Label-free probe of HIV-1 TAT peptide binding to mimetic membranes

The transacting activator of transduction (TAT) protein plays a key role in the progression of AIDS. Studies have shown that a +8 charged sequence of amino acids in the protein, called the TAT peptide, enables the TAT protein to penetrate cell membranes. To probe mechanisms of binding and translocation of the TAT peptide into the cell, investigators have used phospholipid liposomes as cell membrane mimics. We have used the method of surface potential sensitive second harmonic generation (SHG), which is a label-free and interface-selective method, to study the binding of TAT to anionic 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-1′-rac-glycerol (POPG) and neutral 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) liposomes. It is the SHG sensitivity to the electrostatic field generated by a charged interface that enabled us to obtain the interfacial electrostatic potential. SHG together with the Poisson–Boltzmann equation yielded the dependence of the surface potential on the density of adsorbed TAT. We obtained the dissociation constants K_d for TAT binding to POPC and POPG liposomes and the maximum number of TATs that can bind to a given liposome surface. For POPC K_d was found to be 7.5 ± 2 μM, and for POPG K_d was 29.0 ± 4.0 μM. As TAT was added to the liposome solution the POPC surface potential changed from 0 mV to +37 mV, and for POPG it changed from −57 mV to −37 mV. A numerical calculation of K_d, which included all terms obtained from application of the Poisson–Boltzmann equation to the TAT liposome SHG data, was shown to be in good agreement with an approximated solution.The HIV type 1 (HIV-1) transacting activator of transduction (TAT) is an important regulatory protein for viral gene expression (1–3). It has been established that the TAT protein has a key role in the progression of AIDS and is a potential target for anti-HIV vaccines (4). For the TAT protein to carry out its biological functions, it needs to be readily imported into the cell. Studies on the cellular internalization of TAT have led to the discovery of the TAT peptide, a highly cationic 11-aa region (protein transduction domain) of the 86-aa full-length protein that is responsible for the TAT protein translocating across phospholipid membranes (5–8). The TAT peptide is a member of a class of peptides called cell-penetrating peptides (CPPs) that have generated great interest for drug delivery applications (ref. 9 and references therein). The exact mechanism by which the TAT peptide enters cells is not fully understood, but it is likely to involve a combination of energy-independent penetration and endocytosis pathways (8, 10). The first step in the process is high-affinity binding of the peptide to phospholipids and other components on the cell surface such as proteins and glycosaminoglycans (1, 9).The binding of the TAT peptide to liposomes has been investigated using a variety of techniques, each of which has its own advantages and limitations. Among the techniques are isothermal titration calorimetry (9, 11), fluorescence spectroscopy (12, 13), FRET (12, 14), single-molecule fluorescence microscopy (15, 16), and solid-state NMR (17). Second harmonic generation (SHG), as an interface-selective technique (18–24), does not require a label, and because SHG is sensitive to the interface potential, it is an attractive method to selectively probe the binding of the highly charged (+8) TAT peptide to liposome surfaces. Although coherent SHG is forbidden in centrosymmetric and isotropic bulk media for reasons of symmetry, it can be generated by a centrosymmetric structure, e.g., a sphere, provided that the object is centrosymmetric over roughly the length scale of the optical coherence, which is a function of the particle size, the wavelength of the incident light, and the refractive indexes at ω and 2ω (25–30). As a second-order nonlinear optical technique SHG has symmetry restrictions such that coherent SHG is not generated by the randomly oriented molecules in the bulk liquid, but can be generated coherently by the much smaller population of oriented interfacial species bound to a particle or planar surfaces. As a consequence the SHG signal from the interface is not overwhelmed by SHG from the much larger populations in the bulk media (25–28).The total second harmonic electric field, E_2ω, originating from a charged interface in contact with water can be expressed as (31–33)E2ω∝∑iχc,i(2)EωEω+∑jχinc,j(2)EωEω+χH2O(3)EωEωΦ,[1]where χc,i(2) represents the second-order susceptibility of the species i present at the interface; χinc,j(2) represents the incoherent contribution of the second-order susceptibility, arising from density and orientational fluctuations of the species j present in solution, often referred to as hyper-Rayleigh scattering; χH2O(3) is the third-order susceptibility originating chiefly from the polarization of the bulk water molecules polarized by the charged interface; Φ is the potential at the interface that is created by the surface charge; and E_ω is the electric field of the incident light at the fundamental frequency ω. The second-order susceptibility, χc,i(2), can be written as the product of the number of molecules, N, at the surface and the orientational ensemble average of the hyperpolarizability α_i⁽²⁾ of surface species i, yielding χc,i(2)=N〈αi(2)〉 (18). The bracket ?? indicates an orientational average over the interfacial molecules. The third term in Eq. 1 depicts a third-order process by which a second harmonic field is generated by a charged interface. This term is the focus of our work. The SHG signal is dependent on the surface potential created by the electrostatic field of the surface charges, often called the χ⁽³⁾ contribution to the SHG signal. The χ⁽³⁾ method has been used to extract the surface charge density of charged planar surfaces and microparticle surfaces, e.g., liposomes, polymer beads, and oil droplets in water (21, 25, 34–39).In this work, the χ⁽³⁾ SHG method is used to explore a biomedically relevant process. The binding of the highly cationic HIV-1 TAT peptide to liposome membranes changes the surface potential, thereby enabling the use of the χ⁽³⁾ method to study the binding process in a label-free manner. Two kinds of liposomes, neutral 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) and anionic 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-1′-rac-glycerol (POPG), were investigated. The chemical structures of TAT, POPC, and POPG lipids are shown in Scheme 1.Open in a separate windowScheme 1.Chemical structures of HIV-1 TAT (47–57) peptide and the POPC and POPG lipids.     

Fracture of model end-linked networks

Advances in polymer chemistry over the last decade have enabled the synthesis of molecularly precise polymer networks that exhibit homogeneous structure. These precise polymer gels create the opportunity to establish true multiscale, molecular to macroscopic, relationships that define their elastic and failure properties. In this work, a theory of network fracture that accounts for loop defects is developed by drawing on recent advances in network elasticity. This loop-modified Lake–Thomas theory is tested against both molecular dynamics (MD) simulations and experimental fracture measurements on model gels, and good agreement between theory, which does not use an enhancement factor, and measurement is observed. Insight into the local and global contributions to energy dissipated during network failure and their relation to the bond dissociation energy is also provided. These findings enable a priori estimates of fracture energy in swollen gels where chain scission becomes an important failure mechanism.

Models that link materials structure to macroscopic behavior can account for multiple levels of molecular structure. For example, the statistical, affine deformation model connects the elastic modulus E to the molecular structure of a polymer chain,Eaff=3νkbT(ϕo13Roϕ13R)2,[1]where ν is density of chains, ϕ is polymer volume fraction, R is end-to-end distance, ϕo and R_o represent the parameters taken in the reference state that is assumed to be the reaction concentration in this work, and k_bT is the available thermal energy where k_b is Boltzmann’s constant and T is temperature (1–6). Refinements to this model that account for network-level structure, such as the presence of trapped entanglements or number of connections per junction, have been developed (7–11). Further refinements to the theory of network elasticity have been developed to account for dynamic processes such as chain relaxation and solvent transport (12–17). Together these refinements link network elasticity to chain-level molecular structure, network-level structure, and the dynamic processes that occur at both size scales.While elasticity has been connected to multiple levels of molecular structure, models for network fracture have not developed to a similar extent. The fracture energy G_c typically relies upon the large strain deformation behavior of polymer networks, making it experimentally difficult to separate the elastic energy released upon fracture from that dissipated through dynamic processes (18–26). In fact, most fracture theories have been developed at the continuum scale and have focused on modeling dynamic dissipation processes (27). An exception to this is the theory of Lake and Thomas that connects the elastic energy released during chain scission to chain-level structure,Gc,LT=ChainsArea×Energy DissipatedChain=νRoNU,[2]where NU is the total energy released when a chain ruptures in which N represents the number of monomer segments in the chain and U the energy released per monomer (26).While this model was first introduced in 1967, experimental attempts to verify Lake–Thomas theory as an explicit model, as summarized in SI Appendix, have been unsuccessful. Ahagon and Gent (28) and Gent and Tobias (29) attempted to do this on highly swollen networks at elevated temperature but found that, while the scalings from Eq. 2 work well, an enhancement factor was necessary to observe agreement between theory and experiment. This led many researchers to conclude that Lake–Thomas theory worked only as a scaling argument. In 2008, Sakai et al. (30) introduced a series of end-linked tetrafunctional, star-like poly(ethylene glycol) (PEG) gels. Scattering measurements indicated a lack of nanoscale heterogeneities that are characteristic of most polymer networks (30–32). Fracture measurements on these well-defined networks were performed and it was again observed that an enhancement factor was necessary to realize explicit agreement between experiment and theory (33). Arora et al. (34) recently attempted to address this discrepancy by accounting for loop defects; however, different assumptions were used when inputting U to calculate Lake–Thomas theory values that again required the use of an enhancement factor to achieve quantitative agreement. In this work we demonstrate that refining the Lake–Thomas theory to account for loop defects while using the full bond dissociation energy to represent U yields excellent agreement between the theory and both simulation and experimental data without the use of any adjustable parameters.PEG gels synthesized via telechelic end-linking reactions create the opportunity to build upon previous theory to establish true multiscale, molecular to macroscopic relationships that define the fracture response of polymer networks. This paper combines pure shear notch tests, molecular dynamics (MD) simulations, and theory to quantitatively extend the concept of network fracture without the use of an enhancement factor. First, the control of molecular-level structure in end-linked gel systems is discussed. Then, the choice of molecular parameters used to estimate chain- and network-level properties is discussed. Experimental and MD simulation methods used when fracturing model end-linked networks are then presented. A theory of network fracture that accounts for loop defects is developed, in the context of other such models that have emerged recently, and tested against data from experiments and MD simulations. Finally, a discussion of the local and global energy dissipated during failure of the network is presented.     

