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Device and methods for determination of molecular weight distributions of polymers and distributions of other polymer properties without physical separation

Devices and methods for determining the cumulative distribution of a polymer property in a reactor without physical separation of reaction subcomponents. The device includes a means of measuring an instantaneous property of the polymers being produced in a reaction vessel a plurality of times during a polymerization reaction as well as a means of determining the corresponding change in polymer concentration in the reaction vessel between measurements of the instantaneous polymer property. The device also includes a means of computing a statistical distribution appropriate to the polymer characteristic and applying the statistical distribution to a recently measured instantaneous value of the polymer property so as to have an instantaneous distribution of the polymer property and a means of adding together the instantaneous distributions of the polymer property in order to obtain the cumulative distribution of the polymer property in the reactor.

Reed, Wayne Frederick↗

Linear Viscoelastic Properties of Putative Cyclic Polymers Synthesized by Reversible Radical Recombination Polymerization (R3P)

Linear viscoelastic properties in both melt and solution states are reported for a series of poly(3,6-dioxa-1,8-octanedithiol) (polyDODT) made by reversible radical recombination polymerization (R 3 P) under conditions designed to produce linear (LDODT), cyclic (RDODT) and linear-cyclic mixtures (LRDODT). PolyDODT is amorphous (T g < -50 °C) and highly flexible (entanglement molecular weight M e,lin ≈ 1850 g/mol for LDODT). PolyDODT’s low T g and low M e,lin enable characterization over a wide dynamic range and a wide range of dimensionless weight-average molecular weight Z w = M w /M e,lin . Measurements at temperatures from -57 °C to 100 °C provide up to 18 deades of reduced frequency, which is necessary to characterize RDODT melts with Z w from 23 to 300. The two highest molecular weight polymers in the present RDODT series have such high M w (406k and 556k g/mol) that mass spectrometry, NMR spectroscopy, and even chemical assays for chain ends are unable to rule out up to 2 mol% linear contaminant. By studying the samples in solution (using dilution to reduce Z w ) we could compare their dynamics with those of previously established high-purity polystyrene (PS) rings (limited to Z w ≤ 13.6). RDODT solutions with Z w < 15 (concentrations <5wt% for RDODT-406k and 556k) have dynamic moduli G^* that accord with LCCC-purified PS rings in terms of the frequency dependence (including the absence of a plateau), the progression of shapes of G* as a function of Z w , and the linear scaling of their zero-shear viscosity η0 with M w . The shape of G* as a function of Z w for solutions of RDODT-406k and -556k also accord with lower M w RDODT melts (which have ≤ 1.3mol% linear contaminant). Thus, measurement of the linear viscoelastic properties of appropriate concentrations of high M w (>200k g/mol) putative cyclic polymers, in which linear chains evade spectroscopic detection, may provide an alternative means (though not fully proven) of validation of sample purity. When Z w > 15 (including all seven RDODT melts and eight of their solutions), G* has a rubbery plateau. This suggests that the onset of entanglement-like behavior in rings requires 4-5-fold greater Z w than is required for linear chains. Further, the plateau moduli of RDODT samples are indistinguishable from G N o of the corresponding LDODT (melt or matched-concentration solutions). In entangled linear polymers, the observation that G N o is independent of Z w follows from limitations on lateral fluctuations due to neighboring chains becoming independent of position along a given chain. The present results for RDODT suggest that this holds for sufficiently long endless chains, too. While the RDODT have the same G N o as entangled LDODT, when Z w > 60 the terminal relaxation, if reached at all, of RDODT extends to orders of magnitude lower frequency than an entangled linear polymer of the same Z w . Consequently, the viscosity of RDODT with Z w > 60 increases with Z w much more strongly than the 3.4-power observed for entangled linear polymers. Lastly, these novel polymers, with disulfide-linked backbone and broad relaxation time distribution may prove important in relation to biodegradable elastomers and materials with exceptional low-frequency dissipation, extending at least 12 decades below the onset of the rubbery plateau.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Characterization of two types of polysaccharides from Eremurus hissaricus roots growing in Tajikistan

