Density functional theory for inhomogeneous associating chain fluids

We propose a nonlocal density functional theory for associating chain molecules. The chains are modeled as tangent spheres, which interact via Lennard-Jones (12,6) attractive interactions. A selected segment contains additional, short-ranged, highly directional interaction sites. The theory incorporates an accurate treatment of the chain molecules via the intramolecular potential formalism and should accurately describe systems with strongly varying external fields, e.g., attractive walls. Within our approach we investigate the structure of the liquid-vapor interface and capillary condensation of a simple model of associating chains with only one associating site placed on the first segment. In general, the properties of inhomogeneous associating chains depend on the association energy. Similar to the bulk systems we find the behavior of associating chains of a given length to be in between that for the nonassociating chains of the same length and that for the nonassociating chains twice as large.     

Common Intersection Points of Bulk Modulus for Liquefied Natural Gas (LNG) Mixtures

During recent developments on the theories and experimental techniques of compressed liquids and liquid mixtures, it has been revealed that there exist some regularities. Among these, the regularity found by Huang and O'Connell is that the isotherms of reduced bulk modulus of compressed liquids as a function of molar volume intersect at a common point. This intersection is a useful tool for evaluating the reliability of an equation of state (EOS) for producing equilibrium properties of matter. This paper also deals with an extension of the above regularity to some liquefied natural gas (LNG) mixtures including: N₂+CH₄, N₂+C₂H₆, CH₄+C₂H₆, CH₄+C₃H₈, and CH₄+C₄H₁₀ at different temperatures. The present work gives a theoretical analysis for the common bulk modulus point in terms of a statistical‐mechanical equation of state for mixtures. In addition, we have calculated excess molar volume of N₂+CH₄ mixture in terms of temperature and compared it with experimental values.     

Application of a new simplified SAFT to VLE study of associating and non-associating fluids

A new equation of state based on the Statistical Associating Fluid Theory (SAFT) is presented to study the phase behavior of associating and non-associating fluids. In the new equation of state, the hard sphere contribution to compressibility factor of the simplified version of the SAFT (SSAFT) is replaced with that proposed by Ghotbi and Vera. The Ghotbi–Vera SSAFT (GV-SSAFT) was also extended to study the phase behavior of associating and non-associating mixtures. The GV-SSAFT like the SSAFT equation of state has three adjustable segment parameters for non-associating fluids and five parameters for associating fluids. The experimental data of liquid densities and vapor pressures for pure fluids studied in this work were used to obtain the best values for the parameters of the GV-SSAFT. The results obtained from the GV-SSAFT for liquid densities and vapor pressures of pure associating and non-associating fluids were compared with those obtained from the SSAFT equation of state. The results showed that the GV-SSAFT similar to the SSAFT can accurately correlate the experimental data of liquid density and vapor pressure for systems studied. On the other hand the results obtained from two SAFT-based equations of state are almost identical. In order to show capability of the GV-SSAFT and SSAFT equations of state, they were used to directly calculate heat of vaporization for a number of pure associating and non-associating fluids. Slightly better results for heat of vaporization comparing to the experimental data were obtained from the GV-SSAFT EOS than those obtained from the SSAFT. The GV-SSAFT was also used to study the VLE phase behavior for a number of binary associating and non-associating mixtures. The results also showed that the GV-SSAFT can be successfully used to study the phase behavior of mixtures studied in this work.     

Preparation,rheological and drag reduction properties of hydrophobically associating polyacrylamide polymer

Hydrophobically associating polymer (HAMDP) was synthesized by using acrylamide, acrylic acid, 2-acrylamido-2-methylpropane sulfonic acid and dodecyl 2-methylacrylate as main monomers. Dynamic rheometer and self-made simulation evaluation apparatus were used to test the rheological and drag reduction properties of HAMDP. With the mass concentration increased, the apparent viscosity of HAMDP increased. The critical aggregation concentration was 2.29g/L. With the changement of the strain, the elastic modulus was larger than viscous modulus. With the increment of HAMDP, the area of thixotropic loop increased. Compared with commercial polyacrylamide, the drag reduction rate of HAMDP could be up to 62.38%.     