Phase-separating RNA-binding proteins form heterogeneous distributions of clusters in subsaturated solutions

Macromolecular phase separation is thought to be one of the processes that drives the formation of membraneless biomolecular condensates in cells. The dynamics of phase separation are thought to follow the tenets of classical nucleation theory, and, therefore, subsaturated solutions should be devoid of clusters with more than a few molecules. We tested this prediction using in vitro biophysical studies to characterize subsaturated solutions of phase-separating RNA-binding proteins with intrinsically disordered prion-like domains and RNA-binding domains. Surprisingly, and in direct contradiction to expectations from classical nucleation theory, we find that subsaturated solutions are characterized by the presence of heterogeneous distributions of clusters. The distributions of cluster sizes, which are dominated by small species, shift continuously toward larger sizes as protein concentrations increase and approach the saturation concentration. As a result, many of the clusters encompass tens to hundreds of molecules, while less than 1% of the solutions are mesoscale species that are several hundred nanometers in diameter. We find that cluster formation in subsaturated solutions and phase separation in supersaturated solutions are strongly coupled via sequence-encoded interactions. We also find that cluster formation and phase separation can be decoupled using solutes as well as specific sets of mutations. Our findings, which are concordant with predictions for associative polymers, implicate an interplay between networks of sequence-specific and solubility-determining interactions that, respectively, govern cluster formation in subsaturated solutions and the saturation concentrations above which phase separation occurs.

Phase separation of RNA-binding proteins with disordered prion-like domains (PLDs) and RNA-binding domains (RBDs) is implicated in the formation and dissolution of membraneless biomolecular condensates such as RNA–protein (RNP) granules (1–9). Macroscopic phase separation is a process whereby a macromolecule in a solvent separates into a dilute, macromolecule-deficient phase that coexists with a dense, macromolecule-rich phase (10, 11). In a binary mixture, the soluble phase, comprising dispersed macromolecules that are well mixed with the solvent, becomes saturated at a concentration designated as c_sat. Above c_sat, for total macromolecular concentrations c_tot that are between the binodal and spinodal, phase separation of full-length RNA-binding proteins and PLDs is thought to follow classical nucleation theory (12–15).In classical nucleation theories, clusters representing incipient forms of the new dense phase form within dispersed phases of supersaturated solutions defined by c_tot > c_sat (16, 17). In the simplest formulation of classical nucleation theory (16–18), the free energy of forming a cluster of radius a is ΔF=−4π3a3Δμρn+4πa2γ. Here, Δµ is the difference in the chemical potential between the one-phase and two-phase regimes (see discussion in SI Appendix), which is negative in supersaturated solutions and positive in subsaturated solutions; ρ_n is the number of molecules per unit volume, and γ is the interfacial tension between dense and dilute phases. At temperature T, in a seed-free solution, the degree of supersaturation s is defined as s≡ΔμRT=ln(ctotcsat), where R is the ideal gas constant. Here, s is positive for c_tot > c_sat, and, as s increases, cluster formation becomes more favorable. Above a critical radius a*, the free energy of cluster formation can overcome the interfacial penalty, and the new dense phase grows in a thermodynamically downhill fashion. Ideas from classical nucleation theory have been applied to analyze and interpret the dynamics of phase separation in supersaturated solutions (12, 13, 15). Classical nucleation theories stand in contrast to two-step nucleation theories that predict the existence of prenucleation clusters in supersaturated solutions (19–22). These newer theories hint at the prospect of there being interesting features in subsaturated solutions, where c_tot < c_sat and s < 0.The subsaturated regime, where s is negative, corresponds to the one-phase regime. Ignoring the interfacial tension, the free energy of realizing clusters with n molecules in subsaturated solutions is: ΔF = –nΔµ. Therefore, the probability P(n) of forming a cluster of n molecules in a subsaturated solution is proportional to exp(sn). Accordingly, the relative probability P(n)/P(1) of forming clusters with n molecules will be exp(s(n – 1)). This quantity, which may be thought of as the concentration of clusters with n molecules, is negligibly small for clusters with more than a few molecules. This is true irrespective of the degree of subsaturation, s. Is this expectation from classical nucleation theories valid? We show here that subsaturated solutions feature a rich distribution of species not anticipated by classical nucleation theories. We report results from measurements of cluster size distributions in subsaturated solutions of phase-separating RNA-binding proteins from the FUS-EWSR1-TAF15 (FET) family. We find that these systems form clusters in subsaturated solutions, and that the cluster sizes follow heavy-tailed distributions. The abundant species are always small clusters. However, as total macromolecular concentration (c_tot) increases, the distributions of cluster sizes shift continuously toward larger values. We discuss these findings in the context of theories for associative polymers (9, 23–30).     

Nature of dynamic gradients,glass formation,and collective effects in ultrathin freestanding films

Molecular, polymeric, colloidal, and other classes of liquids can exhibit very large, spatially heterogeneous alterations of their dynamics and glass transition temperature when confined to nanoscale domains. Considerable progress has been made in understanding the related problem of near-interface relaxation and diffusion in thick films. However, the origin of “nanoconfinement effects” on the glassy dynamics of thin films, where gradients from different interfaces interact and genuine collective finite size effects may emerge, remains a longstanding open question. Here, we combine molecular dynamics simulations, probing 5 decades of relaxation, and the Elastically Cooperative Nonlinear Langevin Equation (ECNLE) theory, addressing 14 decades in timescale, to establish a microscopic and mechanistic understanding of the key features of altered dynamics in freestanding films spanning the full range from ultrathin to thick films. Simulations and theory are in qualitative and near-quantitative agreement without use of any adjustable parameters. For films of intermediate thickness, the dynamical behavior is well predicted to leading order using a simple linear superposition of thick-film exponential barrier gradients, including a remarkable suppression and flattening of various dynamical gradients in thin films. However, in sufficiently thin films the superposition approximation breaks down due to the emergence of genuine finite size confinement effects. ECNLE theory extended to treat thin films captures the phenomenology found in simulation, without invocation of any critical-like phenomena, on the basis of interface-nucleated gradients of local caging constraints, combined with interfacial and finite size-induced alterations of the collective elastic component of the structural relaxation process.

