Monomer Fluid Research Articles

Thermodynamic properties of hard-core attractive Yukawa fluids: Single-component monomers, binary mixtures and chains

The first three perturbation terms in the inverse temperature expansion of the Helmholtz free energy of hard-core attractive Yukawa (HCAY) monomer fluids have been determined from computer simulation for several values of the range parameter. The predictions of the resulting perturbation theory for the equation of state and the excess energy are shown to be in excellent agreement with simulation data that are also reported. The theory accurately predicts also the simulation data for the liquid–vapour coexistence densities reported in the literature. Extension of the theory to HCAY binary mixtures is achieved by mapping the mixture to an effective single-component fluid and successfully compared with the simulation data reported in this work. The combination of the theory for the single-component fluid of monomers with a version of the Wertheim thermodynamic perturbation theory (TPT) also provides satisfactory results for HCAY chain fluids.

A Fast Method for Group Rendering Based on SPH

In large-scale combat simulations, operational entities appear in groups. These groups have the overall unity of action and the monomers have the characteristics of independent action in a certain extent. In this paper, we focus on a rapid group rendering method based on Smooth Particle Hydrodynamics (SPH). This method uses the two attributes of discrete monomer and continuous fluid to represent individuals and groups, proposes an autonomous behavior model for each monomer in the group, and studies task-based monomer behavior planning algorithms. On the basis of continuous dynamics, bi-directional distance variation constraints are introduced to accelerate population mapping. The simulation results show that the scheme can effectively improve the drawing speed of the group target.

Assembly of particle strings via isotropic potentials.

Assembly of spherical colloidal particles into extended structures, including linear strings, in the absence of directional interparticle bonding interactions or external perturbation could facilitate the design of new functional materials. Here, we use methods of inverse design to discover isotropic pair potentials that promote the formation of single-stranded, polydisperse strings of colloids "colloidomers" as well as size-specific, compact colloidal clusters. Based on the designed potentials, a simple model pair interaction with a short-range attraction and a longer-range repulsion is proposed which stabilizes a variety of different particle morphologies including (i) dispersed fluid of monomers, (ii) ergodic short particle chains as well as porous networks of percolated strings, (iii) compact clusters, and (iv) thick cylindrical structures including trihelical Bernal spirals.

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.

Nanometer-Resolved Fluidity of an Oleophilic Monomer between Silica Surfaces Modified with Fluorinated Monolayers for Nanoimprinting

Ultraviolet (UV) nanoimprinting has the potential to fabricate sub-15 nm resin patterns, but the interfacial fluidity of organic monomers near monomer liquid/mold solid interfaces related to filling nanoscale mold recesses with UV-curable resins still remains unclear. In this study, we demonstrated that surface forces and resonance shear measurements were helpful to select a surface modifier appropriate for silica mold surfaces for UV nanoimprinting with the low-viscosity monomer 1,10-decanediol diacrylate. Surface forces between silica surfaces mediated with the diacrylate monomer and fluidities of the monomer were investigated with nanometer resolution. Chemical vapor surface modification of silica surfaces with chlorodimethyl(3,3,3-trifluoropropyl)silane (FAS3-Cl) and tridecafluoro-1,1,2,2-tetrahydrooctyltrimethoxysilane (FAS13) gave fluorinated silica surfaces with root-mean-square roughness of less than 0.24 nm suitable for the measurements. When the distance D between two silica surfaces was decreased stepwise in the range of 0-30 nm, monomer viscosity between cleaned silica surfaces increased markedly at D < 6 nm. Surface modification with FAS3-Cl suppressed this increase of interfacial monomer viscosity. In contrast, FAS13-modified silica surfaces caused a jump-in phenomenon at approximately D = 7-9 nm, suddenly decreasing to D = 1 nm as the monomer fluid layer was squeezed out. We concluded that FAS3-Cl was appropriate as a fluorinated surface modifier for silica molds used in UV nanoimprinting with an oleophilic low-viscosity monomer, because the chemisorbed monolayer maintained low monomer viscosity near the surface/monomer interface, in addition to its low surface free energy and short CF3CH2CH2- group.

