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At least 163 records · Page 9

Thick strings, the liquid crystal blue phase, and cosmological large-scale structure

A phenomenological model based on the liquid crystal blue phase is proposed as a model for a late-time cosmological phase transition. Topological defects, in particular thick strings and/or domain walls, are presented as seeds for structure formation. It is shown that the observed large-scale structure, including quasi-periodic wall structure, can be well fitted in the model without violating the microwave background isotropy bound or the limits from induced gravitational waves and the millisecond pulsar timing. Furthermore, such late-time transitions can produce objects such as quasars at high redshifts. The model appears to work with either cold or hot dark matter.

Luo, Xiaochun↗

Study of self-assembly behavior and ionic conductivity of conjugated liquid crystals with T-shaped facial-polyphilic structure

The unique self-assembly of liquid crystals (LCs), combined with their potential application as organic semiconductors, has become a focus of recent research. Here, a joint experimental and computational study of the self-assembly and ionic conduction was carried out on a series of T-shaped conjugated LCs consisting of three incompatible components. By extending the EOn side-chain length, several experimental evaluations confirmed a decrease of the order-disorder transition temperature, while coarse-grained simulations revealed a structural evolution from a smectic phase to a columnar phase. Ionic conductivity of these molecules was achieved by adding Li salt, leading to a maximum conductivity of 1.1 × 10 −3 siemens per centimeter observed at 120°C. All-atom simulations were performed to examine the Li-ion solvation environment and to evaluate the intrachain and interchain Li-ion hopping mechanisms. The molecule with a long EOn side chain was found to generate a densely distributed network of Li-ion solvation sites, which can facilitate effective interchain hopping to promote ion transport.

Liu, Ziwei [Cornell Univ., Ithaca, NY (United Stat↗

Processing-Dependent Structure and Poroelasticity of Nafion in Liquid Water

Ionomers act as the solid polymer electrolyte membrane in many modern electrochemical devices, yet the role of their nanostructure in modulating the poroelastic response remains poorly understood, especially in liquid water, where few techniques can measure simultaneous transport-mechanical properties. Poroelastic Relaxation Indentation (PRI) is uniquely suited for measuring time-dependent transport-mechanical properties of porous solids, specifically hydraulic diffusivity, elastic modulus, Poisson’s ratio, and intrinsic permeability, for porous solids. While ionomers such as Nafion are not porous in the typical sense, Nafion has a nanophase-segregated structure that, when fully swollen in liquid water, behaves as a poroelastic solid with a coupled mechanical-transport response. Using a poroelastic framework, we investigate how casting and pretreatment of Nafion membranes alter their poroelastic response in liquid environments. We characterize both extruded and dispersion-cast Nafion membranes pretreated in water at 25 or 100 °C and relate the mechanical-transport properties to the ionomer structure via hydrophilic and intercrystalline domain spacing measured using Small-Angle X-ray Scattering (SAXS). At 25 °C, dispersion-cast membranes exhibit distinctly lower hydraulic diffusivity and intrinsic permeability than extruded membranes but with comparable mechanical properties. Pretreatment at 100 °C increases hydrophilic domain spacing, improving transport but at the expense of mechanical stiffness. Dispersion-cast membranes respond more strongly to pretreatment than extruded membranes. Using the Carman-Kozeny pore network model and the hydrophilic domain-spacing, we estimate the pore radius and tortuosity to show how pretreatment reduces structure-related tortuosity differences between dispersion-cast and extruded membranes. Here, in this work, we show that nanophase-segregated materials such as Nafion can be rigorously characterized using poroelasticity, resulting in physically meaningful transport-mechanical properties. Coupling PRI with SAXS provides insights into the nanostructural features that govern the coupled mechanical-transport response. By establishing PRI for a nanophase-segregated material, this approach opens avenues for this technique’s application in other hydrated polymeric materials not typically considered to be poroelastic.

