Bennett D. Marshall

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

We apply Wertheims 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 density functional theory for patchy colloids based on Wertheim's association theory: beyond the single bonding condition.

In the framework of Wertheims 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.

Thermodynamic perturbation theory for associating fluids with small bond angles: Effects of steric hindrance, ring formation, and double bonding

We develop a comprehensive approach to model associating fluids with small bond angles using Wertheims perturbation theory. We show theoretically and through Monte Carlo simulations that as bond angle is varied various modes of association become dominant. The theory is shown to be in excellent agreement with Monte Carlo simulation for the prediction of the internal energy, pressure, and fractions in rings and chains, double bonded over the full range of bond angles.

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.

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.

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.

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 Wertheims 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.

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 Wertheims perturbation theory. The first represents a slightly approximate general branched chain solution of Wertheims 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.

Effect of bond rigidity and molecular structure on the self-assembly of amphiphilic molecules using second-order classical density functional theory.

Second-order classical density functional theory is applied to assess the effect of surfactant properties on the interfacial structure and interfacial tension of a planar oil/water interface. Specifically the affect of the relative locations of the hydrophobic and hydrophilic portions, rigidity vs flexibility, and bond angle of the surfactant are investigated. It is found that bond angle and branching significantly affect the tendency of a surfactant to adsorb on the interface and the degree to which the interfacial tension is lowered.

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.