Spatially heterogeneous dynamics in glass-forming liquids confined to nanoscale domains (1–7) play a major role in determining the properties of molecular, polymeric, colloidal, and other glass-forming materials (8), including thin films of polymers (9, 10) and small molecules (11–15), small-molecule liquids in porous media (2, 4, 16, 17), semicrystalline polymers (18, 19), polymer nanocomposites (20–22), ionomers (23–25), self-assembled block and layered (26–33) copolymers, and vapor-deposited ultrastable molecular glasses (34–36). Intense interest in this problem over the last 30 y has also been motivated by the expectation that its understanding could reveal key insights concerning the mechanism of the bulk glass transition.Considerable progress has been made for near-interface altered dynamics in thick films, as recently critically reviewed (1). Large amplitude gradients of the structural relaxation time, τ(z,T), converge to the bulk value, τ_bulk(T), in an intriguing double-exponential manner with distance, z, from a solid or vapor interface (13, 37–42). This implies that the corresponding effective activation barrier, F_total(z,T,H) (where H is film thickness), varies exponentially with z, as does the glass transition temperature, T_g (37). Thus the fractional reduction in activation barrier, ε(z,H), obeys the equation ε(z,H)≡1−Ftotal(z,T,H)/Ftotal,bulk(T)=ε0⁡exp(−z/ξF), where F_total,bulk(T) is the bulk temperature-dependent barrier and ξ_F a length scale of modest magnitude. Although the gradient of reduction in absolute activation barriers becomes stronger with cooling, the amplitude of the fractional reduction of the barrier gradient, quantified by ε₀, and the range ξ_F of this gradient, exhibit a weak or absent temperature dependence at the lowest temperatures accessed by simulations (typically with the strength of temperature dependence of ξ_F decreasing rather than increasing on cooling), which extend to relaxation timescales of order 10⁵ ps. This finding raises questions regarding the relevance of critical-phenomena–like ideas for nanoconfinement effects (1). Partially due to this temperature invariance, coarse-grained and all-atom simulations (1, 37, 42, 43) have found a striking empirical fractional power law decoupling relation between τ(z,T) and τ_bulk(T):τ(T,z)τbulk(T)∝(τbulk(T))−ε(z).[1]Recent theoretical analysis suggests (44) that this behavior is consistent with a number of experimental data sets as well (45, 46). Eq. 1 also corresponds to a remarkable factorization of the temperature and spatial location dependences of the barrier:Ftotal(z,T)=[1−ε(z)]Ftotal,bulk(T).[2]This finding indicates that the activation barrier for near-interface relaxation can be factored into two contributions: a z-dependent, but T-independent, “decoupling exponent,” ε(z), and a temperature-dependent, but position-insensitive, bulk activation barrier, F_total,bulk(T). Eq. 2 further emphasizes that ε(z) is equivalent to an effective fractional barrier reduction factor (for a vapor interface), 1−Ftotal(z,T,H)/Ftotal,bulk(T), that can be extracted from relaxation data.In contrast, the origin of “nanoconfinement effects” in thin films, and how much of the rich thick-film physics survives when dynamic gradients from two interfaces overlap, is not well understood. The distinct theoretical efforts for aspects of the thick-film phenomenology (44, 47–50) mostly assume an additive summation of one-interface effects in thin films, thereby ignoring possibly crucial cooperative and whole film finite size confinement effects. If the latter involve phase-transition–like physics as per recent speculations (14, 51), one can ask the following: do new length scales emerge that might be truncated by finite film size? Alternatively, does ultrathin film phenomenology arise from a combination of two-interface superposition of the thick-film gradient physics and noncritical cooperative effects, perhaps in a property-, temperature-, and/or thickness-dependent manner?Here, we answer these questions and establish a mechanistic understanding of thin-film dynamics for the simplest and most universal case: a symmetric freestanding film with two vapor interfaces. We focus on small molecules (modeled theoretically as spheres) and low to medium molecular weight unentangled polymers, which empirically exhibit quite similar alterations in dynamics under “nanoconfinement.” We do not address anomalous phenomena [e.g., much longer gradient ranges (29), sporadic observation of two distinct glass transition temperatures (52, 53)] that are sometimes reported in experiments with very high molecular weight polymers and which may be associated with poorly understood chain connectivity effects that are distinct from general glass formation physics (54–56).We employ a combination of molecular dynamics simulations with a zero-parameter extension to thin films of the Elastically Cooperative Nonlinear Langevin Equation (ECNLE) theory (57, 58). This theory has previously been shown to predict well both bulk activated relaxation over up to 14 decades (44–46) and the full single-gradient phenomenology in thick films (1). Here, we extend this theory to treat films of finite thickness, accounting for coupled interface and geometric confinement effects. We compare predictions of ECNLE theory to our previously reported (37, 43) and new simulations, which focus on translational dynamics of films comprised of a standard Kremer–Grest-like bead-spring polymer model (see SI Appendix). These simulations cover a wide range of film thicknesses (H, from 4 to over 90 segment diameters σ) and extend to low temperatures where the bulk alpha time is ∼0.1 μs (10⁵ Lennard Jones time units τ_LJ).The generalized ECNLE theory is found to be in agreement with simulation for all levels of nanoconfinement. We emphasize that this theory does not a priori assume any of the empirically established behaviors discovered using simulation (e.g., fractional power law decoupling, double-exponential barrier gradient, gradient flattening) but rather predicts these phenomena based upon interfacial modifications of the two coupled contributions to the underlying activation barrier– local caging constraints and a long-ranged collective elastic field. It is notable that this strong agreement is found despite the fact the dynamical ideas are approximate, and a simple hard sphere fluid model is employed in contrast to the bead-spring polymers employed in simulation. The basic unit of length in simulation (bead size σ) and theory (hard sphere diameter d) are expected to be proportional to within a prefactor of order unity, which we neglect in making comparisons.As an empirical matter, we find from simulation that many features of thin-film behavior can be described to leading order by a linear superposition of the thick-film gradients in activation barrier, that is:ε(z,H)=1−Ftotal(z,T,H)/Ftotal,bulk(T)≈ε0[exp(−z/ξF)+exp(−(H−z)/ξF)],[3]where the intrinsic decay length ξ_F is unaltered from its thick-film value and where ε₀ is a constant that, in the hypothesis of literal gradient additivity, is invariant to temperature and film thickness. We employ this functional form [originally suggested by Binder and coworkers (59)], which is based on a simple superposition of the two single-interface gradients, as a null hypothesis throughout this study: this form is what one expects if no new finite-size physics enters the thin-film problem relative to the thick film.However, we find that the superposition approximation progressively breaks down, and eventually entirely fails, in ultrathin films as a consequence of the emergence of a finite size confinement effect. The ECNLE theory predicts that this failure is not tied to a phase-transition–like mechanism but rather is a consequence of two key coupled physical effects: 1) transfer of surface-induced reduction of local caging constraints into the film, and 2) interfacial truncation and nonadditive modifications of the collective elastic contribution to the activation barrier.     

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.     

Photon gating in four-dimensional ultrafast electron microscopy

Ultrafast electron microscopy (UEM) is a pivotal tool for imaging of nanoscale structural dynamics with subparticle resolution on the time scale of atomic motion. Photon-induced near-field electron microscopy (PINEM), a key UEM technique, involves the detection of electrons that have gained energy from a femtosecond optical pulse via photon–electron coupling on nanostructures. PINEM has been applied in various fields of study, from materials science to biological imaging, exploiting the unique spatial, energy, and temporal characteristics of the PINEM electrons gained by interaction with a “single” light pulse. The further potential of photon-gated PINEM electrons in probing ultrafast dynamics of matter and the optical gating of electrons by invoking a “second” optical pulse has previously been proposed and examined theoretically in our group. Here, we experimentally demonstrate this photon-gating technique, and, through diffraction, visualize the phase transition dynamics in vanadium dioxide nanoparticles. With optical gating of PINEM electrons, imaging temporal resolution was improved by a factor of 3 or better, being limited only by the optical pulse widths. This work enables the combination of the high spatial resolution of electron microscopy and the ultrafast temporal response of the optical pulses, which provides a promising approach to attain the resolution of few femtoseconds and attoseconds in UEM.In ultrafast electron microscopy (UEM) (1–3), electrons generated by photoemission at the cathode of a transmission electron microscope are accelerated down the microscope column to probe the dynamic evolution of a specimen initiated by an ultrafast light pulse. The use of femtosecond lasers to generate the electron probe and excite the specimen has made it possible to achieve temporal resolution on the femtosecond time scale, as determined by the cross-correlation of the optical and electron pulses. One important method in the UEM repertoire is photon-induced near-field electron microscopy (PINEM) (4, 5), in which the dynamic response detected by the electron probe is the pump-induced charge density redistribution in nanoscale specimens (6).Photon–electron coupling is the basic building block of PINEM, which takes place in the presence of nanostructures when the energy-momentum conservation condition is satisfied (4, 5). This coupling leads to inelastic gain/loss of photon quanta by electrons in the electron packet, which can be resolved in the electron energy spectrum (5, 7, 8). This spectrum consists of discrete peaks, spectrally separated by multiples of the photon energy (n?ω), on the higher and lower energy sides of the zero loss peak (ZLP) (4) (Fig. 1). The development of PINEM enables the visualization of the spatiotemporal dielectric response of nanostructures (9), visualization of plasmonic fields (4, 5) and their spatial interferences (10), imaging of low atomic number nanoscale materials (11), characterization of ultrashort electron packets (12, 13), and imaging of different biological structures (14).Open in a separate windowFig. 1.Concept of photon gating in 4D electron microscopy. (A) The microscope column with one electron (dark blue) and two optical (red) pulses focused onto the specimen. The wavefunctions of the three pulses are schematically shown at the top. One optical pulse is coincident with the electron pulse at the specimen to generate a PINEM signal. The resulting light blue PINEM pulse is sliced out from other electrons for detection as an energy spectrum, an image, or a diffraction signal (see the text). The second optical pulse initiates the dynamics to be probed. (B) Electron energy spectrum generated at the specimen plane when optical and electron pulses arrive simultaneously. The gain energy range is shaded light blue. (C) Illustration for the temporal pulse sequence, two optical and one electron pulse for ultrafast time-resolved PINEM measurements.As shown by Park et al. (5), the PINEM intensity (I_PINEM) is given by the square modulus of the field integral F˜0 (i.e., IPINEM∝|F˜0|2), in the weak interaction limit. The near field of a nanoparticle leads to the scattering of the electron packet, which can be treated rigorously using the Schrödinger equation/Mie scattering theory. It follows that PINEM images the object and displays its field characteristics depending on its shape, the polarization and wavelength of optical excitation, and the width of pulses used. For a spherical nanoparticle, the field integral at point (x, y) in the specimen plane is simplified to give (6)F˜0≈−iE˜0⁡cos⁡ϕχs 23 a3(Δk)2K[Δkb],[1]where E˜0 is the electric field amplitude of the incident light, ? the light polarization angle, a the particle radius, b=x2+y2 the impact parameter, K the modified Bessel function of the second type, Δk the momentum change of the electron, and χ_s = 3(ε ? 1)/(ε + 2), where χ_s is the material susceptibility and ε the dielectric function.In previous studies of the parameters in Eq. 1, only E˜0 was time dependent. The PINEM intensity, at a given point in space, was a function only of the time delay between the optical and electron pulses, providing, for the pulse lengths currently used, a cross-correlation profile when this delay was scanned across the time of temporal coincidence, or t = 0 (4, 5, 9, 13). Hitherto, PINEM has not been used to study the ultrafast dynamics of matter. Here, we follow the strategy of using the PINEM gain electrons generated by a first optical pulse, whose delay relative to the electron pulse is maintained at t = 0, to probe dynamics initiated by introduction of a second optical pulse on the specimen, as proposed theoretically in ref. 15. By this approach, we were able to optically gate the electron pulse (i.e., create an electron pulse that only lasts for the duration of the optical pulse) and achieve significant enhancement of the temporal resolution (see the second paragraph below).The concept of the experiment is illustrated by Fig. 1A, in which the electron pulse in blue and one optical pulse (P₁) in red are shown arriving at the specimen plane simultaneously. Interaction between photon and electron in the presence of the specimen “slices out” the light blue pulse of gain electrons, which are separated from all other electrons by energy dispersion or filtering to be detected according to microscope settings in spectroscopy, imaging, or diffraction mode, as illustrated schematically at the bottom of the column. Note, it is possible to obtain PINEM diffraction, but this is not the subject of this paper. A second, or pump, optical pulse (P₂) is shown below the specimen, having already triggered the dynamics of interest. A series of time axes is plotted in Fig. 1C showing examples of characteristic sequences of pulse arrival times at the specimen plane during the experiment, with the pump arrival defining the zero of time.A striking feature of this technique that was alluded to above is the potential for high temporal resolution, unlimited by the electron pulse duration, because the optical pulse acts as a temporal gate for a longer electron pulse. In the weak interaction limit, the duration of the pulse of PINEM electrons emulates that of the optical pulse that created it (15), as clearly shown in Fig. 1A. When these photon-gated electrons are used to probe dynamics triggered by a second ultrafast optical pulse, the time resolution is determined by the cross-correlation of the two optical pulses. This paves the way for the realization of attosecond electron microscopy, as done in all-optical spectroscopy (16) but with the spatial resolution being that of atomic motions. As suggested in Fig. 1A, we envisage the use of the photon-gated electron pulses, in imaging or in diffraction mode, for the study of a variety of optically initiated material processes, either of the nanostructure or of its surrounding media.The PINEM signal can be directly monitored to detect changes in any of the specimen optical or physical properties expressed in Eq. 1. Here, we demonstrate the use of the time-resolved PINEM technique where it is shown that the photoinduced dielectric response of VO₂—which is strongly related to the lattice symmetry (17)—manifests itself in a change in PINEM intensity. We relate the changes in optical properties of the polycrystalline VO₂ nanoparticles to the phase transition dynamics from initial (monoclinic) insulator phase to (tetragonal) metal phase, the subject of numerous previous studies.Vanadium dioxide has been discussed as an active metamaterial (18) and one of the best candidates for solid-state ultrafast optical switches in photonics applications (19, 20) due to its unique structural photoinduced phase transition behavior (21). This phase transition has been examined by investigating the change in the heat capacity through thermal excitation (22, 23), whereas its ultrafast dynamics has been studied by optical spectroscopy (24, 25), THz spectroscopy (26, 27), X-ray diffraction (28, 29), ultrafast electron crystallography (30), and electron microscopy (31).     