Comparison between the statistical associating fluid theory for variable range potentials (SAFT-VR) and the first-order mean spherical approximation (FMSA) equations of state for Mie (α, 6) fluids

The respective accuracies of three recent analytical equations of state (EOS) (i.e. analytical representations of the Helmholtz free energy and compressibility factor Z) for the Mie(α,6) monomer fluids are evaluated by comparing the residual Helmholtz free energy, its Barker-Henderson (BH) perturbation terms and Z with the corresponding numerical simulations for the Mie(8,6), Mie(12,6), Mie(20,6) and Mie(30,6) fluids. Two of these EOS stem from the recent enhanced statistical associating fluid theory with variable range potentials (SAFT-VR Mie 2013), with two proposed parameterizations for the free energy first-order BH perturbation term of the Sutherland potentials building up the Mie potential. The third EOS uses a new mapping between the Mie(α,6) and a two-Yukawa potential, for which the first-order mean spherical approximation (FMSA) can be used to obtain analytically the free energy and pressure of the Mie(α,6) fluids up to second order.

Linear, cyclic and branched Lennard-Jones chain quartic equation of state templates for associating fluid model development

Two new cubic equations of state (EOS's) for the pure Lennard-Jones (LJ) monomer fluid are constructed using molecular simulation data for compressibility factor Z versus packing fraction η isotherms. Simulation data for the LJ monomer and dimer pair correlation function at contact value derivatives are fit to extended (quartic) forms of these EOS's and used within the framework of Wertheim's first-order thermodynamic perturbation theory (TPT1) for both the monomer and dimer reference fluid to obtain ten new quartic in molar volume EOS's for straight, cyclic and branched LJ chain fluid isotherms. Predicted Z vs. η for the new equations is compared to simulation data and predictions from much more complex published models. Results show that these simpler equations are much easier to use, with minimal loss in accuracy. Finally, the LJ framework for individual cyclic chains is used in the Marshall–Chapman methodology for branched chains to derive two new LJ TPT1-D platforms and four new equations of state for “branched and fused rings”. The models presented in this paper serve as a foundation for the development of molecularly-based EOS's for real fluids with “soft” intermolecular and intramolecular potentials.

The A in SAFT: developing the contribution of association to the Helmholtz free energy within a Wertheim TPT1 treatment of generic Mie fluids

An accurate representation of molecular association is a vital ingredient of advanced equations of state (EOSs), providing a description of thermodynamic properties of complex fluids where hydrogen bonding plays an important role. The combination of the first-order thermodynamic perturbation theory (TPT1) of Wertheim for associating systems with an accurate description of the structural and thermodynamic properties of the monomer fluid forms the basis of the statistical associating fluid theory (SAFT) family of EOSs. The contribution of association to the free energy in SAFT and related EOSs is very sensitive to the nature of intermolecular potential used to describe the monomers and, crucially, to the accuracy of the representation of the thermodynamic and structural properties. Here we develop an accurate description of the association contribution for use within the recently developed SAFT-VR Mie framework for chain molecules formed from segments interacting through a Mie potential [T. Lafitte, A. Apostolakou, C. Avendaño, A, Galindo, C. S. Adjiman, E. A. Müller, and G. Jackson, J. Chem. Phys. 139, 154504 (2013)]. As the Mie interaction represents a soft-core potential model, a method similar to that adopted for the Lennard-Jones potential [E. A. Müller and K. E. Gubbins, Ind. Eng. Chem. Res. 34, 3662 (1995)] is employed to describe the association contribution to the Helmholtz free energy. The radial distribution function (RDF) of the Mie fluid (which is required for the evaluation of the integral at the heart of the association term) is determined for a broad range of thermodynamic conditions (temperatures and densities) using the reference hyper-netted chain (RHNC) integral-equation theory. The numerical data for the association kernel of Mie fluids with different association geometries are then correlated for a range of thermodynamic states to obtain a general expression for the association contribution which can be applied for varying values of the Mie repulsive exponent. The resulting SAFT-VR Mie EOS allows for a much improved description of the vapour-liquid equilibria and single-phase properties of associating fluids such as water, methanol, ammonia, hydrogen sulphide, and their mixtures. A comparison is also made between the theoretical predictions of the degree of association for water and the extent of hydrogen bonding obtained from molecular simulations of the SPC/E and TIP4P/2005 atomistic models.

