Erratum: Cooperative Gas Adsorption without a Phase Transition in Metal-Organic Frameworks [Phys. Rev. Lett. 121, 015701 (2018)].

This corrects the article DOI: 10.1103/PhysRevLett.121.015701.

The dimensional evolution of structure and dynamics in hard sphere liquids.

The formulation of the mean-field infinite-dimensional solution of hard sphere glasses is a significant milestone for theoretical physics. How relevant this description might be for understanding low-dimensional glass-forming liquids, however, remains unclear. These liquids indeed exhibit a complex interplay between structure and dynamics, and the importance of this interplay might only slowly diminish as dimension d increases. A careful numerical assessment of the matter has long been hindered by the exponential increase in computational costs with d. By revisiting a once common simulation technique involving the use of periodic boundary conditions modeled on Dd lattices, we here partly sidestep this difficulty, thus allowing the study of hard sphere liquids up to d = 13. Parallel efforts by Mangeat and Zamponi [Phys. Rev. E 93, 012609 (2016)] have expanded the mean-field description of glasses to finite d by leveraging the standard liquid-state theory and, thus, help bridge the gap from the other direction. The relatively smooth evolution of both the structure and dynamics across the d gap allows us to relate the two approaches and to identify some of the missing features that a finite-d theory of glasses might hope to include to achieve near quantitative agreement.

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.

Finite Dimensional Vestige of Spinodal Criticality above the Dynamical Glass Transition.

Finite dimensional signatures of spinodal criticality are notoriously difficult to come by. The dynamical transition of glass-forming liquids, first described by mode-coupling theory, is a spinodal instability preempted by thermally activated processes that also limit how close the instability can be approached. We combine numerical tools to directly observe vestiges of the spinodal criticality in finite dimensional glass formers. We use the swap Monte Carlo algorithm to efficiently thermalize configurations beyond the mode-coupling crossover, and analyze their dynamics using a scheme to screen out activated processes, in spatial dimensions ranging from d=3 to d=10. We observe a strong softening of the mean-field square-root singularity in d=3 that is progressively restored as d increases above d=8, in surprisingly good agreement with perturbation theory.

Effect of processing and end groups on the crystal structure of polypeptoids studied by cryogenic electron microscopy at atomic length scales.

Cryogenic electron microscopy at atomic length scales was used to study the structure of self-assembled crystalline nanosheets obtained from a series of polypeptoids with the same chain architecture but with different end groups. While long-range order is enhanced by slowing down the self-assembly process, the dominant crystalline motif was found to be a sensitive function of both processing details and end group chemistry. In some cases, adjacent rows of polypeptoid molecules adopt anti-parallel V-shaped side chain conformations. In other cases, adjacent rows of polypeptoid molecules adopt parallel V-shaped side chain conformations. Interestingly, the unit cell is rectangular in both cases with dimensions a = 4.5 Å and c = 50 Å. In all cases, long-range order, quantified by the average number of concatenated unit cells of the same type, is more prevalent along the a direction.

Universal Relationship between Molecular Structure and Crystal Structure in Peptoid Polymers and Prevalence of the cis Backbone Conformation.

Peptoid polymers are often crystalline in the solid-state as examined by X-ray scattering, but thus far, there has been no attempt to identify a common structural motif among them. In order to probe the relationship between molecular structure and crystal structure, we synthesized and analyzed a series of crystalline peptoid copolymers, systematically varying peptoid side-chain length (S) and main-chain length (N). We also examined X-ray scattering data from 18 previously reported peptoid polymers. In all peptoids, we found that the unit cell dimensions, a, b, and c, are simple functions of S and N: a (Å) = 4.55, b (Å) = [2.98]N + 0.35, and c (Å) = [1.86]S + 5.5. These relationships, which apply to both bulk crystals and self-assembled nanosheets in water, indicate that the molecules adopt extended, planar conformations. Furthermore, we performed molecular dynamics simulations (MD) of peptoid polymer lattices, which indicate that all backbone amides adopt the cis conformation. This is a surprising conclusion, because previous studies on isolated molecules indicated an energetic preference for the trans conformer. This study demonstrates that when packed into supramolecular lattices or crystals, peptoid polymers prefer to adopt a regular, extended, all-cis secondary structure.

Cooperative Gas Adsorption without a Phase Transition in Metal-Organic Frameworks.

