be defined such that the heat capacity C_xT(S/T)_x is negative, even when the canonical ensemble [i.e., at fixed T=(U/S)_Y and YX] is stable. This implies an extension of the classical theory of polytropes from ideal gases to general fluids. As examples of negative heat capacity systems we treat blackbody radiation and general gas systems with nonsingular _T. For the case of a simple ideal gas we even exhibit an apparatus which enforces a constraint X(p, V)=const that makes C_x<0. We then show that it is possible to infer the statistical mechanics of canonicallyunstable systems-for which even the traditional heat capacities are negative-by imposing constraints that stabilize the associated noncanonical ensembles. Two explicit models are discussed.     

A modified soft-core fluid model for the direct correlation function of the square-shoulder and square-well fluids

We propose a simple analytical expression of the direct correlation function for the square-shoulder and square-well fluids. Our approximation is based on an ansatz for the direct correlation function of a modified soft-core fluid, whose parameters are adjusted by fitting the data obtained from Monte Carlo computer simulations. Moreover, it is complemented with a Wertheim-like parametrization to reproduce correctly the direct correlation inside the hard-core. We demonstrate that this approach is in quantitative agreement with the numerical solution of the Ornstein–Zernike equation within the Percus–Yevick approximation. We also show that our results are accurate in a large regime of densities for different interaction ranges and potential strengths. Therefore, this opens up the possibility of introducing the square-shoulder or the square-well potentials as new reference systems in advanced theoretical approximations.     

A self-consistent approach for modelling the interfacial properties and phase diagrams of Yukawa,Lennard-Jones and square-well fluids

A self-consistent density-functional approach is presented for describing the phase behaviour and interfacial tensions of van der Waals fluids represented by the hard-core Yukawa (HCY), Lennard-Jones (LJ) and square-well (SW) potentials. The excess Helmholtz energy functional is formulated in terms of a modified fundamental measure theory (MFMT) for the short-ranged repulsion and a density-gradient expansion for the van der Waals attractions. Analytical expressions for the direct correlation functions of uniform fluids are utilized to take into account the effect of van der Waals’ attraction on intermolecular correlations. For bulk phases, the density functional theory is reduced to an equation of state (EOS) that provides accurate saturation pressures and vapour–liquid phase diagrams. Near the critical region, the long-range fluctuations can be corrected by using the renormalization group (RG) theory. With the same set of molecular parameters, the theory also yields satisfactory surface tensions and interfacial density profiles at all relevant temperatures.     

Heat capacity of isolated clusters

The character of interaction between thermal (vibrational) and configurational cluster excitations is considered under adiabatic conditions when a cluster is a member of a microcanonical ensemble. The hierarchy of equilibration times determines the character of atomic equilibrium in the cluster. The behavior of atoms in the cluster can be characterized by two effective (mean) temperatures, corresponding to the solid and liquid aggregate states, because the typical time for equilibration of atomic motion is less than the transition time between aggregate states. If the cluster is considered for a time much longer than the typical dwell time in either phase, then it is convenient to characterize the system by only one temperature, which is determined from the statistical-thermodynamic long-time average. These three temperatures are not far apart, nor are the cluster heat capacities evaluated on the basis of these definitions of temperature. The heat capacity of a microcanonical ensemble may be negative for two coexisting phases if the mean temperature is defined in terms of the mean kinetic energy, rather than as the derivative of energy with respect to microcanonical entropy. However, if the configurational excitation energy is smaller than the total excitation energy separating the phases, then the two-state model predicts a positive heat capacity under either definition of temperature. Moreover, if the cluster is sufficiently large, then the maximum values of the microcanonical and canonical heat capacities are equal.     

“Negative heat capacity” of stratified fluids

In “doubly nonequilibrium” fluids (e.g., solutions with stratified temperature and impurity concentration in the gravitational field), situations are possible when the addition of heat decreases temperature and vice versa. This is demonstrated by the simple example of a convection problem.     

Broad-band band-pass filter with variable center frequency and band width

This paper describes a new type of broad-band band-pass filter in which both the center frequency and band width are variable. The filter is composed of four balanced mixers, two local oscillators, an amplifier, and high-pass and low-pass filters. The center frequency and band width can be varied by changing the frequencies of two local oscillators. The center frequency is variable in the range 2–16 GHz, and the band width in the range 20–800 MHz.     

Heat capacity of high-pressure ice polymorphs

The isobaric heat capacity C_P of high-pressure water ice polymorphs (ices III, V, VI, and VII) is calculated using P-V-T equations of state of ices, jump condition for C_P on the lines of phase transition, and the equations of the lines of phase transition on the P-T diagram of water substance.     

An automatically controlled Nd:YAG laser with variable pulse width

The development of a high-energy, pulsed Nd:YAG laser system for materials-processing and medical applications is reported here. A variable pulse width in the range of 0.3–10 ms and a variable pulse repetition rate up to 50 pps are provided. An automatic operation system using a microprocessor-based driver/ controller enables safe operation of the laser system and automatic material processing when integrated in a laser/robot system.