Modeling the instantaneous normal mode spectra of liquids as that of unstable elastic media

We study the instantaneous normal mode (INM) spectrum of a simulated soft-sphere liquid at different equilibrium temperatures T. We find that the spectrum of eigenvalues ρ(λ) has a sharp maximum near (but not at) λ=0 and decreases monotonically with |λ| on both the stable and unstable sides of the spectrum. The spectral shape strongly depends on temperature. It is rather asymmetric at low temperatures (close to the dynamical critical temperature) and becomes symmetric at high temperatures. To explain these findings we present a mean-field theory for ρ(λ), which is based on a heterogeneous elasticity model, in which the local shear moduli exhibit spatial fluctuations, including negative values. We find good agreement between the simulation data and the model calculations, done with the help of the self-consistent Born approximation (SCBA), when we take the variance of the fluctuations to be proportional to the temperature T. More importantly, we find an empirical correlation of the positions of the maxima of ρ(λ) with the low-frequency exponent of the density of the vibrational modes of the glasses obtained by quenching to T=0 from the temperature T. We discuss the present findings in connection to the liquid to glass transformation and its precursor phenomena.

The investigation of the potential energy surface (PES) V(r1(t)…rN(t)) of a liquid (made up of N particles with positions r1(t)…rN(t) at a time instant t) and the corresponding instantaneous normal modes (INMs) of the (Hessian) matrix of curvatures has been a focus of liquid and glass science since the appearance of Goldstein’s seminal article (1) on the relation between the PES and the liquid dynamics in the viscous regime above the glass transition (2–27).The PES has been shown to form a rather ragged landscape in configuration space (8, 28, 29) characterized by its stationary points. In a glass these points are minima and are called “inherent structures.” The PES is believed to contain important information on the liquid–glass transformation mechanism. For the latter a complete understanding is still missing (28, 30, 31). The existing molecular theory of the liquid–glass transformation is mode-coupling theory (MCT) (32, 33) and its mean-field Potts spin version (28, 34). MCT predicts a sharp transition at a temperature TMCT>Tg, where T_g is the temperature of structural arrest (glass transition temperature). MCT completely misses the heterogeneous activated relaxation processes (dynamical heterogeneities), which are evidently present around and below T_MCT and which are related to the unstable (negative-λ) part of the INM spectrum (28, 30).Near and above T_MCT, apparently, there occurs a fundamental change in the PES. Numerical studies of model liquids have shown that minima present below T_MCT change into saddles, which then explains the absence of activated processes above T_MCT (2–24). Very recently, it was shown that T_MCT is related to a localization–delocalization transition of the unstable INM modes (25, 26).The INM spectrum is obtained in molecular dynamic simulations by diagonalizing the Hessian matrix of the interaction potential, taken at a certain time instant t:Hijαβ(t)=∂2∂xi(α)∂xj(β)V{r1(t)…rN(t)},[1]with ri=(xi(1),xi(2),xi(3)). For large positive values of the eigenvalues λ_j (j=1…N, N being the number of particles in the system) they are related to the square of vibrational frequencies λj=ωj2, and one can consider the Hessian as the counterpart of the dynamical matrix of a solid. In this high-frequency regime one can identify the spectrum with the density of vibrational states (DOS) of the liquid viag(ω)=2 ωρ(λ(ω))=13N∑jδ(ω−ωj) .[2]For small and negative values of λ this identification is not possible. For the unstable part of the spectrum (λ<0) it has become common practice to call the imaginary number λ=iω˜ and define the corresponding DOS asg(ω˜)≡2 ω˜ρ(λ(ω˜)).[3]This function is plotted on the negative ω axis and the stable g(ω), according to [2], on the positive axis. However, the (as we shall see, very interesting) details of the spectrum ρ(λ) near λ = 0 become almost completely hidden by multiplying the spectrum with |ω|. In fact, it has been demonstrated by Sastry et al. (6) and Taraskin and Elliott (7) already 2 decades ago that the INM spectrum of liquids, if plotted as ρ(λ) and not as g(ω) according to [2] and [3], exhibits a characteristic cusp-like maximum at λ = 0. The shape of the spectrum changes strongly with temperature. This is what we find as well in our simulation and what we want to explore further in our present contribution.In the present contribution we demonstrate that the strong change of the spectrum with temperature can be rather well explained in terms of a model, in which the instantaneous harmonic spectrum of the liquid is interpreted to be that of an elastic medium, in which the local shear moduli exhibit strong spatial fluctuations, which includes a large number of negative values. Because these fluctuations are just a snapshot of thermal fluctuations, we assume that they are obeying Gaussian statistics, the variance of which is proportional to the temperature.Evidence for a characteristic change in the liquid configurations in the temperature range above T_g has been obtained in recent simulation studies of the low-frequency vibrational spectrum of glasses, which have been rapidly quenched from a certain parental temperature T*. If T* is decreased from high temperatures toward T_MCT, the low-frequency exponent of the vibrational DOS of the daughter glass (quenched from T* to T = 0) changed from Debye-like g(ω)∝ω2 to g(ω)∝ωs with s > 2. In our numerical investigation of the INM spectra we show a correlation of some details of the low-eigenvalue features of these spectra with the low-frequency properties of the daughter glasses obtained by quenching from the parental temperatures.The stochastic Helmholtz equations (Eq. 7) of an elastic model with spatially fluctuating shear moduli can be readily solved for the averaged Green’s functions by field theoretical techniques (35–37). Via a saddle point approximation with respect to the resulting effective field theory one arrives at a mean-field theory (self-consistent Born approximation [SCBA]) for the self-energy of the averaged Green’s functions. The SCBA predicts a stable spectrum below a threshold value of the variance. Restricted to this stable regime, this theory, called heterogeneous elasticity theory (HET), was rather successful in explaining several low-frequency anomalies in the vibrational spectrum of glasses, including the so-called boson peak, which is an enhancement at finite frequencies over the Debye behavior of the DOS g(ω)∝ω2 (37–41). We now explore the unstable regime of this theory and compare it to the INM spectrum of our simulated soft-sphere liquid.^*We start Results by presenting a comparison of the simulated spectra of the soft-sphere liquid with those obtained by the unstable version of HET-SCBA theory. We then concentrate on some specific features of the INM spectra, namely, the low-eigenvalue slopes and the shift of the spectral maximum from λ = 0. Both features are accounted for by HET-SCBA. In particular, we find an interesting law for the difference between the slopes of the unstable and the stable parts of the spectrum, which behaves as T−2/3, which, again, is accounted for by HET-SCBA.In the end we compare the shift of the spectral maximum with the low-frequency exponent of the DOS of the corresponding daughter glasses and find an empirical correlation. We discuss these results in connection with the saddle to minimum transformation near T_MCT.     

