Hysteresis curves reveal the microscopic origin of cooperative CO2 adsorption in diamine-appended metal-organic frameworks.

Diamine-appended metal-organic frameworks (MOFs) of the form Mg2(dobpdc)(diamine)2 adsorb CO2 in a cooperative fashion, exhibiting an abrupt change in CO2 occupancy with pressure or temperature. This change is accompanied by hysteresis. While hysteresis is suggestive of a first-order phase transition, we show that hysteretic temperature-occupancy curves associated with this material are qualitatively unlike the curves seen in the presence of a phase transition; they are instead consistent with CO2 chain polymerization, within one-dimensional channels in the MOF, in the absence of a phase transition. Our simulations of a microscopic model reproduce this dynamics, providing a physical understanding of cooperative adsorption in this industrially important class of materials.

Avidity and surface mobility in multivalent ligand-receptor binding.

Targeted drug delivery relies on two physical processes: the selective binding of a therapeutic particle to receptors on a specific cell membrane, followed by transport of the particle across the membrane. In this article, we address some of the challenges in controlling the thermodynamics and dynamics of these two processes by combining a simple experimental system with a statistical mechanical model. Specifically, we characterize and model multivalent ligand-receptor binding between colloidal particles and fluid lipid bilayers, as well as the surface mobility of membrane-bound particles. We show that the mobility of the receptors within the fluid membrane is key to both the thermodynamics and dynamics of binding. First, we find that the particle-membrane binding free energy-or avidity-is a strongly nonlinear function of the ligand-receptor affinity. We attribute the nonlinearity to a combination of multivalency and recruitment of fluid receptors to the binding site. Our results also suggest that partial wrapping of the bound particles by the membrane enhances avidity further. Second, we demonstrate that the lateral mobility of membrane-bound particles is also strongly influenced by the recruitment of receptors. Specifically, we find that the lateral diffusion coefficient of a membrane-bound particle is dominated by the hydrodynamic drag against the aggregate of receptors within the membrane. These results provide one of the first direct validations of the working theoretical framework for multivalent interactions. They also highlight that the fluidity and elasticity of the membrane are as important as the ligand-receptor affinity in determining the binding and transport of small particles attached to membranes.

Unconstrained peptoid tetramer exhibits a predominant conformation in aqueous solution.

Conformational control in peptoids, N-substituted glycines, is crucial for the design and synthesis of biologically-active compounds and atomically-defined nanomaterials. While there are a growing number of structural studies in solution, most have been performed with conformationally-constrained short sequences (e.g., sterically-hindered sidechains or macrocyclization). Thus, the inherent degree of heterogeneity of unconstrained peptoids in solution remains largely unstudied. Here, we explored the folding landscape of a series of simple peptoid tetramers in aqueous solution by NMR spectroscopy. By incorporating specific 13 C-probes into the backbone using bromoacetic acid-2-13 C as a submonomer, we developed a new technique for sequential backbone assignment of peptoids based on the 1,n-Adequate pulse sequence. Unexpectedly, two of the tetramers, containing an N-(2-aminoethyl)glycine residue (Nae), had preferred conformations. NMR and molecular dynamics studies on one of the tetramers showed that the preferred conformer (52%) had a trans-cis-trans configuration about the three amide bonds. Moreover, >80% of the ensemble contained a cis amide bond at the central amide. The backbone dihedral angles observed fall directly within the expected minima in the peptoid Ramachandran plot. Analysis of this compound against similar peptoid analogs suggests that the commonly used Nae monomer plays a key role in the stabilization of peptoid structure via a side-chain-to-main-chain interaction. This discovery may offer a simple, synthetically high-yielding approach to control peptoid structure, and suggests that peptoids have strong intrinsic conformational preferences in solution. These findings should facilitate the predictive design of folded peptoid structures, and accelerate application in areas ranging from drug discovery to biomimetic nanoscience.

Stereochemistry of polypeptoid chain configurations.

