Square-well Potential Research Articles

Application of the SAFT-VR equation of state to vapor–liquid equilibrium calculations for pure components and binary mixtures using the Sutherland potential

An equation of state based on the statistical associating fluid theory for potentials of variable range (SAFT-VR) has been applied to model 35 pure associating and non-associating fluids and 15 binary mixtures. The pure components consist of alkanes, alcohols, water, aromatics and polar or multi-polar compounds like ammonia and H 2S. In contrast to other attempts which have used the SAFT-VR model for various thermodynamic calculations using the square-well or Yukawa potentials, the short-range dispersion interactions have been accounted for here using the Sutherland potential, while hydrogen bonding interactions are explicitly taken into account as in other versions of the SAFT approach. The Sutherland potential is particularly useful for modeling the interactions among multi-polar species. Model parameters for the pure components have been optimized by fitting available experimental data on vapor pressure, saturated vapor density and saturated liquid density for temperatures ranging from near the triple point up to reduced temperatures of 0.9. The effect of several simplifying assumptions aimed at reducing the number of model parameters has been investigated, and the resulting trends in parameters has been discussed. Binary interaction coefficients have been obtained for the binary systems by fitting experimental data on vapor–liquid equilibrium pressure and phase concentrations. Results have been compared to those obtained using other versions of the SAFT-VR model.

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.

Penetrable-square-well fluids: Analytical study and Monte Carlo simulations

We study structural and thermophysical properties of a one-dimensional classical fluid made of penetrable spheres interacting via an attractive square-well potential. Penetrability of the spheres is enforced by reducing from infinite to finite the repulsive energy barrier in the pair potentials As a consequence, an exact analytical solution is lacking even in one dimension. Building upon previous exact analytical work in the low-density limit [A. Santos, R. Fantoni, and A. Giacometti, Phys. Rev. E 77, 051206 (2008)], we propose an approximate theory valid at any density and in the low-penetrable regime. By comparison with specialized Monte Carlo simulations and integral equation theories, we assess the regime of validity of the theory. We investigate the degree of inconsistency among the various routes to thermodynamics and explore the possibility of a fluid-fluid transition. Finally we locate the dependence of the Fisher-Widom line on the degree of penetrability. Our results constitute the first systematic study of penetrable spheres with attractions as a prototype model for soft systems.

Modeling the phase behavior of polydisperse rigid rods with attractive interactions with applications to single-walled carbon nanotubes in superacids

The phase behavior of rodlike molecules with polydisperse length and solvent-mediated attraction and repulsion is described by an extension of the Onsager theory for rigid rods. A phenomenological square-well potential is used to model these long-range interactions, and the model is used to compute phase separation and length fractionation as a function of well depth and rod concentration. The model closely captures experimental data points for isotropic/liquid crystalline phase coexistence of single-walled carbon nanotubes (SWCNTs) in superacids. The model also predicts that the isotropic-biphasic boundary approaches zero as the acid strength diminishes, with the possibility of coexistence of isotropic and liquid crystalline phases at very low concentrations; this counterintuitive prediction is confirmed experimentally. Experimental deviations from classical theories for rodlike liquid crystals are explained in terms of polydispersity and the balance between short-range repulsion and long-range attractions. The predictions of the model also hold practical importance for applications of SWCNT/superacid solutions, particularly in the processing of fibers and films from liquid crystalline SWCNT/superacid mixtures.