Cooperative adsorption of gases by porous frameworks, which permits more efficient uptake and removal than the more usual noncooperative (Langmuir-type) adsorption, usually results from a phase transition of the framework. Here we show how cooperativity emerges in the class of metal-organic frameworks mmen-M_{2}(dobpdc) in the absence of a phase transition. Our study provides a microscopic understanding of the emergent features of cooperative binding, including the position, slope, and height of the isotherm step, and indicates how to optimize gas storage and separation in these materials.

Selective gas capture via kinetic trapping.

Conventional approaches to the capture of CO2 by metal-organic frameworks focus on equilibrium conditions, and frameworks that contain little CO2 in equilibrium are often rejected as carbon-capture materials. Here we use a statistical mechanical model, parameterized by quantum mechanical data, to suggest that metal-organic frameworks can be used to separate CO2 from a typical flue gas mixture when used under nonequilibrium conditions. The origin of this selectivity is an emergent gas-separation mechanism that results from the acquisition by different gas types of different mobilities within a crowded framework. The resulting distribution of gas types within the framework is in general spatially and dynamically heterogeneous. Our results suggest that relaxing the requirement of equilibrium can substantially increase the parameter space of conditions and materials for which selective gas capture can be effected.

Strategies to Modulate the Copper Oxidation State Toward Selective C2+ Production in the Electrochemical CO2 Reduction Reaction.

The electrochemical reduction of CO2 to form value-added chemicals receives considerable attention in recent years. Copper (Cu) is recognized as the only element capable of electro-reducing CO2 into hydrocarbons with two or more carbon atoms (C2+), but the low product selectivity of the Cu-based catalyst remains a major technological challenge to overcome. Therefore, identification of the structural features of Cu-based catalysts is of great importance for the highly selective production of C2+ products (ethylene, ethanol, n-propanol, etc.), and the oxidation state of Cu species in the catalysts is found critical to the catalyst performance. This review introduces recent efforts to fine-tune the oxidation state of Cu to increase carbon capture and produce specific C2+ compounds, with the intention of greatly expediting the advance in the catalyst designs. It also points to the remaining challenges and fruitful research directions for the development of Cu-based catalysts that can shape the practical CO2 reduction technology.

Bypassing sluggishness: SWAP algorithm and glassiness in high dimensions.

The recent implementation of a swap Monte Carlo algorithm (SWAP) for polydisperse glass forming mixtures bypasses computational sluggishness and closes the gap between experimental and simulation timescales in physical dimensions d=2 and 3. Here, we consider suitably optimized systems in d=2,3,⋯,8 to obtain insights into the performance and underlying physics of SWAP. We show that the speedup obtained decays rapidly with increasing the dimension. SWAP nonetheless delays systematically the onset of the activated dynamics by an amount that remains seemingly finite in the limit d→∞. This shows that the glassy dynamics in high dimensions d>3 is now computationally accessible using SWAP, thus opening the door for the systematic consideration of finite-dimensional deviations from the mean-field description.

Shape-Dependent Photocatalytic Activity of Hydrothermally Synthesized Cadmium Sulfide Nanostructures.

The effective surface area of the nanostructured materials is known to play a prime role in catalysis. Here we demonstrate that the shape of the nanostructured materials plays an equally important role in their catalytic activity. Hierarchical CdS microstructures with different morphologies such as microspheres assembled of nanoplates, nanorods, nanoparticles, and nanobelts are synthesized using a simple hydrothermal method by tuning the volume ratio of solvents, i.e., water or ethylenediamine (en). With an optimum solvent ratio of 3:1 water:en, the roles of other synthesis parameters such as precursor's ratio, temperature, and precursor combinations are also explored and reported here. Four selected CdS microstructures are used as photocatalysts for the degradation of methylene blue and photoelectrochemical water splitting for hydrogen generation. In spite of smaller effective surface area of CdS nanoneedles/nanorods than that of CdS nanowires network, the former exhibits higher catalytic activity under visible light irradiation which is ascribed to the reduced charge recombination as confirmed from the photoluminescence study.

The Ramachandran Number: An Order Parameter for Protein Geometry.

