Disclinations in systems of amphiphilic molecules: Cubic structures

Possible ordered geometrical configurations with bicontinuous or cellular topologies, optimizing the frustration of a periodic system of frustrated fluid films, are analyzed in terms of topological defects. The solutions found have the same symmetries as those observed for cubic phases of amphiphilic molecules. This agreement leads to consider the latter as structures of defects of rotation, or disclinations.     

Geometric frustration phases of diblock copolymers in nanoparticles

The geometric frustration phases are investigated for diblock copolymers in nanoparticles with neutral surfaces using real-space self-consistent field theory. First, a rich variety of geometric frustration phases with specific symmetries are observed in the polymer nanoparticles with invariable diameters by constructing the phase diagrams arranged as the volume fraction and Flory-Huggins interaction parameter. Most of the space in the phase diagram is filled with phases with strong symmetries, such as spherical or cubic symmetries, while a number of asymmetric or axisymmetric phases are located in a narrow space in the diagram. Then the geometric frustration phases are examined systematically for the diblock copolymers with special polymer parameters, and a rich variety of novel frustration phases with multilayered structures are observed by varying the diameters of the nanoparticles. Furthermore, the investigations on the free energies indicate that the transitions between these frustrated phases are first-order, and the formation mechanism of the frustration phases is reasonably elucidated.     

Cubic phases as structures of disclinations

We look for possible ordered geometrical configurations with bicontinuous or cellular topologies, optimizing the frustration of a periodic system of frustrated fluid films. The solutions found have the same symmetries as those observed for cubic phases of amphiphilic molecules. This agreement leads to consider cubic structures as structures of defects of rotation, or disclinations.This paper was presented at the workshop Ringing gels and Cubic phases, University of Bayreuth, October 25–26th, 1988.     

Frustration Sculpts the Early Stages of Protein Folding

The funneled energy landscape theory implies that protein structures are minimally frustrated. Yet, because of the divergent demands between folding and function, regions of frustrated patterns are present at the active site of proteins. To understand the effects of such local frustration in dictating the energy landscape of proteins, here we compare the folding mechanisms of the two alternative spliced forms of a PDZ domain (PDZ2 and PDZ2as) that share a nearly identical sequence and structure, while displaying different frustration patterns. The analysis, based on the kinetic characterization of a large number of site‐directed mutants, reveals that although the late stages for folding are very robust and biased by native topology, the early stages are more malleable and dominated by local frustration. The results are briefly discussed in the context of the energy‐landscape theory.     

Hopf fibrations and frustrated matter

Frustrated order appear in different scientific contexts like complex crystals, amorphous materials, liquid crystals, foams and even biological organizations, with scales ranging from the atomic level up to macroscopic scales. In this article, we shall first review several cases where it is possible to release frustration and allows for an unfrustrated structural model by curving the underlying Euclidean space into a positively curved space, the hypersphere S ³. The real Euclidean structure is then analyzed in terms ordered regions interrupted by topological defects, whose presence and density is directly related to the change of curvature from S ³ to R ³. We then focus on a rather fascinating geometrical structure, the Hopf fibration, which can be defined on the hypersphere, and show how this tool is very well suited to describe the defect geometries (both linear, helicoidal and bidimensional) which arises from the decurving procedure.     

Molecular design of flexible liquid crystal oligomers stabilising the chiral frustrated phases

ABSTRACT

Chirality induces structural frustration in liquid crystal systems, producing various kinds of chiral frustrated phases, for example, twist grain boundary (TGB) phases, blue phases (BPs) and dark conglomerate (DC) phases. Almost all molecules exhibiting these frustrated phases have a rigid shape. Especially, a bent–core unit is regarded as a key structure for BPs and DC phases. This paper describes that some flexible liquid crystal oligomers being far from a rigid bent–core molecule stabilise these phases. The LC oligomers have a supermolecular structure in which mesogenic units are connected via flexible spacers. By designing intermolecular interactions, they can exhibit various molecular packing structures in the liquid-crystalline phases as follows: chiral dimers inducing TGB phases, U-shaped and T-shaped oligomers stabilising BPs and achiral liquid crystal trimers exhibiting DC phases. I discuss how the designed liquid crystal oligomers produce the chiral frustrated phases.     

