Modeling Lower Critical Solution Temperature Behavior of Associating Dendrimers Using Density Functional Theory

We study the phase behavior of associating dendrimers in explicit solvents using classical density functional theory. The existence of association enables uptake of solvent inside the dendrimer even for unfavorable Lennard-Jones interaction between the solvent and dendrimer. Depending on the distributions of associating sites, the dendrimer conformation can be either dense-core or dense-shell. The conformation of the associating dendrimer is greatly affected by the temperature. Due to the interplay between association interaction and Lennard-Jones attractions, we find the lower critical solution temperature (LCST) behavior of dendrimer conformation and study how it changes as the dendrimer size or solvent size changes. The dendrimer in our study displays no LCST behavior at low generations, and it has a maximum LCST at G4. Moreover, increasing the solvent chain length decreases the LCST. For solvents with self-association, the competition between solvent-solvent association and solvent-dendrimer association also tends to reduce the LCST. Qualitatively consistent with experiments, our results provide insight into the molecular mechanism of the LCST behavior of associating dendrimers.

Competitive Sorption of CO2 with Gas Mixtures in Nanoporous Shale for Enhanced Gas Recovery from Density Functional Theory

CO₂ competitive sorption with shale gas under various conditions from simple to complex pore characteristics is studied using a molecular density functional theory (DFT) that reduces to perturbed chain-statistical associating fluid theory in the bulk fluid region. The DFT model is first verified by grand canonical Monte Carlo simulation in graphite slit pores for pure and binary component systems at different temperatures, pressures, pore sizes, and bulk gas compositions for methane/ethane with CO₂. Then, the model is utilized in multicomponent systems that include CH₄, C₂H₆, and C3+ components of different compositions. It is shown that the selectivity of CO₂ decreases with increases in temperature, pressure, nanopore size, and average molecular weight of shale gas. Extending the model to more realistic situations, we consider the impact of water present in the pore and consider the effect of permeation of fluid molecules into the kerogen that forms the pore walls. The water-graphite interaction is calibrated with contact angle from molecular simulation data from the literature. The kerogen pore model prediction of gas absolute sorption is compared with experimental and molecular simulation values in the literature. It is shown that the presence of water reduces the CO₂ adsorption but improves the CO₂ selectivity. The dissolution of gases into the kerogen matrix also leads to the increase in CO₂ selectivity. The effect of kerogen type and maturity on the gas sorption amount and CO₂ selectivity is also studied. The associated mechanisms are discussed to provide fundamental understanding for gas recovery by CO₂.

Bond cooperativity and ring formation in hydrogen fluoride thermodynamic properties: A two-density formalism framework

In this work, we develop a thermodynamic perturbation theory using a two-density formalism framework to model the bond cooperativity effect for associating hard sphere and Lennard-Jones fluids. The theory predictions are compared with Monte Carlo simulation results and they are in excellent agreement. We incorporate bond angle dependent ring formation into the theory to calculate hydrogen fluoride thermodynamic properties. The liquid density and vapor pressure obtained by the theory are in good agreement with the experimental data. Comparing the thermo-physical properties of hydrogen fluoride calculated by this theory with previous studies reveals the importance of bond angle dependent ring formation and cooperative hydrogen bonding to capture its anomalous behavior especially in the vapor phase. The cooperativity ratio obtained in our model is close to the values reported by previous quantum studies.

A cluster size distribution theory to study the thermodynamics and phase behavior of multi-bonding single site solutes in patchy colloidal mixtures

We study binary mixtures of multi-bonding single site solute particles in a solvent comprising patchy colloid particles. The particles in the mixture interact by very short-ranged attraction and hard-sphere repulsion. The attractive patch on the solute can bond with multiple solvent particles, whereas the patch on the solvent is restricted to bond only once. From a quasi-chemical analysis of association, in the hard-sphere reference we develop an accurate multi-body correlation information for the distribution of solvent particles over the patch region of the solute. We use this information within Wertheim's multi-density formalism to develop a cluster size distribution theory that is capable of capturing the physics of multi-body association for any geometry of association sites on the solute. We use this general framework to study a mixture containing Janus solutes and one- or two-patch solvent particles over a range of concentration of the solute and association strengths. We find that a mixture of two-patch solvent (with both patches of the same kind) and multi-bonding solutes with different patch geometries can have a vapor-liquid equilibrium, although the pure components themselves cannot phase separate. The liquid state occurs at very low densities, forming a so-called empty liquid. For the relative association strengths studied in this work, we observe that the vapor-liquid coexistence curve broadens as the concentration of the patchy solvent particles in the liquid phase is increased. The pressure-composition phase equilibrium curves show negative azeotropes for these mixtures. We also observe that, for these mixtures, as the size of the patch on the solute particles is decreased, the critical temperature and the critical packing fraction decreases.