Three-dimensional protein structures usually contain regions of local order, called secondary structure, such as α-helices and ß-sheets. Secondary structure is characterized by the local rotational state of the protein backbone, quantified by two dihedral angles called ϕ and ψ. Particular types of secondary structure can generally be described by a single (diffuse) location on a two-dimensional plot drawn in the space of the angles ϕ and ψ, called a Ramachandran plot. By contrast, a recently-discovered nanomaterial made from peptoids, structural isomers of peptides, displays a secondary-structure motif corresponding to two regions on the Ramachandran plot [Mannige et al., Nature 526, 415 (2015)]. In order to describe such 'higher-order' secondary structure in a compact way we introduce here a means of describing regions on the Ramachandran plot in terms of a single Ramachandran number, [Formula: see text], which is a structurally meaningful combination of ϕ and ψ. We show that the potential applications of [Formula: see text] are numerous: it can be used to describe the geometric content of protein structures, and can be used to draw diagrams that reveal, at a glance, the frequency of occurrence of regular secondary structures and disordered regions in large protein datasets. We propose that [Formula: see text] might be used as an order parameter for protein geometry for a wide range of applications.

Asymptotic behavior of the isotropic-nematic and nematic-columnar phase boundaries for the system of hard rectangles on a square lattice.

A system of hard rectangles of size m×mk on a square lattice undergoes three entropy-driven phase transitions with increasing density for large-enough aspect ratio k: first from a low-density isotropic to an intermediate-density nematic phase, second from the nematic to a columnar phase, and third from the columnar to a high-density sublattice phase. In this paper we show, from extensive Monte Carlo simulations of systems with m=1,2, and 3, that the transition density for the isotropic-nematic transition is ≈A(1)/k when k≫1, where A(1) is independent of m. We estimate A(1)=4.80±0.05. Within a Bethe approximation and virial expansion truncated at the second virial coefficient, we obtain A(1)=2. The critical density for the nematic-columnar transition when m=2 is numerically shown to tend to a value less than the full packing density as k(-1) when k→∞. We find that the critical Binder cumulant for this transition is nonuniversal and decreases as k(-1) for k≫1. However, the transition is shown to be in the Ising universality class.

Phase transitions in a system of hard rectangles on the square lattice.

The phase diagram of a system of monodispersed hard rectangles of size m × mk on a square lattice is numerically determined for m = 2,3 and aspect ratio k = 1,2,...,7. We show the existence of a disordered phase, a nematic phase with orientational order, a columnar phase with orientational and partial translational order, and a solidlike phase with sublattice order, but no orientational order. The asymptotic behavior of the phase boundaries for large k is determined using a combination of entropic arguments and a Bethe approximation. This allows us to generalize the phase diagram to larger m and k, showing that for k ≥ 7, the system undergoes three entropy-driven phase transitions with increasing density. The nature of the different phase transitions is established and the critical exponents for the continuous transitions are determined using finite size scaling.

Controlled synthesis and catalytic activity of copper sulfide nanostructured assemblies with different morphologies.

A simple, template-free and mild solution chemistry route was employed to synthesize diverse copper sulfide (CuS) nanostructured assemblies at 70 °C by varying the solvent (water or ethylene glycol, or their ratios (3:1, 1:1 and 1:3)). The CuS structures in the shape of spheres and nanotubes were found to be assemblies of either nanoplates or nanoparticles. The nanotube formation was elaborately studied by varying the synthesis parameters such as temperature, reaction duration, precursor's ratio, and counterions. Counterions such as NO3(-) and SO4(2-) were found to be suitable for nanotube formation whereas in the presence of Cl(-) and OAc(-) ions, CuS flake-like and nanoparticle assemblies are obtained, respectively. The optical bandgaps for the CuS with different morphologies were measured to be in the range of 1.88-2.16 eV. The bandgap of CuS in the visible region of electromagnetic radiation prompted it to be used as photocatalyst in the past under natural light. However, we demonstrate here the similar catalytic performance of as-synthesized CuS nanostructures for the degradation of methylene blue in the dark, suggesting that light does not play a role in its catalytic behavior.

Reentrant disordered phase in a system of repulsive rods on a Bethe-like lattice.

We solve exactly a model of monodispersed rigid rods of length k with repulsive interactions on the random locally tree-like layered lattice. For k≥4 we show that with increasing density, the system undergoes two phase transitions: first, from a low-density disordered phase to an intermediate density nematic phase and, second, from the nematic phase to a high-density reentrant disordered phase. When the coordination number is four, both phase transitions are continuous and in the mean field Ising universality class. For an even coordination number larger than four, the first transition is discontinuous, while the nature of the second transition depends on the rod length k and the interaction parameters.