Predicting adsorption isotherms of asphaltenes in porous materials

In this paper we present a molecular thermodynamics approach for the modeling of adsorption isotherms of asphaltenes adsorbed on Berea sandstone, Bedford limestone and dolomite rock, using a model for bulk asphaltenes precipitation and a quasi-two-dimensional approach for confined fluids [E. Buenrostro-González, C. Lira-Galeana, A. Gil-Villegas, J. Wu, AIChE J., 50 (2004) 2552–2570; A. Martínez, M. Castro, C. McCabe A. Gil-Villegas, J. Chem. Phys. 126 (2007) 074707, respectively], both based on the Statistical Associating Fluid Theory for Potentials of Variable Range [A. Gil-Villegas, A. Galindo, P.J. Whitehead, S.J. Mills, G. Jackson, A.N. Burgess, J. Chem. Phys. 106 (1997) 4168–4186]. The theory is applied to model adsorption isotherms from experimental data of asphaltenes extracted from a dead sample of heavy crude oil from a Mexican reservoir. The theoretical results give the right Langmuir Type II adsorption isotherms observed experimentally. The model requires the determination of ten molecular parameters related to the size of the particles and the square-well potentials used to describe the particle–surface and particle–particle interactions at the bulk and adsorbed phases. Nine parameters are taken from previous published results about the behavior of asphaltenes in bulk phases and the adsorption of several molecular fluids onto activated carbon and graphite surfaces. The remaining parameter, the energy strength of the particle–surface interaction, is adjusted to reproduce the experimental data, obtaining values that are consistent with Molecular Mechanics calculations for asphaltenes adsorbed on different surfaces and solutions. Although the agreement between theory and experiments shows some deviations at low bulk concentrations, the model reproduces adsorption data at high concentrations where other semi-empirical approaches fail.

Electron–electron interaction effects in heliumlike atoms confined in finite external square-well potential

A B-spline-based configuration interaction method is used to compute the energy levels of the ground and a few excited states of heliumlike atoms confined in a finite external square-well potential, as a function of the depth of the confining shell potential. The electron probability density and the dependence of the energy levels in the shell potential are used to account for the electron-electron interaction when the atoms are submitted to such an environment.

A square-well equation of state for aqueous strong electrolyte solutions

A simple and accurate electrolyte-equation of state is introduced for correlation of the mean activity coefficients of strong aqueous electrolyte solutions. The nonelectrolyte contribution of the new electrolyte-equation of state is based on the cubic square-well equation of state, SWEOS, that is composed of the van der Waals repulsive part of EOS and the attractive term is based on the square-well potential. The explicit version of the mean spherical approximation (MSA) is adopted for electrostatic contribution of electrolyte solution. The new electrolyte-equation of state, eEOS, has three adjustable parameters per each salt that are optimized by correlation of the mean activity coefficients of more than 130 binary aqueous electrolyte solutions at 25 °C and 1 bar. Furthermore, the parameters are used for prediction of the osmotic coefficients and densities of several aqueous binary electrolyte solutions at 25 °C. Also the mean activity and osmotic coefficient of a number of electrolytes have been correlated in temperature range of 0–100 °C. Moreover, the ionic specific parameters are obtained for five binary aqueous electrolyte solutions by simultaneous fitting of mean activity, osmotic coefficient and apparent molal volume. The results demonstrate that the new eEOS can be applied for accurate representation of the activity and osmotic coefficients of the aqueous electrolyte solutions at wide range of the electrolyte concentration and temperature of binaries.

Wetting and drying transitions in mean-field theory: Describing the surface parameters for the theory of Nakanishi and Fisher in terms of a microscopic model

The theory of Nakanishi and Fisher [Phys. Rev. Lett. 49, 1565 (1982)] describes the wetting behavior of a liquid and vapor phase in contact with a substrate in terms of the surface chemical potential h(1) and the surface enhancement parameter g. Using density functional theory, we derive molecular expressions for h(1) and g and compare with earlier expressions derived from Landau lattice mean-field theory. The molecular expressions are applied to compare with results from density functional theory for a square-gradient fluid in a square-well fluid-substrate potential and with molecular dynamics simulations.