Like polypeptides, peptoids, or N-substituted glycine oligomers, have intrinsic conformational preferences due to their amide backbones and close spacing of side chain substituents. However, the conformations that peptoids adopt are distinct from polypeptides due to several structural differences: the peptoid backbone is composed of tertiary amide bonds that have trans and cis conformers similar in energy, they lack a backbone hydrogen bond donor, and have an N-substituent. To better understand how these differences manifest in actual peptoid structures, we analyzed 46 high quality, experimentally determined peptoid structures reported in the literature to extract their backbone conformational preferences. One hundred thirty-two monomer dihedral angle pairs were compared to the calculated energy landscape for the peptoid Ramachandran plot, and were found to fall within the expected minima. Interestingly, only two regions of the backbone dihedral angles ϕ and ψ were found to be populated that are mirror images of each other. Furthermore, these two conformers are present in both cis and trans forms. Thus, there are four primary conformers that are sufficient to describe almost all known backbone conformations for peptoid oligomers, despite conformational constraints imposed by a variety of side chains, macrocyclization, or crystal packing forces. Because these conformers are predominant in peptoid structure, and are distinct from those found in protein secondary structures, we propose a simple naming system to aid in the description and classification of peptoid structure.

Design Rules for Self-Assembly of 2D Nanocrystal/Metal-Organic Framework Superstructures.

We demonstrate the guiding principles behind simple two dimensional self-assembly of MOF nanoparticles (NPs) and oleic acid capped iron oxide (Fe3 O4 ) NCs into a uniform two-dimensional bi-layered superstructure. This self-assembly process can be controlled by the energy of ligand-ligand interactions between surface ligands on Fe3 O4 NCs and Zr6 O4 (OH)4 (fumarate)6 MOF NPs. Scanning transmission electron microscopy (TEM)/energy-dispersive X-ray spectroscopy and TEM tomography confirm the hierarchical co-assembly of Fe3 O4 NCs with MOF NPs as ligand energies are manipulated to promote facile diffusion of the smaller NCs. First-principles calculations and event-driven molecular dynamics simulations indicate that the observed patterns are dictated by combination of ligand-surface and ligand-ligand interactions. This study opens a new avenue for design and self-assembly of MOFs and NCs into high surface area assemblies, mimicking the structure of supported catalyst architectures, and provides a thorough fundamental understanding of the self-assembly process, which could be a guide for designing functional materials with desired structure.

Conformations of peptoids in nanosheets result from the interplay of backbone energetics and intermolecular interactions.

The conformations adopted by the molecular constituents of a supramolecular assembly influence its large-scale order. At the same time, the interactions made in assemblies by molecules can influence their conformations. Here we study this interplay in extended flat nanosheets made from nonnatural sequence-specific peptoid polymers. Nanosheets exist because individual polymers can be linear and untwisted, by virtue of polymer backbone elements adopting alternating rotational states whose twists oppose and cancel. Using molecular dynamics and quantum mechanical simulations, together with experimental data, we explore the design space of flat nanostructures built from peptoids. We show that several sets of peptoid backbone conformations are consistent with their being linear, but the specific combination observed in experiment is determined by a combination of backbone energetics and the interactions made within the nanosheet. Our results provide a molecular model of the peptoid nanosheet consistent with all available experimental data and show that its structure results from a combination of intra- and intermolecular interactions.

Growth of defect-free colloidal hard-sphere crystals using colloidal epitaxy.

Using event-driven Brownian dynamics simulations, we investigate the epitaxial growth of hard-sphere crystals with a face-centered-cubic (fcc) structure on the three densest cross-sectional planes of the fcc: (i) fcc (100), (ii) fcc (111), and (iii) fcc (110). We observe that for high settling velocities, large fcc crystals with very few extended defects grow on the fcc (100) template. Our results show good agreement with the experiments of Jensen et al. [Soft Matter 9, 320 (2013)], who observed such large fcc crystals upon centrifugation on an fcc (100) template. We also compare the quality of the fcc crystal formed on the fcc (111) and fcc (110) templates with that of the fcc (100) template and conclude that the latter yields the best crystal. We also briefly discuss the dynamical behavior of stacking faults that occur in the sediments.

Critical Casimir interactions and colloidal self-assembly in near-critical solvents.

A binary solvent mixture close to critical demixing experiences fluctuations whose correlation length, ξ, diverges as the critical point is approached. The solvent-mediated (SM) interaction that arises between a pair of colloids immersed in such a near-critical solvent can be long-ranged and this so-called critical Casimir interaction is well-studied. How a (dense) suspension of colloids will self-assemble under these conditions is poorly understood. Using a two-dimensional lattice model for the solvent and hard disks to represent the colloids, we perform extensive Monte Carlo simulations to investigate the phase behaviour of this model colloidal suspension as a function of colloid size and wettability under conditions where the solvent reservoir is supercritical. Unlike most other approaches, where the solvent is modelled as an implicit background, our model employs an explicit solvent and treats the suspension as a ternary mixture. This enables us to capture important features, including the pronounced fractionation of the solvent in the coexisting colloidal phases, of this complex system. We also present results for the partial structure factors; these shed light on the critical behaviour in the ternary mixture. The degree to which an effective two-body pair potential description can describe the phase behaviour and structure of the colloidal suspension is discussed briefly.