Description of metallic and covalent clusters with icosahedral symmetry: the polytope model

Compact and tetravalent clusters with icosahedral local or global symmetries are generated by mapping from ideal structures in curved space onto a tangent euclidean 3D space. The observed elastic energy of the clusters can thus be interpreted as an intrinsic curvature associated to a frustrated local order. It is then proposed a kind of classification of the very rich family of possible clusters using a limited set of parameters.     

Compounds with the YbFe2O4Structure Type: Frustrated Magnetism and Spin-Glass Behavior

The YbFe₂O₄structure type consists of triangular layers of lanthanide oxygen octahedra stacked with triangular double layers of transition metal oxygen triangular bipyramids. The crystallographic structures determined by neutron diffraction powder profile analysis at 300 and 11 K for new members of this structural family are reported. The compounds are found to be magnetically frustrated, by both lattice geometry and disorder. The magnetic properties of YbCuGaO₄, LuCuGaO₄, LuZnFeO₄, LuCoGaO₄, and LuCuFeO₄reveal the effects of total spin, spin mixing, and interaction between spins on different sublattices on the magnetic frustration. The magnetism is increasingly frustrated as the spin on the magnetic ions is decreased.     

High‐Performance Magnetic Refrigerant Featuring One‐Dimensional Gd‐O Chains and O‐Gd3 Triangles

Magnetic cooling at low temperature has attracted intensive interest in cryogenics research, which may become important as cooling medium for long‐wave photon detectors to support space exploration. Here, we report a Gd‐based quaternary magnetic refrigerant material, Gd₅BSi₂O₁₃, containing chains of face‐shared GdO₉ polyhedra and geometrically frustrated OGd₃ triangles. Magnetic measurements indicate that Gd₅BSi₂O₁₃ exhibits a large magnetocaloric effect (MCE) about 1.74 times that of the practical magnetic refrigerant GGG (−ΔS_m=67.0 J kg⁻¹ K⁻¹). We analyzed the origin of the large MCE by comparing Gd^III‐containing compounds with different structures and concentrations of Gd^III.     

Evidence of a Mixed Magnetic Phase in EuMgGe: A Semi­metallic Zintl Compound with TiNiSi Structure Type

The ternary Zintl phase EuMgGe was synthesized from the elements, and its structure solved by single‐crystal X‐ray diffraction. Chemical bonding is discussed, by means of electronic structure calculations at the DFT level and its physical properties characterized with respect to electronic conductivity, magnetic susceptibility, specific heat capacity, and magnetoresistivity. The compound may be interpreted according to the Zintl‐Klemm concept as (Eu²⁺)(Mg²⁺)(Ge^4–) with isolated germanium anions. Resistivity measurements reveal a semimetallic character, which is consistent with the vanishing energy gap obtained from our calculations. The magnetic susceptibility and the specific heat indicate that two consecutive transitions take place, at 9 and 16 K, and they show evidence of magnetic frustration. A possible physical scenario for this magnetic behavior is discussed based on known models of partially frustrated magnets.     

Computing equilibrium states of cholesteric liquid crystals in elliptical channels with deflation algorithms

We study the problem of a cholesteric liquid crystal confined to an elliptical channel. The system is geometrically frustrated because the cholesteric prefers to adopt a uniform rate of twist deformation, but the elliptical domain precludes this. The frustration is resolved by deformation of the layers or introduction of defects, leading to a particularly rich family of equilibrium configurations. To identify the solution set, we adapt and apply a new family of algorithms, known as deflation methods that iteratively modify the free energy extremisation problem by removing previously known solutions. A second algorithm, deflated continuation, is used to track solution branches as a function of the aspect ratio of the ellipse and preferred pitch of the cholesteric.     