Reaction efficiency of diffusion-controlled processes on finite aperiodic planar arrays. II. Potential effects

We continue our study of diffusion–reaction processes on finite aperiodic lattices, viz., the Penrose lattice and a Girih tiling. Focusing on bimolecular reactions, we mobilize the theory of finite Markov processes to document the effect of attractive forces on the reaction efficiency. Considering both a short-range square-well potential and a longer-range 1/ r S ( S = 4, 6) potential, we find that irreversible reactive encounters between reactants on a Girih platelet are kinetically advantaged relative to processes on a Penrose platelet. This result generalizes the conclusion reached in our earlier study [Roberto A. Garza-López, Aaron Kaufman, Reena Patel, Joseph Chang, Jack Brzezinski, John J. Kozak, Chem. Phys. Lett. 459 (2008) 137] where entropic factors (only) were assessed.

Theoretical study of solvent effects on the coil-globule transition

The coil-globule transition of a polymer in a solvent has been studied using Monte Carlo simulations of a single chain subject to intramolecular interactions as well as a solvent-mediated effective potential. This solvation potential was calculated using several different theoretical approaches for two simple polymer/solvent models, each employing hard-sphere chains and hard-sphere solvent particles as well as attractive square-well potentials between some interaction sites. For each model, collapse is driven by variation in a parameter which changes the energy mismatch between monomers and solvent particles. The solvation potentials were calculated using two fundamentally different methodologies, each designed to predict the conformational behavior of polymers in solution: (1) the polymer reference interaction site model (PRISM) theory and (2) a many-body solvation potential (MBSP) based on scaled particle theory introduced by Grayce [J. Chem. Phys. 106, 5171 (1997)]. For the PRISM calculations, two well-studied solvation monomer-monomer pair potentials were employed, each distinguished by the closure relation used in its derivation: (i) a hypernetted-chain (HNC)-type potential and (ii) a Percus-Yevick (PY)-type potential. The theoretical predictions were each compared to results obtained from explicit-solvent discontinuous molecular dynamics simulations on the same polymer/solvent model systems [J. Chem. Phys. 125, 194904 (2006)]. In each case, the variation in the coil-globule transition properties with solvent density is mostly qualitatively correct, though the quantitative agreement between the theory and prediction is typically poor. The HNC-type potential yields results that are more qualitatively consistent with simulation. The conformational behavior of the polymer upon collapse predicted by the MBSP approach is quantitatively correct for low and moderate solvent densities but is increasingly less accurate for higher densities. At high solvent densities, the PRISM-HNC and MBSP approaches tend to overestimate, while the PRISM-PY approach underestimates the tendency of the solvent to drive polymer collapse.

Generalized van der Waals theory for the twist elastic modulus and helical pitch of cholesterics

We present a generalized van der Waals theory for a lyotropic cholesteric system of chiral spherocylinders based on the classical Onsager theory for hard anisometric bodies. The rods consist of a hard spherocylindrical backbone surrounded with a square-well potential to account for attractive (or soft repulsive) interactions. Long-ranged chiral interactions are described by means of a simple pseudoscalar potential which is appropriate for weak chiral forces of a predominant electrostatic origin. Based on the formalism proposed by Straley [Phys. Rev. A 14, 1835 (1976)], we derive explicit algebraic expressions for the twist elastic modulus and the cholesteric pitch for rods as a function of density and temperature. The pitch varies nonmonotonically with density, with a sharp decrease at low packing fractions and a marked increase at higher packing fractions. A similar trend is found for the temperature dependence. The unwinding of the helical pitch at high densities (or low temperatures) originates from a strong enhancement of the local nematic order and the corresponding increase in the twist elastic resistance associated with near-parallel local rod configurations. This contrasts with the commonly held view that the increase in pitch with decreasing temperature as often observed in cholesterics is due to layer formation resulting from presmectic fluctuations. The increase in pitch with increasing temperature is consistent with an entropic unwinding as the chiral interaction becomes less significant than the thermal energy. The variation of the pitch with density, temperature, and contour length is in qualitative agreement with recent experimental results on colloidal fd rods.

