Moving Dirac nodes by chemical substitution

Dirac fermions play a central role in the study of topological phases, for they can generate a variety of exotic states, such as Weyl semimetals and topological insulators. The control and manipulation of Dirac fermions constitute a fundamental step toward the realization of novel concepts of electronic devices and quantum computation. By means of Angle-Resolved Photo-Emission Spectroscopy (ARPES) experiments and ab initio simulations, here, we show that Dirac states can be effectively tuned by doping a transition metal sulfide, BaNiS2, through Co/Ni substitution. The symmetry and chemical characteristics of this material, combined with the modification of the charge-transfer gap of BaCo1−xNixS2 across its phase diagram, lead to the formation of Dirac lines, whose position in k-space can be displaced along the Γ−M symmetry direction and their form reshaped. Not only does the doping x tailor the location and shape of the Dirac bands, but it also controls the metal-insulator transition in the same compound, making BaCo1−xNixS2 a model system to functionalize Dirac materials by varying the strength of electron correlations.

In the vast domain of topological Dirac and Weyl materials (1–9), the study of various underlying mechanisms (10–15) leading to the formation of nontrivial band structures is key to discovering new topological electronic states (16–23). A highly desirable feature of these materials is the tunability of the topological properties by an external parameter, which will make them suitable in view of technological applications, such as topological field-effect transistors (24). While a thorough control of band topology can be achieved, in principle, in optical lattices (25) and photonic crystals (26) through the wandering, merging, and reshaping of nodal points and lines in k-space (27, 28), in solid-state systems, such a control is much harder to achieve. Proposals have been made by using optical cavities (29), twisted van der Waals heterostructures (30), intercalation (31), chemical deposition (32, 33), impurities (34), and magnetic and electric applied fields (35), both static (36) and time-periodic (17, 37). Here, we prove that it is possible to move and reshape Dirac nodal lines in reciprocal space by chemical substitution. Namely, by means of Angle-Resolved Photo-Emission Spectroscopy (ARPES) experiments and ab initio simulations, we observe a sizable shift of robust massive Dirac nodes toward Γ in BaCo1−xNixS2 as a function of doping x, obtained by replacing Ni with Co. At variance with previous attempts of controlling Dirac states by doping (19, 38), in our work, we report both a reshape and a significant k-displacement of the Dirac nodes.BaCo1−xNixS2 is a prototypical transition metal system with a simple square lattice (39). In BaCo1−xNixS2 , the same doping parameter x that tunes the position of the Dirac nodes also controls the electronic phase diagram, which features a first-order metal-insulator transition (MIT) at a critical substitution level, xcr∼ 0.22 (40, 41), as shown in Fig. 1A. The Co rich side (x=0) is an insulator with columnar antiferromagnetic (AF) order and with local moments in a high-spin (S = 3/2) configuration (42). This phase can be seen as a spin density wave (SDW) made of antiferromagnetically coupled collinear spin chains. Both electron-correlation strength and charge-transfer gap ΔCT increase with decreasing x, as typically found in the late-transition metal series. The MIT at x=0.22 is of interest because it is driven by electron correlations (43) and is associated with a competition between an insulating antiferromagnetic phase and an unconventional paramagnetic semimetal (44), where the Dirac nodes are found at the Fermi level. We show that a distinctive feature of these Dirac states is their dominant d-orbital character and that the underlying band-inversion mechanism is driven by a large d−p hybridization combined with the nonsymmorphic symmetry (NSS) of the crystal (Fig. 1B). It follows that an essential role in controlling the properties of Dirac states is played by electron correlations and by the charge-transfer gap (Fig. 1C), as they have a direct impact on the hybridization strength. This results into an effective tunability of shape, energy, and wave vector of the Dirac lines in the proximity of the Fermi level. Specifically, the present ARPES study unveils Dirac bands moving from M to Γ with decreasing x. The bands are well explained quantitatively by ab initio calculations, in a hybrid density functional approximation suitable for including nonlocal correlations of screened-exchange type, which affect the hybridization between the d and p states. The same functional is able to describe the insulating SDW phase at x=0, driven by local correlations, upon increase of the optimal screened-exchange fraction. These calculations confirm that the Dirac nodes mobility in k-space stems directly from the evolution of the charge-transfer gap, i.e., the relative position between d and p on-site energies. These results clearly suggest that BaCo1−xNixS2 is a model system to tailor Dirac states and, more generally, that two archetypal features of correlated systems, such as the hybrid d−p bands and the charge-transfer gap, constitute a promising playground to engineer Dirac and topological materials using chemical substitution and other macroscopic control parameters.Open in a separate windowFig. 1.Experimental observation of Dirac states in the phase diagram of BaCo1−xNixS2. (A) Phase diagram of BaCo1−xNixS2. The transition lines between the PM, the paramagnetic insulator (PI), and the antiferromagnetic insulator (AFI) are reported. Colored circles indicate the different doping levels x studied in this work. This doping alters the d−p charge-transfer gap (ΔCT). (B) Crystal structure of BaNiS2. Blue, red, and yellow spheres represent the Ni, S, and Ba atoms, respectively. The tetragonal unit cell is indicated by black solid lines. Lattice parameters are a = 4.44 Å and c = 8.93 Å (45). (B, Upper) Projection of the unit cell in the xy plane, containing two Ni atoms. (C) Schematics of the energy levels. The hybridization of d− and p− orbitals creates the Dirac states, and the d−p charge-transfer gap fixes the position of these states in the E−k space. (D) A three-dimensional ARPES map of BaNiS2 (x=1) taken at 70-eV photon energy. The top surface shows the Fermi surface, and the sides of the cube present the band dispersion along high-symmetry directions. The linearly dispersing bands along Γ−M cross each other at the Fermi level, EF, thus creating four Dirac nodes. (E) We observe the oval-shaped section of the linearly dispersing bands on the kx−ky plane for E−EF=−100 meV. The linearly dispersing bands along the major and minor axis of the oval are also shown.     

From hidden order to antiferromagnetism: Electronic structure changes in Fe-doped URu2Si2

In matter, any spontaneous symmetry breaking induces a phase transition characterized by an order parameter, such as the magnetization vector in ferromagnets, or a macroscopic many-electron wave function in superconductors. Phase transitions with unknown order parameter are rare but extremely appealing, as they may lead to novel physics. An emblematic and still unsolved example is the transition of the heavy fermion compound URu2Si2 (URS) into the so-called hidden-order (HO) phase when the temperature drops below T0=17.5 K. Here, we show that the interaction between the heavy fermion and the conduction band states near the Fermi level has a key role in the emergence of the HO phase. Using angle-resolved photoemission spectroscopy, we find that while the Fermi surfaces of the HO and of a neighboring antiferromagnetic (AFM) phase of well-defined order parameter have the same topography, they differ in the size of some, but not all, of their electron pockets. Such a nonrigid change of the electronic structure indicates that a change in the interaction strength between states near the Fermi level is a crucial ingredient for the HO to AFM phase transition.

The transition of URu2Si2 from a high-temperature paramagnetic (PM) phase to the hidden-order (HO) phase below T0 is accompanied by anomalies in specific heat (1–3), electrical resistivity (1, 3), thermal expansion (4), and magnetic susceptibility (2, 3) that are all typical of magnetic ordering. However, the small associated antiferromagnetic (AFM) moment (5) is insufficient to explain the large entropy loss and was shown to be of extrinsic origin (6). Inelastic neutron scattering (INS) experiments revealed gapped magnetic excitations below T0 at commensurate and incommensurate wave vectors (7–9), while an instability and partial gapping of the Fermi surface was observed by angle-resolved photoemission spectroscopy (ARPES) (10–16) and scanning tunneling microscopy/spectroscopy (17, 18). More recently, high-resolution, low-temperature ARPES experiments imaged the Fermi surface reconstruction across the HO transition, unveiling the nesting vectors between Fermi sheets associated with the gapped magnetic excitations seen in INS experiments (14, 19) and quantitatively explaining, from the changes in Fermi surface size and quasiparticle mass, the large entropy loss in the HO phase (19). Nonetheless, the nature of the HO parameter is still hotly debated (20–23).The HO phase is furthermore unstable above a temperature-dependent critical pressure of about 0.7 GPa at T=0, at which it undergoes a first-order transition into a large moment AFM phase where the value of the magnetic moment per U atom exhibits a sharp increase, by a factor of 10 to 50 (6, 24–30). When the system crosses the HO → AFM phase boundary, the characteristic magnetic excitations of the HO phase are either suppressed or modified (8, 31), while resistivity and specific heat measurements suggest that the partial gapping of the Fermi surface is enhanced (24, 27).As the AFM phase has a well-defined order parameter, studying the evolution of the electronic structure across the HO/AFM transition would help develop an understanding of the HO state. So far, the experimental determination of the Fermi surface by Shubnikov de Haas (SdH) oscillations only showed minor changes across the HO → AFM phase boundary (32). Here, we take advantage of the HO/AFM transition induced by chemical pressure in URu2Si2, through the partial substitution of Ru with Fe (33–37), to directly probe its electronic structure in the AFM phase using ARPES. As we shall see, our results reveal that changes in the Ru 4d–U 5f hybridization across the HO/AFM phase boundary seem essential for a better understanding of the HO state.     