Submesoscale dispersion in the vicinity of the Deepwater Horizon spill

Reliable forecasts for the dispersion of oceanic contamination are important for coastal ecosystems, society, and the economy as evidenced by the Deepwater Horizon oil spill in the Gulf of Mexico in 2010 and the Fukushima nuclear plant incident in the Pacific Ocean in 2011. Accurate prediction of pollutant pathways and concentrations at the ocean surface requires understanding ocean dynamics over a broad range of spatial scales. Fundamental questions concerning the structure of the velocity field at the submesoscales (100 m to tens of kilometers, hours to days) remain unresolved due to a lack of synoptic measurements at these scales. Using high-frequency position data provided by the near-simultaneous release of hundreds of accurately tracked surface drifters, we study the structure of submesoscale surface velocity fluctuations in the Northern Gulf of Mexico. Observed two-point statistics confirm the accuracy of classic turbulence scaling laws at 200-m to 50-km scales and clearly indicate that dispersion at the submesoscales is local, driven predominantly by energetic submesoscale fluctuations. The results demonstrate the feasibility and utility of deploying large clusters of drifting instruments to provide synoptic observations of spatial variability of the ocean surface velocity field. Our findings allow quantification of the submesoscale-driven dispersion missing in current operational circulation models and satellite altimeter-derived velocity fields.The Deepwater Horizon (DwH) incident was the largest accidental oil spill into marine waters in history with some 4.4 million barrels released into the DeSoto Canyon of the northern Gulf of Mexico (GoM) from a subsurface pipe over ∼84 d in the spring and summer of 2010 (1). Primary scientific questions, with immediate practical implications, arising from such catastrophic pollutant injection events are the path, speed, and spreading rate of the pollutant patch. Accurate prediction requires knowledge of the ocean flow field at all relevant temporal and spatial scales. Whereas ocean general circulation models were widely used during and after the DwH incident (2–6), such models only capture the main mesoscale processes (spatial scale larger than 10 km) in the GoM. The main factors controlling surface dispersion in the DeSoto Canyon region remain unclear. The region lies between the mesoscale eddy-driven deep water GoM (7) and the wind-driven shelf (8) while also being subject to the buoyancy input of the Mississippi River plume during the spring and summer months (9). Images provided by the large amounts of surface oil produced in the DwH incident revealed a rich array of flow patterns (10) showing organization of surface oil not only by mesoscale straining into the loop current “Eddy Franklin,” but also by submesoscale processes. Such processes operate at spatial scales and involve physics not currently captured in operational circulation models. Submesoscale motions, where they exist, can directly influence the local transport of biogeochemical tracers (11, 12) and provide pathways for energy transfer from the wind-forced mesoscales to the dissipative microscales (13–15). Dynamics at the submesoscales have been the subject of recent research (16–20). However, the investigation of their effect on ocean transport has been predominantly modeling based (13, 21–23) and synoptic observations, at adequate spatial and temporal resolutions, are rare (24, 25). The mechanisms responsible for the establishment, maintenance, and energetics of such features in the Gulf of Mexico remain unclear.Instantaneous measurement of all representative spatiotemporal scales of the ocean state is notoriously difficult (26). As previously reviewed (27), traditional observing systems are not ideal for synoptic sampling of near-surface flows at the submesoscale. Owing to the large spacing between ground tracks (28) and along-track signal contamination from high-frequency motions (29), gridded altimeter-derived sea level anomalies only resolve the largest submesoscale motions. Long time-series ship-track current measurements attain similar, larger than 2 km, spatial resolutions, and require averaging the observations over evolving ocean states (30). Simultaneous, two-point accoustic Doppler current profiler measurements from pairs of ships (25) provide sufficient resolution to show the existence of energetic submesoscale fluctuations in the mixed layer, but do not explicitly quantify the scale-dependent transport induced by such motions at the surface. Lagrangian experiments, centered on tracking large numbers of water-following instruments, provide the most feasible means of obtaining spatially distributed, simultaneous measurements of the structure of the ocean’s surface velocity field on 100-m to 10-km length scales.Denoting a trajectory by x(a, t), where x(a, t₀) = a, the relative separation of a particle pair is given by D(t,D0)=x(a1,t)−x(a2,t)=D0+∫t0tΔv(t′,D0)dt′, where the Lagrangian velocity difference is defined by Δv(t, D₀) = v(a₁, t) − v(a₂, t). The statistical quantities of interest, both practically and theoretically, are the scale-dependent relative dispersion D²(t) = 〈D ⋅ D〉 (averaged over particle pairs) and the average longitudinal or separation velocity, Δv(r), at a given separation, r. The velocity scale is defined by the second order structure function Δv(r)=〈δv2〉, where δv(r) = (v(x + r) − v(x)) ⋅ r/∥r∥ (31, 32) where the averaging is now conditioned on the pair separation r.The applicability of classical dispersion theories (32–34) developed in the context of homogeneous, isotropic turbulence with localized spectral forcing, to ocean flows subject to the effects of rotation, stratification, and complex forcing at disparate length and time scales remains unresolved. Turbulence theories broadly predict two distinct dispersion regimes depending upon the shape of the spatial kinetic energy spectrum, E(k) ∼ k^−β, of the velocity field (35). For sufficiently steep spectra (β ≥ 3) the dispersion is expected to grow exponentially, D ∼ e^λt with a scale-independent rate. At the submesoscales (∼ 100 m–10 km), this nonlocal growth rate will then be determined by the mesoscale motions currently resolved by predictive models. For shallower spectra (1 < β < 3), however, the dispersion is local, D ∼ t^2/(3−β), and the growth rate of a pollutant patch is dominated by advective processes at the scale of the patch. Accurate prediction of dispersion in this regime requires resolution of the advecting field at smaller scales than the mesoscale.Whereas compilations of data from dye measurements broadly support local dispersion in natural flows (36), the range of scales in any particular dye experiment is limited. A number of Lagrangian observational studies have attempted to fill this gap. LaCasce and Ohlmann (37) considered 140 pairs of surface drifters on the GoM shelf over a 5-y period and found evidence of a nonlocal regime for temporally smoothed data at 1-km scales. Koszalka et al. (38) using ??(100) drifter pairs with D₀ < 2 km launched over 18 mo in the Norwegian Sea, found an exponential fit for D²(t) for a limited time (t = 0.5 − 2 d), although the observed longitudinal velocity structure function is less clearly fit by a corresponding quadratic. They concluded that a nonlocal dispersion regime could not be identified. In contrast, Lumpkin and Elipot (39) found evidence of local dispersion at 1-km scales using 15-m drogued drifters launched in the winter-time North Atlantic. It is not clear how the accuracy of the Argos positioning system (150–1,000 m) used in these studies affects the submesoscale dispersion estimates. Schroeder et al. (40), specifically targeting a coastal front using a multiscale sampling pattern, obtained results consistent with local dispersion, but the statistical significance (maximum 64 pairs) remained too low to be definitive.     

Structures and topological defects in pressure-driven lyotropic chromonic liquid crystals

Lyotropic chromonic liquid crystals are water-based materials composed of self-assembled cylindrical aggregates. Their behavior under flow is poorly understood, and quantitatively resolving the optical retardance of the flowing liquid crystal has so far been limited by the imaging speed of current polarization-resolved imaging techniques. Here, we employ a single-shot quantitative polarization imaging method, termed polarized shearing interference microscopy, to quantify the spatial distribution and the dynamics of the structures emerging in nematic disodium cromoglycate solutions in a microfluidic channel. We show that pure-twist disclination loops nucleate in the bulk flow over a range of shear rates. These loops are elongated in the flow direction and exhibit a constant aspect ratio that is governed by the nonnegligible splay-bend anisotropy at the loop boundary. The size of the loops is set by the balance between nucleation forces and annihilation forces acting on the disclination. The fluctuations of the pure-twist disclination loops reflect the tumbling character of nematic disodium cromoglycate. Our study, including experiment, simulation, and scaling analysis, provides a comprehensive understanding of the structure and dynamics of pressure-driven lyotropic chromonic liquid crystals and might open new routes for using these materials to control assembly and flow of biological systems or particles in microfluidic devices.