Unified SAFT-VR theory for simple and chain fluids formed of square-well, triangular-well, Sutherland and Mie segments

The thermodynamic properties of simple and chain fluids, whose molecules interact through the three following basic hard-core intermolecular potentials: the square-well (SW), the triangular-well (TW) and the Sutherland (SU) [−ε(d/r)γ] potentials are presented in a unified mathematical framework. In order to achieve this goal we use the Barker–Henderson perturbation theory with the macroscopic compressibility approximation (BH-MCA) of monomer fluids combined to a simple, analytic expression of the hard-sphere radial distribution function (RDF) derived by Sun [Can. J. Phys. 83 (2005) 55], which allows the first-order perturbation term of the Helmholtz free energy, f1, to be obtained in terms of the same generic analytic function for the three potentials. This function depends on three parameters which assume different values according to the potential considered. Other thermodynamic quantities such as the compressibility factors can be derived from f1, which thus plays a pivotal role in the equation of state (EOS) obtained from perturbation theory. Numerical values of f1 obtained from this generic function are in good agreement with recent Monte Carlo simulations for the three aforementioned basic potentials, as well as with the various parameterizations of f1 in terms of an effective packing fraction ηeff for the square-well and Sutherland potentials commonly used in the statistical associating fluid theory for potentials of variable range (SAFT-VR). For the corresponding chain fluids, Wertheim first-order thermodynamic perturbation theory (TPT1) is used. It requires the SAFT-VR expressions of the potentials RDF at the hard-core contact d, g(d), and its derivative with respect to the packing fraction, which can be expressed in terms of the generic function giving f1. Numerical values of g(d) are also in agreement with the corresponding Monte Carlo results. The equations of state (EOS) of the SW, TW and SU chain fluids are then obtained in simple, analytical forms. The above three basic potentials can then be combined to give more complicated molecular interactions. One important example of combination is studied. It involves the linear combination of two Sutherland potentials with γ=α, β to obtain the Mie(α,β) class of interactions, of which the Lennard–Jones LJ(12,6) or Mie(12,6) is a particular example. Numerical values of: a) the Mie(12,6) first-order perturbation term of the residual Helmholtz free energy, f1Mie, b) the radial distribution function at contact, gMie(σ), [uMie(σ)=0], and c) the reduced pressure or compressibility factor of the monomer, dimer and tetramer Mie(12,6) fluids, obtained from the generic function, f1, corresponding to the combined Sutherland potentials, are compared to Monte Carlo and molecular dynamics simulations and to the recent enhanced SAFT-VR Mie 20013 EOS of Lafitte et al. [J. Chem. Phys. 139 (2013) 154504], whose improvements with respect to the previous SAFT-VR Mie 2006 EOS are highlighted in detail. The results obtained from the generic function f1 are slightly more accurate for the Mie(12,6) monomer fluid, while the results from Lafitte et al., which uses a new f1 parameterization of ηeff for the Sutherland potentials, valid for 5<γ≤100, are more accurate for the Mie(12,6) dimer and tetramer fluids.

Monte Carlo simulation and equation of state for flexible charged hard-sphere chain fluids: polyampholyte and polyelectrolyte solutions.

The thermodynamic modeling of flexible charged hard-sphere chains representing polyampholyte or polyelectrolyte molecules in solution is considered. The excess Helmholtz energy and osmotic coefficients of solutions containing short polyampholyte and the osmotic coefficients of solutions containing short polyelectrolytes are determined by performing canonical and isobaric-isothermal Monte Carlo simulations. A new equation of state based on the thermodynamic perturbation theory is also proposed for flexible charged hard-sphere chains. For the modeling of such chains, the use of solely the structure information of monomer fluid for calculating the chain contribution is found to be insufficient and more detailed structure information must therefore be considered. Two approaches, i.e., the dimer and dimer-monomer approaches, are explored to obtain the contribution of the chain formation to the Helmholtz energy. By comparing with the simulation results, the equation of state with either the dimer or dimer-monomer approach accurately predicts the excess Helmholtz energy and osmotic coefficients of polyampholyte and polyelectrolyte solutions except at very low density. It also well captures the effect of temperature on the thermodynamic properties of these solutions.

Comparison of several classical density functional theories for the adsorption of flexible chain molecules into cylindrical nanopores

Adsorption of flexible oligomers into narrow cylindrical pores has been studied by means of several versions of classical density functional theory (CDFT) and Monte Carlo simulation. The adsorption process is interesting to study due to the competition between the entropic depletion of oligomers from the pores and the wall-oligomer attraction. It is also challenging to describe using current CDFTs, which tend to overestimate the amount of the adsorbed fluid. From a comparison of several different CDFT approaches, we find that this is due to the assumption of ideal or freely jointed chain conformations. Moreover, it is demonstrated that it is impossible to obtain a reasonable description of the adsorption isotherms without taking into account accurate contact values in the distribution functions describing the structure of the reference monomer fluid. At low densities, more accurate result are obtained in comparison with Monte Carlo simulation data when accurate contact values are incorporated into the theory rather than the more commonly used hard-sphere contact value. However, even the CDFT with accurate contact values still overestimates the amount of the adsorbed fluid due to the ideal or freely jointed chain approximation, used for the description of chain conformations in most CDFT approaches. We find that significant improvement can achieved by employing self-consistent field theory, which samples self-avoiding chain conformations and decreases the number of possible chain conformations, and, consequently, the amount of the adsorbed fluid.