Density functional study of dendrimer molecules in solvents of varying quality

Modified inhomogeneous statistical associating fluid theory (iSAFT) density functional theory is extended to dendrimer molecules in solvents of varying quality. The detailed structures of isolated dendrimers in implicit solvent are calculated and have a semi-quantitative agreement with simulation results available in the literature. The dendrimers form dense-core structures under all conditions, while their radius of gyration follows different scaling laws. Factors that affect the quality of the solvent are systematically studied in the explicit solvent case. It is found that the solvent size, density, chemical affinity and temperature all play a role in determining a solvent to be good or poor. New molecular dynamics simulations are performed to validate the iSAFT results. Our results provide insight into the phase behavior of dendrimer solutions as well as guidance in practical applications.

Mini-grand canonical ensemble: Chemical potential in the solvation shell

Quantifying the statistics of occupancy of solvent molecules in the vicinity of solutes is central to our understanding of solvation phenomena. Number fluctuations in small solvation shells around solutes cannot be described within the macroscopic grand canonical framework using a single chemical potential that represents the solvent bath. In this communication, we hypothesize that molecular-sized observation volumes such as solvation shells are best described by coupling the solvation shell with a mixture of particle baths each with its own chemical potential. We confirm our hypotheses by studying the enhanced fluctuations in the occupancy statistics of hard sphere solvent particles around a distinguished hard sphere solute particle. Connections with established theories of solvation are also discussed.

Modeling micelle formation and interfacial properties with iSAFT classical density functional theory

Surfactants reduce the interfacial tension between phases, making them an important additive in a number of industrial and commercial applications from enhanced oil recovery to personal care products (e.g., shampoo and detergents). To help obtain a better understanding of the dependence of surfactantproperties on molecular structure, a classical density functional theory, also known as interfacial statistical associating fluid theory, has been applied to study the effects of surfactant architecture on micelle formation and interfacial properties for model nonionic surfactant/water/oil systems. In this approach, hydrogen bonding is explicitly included. To minimize the free energy, the system minimizes interactions between hydrophobic components and hydrophilic components with water molecules hydrating the surfactant head group. The theory predicts micellar structure, effects of surfactant architecture on critical micelle concentration, aggregation number, and interfacial tension isotherm of surfactant/water systems in qualitative agreement with experimental data. Furthermore, this model is applied to study swollen micelles and reverse swollen micelles that are necessary to understand the formation of a middle-phase microemulsion.

NMR spin-rotation relaxation and diffusion of methane

The translational diffusion-coefficient and the spin-rotation contribution to the ¹H NMR relaxation rate for methane (CH₄) are investigated using MD (molecular dynamics) simulations, over a wide range of densities and temperatures, spanning the liquid, supercritical, and gas phases. The simulated diffusion-coefficients agree well with measurements, without any adjustable parameters in the interpretation of the simulations. A minimization technique is developed to compute the angular velocity for non-rigid spherical molecules, which is used to simulate the autocorrelation function for spin-rotation interactions. With increasing diffusivity, the autocorrelation function shows increasing deviations from the single-exponential decay predicted by the Langevin theory for rigid spheres, and the deviations are quantified using inverse Laplace transforms. The ¹H spin-rotation relaxation rate derived from the autocorrelation function using the "kinetic model" agrees well with measurements in the supercritical/gas phase, while the relaxation rate derived using the "diffusion model" agrees well with measurements in the liquid phase. ¹H spin-rotation relaxation is shown to dominate over the MD-simulated ¹H-¹H dipole-dipole relaxation at high diffusivity, while the opposite is found at low diffusivity. At high diffusivity, the simulated spin-rotation correlation time agrees with the kinetic collision time for gases, which is used to derive a new expression for ¹H spin-rotation relaxation, without any adjustable parameters.

