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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Bridging knowledge gaps in liquid- and vapor-fed CO 2 electrolysis through active electrode area

Increased use of gas diffusion electrodes for CO 2 electroreduction widens the experimental phase space that was previously inaccessible using foil electrodes, raising fundamental questions over the impacts of key variables that translate between liquid- and vapor-fed CO 2 electrolysis systems. This work focuses on studying the interplay of current-potential profiles and electrochemically active surface area (ECSA) by implementing a Cu nanoflower catalyst morphology. The results show decreased overpotentials as much as 460 and 174 mV for foil and gas diffusion electrodes, respectively, while maintaining or improving multi-carbon product current density. Furthermore, these overpotential shifts and product activities normalized by ECSA lead to current-potential relationships akin to those of the Tafel description, which are found through a continuum model to be useful for describing the roughness dependence for both liquid- and vapor-fed systems. This analysis establishes a holistic approach for establishing catalyst design criteria to improve materials development for CO 2 .

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Tungsten-dioxo single-site heterogeneous catalyst on carbon: synthesis, structure, and catalysis

This study investigates the application of a novel third-row metal, tungsten, to carbon-supported single-site metal-oxo heterogeneous catalysis. Tungsten is a green and earth-abundant metal, but an unexplored candidate in this role. The carbon (AC = activated carbon)-supported tungsten dioxo complex, AC/WO 2 was prepared via grafting of (DME)WO 2 Cl 2 (DME = 1,2-dimethoxyethane) onto high-surface-area activated carbon. AC/WO 2 was fully characterized by ICP-OES, XPS, EXAFS, XANES, SMART-EM, and DFT. W 4d 7/2 XPS and W L III -Edge XANES assign the oxidation state as W(VI), while EXAFS reveals two W=O double and two W–O single bonds at distances of 1.73 and 1.92 Å, respectively. These data align well with DFT computational results, supporting the structure as Carbon(–μ-O–) 2 M(=O) 2 . SMART-EM verifies that single W(VI) catalytic sites are bonded in an out-of-plane manner. The catalytic performance of air- and water-stable AC/WO 2 is compared to that of AC/MoO 2 . AC/WO 2 is more active and selective than the molybdenum analog in mediating alcohol dehydration of various substrates, and is recyclable. Notably, AC/WO 2 is an effective and recyclable catalyst for primary aliphatic alcohol dehydration and forms no dehydrogenation side products in contrast to AC/MoO 2 . However, AC/WO 2 is less effective in epoxidation and PET depolymerization. Overall, this work demonstrates the potential of carbon-supported third row metals for future studies.

02 PETROLEUM↗
DOE OSTI2022

Membrane‐electrode assembly design parameters for optimal CO 2 reduction

Commercial-scale generation of carbon-containing chemicals and fuels by means of electrochemical CO 2 reduction (CO 2 R) requires electrolyzers operating at high current densities and product selectivities. Membrane-electrode assemblies (MEAs) have been shown to be suitable for this purpose. In such devices, the cathode catalyst layer controls both the rate of CO 2 R and the distribution of products. In this study, we investigate how the ionomer-to-catalyst ratio (I:Cat), catalyst loading, and catalyst-layer thickness influence the performance of a cathode catalyst layer containing Ag nanoparticles supported on carbon. In this paper, we explore how these parameters affect the cell performance and establish the role of the exchange solution (water vs. CsHCO 3 ) behind the anode catalyst layer in cell performance. We show that a high total current density is best achieved using an I:Cat ratio of 3 at a Ag loading of 0.01–0.1 mg Ag /cm 2 and with a 1.0 M solution of CsHCO 3 circulated behind the anode catalyst layer. For these conditions, the optimal CO partial current density depends on the voltage applied to the MEA. The work also reveals that the performance of the cathode catalyst layer is limited by a combination of the electrochemically active surface area and the degree to which mass transfer of CO 2 to the surface of the Ag nanoparticles and the transport of OH – anions away from it limit the overall catalyst activity. Hydration of the ionomer in the cathode catalyst layer is found not to be an issue when using an exchange solution. The insights gained allowed for a Ag CO 2 R MEA that operates between 200 mA/cm 2 and 1 A/cm 2 with CO faradaic efficiencies of 78–91%, and the findings and understanding gained herein should be applicable to a broad range of CO 2 R MEA-based devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Atomically Dispersed Iron–Nitrogen Sites on Hierarchically Mesoporous Carbon Nanotube and Graphene Nanoribbon Networks for CO 2 Reduction

