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At least 37 records · Page 2

Transport of colloidal particles in microscopic porous medium analogs with surface charge heterogeneity: experiments and fundamental role of single-bead deposition

Understanding colloid transport in subsurface environments is challenging due to complex interactions between colloids, ground water, and porous media over several length scales. Here, we study the transport of colloidal particles through bead-assembled microfluidic porous media analogs (PMAs) with surface charge heterogeneity. The pore-scale dynamics of colloidal particle deposition were measured, as well as the breakthrough curves (BTC) and retention profiles (RP) of deposited colloidal particles at the scale of the entire PMA. From pore-scale experiments, the maximum surface coverage (?max = 0.51) was measured directly, from which the surface blocking function and deposition coefficient (kpore = 3.56 s-1) were obtained. Using these pore-scale parameters, the transport of colloidal particles was modeled using a one-dimensional advection-dispersion equation under the assumption of irreversible adsorption between oppositely charged beads and colloids, showing good agreement with experimental data. This work presents a new approach to fabricate chemically heterogeneous porous media in a microfluidic device that enables direct measurements of pore-scale colloidal deposition. The approach allows a quantitative prediction of colloidal breakthrough and retention via coupling of direct measurements and an advection-dispersion-deposition model.

Guo, Yang↗

Temperature-responsive smart tracers for field-measurement of inter-well thermal evolution: Heterogeneous kinetics and field demonstration

Temperature-responsive smart tracers enable advanced warning of a “premature thermal breakthrough” and may therefore improve reservoir management and reduce financial risk. A successful calculation of inter-well fluid temperatures requires that temperature-dependent kinetics are known, which typically result from homogeneous batch reactor experiments. However, recent meso-scale field experiments at the Altona Field Laboratory involving fluid flow in a discretely-fractured reservoir suggest that silica-fluid interfaces may accelerate hydrolysis kinetics. Here, the Arrhenius parameters of phenyl acetate hydrolysis are investigated under heterogeneous reaction conditions in packed-bed column experiments. The breakthrough curve of the reaction product is compared to an inert reference tracer (carbon-cored nanoparticles). Temperatures experienced during field testing ranging from 10 to 40 °C were studied using a phosphate buffer solution to maintain a near-neutral pH, as found in the reservoir. The empirically-determined pre-exponential factor and activation energy values are subsequently used in a first-order kinetic model to improve calculations of effective reservoir temperatures for these meso-scale field tests. Here, the results suggest that hydrolysis reactions can directly monitor inter-well reservoir temperatures, but only if the influence of solid-fluid interactions are carefully accounted for.

15 GEOTHERMAL ENERGY↗

The Influence of Aqueous Dispersivity on Transport of Radiological Material at LANL MDA G - 20450

Aqueous dispersivity is a phenomenon by which a solute moving in groundwater mixes with water that does not contain the solute and becomes diluted. Solutes take paths of varying lengths through pore networks or experience slower velocities due to interactions with pore walls. Aqueous dispersivity leads to breakthrough curves with earlier arrival than expected in purely advective systems and persistent 'tails,' or late-arriving, dilute concentrations of the solute. Dispersivity can be longitudinal (in the direction of flow) or transverse (orthogonal to flow). LANL has disposed of radioactive material at Material Disposal Area (MDA) G since the late 1950's. Most of the disposed materials at MDA G are low-level waste (LLW), but other types of radioactive wastes are disposed or stored at the site. For example, there is a collection of remote-handled transuranic waste (RH-TRU) waste in 33 shafts, which were intended to be stored retrievably. Aqueous-phase radionuclides included in models of contaminant transport at MDA G are subject to dispersive processes in porous media of the vadose zone and saturated zone. To model dispersivity at MDA G probabilistically, we created site-specific distributions of aqueous dispersivity. First, we performed a comprehensive review of peer-reviewed publications, reports from other performance assessments of MDA G, and documentation from sites that were considered similar based on expert opinion, such as Yucca Mountain. Data were included from a wide range of sources, so that distributions developed based on the data reflect the current state of knowledge in properties of the subsurface environment. Data were grouped based on value type (e.g., determined via experiment or used in a different model), rock type, zone type (saturated or unsaturated), and site, and were weighted in the distributions according to their relevance to the site and zone type. We combined Monte Carlo simulation and bootstrapping techniques to produce approximate distributions of mean aqueous dispersivity. Distributions of dispersivity for saturated and unsaturated zone transport are differentiated by data weight and the length scales over which transport occurs. We find that underestimating or disregarding transverse dispersivity may lead to overstating simulated well capture in the saturated zone at MDA G. Neglecting transverse dispersivity is a common assumption due in part to use of one-dimensional transport models that do not consider solute spreading orthogonal to flow. Also, we find that variability in longitudinal dispersivity is associated with substantial travel time alterations in the MDA G unsaturated zone and in simulated contaminant breakthrough times at a downstream observation plane in the MDA G saturated zone. Finally, at large scales (>1000 m), a linear trend between the dispersivity coefficient and length over which transport occurs may overestimate the dispersivity coefficient. Future modeling work with application to solute spreading could include interacting advective and diffusive zones in the highly fractured basalt below MDA G. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Synthesis of Ionic Ultramicroporous Polymers for Selective Separation of Acetylene from Ethylene

