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At least 163 records · Page 9

Light Hydrocarbon Separations Using Porous Organic Framework Materials

Light hydrocarbons (C 1 –C 3 ) are used as basic energy feedstocks and as commodity organic compounds for the production of many industrially necessary chemicals. Due to the nature of the raw materials and production processes, light hydrocarbons are generated as mixtures, but the high-purity single-component products are of vital importance to the petrochemical industry. Consequently, the separation of these C 1 –C 3 products is a crucial industrial procedure that comprises a significant share of the total global energy consumption per year. As a complement to traditional separation methods (distillation, partial hydrogenation, etc.), adsorptive separations using porous solids have received widespread attention due to their lower energy costs and higher efficiency. Extensive research has been devoted to the use of porous materials such as zeolites and metal-organic frameworks (MOFs) as solid adsorbents for these key separations, owing to the high porosity, tunable pore structures, and unsaturated metal sites present in these materials. Recently, porous organic framework (POF) materials composed of organic building blocks linked by covalent bonds have also shown excellent properties in light hydrocarbon adsorption and separation, sparking interest in the use of these materials as adsorbents in separation processes. In this Minireview we summarize the recent advances in the use of POFs for light hydrocarbon separations, including the separation of mixtures of methane/ethane, methane/propane, ethylene/ethane, acetylene/ethylene, and propylene/propane, while highlighting the relationships between the structural features of these materials and their separation performances. Finally, the difficulties, challenges, and opportunities associated with leveraging POFs for light hydrocarbon separations are discussed to conclude the review.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High resolution mobility spectrometry in a co-axial platform

Ion mobility spectrometry is an analytical technique that separate ions in the gas phase based on their interaction with a neutral buffer gas. Ion mobility spectrometry performs separations quickly (typically less than a second) and the ion mobilities are very reproducible across different laboratories. This project aimed at evaluating the performance of a new ion mobility device. The new device relies on conducting ion mobility separation in a curved geometry. The project explored the operation landscape of the device using ion trajectory simulations then fabricated and experimentally demonstrated the device's performance. Ion trajectory simulations on a set of tetraalkylammonium and phosphazene ions indicate that ions traveling a curved path length undergo mobility separation that is similar to a straight path. The ion mobility resolution of the curved device was found to be similar to that of a straight path of a similar length. The experimental validation of the new device confirmed the device's ability to separate ions according to their mobilities. Sets of mixtures (tetraalkylammonium ions, phosphazene ions, and peptide ions) were evaluated for separation and transmission.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Inline small-angle X-ray scattering-coupled chromatography under extreme hydrostatic pressure

As continuing discoveries highlight the surprising abundance and resilience of deep ocean and subsurface microbial life, the effects of extreme hydrostatic pressure on biological structure and function have attracted renewed interest. Biological small-angle X-ray scattering (BioSAXS) is a widely used method of obtaining structural information from biomolecules in solution under a wide range of solution conditions. Due to its ability to reduce radiation damage, remove aggregates, and separate monodisperse components from complex mixtures, size-exclusion chromatography-coupled SAXS (SEC-SAXS) is now the dominant form of BioSAXS at many synchrotron beamlines. While BioSAXS can currently be performed with some difficulty under pressure with non-flowing samples, it has not been clear how, or even if, continuously flowing SEC-SAXS, with its fragile media-packed columns, might work in an extreme high-pressure environment. Here we show, for the first time, that reproducible chromatographic separations coupled directly to high-pressure BioSAXS can be achieved at pressures up to at least 100 MPa and that pressure-induced changes in folding and oligomeric state and other properties can be observed. Further, the apparatus described here functions at a range of temperatures (0°C–50°C), expanding opportunities for understanding biomolecular rules of life in deep ocean and subsurface environments.