Eremurus Hissaricus (E.hissaricus) is a native plant of Tajikistan that has been used in traditional medicine and whose raw components have been identified as having potential for the domestic economy. We have found that carbohydrates comprise 80–85% of the root biomass, from which we have characterized two types of polysaccharides: A water-soluble polysaccharide (WSP) and an acid-soluble polysaccharide (ASP), with 23% and 8% yields, respectively. The results from FTIR, HPAEC-PAD, HPSEC, methylation linkage analysis and NMR spectroscopy ( 1 H, 13 C, zTOCSY, HSQC, HSQCTOXY and HMBC) demonstrated that WSP has a backbone of (1 → 4)-linked β-d-mannopyranosyl and β-d-glucopyranosyl residues in a 1.5:1 M ratio, having acetylated groups, with weight-average molecular weights of 495 kDa. Analyses of ASP indicate that it is comprised of d-galactose, d-mannose, and d-glucose in a molar ratio of 1.8: 1.6: 1.0, which is consistent with a branched galactoglucomannan polysaccharide with (1 → 4)-linked β-pyranose configurations, and weight-average molecular weight of 179 kDa. The FTIR absorption bands in the region of 875–890 cm 1 and NMR spectroscopy data confirm the presence of β-pyranose configuration of main polysaccharide backbone in the both ASP and WSP samples. These polysaccharides are an available raw material with the potential for use in a number of industrial applications.

59 BASIC BIOLOGICAL SCIENCES↗

Process Variability Effects on Tensile Response in Injection Molded, Fluorinated Thermoplastics

The mechanical properties of fluorinated thermoplastics (i.e., tensile strength and elongation) can vary with changes in injection molding processing parameters. Four fluoropolymers are examined: poly(vinylidene fluoride) (PVDF) and random poly(vinylidene fluoride-co-chlorotrifluoroethylene) (PVDF-CTFE) with three CTFE concentrations. Dog bones were manufactured with various cylinder dwell times and mold cooling times to assess the manufacturing sensitivity to the tensile response. Dwell and cooling times increasingly impact mechanical performance as CTFE concentration increases. Specimens exhibit higher tensile strength as a function of injection order. The first injected specimen exhibits the lowest tensile strength and highest elongation in all copolymers. This trend becomes more pronounced among fluoropolymers with higher CTFE concentration and lower weight-averaged molecular weight. Parallel plate rheology was used to obtain the zero-shear viscosity as a function of material type, process, and injection order. We found that in the copolymers, the first injected sample exhibited a lower zero-shear viscosity than the next, which indicates a lower molecular weight in the first injected specimen. This phenomenon was not presented for the PVDF homopolymer. Copolymer mechanical uncertainties are hypothesized to result from the shorter molecular weight chains extruding out of the specimens' sides as a flash due to higher mobility with CTFE segments.

36 MATERIALS SCIENCE↗

Process Variability Effects on Tensile Response in Injection Molded, Fluorinated Thermoplastics

The mechanical properties of fluorinated thermoplastics (i.e., tensile strength and elongation) can vary with changes in injection molding processing parameters. Four fluoropolymers are examined: poly(vinylidene fluoride) (PVDF) and random poly(vinylidene fluoride-co-chlorotrifluoroethylene) (PVDF-CTFE) with three CTFE concentrations. Dog bones were manufactured with various cylinder dwell times and mold cooling times to assess the manufacturing sensitivity to the tensile response. Dwell and cooling times increasingly impact mechanical performance as CTFE concentration increases. Specimens exhibit higher tensile strength as a function of injection order. The first injected specimen exhibits the lowest tensile strength and highest elongation in all copolymers. This trend becomes more pronounced among fluoropolymers with higher CTFE concentration and lower weight-averaged molecular weight. Parallel plate rheology was used to obtain the zero-shear viscosity as a function of material type, process, and injection order. We found that in the copolymers, the first injected sample exhibited a lower zero-shear viscosity than the next, which indicates a lower molecular weight in the first injected specimen. This phenomenon was not present for the PVDF homopolymer. Copolymer mechanical uncertainties are hypothesized to result from the shorter molecular weight chains extruding out of the specimens’ sides as a flash due to higher mobility with CTFE segments.