Ultrasensitive multispecies spectroscopic breath analysis for real-time health monitoring and diagnostics

Breath analysis enables rapid, noninvasive diagnostics, as well as long-term monitoring of human health, through the identification and quantification of exhaled biomarkers. Here, we demonstrate the remarkable capabilities of mid-infrared (mid-IR) cavity-enhanced direct-frequency comb spectroscopy (CE-DFCS) applied to breath analysis. We simultaneously detect and monitor as a function of time four breath biomarkers—CH3OH, CH4, H2O, and HDO—as well as illustrate the feasibility of detecting at least six more (H2CO, C2H6, OCS, C2H4, CS2, and NH3) without modifications to the experimental apparatus. We achieve ultrahigh detection sensitivity at the parts-per-trillion level. This is made possible by the combination of the broadband spectral coverage of a frequency comb, the high spectral resolution afforded by the individual comb teeth, and the sensitivity enhancement resulting from a high-finesse cavity. Exploiting recent advances in frequency comb, optical coating, and photodetector technologies, we can access a large variety of biomarkers with strong carbon–hydrogen-bond spectral signatures in the mid-IR.

Breath analysis is an exceptionally promising and rapidly developing field of research, which examines the molecular composition of exhaled breath (1–6). The hundreds of different gases that are present in exhaled breath include inorganic compounds, as well as volatile organic compounds (VOCs), and can either result from internal metabolic activity (endogenous emissions) or external factors, such as food consumption or environmental exposure (exogenous emissions). Despite its distinctive advantages of being a rapid, noninvasive technique and its long history dating back to Hippocrates, breath analysis has not yet been as widely deployed for routine diagnostics and monitoring as other methods, such as blood-based analysis. This is partly due to the experimental challenges of dealing with extremely small amounts of gas-phase molecules—in the parts-per-million (ppm) to parts-per-billion (ppb) range for most VOCs—and partly due to the relative scarcity of large-scale clinical studies that can reliably correlate specific diseases with biomarkers present in breath. Nevertheless, through close collaborations between instrument developers, breath-analysis experts, and clinicians, the field of breath analysis is fast approaching its goal of enabling real-time, noninvasive early detection and long-term monitoring of temporary and permanent health conditions (1, 3). Several biomarkers present in breath have been associated with specific conditions—for instance, nitrogen monoxide with asthma, acetone with diabetes, and ammonia with renal failure (5)—and breath is increasingly being used to track diseases and infections, both bacterial and viral (7). Recently, three studies have demonstrated the use of breath analysis to discriminate between SARS-CoV-2–infected patients and patients affected by other conditions (including asthma, chronic obstructive pulmonary disease, bacterial pneumonia, and cardiac conditions) (8, 9) or influenza A-infected patients (10). The possibility of real-time testing for highly infectious diseases in a noninvasive manner, without the need for chemical reagents and complex laboratory facilities, is particularly appealing in view of the current global pandemic.Technologies being explored and adopted for breath analysis include mass spectrometry, nanomaterial-based sensors, and laser spectroscopy. To date, the most widely used analytical technique in breath research is gas chromatography combined with mass spectrometry, which allows for the sensitive detection of hundreds of exhaled molecules, albeit with relatively long analysis times (tens of minutes) limited by the elution time of the various species. On the other hand, selected ion-flow-tube mass spectrometry and proton-transfer reaction mass spectrometry allow for real-time breath analysis at the expense of a reduced number of simultaneously detectable molecules (11). Sensor arrays offer an inexpensive and practical alternative for identifying the presence of a class of compounds based on their functional groups, but they generally do not permit identification of the specific molecules present in the samples (9, 12). Laser spectroscopy is intrinsically fast (≪ second timescale), allowing breath-cycle-resolved (i.e., respiratory-phase-resolved) sampling of breath with high precision and absolute accuracy. Achieving high sensitivity requires both signal enhancement and noise reduction: The former is attained by using multipass cells or high-finesse cavities, while the latter is accomplished through intensity or frequency-modulation techniques. Among others, tunable diode laser absorption spectroscopy, cavity ring-down spectroscopy, cavity-enhanced absorption spectroscopy, and photoacoustic spectroscopy have all successfully been employed in breath analysis, but are typically limited in tunability and therefore in the number of detectable analytes (1). Cavity-enhanced direct-frequency comb spectroscopy (CE-DFCS) offers substantially enhanced capabilities for the simultaneous detection of multiple species due to the combination of high spectral resolution, wide spectral coverage, and high sensitivity (13–18). An early study from 2008 demonstrated this by detecting carbon monoxide, carbon dioxide, methane, ammonia, and water in breath samples by CE-DFCS (19). This previous work measured vibrational (mainly first) overtone transitions in the near-infrared (near-IR) region of the spectrum, from 1.5 μm to 1.7 μm.Here, we report a 2-orders-of-magnitude improvement in the detection sensitivity for multiple species relevant to breath analysis by using CE-DFCS in the mid-infrared (mid-IR) molecular fingerprint region (3.4−3.6 μm). We gain access to fundamental vibrational transitions, as well as employ higher-finesse mid-IR cavity mirrors (15, 20), compared to previous work in this spectral region (21). Exploiting recent advances in frequency comb, high-reflectivity optical coating, and photodetector technologies, we can detect a large variety of biomarkers simultaneously, sensitively, and unambiguously, providing exciting prospects to connect breath to a range of biological functions and diseases.     

Glasses denser than the supercooled liquid

When aged below the glass transition temperature, Tg, the density of a glass cannot exceed that of the metastable supercooled liquid (SCL) state, unless crystals are nucleated. The only exception is when another polyamorphic SCL state exists, with a density higher than that of the ordinary SCL. Experimentally, such polyamorphic states and their corresponding liquid–liquid phase transitions have only been observed in network-forming systems or those with polymorphic crystalline states. In otherwise simple liquids, such phase transitions have not been observed, either in aged or vapor-deposited stable glasses, even near the Kauzmann temperature. Here, we report that the density of thin vapor-deposited films of N,N′-bis(3-methylphenyl)-N,N′-diphenylbenzidine (TPD) can exceed their corresponding SCL density by as much as 3.5% and can even exceed the crystal density under certain deposition conditions. We identify a previously unidentified high-density supercooled liquid (HD-SCL) phase with a liquid–liquid phase transition temperature (TLL) ∼35 K below the nominal glass transition temperature of the ordinary SCL. The HD-SCL state is observed in glasses deposited in the thickness range of 25 to 55 nm, where thin films of the ordinary SCL have exceptionally enhanced surface mobility with large mobility gradients. The enhanced mobility enables vapor-deposited thin films to overcome kinetic barriers for relaxation and access the HD-SCL state. The HD-SCL state is only thermodynamically favored in thin films and transforms rapidly to the ordinary SCL when the vapor deposition is continued to form films with thicknesses more than 60 nm.

