A molecular equation of state for alcohols which includes steric hindrance in hydrogen bonding.

In this paper, we develop the first equation of state for alcohol containing mixtures which includes the effect of steric hindrance between the two electron lone pair hydrogen bond acceptor sites on the alcohol's hydroxyl oxygen. The theory is derived for multi-component mixtures within Wertheim's multi-density statistical mechanics in a second order perturbation theory. The accuracy of the new approach is demonstrated by application to pure methanol and ethanol and binary ethanol/water mixtures. It is demonstrated that the new approach gives a substantial improvement in the prediction of the hydrogen bonding structure of both pure alcohol and alcohol/water mixtures, as compared to conventional approaches which do not include steric effects between the alcohol association sites. Finally, it is demonstrated that the inclusion of steric effects allows for more accurate binary phase equilibria and heats of mixing prediction with water.

A general mixture equation of state for double bonding carboxylic acids with ≥2 association sites.

In this paper, we obtain the first general multi-component solution to Wertheim's thermodynamic perturbation theory for the case that molecules can participate in cyclic double bonds. In contrast to previous authors, we do not restrict double bonding molecules to a 2-site association scheme. Each molecule in a multi-component mixture can have an arbitrary number of donor and acceptor association sites. The one restriction on the theory is that molecules can have at most one pair of double bonding sites. We also incorporate the effect of hydrogen bond cooperativity in cyclic double bonds. We then apply this new association theory to 2-site and 3-site models for carboxylic acids within the polar perturbed chain statistical associating fluid theory equation of state. We demonstrate the accuracy of the approach by comparison to both pure and multi-component phase equilibria data. It is demonstrated that the 3-site association model gives substantially a different hydrogen bonding structure than a 2-site approach. We also demonstrate that inclusion of hydrogen bond cooperativity has a substantial effect on a liquid phase hydrogen bonding structure.

A theory for the effect of patch/non-patch attractions on the self-assembly of patchy colloids.

In this paper, we develop a thermodynamic perturbation theory to describe the self-assembly of patchy colloids which exhibit both patch-patch attractions as well as patch/non-patch attractions. That is, patches attract other patches as well as the no patch region (we call this region Ψ). In general, the patch-patch and patch-Ψ attractions operate on different energy scales allowing for a competition between different modes of attraction. This competition may result in anomalous thermodynamic properties. As an application, we tune the patch parameters to reproduce the liquid density (suitably scaled) maximum of water. It is then shown that the liquid branch of the colloids phase diagram has liquid densities consistent with both saturated and super-cooled liquid water. Finally, it is shown that the colloids reproduce water's anomalous minimum in isothermal compressibility and negative volume expansivity.

A second order thermodynamic perturbation theory for hydrogen bond cooperativity in water.

It has been extensively demonstrated through first principles quantum mechanics calculations that water exhibits strong hydrogen bond cooperativity. Equations of state developed from statistical mechanics typically assume pairwise additivity, meaning they cannot account for these 3-body and higher cooperative effects. In this paper, we extend a second order thermodynamic perturbation theory to correct for hydrogen bond cooperativity in 4 site water. We demonstrate that the theory predicts hydrogen bonding structure consistent spectroscopy, neutron diffraction, and molecular simulation data. Finally, we implement the approach into a general equation of state for water.

Dual chain perturbation theory: A new equation of state for polyatomic molecules.

In the development of equations of state for polyatomic molecules, thermodynamic perturbation theory (TPT) is widely used to calculate the change in free energy due to chain formation. TPT is a simplification of a more general and exact multi-density cluster expansion for associating fluids. In TPT, all contributions to the cluster expansion which contain chain-chain interactions are neglected. That is, all inter-chain interactions are treated at the reference fluid level. This allows for the summation of the cluster theory in terms of reference system correlation functions only. The resulting theory has been shown to be accurate and has been widely employed as the basis of many engineering equations of state. While highly successful, TPT has many handicaps which result from the neglect of chain-chain contributions. The subject of this document is to move beyond the limitations of TPT and include chain-chain contributions to the equation of state.

On the cooperativity of association and reference energy scales in thermodynamic perturbation theory.

Equations of state for hydrogen bonding fluids are typically described by two energy scales. A short range highly directional hydrogen bonding energy scale as well as a reference energy scale which accounts for dispersion and orientationally averaged multi-pole attractions. These energy scales are always treated independently. In recent years, extensive first principles quantum mechanics calculations on small water clusters have shown that both hydrogen bond and reference energy scales depend on the number of incident hydrogen bonds of the water molecule. In this work, we propose a new methodology to couple the reference energy scale to the degree of hydrogen bonding in the fluid. We demonstrate the utility of the new approach by showing that it gives improved predictions of water-hydrocarbon mutual solubilities.

Thermodynamic perturbation theory for associating fluids confined in a one-dimensional pore.

