Square-well Chain Research Articles

Predicting phase coexistence and adsorption isotherms of classical and quantum fluids using the microcanonical-ensemble perturbation theory (MEPT)

The Microcanonical-Ensemble Perturbation Theory (MEPT) of Sastre et al. (2018) [7] has been extended to study the vapor-liquid phase coexistence of binary and ternary mixtures of fluids. The attractive interactions between chains of molecules are represented as monomer segments interacting via a square-well pair potential. Calculations for the thermodynamic properties and phase behavior of square-well monomer chains are considered and compared with experimental data. Molecular parameters have been obtained to model the phase behavior of real fluids such as n-alkanes (from C1 to C12), nitrogen, perfluoromethane, carbon dioxide, i-butane, i-pentane, neon, and hydrogen. Furthermore, the capability of the MEPT approach in predicting critical and azeotropic lines of binary and ternary mixtures is explored. The results demonstrate that the MEPT approach provides a robust description of the phase behavior of mixtures containing chains of fluids. Additionally, we have integrated the MEPT approach with the two-dimensional Statistical Associating Fluid Theory for fluids interacting via variable range potentials (SAFT-VR-2D) to investigate the effect of quantum contributions on both phase behavior and adsorption. Remarkable improvements are observed when both higher order perturbation terms of the Helmholtz free energy and quantum contributions are included in the predictions of the phase behavior of quantum fluids such as neon and hydrogen. In all cases, the theoretical results exhibit favorable comparisons with experimental data in a wide range of compositions, pressures, and temperatures.

Equation of state with quantum effects for square-well chain fluid with variable range

Equation of state with quantum effects for square-well chain fluid with variable range

Interfacial properties of square-well chains from molecular dynamics simulation

ABSTRACT Square-well (SW) potential is likely the simplest potential describing attractive and repulsive interactions. However, its discontinuous functional form makes it difficult to be used in Molecular Dynamics (MD) simulation, particularly with commercial MD packages. Recently, Zerón and collaborators [Mol. Phys. 116, 3355 (2018)] have presented a parameterisation of the SW potential that allows its use for simulation packages since the intermolecular potential and force are described by continuous mathematical functions. It was validated for SW spheres. In this work, we use this reported continuous SW potential to describe for the first time the equilibrium and interfacial properties of SW chains, with potential ranges of and 1.75. Simulations for tetramers interacting with are compared with available computational data in the literature, which has allowed to validate the method for molecular chain systems. Besides, a systematic study for the potential range of has not been addressed so far, which represents valuable information for instance to discern whether different microscopic theories are capable of describing this type of system. In particular, we assess the effect of temperature, chain length, and potential range on the calculated properties, namely density profiles, coexistence densities, vapour pressures, surface tensions and critical points. Overall, with increasing the chain length, the width of the envelope of the coexistence phase increases, which results in an increase of the surface tension as well as the critical temperature at the same time that the vapour pressure and the interfacial width decrease.

Experimental Determination and Modeling of Density, Viscosity, and Surface Tension for Sulfolane + Ethyl Acetate and + n-Propyl Acetate

The density, viscosity, and surface tension for the binary mixtures of sulfolane + ethyl acetate and + n-propyl acetate were measured at the atmospheric pressure and temperature ranging from 308.15 to 328.15 K. The linear equation and Andrade model were successfully used to correlate the experimental density and viscosity, respectively. On the basis of the experimental data, the viscosity energy barrier and the surface entropy/enthalpy were further obtained. The calculation of the molecular interaction energy using the Dmol3 module in Materials Studio software shows that the interaction energy in sulfolane + ethyl acetate is slightly greater than one in sulfolane + n-propyl acetate, which is consistent with the experimental observation. In addition, each experimental property of density, viscosity, and surface tension can well be reproduced by the square-well chain fluid with variable range (SWCF-VR) equation of state with one different binary adjustable parameter.

Effects of macromolecular crowding on the folding of a polymer chain: A Wang–Landau simulation study

A flexible polymer chain in the presence of inert macromolecular crowders will experience a loss of configurational entropy due to the crowder excluded volume. This entropy reduction will be most pronounced in good solvent conditions where the chain assumes an expanded coil conformation. For polymers that undergo a folding transition from a coil to a compact ordered state, as is the case for many globular proteins, macromolecular crowding is expected to stabilize the folded state and thereby shift the transition location. Here, we study such entropic stabilization effects for a tangent square-well sphere chain (monomer diameter σ) in the presence of hard-sphere (HS) crowders (diameter D ≥ σ). We use the Wang-Landau simulation algorithm to construct the density of states for this chain in a crowded environment and are thus able to directly compute the reduction in configurational entropy due to crowding. We study both a chain that undergoes all-or-none folding directly from the coil state and a chain that folds via a collapsed-globule intermediate state. In each case, we find an increase in entropic stabilization for the compact states with an increase in crowder density and, for fixed crowder density, with a decrease in crowder size (concentrated, small crowders have the largest effect). The crowder significantly reduces the average size for the unfolded states while having a minimal effect on the size of the folded states. In the athermal limit, our results directly provide the confinement free energy due to crowding for a HS chain in a HS solvent.