Glasses are formed when the structural relaxations in supercooled liquids (SCLs) become too slow, causing the system to fall out of equilibrium at the glass transition temperature (Tg). The resulting out-of-equilibrium glass state has a thermodynamic driving force to evolve toward the SCL state through physical aging (1). At temperatures just below Tg, the extent of equilibration is limited by the corresponding SCL state, while at much lower temperatures, equilibration is limited by the kinetic barriers for relaxation. As such, the degree of thermodynamic stability achieved through physical aging is limited (2).Physical vapor deposition (PVD) is an effective technique to overcome kinetic barriers for relaxation to produce thermodynamically stable glasses (3–10). The accelerated equilibration in these systems is due to their enhanced surface mobility (11–14). During PVD, when the substrate temperature is held below Tg, molecules or atoms can undergo rearrangements and adopt more stable configurations at the free surface and proximate layers underneath (13). After the molecules are buried deeper into the film, their relaxation dynamics significantly slow down, which prevents further equilibration. Through this surface-mediated equilibration process, stable glasses can achieve low-energy states on the potential energy landscape that would otherwise require thousands or millions of years of physical aging (2, 3, 15, 16).As such, the degree of enhanced surface mobility and mobility gradients are critical factors in the formation of stable glasses (3, 11, 17, 18). While the effect of film thickness on the surface mobility and gradients of liquid-quenched (LQ) glasses has been studied in the past (19, 20), there are limited data on the role of film thickness in the stability of vapor-deposited glasses. In vapor-deposited toluene, it has been shown that decreasing the film thickness from 70 to 5 nm can increase the thermodynamic stability but decrease the apparent kinetic stability (5, 6). In contrast, thin films covered with a top layer of another material do not show a significant evidence of reduced kinetic stability (21), indicating the nontrivial role of mobility gradients in thermal and kinetic stability.Stable glasses of most organic molecules, with short-range intramolecular interactions, have properties that are indicative of the same corresponding metastable SCL state as LQ and aged glasses, without any evidence of the existence of generic liquid–liquid phase transitions that can potentially provide a resolution for the Kauzmann entropy crisis (22). The Kauzmann crisis occurs at the Kauzmann temperature (TK), where the extrapolated SCL has the same structural entropy as the crystal, producing thermodynamically impossible states just below this temperature. Recently, Beasley et al. (16) showed that near-equilibrium states of ethylbenzene can be produced using PVD down to 2 K above TK and hypothesized that any phase transition to an “ideal glass” state to avoid the Kauzmann crisis must occur at TK.In some glasses of elemental substances (23, 24) and hydrogen-bonding compounds (25, 26), liquid–liquid phase transitions can occur between polyamorphic states with distinct local packing structures that correspond to polymorphic crystalline phases. For example, at high pressures, high- and low-density supercooled water phases are interconvertible through a first-order phase transition (27, 28). Recent studies have demonstrated that such polyamorphic states can also be accessed through PVD in hydrogen-bonding systems with polymorphic crystal states at depositions above the nominal Tg (29, 30). However, these structure-specific transitions do not provide a general resolution for the Kauzmann crisis.Here, we report the observation of a liquid–liquid phase transition in vapor-deposited thin films of N,N′-bis(3-methylphenyl)-N,N′-diphenylbenzidine (TPD). TPD is a molecular glass former with only short-range intermolecular interactions. When thin films of TPD are vapor deposited onto substrates held at deposition temperatures (Tdep) below the nominal glass transition temperature of bulk TPD, Tg (bulk), films in the thickness range of 25 nm<h<55 nm achieve a high-density supercooled liquid (HD-SCL) state, which has not been previously observed. The liquid–liquid phase transition temperature (TLL) between the ordinary SCL and HD-SCL states is measured to be TLL≃Tg(bulk)−35 K. The density of thin films deposited below TLL tangentially follows the HD-SCL line, which has a stronger temperature dependence than the ordinary SCL. When vapor deposition is continued to produce thicker films (h>60 nm), the HD-SCL state transforms into the ordinary SCL state, indicating that the HD-SCL is only thermodynamically favored in the thin-film geometry. This transition is qualitatively different from the previously reported liquid–liquid phase transitions, as it is not related to a specific structural motif in TPD crystals, and it can only be observed in thin films, indicating that the energy landscape of thin films is favoring this high-density state.We observe an apparent correlation between enhanced mobility gradients in LQ thin films of TPD and the thickness range where HD-SCL states are produced during PVD. We hypothesize that enhanced mobility gradients are essential in providing access to regions of the energy landscape corresponding to the HD-SCL state, which are otherwise kinetically inaccessible. This hypothesis should be further investigated to better understand the origin of this phenomenon.     

Grain boundary formation through particle detachment during coarsening of nanoporous metals

Grain boundary formation during coarsening of nanoporous gold (NPG) is investigated wherein a nanocrystalline structure can form by particles detaching and reattaching to the structure. MicroLaue and electron backscatter diffraction measurements demonstrate that an in-grain orientation spread develops as NPG is coarsened. The volume fraction of the NPG sample is near the limit of bicontinuity, at which simulations predict that a bicontinuous structure begins to fragment into independent particles during coarsening. Phase-field simulations of coarsening using a computationally generated structure with a volume fraction near the limit of bicontinuity are used to model particle detachment rates. This model is tested by using the measured NPG structure as an initial condition in the phase-field simulations. We predict that up to ∼5% of the NPG structure detaches as a dealloyed Ag75Au25 sample is annealed at 300 °C for 420 min. The quantity of volume detached is found to be highly dependent on the volume fraction and volume fraction homogeneity of the nanostructure. As the void phase in the experiments cannot support independent particles, they must fall and reattach to the structure, a process that results in the formation of new grain boundaries. This particle reattachment process, along with other classic processes, leads to the formation of grain boundaries during coarsening in nanoporous metals. The formation of grain boundaries can impact a variety of applications, including mechanical strengthening; thus, the consideration and understanding of particle detachment phenomena are essential when studying nanoporous metals.

Nanoporous metals are prototypical bicontinuous structures with a network of pores and ligaments. They are created by a number of metallic dealloying processes (1–6) allowing nearly any bulk metal to be transformed into a bicontinuous two-phase mixture of metal and void phase (7). These metals have a large interfacial area per volume enabling exciting applications in oxygen reduction (8), electromechanical devices (9), battery electrodes (10), actuators (11), and catalysts (12). Given the large surface area per volume, nanoporous structures frequently undergo coarsening when annealed at elevated temperatures. Nanoporous metals coarsen by surface diffusion (13–15), a process where the characteristic length, L, increases in time, t, according to the power law L∼t1/4 (16). Coarsening decreases the total interfacial energy of the structure, which greatly affects its material properties. For instance, coarsening is used to select the length scale in the structure, which alters the sizes of pores and ligaments (7, 17–20), ultimately impacting optical, chemical, and mechanical properties (21, 22), such as the elastic modulus (23). Nanoporous gold (NPG) often serves as a prototype for studying nanoporous metals (7). This paper investigates grain boundary formation as NPG coarsens and shows that the formation of a significant number of these boundaries is from particle detachment and subsequent reattachment.Metallic samples prior to dealloying have grain sizes on the order of 10 to 100 μm (24). Dealloying and annealing of bulk nanoporous metals are typically believed to preserve the grain orientation of the original metallic sample. This was demonstrated through electron backscatter diffraction (EBSD) measurements (1) and scanning electron microscopy (SEM) images (25) for NPG. However, these techniques provide information only about the external surfaces, not the bulk structure. The formation of an in-grain orientation spread would demonstrate that nanoporous metals can develop nanocrystallinity. Some recent work has observed a developed nanocrystalline structure in nanoporous metallic samples after dealloying and annealing. Sun et al. (26) observed grain boundary formation during annealing of NPG but assumed that the varying orientations formed due to the small grain size in the original alloy. High-resolution transmission electron microscopy (HRTEM) (27) and X-ray diffraction (28) were used to identify a nanocrystalline structure in NPG postdealloying. Nanocrystalline structures have also been identified in nanoporous platinum (29) and copper (30) postdealloying. Theories of how these grain boundaries form during dealloying and annealing have not been fully investigated. Dealloyed NPG samples have been shown to contain lattice dislocations (24). It is possible that there are driving forces for dislocations to form low-angle grain boundaries in the structure when coarsening at elevated temperatures.Coarsening of nanoporous metals is often compared to simulations that coarsen computationally generated (CG) bicontinuous structures, e.g., those formed in simulations of spinodal decomposition (31). Evolution of these structures has been studied with phase-field (31–35) and kinetic Monte Carlo (KMC) (36–38) methods. In certain volume fraction ranges, particle detachment is observed during simulations of coarsening, altering the topology of the structure. This breaking of ligaments in the structure is due to a Rayleigh–Plateau instability (38), the same mechanism causing ligament pinch-off (a ligament breaking in one place) during coarsening of nanoporous metals (13, 39, 40). The topology of an object in three dimensions (3D) is quantified by the Betti numbers: β0, the number of independent objects; β1, the number of handles (genus); and β2, the number of enclosed voids in the structure. Assuming no enclosed voids, the Euler characteristic of a 3D structure is given by χ=β0−β1 (41). When a particle detaches from the microstructure, β0 increases by 1. As particles detach from the end of ligaments, β1 remains the same. If a ligament breaks in one place (a process that is referred to as a ligament pinch-off), β1 decreases by 1 and β0 remains the same. Here we define particle detachment as the process of creating small (in size when compared to the main bicontinuous structure) isolated bodies.Simulations have demonstrated that the topology of a structure has a strong dependence on the minority phase volume fraction, ϕ, and can vary drastically within a small range of ϕ (34, 38). Using KMC, Li et al. (38) investigated coarsening via surface diffusion of structures initialized as leveled Gaussian random fields with ϕ of 22, 25, and 27% and increments of 5% from 30 to 50%. By investigating the topology, they found that structures with a ϕ lower than 30% are evolving toward a particle-dominated system, while structures with a ϕ higher than 40% are evolving as a fully connected system (β0=1). As the topological changes are related to how particles detach, we establish two regimes of topological evolution. In the particle-dominated regime (low ϕ), the structure evolves toward a state where the number of handles (β1) is either zero or low compared to the number of particles (β0). In the ligament-dominated regime (high ϕ), the structure evolves toward a state where there is a low number of particles (β0) compared to the number of handles (β1). In between these regimes (intermediate ϕ), the structure evolves to a state with an intermediate number of particles and handles, and any transition to the particle-dominated regime or the ligament-dominated regime occurs too slowly to be feasibly observed. We define this approximate boundary between regimes as the limit of bicontinuity, as the structure begins to break up while still maintaining a high degree of connectivity. Due to the approximate nature of this definition, a range of ϕ (e.g., 30 to 35%) may be considered to be “at” the limit of bicontinuity. We are most likely to observe particle detachment in structures with a ϕ at the limit of bicontinuity, where β0 might be stable or increasing throughout coarsening (signifying particle detachment) while a majority of the solid volume is contained in the main bicontinuous structure. Simulations with a ϕ in the range 30 to 35% have not yet been extensively studied despite the many coarsening experiments of nanoporous metals that are within this range.Experiments commonly study NPG samples with a ϕ between 25 and 36% postdealloying and report fully connected bicontinuous structures (17, 19, 20, 42–47). In this case, the minority phase volume fraction, ϕ, corresponds to the gold volume fraction. These ϕ values are just below or at the limit of bicontinuity predicted by simulation. However, the stability of the structures during coarsening is not always investigated, especially at lower ϕ. Detachment of particles from the bicontinuous structure can be kinetically inhibited due to short coarsening times or slow coarsening rates. However, experiments that coarsen NPG for sufficiently long times such that the mean ligament diameter increased by a factor of 16 have still reported fully connected bicontinuous structures (19, 20). The bicontinuity does not necessarily indicate that disconnections do not occur during the evolution; since the vapor phase cannot support independent particles, any particles that detach would presumably fall under their own weight and reattach elsewhere, leading to a fully connected bicontinuous structure and the formation of grain boundaries.As the ϕ of many NPG samples is at the limit of bicontinuity, we show that particles detach as NPG coarsens, and we hypothesize that the reattachment of particles leads to the formation of many of the grain boundaries that are observed in the microstructure. The results of microLaue and EBSD measurements of coarsened NPG samples with a ϕ at the limit of bicontinuity identify large in-grain orientation spreads that develop during coarsening. Phase-field simulations of coarsening of a CG bicontinuous structure with a ϕ at the limit of bicontinuity are conducted to investigate how particle detachment occurs in this regime. Subsequently, the morphology of the CG and NPG structures is characterized to search for evidence of particle reattachment phenomena. A coarsened NPG structure is then used as an initial condition in a phase-field simulation to observe how particle detachment would occur if the sample had continued to coarsen. These calculations that begin with the experimentally measured structure have identified the critical role of volume fraction homogeneity in particle detachment phenomena.     