In this paper, a new theory is developed for the self-assembly of associating molecules confined to a single spatial dimension, but allowed to explore all orientation angles. The interplay of the anisotropy of the pair potential and the low dimensional space results in orientationally ordered associated clusters. This local order enhances association due to a decrease in orientational entropy. Unlike bulk 3D fluids which are orientationally homogeneous, association in 1D necessitates the self-consistent calculation of the orientational distribution function. To test the new theory, Monte Carlo simulations are performed and the theory is found to be accurate. It is also shown that the traditional treatment in first order perturbation theory fails to accurately describe this system. The theory developed in this paper may be used as a tool to study hydrogen bonding of molecules in 1D zeolites as well as the hydrogen bonding of molecules in carbon nanotubes.

Thermodynamic perturbation theory for self-assembling mixtures of divalent single patch colloids.

In this work we extend Wertheim's thermodynamic perturbation theory (TPT) to binary mixtures (species A and species B) of patchy colloids were each species has a single patch which can bond a maximum of twice (divalent). Colloids are treated as hard spheres with a directional conical association site. We restrict the system such that only patches between unlike species share attractions; meaning there are AB attractions but no AA or BB attractions. The theory is derived in Wertheim's two density formalism for one site associating fluids. Since the patches are doubly bondable, associated chains, of all chain lengths, as well as 4-mer rings consisting of two species A and two species B colloids are accounted for. With the restriction of only AB attractions, triatomic rings of doubly bonded colloids, which dominate in the corresponding pure component case, cannot form. The theory is shown to be in good agreement with Monte Carlo simulation data for the structure and thermodynamics of these patchy colloid mixtures as a function of temperature, density, patch size and composition. It is shown that 4-mer rings dominate at low temperature, inhibiting the polymerization of the mixture into long chains. Mixtures of this type have been recently synthesized by researchers. This work provides the first theory capable of accurately modeling these mixtures.

Resummed thermodynamic perturbation theory for bond cooperativity in associating fluids with small bond angles: effects of steric hindrance and ring formation.

In this paper we develop a thermodynamic perturbation theory for two site associating fluids which exhibit bond cooperativity (system energy is non-pairwise additive). We include both steric hindrance and ring formation such that the equation of state is bond angle dependent. Here, the bond angle is the angle separating the centers of the two association sites. As a test, new Monte Carlo simulations are performed, and the theory is found to accurately predict the internal energy as well as the distribution of associated clusters as a function of bond angle.

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.

Molecular theory for self assembling mixtures of patchy colloids and colloids with spherically symmetric attractions: the single patch case.

In this work we develop a new theory to model self assembling mixtures of single patch colloids and colloids with spherically symmetric attractions. In the development of the theory we restrict the interactions such that there are short ranged attractions between patchy and spherically symmetric colloids, but patchy colloids do not attract patchy colloids and spherically symmetric colloids do not attract spherically symmetric colloids. This results in the temperature, density, and composition dependent reversible self assembly of the mixture into colloidal star molecules. This type of mixture has been recently synthesized by grafting of complimentary single stranded DNA [L. Feng, R. Dreyfus, R. Sha, N. C. Seeman, and P. M. Chaikin, Adv. Mater. 25(20), 2779-2783 (2013)]. As a quantitative test of the theory, we perform new monte carlo simulations to study the self assembly of these mixtures; theory and simulation are found to be in excellent agreement.

Three new branched chain equations of state based on Wertheim's perturbation theory.

In this work, we present three new branched chain equations of state (EOS) based on Wertheim's perturbation theory. The first represents a slightly approximate general branched chain solution of Wertheim's second order perturbation theory (TPT2) for athermal hard chains, and the second represents the extension of first order perturbation theory with a dimer reference fluid (TPT1-D) to branched athermal hard chain molecules. Each athermal branched chain EOS was shown to give improved results over their linear counterparts when compared to simulation data for branched chain molecules with the branched TPT1-D EOS being the most accurate. Further, it is shown that the branched TPT1-D EOS can be extended to a Lennard-Jones dimer reference system to obtain an equation of state for branched Lennard-Jones chains. The theory is shown to accurately predict the change in phase diagram and vapor pressure which results from branching as compared to experimental data for n-octane and corresponding branched isomers.

Resummed thermodynamic perturbation theory for bond cooperativity in associating fluids.

We develop a resummed thermodynamic perturbation theory for bond cooperativity in associating fluids by extension of Wertheim's multi-density formalism. We specifically consider the case of an associating hard sphere with two association sites and both pairwise and triplet contributions to the energy, such that the first bond in an associated cluster receives an energy -ε((1)) and each subsequent bond in the cluster receives an energy -ε((2)). To test the theory we perform new Monte Carlo simulations for potentials of this type. Theory and simulation are found to be in excellent agreement. We show that decreasing the energetic benefit of hydrogen bonding can actually result in a decrease in internal energy in the fluid. We also predict that when ε((1)) = 0 and ε((2)) is nonzero there is a transition temperature where the system transitions from a fluid of monomers to a mixture of monomers and very long chains.