36 MATERIALS SCIENCE↗

Bioconversion of Homogeneous Linear C-Lignin to Polyhydroxyalkanoates

Here, the bioconversion of homogeneous linear catechyl lignin (C-lignin) to polyhydroxyalkanoates (PHA) was examined for the first time in this study. C-lignins from vanilla, euphorbia, and candlenut seed coats (denoted as C1, C2, and C3, respectively) varied in their molecular structures, which showed different molecular weight distributions, etherification degrees, and contents of hydroxyl groups. A notable amount of nonetherified catechol units existed within C1 and C2 lignins, and these catechol units were consumed during fermentation. These results suggested that the nonetherified catechol structure was readily converted by Pseudomonas putida KT2440. Since the weight-average molecular weight of C2 raw lignin was 26.7% lower than that of C1, the bioconversion performance of C2 lignin was more outstanding. The P. putida KT2440 cell amount reached the maximum of 9.3 × 10 7 CFU/mL in the C2 medium, which was 37.9 and 82.4% higher than that in the C1 and C3 medium, respectively. Accordingly, PHA concentration reached 137 mg/L within the C2 medium, which was 41.2 and 149.1% higher than the C1 and C3 medium, respectively. Overall, C-lignin, with a nonetherified catechol structure and low molecular weight, benefits its microbial conversion significantly.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Impacts of Hydrogen Bond Donor Structures in Phenolic Aldehyde Deep Eutectic Solvents on Pretreatment Efficiency

As a green solvent for biomass processing, deep eutectic solvents (DESs) have shown effectiveness in biomass processing. Here, in this study, phenolic aldehydes with different numbers of methoxy groups, including 4-hydroxybenzaldehyde (HBA, no methoxy), vanillin (VA, monomethoxy), and syringaldehyde (SA, dimethoxy) were employed to synthesize DESs with choline chloride (ChCl). The presence of methoxy groups in the hydrogen bond donor structure affected DES properties, as well as biomass pretreatment performance. The high thermal stability of phenolic aldehyde DESs was shown with over 225 °C onset temperature. The hydrogen bond donor with one aldehyde and one hydroxyl group at the para position without a methoxy group (ChCl-HBA) showed the highest xylan removal and delignification, reaching 59.3 and 88.0%, respectively, leading to the highest enzymatic hydrolysis yield. Sonication after pretreatment further enhanced the hydrolysis yields, achieving 83.3% glucan conversion and 50.1% xylan conversion. In the lignin-rich fraction, the recovered lignin showed a low weight–average molecular weight under 2100 g/mol with a relatively uniform molecular weight dispersity below 1.5. This study provides insights into how the chemical structure of hydrogen bond donors in DESs affects biomass processing and paves the way for designing effective lignin-derived DES in future biorefinery processes.

09 BIOMASS FUELS↗

Methods of recovering lignin and other products from biomass

Methods of recovering lignin products and other products from biomass. The method comprises adding a chemical agent to a stored biomass comprising lignin to form a chemically-treated biomass. The chemical agent comprises an acid, a base, an inorganic salt, or a combination of the inorganic salt and one of the acid or the base. The chemically-treated biomass is stored under anaerobic conditions. Lignin products, such as high molecular weight lignin, medium molecular weight lignin, or low molecular weight lignin, are recovered from the chemically-treated biomass. Additional methods of recovering lignin products and other products from biomass are disclosed.

09 BIOMASS FUELS↗

Synthesis and characterization of biobased copolyesters based on pentanediol: (2) Poly(pentylene adipate–co–terephthalate)

Traditionally, most flexible food packaging is made of linear low-density polyethylene (LLDPE) which cannot easily be recycled, nor will it degrade in a reasonable timescale. In this work, a biobased biodegradable polyester alternative was investigated as a possible replacement for LLDPE. High molecular weight poly (pentylene adipate-co-terephthalate) with a 40/60 adipic acid/terephthalic acid mole ratio was synthesized using direct esterification and polycondensation. Glycerol and hexane-1,2,5,6-tetrol were added as branching agents to better match the structure of the LLDPE which in turn might help the ability of these materials in film-blowing. Thermal, mechanical, and rheological properties of the copolyesters were thoroughly investigated. All copolyesters had a weight-average molecular weight of over 140,000 g/mol, which is necessary for proper rheology, and were thermally stable up to 350°C. Here, the addition of branching agents led to a slight decrease in crystallinity, d-spacing, melting temperature, enthalpy of melting, stress at break, and elongation at break. However, an increase in Young's modulus and complex viscosity at high frequency were observed compared to PPeAT60 without branching agent added. Although the improved crystallinity and mechanical properties of the copolyesters made them viable for film-blowing, the slow crystallization rate creates a major challenge.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effect of Macro- and Microstructures on Catalytic Hydrogenolysis of Polyolefins