Atomically dispersed metal and nitrogen co-doped carbon (M-N/C) catalysts hold great promise for electrochemical CO 2 conversion. However, there is a lack of cost-effective synthesis approaches to meet the goal of economic mass production of single-atom M-N/C with desirable carbon support architecture for efficient CO 2 reduction. Herein, we report facile transformation of commercial carbon nanotube (CNT) into isolated Fe-N 4 sites anchored on carbon nanotube and graphene nanoribbon (GNR) networks (Fe-N/CNT@GNR). The oxidization-induced partial unzipping of CNT results in the generation of GNR nanolayers attached to the remaining fibrous CNT frameworks, which reticulates a hierarchically mesoporous complex and thus enables a high electrochemical active surface area and smooth mass transport. The Fe residues originating from CNT growth seeds serve as Fe sources to form isolated Fe-N-4 moieties located at the CNT and GNR basal plane and edges with high intrinsic capability of activating CO 2 and suppressing hydrogen evolution. The Fe-N/CNT@GNR delivers a stable CO Faradaic efficiency of 96% with a partial current density of 22.6 mA cm -2 at a low overpotential of 650 mV, making it one of the most active M-N/C catalysts reported. This work presents an effective strategy to fabricate advanced atomistic catalysts and highlights the key roles of support architecture in single-atom electrocatalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Microwave Heating of Nanocrystals for Rapid, Low-Aggregation Intermetallic Phase Transformations

The use of intermetallic Pt–Co nanocrystals (NCs) for the electrocatalytic oxygen reduction reaction is quickly gaining interest thanks to the higher electrochemical stability of the intermetallic L1 o phase compared to a random alloy A1 phase. However, the thermal treatment that enables the intermetallic phase transformation also causes considerable NC aggregation, resulting in a significant loss of electrochemically active surface area. Herein, we report the use of microwave radiation to induce the intermetallic phase transformation in Cu-doped Pt–Co NCs. We demonstrate that microwave radiation reduces NC aggregation while allowing for a complete phase transformation in only 30 s. Furthermore, these microwave-treated NCs demonstrate higher mass activity for the oxygen reduction reaction while maintaining electrochemical stability similar to the thermally annealed samples.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Operando carbon corrosion measurements in fuel cells using boron-doped carbon supports

Carbonaceous materials are the most common catalyst supports in proton exchange membrane fuel cell (PEMFCs), yet their corrosion is one of the limiting factors in achieving high durability. Herein, we doped carbon supports with boron (B) to increase the corrosion-resistance of the support. Two types of B-doped carbons were synthesized and studied as platinum support materials. Further, they varied in their morphologies, surface areas, and the types of boron species. The durability of Pt/B-doped carbon catalysts was investigated using the US-DOE catalysts’ supports accelerated stress test (AST) and a mass-spectrometer connected to the fuel cell effluent stream to quantify the mass of corroded carbon support in operando. The addition of boron to the carbon increased the stability of Pt catalysts in long-term usage of PEMFC. After 4000 AST cycles, more than 50% of initial current density was preserved for the boron-containing systems, while less than 30% of it remained with Vulcan carbon (Pt/V). Also, the Pt/B-doped carbon samples demonstrated better electrochemical active surface area (ECSA) stability when compared to Pt/V. Carbon loss measurements showed that B-doped carbons have higher resistance to electrochemical corrosion than unmodified carbon. Specifically, the substitutional boron-doped carbon demonstrated an extremely high stability and low corrosion rate.