Collapse-driven self-assembly of multiblock chains: A Monte Carlooff-lattice study

Abstract We perform off-lattice Monte Carlo simulations for multiblock chains, ( 5 A - 5 B ) n , with n = 10 , 20 , 30 , 40 , 50 , and 60 , in an implicit selective solvent, using a discontinuous square-well potential. We present selected thermodynamic and structural properties as a function of the reduced temperature, such as the reduced energy per segment, the reduced heat capacity, and the mean-squared radius of gyration. We observe that the collapse-driven self-assembled structure is not spherical above certain value of chain length, N, and develops a non-spherical globular structure with multiple cores.

Driven on- and off-lattice gas

An on- and off-lattice analog of the driven lattice gas has been studied by molecular-dynamics simulation. In the model, particles move on a two-dimensional lattice potential under a constant driving force. They also interact with each other by an attractive square-well pair potential. A heat bath removes as heat the work done by the driving field. The case of zero field recovers equilibrium two-dimensional lattice and continuous-space results. With nonzero field and a strong lattice potential, the system is comparable to the driven lattice gas. As in the driven lattice gas, the anisotropic single-strip configuration persists to higher kinetic energy as the field strength increases. In the case of zero lattice strength, the model reduces to an off-lattice two-dimensional driven square-well fluid. Single-strip steady states are not observed off lattice.

Inner segment radial distribution functions at contact point for chain-like molecules

Here we present, by simple geometric arguments, a proposal to calculate the radial distribution function at the contact point (RDF) between inner chain segments for chain-like molecules. Segments are identified as disconnected spheres, dimmer segments, or inner chain segments according to the number of adjacent joined spheres. The RDF expressions are based on three main considerations: a) the segment-surface area available for contact is additive for the two segments correlated by the RDF; b) the RDFs between segments with the same segment-surface area are considered equal; c) the effect of chain length on the RDF is neglected. In order to test the proposed equations, canonical ensemble Monte Carlo simulations were performed in order to obtain the RDF of segments in mixtures involving monomers, dimers, and n-mer chains ( n = 4, 8, and 16), where each chain is composed of freely-jointed tangent spheres interacting by the square-well potential. Even though we present very simple equations, the calculated RDFs are in very good agreement with those obtained from molecular simulations. The assumption that adjacent segments respond to the major contribution for the contact correlation function is confirmed at all conditions. The results indicate that the approach presented here can be useful for improving calculations of thermodynamic properties of chain molecules.

Exact nonlinear Bloch-state solutions for Bose–Einstein condensates in a periodic array of quantum wells

A set of exact closed-form Bloch-state solutions to the stationary Gross–Pitaevskii equation are obtained for a Bose–Einstein condensate in a one-dimensional periodic array of quantum wells, i.e. a square-well periodic potential. We use these exact solutions to comprehensively study the Bloch band, the compressibility, effective mass and the speed of sound as functions of both the potential depth and interatomic interaction. According to our study, a periodic array of quantum wells is more analytically tractable than the sinusoidal potential and allows an easier experimental realization than the Krönig–Penney potential, therefore providing a useful theoretical model for understanding Bose–Einstein condensates in a periodic potential.

Stokes−Einstein Relation in Two- and Three-Dimensional Fluids

The Stokes−Einstein relation, relating the self-diffusion coefficient D to the shear viscosity η (D = kBT/2πησ), is tested for two- and three-dimensional fluids. The influence of attractive potential and temperature on the validity of the Stokes−Einstein relation by employing square-well potential is analyzed. A breakdown of the Stokes−Einstein relation is observed at low temperatures for three-dimensional fluid by using the Nigra and Evans(11) model and with that obtained from the velocity autocorrelation function(10) and for two-dimensional fluids by using the Garcia−Rojo et al.(12) model for hard discs.