Shen, Margaret [University of California, Berkeley↗

Neutrino beam bunch structure reconstruction with precision timing in the ICARUS liquid argon time projection chamber

The ICARUS detector has been operating smoothly since 2021 as the far detector in the Short Baseline Neutrino (SBN) program at Fermilab, collecting neutrino interactions from both the Booster Neutrino Beam (BNB) and off-axis from the Neutrinos at the Main Injector (NuMI) beam. Analysis of neutrino interactions in ICARUS requires mitigation of substantial cosmogenic backgrounds. This is achieved by using an external Cosmic Ray Tagger (CRT) and a Photomultiplier Tube (PMT) system embedded in the liquid argon. The intrinsic neutrino beam bunch structure, inherited time structure from the Radio Frequency (RF) system used to accelerate the protons, can be resolved at the ICARUS detector using precise timing information. Located at shallow depth, ICARUS is exposed to a high flux of cosmic rays that can be mistaken for neutrino interactions. To mitigate this background, the CRT and a 3-meter-thick concrete overburden were installed. To better model backgrounds, ICARUS makes use of an overlay technique where simulated neutrino events are superimposed on detector beam-off data. PMTs installed within a Time Projection Chamber detect argon scintillation light emitted by high energy charged particles passing through the chamber and provide the event timing of neutrino interactions. The nanosecond-level beam bunch structure is reconstructed with the PMT system and can be used to further understand backgrounds and enhance neutrino physics capabilities. In this thesis, I will discuss background mitigation techniques using precision timing and present a novel technique to select neutrino events from our unbiased data stream using the beam bunch structure.

Heggestuen, Anna [Colorado State U.] (ORCID:000000↗

Physics and Chemistry of Te and HgTe-based Ternary Melts

Historically, the theoretical treatment of the liquid phases has always been more difficult and complicated than that for solid and gas phases. A liquid has no lattice structure as crystalline solids and the atoms/molecules in the liquid can migrate through it relatively rapidly. On the other hand, it is also interacting with many other atoms/molecules so that the simplifications of the kinetic theory of gases cannot be employed. For more complicated liquids, such as the liquids of high ionicity and those containing hydrogen bonds and electric dipoles, the understanding is far from complete. At the same time, accurate information on the physics and chemistry of semiconductor melts is needed for the quantitative descriptions of the process of crystal growth from melt. The pre-crystallization phenomena in the liquid phase are critical because the properties of the grown crystals depend on the state and structure of the melt as well as the thermal history of the melt during solidification process. However, the data on the liquid phase, such as thermophysical properties of semiconductor melts are scarce, especially for the HgTe-based II-VI ternary compound semiconductors because of their high vapor pressure and extreme toxicity. Analysis of the thermophysical properties of the melt can provide information about structural transitions of the melt during the solidification process. From a broader point of view, the structure of liquids is much more complicated than the crystalline solids, especially the relaxation behavior through different thermal histories. The theory of hetero-phase fluctuations of liquids is applicable to any many-body systems including condensed-matter physics, field theory, physics of nuclear-matter, cosmology, biology and even sociology. This book summarizes the physics and chemistry from the experimental measurements and theoretical analyses of phase diagram, thermodynamic properties, density, thermal conductivity, viscosity, and electrical conductivity on the binary, pseudo-binary and ternary melts of the most advanced IR-detector material systems of HgCdTe and HgZnTe as well as the analyses of these results. The main objectives of this study are: (1) to provide the phase diagrams and thermodynamic properties of Hg-Cd-Te and Hg-Zn-Te systems through quantitatively fitting the experimental data by assuming an associated solution model for the liquid phase, (2) to experimentally measure the thermophysical properties of the Hg-Cd-Te and Hg-Zn-Te melts, including density, viscosity, electrical conductivity and thermal conductivity as functions of temperature and composition and (3) to enhance the fundamental knowledge of hetero-phase fluctuations and relaxation phenomena in the melts and extend our understanding of the solidification process in order to interpret the experimental results of crystal growth so as to improve the melt growth processes of the compound semiconductor. The physics and chemistry of Te and HgTe-based ternary melts were explored through the studies of the structural transformation during melting, the supercooling during solidification, the relaxation phenomena after rapid cooling of the melts and the metal-semiconductor transition in the melts through the analyses of electrical conductivity and Lorenz number. An in-depth study on the thermophysical properties and their time-dependent structural dynamic processes taking place in the vicinity of the solid-liquid phase transition of the narrow homogeneity range HgTe-based ternary semiconductors as well as the analysis of the homogenization process in the melt will also be presented.