Stabilizing the hexagonal close packed structure of hard spheres with polymers: Phase diagram, structure, and dynamics.

We study the phase behaviour of a binary mixture of colloidal hard spheres and freely jointed chains of beads using Monte Carlo simulations. Recently Panagiotopoulos and co-workers predicted [Nat. Commun. 5, 4472 (2014)] that the hexagonal close packed (HCP) structure of hard spheres can be stabilized in such a mixture due to the interplay between polymer and the void structure in the crystal phase. Their predictions were based on estimates of the free-energy penalty for adding a single hard polymer chain in the HCP and the competing face centered cubic (FCC) phase. Here we calculate the phase diagram using free-energy calculations of the full binary mixture and find a broad fluid-solid coexistence region and a metastable gas-liquid coexistence region. For the colloid-monomer size ratio considered in this work, we find that the HCP phase is only stable in a small window at relatively high polymer reservoir packing fractions, where the coexisting HCP phase is nearly close packed. Additionally we investigate the structure and dynamic behaviour of these mixtures.

Critical casimir forces and colloidal phase transitions in a near-critical solvent: a simple model reveals a rich phase diagram.

From experimental studies, it is well known that colloidal particles suspended in a near-critical binary solvent exhibit interesting aggregation phenomena, often associated with colloidal phase transitions and assumed to be driven by long-ranged solvent-mediated (SM) interactions (critical Casimir forces), set by the (diverging) correlation length of the solvent. We present the first simulation and theoretical study of an explicit model of a ternary mixture that mimics this situation. Both the effective SM pair interactions and the full ternary phase diagram are determined for Brownian disks suspended in an explicit two-dimensional supercritical binary liquid mixture. Gas-liquid and fluid-solid transitions are observed in a region that extends well away from criticality of the solvent reservoir. We discuss to what extent an effective pair-potential description can account for the phase behavior we observe. Our study provides a fresh perspective on how proximity to the critical point of the solvent reservoir might influence colloidal self-assembly.

Dynamic mean field theory for lattice gas models of fluids confined in porous materials: higher order theory based on the Bethe-Peierls and path probability method approximations.

Recently we have developed a dynamic mean field theory (DMFT) for lattice gas models of fluids in porous materials [P. A. Monson, J. Chem. Phys. 128(8), 084701 (2008)]. The theory can be used to describe the relaxation processes in the approach to equilibrium or metastable states for fluids in pores and is especially useful for studying system exhibiting adsorption/desorption hysteresis. In this paper we discuss the extension of the theory to higher order by means of the path probability method (PPM) of Kikuchi and co-workers. We show that this leads to a treatment of the dynamics that is consistent with thermodynamics coming from the Bethe-Peierls or Quasi-Chemical approximation for the equilibrium or metastable equilibrium states of the lattice model. We compare the results from the PPM with those from DMFT and from dynamic Monte Carlo simulations. We find that the predictions from PPM are qualitatively similar to those from DMFT but give somewhat improved quantitative accuracy, in part due to the superior treatment of the underlying thermodynamics. This comes at the cost of greater computational expense associated with the larger number of equations that must be solved.

Dynamics of capillary condensation in lattice gas models of confined fluids: a comparison of dynamic mean field theory with dynamic Monte Carlo simulations.

This article addresses the accuracy of a dynamic mean field theory (DMFT) for fluids in porous materials [P. A. Monson, J. Chem. Phys. 128, 084701 (2008)]. The theory is used to study the relaxation processes of fluids in pores driven by step changes made to a bulk reservoir in contact with the pore. We compare the results of the DMFT to those obtained by averaging over large numbers of dynamic Monte Carlo (DMC) simulation trajectories. The problem chosen for comparison is capillary condensation in slit pores, driven by step changes in the chemical potential in the bulk reservoir and involving a nucleation process via the formation of a liquid bridge. The principal difference between the DMFT results and DMC is the replacement of a distribution of nucleation times and location along the pore for the formation of liquid bridges by a single time and location. DMFT is seen to yield an otherwise qualitatively accurate description of the dynamic behavior.