Phase Equilibria of Polydisperse Square-Well Chain Fluid Confined in Random Porous Media: TPT of Wertheim and Scaled Particle Theory.

Extension of Wertheim's thermodynamic perturbation theory and its combination with scaled particle theory is proposed and applied to study the liquid-gas phase behavior of polydisperse hard-sphere square-well chain fluid confined in the random porous media. Thermodynamic properties of the reference system, represented by the hard-sphere square-well fluid in the matrix, are calculated using corresponding extension of the second-order Barker-Henderson perturbation theory. We study effects of polydispersity and confinement on the phase behavior of the system. While polydispersity causes increase of the region of phase coexistence due to the critical temperature increase, confinement decreases the values of both critical temperature and critical density making the region of phase coexistence smaller. This effect is enhanced with the increase of the size ratio of the fluid and matrix particles. The increase of the average chain length at fixed values of polydispersity and matrix density shifts the critical point to a higher temperature and a slightly lower density.

The role of higher-order terms in perturbation approaches to the monomer and bonding contributions in a SAFT-type equation of state for square-well chain fluids

ABSTRACTA perturbation theory for square-well chain fluids is developed within the scheme of the (generalised) Wertheim thermodynamic perturbation theory. The theory is based on the Pavlyukhin parametrisations [Y. T. Pavlyukhin, J. Struct. Chem. 53, 476 (2012)] of their simulation data for the first four perturbation terms in the high temperature expansion of the Helmholtz free energy of square-well monomer fluids combined with a second-order perturbation theory for the contact value of the radial distribution function of the square-well monomer fluid that enters into bonding contribution. To obtain the latter perturbation terms, we have performed computer simulations in the hard-sphere reference system. The importance of the perturbation terms beyond the second-order one for the monomer fluid and of the approximations of different orders in the bonding contribution for the chain fluids in the predicted equation of state, excess energy and liquid–vapour coexistence densities is analysed.

Note: Rigorous results for the partition function of a square-well chain in hard-sphere solvent.

First Page

Polymer Folding in Slitlike Nanoconfinement

A flexible homopolymer chain with sufficiently short-range interactions undergoes a discontinuous transition from an expanded coil to a compact crystallite analogous to the all-or-none folding transition exhibited by fast-folding proteins. In this work we investigate the effects of both tethering and confinement on this type of folding transition. In particular, we study a flexible square-well N-mer chain (monomer diameter σ) located between two hard walls forming a slitlike pore (width W) with the chain end tethered to one wall. We carry out Monte Carlo simulations with Wang–Landau sampling to construct the single-chain density of states and use both microcanonical and canonical analyses to characterize phase transitions. We find that in a very wide pore (W > Nσ) the all-or-none folding transition is only slightly affected by the tethering. As the pore width is reduced to near the size of the folded polymer chain (W ≈ N1/3σ) there is a modest entropy reduction for the unfolded states leading to a stabili...

Vapour-liquid interfacial properties of square-well chains from density functional theory and Monte Carlo simulation.

The statistical associating fluid theory for attractive potentials of variable range (SAFT-VR) density functional theory (DFT) developed by [Gloor et al., J. Chem. Phys., 2004, 121, 12740-12759] is used to predict the interfacial behaviour of molecules modelled as fully-flexible square-well chains formed from tangentially-bonded monomers of diameter σ and potential range λ = 1.5σ. Four different model systems, comprising 4, 8, 12, and 16 monomers per molecule, are considered. In addition to that, we also compute a number of interfacial properties of molecular chains from direct simulation of the vapour-liquid interface. The simulations are performed in the canonical ensemble, and the vapour-liquid interfacial tension is evaluated using the wandering interface (WIM) method, a technique based on the thermodynamic definition of surface tension. Apart from surface tension, we also obtain density profiles, coexistence densities, vapour pressures, and critical temperature and density, paying particular attention to the effect of the chain length on these properties. According to our results, the main effect of increasing the chain length (at fixed temperature) is to sharpen the vapour-liquid interface and to increase the width of the biphasic coexistence region. As a result, the interfacial thickness decreases and the surface tension increases as the molecular chains get longer. The interfacial thickness and surface tension appear to exhibit an asymptotic limiting behaviour for long chains. A similar behaviour is also observed for the coexistence densities and critical properties. Agreement between theory and simulation results indicates that SAFT-VR DFT is only able to predict qualitatively the interfacial properties of the model. Our results are also compared with simulation data taken from the literature, including the vapour-liquid coexistence densities, vapour pressures, and surface tension.