Crystallographic B-factors highlight energetic frustration in aldolase folding

Kinetic simulations of the folding and unfolding of the mammalian TIM barrel protein aldolase were conducted to determine if a minimalist monomeric Gō model, using the native structure to determine attractive energies in the protein chain, could capture the experimentally determined folding pathway. The folding order, that is, the order in which different secondary structures fold, between the Gō model simulations and that from hydrogen-deuterium exchange experiments, did not agree. To explain this discrepancy, two alternate variant of the basic Gō model were simulated: (1) a monomer Gō model with native contact energies weighted by a statistical potential (SP model) and (2) a monomer Gō model with native contact energies inversely weighted by crystallographic B factors (B model). The B model demonstrated the best agreement between simulation and experiments. The success of the B model is attributed to the ability of B factors to highlight local energetic frustration in the aldolase structure which results in weaker native contacts in these frustrated regions. The predictive success of the B model also reveals the potential use of B factor information for energetic weighting in general protein modeling.     

Magnetic structures of the M2TbF6 (M=Li, K, Rb) fluorides: A complex behavior resulting from frustration

Neutron powder diffraction has been performed on Li₂TbF₆, K₂TbF₆ and Rb₂TbF₆ fluoroterbates. Incommensurate long-range magnetic order is observed below T_N=2.02, 1.60 and 2.07 K. The square-modulating of the magnetic structures can be correlated with the geometric frustration induced by the pseudo-hexagonal packing of the [TbF₆]²⁻ chains in these hexafluorides. This frustration and the magnetic interactions are discussed on the basis of experimental data and topological considerations. The magnetic structures encountered in this series, and the particular thermal evolution of the Li₂TbF₆ magnetic structure may result from the competition between the magnetic interactions taking place in the chains and the magnetic interactions coupling the chains.     

Evolution of the crystal and magnetic structure of the R2MnRuO7 (R = Tb, Dy, Ho, Er, Tm, Yb, Lu, and Y) family of pyrochlore oxides

The members of the family of pyrochlore oxides with the formula R(2)MnRuO(7) (R = Tb, Dy, Ho, Er, Tm, Yb, Lu and Y) have been synthesized and characterized. Polycrystalline samples were prepared by a soft chemistry procedure involving citrates of the different metal ions, followed by thermal treatments in air or O(2) pressure. The crystallographic and magnetic structures have been analysed from X-ray diffraction (XRD) and neutron powder diffraction (NPD) data, in complement with magnetic measurements; the evolution along the series of the crystallographic parameters (unit-cell parameters, bond distances and angles) is discussed. In R(2)MnRuO(7) pyrochlores, Mn and Ru ions statistically occupy the 16c sites in a cubic unit cell with space group Fd ?3m, which defines an intrinsic frustrated three-dimensional system. In all the cases, the low-temperature NPD data unveils an antiferromagnetic coupling of two subsets of Mn(4+)/Ru(4+) spins, indicating that the magnetic frustration is partially relieved by the random distribution of Mn and Ru over the 16c sites. At lower temperatures there is a polarization of the R(3+) magnetic moments, which also participate in the magnetic structure, when a magnetic rare earth is present.     

Divergent effects of static disorder and hole doping in geometrically frustrated β-CaCr2O4

The gallium substituted and calcium deficient variants of geometrically frustrated β-CaCr₂O₄, β-CaCr_2-2xGa_2xO₄ (0.02≤x≤0.25) and β-Ca_1−yCr₂O₄ (0.075≤y≤0.15), have been investigated by X-ray powder diffraction, magnetization and specific heat measurements. This allows for a direct comparison of the effects, in a geometrically frustrated magnet, of the static disorder that arises from non-magnetic substitution and the dynamic disorder that arises from hole doping. In both cases, disturbing the Cr³⁺ lattice results in a reduction in the degree of magnetic frustration. On substitution of Ga, which introduces disorder without creating holes, a gradual release of spins from ordered antiferromagnetic states is observed. In contrast, in the calcium-deficient compounds the introduction of holes induces static ferrimagnetic ordering and much stronger perturbations of the β-CaCr₂O₄ host.     