25 ENERGY STORAGE↗
DOE OSTI2022

Implications of Local Cathode Structure in Solid-State Batteries

Solid-state batteries (SSBs) are promising candidates for energy storage systems—specifically for automotive applications—owing to their higher energy density and supreme safety. SSBs currently must improve area-specific cathode loadings as well as the electro-chemo-mechanical stability at high voltages. Composite cathodes in SSBs are comprised of active material, ion and electronic conductors, binders, and electronic conducting materials. In addition to experimental limitations with engineering thick cathode architectures, low utilization and chemomechanical degradation of the cathodes limit the performance of composite cathodes. Composite cathodes must optimize several parameters simultaneously to achieve high performances that include loading, electrochemically active surface area, mechanical resilience, and porosity. This chapter summarizes the current state-of-the-art applications with regard to composite cathodes for SSBs and provides insights into cathode architectures using geometric packing models. Tailoring ion and electron transport pathways within the electrode while mitigating operational stresses is crucial for achieving energy-dense cathode structres for SSBs.

Dixit, Marm↗
DOE OSTI2022

Nanostructured carbon as highly efficient and stable anodes for ethylene production and power generation in protonic ceramic electrochemical cells

Protonic ceramic electrochemical cells (PCECs) have the potential in reducing the energy input and carbon emissions in ethylene production from ethane dehydrogenation. The performance of conventional perovskite-based anode materials for ethane conversion in PCECs is limited by their low active surface area and proneness to coke deposition. In this work, for the first time, we demonstrate the use of aligned carbon nanotube forests (CNTFs) as a novel anode material for an ethane fueled PCEC to co-produce ethylene and electricity. The CNTF electrode was grown on the electrolyte by the chemical vapor deposition (CVD) method. Highly dispersed iron carbide nanoparticles are formed in situ on the CNTFs during the CVD process, acting as highly active catalysts for ethane dehydrogenation. The novel PCECs show superior catalytic and electrochemical performances to that using conventional perovskite-based anodes. The cell also exhibits excellent durability and anti-coking abilities within 100 h test. This work showcases the promising application of nanostructured carbon, a new class of non-perovskite materials, as the multifunctional electrode materials for PCECs.

03 NATURAL GAS↗
DOE OSTI2021

Layer-structured triple-conducting electrocatalyst for water-splitting in protonic ceramic electrolysis cells: Conductivities vs. activity

Electron, proton and oxygen-triple-conducting materials are becoming the dominant steam electrode candidate to break the rate limit on the water-splitting reaction that throttles the performance of protonic ceramic electrolysis cells (PCECs). In this study, based on Pr 2 NiO 4+δ Ruddlesden-Popper phase, we manipulate these conductivities by Pr-site Ba substitution to probe the correlation of each conductivity with the kinetics of the elementary reaction steps. It is found that the proton conductivity is vital to sustain an extended active surface area for faster adsorption of reactants and desorption of products. The effect of oxygen conductivity is surprisingly found insignificant in the water-splitting reaction. On the contrary, surface oxygen removal is discovered as the most rate-limiting process. The electronic conductivity is not a direct limiting factor. However, an electron transfer process between the current collector and the electrode junction could introduce extra resistance that is perceptible at a high operating temperature range. The best water-splitting activity is obtained on a proton conductivity/oxygen surface desorption capability well-balanced sample after Ba substitution. As a result, a water-splitting reaction resistance of 0.022 Ωcm 2 , a current density of 1.96 A/cm 2 at 700 °C is achieved on Pr 1.7 Ba 0.3 NiO 4+δ , one of the best performances for PCECs.

25 ENERGY STORAGE↗
DOE OSTI2021

Catalytic Activity and Water Stability of the MgO(111) Surface for 2-Pentanone Condensation

Nanomaterials derived from earth-abundant metal oxides have gained tremendous interest as catalysts; although, water stability remains a challenge. This study examines MgO(111) surfaces for 2-pentanone condensation and their evolution during D2O hydration. Catalyst screening confirmed the high activity of fresh MgO(111) for 2-pentanone condensation relative to conventionally prepared MgO(100). Computational modeling suggests that the (111) surface is readily hydroxylated, and that surface hydroxyls help stabilize the surface and reduce the barrier for 2-pentanone condensation. Vapor-phase D2O hydration after 3 min increased MgO(111) hydroxyls and retained surface area and activity; however, after 1 h, deuteroxide formation reduced the surface area and activity by >30 %. After 24 h, deuteroxide growth slowed down, and surface area and activity remained stable. This suggests MgO(111)-derived hydroxide may be the dominant surface responsible for 2-pentanone condensation following water exposure. Thermal regeneration of the 24-h sample restored 86 % of the surface area and 94 % of the activity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Hydrogen Recombiner Catalyst Evaluations for Waste Storage