Thermophysical properties↗

Structure, Hydrodynamics, and Phase Transition of Freely Suspended Liquid Crystals

Smectic liquid crystals are phases of rod shaped molecules organized into one dimensionally (1D) periodic arrays of layers, each layer being between one and two molecular lengths thick. In the least ordered smectic phases, the smectics A and C, each layer is a two dimensional (2D) liquid. Additionally there are a variety of more ordered smectic phases having hexatic short range translational order or 2D crystalline quasi long range translational order within the layers. The inherent fluid-layer structure and low vapor pressure of smectic liquid crystals enable the long term stabilization of freely suspended, single component, layered fluid films as thin as 30A, a single molecular layer. The layering forces the films to be an integral number of smectic layers thick, quantizing their thickness in layer units and forcing a film of a particular number of layers to be physically homogeneous with respect to its layer structure over its entire area. Optical reflectivity enables the precise determination of the number of layers. These ultrathin freely suspended liquid crystal films are structures of fundamental interest in condensed matter and fluid physics. They are the thinnest known stable condensed phase fluid structures and have the largest surface-to-volume ratio of any stable fluid preparation, making them ideal for the study of the effects of reduced dimensionality on phase behavior and on fluctuation and interface phenomena. Their low vapor pressure and quantized thickness enable the effective use of microgravity to extend the study of basic capillary phenomena to ultrathin fluid films. Freely suspended films have been a wellspring of new liquid crystal physics. They have been used to provide unique experimental conditions for the study of condensed phase transitions in two dimensions. They are the only system in which the hexatic has been unambiguously identified as a phase of matter, and the only physical system in which fluctuations of a 2D XY system and Kosterlitz Thouless phase transition has been observed and 2D XY quasi long range order verified. Smectic films have enabled the precise determination of smectic layer electron density and positional fluctuation profile and have been used to show that the interlayer interactions in anti-ferroelectric tilted smectics do not extend significantly beyond nearest neighbors. The interactions which are operative in liquid crystals are generally weak in comparison to those in crystalline phases, leading to the facile manipulation of the order in liquid crystals by external agents such as applied fields and surfaces. Effects arising from weak ordering are significantly enhanced in ultrathin free films and filaments wherein the intermolecular coupling is effectively reduced by loss of neighbors. Over the past four years this research, which we now detail, has produced a host of exciting new discoveries and unexpected results, maintaining the position of the study of freely suspended liquid crystal structures as one of most exciting and fruitful areas of complex fluid physics. In addition, several potentially interesting microgravity free film experiments have been identified.

Clark, Noel A.↗

Molecular dynamics based study on the effects of cation size on the local structure and diffusion in polymerized ionic liquids

We have used coarse-grained molecular dynamics simulations to understand the effect of cation size on ion diffusion in polymerized ionic liquids at temperatures well above the glass transition temperature of the polymers. We investigated dependencies of the diffusion constant on the cation radius and static dielectric constant and interpreted these results in terms of underlying structural changes, and decoupling phenomenon. We have found non-monotonic effects of the cation radius on the diffusion constant, with a maximum at an intermediate radius resulting from two different size dependent effects. Changes in the radial distribution functions characterizing spatial distribution of cations with respect to anions result in a monotonic increase in the coordination number. This yields an increase in the effective interaction energy as a function of cation radius, which can explain the decrease in the diffusion constant. This increase is counteracted at small cation radii by a corresponding increase in decoupling of cation and anion dynamics. In addition, the diffusion constant is found to increase on increasing the static dielectric constant for all radii of the cations. These results highlight the significant role of decoupling in designing polymerized ionic liquids with an enhanced diffusion constant of cations.

Gillespie, Colin [ORNL] (ORCID:0000000320287080)↗

Evaluation of the Transient Liquid Phase (TLP) Bonding Process for Ti3Al-Based Honeycomb Core Sandwich Structure