Lyotropic chromonic liquid crystals (LCLCs) are aqueous dispersions of organic disk-like molecules that self-assemble into cylindrical aggregates, which form nematic or columnar liquid crystal phases under appropriate conditions of concentration and temperature (1–6). These materials have gained increasing attention in both fundamental and applied research over the past decade, due to their distinct structural properties and biocompatibility (4, 7–14). Used as a replacement for isotropic fluids in microfluidic devices, nematic LCLCs have been employed to control the behavior of bacteria and colloids (13, 15–20).Nematic liquid crystals form topological defects under flow, which gives rise to complex dynamical structures that have been extensively studied in thermotropic liquid crystals (TLCs) and liquid crystal polymers (LCPs) (21–29). In contrast to lyotropic liquid crystals that are dispersed in a solvent and whose phase can be tuned by either concentration or temperature, TLCs do not need a solvent to possess a liquid-crystalline state and their phase depends only on temperature (30). Most TLCs are shear-aligned nematics, in which the director evolves toward an equilibrium out-of-plane polar angle. Defects nucleate beyond a critical Ericksen number due to the irreconcilable alignment of the directors from surface anchoring and shear alignment in the bulk flow (24, 31–33). With an increase in shear rate, the defect type can transition from π-walls (domain walls that separate regions whose director orientation differs by an angle of π) to ordered disclinations and to a disordered chaotic regime (34). Recent efforts have aimed to tune and control the defect structures by understanding the relation between the selection of topological defect types and the flow field in flowing TLCs. Strategies to do so include tuning the geometry of microfluidic channels, inducing defect nucleation through the introduction of isotropic phases or designing inhomogeneities in the surface anchoring (35–39). LCPs are typically tumbling nematics for which α2α3 < 0, where α2 and α3 are the Leslie viscosities. This leads to a nonzero viscous torque for any orientation of the director, which allows the director to rotate in the shear plane (22, 29, 30, 40). The tumbling character of LCPs facilitates the nucleation of singular topological defects (22, 40). Moreover, the molecular rotational relaxation times of LCPs are longer than those of TLCs, and they can exceed the timescales imposed by the shear rate. As a result, the rheological behavior of LCPs is governed not only by spatial gradients of the director field from the Frank elasticity, but also by changes in the molecular order parameter (25, 41–43). With increasing shear rate, topological defects in LCPs have been shown to transition from disclinations to rolling cells and to worm-like patterns (25, 26, 43).Topological defects occurring in the flow of nematic LCLCs have so far received much more limited attention (44, 45). At rest, LCLCs exhibit unique properties distinct from those of TLCs and LCPs (1, 2, 4–6, 44). In particular, LCLCs have significant elastic anisotropy compared to TLCs; the twist Frank elastic constant, K2, is much smaller than the splay and bend Frank elastic constants, K1 and K3. The resulting relative ease with which twist deformations can occur can lead to a spontaneous symmetry breaking and the emergence of chiral structures in static LCLCs under spatial confinement, despite the achiral nature of the molecules (4, 46–51). When driven out of equilibrium by an imposed flow, the average director field of LCLCs has been reported to align predominantly along the shear direction under strong shear but to reorient to an alignment perpendicular to the shear direction below a critical shear rate (52–54). A recent study has revealed a variety of complex textures that emerge in simple shear flow in the nematic LCLC disodium cromoglycate (DSCG) (44). The tumbling nature of this liquid crystal leads to enhanced sensitivity to shear rate. At shear rates γ˙<1 s−1, the director realigns perpendicular to the flow direction adapting a so-called log-rolling state characteristic of tumbling nematics. For 1 s−1<γ˙<10 s−1, polydomain textures form due to the nucleation of pure-twist disclination loops, for which the rotation vector is parallel to the loop normal, and mixed wedge-twist disclination loops, for which the rotation vector is perpendicular to the loop normal (44, 55). Above γ˙>10 s−1, the disclination loops gradually transform into periodic stripes in which the director aligns predominantly along the flow direction (44).Here, we report on the structure and dynamics of topological defects occurring in the pressure-driven flow of nematic DSCG. A quantitative evaluation of such dynamics has so far remained challenging, in particular for fast flow velocities, due to the slow image acquisition rate of current quantitative polarization-resolved imaging techniques. Quantitative polarization imaging traditionally relies on three commonly used techniques: fluorescence confocal polarization microscopy, polarizing optical microscopy, and LC-Polscope imaging. Fluorescence confocal polarization microscopy can provide accurate maps of birefringence and orientation angle, but the fluorescent labeling may perturb the flow properties (56). Polarizing optical microscopy requires a mechanical rotation of the polarizers and multiple measurements, which severely limits the imaging speed. LC-Polscope, an extension of conventional polarization optical microscopy, utilizes liquid crystal universal compensators to replace the compensator used in conventional polarization microscopes (57). This leads to an enhanced imaging speed and better compensation for polarization artifacts of the optical system. The need for multiple measurements to quantify retardance, however, still limits the acquisition rate of LC-Polscopes.We overcome these challenges by using a single-shot quantitative polarization microscopy technique, termed polarized shearing interference microscopy (PSIM). PSIM combines circular polarization light excitation with off-axis shearing interferometry detection. Using a custom polarization retrieval algorithm, we achieve single-shot mapping of the retardance, which allows us to reach imaging speeds that are limited only by the camera frame rate while preserving a large field-of-view and micrometer spatial resolution. We provide a brief discussion of the optical design of PSIM in Materials and Methods; further details of the measurement accuracy and imaging performance of PSIM are reported in ref. 58.Using a combination of experiments, numerical simulations and scaling analysis, we show that in the pressure-driven flow of nematic DSCG solutions in a microfluidic channel, pure-twist disclination loops emerge for a certain range of shear rates. These loops are elongated in the flow with a fixed aspect ratio. We demonstrate that the disclination loops nucleate at the boundary between regions where the director aligns predominantly along the flow direction close to the channel walls and regions where the director aligns predominantly perpendicular to the flow direction in the center of the channel. The large elastic stresses of the director gradient at the boundary are then released by the formation of disclination loops. We show that both the characteristic size and the fluctuations of the pure-twist disclination loops can be tuned by controlling the flow rate.     

Direct visualization of polaron formation in the thermoelectric SnSe

SnSe is a layered material that currently holds the record for bulk thermoelectric efficiency. The primary determinant of this high efficiency is thought to be the anomalously low thermal conductivity resulting from strong anharmonic coupling within the phonon system. Here we show that the nature of the carrier system in SnSe is also determined by strong coupling to phonons by directly visualizing polaron formation in the material. We employ ultrafast electron diffraction and diffuse scattering to track the response of phonons in both momentum and time to the photodoping of free carriers across the bandgap, observing the bimodal and anisotropic lattice distortions that drive carrier localization. Relatively large (18.7 Å), quasi-one-dimensional (1D) polarons are formed on the 300-fs timescale with smaller (4.2 Å) 3D polarons taking an order of magnitude longer (4 ps) to form. This difference appears to be a consequence of the profoundly anisotropic electron–phonon coupling in SnSe, with strong Fröhlich coupling only to zone-center polar optical phonons. These results demonstrate a high density of polarons in SnSe at optimal doping levels. Strong electron-phonon coupling is critical to the thermoelectric performance of this benchmark material and, potentially, high performance thermoelectrics more generally.

Thermoelectric materials convert a difference in temperature into an electrical potential (i.e., the thermoelectric effect) and promise to become increasingly important components of energy-harvesting devices and technologies (1–3). This could make a significant contribution to sustainability efforts by enabling electrical power generation from otherwise wasted heat. Unfortunately, the combination of thermal and electrical properties that leads to high thermoelectric performance is not found in naturally occurring materials (4); efficient thermoelectrics must be engineered. The figure of merit for thermoelectric efficiency is ZT=(S2σ/κ)T, where T is the absolute temperature, S is the Seebeck coefficient (induced voltage per temperature gradient), σ is the electrical conductivity, and κ is the thermal conductivity. Historically, increasing ZT has consisted in starting with compounds with a high Seebeck coefficient (e.g., selenides), and then selecting for good electrical conductivity and low thermal conductivity. In this sense, the ideal thermoelectric has been referred to as a “phonon glass–electron crystal” (5)—a concept that, interestingly, also seems to apply to lead halide perovskite light-harvesting materials (6). Nanostructuring has also been explored as a way to further reduce the thermal conductivity of thermoelectrics without significantly impacting electrical conductivity (7), but concerns regarding manufacturing and longevity favor the use of bulk materials (8). In practice, attempts to optimize the performance of bulk thermoelectric materials by favorably influencing a single parameter have not been a successful strategy, because the key properties are all interdependent (7). Thus, developing a more sophisticated understanding of the fundamental interdependencies between key material parameters (S, σ, and κ) is widely recognized as critical to the development of high-performance thermoelectrics.Recently, tin selenide (SnSe) has been shown to exhibit remarkable thermoelectric efficiency, while also being non–lead based and composed of earth-abundant elements (9–11). Its high performance owes to three factors: 1) an anomalously low lattice thermal conductivity ¡1 W·m−1 ·K⁻¹ (9) at room temperature that decreases even further at higher temperature, 2) an electrical conductivity that increases notably above 600 K, and 3) a high Seebeck coefficient. These factors combine to yield a profound enhancement in thermoelectric performance in SnSe above 600 K, from ZT≈0.1 to a maximum ZT > 2 at 800 K (9, 10). In the case of undoped SnSe, this enhancement is associated with a second-order Pnma→Cmcm phase transition (Fig. 1 A and B) of a displacive character (15) but, at a microscopic level, is related to changes in the character of the electron–phonon (16) and phonon–phonon (17) interactions that control electrical and thermal transport in the material.Open in a separate windowFig. 1.(A) SnSe has a layered orthorhombic structure in the Pnma phase at room temperature. (B) The Pnma structure is derived from 3D distortion of the higher-symmetry (distorted rock salt) Cmcm phase, which is stable above 750 K. Crystallographic directions are all given with respect to the low-temperature Pnma phase, and structures were rendered using Visualization for Electronic and Structural Analysis (VESTA) (12). (C) Diagram of the electronic structure of Pnma SnSe in the b⋆–c⋆ plane at 300 K. Three distinct valleys are present in both the valence and conduction bands: at Γ, 2/3 Y, and 3/4 Z (13). Photoexcitation at 800 nm (1.55 eV) photodopes electrons and holes into all three valleys. (D) Schematic (single valley) band structure diagram immediately following photoexcitation, which generates delocalized conduction band electrons (equivalent picture for holes not shown). (E) Schematic band structure diagram after carrier localization indicating a polaron peak below the Fermi energy E_F. (F) Configuration coordinate showing the free energy of the system as carriers self-localize via phonon dressing; that is, the generation of a local lattice distortion (14). The phonon wavevector dependence of this dressing process is probed directly through the UEDS experiments reported here.Unlike most previous studies, which have attempted to understand the enhancement of thermoelectric properties in SnSe in terms of lattice anharmonicity and the Pnma→Cmcm phase transition (17–20), in this work, we focus on the momentum dependence of electron–phonon coupling in the Pnma phase specifically (21). We seek to develop a full understanding of the carrier–lattice interactions that may also contribute to thermoelectric performance. To this end, we use ultrafast electron diffraction (UED) and ultrafast electron diffuse scattering (UEDS) (22–26) to directly probe electron–phonon interactions in momentum and time following the photodoping of carriers (Fig. 1C). A feature of these ultrafast measurements is that they freeze out changes in electronic and phonon band structure that result from in-plane thermal expansion (temperature-dependent lattice constants), uncoupling those effects from those due exclusively to the photodoped carriers that are the subject of our investigations. The results presented here clearly reveal profoundly momentum-dependent electron–phonon coupling in SnSe, as is expected from Fröhlich coupling in a polar lattice (16). However, the ultrafast diffuse scattering signals also show clear signatures of the “phonon dressing” (lattice distortion) that drives photocarrier localization and polaron formation (Fig. 1 D–F), even at high levels of photocarrier doping [equivalent to the doping levels previously used to optimize the power factor in SnSe (10)].     