59 BASIC BIOLOGICAL SCIENCES↗

Supramolecular Assembly of Lanthanide-Binding Tag Peptides for Aqueous Separation of Rare Earth Elements

Selective and eco-friendly separation and purification methods for rare earth elements (REEs) are necessary to meet the increasing demand for these valuable metals, which are extensively used in modern electronics and clean energy technologies. Mining feedstocks consist of REE mixtures as stable trivalent cations (Ln 3+ ) that are difficult to separate due to their identical charge and similar size. Lanthanide-binding tags (LBTs), peptide chelates that coordinate Ln 3+ in binding pockets, show promise as selective, high-affinity extractants. We demonstrate that the LBT variant LBTLLA 5– , designed for high selectivity for Tb 3+ , is an effective extractant, forming complexes with REEs in solution that subsequently organize into self-assembling structures rich in Ln 3+ . These structures condense into aggregates that can be separated, enabling an efficient, all-aqueous, eco-friendly separation process. The self-assembled structures are studied using dynamic light scattering, ζ-potential measurements, transmission electron microscopy, anomalous small-angle X-ray scattering, inductively coupled plasma optical emission spectroscopy, and ultraviolet–visible absorption spectroscopy, which confirm LBTLLA 5– peptide-REE ion binding and the further assembly of micron-scale structures rich in REEs. Molecular dynamics simulations reveal the interactions promoting aggregation as well as the integrity of the binding pocket upon self-assembly. We find that LBTLLA 5– :Ln 3+ complexes recruit excess cations within the macrostructures, and we demonstrate that aggregation and selective separation can be controlled by manipulating the metal-peptide ratio in solution. Furthermore, we demonstrate separation from equimolar mixtures of REE pairs Tb 3+ -Lu 3+ and Tb 3+ -La 3+ , supporting the application of LBT peptides as a platform for the selective separation of REEs.

LBT peptides↗

Structurally Driven Selective Adsorption of Hydrocarbons by Metal Substitution in Isostructural Rare-Earth Metal–Organic Frameworks

The design and realization of highly selective nanoporous materials are necessary to target critical separations across industries. By leveraging pore size, pore shape, and linker functionalization, the design of nanoporous solid adsorbents will enable the rapid production of energy efficient separation materials for high-value gas mixtures. This study uses a combination of modeling, synthesis, and gas adsorption testing to investigate a new class of small-pore isostructural rare-earth (RE) 2,5-dihydroxyterephthalic acid (DOBDC) metal–organic frameworks (MOFs) (RE: Pr-, Gd-, Er-, Yb; DOBDC = 2,5-dihydroxyterephthalic acid) and their adsorption selectivity for acetylene/ethylene mixtures. Density functional theory simulations identified that selective binding of acetylene over ethylene in the Gd-, Er-, and Yb-DOBDC MOFs was due to hydrogen-bonding between acetylene and the linker hydroxyl. Adsorption experiments validated the computational results by identifying mechanisms that control the acetylene/ethylene adsorption selectivity and high acetylene adsorption. Furthermore, dynamic column breakthrough experiments with the Gd-DOBDC MOF validated the simulations and indicated that ethylene can be separated from acetylene in a mixture containing 1 vol % acetylene and 39 vol % ethylene (balance argon). In conclusion, the results highlight the complexity of gas binding in functional porous materials and how combining modeling and experiment enables a fundamental understanding of gas–framework interactions that can be leveraged for the design of future separation materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Temperature Effects in Flexible Adsorption Processes for Amorphous Microporous Polymers

A collection of atomistic molecular simulations is reported that illustrate the impact of adsorption temperature on species uptake and adsorbate-induced structural rearrangement for amorphous polymers of intrinsic microporosity. Temperature-sensitive structural rearrangement is evaluated by contrasting two methods: standard grand canonical Monte Carlo simulations using a rigid framework approximation and a combined Monte Carlo/molecular dynamics approach that fully incorporates framework flexibility. We report single-component gas phase adsorption isotherms for CH 4 , C 2 H 4 , C 2 H 6 , C 3 H 6 , C 3 H 8 , and CO 2 across a temperature range of 250–400 K for models of an archetypal polymer of intrinsic microporosity, PIM-1. A quadratic model is presented that captures two main mechanisms of temperature-dependent adsorption-induced deformation of PIM-1 up to a relative swelling of 1.15: thermal expansion and an increased propensity to swell as a function of species uptake. Two case studies are reported that highlight the critical role of operating temperature in industrial storage and separation applications. The first study focuses on methane storage and delivery applications using a pressure–temperature swing adsorption application (PTSA). We demonstrate that larger working capacities are accompanied by increased volumetric strain between adsorption–desorption steps. The second case study considers PIM-1 as an adsorbent to separate an exemplar ternary syngas mixture at operating temperatures ranging 300–550 K. Here, a temperature threshold of ~400 K is identified, beyond which adsorption-induced PIM-1 swelling is negligible and the solubility selectivity-loading curve transitions to exhibiting a nearly linear relationship.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Framework for predicting the fractionation of complex liquid feeds via polymer membranes