Resummed thermodynamic perturbation theory for central force associating potential. Multi-patch models

A resummed thermodynamic perturbation theory for associating fluids with multiply bondable central force associating potential is extended for the fluid with multiple number of multiply bondable associating sites. We consider a multi-patch hard-sphere model for associating fluids. The model is represented by the hard-sphere fluid system with several spherical attractive patches on the surface of each hard sphere. Resummation is carried out to account for blocking effects, i.e., when the bonding of a particle restricts (blocks) its ability to bond with other particles. Closed form analytical expressions for thermodynamical properties (Helmholtz free energy, pressure, internal energy, and chemical potential) of the models with arbitrary number of doubly bondable patches at all degrees of the blockage are presented. In the limiting case of total blockage, when the patches become only singly bondable, our theory reduces to Wertheim's thermodynamic perturbation theory (TPT) for polymerizing fluids. To validate the accuracy of the theory we compare to exact values, for the thermodynamical properties of the system, as determined by Monte Carlo computer simulations. In addition we compare the fraction of multiply bonded particles at different values of the density and temperature. In general, predictions of the present theory are in good agreement with values for the model calculated using Monte Carlo simulations, i.e., the accuracy of our theory in the case of the models with multiply bondable sites is similar to that of Wertheim's TPT in the case of the models with singly bondable sites.     

Size effect on the rheological behavior of nanoparticle suspensions in associating polymer solutions

Associating polymers are hydrophilic long-chain molecules containing a small amount of hydrophobic groups and tend to create bonds between chains by reversible associating interactions. The effects of associating polymer on the steady-shear viscosity and dynamic viscoelasticity are studied for suspensions of silica nanoparticles with diameters of 8, 18, and 25 nm. The silica particles of 8 nm are entrapped in the transient network of associating polymer by reversible adsorption. The enhancement of network results in the high viscosity with a Newtonian flow profile in the limit of zero shear rate. In suspensions of 25 nm silica, the hydrophobes extending from the chains adsorbed onto different particles can form a micelle by association interactions. The multichain bridging gave rise to the shear-thinning flow and high storage modulus at low frequencies. The suspensions of 25 nm silica are characterized as flocculated systems. Because of intermediate curvature, the flexible bridges are formed between silica particles of 18 nm. When the flexible bridges are highly extended within the lifetime in shear fields, the suspensions show shear-thickening flow. The shear-thickening flow can be attributed to the elastic effect of flexible bridges.     

Monte Carlo study of interfacial properties of associating fluids

Canonical Monte Carlo Simulations have been performed to calculate liquid-vapor properties of the associating square well and Lennard-Jones fluids with one and two sites. Simulations were carried out by using several values of reduced temperatures and association energies. The orthobaric densities, as well as the surface tension of associating square well fluids, were calculated and compared with those reported previously in literature; a good agreement was found among them. Results of surface tension of two-sites associating Lennard-Jones fluids are presented here for the first time.     

Thermodynamic properties for liquid mercury using GMA equation of state

The important known regularities and thermodynamic properties of liquid mercury have been studied based on the average potential energy. Recognised regularities, the linearity of Zeno contour, bulk modulus and secant bulk modulus as functions of temperature, isochors of pressure versus temperature and near linearity of the inverse isobaric expansion coefficient have been investigated, all evaluated using the Goharshadi–Morsali–Abbaspour equation of state. The validity of the equation of state in predicting thermophysical properties is confirmed by a statistical parameter, absolute average deviation, with a maximum value of 0.41, showing excellent agreement with the experiment at temperatures between 293.15 and 323.15?K from low to high pressures.     