Taylor’s law of fluctuation scaling for semivariances and higher moments of heavy-tailed data

We generalize Taylor’s law for the variance of light-tailed distributions to many sample statistics of heavy-tailed distributions with tail index α in (0, 1), which have infinite mean. We show that, as the sample size increases, the sample upper and lower semivariances, the sample higher moments, the skewness, and the kurtosis of a random sample from such a law increase asymptotically in direct proportion to a power of the sample mean. Specifically, the lower sample semivariance asymptotically scales in proportion to the sample mean raised to the power 2, while the upper sample semivariance asymptotically scales in proportion to the sample mean raised to the power (2−α)/(1−α)>2. The local upper sample semivariance (counting only observations that exceed the sample mean) asymptotically scales in proportion to the sample mean raised to the power (2−α2)/(1−α). These and additional scaling laws characterize the asymptotic behavior of commonly used measures of the risk-adjusted performance of investments, such as the Sortino ratio, the Sharpe ratio, the Omega index, the upside potential ratio, and the Farinelli–Tibiletti ratio, when returns follow a heavy-tailed nonnegative distribution. Such power-law scaling relationships are known in ecology as Taylor’s law and in physics as fluctuation scaling. We find the asymptotic distribution and moments of the number of observations exceeding the sample mean. We propose estimators of α based on these scaling laws and the number of observations exceeding the sample mean and compare these estimators with some prior estimators of α.

Heavy-tailed nonnegative random variables with infinite moments, such as nonnegative stable laws with index α in (0,1), have theoretical and practical importance [e.g., Carmona (1), Feller (2), Resnick (3), and Samorodnitsky and Taqqu (4)]. Heavy-tailed nonnegative random variables with some or all infinite moments have been claimed to arise empirically in finance [operational risks in Nešlehová et al. (5)], economics [income distributions in Campolieti (6) and Schluter (7); returns to technological innovations in Scherer et al. (8) and Silverberg and Verspagen (9)], demography [city sizes in Cen (10)], linguistics [word frequencies in Bérubé et al. (11)], and insurance [economic losses from earthquakes in Embrechts et al. (12) and Ibragimov et al. (13)]. Partial reviews are in Carmona (1) and Ibragimov (14).Brown et al. (15) (hereafter BCD) showed that when a random sample is drawn from a nonnegative stable law with index α∈(0,1), the sample variance is asymptotically (as the sample size n goes to ∞) proportional to the sample mean raised to a power that is an explicit function of α (Eqs. 11 and 13). This relationship generalizes to stable laws with infinite moments a widely observed power-law relationship between the variance and the mean in families of distributions with finite population mean and finite population variance. This power-law relationship is commonly known as Taylor’s law in ecology [Taylor (16, 17)] and as fluctuation scaling in physics [Eisler et al. (18)].To the two ingredients combined by BCD (nonnegative stable laws with infinite moments and Taylor’s law), this paper adds two more ingredients. We establish scaling relationships that generalize the usual Taylor’s law, for light-tailed distributions, to many functions of the sample in addition to the variance, including all positive absolute and central moments, upper and lower semivariances, and several measures of risk-adjusted investment performance such as the Sortino, Sharpe, and Farinelli–Tibiletti ratios. In addition, based on these scaling relationships, we propose several estimators of the index α of a nonnegative stable law with infinite first moment.Section 1 defines most of the sample functions studied here. Section 2 gives background on Taylor’s law, semivariances, and nonnegative stable laws, including key prior results from BCD. Section 3 establishes that the lower sample semivariance, the upper sample semivariance, the local lower sample semivariance, and the local upper sample semivariance are asymptotically each a power of the sample mean with explicitly given exponents. These results are the core of the paper. When investment returns obey a nonnegative heavy-tailed law with index α∈(0,1), these results reveal the asymptotic behavior of the Sharpe ratio, the Sortino ratio, and the Farinelli–Tibiletti ratio. Section 4 extends these results to higher central and noncentral moments and various indices of volatility. Section 5 analyzes the number of observations from a stable law or an approximately stable (i.e., regularly varying) law that exceed the sample mean. Section 6 proposes and compares estimators of α by simulation. SI Appendix gives all proofs of results stated in the text and additional numerical simulations.     

Dynamic rupture initiation and propagation in a fluid-injection laboratory setup with diagnostics across multiple temporal scales

Fluids are known to trigger a broad range of slip events, from slow, creeping transients to dynamic earthquake ruptures. Yet, the detailed mechanics underlying these processes and the conditions leading to different rupture behaviors are not well understood. Here, we use a laboratory earthquake setup, capable of injecting pressurized fluids, to compare the rupture behavior for different rates of fluid injection, slow (megapascals per hour) versus fast (megapascals per second). We find that for the fast injection rates, dynamic ruptures are triggered at lower pressure levels and over spatial scales much smaller than the quasistatic theoretical estimates of nucleation sizes, suggesting that such fast injection rates constitute dynamic loading. In contrast, the relatively slow injection rates result in gradual nucleation processes, with the fluid spreading along the interface and causing stress changes consistent with gradually accelerating slow slip. The resulting dynamic ruptures propagating over wetted interfaces exhibit dynamic stress drops almost twice as large as those over the dry interfaces. These results suggest the need to take into account the rate of the pore-pressure increase when considering nucleation processes and motivate further investigation on how friction properties depend on the presence of fluids.