Frustration and hydrophobicity interplay in protein folding and protein evolution

A lattice model is used to study mutations and compacting effects on protein folding rates and folding temperature. In the context of protein evolution, we address the question regarding the best scenario for a polypeptide chain to fold: either a fast nonspecific collapse followed by a slow rearrangement to form the native structure or a specific collapse from the unfolded state with the simultaneous formation of the native state. This question is investigated for optimized sequences, whose native state has no frustrated contacts between monomers, and also for mutated sequences, whose native state has some degree of frustration. It is found that the best scenario for folding may depend on the amount of frustration of the native structure. The implication of this result on protein evolution is discussed.     

Role of the spin magnitude of the magnetic ion in determining the frustration and low-temperature properties of kagome lattices

In view of the variety of low-temperature magnetic properties reported recently for kagome lattices with transition-metal ions in different oxidation states, we have investigated the low-energy spectrum and low-temperature thermodynamic properties of antiferromagnetic kagome lattices with varying magnitudes of site spins, employing quantum many-body Heisenberg models. The ground state and the low-lying excitation spectrum are found to depend strongly on the nature of the spin magnitude of the magnetic ions. The system remains highly frustrated if spins are half-odd-integer in magnitude, while the frustration is very weak or almost absent for integer spins or mixed-spin systems. In fact, for a mixed-spin kagome system with a certain magnitude, the whole system behaves as a classical magnet with a ferrimagnetic ground state without any frustration. These theoretical findings are consistent with a few experimental observations recently reported in the literature and would be of value in designing new kagome systems with unusual and interesting low-temperature magnetic properties.     

Frustrated magnetism in the S = 1 kagomé lattice BaNi3(OH)2(VO4)2

Frustrated magnets with integer spin are predicted to have exotic physical properties including spin nematicity, yet few are known to exist. We report a new, frustrated S = 1 magnet, BaNi(3)(OH)(2)(VO(4))(2), which is the structural analogue of the mineral vesignieite. Magnetic frustration arises from a competition between ferromagnetic and antiferromagnetic ordering leading to a glassy transition at 19 K.     

Nematodynamics and structures in junctions of cylindrical micropores

ABSTRACT

We explore equilibrium structures and flow-driven deformations of nematic liquid crystals confined to 3D junctions of cylindrical micropores with homeotropic surface anchoring. The topological state of the nematic ordering field in such basic unit of porous networks is controlled by nematic orientation profiles in individual pores, anchoring frustration along the edges of joining pores and coupling to the material flow field. We numerically investigate formation of the flow-aligned configurations in single cylindrical pores and pore junctions. Depending on the arrangement of inlet and outlet flows in the junction, we demonstrate existence of numerous stationary nematic configurations, characterised by specific bulk defects and surface disclinations along joining edges. Observed bulk defects are nonsingular escaped structures, disclinations in the form of loops or disclination lines pinned to the joining edges of the pores. Furthermore, we show examples of defect dynamics during the flow-induced topological transformations.     

Evidence for Genuine Bimetallic Frustrated Lewis Pair Activation of Dihydrogen with Gold(I)/Platinum(0) Systems

A joint experimental/computational effort to elucidate the mechanism of dihydrogen activation by a gold(I)/platinum(0) metal-only frustrated Lewis pair (FLP) is described herein. The drastic effects on H₂ activation derived from subtle ligand modifications have also been investigated. The importance of the balance between bimetallic adduct formation and complete frustration has been interrogated, providing for the first time evidence for genuine metal-only FLP reactivity in solution. The origin of a strong inverse kinetic isotopic effect has also been clarified, offering further support for the proposed bimetallic FLP-type cleavage of dihydrogen.