The suitability of using transient liquid phase (TLP) bonding to fabricate honeycomb core sandwich panels with Ti-14Al-21Nb (wt%) titanium aluminide (T3Al) face sheets for high-temperature hypersonic vehicle applications was evaluated. Three titanium alloy honeycomb cores and one Ti3Al alloy honeycomb core were investigated. Edgewise compression (EWC) and flatwise tension (FWT) tests on honeycomb core sandwich specimens and tensile tests of the face sheet material were conducted at temperatures ranging from room temperature to 1500 F. EWC tests indicated that the honeycomb cores and diffusion bonded joints were able to stabilize the face sheets up to and beyond the face sheet compressive yield strength for all temperatures investigated. The specimens with the T3Al honeycomb core produced the highest FWT strengths at temperatures above 1000 F. Tensile tests indicated that TLP processing conditions resulted in decreases in ductility of the Ti-14Al-21Nb face sheets. Microstructural examination showed that the side of the face sheets to which the filler metals had been applied was transformed from equiaxed alpha2 grains to coarse plates of alpha2 with intergranular Beta. Fractographic examination of the tensile specimens showed that this transformed region was dominated by brittle fracture.

Bird, R. Keith↗

Experimental studies of effects of tilt and structural asymmetry on vibration characteristics of thin-wall circular cylinders partly filled with liquid

The effects of tilt and structural asymmetry on the vibration characteristics of partly liquid-filled thin-wall cylinders were experimentally studied. It was found that tilting the longitudinal axis of a partly filled axisymmetric cylinder from the vertical could markedly reduce its resonant frequencies and change significantly the shape of the circumferential modes. For the minimum frequency modes, vibratory motion occurred only on that side of the cylinder where the liquid was deepest. An empirical equation was derived that gives the equivalent liquid depth of an untilted cylinder having the same minimum resonant frequency as a tilted, partly filled cylinder. Circumferential mode shapes of an untilted asymmetric cylinder were similar to those of the tilted, partly filled axisymmetric cylinder. Vibratory motion in the minimum frequency modes occurred in most instances only on the side of minimum thickness. Correlation between test data and results from a reformulated NASTRAN hydroelastic analysis was excellent.

Herr, R. W.↗

Double-Helical Tiled Chain Structure of the Twist-Bend Liquid Crystal Phase in CB7CB

The twist-bend nematic liquid crystal phase is a three-dimensional fluid in which achiral bent molecules spontaneously form an orientationally ordered, macroscopically chiral, heliconical winding of a ten nanometer-scale pitch in the absence of positional ordering. Here, the structure of the twist-bend phase of the bent dimer CB7CB and its mixtures with 5CB is characterized, revealing a hidden invariance of the self-assembly of the twist-bend structure of CB7CB, such that over a wide range of concentrations and temperatures, the helix pitch and cone angle change as if the ground state for a pitch of the TB helix is an inextensible heliconical ribbon along the contour formed by following the local molecular long axis (the director). Remarkably, the distance along the length for a single turn of this helix is given by 2πR mol , where R mol is the radius of bend curvature of a single all-trans CB7CB molecule. This relationship emerges from frustrated steric packing due to the bent molecular shape: space in the fluid that is hard to fill attracts the most flexible molecular subcomponents, a theme of nanosegregation that generates self-assembled, oligomer-like correlations of interlocking bent molecules in the form of a brickwork-like tiling of pairs of molecular strands into duplex double-helical chains. At higher temperatures in the twist-bend phase, the cone angle is small, the director contour is nearly along the helix axis z, and the duplex chains are sequences of biaxial elements formed by overlapping half-molecule pairs, with an approximately 45° rotation of the biaxis between each such element along the chain.

36 MATERIALS SCIENCE↗

Theory of Ion-Mediated Segmental Localization, Activated Structural Relaxation, and the Glass Transition in Polymerized Ionic Liquids

Here we combine polymer integral equation theory for structural correlations with a force-level theory for activated segmental relaxation to construct a microscopic theory for how ions modify the onset of segmental localization, the polymer alpha relaxation time, and glass transition temperature, T g , in dry polymerized ionic liquids (PolyILs). Our most important findings concerning the behavior of T g are (i) a weak dependence on anion–cation Coulomb attraction strength due to strong decoupling of ion and segmental dynamics, (ii) strong reduction with increasing mobile ion size due to both plasticization effects and weakening of ion-modified monomer caging, and (iii) increase with backbone rigidity and intrachain dynamic cooperativity. We quantitatively estimate T g variations as ion size and polymer static and dynamic rigidity are widely varied. The experimental data of 19 PolyILs are organized into a specific pattern consistent with the theoretical predictions with glass transition temperatures varying over a very wide range (~250 K) as observed experimentally. Based on the theoretical results, suggestions are made concerning the search for high conductivity Li- or Na-based PolyILs based on further lowering of T g via new polymer synthesis. Calculations of the alpha time as a function of packing fraction reveal the dynamic fragility increases for larger mobile ions, a more flexible backbone, and/or a smaller degree of intrachain dynamic cooperativity, as a consequence of the increasing importance of collective elasticity in determining the activation barrier. An analysis of transient segmental localization and a crossover to activated dynamics reveals similar, but not identical, trends as predicted at the laboratory vitrification timescale.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