Radiolysis of water in nuclear waste storage generates hydrogen gas that can accumulate within sludge style waste and be rapidly released during agitation events, creating a significant flammability hazard. Engineering controls are therefore required to limit hydrogen concentrations during both quiescent storage and transient disturbances. Catalytic recombination of hydrogen in waste storage offgas is a proven mitigation strategy, maintaining hydrogen levels below flammability limits and managing sudden concentration spikes. Conventional recombiners rely on platinum and/or palladium catalysts, with development efforts focused on extending service life, increasing active surface area, and ensuring safe deployment in radioactive environments. Savannah River National Laboratory (SRNL) is evaluating a newly developed hydrogen recombiner catalyst from Canadian Nuclear Laboratories as a cost-effective and durable alternative for nuclear waste applications. Testing was conducted in SRNL’s Shielded Cells facility, which enables reduced-scale experimental modeling under radiation fields and near-use-case conditions relevant to radioactive waste storage. Catalyst performance was evaluated using a custom offgas characterization system designed for near-zero flow conditions. The experimental apparatus consisted of a gas-tight 2.7 L PTFE vessel equipped with temperature monitoring, gas flow controls, and a variable-speed mixer to simulate sludge agitation. Offgas composition was monitored using a dedicated gas chromatograph with argon carrier gas and a krypton internal standard. Measurements were obtained for an empty vessel, the vessel containing a well characterized radioactive tank waste sample, and the same configuration with the candidate catalyst installed. Results demonstrate that the new catalyst effectively reduced hydrogen concentrations in the offgas within the constraints of the experimental design. In addition to confirming catalytic activity, the testing provided valuable insights into experimental optimization and considerations for future performance evaluations. These findings support the potential scalability of the technology and highlight its applicability to broader nuclear waste management operations, offering improved safety and reduced operational costs through enhanced catalyst durability and lower replacement frequency.

Tener, Zachary P. [Savannah River National Laborat↗
DOE OSTI2025

Optimization of La 2 NiO 4+δ Electrolysis Cell Oxygen Electrode through Surfactant-Enabled LaCoO 3±δ Nanocatalyst Deposition

Lanthanum nickelate (LNO) has shown promise as a Cr-resistant air electrode material for SOECs but has suboptimal surface oxygen exchange properties. Nanocoating of the LNO surface with lanthanum cobaltite (LCO) was chosen to improve cell performance as a surface oxygen conductor. The work focused on the implementation of a two-step nano-LCO film deposition utilizing catechol molecules in a porous LNO electrode. The subgoals of the work were to maintain nanosized LCO particles/ grains to increase active surface area and to control the regularity/ homogeneity of the coating across the microstructure. To achieve these goals, a novel surfactant-enhanced liquid infiltration method was utilized, where nucleation sites were spread across the electrode structure to control the location and size of LCO particles. Various catechol surfactant compositions were evaluated for their ability to control the kinetics of nanoparticle deposition and the homogeneity of the coating. Chelated LCO was characterized by X-ray diffraction (XRD), which found a substantial improvement in LCO formation with surfactant addition and determined polymerized norepinephrine to be the best-performing surfactant, with 88.4% pure LCO formed at low temperature. X-ray photoelectron spectroscopy (XPS) confirmed LCO nanostructures formed by the two-step infiltration process, showing no impurities and a stable perovskite structure. Deposition kinetics were analyzed using atomic force microscopy (AFM), correlating infiltration times and solution molarity to nanoparticle size and distribution, the results of which were confirmed in symmetrical cell samples by scanning electron microscopy (SEM). Electrochemical impedance spectroscopy (EIS) testing demonstrated substantial improvements in polarization resistance, where the nanocoating reduced the resistance by ∼55% to 0.152 Ω·cm 2 at 700 °C and 0.039 Ω·cm 2 at 800 °C. Electrical conductivity relaxation (ECR) at this temperature confirmed an improved surface oxygen exchange coefficient of the LCO + LNO heterostructure predicted by the Bode data from EIS, alongside a reduction in activation energy by about 30%.