Accurate statistical associating fluid theory for chain molecules formed from Mie segments

A highly accurate equation of state (EOS) for chain molecules formed from spherical segments interacting through Mie potentials (i.e., a generalized Lennard-Jones form with variable repulsive and attractive exponents) is presented. The quality of the theoretical description of the vapour-liquid equilibria (coexistence densities and vapour pressures) and the second-derivative thermophysical properties (heat capacities, isobaric thermal expansivities, and speed of sound) are critically assessed by comparison with molecular simulation and with experimental data of representative real substances. Our new EOS represents a notable improvement with respect to previous versions of the statistical associating fluid theory for variable range interactions (SAFT-VR) of the generic Mie form. The approach makes rigorous use of the Barker and Henderson high-temperature perturbation expansion up to third order in the free energy of the monomer Mie system. The radial distribution function of the reference monomer fluid, which is a prerequisite for the representation of the properties of the fluid of Mie chains within a Wertheim first-order thermodynamic perturbation theory (TPT1), is calculated from a second-order expansion. The resulting SAFT-VR Mie EOS can now be applied to molecular fluids characterized by a broad range of interactions spanning from soft to very repulsive and short-ranged Mie potentials. A good representation of the corresponding molecular-simulation data is achieved for model monomer and chain fluids. When applied to the particular case of the ubiquitous Lennard-Jones potential, our rigorous description of the thermodynamic properties is of equivalent quality to that obtained with the empirical EOSs for LJ monomer (EOS of Johnson et al.) and LJ chain (soft-SAFT) fluids. A key feature of our reformulated SAFT-VR approach is the greatly enhanced accuracy in the near-critical region for chain molecules. This attribute, combined with the accurate modeling of second-derivative properties, allows for a much improved global representation of the thermodynamic properties and fluid-phase equilibria of pure fluids and their mixtures.

Bone cement and the implications for anaesthesia

Poly(methyl methacrylate) (PMMA) was developed in 1928 and was first marketed under the name of ‘Plexiglas’. Since then, PMMA has been used in a huge number of applications, including transparent glass substitutes in windows, semiconductor research, and for the bodies of electric guitars. PMMA has a good degree of biocompatibility, which has made it an important component of replacement intraocular lenses, dentures, and dental filling composite materials. In orthopaedic surgery, PMMA bone cement is used to affix implants and to remodel lost bone. The medical orthopaedic use of PMMA is universally credited to Sir John Charnley, who was inspired by his dentist to use dental acrylic for prosthetic fixation in total hip replacement (THR) procedures in 1957. In 1965, he began to use bone cement (CMW Bone Cement TM ) that was developed specifically for THRs rather than dental acrylic. Bone cement is now routinely used in a variety of orthopaedic procedures. The microscopic structure of bone cement comprises two substances glued together. The so-called ‘pearls’ in bone cement consist of small particles of pre-polymerized PMMA, which are present as white powder. The second substance is a liquid monomer of methyl methacrylate (MMA). Both substances are mixed together in theatre after the addition of a catalyst that initiates the polymerization of the monomer fluid. When the bone cement hardens, the individual pearls are entrapped and glued within the net of the polymerized monomer, but no chemical binding occurs between the pearls and the polymerized

Application of a renormalization-group treatment to the statistical associating fluid theory for potentials of variable range (SAFT-VR)