Adsorption and Phase Behavior of Pure/Mixed Alkanes in Nanoslit Graphite Pores: An iSAFT Application

The prediction of fluid phase behavior in nanoscale pores is critical for shale gas/oil development. In this work, we use a molecular density functional theory (DFT) to study the effect of molecular size and shape on partitioning to graphite nanopores as a model of shale. Here, interfacial statistical associating fluid theory (iSAFT) is applied to model alkane (C₁ - C₈) adsorption/desorption/phase behavior in graphite slit pores for both pure fluids and mixtures. The pure component parameters were fit to the bulk saturated liquid density and vapor pressure data in selected temperature ranges. The potential of interaction between the fluid and graphite is modeled with a Steele 10-4-3 potential that is fit to the potential of mean force from single-molecule simulations. Good agreement is found between theory and molecular simulation for the density distributions of pure components in slit pores. The critical properties of methane, ethane, and their mixtures as well as the shift in bubble point and dew point densities were studied, showing good agreement with simulation. The competitive adsorption of mixtures of normal and branched alkanes in graphite pores was also studied. Heavier components more strongly adsorb up to the point that the entropic penalty due to confinement reduces adsorption.

Thermodynamics of mixtures of patchy and spherical colloids of different sizes: A multi-body association theory with complete reference fluid information

We present a theory to predict the structure and thermodynamics of mixtures of colloids of different diameters, building on our earlier work [A. Bansal et al., J. Chem. Phys. 145, 074904 (2016)] that considered mixtures with all particles constrained to have the same size. The patchy, solvent particles have short-range directional interactions, while the solute particles have short-range isotropic interactions. The hard-sphere mixture without any association site forms the reference fluid. An important ingredient within the multi-body association theory is the description of clustering of the reference solvent around the reference solute. Here we account for the physical, multi-body clusters of the reference solvent around the reference solute in terms of occupancy statistics in a defined observation volume. These occupancy probabilities are obtained from enhanced sampling simulations, but we also present statistical mechanical models to estimate these probabilities with limited simulation data. Relative to an approach that describes only up to three-body correlations in the reference, incorporating the complete reference information better predicts the bonding state and thermodynamics of the physical solute for a wide range of system conditions. Importantly, analysis of the residual chemical potential of the infinitely dilute solute from molecular simulation and theory shows that whereas the chemical potential is somewhat insensitive to the description of the structure of the reference fluid, the energetic and entropic contributions are not, with the results from the complete reference approach being in better agreement with particle simulations.

Molecular dynamics simulations of NMR relaxation and diffusion of bulk hydrocarbons and water

Molecular dynamics (MD) simulations are used to investigate ¹H nuclear magnetic resonance (NMR) relaxation and diffusion of bulk n-C₅H₁₂ to n-C₁₇H₃₆ hydrocarbons and bulk water. The MD simulations of the ¹H NMR relaxation times T_1,2 in the fast motion regime where T₁=T₂ agree with measured (de-oxygenated) T₂ data at ambient conditions, without any adjustable parameters in the interpretation of the simulation data. Likewise, the translational diffusion D_T coefficients calculated using simulation configurations agree with measured diffusion data at ambient conditions. The agreement between the predicted and experimentally measured NMR relaxation times and diffusion coefficient also validate the forcefields used in the simulation. The molecular simulations naturally separate intramolecular from intermolecular dipole-dipole interactions helping bring new insight into the two NMR relaxation mechanisms as a function of molecular chain-length (i.e. carbon number). Comparison of the MD simulation results of the two relaxation mechanisms with traditional hard-sphere models used in interpreting NMR data reveals important limitations in the latter. With increasing chain length, there is substantial deviation in the molecular size inferred on the basis of the radius of gyration from simulation and the fitted hard-sphere radii required to rationalize the relaxation times. This deviation is characteristic of the local nature of the NMR measurement, one that is well-captured by molecular simulations.

A density functional theory for association of fluid molecules with a functionalized surface: fluid-wall single and double bonding

In this manuscript we extend Wertheim's two-density formalism beyond its first order to model a system of fluid molecules with a single association site close to a planar hard wall with association sites on its surface in a density functional theory framework. The association sites of the fluid molecules are small enough that they can form only one bond, while the wall association sites are large enough to bond with more than one fluid molecule. The effects of temperature and of bulk fluid and wall site densities on the fluid density profile, extent of association, and competition between single and double bonding of fluid segments at the wall sites versus distance from the wall are presented. The theory predictions are compared with new Monte Carlo simulation results and they are in good agreement. The theory captures the surface coverage over wide ranges of temperature and bulk density by introducing the effect of steric hindrance in fluid association at a wall site.