Deposition↗
DOE OSTI2024

A Three–Dimensional Nanoscale View of Electrocatalyst Degradation in Hydrogen Fuel Cells

The loss of platinum (Pt) electrochemically active surface area (ECSA) is a critical degradation mode that often becomes a limiting factor for heavy-duty proton exchange membrane fuel cell vehicles. High surface area carbon supports have been shown to improve Pt dispersion and limit detrimental ionomer-electrocatalyst interactions due to their large interior pore volume. Here, in this work, using automated scanning transmission electron tomography, the degradation of nanoparticles located on the interior versus exterior surfaces of the carbon support is compared following a catalyst-specific accelerated stress test (AST) of 90,000 voltage cycles between 0.6 V to 0.95 V. The results reveal a notable increase in median particle size for both interior and exterior Pt catalyst particles, with a slightly higher increase in particle size distribution and loss of specific surface area for the particles located on the exterior carbon surface. The fraction of Pt nanoparticles that reside within the interior of the carbon support also increased following the AST test, accompanied by evidence of an increase in average carbon mesopore size. Here, the results shed light on the degradation mechanisms affecting electrochemical properties and the enhanced particle accessibility at lower relative humidity.

08 HYDROGEN↗
DOE OSTI2022

Super-porous Pt/CuO/Pt hybrid platform for ultra-sensitive and selective H 2 O 2 detection

A super-porous Pt/CuO/Pt hybrid electrode is demonstrated with extremely high sensing performance parameters for the hydrogen peroxide (H 2 O 2 ) detection. A unique physiochemical approach is adapted for the fabrication of 3-D super-porous Pt/CuO/Pt sensing platform. Here, the super-porous Pt/CuO/Pt hybrid platform demonstrates a superior sensitivity of 16,694 µA mM -1 cm -2 with a limit of detection of 2.91 nM (S/N = 3). It also demonstrates an excellent selectivity against the interfering molecules such as NaCl, fructose, ascorbic acid, citric acid, dopamine and glucose with a wide linear range. The demonstrated performance ranks the Pt/CuO/Pt hybrid platform as one of the best H 2 O 2 sensors as summarized in the Table 2. The super-porous CuO layer is fabricated by a dynamic hydrogen bubbling technique of electrochemical deposition and metallic Pt NP decoration is achieved by the physical vapor deposition (PVD) and post-annealing. The super-porous CuO layer offers a drastically improved electrochemical active surface area, and the Pt NP decoration offers a significantly improved conductivity and improved charge accumulation for the H 2 O 2 reduction. The DFT simulations confirm the predominance of CuO over Cu 2 O and Pt over Pd for the H 2 O 2 detection based on the adsorption energy, density of states and charge accumulation calculations.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Ultrathin platinum nanowire based electrodes for high-efficiency hydrogen generation in practical electrolyzer cells

Significant reduction of noble metal catalyst loading and simplification of electrode fabrication are urgently needed in order to lower the cost of proton exchange membrane electrolyzer cells (PEMECs) for large-scale hydrogen production. Herein, we report an integrated electrode design comprising in-situ grown platinum nanowires (PtNW) on ultrathin titanium liquid/gas diffusion layers (LGDLs) via a cost-effective and green chemical synthesis approach. The ultrathin integrated PtNW electrodes showed a low cell voltage of 1.643 V and high efficiency of 90.08% at 1000 mA cm -2 using about 15 times lower catalyst loadings than a conventional catalyst-coated membrane in PEMEC tests. Ex-situ electrochemical characterizations and microscale visualizations further reveal that PtNW electrodes display highly efficient hydrogen evolution reactions and excellent electrode durability due to high active surface area, favorable bubble detachment, and structural stability. This work provides new insights into catalyst layer design and facile ultrathin electrode fabrication for more compact and low-cost PEM electrolyzers, fuel cells and other systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Indirect electrochemical method for high accuracy quantification of protein adsorption on gold surfaces

