Wertheim Association Theory Research Articles

A general framework for modelling association

A general formulation of association theory is presented which, unlike Wertheim's association theory as proposed in the Statistical Associating Fluid Theory, allows association strengths to vary with different sizes of oligomer. It is shown that association theory is governed by a few simple relationships which apply in all cases. The formulation is compatible with any equation of state. Potential applications are suggested.

Condensation and Demixing in Solutions of DNA Nanostars and Their Mixtures.

We present a numerical/theoretical approach to efficiently evaluate the phase diagram of self-assembling DNA nanostars. Combining input information based on a realistic coarse-grained DNA potential with the Wertheim association theory, we derive a parameter-free thermodynamic description of these systems. We apply this method to investigate the phase behavior of single components and mixtures of DNA nanostars with different numbers of sticky arms, elucidating the role of the system functionality and of salt concentration. Specifically, we evaluate the propensity to demix, the gas–liquid phase boundaries and the location of the critical points. The predicted critical parameters compare very well with existing experimental results for the available compositions. The approach developed here is very general, easily extensible to other all-DNA systems, and provides guidance for future experiments.

Hyperbranched polymers as phase forming components in aqueous two-phase extraction

This work focusses on the experimental and theoretical investigation of the partitioning of a l-serine in an aqueous two-phase system (ATPS) based on a hyperbranched polymer. As a model ATPS, a polymer system containing a hyperbranched polyesteramide and dextran was chosen. The partitioning of l-serine in this ATPS was studied and compared with the partitioning of l-serine in a conventional ATPS consisting of polyethylene glycol (PEG) and dextran. For the thermodynamic modelling of these ATPS’s the Lattice Cluster Theory (LCT) in combination with the Wertheim association theory was used. The LCT allows the incorporation of the hyperbranched polymer architecture in the Helmholtz free energy and the Wertheim association theory considers the influence of the polar groups. As a result, it can be stated that in both ATPS, l-serine is mainly partitioned into the dextran-enriched phase, but in the ATPS based on the hyperbranched polyesteramide and dextran, the l-serine concentration in the dextran-enriched phase is higher. The partitioning of l-serine could be predicted by the used thermodynamic model on basis of the solubility experiments carried out for l-serine in aqueous solutions of phase forming components. Further, this work represents the first application of the used thermodynamic model on a quaternary system.

Investigation of interfacial properties of aqueous two-phase systems by density gradient theory: Dedicated to Prof. Sabine Enders on her 50th birthday and in honor of her previous scientific impact

In this work the interfacial properties of aqueous two-phase systems (ATPS) consisting of an aqueous solution of polyethylene glycol (PEG) and dextran with different molar masses were investigated. To calculate the interfacial properties the density gradient theory was combined with the lattice cluster theory and the Wertheim association theory. With help of this thermodynamic model the liquid–liquid equilibria of the investigated ATPS were calculated in a molar mass range of PEG from 4000 to 20,000g/mol and of dextran from 10,000 to 500,000g/mol; whereas the thermodynamic model was fitted to the phase equilibrium in several selected ATPS. Phase equilibria in all other systems were predicted in a good accordance with experimental data.On the basis of the modelled phase equilibria the interfacial tension was calculated by the density gradient theory in an excellent agreement with experimental data. Moreover, the concentration profile of the phase forming components across the interface was calculated and it could be seen that there is no accumulation of any component in the interface and that the length of interfacial region depends on PEG molar mass.

PC-SAFT modeling of asphaltene phase behavior in the presence of nonionic dispersants