Here, polyethylenes of varying molecular weight and branch density, as well as polypropylenes of varying molecular weight and tacticity, were catalytically converted to lower-molecular-weight liquid products to showcase how these various properties in a mixed waste plastic stream could affect the final product. A Pt nanoparticle on a strontium titanate nanocuboid (Pt/STO) catalyst was used under solvent-free conditions in the presence of 170 psi of H 2 at 300 °C for hydrogenolysis. The initial molecular weight of polyethylene was found to have a moderate effect on the yield to the final product (ranging from 55 wt% for M n ~ 7600 Da to 67 wt% for M n ~ 50,950 Da). The microstructure, defined as the length and density of branches in a polymer, of higher-molecular-weight polymers was the dominant factor in determining the yield (ranging from 67 wt% for M n ~ 50,950 Da for linear low-density polyethylene (LLDPE) with C 2 branches to 97 wt% for M n ~ 38,850 Da for LLDPE with C 6 branches). The same products (M n = C 29 –C 46 , Ð = 1.1–1.6) and distribution of undesired light gases (C 1 –C 4 ≈ 90 mol%, C 5 –C 8 ≈ 10 mol%) are obtained from conversions of PE of varying molecular weight. The tacticity of polypropylene at a given molecular weight had a significant effect on the molecular weight of the final product, while not strongly affecting conversion. Hydrogenolysis of isotactic polypropylene (iPP) produced ≈C 18 with a wider polydispersity (Ð ~ 1.4) compared to the narrow ≈C 64 (Ð ~ 1.0) and ≈C 54 (Ð ~ 1.0) products from atactic (aPP) and syndiotactic (sPP) polypropylene, respectively. The stereochemistry of the methyl groups dictates the shape and structure of the polymer in the melt, which in turn affects how the hydrocarbon chain interacts with the catalyst surface, thereby impacting the number of C–C scissions. These results show how various characteristics such as the molecular weight and structure of a waste plastic stream could affect the final product.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multifunctional Tunable Polymethacrylates for Enhanced Shear Stability and Wear Prevention

This paper describes the design, synthesis, and characterization of linear, polar, and non-polar polymethacrylates designed for use as lubricant viscosity index improvers with enhanced shear and anti-wear resistance. The polymers were prepared via Reversible Addition-Fragmentation Chain Transfer (RAFT) to obtain relatively low, narrow, molecular weights, with random polar moieties. The resulting polymers were evaluated as oil solutions to determine their viscosity index, shear stability performance, and antiwear characteristics. The polymers had molecular weights (Mw) ranging from 120-170 kDa, and the resulting viscosity indexes (VIs) in general tracked the Mw. Although the VIs were modest (140-189), all polymers displayed higher values than a commercial product designed for similar applications, both at 2% (w/w) and when kinematic viscosities (KVs) were normalized to the lowest KV100 of ~5cSt. One of the imidazole-containing polymers displayed an anomalously high VI for a low apparent Mw. As hypothesized, many of the polar polymers demonstrated substantial wear reduction compared to the non-polar homopolymers or a commercial benchmark. The low-molecular-weight imidazole-containing polymer produced less than 4% of the wear displayed by the commercial standard. The higher molecular weight polymers containing imidazole, hydroxy group and amino group also produced as little as 10% of the wear shown by the benchmark. The strategy demonstrated the benefit of low, narrow, molecular weight polymers to achieve good shear stability in viscosity modifiers while minimizing wear, rendering them suitable for fluid-power applications.

friction modifiers↗

Liquid bicontinuous stabilized assemblies by interfacial jamming of nanoparticles

A method for preparing a stabilized assembly includes combining a first liquid phase including nanoparticles and a second, immiscible liquid phase, dissolving in the second phase a first end-functionalized polymer having a first molecular weight, and a second end-functionalized polymer having a second molecular weight, wherein the second molecular weight is greater than the first molecular weight, applying a shearing external deformation field to increase the surface area of the first phase to create a new interface, wherein the nanoparticle surfactants form a disordered, jammed assembly at the new interface, and releasing the shearing external deformation field. The polymer and the nanoparticles can interact at an interface through ligand interactions to form nanoparticle surfactants and upon releasing the external deformation field the jammed assembly at the new interface traps the first phase in a deformed state having the first liquid phase and the second liquid phase as interpenetrating domains.