The separation of complex liquid hydrocarbon mixtures was recently demonstrated using the glassy polymer SBAD-1, showing that small molecule fractionation is possible by such organic membrane materials. Here, in this work, we develop a framework that will enable workable predictions of permeate flux and composition in complex hydrocarbon liquids through intrinsically porous glassy polymers. The predictions are made by incorporating experimentally-derived unary sorption and diffusion parameters in a Maxwell-Stefan framework coupled with multicomponent sorption models and various distinct diffusion phenomena. Across the range of sorption and diffusion phenomena considered, both the conventional Flory-Huggins model and the proposed Langmuir + Flory-Huggins sorption model combined with a simple average guest diffusivity or a more complex free-volume theory-based transport resulted in the lowest prediction error for three chosen multicomponent separations. The proposed Maxwell-Stefan framework simply requires pure component transport parameters to allow a fast approximation of the separation of multicomponent liquid hydrocarbon feeds that can potentially be extended to more complex feeds such as crude oil fractions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Separation of Hydrogen Using Pd/Ag Membranes: Experimental and Modeling Results with Potential Application to Direct Internal Recycle

Implementation of fusion energy requires processing the deuterium-tritium (D-T) mixture used to fuel the reaction, and separation of hydrogen isotopes from other gases is imperative. Specifically, the separation of hydrogen isotopes from helium is a matter of importance to the fusion fuel cycle community. Initial testing with a palladium-silver (Pd-Ag) membrane indicates that even moderate vacuum (~100 torr permeate pressure) can provide a high degree of separation (>90%) at a high ratio of H 2 to He. Given the presence of He in many fusion systems, a high technology readiness level (TRL) for Q 2 /He (where Q represents any isotope of hydrogen) separations is needed. This study demonstrates the efficacy of H 2 removal from He via permeation and potential applications for direct internal recycle. Modeling will accompany the experimental campaign to generate a predictive capability and quantify the separation performance. Modeling from previous hydrogen permeation studies has demonstrated that the typical Sieverts’ law fails to predict the measured permeation rates at high hydrogen fluxes. Existing models are being refined to integrate the effects of surface phenomena into permeation predictions, which have been expanded to account for mixtures with large ranges of Q 2 concentrations. These data will improve the TRL of permeators as a separation technology for the fusion fuel cycle.

08 HYDROGEN↗

Structure and Potential–Dependent Selectivity in Redox–Metallopolymers: Electrochemically Mediated Multicomponent Metal Separations

Electro-responsive functional materials can play a critical role in selective metal recovery and recycling due to the need for molecular differentiation between transition metals in complex mixtures. Redox-active metallopolymers are a promising platform for electrochemical separations, offering versatile structural tuning and fast electron transfer. First, through a judicious selection of polymer structure between a main-chain metallopolymer (polyferrocenylsilane) and a pendant-group metallopolymer (polyvinylferrocene), charge-transfer interactions and binding strength toward competing metal ions are tuned, which as a result, dictate selectivity. For example, almost an order of magnitude increase in separation factor between chromate and meta-vanadate can be achieved, depending on polymer structure. Second, these metallopolymer electrodes exhibit potential-dependent selectivity that can even flip ion preference, based solely on electrical means—indicating a control parameter that is orthogonal to structural modifications. Finally, this work presents a framework for evaluating electrochemical separations in multicomponent ion mixtures and elucidates the underlying charge-transfer mechanisms resulting in molecular selectivity through a combination of spectroscopy and electronic structure calculations. Furthermore, the findings demonstrate the applicability of redox-metallopolymers in tailored electrochemical separations for environmental remediation, value-added metal recovery, waste recycling, and even mining processing.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Trailblazing Kr/Xe Separation: The Birth of the First Kr-Selective Material