Structural and Functional Analysis of Transmembrane XI of the NHE1 Isoform of the Na+/H+ Exchanger

The Na(+)/H(+) exchanger isoform 1 is a ubiquitously expressed integral membrane protein that regulates intracellular pH in mammals by extruding an intracellular H(+) in exchange for one extracellular Na(+). We characterized structural and functional aspects of the critical transmembrane (TM) segment XI (residues 449-470) by using cysteine scanning mutagenesis and high resolution NMR. Each residue of TM XI was mutated to cysteine in the background of the cysteine-less protein and the sensitivity to water-soluble sulfhydryl reactive compounds MTSET ((2-(trimethylammonium) ethyl)methanethiosulfonate) and MTSES ((2-sulfonatoethyl) methanethiosulfonate) was determined for those residues with at least moderate activity remaining. Of the residues tested, only proteins with mutations L457C, I461C, and L465C were inhibited by MTSET. The activity of the L465C mutant was almost completely eliminated, whereas that of the L457C and I461C mutants was partially affected. The structure of a peptide representing TM XI (residues Lys(447)-Lys(472)) was determined using high resolution NMR spectroscopy in dodecylphosphocholine micelles. The structure consisted of helical regions between Asp(447)-Tyr(454) and Phe(460)-Lys(471) at the N and C termini of the peptide, respectively, connected by a region with poorly defined, irregular structure consisting of residues Gly(455)-Gly(459). TM XI of NHE1 had a structural similarity to TM XI of the Escherichia coli Na(+)/H(+) exchanger NhaA. The results suggest that TM XI is a discontinuous helix, with residue Leu(465) contributing to the pore.

Determination of atomic scattering lengths from measurements of molecular binding energies near Feshbach resonances

We present an analytic model to calculate the atomic scattering length near a Feshbach resonance from data on the molecular binding energy. Our approach considers finite-range square-well potentials and can be applied near broad, narrow, or even overlapping Feshbach resonances. We test our model on ${\mathrm{Cs}}_{2}$ Feshbach molecules. We measure the binding energy using magnetic-field modulation spectroscopy in a range where one broad and two narrow Feshbach resonances overlap. From the data we accurately determine the Cs atomic scattering length and the positions and widths of two particular resonances.

Monte Carlo Simulation of Surfactant Adsorption on Hydrophilic Surfaces

Monte Carlo simulations have been carried out to study the adsorption behavior of small flexible amphiphilic molecules on solid surfaces from aqueous solutions. A simple coarse-grained solvent-free off-lattice model, with a square-well pair potential and hard core excluded volume effect, has been used. Adsorption isotherms for weakly and strongly hydrophilic homogeneous surfaces have been determined. The adsorbed layer displays a coexistence region with an upper critical point. Below the critical temperature a densely packed patch coexists with a two-dimensional gas-analogous phase. Above the critical temperature, a percolating network forms at higher surfactant concentrations. Depending on the ratio between the strength of the hydrophobic effect and the adsorption energy, a large variety of associates has been observed. Monolayers, bilayers, admicelles, small clusters, and percolating networks as typical associate structures have been found. In the four-region model, which is extended by the coexistence region, a characteristic adsorbed layer structure for each region can be detected. Intermediate structure types have been produced by variation of the adsorption energy.

Effects of pH, salt type, and ionic strength on the second virial coefficients of aqueous bovine serum albumin solutions

The osmotic pressures of aqueous bovine serum albumin (BSA) solutions were measured at different pH (3.6, 4.6, 5.6, and 7.6) in combination with different concentrations (0.01 M, 0.1 M, 1 M, and 3 M) of salts (sodium, pottasium, and lithum) by using a Wescor colloid membrane osmometer. The osmotic second virial coefficients for BSA were determined from the experimental osmotic pressure. Predominant forces between protein molecules were measured at the various pH, ionic strength, and type of salt. These experimental data were utilized to determine the depth of square-well potential, which accounts for specific interactions between protein molecules at various conditions.