The design of highly stable and efficient porous materials is essential for developing breakthrough hydrocarbon separation methods based on physisorption to replace currently used energy-intensive distillation/absorption technologies. Efforts to develop advanced porous materials such as zeolites, coordination frameworks, and organic polymers have met with limited success. Here, a new class of ionic ultramicroporous polymers (IUPs) with high-density inorganic anions and narrowly distributed ultramicroporosity is reported, which are synthesized by a facile free-radical polymerization using branched and amphiphilic ionic compounds as reactive monomers. A covalent and ionic dual-crosslinking strategy is proposed to manipulate the pore structure of amorphous polymers at the ultramicroporous scale. The IUPs exhibit exceptional selectivity (286.1–474.4) for separating acetylene from ethylene along with high thermal and water stability, collaboratively demonstrated by gas adsorption isotherms and experimental breakthrough curves. Modeling studies unveil the specific binding sites for acetylene capture as well as the interconnected ultramicroporosity for size sieving. Finally, the porosity-engineering protocol used in this work can also be extended to the design of other ultramicroporous materials for the challenging separation of other key gas constituents.

36 MATERIALS SCIENCE↗

Visualisation and outlier detection for probability density function ensembles

Abstract Exploratory data analysis (EDA) for functional data—data objects where observations are entire functions—is a difficult problem that has seen significant attention in recent literature. This surge in interest is motivated by the ubiquitous nature of functional data, which are prevalent in applications across fields such as meteorology, biology, medicine and engineering. Empirical probability density functions (PDFs) can be viewed as constrained functional data objects that must integrate to one and be nonnegative. They show up in contexts such as yearly income distributions, zooplankton size structure in oceanography and in connectivity patterns in the brain, among others. While PDF data are certainly common in modern research, little attention has been given to EDA specifically for PDFs. In this paper, we extend several methods for EDA on functional data for PDFs and compare them on simulated data that exhibit different types of variation, designed to mimic that seen in real‐world applications. We then use our new methods to perform EDA on the breakthrough curves observed in gas transport simulations for underground fracture networks.

97 MATHEMATICS AND COMPUTING↗

Markovian transport processes in a heterogeneous, variably saturated watershed: A multi-domain spatial Markov model

Transport processes in watersheds remain challenging to describe accurately with upscaled models because of their intricate complexities at multiple scales that can lead to multi-modal, non-Fickian breakthrough curves. One of the recent advances in solute transport modeling has been the Lagrangian spatial Markov model (SMM), which describes transport using velocity increments and models the correlated transitions between them. The method has been applied previously to saturated porous media and fractured media, but these successful applications suggest it may be useful for describing watershed scale processes as well. An existing, 3-D, heterogeneous variably saturated model of a headwaters catchment and classical random walk particle tracking were used to generate a forward simulation and the resulting transport was analyzed with a spatial Markov framework. Existing SMM methods were used to analyze the transport paths through the complex, unconfined domain and we found that the vadose zone plays an important role in the correlation structure. As such, a new kind of SMM is proposed, termed a multi-domain SMM (MD-SMM), that uses separate correlation models for auto-transitions in the vadose zone and the saturated zone, and for the cross-transitions between them. The MD-SMM improves representation of transport relative to the single domain model and can naturally delineate times when a particle is in the vadose zone or the saturated zone, adding an additional degree of realism to the upscaled model. Lastly, we show that the transition probability matrix for transport in the saturated portion of this unconfined system is approximately Markovian, which is an important validation of the proposed framework.