[... formula ...] triggers the release of astrocytic lactate via mitochondrial pyruvate shunting

Neural activity is accompanied by a transient mismatch between local glucose and oxygen metabolism, a phenomenon of physiological and pathophysiological importance termed aerobic glycolysis. Previous studies have proposed glutamate and K⁺ as the neuronal signals that trigger aerobic glycolysis in astrocytes. Here we used a panel of genetically encoded FRET sensors in vitro and in vivo to investigate the participation of NH4+, a by-product of catabolism that is also released by active neurons. Astrocytes in mixed cortical cultures responded to physiological levels of NH4+ with an acute rise in cytosolic lactate followed by lactate release into the extracellular space, as detected by a lactate-sniffer. An acute increase in astrocytic lactate was also observed in acute hippocampal slices exposed to NH4+ and in the somatosensory cortex of anesthetized mice in response to i.v. NH4+. Unexpectedly, NH4+ had no effect on astrocytic glucose consumption. Parallel measurements showed simultaneous cytosolic pyruvate accumulation and NADH depletion, suggesting the involvement of mitochondria. An inhibitor-stop technique confirmed a strong inhibition of mitochondrial pyruvate uptake that can be explained by mitochondrial matrix acidification. These results show that physiological NH4+ diverts the flux of pyruvate from mitochondria to lactate production and release. Considering that NH4+ is produced stoichiometrically with glutamate during excitatory neurotransmission, we propose that NH4+ behaves as an intercellular signal and that pyruvate shunting contributes to aerobic lactate production by astrocytes.Brain tissue is almost exclusively energized by the oxidation of glucose. However, during neuronal activation, there is a larger increase in local glucose consumption relative to oxygen consumption (1). As this mismatch occurs in the presence of normal or augmented oxygen levels, it has been termed aerobic glycolysis, paralleling the signal detected by functional magnetic resonance imaging (2). Aerobic glycolysis and its associated lactate surge are causally linked to diverse functions of the brain in health and disease (3–10). Two signals are known to trigger aerobic glycolysis in brain tissue: glutamate and K⁺, which are released by active neurons and stimulate glycolysis in astrocytes (11, 12).Neurons produce as much NH4+ as they produce glutamate, both molecules being stoichiometrically linked in the glutamate-glutamine cycle (13). Brain tissue NH4+ increases within seconds of neural activation (14–16) and is quickly released to the interstitium (17, 18) to be captured by astrocytes through K⁺ channels and transporters (19). It is well established that chronic exposure to pathological levels of NH4+ such as those observed during liver failure has a major impact on brain metabolism, but it is not known whether this molecule may affect energy metabolism at physiological levels, particularly within the time scale of synaptic transmission. A previous study showed a reversible rise in brain tissue lactate and cerebral blood flow within minutes of an i.v. infusion of NH4+. In view of this result, NH4+ was speculated to have signaling roles in the brain (20). The aim of the present work was to investigate this possibility.     

The ferroelectric photo ground state of SrTiO3: Cavity materials engineering

Optical cavities confine light on a small region in space, which can result in a strong coupling of light with materials inside the cavity. This gives rise to new states where quantum fluctuations of light and matter can alter the properties of the material altogether. Here we demonstrate, based on first-principles calculations, that such light–matter coupling induces a change of the collective phase from quantum paraelectric to ferroelectric in the SrTiO3 ground state, which has thus far only been achieved in out-of-equilibrium strongly excited conditions [X. Li et al., Science 364, 1079–1082 (2019) and T. F. Nova, A. S. Disa, M. Fechner, A. Cavalleri, Science 364, 1075–1079 (2019)]. This is a light–matter hybrid ground state which can only exist because of the coupling to the vacuum fluctuations of light, a photo ground state. The phase transition is accompanied by changes in the crystal structure, showing that fundamental ground state properties of materials can be controlled via strong light–matter coupling. Such a control of quantum states enables the tailoring of materials properties or even the design of novel materials purely by exposing them to confined light.

Engineering an out-of-equilibrium state of a material by means of strong light fields can drastically change its properties and even induce new phases altogether. This is considered a new paradigm of material design, especially when the collective behavior of particles in quantum materials can be controlled to provide novel functionalities (1, 2). Alternatively to the intense lasers necessary to reach such out-of-equilibrium states, one can achieve strong light–matter coupling by placing the material inside an optical cavity (3–11). A main advantage of this approach is that strong interaction can be achieved at equilibrium, opening up new possibilities for materials manipulation. Among the proposed effects are novel exciton insulator states (12), control of excitonic energy ordering (13), enhanced electron–phonon coupling (14), photon-mediated electron pairing (15–18), enhanced ferroelectricity (19), and multi-quasi-particles hybridization (20). One enticing possibility is, however, to change the ground state of a material and to create a new phase not through excited quasi-particles but truly as the equilibrium state.Here we show that this can be achieved in the paraelectric SrTiO3 as a photo-correlated ferroelectric ground state. This ground state, which we refer to as photo ground state, is the result of the strong coupling between matter and quantum vacuum fluctuations of light. While similar materials of the perovskite family undergo a para- to ferroelectric phase transition at low temperatures, SrTiO3 remains paraelectric (21), because the nuclear quantum fluctuations prevent the emergence of a collective polarization that is characteristic of the ferroelectric phase (22, 23). Alterations to the material that overcome a relatively small activation energy, however, can induce ferroelectricity: for instance, through isotope substitution (24), strain (25, 26), and, most notably, nonlinear excitation of the lattice by strong and resonant terahertz laser pumping (27, 28). In the latter type of experiments, a transient broken symmetry of the structure as well as macroscopic polarization indicative of a transient ferroelectric phase have been observed.By using atomistic calculations, we show that the off-resonant dressing of the lattice of SrTiO3 with the vacuum fluctuations of the photons in a cavity can suppress the nuclear quantum fluctuations in a process that is analogous to the one of dynamical localization (29): As explained in Results and Discussion, the interaction with cavity photons effectively results in an enhancement of the effective mass of the ions, thus slowing them down and reducing the importance of their quantum fluctuations. We further demonstrate that the effect of cavity-induced localization extends to finite temperatures, even when thermal lattice fluctuations overcome the quantum ones. We thus introduce a revisited paraelectric to ferroelectric phase diagram, with the cavity coupling strength as a new dimension.     