A non-additive repulsive contribution in an equation of state: The development for homonuclear square well chains equation of state validated against Monte Carlo simulation.

This work consists of the adaptation of a non-additive hard sphere theory inspired by Malakhov and Volkov [Polym. Sci., Ser. A 49(6), 745-756 (2007)] to a square-well chain. Using the thermodynamic perturbation theory, an additional term is proposed that describes the effect of perturbing the chain of square well spheres by a non-additive parameter. In order to validate this development, NPT Monte Carlo simulations of thermodynamic and structural properties of the non-additive square well for a pure chain and a binary mixture of chains are performed. Good agreements are observed between the compressibility factors originating from the theory and those from molecular simulations.

Wang-Landau simulation of Gō model molecules.

Gō-like models are one of the oldest protein modeling concepts in computational physics and have proven their value over and over for forty years. The essence of a Gō model is to define a native contact matrix for a well-defined low-energy polymer configuration, e.g., the native state in the case of proteins or peptides. Many different potential shapes and many different cut-off distances in the definition of this native contact matrix have been proposed and applied. We investigate here the physical consequences of the choice for this cut-off distance in the Gō models derived for a square-well tangent sphere homopolymer chain. For this purpose we are performing flat-histogram Monte Carlo simulations of Wang-Landau type, obtaining the thermodynamic and structural properties of such models over the complete temperature range. Differences and similarities with Gō models for proteins and peptides are discussed.

A new perturbed-chain equation of state for square-well chains in fluid and solid phases

Considering the hard-chain system as reference, a perturbed-chain equation of state (EOS) is developed. The second-order thermodynamic perturbation theory EOS is applied to the reference system. Monte Carlo simulation data for average intra-molecular and inter-molecular segment-segment radial distribution function of hard-chain systems with a chain length of 3-10 in the range of packing fraction between 0.1 and 0.72, covering both fluid and solid phases, are reported. A disordered solid phase structure is considered in this work. These customized data are used to develop the perturbation term of square-well (SW) attractions. The performance of perturbed-chain EOS is tested against computer simulation data from the literature for compressibility factor and phase equilibrium in the systems of SW chains. Results within good accuracy are obtained for all the test cases. Global vapor-liquid-solid equilibrium diagrams for SW chain systems predicted by the new EOS are reported.

Partition function zeros and phase transitions for a square-well polymer chain

The zeros of the canonical partition functions for flexible square-well polymer chains have been approximately computed for chains up to length 256 for a range of square-well diameters. We have previously shown that such chain molecules can undergo a coil-globule and globule-crystal transition as well as a direct coil-crystal transition. Here we show that each of these transitions has a well-defined signature in the complex-plane map of the partition function zeros. The freezing transitions are characterized by nearly circular rings of uniformly spaced roots, indicative of a discontinuous transition. The collapse transition is signaled by the appearance of an elliptical horseshoe segment of roots that pinches down towards the positive real axis and defines a boundary to a root-free region of the complex plane. With increasing chain length, the root density on the circular ring and in the space adjacent to the elliptical boundary increases and the leading roots move towards the positive real axis. For finite-length chains, transition temperatures can be obtained by locating the intersection of the ellipse and/or circle of roots with the positive real axis. A finite-size scaling analysis is used to obtain transition temperatures in the long-chain (thermodynamic) limit. The collapse transition is characterized by crossover and specific-heat exponents of φ≈0.76(2) and α≈0.66(2), respectively, consistent with a second-order phase transition.

Application of the statistical associating fluid theory for potentials of variable range (SAFT-VR) coupled with renormalisation-group (RG) theory to model the phase equilibria and second-derivative properties of pure fluids

In earlier work, a methodology to couple SAFT-VR with an RG treatment (SAFT-VR+RG) for square-well chain and associating fluids was presented [E. Forte, F. Llovell, L.F. Vega, J.P.M. Trusler, A. Galindo, J. Chem. Phys. 134 (15) (2011) 154102]. The approach is based on a recursive procedure which begins with an initial free energy incorporating only contributions from short-wavelength density fluctuations, which are treated locally. The contribution from long-wavelength fluctuations is incorporated through the iterative procedure based on attractive interactions that incorporate the structure of the fluid following the ideas of perturbation theories and using a mapping that allows integration of the radial distribution function. The resulting SAFT-VR+RG theory provides an equation of state based on the classical SAFT-VR equation and yields the correct critical behaviour without the need for additional adjustable parameters. In this work, the application of this equation to real fluids is presented. The ability of the methodology to reproduce the phase behaviour close to and far from criticality solely through the standard SAFT-VR molecular parameters is demonstrated here. Molecular model parameters for a range of fluids, both non-associating and associating are presented, including the homologous series of n-alkanes, benzene, carbon dioxide, water, light alcohols, ammonia, hydrogen fluoride and hydrogen sulphide. These were determined by comparison with experimental data for vapour pressure and saturated liquid density. Furthermore, the models presented are used to predict second derivative properties for these compounds. Deviations compared with the original SAFT-VR equation are discussed in order to assess further the improvements introduced by the coupled theory to predict these properties. The critical exponents α, β, γ and δ have also been obtained for a number of these fluids and found to be in good agreement with the universal values of the three-dimensional Ising model.