Efficient separation of Kr from Kr/Xe mixtures is pivotal in nuclear waste management and dark matter research. Thus far, scientists have encountered a formidable challenge: the absence of a material with the ability to selectively adsorb Kr over Xe at room temperature. This study presents a groundbreaking transformation of the renowned metal–organic framework (MOF) CuBTC, previously acknowledged for its Xe adsorption affinity, into an unparalleled Kr-selective adsorbent. This achievement stems from an innovative densification approach involving systematic compression of the MOF, where the crystal size, interparticle interaction, defects, and evacuation conditions are synergistically modulated. The resultant densified CuBTC phase exhibits exceptional mechanical resilience, radiation tolerance, and notably an unprecedented selectivity for Kr over Xe at room temperature. Simulation and experimental kinetic diffusion studies confirm reduced gas diffusion in the densified MOF, attributed to its small pore window and minimal interparticle voids. The lighter Kr element demonstrates facile surface passage and higher diffusivity within the material, while the heavier Xe encounters increased difficulty entering the material and lower diffusivity. This Kr-selective MOF not only represents a significant breakthrough in Kr separation but also demonstrates remarkable processability and scalability to kilogram levels. Furthermore, the findings presented herein underscore the transformative potential of engineered MOFs in addressing complex challenges, heralding a new era of Kr separation technologies.

36 MATERIALS SCIENCE↗

Hydrocarbon ladder polymers with ultrahigh permselectivity for membrane gas separations

Membranes have the potential to substantially reduce energy consumption of industrial chemical separations, but their implementation has been limited owing to a performance upper bound—the trade-off between permeability and selectivity. Although recent developments of highly permeable polymer membranes have advanced the upper bounds for various gas pairs, these polymers typically exhibit limited selectivity. We report a class of hydrocarbon ladder polymers that can achieve both high selectivity and high permeability in membrane separations for many industrially relevant gas mixtures. Additionally, their corresponding films exhibit desirable mechanical and thermal properties. Tuning of the ladder polymer backbone configuration was found to have a profound effect on separation performance and aging behavior.

Science & Technology - Other Topics↗

Generalizable Porous Aromatic Framework‐Included Polymer Membranes for Diffusion‐Enhanced Gas Separations

Industrial separation processes account for 10-15% of global energy consumption. Membrane-based processes are less energy-intensive than traditional gas separation technologies; however, enhanced material separation performance and stability for numerous gas mixtures are needed for widespread industrial adoption. This work presents a generalizable strategy for preparing mixed-matrix gas separation membranes exceeding the performance upper bounds of existing polymer membranes for a wide variety of industrial gases. By incorporating robust porous aromatic framework (PAF) particles into various dense commercial polymer matrices, gas diffusivity and solubility can be enhanced. For diverse gas mixtures (e.g., CO2/N2, O2/N2, He/CH4, H2/N2, and C2H4/C2H6), the resulting composite membranes exhibit enhanced gas permeabilities-by as much as 520%-and largely unchanged selectivities even after 6 years of aging under simulated flue gas conditions. These improvements arise from the ultrahigh porosity, excellent chemical compatibility, and unique physicochemical properties of the embedded PAF particles. Functionalizing the PAFs with polyamines also enables composite membranes that achieve among the highest reported performances against plasticization, a common obstacle in commercializing gas separation membranes. Significantly, the PAF-1 particles are readily dispersible in various common membrane casting solvents, suggesting their broader utility as a filler for designing high-performance membranes for many industrial gas separations.