Huang, Caili↗

PolyDODT: a macrocyclic elastomer with unusual properties

The effect of reaction conditions on the structure of poly(3,6-dioxa-1,8-octanedithiol) (polyDODT) made by Reversible Radical Recombination Polymerization (R3P) using triethylamine (TEA), H 2 O 2 and air was investigated. 800 MHz (1 and 2D) NMR was used to investigate the polymer structures. Sensitivity analysis provided direct evidence for high purity cyclic polyDODT up to M n ~ 100 000 g mol –1 . Here, comparative analysis by High Resolution Multidetector Size Exclusion Chromatography (SEC) using integrated data showed that the cycles had lower viscosity and were more compact (both for R g and R h ) than linear samples of similar molecular weight. However, differential data revealed unusual behavior. While lower molecular weight cyclic polymers eluted later and had lower intrinsic viscosity than their linear counterparts at the same molecular weight, at higher molecular weights the polymers showed strange behavior: both the diffusion coefficient measured by Quasielastic Light Scattering (QELS) and Mark–Houwink–Sakurada plots of intrinsic viscosity for linear and cyclic polyDODT were found to converge. R3P, an aqueous based “green” method is capable of producing polymers at the 10–100 g scale in the lab, which will allow more detailed studies of this new class of biodegradable elastomers so further experimentation can be performed to elucidate the reasons for the unusual findings.

36 MATERIALS SCIENCE↗

Cooperativity in the Aldol Condensation Using Bifunctional Mesoporous Silica–Poly(styrene) MCM-41 Organic/Inorganic Hybrid Catalysts

This work explores the efficacy of silica/organic hybrid catalysts, where the organic component is built from linear aminopolymers appended to the silica support within the support mesopores. Specifically, the role of molecular weight and polymer chain composition in amine-bearing atom transfer radical polymerization-synthesized poly(styrene-co-2-(4-vinylbenzyl)isoindoline-1,3-dione) copolymers is probed in the aldol condensation of 4-nitrobenzaldehyde and acetone. Controlled polymerization produces protected amine-containing poly(styrene) chains of controlled molecular weight and dispersity, and a grafting-to thiol–ene coupling approach followed by a phthalimide deprotection step are used to covalently tether and activate the polymer hybrid catalysts prior to the catalytic reactions. Site-normalized batch kinetics are used to assess the role of polymer molecular weight and chain composition in the cooperative catalysis. Lower-molecular-weight copolymers are demonstrated to be more active than catalysts built from only molecular organic components or from higher-molecular-weight chains. Molecular dynamics simulations are used to probe the role of polymer flexibility and morphology, whereby it is determined that higher-molecular-weight hybrid structures result in congested pores that inhibit active site cooperativity and the diffusivity of reagents, thus resulting in lower rates during the reaction.

36 MATERIALS SCIENCE↗

Multijunction organic photovoltaics incorporating solution and vacuum deposited active layers

There is disclosed an organic photovoltaic device comprising at least one first subcell comprising at least one first small molecular weight material deposited by solution processing, and at least one second subcell comprising a weight at least one second small molecular material deposited by vacuum evaporation. Also disclosed herein is a method for preparing an organic photovoltaic device comprising at least one first subcell comprising at least one first small molecular weight material and at least one second subcell comprising at least one second small molecular weight material, the method comprising depositing at least one first small weight material by solution processing; and depositing at least one second small weight material by vacuum evaporation.