Molecular theory for the phase equilibria and cluster distribution of associating fluids with small bond angles.

We develop a new theory for associating fluids with multiple association sites. The theory accounts for small bond angle effects such as steric hindrance, ring formation, and double bonding. The theory is validated against Monte Carlo simulations for the case of a fluid of patchy colloid particles with three patches and is found to be very accurate. Once validated, the theory is applied to study the phase diagram of a fluid composed of three patch colloids. It is found that bond angle has a significant effect on the phase diagram and the very existence of a liquid-vapor transition.

Modeling lower critical solution temperature behavior of associating polymer brushes with classical density functional theory.

We study the lower critical solution temperature (LCST) behavior of associating polymer brushes (i.e., poly(N-isopropylacrylamide)) using classical density functional theory. Without using any empirical or temperature-dependent parameters, we find the phase transition of polymer brushes from extended to collapsed structure with increasing temperature, indicating the LCST behavior of polymer brushes. The LCST behavior of associating polymer brushes is attributed to the interplay of hydrogen bonding interactions and Lennard-Jones attractions in the system. The effect of grafting density and molecular weight on the phase behavior of associating polymer brushes has been also investigated. We find no LCST behavior at low grafting density or molecular weight. Moreover, increasing grafting density decreases the LCST and swelling ratio of polymer brushes. Similarly, increasing molecular weight decreases the LCST but increases the swelling ratio. At very high grafting density, a partial collapsed structure appears near the LCST. Qualitatively consistent with experiments, our results provide insight into the molecular mechanism of LCST behavior of associating polymer brushes.

A Monte Carlo density functional theory for the competition between inter and intramolecular association in inhomogeneous fluids.

A Monte Carlo density functional theory is developed for chain molecules which both intra and intermolecularly associate. The approach can be applied over a range of chain lengths. The theory is validated for the case of an associating 4-mer fluid in a planar hard slit pore. Once validated, the new theory is used to study the effect of chain length and temperature on the competition between intra and intermolecular association near a hard wall. We show that this competition enhances intramolecular association near wall contact and inverts the chain length dependence of the fraction bonded intermolecularly in the inhomogeneous region.

Data-driven predictions of complex organic mixture permeation in polymer membranes.

Membrane-based organic solvent separations are rapidly emerging as a promising class of technologies for enhancing the energy efficiency of existing separation and purification systems. Polymeric membranes have shown promise in the fractionation or splitting of complex mixtures of organic molecules such as crude oil. Determining the separation performance of a polymer membrane when challenged with a complex mixture has thus far occurred in an ad hoc manner, and methods to predict the performance based on mixture composition and polymer chemistry are unavailable. Here, we combine physics-informed machine learning algorithms (ML) and mass transport simulations to create an integrated predictive model for the separation of complex mixtures containing up to 400 components via any arbitrary linear polymer membrane. We experimentally demonstrate the effectiveness of the model by predicting the separation of two crude oils within 6-7% of the measurements. Integration of ML predictors of diffusion and sorption properties of molecules with transport simulators enables for the rapid screening of polymer membranes prior to physical experimentation for the separation of complex liquid mixtures.

Response behavior of diblock copolymer brushes in explicit solvent.

The understanding of phase behavior of copolymer brushes is of fundamental importance for the design of smart materials. In this paper, we have performed classical density functional theory calculations to study diblock copolymer brushes (A-B) in an explicit solvent which prefers the A block to B block. With increasing B-block length (N(B)), we find a structural transition of the copolymer brush from mixed to collapsed, partial-exposed, and exposed structure, which is qualitatively consistent with experiments. The phase transitions are attributed to the interplay between entropic cost of folding copolymer brushes and enthalpic effect of contact between unlike components. In addition, we examine the effect of different parameters, such as grafting density (ρ(g)), the bottom block length (N(A)), and the chain length of solvent (N(S)) on the solvent response of copolymer brushes. The transition chain length (N(B)) increases with decreasing ρ(g) and N(A), and a smaller solvent molecule makes the collapsed structure less stable due to its lower penetration cost. Our results provide the insight to phase behavior of copolymer brushes in selective solvents from a molecular view.

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.

A perturbation density functional theory for the competition between inter and intramolecular association.

Using the framework of Wertheim's thermodynamic perturbation theory we develop the first density functional theory which accounts for intramolecular association in chain molecules. To test the theory new Monte Carlo simulations are performed at a fluid solid interface for a 4 segment chain which can both intra and intermolecularly associate. The theory and simulation results are found to be in excellent agreement. It is shown that the inclusion of intramolecular association can have profound effects on interfacial properties such as interfacial tension and the partition coefficient.