The close connection between fluids and faulting has been revealed by a large number of observations, both in tectonic settings and during human activities, such as wastewater disposal associated with oil and gas extraction, geothermal energy production, and CO₂ sequestration (1–11). On and around tectonic faults, fluids also naturally exist and are added at depths due to rock-dehydration reactions (12–15) Fluid-induced slip behavior can range from earthquakes to slow, creeping motion. It has long been thought that creeping and seismogenic fault zones have little to no spatial overlap. Nonetheless, growing evidence suggests that the same fault areas can exhibit both slow and dynamic slip (16–19). The existence of large-scale slow slip in potentially seismogenic areas has been revealed by the presence of transient slow-slip events in subduction zones (16, 18) and proposed by studies investigating the physics of foreshocks (20–22).Numerical and laboratory modeling has shown that such complex fault behavior can result from the interaction of fluid-related effects with the rate-and-state frictional properties (9, 14, 19, 23, 24); other proposed rheological explanations for complexities in fault stability include combinations of brittle and viscous rheology (25) and friction-to-flow transitions (26). The interaction of frictional sliding and fluids results in a number of coupled and competing mechanisms. The fault shear resistance τres is typically described by a friction model that linearly relates it to the effective normal stress σ^n via a friction coefficient f:τres=f σ^n=f (σn−p),[1]where σn is the normal stress acting across the fault and p is the pore pressure. Clearly, increasing pore pressure p would reduce the fault frictional resistance, promoting the insurgence of slip. However, such slip need not be fast enough to radiate seismic waves, as would be characteristic of an earthquake, but can be slow and aseismic. In fact, the critical spatial scale h* for the slipping zone to reach in order to initiate an unstable, dynamic event is inversely proportional to the effective normal stress (27, 28) and hence increases with increasing pore pressure, promoting stable slip. This stabilizing effect of increasing fluid pressure holds for both linear slip-weakening and rate-and-state friction; it occurs because lower effective normal stress results in lower fault weakening during slip for the same friction properties. For example, the general form for two-dimensional (2D) theoretical estimates of this so-called nucleation size, h*, on rate-and-state faults with steady-state, velocity-weakening friction is given by:h*=(μ*DRS)/[F(a,b)(σn−p)],[2]where μ*=μ/(1−ν) for modes I and II, and μ*=μ for mode III (29); DRS is the characteristic slip distance; and F(a, b) is a function of the rate-and-state friction parameters a and b. The function F(a, b) depends on the specific assumptions made to obtain the estimate: FRR(a,b)=4(b−a)/π (ref. 27, equation 40) for a linearized stability analysis of steady sliding, or FRA(a,b)=[π(b−a)2]/2b, with a/b>1/2 for quasistatic crack-like expansion of the nucleation zone (ref. 30, equation 42).Hence, an increase in pore pressure induces a reduction in the effective normal stress, which both promotes slip due to lower frictional resistance and increases the critical length scale h*, potentially resulting in slow, stable fault slip instead of fast, dynamic rupture. Indeed, recent field and laboratory observations suggest that fluid injection triggers slow slip first (4, 9, 11, 31). Numerical modeling based on these effects, either by themselves or with an additional stabilizing effect of shear-layer dilatancy and the associated drop in fluid pressure, have been successful in capturing a number of properties of slow-slip events observed on natural faults and in field fluid-injection experiments (14, 24, 32–34). However, understanding the dependence of the fault response on the specifics of pore-pressure increase remains elusive. Several studies suggest that the nucleation size can depend on the loading rate (35–38), which would imply that the nucleation size should also depend on the rate of friction strength change and hence on the rate of change of the pore fluid pressure. The dependence of the nucleation size on evolving pore fluid pressure has also been theoretically investigated (39). However, the commonly used estimates of the nucleation size (Eq. 2) have been developed for faults under spatially and temporally uniform effective stress, which is clearly not the case for fluid-injection scenarios. In addition, the friction properties themselves may change in the presence of fluids (40–42). The interaction between shear and fluid effects can be further affected by fault-gauge dilation/compaction (40, 43–45) and thermal pressurization of pore fluids (42, 46–48).Recent laboratory investigations have been quite instrumental in uncovering the fundamentals of the fluid-faulting interactions (31, 45, 49–57). Several studies have indicated that fluid-pressurization rate, rather than injection volume, controls slip, slip rate, and stress drop (31, 49, 57). Rapid fluid injection may produce pressure heterogeneities, influencing the onset of slip. The degree of heterogeneity depends on the balance between the hydraulic diffusion rate and the fluid-injection rate, with higher injection rates promoting the transition from drained to locally undrained conditions (31). Fluid pressurization can also interact with friction properties and produce dynamic slip along rate-strengthening faults (50, 51).In this study, we investigate the relation between the rate of pressure increase on the fault and spontaneous rupture nucleation due to fluid injection by laboratory experiments in a setup that builds on and significantly develops the previous generations of laboratory earthquake setup of Rosakis and coworkers (58, 59). The previous versions of the setup have been used to study key features of dynamic ruptures, including sub-Rayleigh to supershear transition (60); rupture directionality and limiting speeds due to bimaterial effects (61); pulse-like versus crack-like behavior (62); opening of thrust faults (63); and friction evolution (64). A recent innovation in the diagnostics, featuring ultrahigh-speed photography in conjunction with digital image correlation (DIC) (65), has enabled the quantification of the full-field behavior of dynamic ruptures (66–68), as well as the characterization of the local evolution of dynamic friction (64, 69). In these prior studies, earthquake ruptures were triggered by the local pressure release due to an electrical discharge. This nucleation procedure produced only dynamic ruptures, due to the nearly instantaneous normal stress reduction.To study fault slip triggered by fluid injection, we have developed a laboratory setup featuring a hydraulic circuit capable of injecting pressurized fluid onto the fault plane of a specimen and a set of experimental diagnostics that enables us to detect both slow and fast fault slip and stress changes. The range of fluid-pressure time histories produced by this setup results in both quasistatic and dynamic rupture nucleation; the diagnostics allows us to capture the nucleation processes, as well as the resulting dynamic rupture propagation. In particular, here, we explore two injection techniques: procedure 1, a gradual, and procedure 2, a sharp fluid-pressure ramp-up. An array of strain gauges, placed on the specimen’s surface along the fault, can capture the strain (translated into stress) time histories over a wide range of temporal scales, spanning from microseconds to tens of minutes. Once dynamic ruptures nucleate, an ultrahigh-speed camera records images of the propagating ruptures, which are turned into maps of full-field displacements, velocities, and stresses by a tailored DIC) analysis. One advantage of using a specimen made of an analog material, such as poly(methyl meth-acrylate) (PMMA) used in this study, is its transparency, which allows us to look at the interface through the bulk and observe fluid diffusion over the interface. Another important advantage of using PMMA is that its much lower shear modulus results in much smaller nucleation sizes h* than those for rocks, allowing the experiments to produce both slow and fast slip in samples of manageable sizes.We start by describing the laboratory setup and the diagnostics monitoring the pressure evolution and the slip behavior. We then present and discuss the different slip responses measured as a result of slow versus fast fluid injection and interpret our measurements by using the rate-and-state friction framework and a pressure-diffusion model.     

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.     

A new type of half-quantum circulation in a macroscopic polariton spinor ring condensate

We report the observation of coherent circulation in a macroscopic Bose–Einstein condensate of polaritons in a ring geometry. Because they are spinor condensates, half-quanta are allowed in where there is a phase rotation of π in connection with a polarization vector rotation of π around a closed path. This half-quantum behavior is clearly seen in the experimental observations of the polarization rotation around the ring. In our ring geometry, the half-quantum state that we see is one in which the handedness of the spin flips from one side of the ring to the other side in addition to the rotation of the linear polarization component; such a state is allowed in a ring geometry but will not occur in a simply connected geometry. This state is lower in energy than a half-quantum state with no change of the spin direction and corresponds to a superposition of two different elementary half-quantum states. The direction of circulation of the flow around the ring fluctuates randomly between clockwise and counterclockwise from one shot to the next; this fluctuation corresponds to spontaneous breaking of time-reversal symmetry in the system. This type of macroscopic polariton ring condensate allows for the possibility of direct control of the circulation to excite higher quantized states and the creation of Josephson junction tunneling barriers.Ring condensates, analogous to superconducting rings, have received much attention lately (1–9); among other predictions, a ring condensate allows the possibility of macroscopic superposition of states with different circulation. A ring condensate is topologically distinct from a condensate in a simply connected region.With the advance of the field of polariton condensates in the past few years, it is a natural step to create a condensate ring in a microcavity polariton system. The polariton system allows direct, nondestructive observation of the momentum distribution, energy distribution, and spatial distribution of the particles as well as direct measurement of the coherence properties through interferometry. To make a macroscopic ring requires macroscopic transport distances as well as macroscopic coherence length. Macroscopic coherence has been achieved with polaritons with coherent motion over tens of micrometers with lifetimes of 10–20 ps (10, 11) and coherent motion over hundreds of micrometers with lifetimes of 150–200 ps (12–14). One advantage of the long-lifetime polariton systems is that the polaritons can move well away from the laser spot where they are generated, so that the laser can be viewed as a simple source term and does not interact with the condensate. General reviews of previous polariton work with shorter transport distances are in refs. 15–19.The polaritons can be viewed as photons that have been given a small effective mass of the order of 10^?4 times the mass of a vacuum electron and repulsive interactions, which are about 10⁴ times stronger than the typical χ⁽³⁾ nonlinearities of photons in solids. The effective mass comes from the dispersion of the photons in a planar cavity, ℏω=ℏc(k∥2+k⊥)1/2, where k_⊥ is fixed by the width of the cavity, which implies that ℏω≃E0+ℏ2k∥2/2meff with m_eff = ?k_⊥/c for low k_∥. There are two circular polarization modes of the cavity photons corresponding to m = ±1 for the projection of the angular momentum on the z axis perpendicular to the plane. The strong interactions between photons are generated by mixing the photon states with a sharp excitonic resonance in a semiconductor inside the cavity, so that the photons pick up a fraction of the exciton–exciton interaction. Although their interactions are much stronger than the interactions of typical photons in a solid medium, the polaritons are still in the weakly interacting Bose gas regime.The structure for these experiments is a planar cavity, in which the mirrors are distributed Bragg reflectors of AlAs/AlGaAs and the exciton medium consists of GaAs/AlGaAs quantum wells embedded in this cavity. This structure has the same design as that used in previous experiments, which allows coherent transport of polaritons over hundreds of micrometers in the 2D plane of the cavity (12–14). Recent measurements (14) give the cavity lifetime as 135 ps, which corresponds to a polariton lifetime of 200 ps or more. Although this lifetime may seem to be short compared with atoms evaporating from an optical trap on timescales of seconds, the polariton lifetime is sufficient for them to interact many times with each other. In these long-lifetime polariton systems, the ratio of lifetime in the trap to the particle–particle collision time can be of the order of 500:1, comparable with the ratio for cold atom condensates.The lifetime of the polaritons and the strength of the interaction between the polaritons can be tuned by varying the energy difference between the photon states and the exciton states (known as the “detuning”), which leads to a varying degree of mixing of the photons and excitons. Because the planar cavity has a wedge that gives a gradient of cavity width, we can tune the strength of the polariton–polariton interactions simply by choosing different locations on the sample with different cavity width. There is a tradeoff in how much excitonic interaction character to give to the polaritons. Fewer interactions (more photon-like) allow long transport length, whereas more interactions allow better thermalization of the polariton gas through collisions and longer population lifetime.