54 ENVIRONMENTAL SCIENCES↗

Nonparametric, data-based kernel interpolation for particle-tracking simulations and kernel density estimation

Traditional interpolation techniques for particle tracking include binning and convolutional formulas that use pre-determined (i.e., closed-form, parameteric) kernels. In many instances, the particles are introduced as point sources in time and space, so the cloud of particles (either in space or time) is a discrete representation of the Green’s function of an underlying PDE. As such, each particle is a sample from the Green’s function; therefore, each particle should be distributed according to the Green’s function. In short, the kernel of a convolutional interpolation of the particle sample “cloud” should be a replica of the cloud itself. This idea gives rise to an iterative method by which the form of the kernel may be discerned in the process of interpolating the Green’s function. When the Green’s function is a density, this method is broadly applicable to interpolating a kernel density estimate based on random data drawn from a single distribution. We formulate and construct the algorithm and demonstrate its ability to perform kernel density estimation of skewed and/or heavy-tailed data including breakthrough curves.

42 ENGINEERING↗

Catalytic hydrogenation of HMF to BHMF over copper catalysts

2,5-Bis(hydroxymethyl)furan (BHMF) is a bio-derived building block for polyester production, obtained via the hydrogenation of 5-hydroxymethylfurfural (HMF). First-principles thermodynamic equilibrium calculations indicate that this reaction is not thermodynamically limited under relevant conditions (e.g., 100 °C and high H 2 partial pressure). In this work, crude HMF was employed as the feedstock for BHMF synthesis. Initially, acidic impurities and humins were removed from unrefined HMF through filtration using a packed bed of γ-alumina. A comprehensive study of the filtration process is presented, including filtration kinetics, breakthrough curve analysis, and mathematical modeling. The purified HMF was subsequently hydrogenated over a 10 wt% CuZrO 2 catalyst, using ethanol as the reaction solvent. Batch reactions were first performed for collection of kinetic data to guide the transition to continuous flow operation. Kinetic data was collected in a fixed bed reactor at varying contact time, time on stream, temperature, and HMF concentration. This data was used to develop a kinetic model for HMF hydrogenation. Maximum BHMF production rates were achieved at 130 °C, accompanied by minor formation of byproducts from BHMF ring-opening reactions. The BHMF selectivity was 100 % at 100 °C although with lower reaction rates. Furthermore, catalyst stability tests revealed a loss of up to 50 % in catalytic activity within the first 24 h, likely due to the adsorption of HMF-derived oligomers that are not easily removed by filtration.

Crude HMF filtration↗

Encapsulation of highly viscous CO 2 capture solvents for enhanced capture kinetics: Modeling investigation of mass transfer mechanisms

The encapsulation of highly viscous liquid-like Nanoparticle Organic Hybrid Materials (NOHMs) inside a gas permeable polymer to form SIPs (Solvent Impregnated Polymers) significantly enhanced the CO 2 capture kinetics of NOHMs, leading to a remarkable 50-fold increase in CO 2 flux compared to the neat NOHMs. To understand the mechanism for enhanced CO 2 mass transfer within these hybrid materials, kinetic modeling of CO 2 uptake into SIPs containing polyethylenimine functionalized NOHMs, denoted NPEI-SIP, was conducted. CO 2 mass transfer into NPEI-SIP films was found to conform, both qualitatively and quantitatively, with a diffusion-controlled moving front model. The diffusion-controlled model was also used to simulate CO 2 uptake within a fixed bed containing polydisperse NPEI-SIP particles, and this model accurately predicted experimentally measured breakthrough curves at 25 °C and 50 °C. The 50-fold increase in gas flux was shown to be a consequence of the very large CO 2 permeability within the polymer–solvent composite. Furthermore, the increase in gas flux is also dependent on the diffusion–reaction regime in which the chemical solvent operates, and the largest improvement will occur when immobilizing solvents, such as NOHMs, which operate in the instantaneous-reaction regime. The CO 2 capacity (~3 mol CO 2 /kg) and saturation time (~5 min) of 430 μm SIP particles were comparable to popular CO 2 chemisorption materials such as amine grafted silicates, in spite of the slow kinetics of NOHM-I-PEI in liquid form (CO 2 saturation time ~24 h for a 1 mm thin film).