Uliana, Adam A↗

Fluorinated ionic liquids as gas chromatographic stationary phases for the separation of volatile per- and polyfluoroalkyl substances

Background Here, the production of fluorinated organic compounds in the manufacturing, semiconductor, and pharmaceutical industries has increased exponentially over the past decade. This rapid growth has created an urgent need for efficient chromatographic platforms capable of selectively separating these compounds from complex mixtures, not only to support industrial quality control and waste management practices, but also to enable reliable environmental monitoring of volatile fluorinated contaminants. Conventional GC stationary phases lack the fluorophilic interactions needed for highly fluorinated analytes. Consequently, there is a clear demand for specialized stationary phases designed to improve chromatographic retention and selectivity for these compounds. Results Three stationary phases composed of fluorinated ionic liquids (ILs) with varied extent of fluorination were prepared to study fluorophilic interactions with fluorinated/non-fluorinated probe molecules by gas chromatography (GC). IL stationary phases featuring linear and branched perfluoroalkyl moieties, as well as a branched alkyl moiety, were systematically investigated. Chromatographic performance was examined using fluorinated compounds and their hydrocarbon analogs, including CF 3 -substituted aromatics, aliphatic alcohols, fluorotelomer alcohols (FTOHs), and perfluoroalkenes. Measurements on 5 m and 20 m columns revealed that the IL possessing branched alkyl provided stronger dispersive and hydrogen bonding interactions toward non-fluorinated aromatic and long-chain alcohols, whereas the fluorinated ILs enhanced retention of highly fluorinated FTOHs and perfluorodecene. Comprehensive two-dimensional GC (GC × GC), using a nonpolar primary column coupled with secondary columns featuring cross-bonded poly(trifluoropropylmethyl siloxane) (Rtx-200 ms), the branched fluorinated IL, or the branched non-fluorinated IL, highlighted complementary selectivity with the branched fluorinated IL providing the strongest interactions with fluorinated analytes. Significance These results demonstrate that fluorinated IL stationary phases are promising alternatives to conventional polysiloxane stationary phases for improving the separation of per- and polyfluoroalkyl substances and related fluorinated compounds. By correlating IL structure with fluorophilic interactions, this work establishes design principles for GC stationary phases that enable enhanced selectivity for highly fluorinated analytes while maintaining complementary interactions with non-fluorinated compounds.

Comprehensive two-dimensional GC↗

Gamma-ray spectrometry analysis methods for radioisotope dissolution and mixing for nuclear forensics applications

We report the production of surrogate nuclear explosive debris involves the dissolution of irradiated fissile material, elemental isolation, and recombination based on required fission product ratios. Gamma-ray spectrometry is used following each step to assess the radioactive fission product inventory. A high-purity germanium detector is used to measure each sample, and the detector efficiencies are determined prior to sample measurements. Through radiochemical techniques, elements are isolated and recombined into samples with specific fission product ratios. As a result, a matrix-based approach can account for imperfect chemical separations to calculate the proper mixture volumes to obtain intended volatile-to-refractory fission product ratios, or R-values.

07 ISOTOPE AND RADIATION SOURCES↗

Extraction chromatography of 225 Ac and lanthanides on N,N-dioctyldiglycolamic acid /1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide solvent impregnated resin

The alpha-emitter 225 Ac (t 1/2 = 9.92 d) is currently under development for targeted alpha-particle therapy of cancer, and accelerator production of 225 Ac via proton irradiation of thorium targets requires robust separations of 225 Ac from chemically similar fission product lanthanides. Additionally, the lanthanide elements represent critical components in modern technologies, and radiolanthanides such as 140 Nd (t 1/2 = 3.37 d) also have potential application in the field of nuclear medicine. The ionic liquid, 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([Bmim][NTf 2 ]), combined with the diglycolamide extractant, N,N-dioctyldiglycolamic acid (DODGAA), was adsorbed on macroporous resin support to produce a solvent impregnated resin (SIR) that was investigated for separations of 225 Ac and lanthanides. The equilibrium distribution coefficients (Kd) of the rare earth elements (Sc(III), Y(III), Ln(III)), 225 Ac(III), Th(IV), and U(VI) on the prepared DODGAA/[Bmim][NTf 2 ]-SIR were determined from batch adsorption experiments in HCl and HNO 3 media. The DODGAA/[Bmim][NTf2]-SIR exhibited preferential uptake of the heavier lanthanide elements while allowing for the separation of the lighter lanthanides. Column separations utilizing the DODGAA/[Bmim][NTf 2 ]-SIR were effective at separating the lighter lanthanides from each other, and separating 225 Ac from a mixture of lanthanides, 213 Bi, and 225 Ra without the need for additional complexing agents.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Techno-Economic and life cycle assessment of standalone Single-Stream material recovery facilities in the United states