An accurate prediction of phase behavior at conditions far and close to criticality cannot be accomplished by mean-field based theories that do not incorporate long-range density fluctuations. A treatment based on renormalization-group (RG) theory as developed by White and co-workers has proven to be very successful in improving the predictions of the critical region with different equations of state. The basis of the method is an iterative procedure to account for contributions to the free energy of density fluctuations of increasing wavelengths. The RG method has been combined with a number of versions of the statistical associating fluid theory (SAFT), by implementing White's earliest ideas with the improvements of Prausnitz and co-workers. Typically, this treatment involves two adjustable parameters: a cutoff wavelength L for density fluctuations and an average gradient of the wavelet function Φ. In this work, the SAFT-VR (variable range) equation of state is extended with a similar crossover treatment which, however, follows closely the most recent improvements introduced by White. The interpretation of White's latter developments allows us to establish a straightforward method which enables Φ to be evaluated; only the cutoff wavelength L then needs to be adjusted. The approach used here begins with an initial free energy incorporating only contributions from short-wavelength fluctuations, which are treated locally. The contribution from long-wavelength fluctuations is incorporated through an iterative procedure based on attractive interactions which incorporate the structure of the fluid following the ideas of perturbation theories and using a mapping that allows integration of the radial distribution function. Good agreement close and far from the critical region is obtained using a unique fitted parameter L that can be easily related to the range of the potential. In this way the thermodynamic properties of a square-well (SW) fluid are given by the same number of independent intermolecular model parameters as in the classical equation. Far from the critical region the approach provides the correct limiting behavior reducing to the classical equation (SAFT-VR). In the critical region the β critical exponent is calculated and is found to take values close to the universal value. In SAFT-VR the free energy of an associating chain fluid is obtained following the thermodynamic perturbation theory of Wertheim from the knowledge of the free energy and radial distribution function of a reference monomer fluid. By determining L for SW fluids of varying well width a unique equation of state is obtained for chain and associating systems without further adjustment of critical parameters. We use computer simulation data of the phase behavior of chain and associating SW fluids to test the accuracy of the new equation.

Novel cationic pH-responsive poly( N, N-dimethylaminoethyl methacrylate) microcapsules prepared by a microfluidic technique

Novel monodisperse cationic pH-responsive microcapsules are successfully prepared using oil-in-water-in-oil double emulsions as templates by a microfluidic technique in this study. With the use of a double photo-initiation system and the adjustment of pH value of the monomer solution, cross-linked poly( N, N-dimethylaminoethyl methacrylate) (PDM) microcapsules with good sphericity and monodispersity can be effectively fabricated. The obtained microcapsule membranes swell at low pH due to the protonation of N(CH 3) 2 groups in the cross-linked PDM networks. The effects of various preparation parameters, such as pH of the aqueous monomer fluid, concentration of cross-linker, concentration of monomer N, N-dimethylaminoethyl methacrylate (DM) and addition of copolymeric monomer acrylamide (AAm), on the pH-responsive swelling characteristics of PDM microcapsules are systematically studied. The results show that, when the PDM microcapsules are prepared at high pH and with low cross-linking density and low DM monomer concentration, they exhibit high pH-responsive swelling ratios. The addition of AAm in the preparation decreases the swelling ratios of PDM microcapsules. The external temperature has hardly any influence on the swelling ratios of PDM microcapsules when the external pH is less than 7.4. The prepared PDM microcapsules with both biocompatibility and cationic pH-responsive properties are of great potential as drug delivery carriers for tumor therapy. Moreover, the fabrication methodology and results in this study provide valuable guidance for preparation of core–shell microcapsules via free radical polymerization based on synergistic effects of interfacial initiation and initiation in a confined space.

Coaxially Electrospun Fibrillar Structures as Templates and Hosts for Synthesis Processes

This work has demonstrated coaxial electrospun polymeric sheath fibrillar structure as useful tool for hosting chemical reactions within confined volume and potential templating material for the synthesis of extended one-dimensional structures. In addition, this work has successfully demonstrated the novel production of micron sized epoxy fibers via coaxial electrospinning. Epoxy monomer fluids were polymerized within the polyamide 6/6 (PA 66) sheath structures and upon removal of PA 66, long continuous epoxy fibers were revealed.

Modeling the phase behavior, excess enthalpies and Henry's constants of the H 2O + H 2S binary mixture using the SAFT-VR+D approach