36 MATERIALS SCIENCE↗

Dimensionality effects on multicomponent ionic transport and surface complexation in porous media

Coulombic interactions between charged species in pore water and at surface/solution interfaces are of pivotal importance for multicomponent reactive transport in porous media. In this study, we investigate the impact of domain dimensionality on electrostatically coupled dispersion and surface-solution reactions during transport of acidic plumes and major ions in porous media. Column and quasi two-dimensional flow-through experiments were performed, with identical silica porous media and under the same advection-dominated conditions. Equal mass fluxes of different electrolyte solutions (i.e., HCl - pH ~ 2.8, NaBr - 100 mM, HCl - pH ~ 2.8 plus NaBr - 100 mM) were continuously injected in the 1-D and 2-D experiments and breakthrough curves of pH and major ions were measured at the outlet of the domains. The presence of pronounced ionic strength gradients in the transverse direction in the 2-D setup caused distinct retardation and transport behaviors of protons and major ions which were not observed in the one-dimensional column experiments. Furthermore, in the cases of salt electrolytes injection, considerably enhanced release of H + (>61%) from the quartz surface was observed in the multidimensional system compared to the one-dimensional setup. Reactive transport modeling was performed to reproduce the experimental outcomes and to analyse the coupling between transport processes, based on the Nernst-Planck formulation of diffusive/dispersive fluxes and on surface complexation reactions at the solid-solution interface. Electrostatic interactions between Na + , B – , and H + , and deprotonation of the quartz surface upon the formation of sodium outer-sphere complexes, are the primary controllers of the spatial and temporal features displayed by the pH and major ions measurements. The reactive transport simulations allowed us to interpret the experimental observations, to visualize the distribution and spatio-temporal evolution of dissolved and solid species, to identify a spatially heterogeneous zonation of Coulombic interactions with distinct behavior at the fringe and core of the injected plumes in the multidimensional setup, and to quantify the different components of the Nerst-Planck fluxes of the charged solutes. This study demonstrates that the domain dimensionality directly affects electrostatic interactions between charged aqueous species in the pore water and surface complexation reactions at the solid-solution interface. The non-trivial effects of dimensionality on multicomponent ionic transport result in a significantly different behavior in 1-D and 2-D systems.

58 GEOSCIENCES↗

Mechanistic definition and prediction of the mass exchange coefficient between rivers and hyporheic zones: The $α$ of two $Ω$s

Solute transport in interconnected rivers and hyporheic zones is typically modeled through dual-domain models where first-order solute mass transfer between the two domains, Ω R and Ω HZ , is represented by a coefficient α. The transient storage model (TSM) is an example of such an approach. In practice, α is determined by fitting the tails of solute tracer breakthrough curves using a TSM. This approach has led to ambiguity regarding α’s physical meaning and transferability. Here, in this work, we investigated the physical basis for α and tested it with virtual experiments through the fully coupled multiphysics model hyporheicFoam for the Ω R – Ω HZ system. hyporheicFoam explicitly simulated coupled flow and solute transport over a kilometer with centimeter-scale resolution. Model results were analyzed to calculate α following its theoretical definition directly. Using the determined α within a TSM enables accurate reproduction of solute transport, underscoring α’s physical relevance and precision.

54 ENVIRONMENTAL SCIENCES↗

Characterizing the impact of finite matrix block size on conservative particle transport through three-dimensional fracture networks

Mass transfer of solutes between fractures and the surrounding rock matrix exerts a noticeable signature on the tail of travel time distributions. When the width of the matrix is assumed to be infinite and advective transport through the fracture is sufficiently fast, the tails of the travel time distributions exhibit a classically expected slope of ψ(t) ∝ t -3/2 . However, studies have yet to characterize how solute transfer between fractures via diffusion through finite matrix blocks influences the tail’s slope in three-dimensional fractured media. Here, in this study, we assess the impact of finite matrix block size on breakthrough curve shape at different spatio-temporal scales by con ducting particle tracking simulations in three-dimensional discrete fracture networks. We consider a variety of hydrodynamic and geostructural proper ties to determine their relative impact on the resulting travel time distributions. We observe that the impact of matrix diffusion through a finite block on travel time distributions is similar to that of an infinite matrix block when the fracture spacing is sufficiently large, matrix diffusion is relatively weak, or transport is considered at an early control plane distance. We observe that the converse of these conditions, results in deviations from the classical ψ(t) ∝ t -3/2 scaling. These results provide a first step toward developing a metric to assess when finite block size effects are expected to significantly influence transport.