In-situ/operando study of Cu-based nanocatalysts for CO 2 electroreduction using electrochemical liquid cell TEM

The structure of a nanocatalyst during electrocatalytic reactions often deviates from its pristine structure due to intrinsic properties, or physical and chemical adsorption at the catalytic surfaces. Taking Cu-based catalysts for CO 2 electroreduction reactions (CO 2 RR) as an example, they often experience segregation, leaching, and alloying during reactions. With the recent breakthrough development of high-resolution polymer electrochemical liquid cells, in-situ electrochemical liquid cell transmission electron microscopy (EC-TEM) alongside other advanced microscopy techniques, has become a powerful platform for revealing electrocatalysts restructuring at the atomic level. Considering the complex reactions involving electrified solid-liquid interfaces and catalyst structural evolution with intermediates, systematic studies with multimodal approaches are crucial. In this article, we demonstrate a research protocol for the study of electrocatalysts structural evolution during reactions using the in-situ EC-TEM platform. Using Cu and CuAg nanowire catalysts for CO 2 RR as model systems, we describe the experimental procedures and findings. We highlight the platform’s crucial role in elucidating atomic-scale pathways of nanocatalyst restructuring and identifying catalytic active sites, as well as avoiding potential artifacts to ensure unbiased conclusions. Using the multimodal characterization toolbox, we provide the opportunity to correlate the structure of a working catalyst with its performance. Finally, we discuss advancements as well as the remaining gap in elucidating the structural-performance relationship of working catalysts. We expect this article will assist in establishing guidelines for future investigations of complex electrochemical reactions, such as CO 2 RR and other catalytic processes, using the in-situ EC-TEM platform.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Anion-dependent phase behavior of methylimidazolium-based ionic liquids mixed with water: Correlation between local molecular structure and mesoscale behaviors

The mesoscopic phase behavior of decylmethylimidazolium (C 10 mim) ionic liquids (ILs) bearing three monovalent anions—thiocyanate (SCN − ), nitrate (NO 3 − ), and chloride (Cl − )—mixed with water at relatively high IL contents (50–95 wt%) was investigated. Small-angle and wide-angle X-ray scattering (SAXS/WAXS) were employed to follow the evolution of both local and mesoscale structures across this composition range. In the absence of water, C 10 mimSCN and C 10 mimCl behaved as disordered liquids, whereas C 10 mimNO 3 spontaneously formed a hexagonally ordered cylindrical mesophase and displayed a sticky-solid macroscopic appearance. Upon addition of water, C 10 mimSCN remained a viscous liquid and only weakly ordered lamellar domains were observed. This limited ordering is attributed to the lack of hydrogen bonding and weak interaction energy between SCN − anions and C 10 mim + cations. In contrast, the trigonal-planar NO 3 − and point-like Cl − anions promoted the formation of well-defined hexagonal mesophases up to 35–45 wt% water. The formation of hydrogen bonding of the two anions with imidazolium ring protons likely enabled the creation of compact ion clusters that effectively exclude water molecules from the immediate vicinity of the IL aggregates. These findings demonstrate that the interaction energy between ion pairs dictate IL-water interactions and therefore control the transition from disordered liquids to ordered mesophases in IL/water mixtures with high IL contents. In conclusion, the combined SAXS/WAXS analysis reveals a correlation between local intermolecular structure and the emergence of mesoscopic order, providing a systematic framework for tailoring mesoscale structures in alkylimidazolium-based IL/water systems.