Universal scaling behaviour of surface tension of molecular chains

We use and extend the universal relationship recently proposed by Galliero [G. Galliero, J. Chem. Phys. 133, 074705 (2010)], based on a combination of the corresponding-states principle of Guggenheim [E. A. Guggenheim, J. Chem. Phys. 13, 253 (1945)] and the parachor approach of Macleod [J. Macleod, Trans. Faraday Soc. 19, 38 (1923)], to predict the vapour-liquid surface tension of fully flexible chainlike Lennard-Jones molecules. In the original study of Galliero, the reduced surface tension of short-chain molecules formed by up to five monomers is expressed as a unique function of the difference between the liquid and vapour coexistence densities. In this work, we extend the applicability of the recipe and demonstrate that it is also valid for predicting the surface tension of two different chainlike molecular models, namely, linear tangent chains that interact through the Lennard-Jones intermolecular potential and fully flexible chains formed by spherical segments interacting through the square-well potential. Computer simulation data for vapour-liquid surface tension of fully flexible and rigid linear Lennard-Jones, and fluid flexible square-well chains is taken from our previous works. Our results indicate that the universal scaling relationship is able to correlate short- and long-chain molecules with different degrees of flexibility and interacting through different intermolecular potentials.

Density functional theory for the selective adsorption of small molecules on a surface modified with polymer brushes

A density functional method based on weighted density approximation is extended to study the selective adsorption of small molecules on a surface modified with end-grafted square-well chains. The excess part of the Helmholtz free energy functional is divided into two components: the hard sphere repulsion and the square-well attraction. The equation of state for hard sphere chain fluids developed by Liu et al. is used to calculate the repulsive part of the excess Helmholtz free energy functional, and the equation of state for square-well chain fluid with variable range developed by Li et al. is employed to calculate the attractive part. With this theoretical model, we examine the physical properties of the grafted polymer and the selective adsorption of small molecules on the modified surface.

Equation of state of square-well chain fluid with variable range for CO<sub>2</sub> + physical absorption solvent

采用变阱宽方阱链流体(SWCF-VR)状态方程关联了CO 2 在几种常规物理吸收溶剂中的溶解度数据, 得到了二元交互作用参数, 建立了二元交互作用参数与温度的关联式. 结果表明, 采用一个二元交互作用参数, SWCF-VR 方程均能很好地描述CO 2 在常规流体中的溶解度, 尤其能满意再现甲醇低温洗工艺中CO 2 -甲醇的相行为. 利用建立的二元交互作用参数与温度的关联式, 可将SWCF-VR 状态方程拓展应用于预测二元系统气液两相的密度以及CO 2 -物理吸收溶剂多元系统的气液平衡.

Capturing Thermodynamic Behavior of Ionic Liquid Systems: Correlations with the SWCF-VR Equation

An equation of state for square-well chain fluids with variable well-width range (SWCF-VR EoS) [Li et al. Fluid Phase Equilib.2009, 276, 57] was applied to ionic liquid (IL) systems. ILs were treat...

Modeling pVT Properties and Vapor-Liquid Equilibrium of Ionic Liquids Using Cubic-plus-association Equation of State

Combining Peng-Robinson (PR) equation of state (EoS) with an association model derived from shield-sticky method (SSM) by Liu et al., a new cubic-plus-association (CPA) EoS is proposed to describe the thermodynamic properties of pure ionic liquids (ILs) and their mixtures. The new molecular parameters for 25 ILs are obtained by fitting the experimental density data over a wide temperature and pressure range, and the overall average deviation is 0.22%. The model parameter b for homologous ILs shows a good linear relationship with their molecular mass, so the number of model parameters is reduced effectively. Using one temperature-independent binary adjustable parameter k ij , satisfactory correlations of vapor-liquid equilibria (VLE) for binary mixtures of ILs + non-associating solvents and + associating solvents are obtained with the overall average deviation of vapor pressure 2.91% and 7.01%, respectively. In addition, VLE results for ILs + non-associating mixtures from CPA, lattice-fluid (LF) and square-well chain fluids with variable range (SWCF-VR) EoSs are compared.