Thermodynamic controls on rates of iron oxide reduction by extracellular electron shuttles

Anaerobic microbial respiration in suboxic and anoxic environments often involves particulate ferric iron (oxyhydr-)oxides as terminal electron acceptors. To ensure efficient respiration, a widespread strategy among iron-reducing microorganisms is the use of extracellular electron shuttles (EES) that transfer two electrons from the microbial cell to the iron oxide surface. Yet, a fundamental understanding of how EES–oxide redox thermodynamics affect rates of iron oxide reduction remains elusive. Attempts to rationalize these rates for different EES, solution pH, and iron oxides on the basis of the underlying reaction free energy of the two-electron transfer were unsuccessful. Here, we demonstrate that broadly varying reduction rates determined in this work for different iron oxides and EES at varying solution chemistry as well as previously published data can be reconciled when these rates are instead related to the free energy of the less exergonic (or even endergonic) first of the two electron transfers from the fully, two-electron reduced EES to ferric iron oxide. We show how free energy relationships aid in identifying controls on microbial iron oxide reduction by EES, thereby advancing a more fundamental understanding of anaerobic respiration using iron oxides.

The use of iron oxides as terminal electron acceptors in anaerobic microbial respiration is central to biogeochemical element cycling and pollutant transformations in many suboxic and anoxic environments (1–6). To ensure efficient electron transfer to solid-phase ferric iron, Fe(III), at circumneutral pH, metal-reducing microorganisms from diverse phylae use dissolved extracellular electron shuttle (EES), including quinones (7–9), flavins (10–16), and phenazines (17–19), to transfer two electrons per EES molecule from the respiratory chain proteins in the outer membrane of the microbial cell to the iron oxide (17, 20, 21). The oxidized EES can diffuse back to the cell surface for rereduction, thereby completing the catalytic redox cycle involving the EES.The electron transfer from the reduced EES to Fe(III) is considered a key step in overall microbial Fe(III) respiration. Several lines of evidence suggest that the free energy of the electron transfer reaction, ΔrG, controls Fe(III) reduction rates (15, 17, 22, 23). For instance, microbial Fe(III) oxide reduction by dissolved model quinones as EES was accelerated only for quinones with standard two-electron reduction potentials, EH,1,20, that fell into a relatively narrow range of −180±80 mV at pH 7 (24). Furthermore, in abiotic experiments, Fe(III) reduction rates by EES decreased with increasing ΔrG that resulted from increasing either EH,1,20 of the EES (25, 26), the concentration of Fe(II) in the system (27), or solution pH (25, 26, 28). However, substantial efforts to relate Fe(III) reduction rates for different EES species, iron oxides, and pH to the EH,1,20 averaged over both electrons transferred from the EES to the iron oxides were only partially successful (25, 28). Reaction free energies of complex redox processes involving the transfer of multiple electrons can readily be calculated using differences in the reduction potentials averaged over all electrons transferred, and this approach is well established in biogeochemistry and microbial ecology. For kinetic considerations, however, the use of averaged reduction potentials is inappropriate.Herein, we posit that rates of Fe(III) reduction by EES instead relate to the ΔrG of the less exergonic first one-electron transfer from the two-electron reduced EES species to the iron oxide, following the general notion that reaction rates scale with reaction free energies (29). Our hypothesis is based on the fact that, at circumneutral to acidic pH and for many EES, the reduction potential of the first electron transferred to the fully oxidized EES to form the one-electron reduced intermediate semiquinone species, EH,1, is lower than the reduction potential of the second electron transferred to the semiquinone to form the fully two-electron reduced EES species, EH,2 [i.e., EH,1<EH,2 (30–33)]. This difference in one-electron reduction potentials implies that the two-electron reduced EES (i.e., the hydroquinone) is the weaker one-electron reductant for Fe(III) as compared to the semiquinone species. We therefore expect that rates of iron oxide reduction relate to the ΔrG of the first electron transferred from the hydroquinone to Fe(III). The ΔrG of this first electron transfer may even be endergonic provided that the two-electron transfer is exergonic.We verified our hypothesis in abiotic model systems by demonstrating that reduction rates of two geochemically important crystalline iron oxides, goethite and hematite, by two-electron reduced quinone- and flavin-based EES over a wide pH range, and therefore thermodynamic driving force for Fe(III) reduction, correlate with the ΔrG of the first electron transferred from the fully reduced EES to Fe(III). We further show that rates of goethite and hematite reduction by EES reported in the literature are in excellent agreement with our rate data when comparing rates on the basis of the thermodynamics of the less exergonic first of the two electron transfers.     

On randomly changing conformity bias in cultural transmission

Humans and nonhuman animals display conformist as well as anticonformist biases in cultural transmission. Whereas many previous mathematical models have incorporated constant conformity coefficients, empirical research suggests that the extent of (anti)conformity in populations can change over time. We incorporate stochastic time-varying conformity coefficients into a widely used conformity model, which assumes a fixed number n of “role models” sampled by each individual. We also allow the number of role models to vary over time (nt). Under anticonformity, nonconvergence can occur in deterministic and stochastic models with different parameter values. Even if strong anticonformity may occur, if conformity or random copying (i.e., neither conformity nor anticonformity) is expected, there is convergence to one of the three equilibria seen in previous deterministic models of conformity. Moreover, this result is robust to stochastic variation in nt. However, dynamic properties of these equilibria may be different from those in deterministic models. For example, with random conformity coefficients, all equilibria can be stochastically locally stable simultaneously. Finally, we study the effect of randomly changing weak selection. Allowing the level of conformity, the number of role models, and selection to vary stochastically may produce a more realistic representation of the wide range of group-level properties that can emerge under (anti)conformist biases. This promises to make interpretation of the effect of conformity on differences between populations, for example those connected by migration, rather difficult. Future research incorporating finite population sizes and migration would contribute added realism to these models.