Extension of the new proposed association equation of state (AEOS) to associating fluid mixtures

Recently, a new statistical mechanic-based equation of state has been proposed by Mohsen-Nia and Modarress [M. Mohsen-Nia, H. Modarress, Chem. Phys. 336 (2007) 22–26] for associating pure fluids. The new association equation of state (AEOS) was successfully applied to calculate the saturated properties of water, methanol, and ammonia. In this work, the new proposed AEOS is used to evaluate the (vapour + liquid) equilibrium (VLE) of 25 associating pure compounds and the adjusted parameters are reported. The new AEOS is also extended to mixtures containing associating and non-associating compounds. The calculated saturated properties of the pure compounds are compared with those calculated by other AEOSs. The results of VLE calculation for various binary mixtures such as: alcohol/hydrocarbon, alcohol/CO₂, alcohol/aromatic-hydrocarbons, and the quaternary system (H₂O/CH₄/CO₂/H₂S) indicate the capability of the new proposed AEOS for associating pure and mixture calculations.     

Rheological behavior of silica suspensions in aqueous solutions of associating polymer

Associating polymers are hydrophilic long-chain molecules containing a small amount of hydrophobic groups. The aqueous solutions show viscoelastic responses above some critical concentrations because a three-dimensional structure is formed by association of hydrophobic groups. When the associating polymers are added to silica suspensions at low concentrations, the flocculation is induced by bridging mechanisms, and the flow of suspensions become shear-thinning. For suspensions prepared with polymer solutions in which the associating network is developed, the viscosity decreases, shows a minimum, and then increases with increasing particle concentration. The viscosity decrease may arise from the breakdown of associating network due to adsorption of polymer chains onto the silica surfaces. As the particle concentration is increased, the polymer concentration in solution is decreased, and finally, all polymer chains are adsorbed on the surfaces. Beyond this point, the partial coverage of particle surfaces takes place and strong interactions are generated between particles by polymer bridging. Since the stable suspensions are converted to highly flocculated systems, the viscosity is increased and the flow becomes shear-thinning. The concentration effect of silica particles on the viscosity behavior of suspensions can be explained by a combination of viscosity decrease in solution due to polymer adsorption and viscosity increase due to flocculation.     

Linear viscoelastic properties of transient networks formed by associating polymers with multiple stickers

We have developed a single-chain theory that describes dynamics of associating polymer chains carrying multiple associative groups (or stickers) in the transient network formed by themselves and studied linear viscoelastic properties of this network. It is shown that if the average number N of stickers associated with the network junction per chain is large, the terminal relaxation time τ(A) that is proportional to τ(X)N(2) appears. The time τ(X) is the interval during which an associated sticker goes back to its equilibrium position by one or more dissociation steps. In this lower frequency regime ω<1/τ(X), the moduli are well described in terms of the Rouse model with the longest relaxation time τ(A). The large value of N is realized for chains carrying many stickers whose rate of association with the network junction is much larger than the dissociation rate. This associative Rouse behavior stems from the association/dissociation processes of stickers and is different from the ordinary Rouse behavior in the higher frequency regime, which is originated from the thermal segmental motion between stickers. If N is not large, the dynamic shear moduli are well described in terms of the Maxwell model characterized by a single relaxation time τ(X) in the moderate and lower frequency regimes. Thus, the transition occurs in the viscoelastic relaxation behavior from the Maxwell-type to the Rouse-type in ω<1/τ(X) as N increases. All these results are obtained under the affine deformation assumption for junction points. We also studied the effect of the junction fluctuations from the affine motion on the plateau modulus by introducing the virtual spring for bound stickers. It is shown that the plateau modulus is not affected by the junction fluctuations.     

Prediction of global vapor-liquid equilibria for mixtures containing polar and associating components with improved renormalization group theory

Our recently improved renormalization group (RG) theory is further reformulated within the context of density functional theory. To improve the theory for polar and associating fluids, an explicit and complete expression of the theory is derived in which the density fluctuation is expanded up to the third-order term instead of the original second-order term. A new predictive equation of state based on the first-order mean spherical approximation statistical associating fluid theory (FMSA-SAFT) and the newly improved RG theory is proposed for systems containing polar and associating fluids. The calculated results for both pure fluids and mixtures are in good agreement with experimental data both inside and outside the critical region. This work demonstrates that the RG theory incorporated with the solution of FMSA is a promising route for accurately describing the global phase behavior of complex fluids and mixtures.     