58 GEOSCIENCES↗

Understanding How Ligand Functionalization Influences CO2 and N2 Adsorption in a Sodalite Metal–Organic Framework

In this work, a detailed study is conducted to understand how ligand substitution influences the CO2 and N2 adsorption properties of two highly crystalline sodalite metal–organic frameworks (MOFs) known as Cu–BTT (BTT–3 = 1,3,5-benzenetristetrazolate) and Cu–BTTri (BTTri–3 = 1,3,5-benzenetristriazolate). The enthalpy of adsorption and observed adsorption capacities at a given pressure are significantly lower for Cu–BTTri compared to its tetrazole counterpart, Cu–BTT. In situ X-ray and neutron diffraction, which allow visualization of the CO2 and N2 binding sites on the internal surface of Cu–BTTri, provide insights into understanding the subtle differences. As expected, slightly elongated distances between the open Cu2+ sites and surface-bound CO2 in Cu–BTTri can be explained by the fact that the triazolate ligand is a better electron donor than the tetrazolate. The more pronounced Jahn–Teller effect in Cu–BTTri leads to weaker guest binding. The results of the aforementioned structural analysis were complemented by the prediction of the binding energies at each CO2 and N2 adsorption site by density functional theory calculations. In addition, variable temperature in situ diffraction measurements shed light on the fine structural changes of the framework and CO2 occupancies at different adsorption sites as a function of temperature. Finally, simulated breakthrough curves obtained for both sodalite MOFs demonstrate the materials’ potential performance in dry postcombustion CO2 capture. The simulation, which considers both framework uptake capacity and selectivity, predicts better separation performance for Cu–BTT. The information obtained in this work highlights how ligand substitution can influence adsorption properties and hence provides further insights into the material optimization for important separations.

adsorption capacities↗

Predictive Inverse Model for Advective Heat Transfer in a Short–Circuited Fracture: Dimensional Analysis, Machine Learning, and Field Demonstration

Identifying fluid flow maldistribution in planar geometries is a well–established problem in subsurface science/engineering. Of particular importance to the thermal performance of enhanced (or “engineered”) geothermal systems is identifying the existence of nonuniform (i.e., heterogeneous) permeability and subsequently predicting advective heat transfer. Here, machine learning via a genetic algorithm (GA) identifies the spatial distribution of an unknown permeability field in a two–dimensional Hele–Shaw geometry (i.e., parallel plates). The inverse problem is solved by minimizing the L2 norm between simulated residence time distribution (RTD) and measurements of an inert tracer breakthrough curve (BTC) (C–Dot nanoparticle). Principal component analysis (PCA) of spatially correlated permeability fields enabled reduction of the parameter space by more than a factor of 10 and restricted the inverse search to reservoir–scale permeability variations. Thermal experiments and tracer tests conducted at the mesoscale Altona Field Laboratory (AFL) demonstrate that the method accurately predicts the effects of extreme flow channeling on heat transfer in a single bedding–plane rock fracture. However, this is only true when the permeability distributions provide adequate matches to both tracer RTD and frictional pressure loss. Without good agreement to frictional pressure loss, it is still possible to match a simulated RTD to measurements, but subsequent predictions of heat transfer are grossly inaccurate. Here, the results of this study suggest that it is possible to anticipate the thermal effects of flow maldistribution, but only if both simulated RTDs and frictional pressure loss between fluid inlets and outlets are in good agreement with measurements.

