Kinetic Regime Research Articles

The performance of artificial molecular machines relieson theinterplay between molecular design and environmental factors, yethow solvation shapes their energy landscapes and kinetics remainspoorly understood. Here, we combine well-tempered and infrequent metadynamicsto investigate equilibrium shuttling in a minimal [2]­rotaxane inspiredby Borsley’s fuel-driven molecular motor. By systematicallyvarying solvent polarity and hydrogen-bonding capacity, we uncoverdistinct thermodynamic and kinetic regimes that govern macrocyclemotion. In highly polar, hydrogen-bond-accepting media, the macrocycleadopts a symmetric distribution between binding sites, with enthalpicand entropic forces in direct competition. Conversely, in low-polarity,hydrogen-bond-donating environments, the axle undergoes a conformationalcollapse that entropically biases occupancy toward a single stationin the absence of chemical fuel. Despite comparable free-energy barriersacross conditions (9–13 kcal/mol), the transition pathwaysexhibit pronounced solvent-dependent asymmetries and energetic ruggedness.These findings provide a molecular-level framework for understandinghow solvation dictates passive ratchet behavior and offer strategicinsights for designing high-performance molecular machines tailoredto complex media.

Dynamic single-molecule sensing (DSMS) enables real-time monitoring of molecular interactions with exceptional sensitivity and kinetic resolution, offering significant potential for ultrasensitive biomarker detection. However, existing DSMS platforms often require probe redesign or external force modulation to tune binding kinetics, which limits system simplicity and scalability. Here, we report an intrinsically regulated DSMS platform engineered through systematic optimization of nanoparticle size and buffer ionic strength. We first established a theoretical model describing two dominant kinetic regimes─damping-dominated and entropic-confinement-dominated dynamics─and identified a critical inflection point where sensitivity and specificity are balanced. While this model provides insights into kinetic tuning, practical challenges such as nanoparticle heterogeneity and matrix complexity limit its direct application for sensor design. To address this, we empirically optimized a previously developed DSMS system using average binding dwell time and total binding events as two key performance indicators. The optimized platform, featuring 150 nm polystyrene nanoparticles under 150 mM NaCl, achieved femtomolar detection of thrombin and HIV-1 p24 antigen with limits of detection of 213.9 fM and 4.3 fM, respectively. Notably, the platform maintained excellent specificity in diluted serum through dwell-time filtering, highlighting its robustness in complex biological matrices. This work establishes a novel DSMS strategy that enables efficient single-molecule sensing without probe modification or external actuation, paving the way for scalable, high-performance biomarker detection in clinical diagnostics and point-of-care applications.

The phosphine-catalyzed [3 + 2] cycloaddition of allenoateswithenones provides an efficient route to five-membered carbocycles andexhibits regioselectivity that depends on the substituents of thesubstrates. To elucidate the origin of the substituent effects, densityfunctional theory calculations and kinetic modeling are performedon the reactions of unsubstituted/substituted allenoates (2/8) with arylideneoxindoles (e-iii). Nucleophilicattack of PPh3 on the allenoate generates interconvertible Z-, E-, and twisted adducts: the formertwo participate in regioselective [3 + 2] cyclization. For 2, the major γ-regioisomeric product forms via the E-adduct. Kinetic modeling predicts an α:γ ratio of 1:99,consistent with the experimentally observed 10:90 selectivity. Bycontrast, the reaction of 8 yields the α-regioisomervia the Z-adduct. The computed isomer ratio of 99:1agrees with the experimental value of >95:5. The switch in regioselectivityis attributed to the interplay between electronic and steric effects.Secondary orbital interactions favor the γ-[3 + 2] pathway.Substituent-induced steric hindrance is found to elevate the activationbarriers to cyclization, thereby shifting the kinetic regime towardCurtin–Hammett control and modulating regioselectivity. Thesefindings highlight the pivotal role of adduct dynamics in phosphinecatalysis and clarify the conditions under which Curtin–Hammettcontrol governs product selectivity.

The understanding and control of protein crystallization are crucial in structural biology, drug development, and biomaterial design. This study introduces a unified framework for modeling and comparing crystallization kinetics using selected growth functions. Experimental datasets from the literature for four proteins, Lysozyme, Thaumatin, Ribonuclease A, and Proteinase K, under Hanging Drop and Langmuir–Blodgett conditions were analyzed. Five kinetic models, Avrami, Kashchiev, Hill, Logistic, and Generalized Sigmoid (GSM), were fitted to size–time data of the four benchmark proteins. From each fit, four descriptors were extracted: crystallization half-time, time of maximum growth, width at half-maximum, and peak growth rate. These metrics summarize crystallization dynamics and enable cross-comparison of proteins and methods. Langmuir–Blodgett templating accelerated onset and improved synchrony, though the effect varied by protein and model. Logistic, Hill, and GSM models provided consistent fits across most conditions, while Avrami and Kashchiev were more sensitive to early or late deviations. Notably, descriptor extraction remained reliable even with limited or uneven sampling, revealing kinetic regimes such as synchrony, asymmetry, or prolonged nucleation, not evident in raw data. This transferable analytical framework supports quantitative evaluation of crystallization behavior, aiding screening, process optimization, and time-resolved structural studies.