Forrest, Stephen R.↗

Phosphorus speciation analysis of fatty-acid-based feedstocks and fast pyrolysis biocrudes via gel permeation chromatography inductively coupled plasma high-resolution mass spectrometry

Renewable feedstocks, such as lignocelulosic fast pyrolysis oils and both vegetable oil and animal fats, are becoming a viable alternative to petroleum for producing high-quality renewable transportation fuels. However, the presence of phosphorus-containing compounds, mainly from phospholipids, in these renewable feedstocks is known to poison and deactivate hydrotreating catalysts during fuel production. In this work, gel permeation chromatography (GPC) combined with inductively coupled plasma high-resolution mass spectrometry (ICP-HRMS) was used to analyze feedstocks including unprocessed soybean oil, animal fat, and pyrolysis oils from red oak and milorganite to identify phosphorus species. The results have shown the presence of a wide range of different phosphorous compounds among all the samples analysed in this work. The GPC-ICP-HRMS analyses of a vegetable oil and two animal fats have shown different fingerprints based on the molecular weight of each of the samples, highlighting the structural differences among their corresponding phosphorus-containing compounds. While the presence of low-molecular-weight species, such as phospholipids, was expected, several high-molecular-weight species (MW > 10 000 Da) have been found, suggesting that high-molecular-weight micelles or liposomes might have been formed due to the high concentration of phospholipids in these samples. Results obtained through the hydroxylation of a mix of phospholipids (asolectin) and its posterior GPC-ICP-HRMS agree with this hypothesis. With respect to the lignocellulosic catalytic fast pyrolysis oil samples, the GPC-ICP-HRMS results obtained suggest that either aggregation or polymerization reactions might have occurred during the pyrolysis process, yielding phosphorus-containing compounds with an approximate molecular weight above 91 000 kDa. In addition, an aggregation phenomenom has been observed for those phosphorus species present within the fast pyrolysis oils after being stored for 3 months, especially for those pyrolysis oils contaning pre-processed feedstocks, such as milorganite.

09 BIOMASS FUELS↗

Elucidating Polymer Binder Entanglement in Freestanding Sulfide Solid-State Electrolyte Membranes

This study advances the development of flexible, sheet-type sulfide solid-state electrolytes (SSEs) for use in all-solid-state batteries, emphasizing the important and previously insufficiently investigated role of polymer binder entanglement. Here, the molecular weight of polymer binders is pivotal in crafting robust, freestanding SSE films. Our research uncovers a dual impact: higher molecular weight binders bolster the structural integrity of SSE films but elevate grain boundary resistance and diminish critical current density, whereas lower molecular weight poly(isobutylene) films, despite their more uniform distribution, lack the essential strain hardening or strength for sustained active material contact. Crucially, full cells employing higher molecular weight binders demonstrate improved discharge capacity retention, contrasting sharply with the notable capacity degradation in lower molecular weight cells. Our findings not only deepen the comprehension of binder influences in solid-state batteries but also chart a course for refining all-solid-state battery technologies, a key stride for the future of energy storage solutions.

25 ENERGY STORAGE↗

Characterization of the Atmosphere of Super-Earth 55 Cancri e Using High-resolution Ground-based Spectroscopy

The nearby super-Earth 55 Cnc e orbits a bright (V = 5.95 mag) star with a period of -18 hr and a mass of -8M {sub ⊕}. Its atmosphere may be water-rich and have a large-scale height; though, attempts to characterize it have yielded ambiguous results. Here we present a sensitive search for water and TiO in its atmosphere at high spectral resolution using the Gemini North telescope and the GRACES spectrograph. We combine observations with previous observations from Subaru and CFHT, improving the constraints on the presence of water vapor. We adopt parametric models with an updated planet radius based on recent measurements, and use a cross-correlation technique to maximize sensitivity. Our results are consistent with atmospheres that are cloudy or contain minimal amounts of water and TiO. Using these parametric models, we rule out a water-rich atmosphere (VMR ≥ 0.1%) with a mean molecular weight of ≤ 15 g mol{sup -1} at a 3σ confidence level, improving on the previous limit by a significant margin. For TiO, we rule out a mean molecular weight of ≤ 5 g mol{sup -1} with a 3σ confidence level for a VMR greater than 10{sup -8}; for a VMR of greater than 10{sup -7}, the limit rises to a mean molecular weight of ≤ 10 g mol{sup -1}. We can rule out low mean-molecular-weight chemical equilibrium models both including and excluding TiO/VO at very high confidence levels (>10σ). Overall, our results are consistent with an atmosphere with a high mean molecular weight and/or clouds, or no atmosphere.

79 ASTRONOMY AND ASTROPHYSICS↗