42 ENGINEERING↗

On the Reliability of Parameter Inferences in a Multiscale Model for Transport in Stream Corridors

Nonreacting tracer tests capture information about physical processes in transient storage zones including the hyporheic zone (HZ). However, reliably extracting this information from breakthrough curves (BTCs) and distinguishing the effects of in-channel dispersion and transient storage are well-known challenges. Using BTCs from a nonreacting tracer test monitored at multiple locations, we explore ways for reliable parameter estimations. The identifiability of parameters is greatly influenced by the choice of forward and inverse modeling frameworks in addition to the quality of the data. Our forward model is a recently proposed multiscale model that uses subgrid transport models written in the Lagrangian form to represent transport along a diverse set of HZ pathways with a shape-free distribution of travel times. Joint distributions of HZ and channel parameters are estimated using the Markov Chain Monte Carlo technique. Numerical experiments show ambiguity between channel dispersion and HZ transport when the reach length is too short to allow significant solute-HZ interaction, the observation period is too brief to observe the tailing behavior, or the solute source is spread in time. In contrast, we obtained reliable parameter estimates by simultaneously fitting BTCs observed at different locations in the test reach using a single set of HZ parameters and section-specific channel areas and dispersion coefficients. Furthermore, this study demonstrates the estimation of travel time distributions, HZ exchange rates, and channel parameters in a new multiscale approach and offers guidance for extracting reliable parameter estimates from multiple BTCs.

54 ENVIRONMENTAL SCIENCES↗

Hyporheic Exchange Due to Cobbles on Sandy Beds

Hyporheic exchange induced by riverbed topography and roughness provides important ecosystem functions. We investigated how cobble clusters embedded in a finer-grained sand bed affect the near-bed channel flow and the exchange of surface and subsurface water. We tested how the spacing and embeddedness of cobbles altered hyporheic exchange through a three-dimensional fully coupled surface-subsurface model. The 3D modeling framework captured the full physics of the exchange process locating the lateral position of upwelling zones on the side of the cobble. As the cobbles protrude more into the channel, eddies appear downstream, with smaller vortices where cobbles are closer together. In our simulations, hyporheic exchange increased with the spacing and protrusion ratio. The travel time in the hyporheic zone also increased with the protrusion ratio because the hyporheic flow paths are longer when the cobble is more protruded. With different spacings at the highest protrusion ratio, the average slope of early time breakthrough curve was steeper for large spacing settings: the travel time increases as the spacing decreases.

54 ENVIRONMENTAL SCIENCES↗

Effects of Dissolution Regimes on Flow Channelization and Solute Transport in 3D Fracture Networks: Insights From Graph‐Based Reactive Transport Modeling

We investigate how mineral dissolution reshapes flow pathways and solute transport in three‐dimensional discrete fracture networks using a computationally efficient graph‐based reactive transport model. The DFNs are inspired by field‐site observations of fractured carbonate and represent realistic connectivity and structural heterogeneity. Flow is simulated with the Reynolds equation, and dissolution follows first‐order kinetics with diffusive limitations captured through an effective mass‐transfer coefficient. By systematically varying two key dimensionless parameters, the effective Damköhler number (Da), governing reaction versus advection rates, and a transport parameter (Da), analogous to the Thiele modulus, distinct flow channelization regimes emerge: mildly channelized at low G, highly channelized at intermediate Da, and extreme wormhole formation at high Da and low G. Eulerian and Lagrangian analyses, including breakthrough curves, particle tortuosity, dispersivity, and flow channeling indicators quantitatively characterize the progression of dissolution‐driven network restructuring. Across all regimes, initial fracture heterogeneity persists. The results underscore how the interplay between this initial structure, advection, reaction, and diffusion critically shapes subsurface flow pathways, with implications for applications ranging from groundwater remediation to enhanced geothermal systems.

54 ENVIRONMENTAL SCIENCES↗

Asymmetric rotations slow down diffusion under confinement

Translation and rotation are the two most fundamental forms of diffusion, yet their coupling mechanism is not clear, especially under confinement. Here, we provided evidence of the coupling between rotation and translation using a substituted benzene molecule as an example. A counterintuitive behavior was observed where the movement of the smaller molecule with an asymmetric shape was unexpectedly slower than the larger one with a symmetric shape in confined channels of zeolite. We showed that this diffusion behavior was caused by the presence of the specific and selective interaction of the asymmetric guest with the pores, which increased the local restricted residence time, thus inhibiting the translation under confinement, as further confirmed by dynamic breakthrough curves, uptake measurements, quasi-elastic neutron scattering, and 2 H solid-state NMR techniques. Our work correlated asymmetric rotation and diffusion under a confined environment, which enriched our understanding of the coupling between rotation and translation and could shed light on a fundamental understanding of the diffusion process.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