We demonstrate the use of copper underpotential deposition (UPD) for measurement of the electrochemically active surface area of a protein-modified gold electrode. The kinetics of adsorption and the subsequent structural rearrangement of β-casein, as a model protein, on the surface of a gold electrode have been followed over time. The protein-free surface area was determined by measuring the charge derived from UPD copper deposition on the non-blocked surface area at different stages of adsorption. The behaviour of β-casein adsorption as a function of surface roughness and the microstructure of the gold electrode, as well as the concentration of the protein solution, are studied using this method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Enabling high rate capability, low internal resistance, and excellent cyclability for vanadium redox flow batteries utilizing ultrafast laser-structured graphite felt

The electrochemical performance of vanadium redox flow batteries (VRFBs) was enhanced via laser-patterned graphite felt (GF) electrodes. The laser-structured GF electrodes engineered via preparing a series of well-ordered microscopic channel structures with an average width of 200 μm, creating a three-dimensional carbon framework. The ultrafast laser patterning increased the porosity by 10%, as compared to pristine electrode. The analysis of the overpotential distribution using electrochemical impedance spectroscopy revealed that the electrode polarization involving charge transfer and diffusion resistance is strongly alleviated with the aid of carbon micro-perforation. The advanced design of laser-structured GF electrode also exhibits high rate capability, low internal resistance, and excellent cyclability. The improved performance was attributed to the synergistic effect involving (i) high electrochemically active surface area for rapid electrochemical reactions (i.e., V(II)/V(III) and V(IV)/V(V) redox couples) and (ii) excellent transport properties for facile electron/ion/species transport. The micro-scale channels created with the laser-ablation technique act as capillary structures and enabled homogeneous and rapid wetting of GF electrodes as formulated with the classical Washburn equation. The VRFB equipped with the laser-structured GF electrodes delivered a high discharge capacity with exceptional capacity retention upon extended cycling (>84.9%). In conclusion, accordingly, the design of laser-structured electrode paves the pathway towards finely tuning the electrode internal microstructure for improved cyclability, durability, and capacity retention in various electrochemical energy storage/conversion devices (e.g. all-vanadium redox flow batteries).

25 ENERGY STORAGE↗
DOE OSTI2025

The role of the Pt-group dehydrogenation catalyst in alkane metathesis for polyolefin deconstruction

Recent proposed approaches in the depolymerization of waste plastics employ an olefin intermediate to produce alkanes or alkenes using olefin metathesis in tandem chemistry. Here, in this study, we investigated the role of the dehydrogenation catalyst on reaction rate, kinetics, and product distribution in heterogeneous tandem dehydrogenation and olefin metathesis (alkane metathesis) of three different alkane reactants, including polyethylene. We found that many properties to which alkane dehydrogenation rates were sensitive-including metal composition, nanoparticle size, and surface doping of Re species also controlled activity in Tandem D/OM. When comparing Pd, Pt, and Pt 3 Sn 1 , supported Pd in tandem with a Re 2 O 7 olefin metathesis catalyst showed four-fold higher activity (surface area basis) compared to Pt or Pt 3 Sn 1 catalysts on the same support, mainly due to differences in the rate of hydrogenation. Catalyst preparation resulted in metal nanoparticles partially covered by ReO x , as seen from elemental mapping. Co-location of Re 2 O 7 and Pd correlated with increased rates of hydrogenation (i.e., an increase in the rate of alkane formation and simultaneous lowering of the rate of alkene formation), with a reaction order in catalyst study that further supported this conclusion. The Pd and Re 2 O 7 system displayed marked improvement compared to Pt or Pt 3 Sn 1 with Re 2 O 7 , and previous work, in the depolymerization rate of a linear polyethylene feedstock, with over 94 % reduction in polymer molecular weight in 15 h at 190 °C using less catalyst and increased reactant loadings, while keeping solvent to polymer consumption below 2.5.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