Structure and anomalous solubility for hard spheres in an associating lattice gas model

In this paper we investigate the solubility of a hard-sphere gas in a solvent modeled as an associating lattice gas. The solution phase diagram for solute at 5% is compared with the phase diagram of the original solute free model. Model properties are investigated both through Monte Carlo simulations and a cluster approximation. The model solubility is computed via simulations and is shown to exhibit a minimum as a function of temperature. The line of minimum solubility (TmS) coincides with the line of maximum density (TMD) for different solvent chemical potentials, in accordance with the literature on continuous realistic models and on the "cavity" picture.     

Viscosity behavior of silica suspensions flocculated by associating polymers

Associating polymers are hydrophilic long-chain molecules containing a small number of hydrophobic groups, and act as flocculants in aqueous suspensions. The effects of associating and nonassociating polymers on viscosity behavior are studied for silica suspensions. Since flocculation is induced by polymer bridging, the viscosity behavior is converted from Newtonian to shear-thinning profiles. The additions of surfactant cause an increase in viscosity for suspensions prepared with associating polymer, whereas the flow behavior of suspensions with nonassociating polymer is not significantly influenced. In adsorption of associating polymers onto silica particles, the chain may adopt a conformation with a water-soluble backbone attached to the particle surfaces. The hydrophobic groups extending from the chains adsorbed onto different particles can form a micelle by association with surfactant. Therefore, the bridging flocculation is enhanced by surfactant. The cooperative micellar formation between associating polymer and surfactant is responsible for viscosity increase in suspensions.     

Bulk and interfacial wetting behavior of binary mixtures induced by associating between unlike-pair molecules

The statistical associating fluid theory of Wertheim is applied to describe binary mixtures with associating between unlike-pair molecules. The phase behavior of this binary mixture would fall into five different types (I, II, III, V, and VI) of the classification scheme of van Konynenburg and Scott by varying the associating strength and the energy parameters. Both interfacial wetting behavior and wetting transitions are carefully examined in all the vapor-liquid-liquid (gamma-beta-alpha) three-phase-coexisting regions of the binary mixtures. The global wetting behavior and wetting transitions are delineated by scanning the parameter space. In certain regions, the middle beta phase exhibits interfacial phase transitions sequentially, nonwetting --> partial-wetting --> nonwetting, at the interface separating lower alpha and upper gamma phases along with increasing temperature.     

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.     

Virial coefficients and inversion curve of simple and associating fluids

Free energy simulation method is applied to calculate the virial coefficients of square-well (SW) fluids of variable well-width and square-well based dimer forming associating fluids. In this approach, Monte Carlo sampling is performed on a number of molecules equal to the order of integral, and configurations are weighted according to the absolute value of the integrand. An umbrella-sampling average yields the value of the cluster integral in reference to a known integral. By using this technique, we determine the virial coefficients up to B₆ for SW fluid with variable potential range from λ = 1.25 to λ = 3.0 and model associating fluids with different association strengths: ?_af = 0.0, 8.0, 16.0 and 22.0. These calculated values for SW fluids are in good agreement with the literature. We examine these coefficients in the context of the virial equation of state (VEOS) of SW fluids. VEOS up to B₄ or up to B₆ describes the PVT behavior along the saturated vapor line better than the series that includes B₅. We used these coefficients to find the critical properties of SW fluids and compared with the literature values. Boyle temperature is also determined and is found to increase with the increase in the well-extent and associating strength. We also report Joule–Thomson inversion curve for Lennard–Jones fluid and SW fluids using different truncated VEOS and compared with that predicted from established EOS.