Cavalli-Sforza and Feldman (1) studied the finite population dynamics of a trait whose transmission from one generation to the next depended on the mean value of that trait in the population. This “group transmission” constrained the within-group variability but could lead to increasing variance in the average trait value between groups. Other analyses of cultural transmission biases have incorporated characteristics of trait variation, such as the quality, and characteristics of transmitters, including success and prestige (2). Another class of transmission biases is couched in terms of the frequencies of the cultural variants in the population (3). These “frequency-dependent” biases include conformity and anticonformity, which occur when a more common variant is adopted at a rate greater or less than its population frequency, respectively (4).Humans have exhibited conformity in mental rotation (5), line discrimination (6), and numerical discrimination tasks (7). Anticonformity has been exhibited by young children performing numerical discrimination (7). Unbiased frequency-dependent transmission, known as random copying (8), has been suggested to account for choices of dog breeds (9), Neolithic pottery motifs, patent citations, and baby names (10, 11). However, baby name distributions appear more consistent with frequency-dependent (8, 12) and/or other (13, 14) biases.In nonhuman animals, conformity has been observed in nine-spined sticklebacks choosing a feeder (15) and great tits solving a puzzle box (16, 17) (but see ref. 18). Fruit flies displayed both conformist and anticonformist bias with respect to mate choice (19) (but these authors used a different definition of anticonformity from that of ref. 4, which we use, and therefore did not consider these behaviors to be anticonformist).Asch (20, 21) used a different definition of conformity from ref. 4, namely “the overriding of personal knowledge or behavioral dispositions by countervailing options observed in others” (ref. 22, p. 34). Aschian conformity (22) has been observed in chimpanzees (23, 24), capuchin monkeys (25, 26) (but see ref. 27), vervet monkeys (28), and great tits (16). It has also been empirically tested in at least 133 studies of humans and, in the United States, has declined from the 1950s to the 1990s (29).Temporal variation may also occur in forms of conformity other than Aschian. In ref. 12, popular US baby names from 1960 to 2010 show a concave turnover function indicative of negative frequency-dependent bias, but male baby names from earlier decades (1880 to 1930) show a convex turnover indicative of positive frequency-dependent or direct bias. However, most previous mathematical models of conformity have incorporated constant, rather than time-dependent, conformity coefficients.Cavalli-Sforza and Feldman (ref. 3, chap. 3) and Boyd and Richerson (ref. 4, chap. 7) studied models of frequency-dependent transmission of a cultural trait with two variants. Boyd and Richerson (4) incorporated conformist and anticonformist bias through a conformity coefficient denoted by D. In their simplest model, if the frequency of variant A is p and that of variant B is 1−p, then the frequency of variant A in the offspring generation, p′, isp′=p+Dp(1−p)(2p−1),[1]where D>0 entails conformity (A increases if its frequency is p>12), D<0 entails anticonformity, D=0 entails random copying, and −2<D<1. In this model, each offspring samples the cultural variants of n=3 members of the parental generation (hereafter, role models). Sampling n>3 role models requires different constraints and, if n>4, there are multiple conformity coefficients (Eq. 19).Many subsequent models have built upon Boyd and Richerson’s (4) simplest model (Eq. 1). These have incorporated individual learning, information inaccuracy due to environmental change (30–34), group selection (35), and other transmission biases, including payoff bias (36), direct bias, and prestige bias (37). Other models, which include a single conformity coefficient and preserve the essential features of Eq. 1, incorporate individual learning, environmental variability (32, 38), group selection (39), and multiple cultural variants (38).In agent-based statistical physics models, the up and down spins of an electron are analogous to cultural variants A and B (40, 41). Individuals are nodes in a network and choose among a series of actions with specified probabilities, such as independently acquiring a spin, or sampling neighboring individuals and adopting the majority or minority spin in the sample. The number of sampled role models can be greater than three (42, 43). (Anti)conformity may occur if all (42–47), or if at least r (40, 48), sampled individuals have the same variant. In contrast, Boyd and Richerson’s (4) general model (Eq. 19) allows, for example, stronger conformity to a 60% majority of role models and weaker conformity or anticonformity to a 95% majority (in humans, this might result from a perceived difference between “up-and-coming” and “overly popular” variants).In Boyd and Richerson’s (4) general model, individuals sample n role models, which is more realistic than restricting n to 3 (as in Eq. 1); individuals may be able to observe more than three members of the previous generation. With n>4, different levels of (anti)conformity may occur for different samples j of n role models with one variant. In addition to the example above with 60 and 95% majorities, other relationships between the level of conformity and the sample j of n are possible. For example, the strength of conformity might increase as the number of role models with the more common variant increases. In a recent exploration of Boyd and Richerson’s (4) general model, we found dynamics that departed significantly from those of Eq. 1 (49). If conformity and anticonformity occur for different majorities j of n role models (i.e., j>n2), polymorphic equilibria may exist that were not possible with Eq. 1. In addition, strong enough anticonformity can produce nonconvergence: With as few as 5 role models, stable cycles in variant frequencies may arise, and with as few as 10 role models, chaos is possible. Such complex dynamics may occur with or without selection.Here, we extend both Boyd and Richerson’s (4) simplest (Eq. 1) and general (Eq. 19) models to allow the conformity coefficient(s) to vary randomly across generations, by sampling them from probability distributions. Although some agent-based models allow individuals to switch between “conformist” and “non-” or “anticonformist” states over time (40, 42, 47, 50, 51), to our knowledge, random temporal variation in the conformity coefficients themselves has not been modeled previously. In reality, the degree to which groups of individuals conform may change over time, as illustrated by the finding that young children anti-conformed while older children conformed in a discrimination task (7); thus, it seems reasonable to expect that different generations may also exhibit different levels of conformity. Indeed, generational changes have occurred for Aschian conformity (29) and possibly in frequency-dependent copying of baby names (12). Our stochastic model may therefore produce more realistic population dynamics than previous deterministic models, and comparisons between the two can suggest when the latter is a reasonable approximation to the former.We also allow the number of role models, nt, to vary over time. Agent-based conformity models have incorporated temporal (43) and individual (43, 45, 46) variation in the number of sampled individuals, whereas here, all members of generation t sample the same number nt of role models. Causes of variation in nt are not explored here, but there could be several. For instance, different generations of animals may sample different numbers of role models due to variation in population density. In humans, changes in the use of social media platforms or their features may cause temporal changes in the number of observed individuals. For example, when Facebook added the feature “People You May Know,” the rate of new Facebook connections in a New Orleans dataset nearly doubled (52).In the stochastic model without selection, regardless of the fluctuation in the conformity coefficient(s), if there is conformity on average, the population converges to one of the three equilibria present in Boyd and Richerson’s (4) model with conformity (D(j)>0 for n2<j<n in Eq. 19). These are p*=1 (fixation on variant A), p*=0 (fixation on variant B), and p*=12 (equal representation of A and B). However, their stability properties may differ from those in the deterministic case. In Boyd and Richerson’s (4) model with random copying, every initial frequency p0 is an equilibrium. Here, with random copying expected and independent conformity coefficients, there is convergence to p*=0,12, or 1. In this case, and in the case with conformity expected, convergence to p*=0,12, or 1 also holds with stochastic variation in the number of role models, nt. With either stochastic or constant weak selection in Boyd and Richerson’s (4) simplest model (Eq. 1) and random copying expected, there is convergence to a fixation state (p*=0 or 1). Finally, with anticonformity in the deterministic model or anticonformity expected in the stochastic model, nonconvergence can occur.     

Carbon dioxide as a line active agent: Its impact on line tension and nucleation rate

By considering a water capillary bridge confined between two flat surfaces, we investigate the thermodynamics of the triple line delimiting this solid–liquid–vapor system when supplemented in carbon dioxide. In more detail, by means of atom-scale simulations, we show that carbon dioxide accumulates at the solid walls and, preferably, at the triple lines where it plays the role of a line active agent. The line tension of the triple line, which is quantitatively assessed using an original mechanical route, is shown to be driven by the line excess concentrations of the solute (carbon dioxide) and solvent (water). Solute accumulation at the lines decreases the negative line tension (i.e., more negative) while solvent depletion from the lines has the opposite effect. Such an unprecedented quantitative assessment of gas-induced line tension modifications shows that the absolute value of the negative line tension increases upon increasing the carbon dioxide partial pressure. As a striking example, for hydrophilic surfaces, the line tension is found to increase by more than an order of magnitude when the carbon dioxide pressure exceeds 3 MPa. By considering the coupling between line and surface effects induced by gaseous adsorption, we hypothesize from the observed gas concentration-dependent line tension a nontrivial impact on heterogeneous nucleation of nanometric critical nuclei.