The high-pressure phase diagram and other thermodynamic properties of the binary systems of water + hydrogen sulphide have been examined using the SAFT-VR+D equation of state [Zhao and McCabe, J. Chem. Phys. 125 (2006) 104504]. The SAFT-VR+D approach is based on a version of the statistical associating fluid theory that was developed to model dipolar fluids by explicitly accounting for dipolar interactions and their effect on the thermodynamics and structure of a fluid. In the SAFT-VR+D equation this is achieved through the use of the generalized mean spherical approximation (GSMA) to describe a monomer fluid of dipolar square-well segments. In the present work, we further develop the SAFT-VR+D equation to study mixtures of dipolar associating fluids of arbitrary size using the analytical solution of the Ornstein–Zernike equation due to Cummings and Blum [J. Chem. Phys. 84, 1833 (1986)]. The high-pressure phase diagram and other thermodynamic properties of the water + hydrogen sulphide binary mixture are then examined. Both components, hydrogen sulphide and water, are naturally modeled as associating spherical molecules with four off-centre sites to mimic hydrogen bonding and an embedded dipole moment ( μ) to describe their polarity. Using simple Lorentz–Berthelot combining rules, the theory is able to predict the phase behavior of the H 2O + H 2S system from pure component parameters. Specifically, type III phase behavior according to the classification of Scott and van Konynenburg is observed, with a three-phase line at low temperatures that terminates at an upper critical end point and two separate critical lines, one at high temperatures that runs continuously from a gas–liquid critical line to a liquid–liquid critical line at high pressures and a second gas–liquid critical line located at low temperatures. The phase behavior predicted by the SAFT-VR+D approach is in excellent agreement with the experimental data, without requiring any fitted binary interaction parameters. In addition, the theory is also able to describe the excess molar enthalpies and the most important features of the Henry's constants as a function of temperature.

Phase behavior of dipolar fluids from a modified statistical associating fluid theory for potentials of variable range

A statistical associating fluid theory for potentials of variable range to model dipolar fluids is presented. The new theory, termed the SAFT-VR+D equation (the statistical associating fluid theory for potentials of variable range plus dipole), explicitly accounts for dipolar interactions and their effect on the structure of the fluid. This is achieved through the use of the generalized mean spherical approximation (GMSA) to describe a reference fluid of dipolar square-well segments. Isothermal-isobaric and Gibbs ensemble Monte Carlo simulations have been performed in order to test the new theoretical approach. Predictions for the thermodynamic properties and phase behavior of dipolar square-well monomer and chain fluids, in which one or more segments are dipolar, are considered and compared with new computer simulation data. The results show that the equation of state in general provides a good description of the phase behavior of dipolar monomer and chain fluids. Some deviations are seen between the simulation data and theoretical predictions for monomer fluids with large dipole moments and for molecules composed of segments with dipoles in different orientations. This is addressed through the replacement of the GMSA by the linearized exponential approximation.

Capillary condensation of short-chain molecules

A density-functional study of capillary condensation of fluids of short-chain molecules confined to slitlike pores is presented. The molecules are modeled as freely jointed tangent spherical segments with a hard core and with short-range attractive interaction between all the segments. We investigate how the critical parameters of capillary condensation of the fluid change when the pore width decreases and eventually becomes smaller than the nominal linear dimension of the single-chain molecule. We find that the dependence of critical parameters for a fluid of dimers and of tetramers on pore width is similar to that of the monomer fluid. On the other hand, for a fluid of chains consisting of a larger number of segments we observe an inversion effect. Namely, the critical temperature of capillary condensation decreases with increasing pore width for a certain interval of values of the pore width. This anomalous behavior is also influenced by the interaction between molecules and pore walls. We attribute this behavior to the effect of conformational changes of molecules upon confinement.

Generalized equation of state for square-well potentials of variable range

An equation of state for square-well fluids of short and long potential range λ is presented and compared with Gibbs ensemble and canonical Monte Carlo simulation data; vapour–liquid coexistence densities, vapour pressures, internal energies and contact radial distribution functions are examined. The equation is an extension of that presented in previous work for the reference monomer fluid in the SAFT-VR approach [GIL-VILLEGAS et al., 1997, J. chem. Phys., 106, 4168]. The Helmholtz free energy is written as a high-temperature expansion up to second order, where simple expressions are obtained for the mean attractive energy and the fluctuation term using the mean-value theorem and a mapping of radial distribution functions. In previous work the range of the square-well potential was limited to λ ≤ 1.8. In this work we show that the phase behaviour of such a fluid is far from the expected long-range limits given by the mean-field and van der Waals approximations. We extend the applicability of the equation of state to ranges up to λ = 3, and show that, in this case, the phase behaviour of the fluid is essentially that of a fluid of infinite potential range (van der Waals limit). At short ranges (λ < 1.8) the calculated coexistence is virtually identical to that of the previous approach, hence ensuring that its application within a SAFT-VR framework is consistent with previous work. The extension of the approach to longer ranges is of interest in the context of modelling of polar fluids, and in the implementation of cross-over approaches to treat the critical region.