36 MATERIALS SCIENCE↗

A shear sensitive monomer-polymer liquid crystal system for wind tunnel applications

Characteristics of a liquid crystal system, comprised of a shear-sensitive cholesteric-monomer liquid crystal thin-film coated on a liquid-crystal polymer substrate, are described. The system provides stable Grandjean texture, a desirable feature for shear-stress measurements using selective reflection from the monomer liquid-crystal helix structure. Impingement of gas or air flow on the monomer liquid-crystal free surface changes the wavelength of the selective reflection for an incident white light from red toward blue with increase in the rate of gas flow. The contrast of the selectively reflected light improves considerably by providing a thin black coating of about 5 microns at the monomer-polymer interface. The coating thickness is such that the steric interactions are still sufficiently strong to maintain Grandjean texture. For a small angle of incidence of a monochromatic light, the measurement of the reflected light intensity normal to the monomer-polymer liquid-crystal interface enables the determination of the wavelength for selective reflection as a function of the gas-flow differential pressure applied in the plane of the interface. The variation of the wavelength with the pressure is linear with a slope of about 2 nm/mmHg. Furthermore, the shear-stress effects are reversible unlike for monomer liquid crystal-metal systems used for flow visualization on wind-tunnel model surfaces. The present system offers a suitable method for direct on-line measurement of shear stress field from measurements of the wavelength for selective reflection for an incident white light.

Parmar, D. S.↗

Analytical Solution and Physics of a Propellant Damping Device

NASA design teams have been investigating options for "detuning" Ares I to prevent oscillations originating in the vehicle solid-rocket main stage from synching up with the natural resonance of the rest of the vehicle. An experimental work started at NASA MSFC center in 2008 using a damping device showed great promise in damping the vibration level of an 8 resonant tank. However, the mechanisms of the vibration damping were not well understood and there were many unknowns such as the physics, scalability, technology readiness level (TRL), and applicability for the Ares I vehicle. The objectives of this study are to understand the physics of intriguing slosh damping observed in the experiments, to further validate a Computational Fluid Dynamics (CFD) software in propellant sloshing against experiments with water, and to study the applicability and efficiency of the slosh damper to a full scale propellant tank and to cryogenic fluids. First a 2D fluid-structure interaction model is built to model the system resonance of liquid sloshing and structure vibration. A damper is then added into the above model to simulate experimentally observed system damping phenomena. Qualitative agreement is found. An analytical solution is then derived from the Newtonian dynamics for the thrust oscillation damper frequency, and a slave mass concept is introduced in deriving the damper and tank interaction dynamics. The paper will elucidate the fundamental physics behind the LOX damper success from the derivation of the above analytical equation of the lumped Newtonian dynamics. Discussion of simulation results using high fidelity multi-phase, multi-physics, fully coupled CFD structure interaction model will show why the LOX damper is unique and superior compared to other proposed mitigation techniques.

Yang, H. Q.↗

Tethered from the Head and from the Tail: The Structure of Hydroxyl-Functionalized Ionic Liquids

Ionic liquids with special functionalities are synthesized with the specific purpose of creating new patterns of interaction in the condensed phase. This Letter discusses the case of alcohol-functionalized ILs, the so-called HFILs, which are part of the larger cohort of task-specific ionic liquids. We find that this small chemical modification can cause massive changes in the liquid landscape when the cationic tails are longer. For prototypical ionic liquids, larger alkyl tails act as separators of charge networks, but in the case of HFILs these become physical charge network linkers. The OH functionality adds a large repertoire of interactions and correlations that were mostly unavailable to traditional ILs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Experimental and Theoretical Studies of Wetting and Multilayer Adsorption

The recent work with partially miscible binary liquid mixtures has established that the structure of the liquid-vapor interface can undergo a first-order phase transition from incomplete to complete wetting of the vapor as the temperature is raised. A discontinuity in the change of interfacial tension as a function of temperature at the phase transition has been predicted to occur in many systems and to play an important role in the growth of uniform composites from alloy melts at monotectic points. These measurements are the first to establish the order of the transition. Studies of capillary rise in SF6 in a unique interferometer have led to the first measurements of the thickness of wetting layers (or equivalently, multilayer adsorbed films) on a solid surface near a liquid-vapor critical point. Instabilities in wetting layers were observed. A theory for the instabilities is being developed and will be checked by both static and dynamic optical experiments. The effect of gravity on the apparent thickness of interfaces (as measured by ellipsometry) is under study.

Moldover, M. R.↗