Line tension, a concept introduced by Gibbs, is still mostly considered as an academic curiosity. Like excess quantities at an interface (e.g., surface tension), lines separating several interfaces may also be endowed with excess quantities. In particular, the excess free energy per unit length of such a line—the so-called line tension—can be seen as a force with the underlying picture of the tension acting in a molecularly thin thread. It has been long considered that such a force contributes only at the molecular or maybe the nanometer scale. Yet, line tension is now recognized as a crucial parameter even in physical, chemical, and biological systems where it was probably the least expected [e.g., phase separation within a lipid layer and nucleation of rafts within a biological membrane (1, 2)]. Line tension effects are also directly involved in heterogeneous nucleation due to the presence of a triple line between the nucleus and the preexisting phases (3). For instance, it has been shown theoretically that the line tension may contribute to water condensation on atmospheric aerosols and cloud formation (4) [various atmospheric aerosols can originate from multicomponent nucleation of trace condensable vapors—in particular, water, acids, bases, and organics (5, 6)].Despite its now broadly acknowledged role in both science and engineering fields, the accurate determination of line tension is still a matter of debate even for a triple line involving vapor/liquid equilibrium for a single fluid on a well-defined solid surface. Thermodynamically, the line tension can be positive or negative while preserving the coexistence of the adjacent phases (7). In the particular case of solid/liquid/vapor triple lines, a negative sign is mainly expected, except for a system close to the wetting transition, with magnitude of the order of a few piconewtons (8–16). For instance, for ordered hydrophobic nanopores of a few nanometers in diameter, it has been shown experimentally and confirmed numerically that large drying pressures of more than 200 bar are induced by a negative line tension. In fact, such a negative line tension favors the emergence of a gas nucleus at the origin of the drying process (12, 13). This example shows that the line tension, which balances with surface and bulk thermodynamic contributions, acts as a lever controlling the stability of confined fluids (17).In 1982, Rowlinson and Widom (7) envisioned theoretically adsorption at a triple line separating three phases and its impact on line tension. More recently, some authors have suggested that line tension could be lowered by using line active molecules—the so-called lineactants [namely surfactants that present specific affinity for the line in addition to their affinity for the interface (18)]. Such adsorption effects on three-phase coexistence are also central to the physics of oversolubility aspects, which refer to the large gas solubility increase in liquids confined in nanoporous solids (19–21). In this context, we stress that the thermodynamics of a mixture of water and noncondensable soluble gases near solid surfaces as well as the phase transition kinetics in such a mixture remain to be investigated. Among numerous examples, such aspects are related to important issues in the context of climate change and energy transition: CO2 geological capture in aquifers (22–25), formation and stability of gas clathrates [methane hydrate trapped in seafloor and rocks corresponds to critical amounts of greenhouse gases potentially harmful to the environment (26–28)], water electrolysis, and fuel cells [which involve a confined reactive zone with nucleating bubbles or droplets (29, 30)].Up to now, when addressing these specific topics and, more generally, the question of the state of a confined water/gas mixture [either for technological or for scientific problems (31)], the role of line tension has been often overlooked (9). A consensus has started to emerge concerning the line tension of a solid/liquid/vapor triple line involving a single fluid. However, the case of a fluid mixture with potential accumulation of one species at the triple line is still an open problem. While a few experiments suggest that dissolved gas may accumulate at solid interfaces and consequently impact nucleation (32–36), there are no quantitative data concerning their contribution to a triple line. Key questions relevant to this complex problem include the following: Does a gas solute behave as a line active agent at a triple line? Would such solute excess at the line impact heterogeneous nucleation rates? Here, we address these questions using molecular dynamics simulations for a liquid droplet confined between two surfaces and supplemented with a noncondensable gas. In more detail, this paper is focused on water/CO2 mixtures—a key system of interest for applied and basic sciences—in contact with either hydrophilic or hydrophobic surfaces. We aim at addressing the pivotal role of adsorption at the triple line and its coupling with adsorption at the solid surfaces. We do not consider any chemical reaction such as the formation of a small amount of carbonic acid from the dissolution of CO2 in water (which is known to occur in real systems). We believe that a confined CO2/water mixture is a prototypical example with results that should also pertain to many other common systems (corresponding to solute/solvent couples with a low solubility). Moreover, while the present work is limited to a specific mixture for feasibility purposes, in addition to varying the gas pressure in a large range, we tune the hydrophobicity/hydrophilicity of the solid surface to cover the diversity of situations that can be met experimentally. However, in any case, while we think that our model subclass is representative of a larger set of systems corresponding to weakly soluble gases, we recognize here that other systems could display a different behavior with additional complexity.In practice, we consider an infinite water liquid droplet confined between two flat solid surfaces—hence forming four straight triple lines that are the locus of specific molecular structuring (Fig. 1). The solid surfaces are formed using two structureless dispersive walls that interact with the fluid through an external 9–3 Lennard-Jones potential as detailed in Materials and Methods. The droplet, which is invariant by translation in the y direction, is modeled as a finite system confined in a fully periodic rectangular box. The system is made up of water molecules in the liquid state (solvent) and of CO2 molecules (solute) in the gas state and partly solubilized in water. This fluid mixture is considered at constant temperature, constant numbers of solvent and solute molecules, and constant volume defined by the rectangular box. Molecular simulations are performed using Large-scale Atomic/Molecular Massively Parallel Simulator software (37) with a Verlet integration algorithm coupled to a Nosé–Hoover thermostat. The two curved liquid–gas interfaces intersect the solid walls along the triple lines with a contact angle θY. The distance h between the walls is such that disjoining pressure effects are negligible (SI Appendix, section 5). As the triple line is straight, its tension does not contribute to the contact angle (15) so that θY corresponds to Young’s contact angle. The thermodynamic properties of the system—in particular, the line tension and line excess concentrations—are studied as a function of the solute partial pressure in the gas phase. To determine the line tension of the straight solid/liquid/gas triple lines, we use a recently introduced mechanical methodology that offers unprecedented sensitivity and reliability (15). The line tension is directly extracted from force measurements. More precisely, as detailed in Materials and Methods, the specific contribution of the line in the y direction is separated from the bulk and surface contributions determined using force measurements in the x and z directions as the line tension is not acting in these directions (15) (Fig. 1). The line excess concentrations are readily obtained by subtracting bulk and surface excess quantities from the total amount of fluid molecules for each species. The measurement approach is further detailed in Materials and Methods.Open in a separate windowFig. 1.Setup consisting of a liquid (dark blue) in contact with a partially soluble gas confined between two solid walls (perpendicular to the z direction). Solid/fluid and liquid–gas interfaces are separated by distances h and l, respectively. The dependence of the line tension τ on the adsorption of molecules at the straight contact lines (in red; Inset) is estimated from the forces Σx, Σy, and Σz exerted along x, y, and z.     

Statistical analysis of ENDOR spectra

Electron–nuclear double resonance (ENDOR) measures the hyperfine interaction of magnetic nuclei with paramagnetic centers and is hence a powerful tool for spectroscopic investigations extending from biophysics to material science. Progress in microwave technology and the recent availability of commercial electron paramagnetic resonance (EPR) spectrometers up to an electron Larmor frequency of 263 GHz now open the opportunity for a more quantitative spectral analysis. Using representative spectra of a prototype amino acid radical in a biologically relevant enzyme, the Y122• in Escherichia coli ribonucleotide reductase, we developed a statistical model for ENDOR data and conducted statistical inference on the spectra including uncertainty estimation and hypothesis testing. Our approach in conjunction with ¹H/²H isotopic labeling of Y122• in the protein unambiguously established new unexpected spectral contributions. Density functional theory (DFT) calculations and ENDOR spectral simulations indicated that these features result from the beta-methylene hyperfine coupling and are caused by a distribution of molecular conformations, likely important for the biological function of this essential radical. The results demonstrate that model-based statistical analysis in combination with state-of-the-art spectroscopy accesses information hitherto beyond standard approaches.