This study introduced a new method to characterize asphaltenes in PC-SAFT equation of state (EOS) and correctly model the effect of nonionic dispersants on the thermodynamic behavior of asphaltenes. Our approach is to combine microscale parameters from Molecular Dynamics (MD) simulations with Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) to develop a comprehensive model that enables the prediction of macroscopic behavior such as the amount and onset of asphaltene precipitation at various pressures, temperatures, and fluid compositions. More specifically, association parameters were considered for asphaltene molecules and determined by equating the Gibbs energy of association calculated by PC-SAFT EOS to the one obtained from MD simulations. A correlation was derived to relate the association energy parameter (ɛAB) of asphaltenes to the molar weight of their aromatic cores. Our model showed that asphaltene association energy is affected by temperature and solvent type and is inversely proportional to the solubility parameter of the medium. The hetero-segment approach in PC-SAFT EOS was adopted to accurately characterize asphaltene molecules and their non-association parameters in PC-SAFT were determined based on the molecular weight and aromaticity factor of asphaltenes. Moreover, the average aggregation number of asphaltene nanoaggregates was calculated using the Wertheim association theory. This model was applied to predict asphaltene precipitation envelopes for three different live crude oils and showed excellent agreement with experimental data in the literature. Additionally, the model could correctly predict the amount of asphaltene precipitation upon addition of nonionic dispersants.

Novel aqueous two-phase system based on a hyperbranched polymer

Hyperbranched polymers have increased attention because of their branched structure and the wide range of different functional groups. Because of this feature hyperbranched polymers show an excellent applicability for aqueous two-phase systems (ATPS). In this work an ATPS consisting of a PEG-functionalized hyperbranched polyesteramide+water+Dextran T40 is compared to an ATPS consisting of PEG8000+Dextran T40+water. In addition to the experimental investigation of the ATPS, they will also be modeled using the lattice cluster theory (LCT) in combination with Wertheim theory. The LCT allows the direct incorporation of the polymer architecture in the Helmholtz free energy, so all derived properties are dependent on chain architecture. A multicomponent version of LCT for incompressible polymer solutions/blends is presented in this work. To consider associative interactions the LCT is combined with Wertheim association theory. To obtain the model binary interaction parameters of the hyperbranched polymer+water the subsystem hyperbranched polymer+water was experimentally estimated, and for the subsystem PEG8000–water experimental data from literature were used, the parameters were fitted in both cases. So both ATPS could be modeled. In addition to the phase behavior, the kinematic viscosity of both ATPS was compared.

A density functional theory for patchy colloids based on Wertheim's association theory: Beyond the single bonding condition

In the framework of Wertheim's theory, we develop the first classical density functional theory for patchy colloids where the patch can bond more than once. To test the theory we perform new Monte Carlo simulations for the model system of patchy colloids in a planar slit pore. The theory is shown to be in excellent agreement with simulation for the density profiles and bonding fractions. It is also shown that the theory obeys the wall contact rule by accurately predicting bulk pressures from the wall contact density.

Publisher's Note: “Wertheim's association theory applied to one site patchy colloids: Beyond the single bonding condition” [J. Chem. Phys. 137, 104909 (2012)

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Wertheim's association theory applied to one site patchy colloids: Beyond the single bonding condition

We apply Wertheim's theory to develop an equation of state for one site patchy colloids where the patch can bond multiple times. We allow for the possibility of ring formation without the introduction of empirical parameters and show that for moderate patch coverage the infinite series of chain graphs is well represented by the first two terms. The theory is found to be in excellent agreement with new NVT and NPT Monte Carlo simulations. The approach described here can easily be converted to the form of a density functional theory to describe inhomogeneous patchy colloid systems.

Phase behavior of hyperbranched polymer solutions in mixed solvents

Hyperbranched polymers get more and more interesting for several applications due to their tailor-made properties influenced by the architecture and the functional groups of the polymer. The liquid–liquid phase behavior of hyperbranched polymer solutions is an important issue for various applications. Until now, the calculations of these phase equilibria are limited to solutions of hyperbranched polymers in a single solvent using Lattice Cluster theory (LCT). The LCT permits the incorporation of the architecture of the polymer directly in thermodynamic properties, as the Helmholtz energy, without any additional adjustable parameter. This papers aims at the extension of the LCT to ternary systems made from hyperbranched polymer (Boltorn H20), water and propanol. The derived expression for the Helmholtz energy allows for the first time the prediction of miscibility gaps in the ternary system based on experimental data of the binary subsystems. Additionally to the architecture of hyperbranched polymers also the functional groups of hyperbranched polymers play an important role in phase equilibrium. In order to include the association phenomena in the theoretical framework, a modified version of the Wertheim association theory is used. However, during the application of this approach the model lost its predictive power, because ternary data must be used for the parameter estimation procedure. Nevertheless, the combined theory is able to model the experimental phase behavior within the experimental accuracy.