Material Recovery Facilities (MRFs) are crucial players in achieving a circular economy. MRFs receive complex waste streams and separate valuable recyclables from these mixtures. This study conducts techno-economic analysis (TEA) to estimate the net present value (NPV) and life cycle assessment (LCA) to estimate different environmental impacts of a commercial scale standalone, single-stream MRF to assess the economic feasibility and environmental impacts of recovering valuable recyclables from an MRF processing 120,000 tonnes per year (t/y). The TEA employs a discounted cash flow rate of return (DCFROR) analysis over a 20-year facility lifetime, along with a sensitivity analysis on the impact of different operating and economic parameters. Results show that the total fixed cost of building the MRF facility is $\$ $23 MM, and the operating cost is $\$ $45.48/tonne. Further the NPV of the MRF can vary from $\$ $3.57 MM to $\$ $60 MM, while 100-year global warming potential can range from 5.98 to 8.53 kg carbon dioxide equivalents (CO2-eq) per tonne of MSW. We have also found that MSW composition (arising from regional effects) significantly impacts costs, 100-year global warming potential, and other impact categories such as acidification potential, eutrophication potential, ecotoxicity, ozone depletion, photochemical oxidation, carcinogenic effects, and non-carcinogenic effects. Sensitivity and uncertainty analysis indicate that waste composition and market prices significantly impact the profitability of the MRF, and the waste composition mostly impacts global warming potential. Our analysis also indicates that facility capacity, fixed capital cost, and waste tipping fees are vital parameters that affect the economic viability of MRF operations.

36 MATERIALS SCIENCE↗

Liquid-induced topological transformations of cellular microstructures

The fundamental topology of cellular structures—the location, number and connectivity of nodes and compartments—can profoundly affect their acoustic, electrical5, chemical, mechanical and optical properties, as well as heat, fluid and particle transport. Approaches that harness swelling, electromagnetic actuation and mechanical instabilities in cellular materials have enabled a variety of interesting wall deformations and compartment shape alterations, but the resulting structures generally preserve the defining connectivity features of the initial topology. Achieving topological transformation presents a distinct challenge for existing strategies: it requires complex reorganization, repacking, and coordinated bending, stretching and folding, particularly around each node, where elastic resistance is highest owing to connectivity. Here we introduce a two-tiered dynamic strategy that achieves systematic reversible transformations of the fundamental topology of cellular microstructures, which can be applied to a wide range of materials and geometries. Our approach requires only exposing the structure to a selected liquid that is able to first infiltrate and plasticize the material at the molecular scale, and then, upon evaporation, form a network of localized capillary forces at the architectural scale that ‘zip’ the edges of the softened lattice into a new topological structure, which subsequently restiffens and remains kinetically trapped. Reversibility is induced by applying a mixture of liquids that act separately at the molecular and architectural scales (thus offering modular temporal control over the softening–evaporation–stiffening sequence) to restore the original topology or provide access to intermediate modes. Guided by a generalized theoretical model that connects cellular geometries, material stiffness and capillary forces, we demonstrate programmed reversible topological transformations of various lattice geometries and responsive materials that undergo fast global or localized deformations. In conclusion, we then harness dynamic topologies to develop active surfaces with information encryption, selective particle trapping and bubble release, as well as tunable mechanical, chemical and acoustic properties.

42 ENGINEERING↗

Arrested coarsening and large density fluctuations in driven particle mixtures in two dimensions

Abstract Using molecular dynamics simulations, we study a driven, nonadditive binary mixture of spherical particles confined to move in two dimensions and immersed in an explicit solvent consisting of point particles with purely repulsive interactions. We show that, without a drive, the mixture of spherical particles phase separates and coarsens with kinetics consistent with an Ising-like conserved dynamics. Conversely, when the drive is applied, the coarsening is arrested and the system develops large density fluctuations. We show that the drive creates domains of a characteristic size which decreases with an increasing force. Furthermore, we find that these domains are anisotropic and can be oriented either parallel or perpendicular to the drive direction. Finally, we connect our findings to existing theories of strongly-driven systems, pointing out the importance of introducing the explicit solvent particles to break the Galilean invariance of the system.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