Structural information at atomic resolution is essential for many areas of physics, chemistry, and biology. Electron spin resonance (ESR) or electron paramagnetic resonance (EPR) (1) belongs to a pool of methods, including nuclear magnetic resonance, optical spectroscopy, X-ray diffraction, and cryo-electron microscopy, which can deliver this information. For biophysical applications, the EPR-based electron–nuclear double resonance (ENDOR) technique is particularly suited for mechanistic studies involving endogenous paramagnetic centers, such as redox-active amino acid radical intermediates or metal ions and clusters, as it measures the hyperfine (hf) interaction between these centers and their surrounding magnetic nuclei (2), providing information on the protein architecture and establishing structural to functional relationships. The method has identified and characterized a wealth of paramagnetic intermediates in enzymes; for recent examples see refs. 3–7. Moreover, ENDOR spectroscopy has recently been proposed as a method of choice to measure molecular distances in the angstrom to nanometer range by ¹⁹F spin labeling (8), bridging a critical gap in pulse EPR-based distance measurements in biomolecules and complementing ¹⁹F-based NMR spectroscopy (9, 10).ENDOR spectra of magnetic nuclei are usually recorded in the solid state (a frozen solution of a biological sample) at very low temperatures (T < 80 K) and thus display the full anisotropy of magnetic interactions, resulting in very broad lines. The signals are recorded as a change of the EPR electron-spin echo (11), which is sensitive to drifts in experimental conditions, particularly at low temperatures. Therefore, a model-free analysis of the observed signals constitutes one of the main challenges of ENDOR spectroscopy. In the last decade, progress in EPR instrumentation enabled the implementation of pulsed EPR spectrometers operating in the quasi-optical regime (12). We have recently reported a ¹H ENDOR study of the essential Y122• in the wild-type (WT) β2 subunit of Escherichia coli ribonucleotide reductase (RNR) (Fig. 1A), using a commercial instrument (13) operating at 9.4 T/263 GHz. The strong orientation selection (hole burning) under high field/frequency conditions leads to sharpening of the spectra, strongly facilitating their analysis. We demonstrated the effect with the ¹H spectrum of Y122•, illustrated in Fig. 1B, where the sharp peaks were attributed to internal ¹Hs of the radical. Additional broad resonances became visible, whose attribution presents additional challenges. From visual inspection alone, the significance of these signals could not be inferred given their shallow line shapes and the difficulty to separate them from unknown baseline distortions.Open in a separate windowFig. 1.(A) Structure of Y122 and surrounding amino acids in the E. coli RNR WT-β2 subunit from PDB 1mxr (22) in the reduced state (phenolic proton omitted). Highlighted are interactions with two protons at distances <3 Å from the tyrosine oxygen. Protons were added with Pymol 2.2.2 in positions determined by the overall orientation of the amino acids. The O-O distance (3.8 Å) to the water molecule coordinating the proximal Fe ion is highlighted as well. (B) The 263-GHz ¹H Davies ENDOR spectrum of Y122• adapted from ref. 13. Marked are resonances of the ring protons. Unknown broad features (asterisks) became observable only at 263 GHz. (Inset) Structure of a Y• with labeling of the internal protons.The structure and function of amino acid radicals, particularly Y• in prototype biological machineries such as RNRs or photosystem II, have been the focus of several studies since the 1990s, due to their representative role in biological redox reactions and proton-coupled electron transfer (14, 15). In class Ia RNRs, the Y•/diiron cofactor is essential for enzyme activity and thus for cell survival (16). In contrast to nonprotein Y• model systems (17, 18), the conformation of Y•s in proteins appeared much more constrained (19, 20). This finding was rationalized as due to the interaction with the protein environment that confers redox properties and thus governs biological function. Nevertheless, the mechanism of action of Y• at the diiron cluster in class Ia RNRs remains puzzling. The current model for initiating nucleotide reduction requires that Y122• (E. coli numbering) is reduced in combination with protonation by a water molecule bound to the diferric cluster (16, 21) when the RNR subunits β2, α2 are mixed with substrate and allosteric effector. In all structures of β2 alone, however, the distance between the oxygen of the water and the oxygen of Y122• is too long for this step [3.8 Å in Protein Data Bank (PDB) 1mxr (22); Fig. 1A]. Thus, the model requires a conformational change to shorten this distance, for which to date no experimental evidence exists.Statistical methods are valuable to support the interpretation of biophysical experiments (23, 24). They have already been introduced in EPR spectroscopy for the analysis of distance measurements and distance distributions (25, 26). While adding uncertainty quantification to general spectroscopic practice, these works still hinge on assumptions about functions of interest, whether explicitly made through a Bayesian prior distribution or implicitly included in a choice of a penalization functional or thresholding procedure, some of which are hard to verify in practice. Additionally, ENDOR targets a different object of interest as it uses a different physical method. Therefore, a statistical analysis of ENDOR signals requires different methodology and has been less explored, possibly also due to a high incidence of systematic errors that are hard to model. In this contribution we aim at a statistical model that does not hinge on any specific assumptions regarding the functions of interest, in particular not on any that are hard to verify. Hence, our statistical model can be generalized to other biophysical experiments. In particular, our statistical approach includes careful statistical checking of distributional assumptions and thus lays a strong foundation for our statistical hypothesis tests. Recent advances in microwave (mw) technology, which allow for long-term signal stability and thus accumulation of large datasets, now provide the opportunity to gain additional information from quantitative ENDOR analysis. In this context, development of statistical methods that disentangle signals from noise and systematic error without having to rely on any assumptions regarding the spectrum and that report uncertainty estimates becomes mandatory.The topic of this paper is a statistical analysis of ENDOR spectra and its representative application to assess the significance of broad spectral features observed in the 263-GHz ¹H spectra of the E. coli RNR Y122•. We present a statistical model for the experimental data, which is used to extract the “most likely signal.” This model takes advantage of the information hidden in each individual scan (or batch) of the spectrum that is usually lost in the process of signal averaging. The treatment presents estimation of the uncertainty in the ENDOR spectra and permits subsequent statistical tests. The mathematical approach combined with spectroscopy of various isotopically labeled mutants of Y122• ultimately uncovered a distribution of conformations of Y122•, yielding insight into the mechanism of action of this essential radical.     

Layering transitions and metastable structures of cholesteric liquid crystals in cylindrical confinement

Our study of cholesteric lyotropic chromonic liquid crystals in cylindrical confinement reveals the topological aspects of cholesteric liquid crystals. The double-twist configurations we observe exhibit discontinuous layering transitions, domain formation, metastability, and chiral point defects as the concentration of chiral dopant is varied. We demonstrate that these distinct layer states can be distinguished by chiral topological invariants. We show that changes in the layer structure give rise to a chiral soliton similar to a toron, comprising a metastable pair of chiral point defects. Through the applicability of the invariants we describe to general systems, our work has broad relevance to the study of chiral materials.

Chiral liquid crystals (LCs) are ubiquitous, useful, and rich systems (1–4). From the first discovery of the liquid crystalline phase to the variety of chiral structures formed by biomolecules (5–9), the twisted structure, breaking both mirror and continuous spatial symmetries, is omnipresent. The unique structure also makes the chiral nematic (cholesteric) LC, an essential material for applications utilizing the tunable, responsive, and periodic modulation of anisotropic properties.The cholesteric is also a popular model system to study the geometry and topology of partially ordered matter. The twisted ground state of the cholesteric is often incompatible with confinement and external fields, exhibiting a large variety of frustrated and metastable director configurations accompanying topological defects. Besides the classic example of cholesterics in a Grandjean−Cano wedge (10, 11), examples include cholesteric droplets (12–16), colloids (17–19), shells (20–22), tori (23, 24), cylinders (25–29), microfabricated structures (30, 31), and films between parallel plates with external fields (32–40). These structures are typically understood using a combination of nematic (achiral) topology (41, 42) and energetic arguments, for example, the highly successful Landau−de Gennes approach (43). However, traditional extensions of the nematic topological approach to cholesterics are known to be conceptually incomplete and difficult to apply in regimes where the system size is comparable to the cholesteric pitch (41, 44).An alternative perspective, chiral topology, can give a deeper understanding of these structures (45–47). In this approach, the key role is played by the twist density, given in terms of the director field n by n⋅∇×n. This choice is not arbitrary; the Frank free energy prefers n⋅∇×n≈−q0=2π/p0 with a helical pitch p0, and, from a geometric perspective, n⋅∇×n≠0 defines a contact structure (48). This allows a number of new integer-valued invariants of chiral textures to be defined (45). A configuration with a single sign of twist is chiral, and two configurations which cannot be connected by a path of chiral configurations are chirally distinct, and hence separated by a chiral energy barrier. Within each chiral class of configuration, additional topological invariants may be defined using methods of contact topology (45–48), such as layer numbers. Changing these chiral topological invariants requires passing through a nonchiral configuration. Cholesterics serve as model systems for the exploration of chirality in ordered media, and the phenomena we describe here—metastability in chiral systems controlled by chiral topological invariants—has applicability to chiral order generally. This, in particular, includes chiral ferromagnets, where, for example, our results on chiral topological invariants apply to highly twisted nontopological Skyrmions (49, 50) (“Skyrmionium”).Our experimental model to explore the chiral topological invariants is the cholesteric phase of lyotropic chromonic LCs (LCLCs). The majority of experimental systems hitherto studied are based on thermotropic LCs with typical elastic and surface-anchoring properties. The aqueous LCLCs exhibiting unusual elastic properties, that is, very small twist modulus K2 and large saddle-splay modulus K24 (51–56), often leading to chiral symmetry breaking of confined achiral LCLCs (53, 54, 56–61), may enable us to access uncharted configurations and defects of topological interests. For instance, in the layer configuration by cholesteric LCLCs doped with chiral molecules, their small K2 provides energetic flexibility to the thickness of the cholesteric layer, that is, the repeating structure where the director n twists by π. The large K24 affords curvature-induced surface interactions in combination with a weak anchoring strength of the lyotropic LCs (62–64).We present a systematic investigation of the director configuration of cholesteric LCLCs confined in cylinders with degenerate planar anchoring, depending on the chiral dopant concentration. We show that the structure of cholesteric configurations is controlled by higher-order chiral topological invariants. We focus on two intriguing phenomena observed in cylindrically confined cholesterics. First, the cylindrical symmetry renders multiple local minima to the energy landscape and induces discontinuous increase of twist angles, that is, a layering transition, upon the dopant concentration increase. Additionally, the director configurations of local minima coexist as metastable domains with point-like defects between them. We demonstrate that a chiral layer number invariant distinguishes these configurations, protects the distinct layer configurations (45), and explains the existence of the topological defect where the invariant changes.