Density functional theory for non-uniform associating ionic fluids

We discuss a density functional approach of non-uniform electrolytes that includes the term that takes into account the formation of associated ionic pairs. The theory is based on a fundamental measurement theory of hard-spheres, the theory of Gillespie et al. [D. Gillespie, W. Nonner, R.S. Eisenberg, J. Phys.: Condens. Matter 14 (2002) 12129] which leads to a more accurate description of the electrostatic part of the grand potential and on the Wertheim theory of association. The results of model calculations indicate that at low temperatures the inclusion of the associative term in the grand potential leads to the structure of the double layer, which differs from the structure evaluated by neglecting the association. However, these differences become negligibly small at high temperatures.

The solution of the Wertheim association theory for molecular liquids: Application to hydrogen fluoride

A general numerical method for solving the Wertheim association theory in the case of fully anisotropic polyatomic rigid molecules is proposed. In order to handle the nonspherical shapes of the molecules, the Wertheim association theory is combined with the rotational invariant approach of the molecular Ornstein–Zernike (MOZ) method. Therefore, this approach is called the WMOZ method. It is carried out in the association hypernetted chain (AHNC) approximation which is the only approximation and which consists of the neglect of the bridge functions. The method of solution is implemented by translating the set operations appearing in the Wertheim association theory into an algebraic formalism developed through a one-to-one correspondence between subsets and binary numbers. The Wertheim association theory is explicitly solved for hydrogen fluoride using two interaction site models. For these models, site–site distribution functions, internal excess energies, and dielectric constants obtained by the MOZ and WMOZ methods are compared to the exact molecular dynamics results. The WMOZ method strongly improves the structural description of the H bonding in comparison with the MOZ approximation. The quality of the dielectric and thermodynamic results obtained by the WMOZ approach is discussed in comparison with the simulation values. To our knowledge, this is the first solution of the Wertheim association theory for a liquid of particles of nonspherical shapes.

Shear thinning vs shear thickening in associating fluids

When one-bond Frenkel dumbbells are allowed to dimerize, as analyzed using the Wertheim theory of association, the resulting fluid exhibits shear thinning or shear thickening behaviors. In contrast, when Gaussian chains undergo shear-assisted association, only shear thickening is possible. The present theory of shear-induced association of non-Newtonian fluids is applied to interpret the shear thickening seen in equimolar solutions of the CTAB (cetyl trimethyl ammonium bromide) micelles and sodium salicylate. Also derived in this study are the frequency dependent Newtonian viscosity and the non-Newtonian viscosity for a dilute Brownian suspension of two-bond freely jointed Frenkel dumbbells.

Shear-induced dimerization

The Yamada–Kawasaki theory of nonlinear response was applied to the calculation of the frequency and shear-rate dependent shear viscosity of a dilute Brownian suspension of harmonically bound dumbbells. When the dumbbells were allowed to dimerize, as implemented by the Wertheim theory of association, the resulting fluid displayed exhibited shear-thinning and shear-thickening regimes. Head-to-head dimerization led to shear thinning, and for shear thickening to occur, the rotational correlation time of the dimers must be commensurate with those of the monomers. The present findings were evaluated in light of the observed shear-induced coagulation in micellar solutions.

Replica Ornstein-Zernike theory for chemically associating fluids with directional forces in disordered porous media: Smith-Nezbeda model in a hard sphere matrix

The associative replica Ornstein-Zernike equations, supplemented by the associative hypernetted chain approximation are used to describe the Smith-Nezbeda model for an associating fluid adsorbed in a disordered hard sphere matrix. These equations have been developed by combining the replica Ornstein-Zernike equations with the Wertheim theory of association in fluids. The pair distribution functions and fraction of unbonded species are calculated. Also investigated is the influence of the association on the equation of state and the chemical potential of the absorbed fluid.

Density profiles of a model of dimerizing hard spheres in contact with a crystalline surface: application of Wertheim's theory of association

Density profiles of a model of dimerizing hard spheres in contact with a crystalline surface: application of Wertheim's theory of association