Despite significant attention directed toward affinity hydrogels as promising platforms for the controlled storage of therapeutic molecular cargo, the loading process remains incompletely understood. Notably, the direct link between surface-level binding interactions and bulk cargo uptake into these hydrogels remains unresolved. Here, we propose a coupling framework for the interplay between microscopic polymer-cargo interfacial interactions and macroscopic bulk uptake dynamics. In contrast to conventional empirical models, our approach explicitly integrates cargo-polymer interaction, enabling the identification of performance limits. Kinetically, we resolve the characteristic loading time as the system transitions between bulk-dominated and hydrogel-dominated kinetic regimes as a function of polymer-cargo binding affinity. Thermodynamically, we demonstrate that cargo permeability within the hydrogel is governed by the product of equilibrium partitioning and diffusivity, thereby revealing water-mediated modulation of cargo uptake efficacy. Collectively, by bridging microscale interactions with macroscale system behavior governing molecular cargo loading in affinity hydrogels, we re-highlight their potential as promising therapeutic storage as well as delivery platforms.

Physisorption is a reversible exothermic phenomenon wheremolecularkinetic energy is limited and interactions between guest moleculesand materials are favored at low temperatures. However, in certainultramicroporous materials, physisorption can be impacted by subtlestructural changes on decreasing temperature that slows or even stopsadsorbate diffusion, circumventing thermodynamic expectations. Theseunique ultramicroporous materials are described as temperature-regulatedgating adsorbents and, given their special properties, can facilitatemix-and-match gas separations by simply controlling temperature. Todate, though understood to be remarkably useful, there is still ambiguityabout how best to identify, characterize, and rationalize the performanceof these materials. To address this issue, we provide a practicalanalytical framework of a model gating material, Al­(HCOO)3 (ALF). Our work illustrates how the gating effect in ALF originatesfrom the changing dynamics of the formate linkers that define theapertures between porous cavities. As formate dynamics increase withtemperature, new kinetic adsorption regimes for an adsorbate can beaccessed, marked by kinetic inflection temperatures (KITs). Identificationof these temperatures allows kinetic or absolute gating separationsto be devised without exhaustive experimentation. However, thoughan elevated temperature regime may promote fast diffusion for an adsorbate,adsorption quantities can be minimal if thermodynamics of adsorptionhave been overcome. By using gas sorption studies with noble gases,H2, N2, O2, CO2, and C2H2, as well as crystallography, spectroscopy, andmodeling, our work elucidates how the convoluted effects of thermodynamicsand kinetics affect a system like ALF and how they can be leveragedfor separation design.

A semi-analytic model formalism is systematically developed to analyze the effects of kappa-distributed lighter constituents and the resulting kappa-modified polarization force on the Jeans instability in EiBI-gravitating dust molecular clouds (DMCs). The lighter constituents (electrons and ions) are considered to follow non-thermal kappa-velocity distribution. The constitutive massive dust grains are treated as EiBI-gravitating fluids. A generalized linear quadratic dispersion relation is derived using spherical normal mode analysis without any quasi-classic approximation. The resulting dispersion relation is analyzed in both the hydrodynamic and kinetic regimes along with their corresponding modified instability criteria. The characteristics of oscillatory and propagatory modes are illustratively analyzed. It is seen that the EiBI gravity introduces a new velocity term, the EiBI-induced velocity, in the dispersion relation. In contrast, the non-thermal kappa-distributed constituents significantly enhance the polarization force against their respective Maxwellian counterparts. The kappa-modified polarization force and the negative EiBI gravity parameter have destabilizing influences, unlike that with the positive EiBI parameter. An enhanced polarization interaction parameter and positive EiBI parameter reduce the real normalized frequency. Consequently, the phase velocity exhibits strong dispersion, increasing with the wavenumber until reaching saturation, after which it transitions into a weakly dispersive regime. These findings provide new theoretical insights on the gravitational collapse mechanisms in the ultracompact Hii regions of dense DMCs towards bounded structure formation.

The linear Rayleigh-Taylor (R-T) instability and the propagation of the internal waves are analytically studied in ultra-relativistic degenerate viscoelastic quantum fluids. A generalized hydrodynamic fluid model is considered composed of strongly coupled non-degenerate ions and weakly coupled ultra-relativistic degenerate electrons with their radiation effects in the presence of a uniform magnetic field and vertically downward gravity. The impact of quantum corrections and the fluid rotation is included in the momentum transport equation in terms of the Bohm potential and the Coriolis force. A generalized dispersion relation is derived using the normal mode method and discussed for two different cases of interest, namely hydrodynamic and kinetic regimes. The numerical investigation reveals that the thermal radiation of the ultra-relativistic degenerate electrons, quantum correction, and compressible viscoelastic speed significantly suppress the onset of R-T instability in the medium. In contrast, the high-strength magnetic field strongly supports the excitation of R-T instability in the configuration. The rotation of the fluid remarkably reduces the instability growth rate without modifying the instability criterion. The outcomes are useful for understanding the R-T instability excitation and internal wave propagation in different dense astrophysical plasma environments, such as the core of white dwarfs.

Abstract Turbulence is a complex physical process prevalent in modern physics, particularly in ionized environments like interstellar gas, where magnetic fields play a dynamic role. However, the precise influence of magnetic fields in such settings remains unclear. We employ the Alfvén Mach number, ${\cal M}_{\rm A} = \sqrt{E_{\rm k}/E_B}$, to gauge the magnetic field’s significance relative to turbulent motion, uncovering diverse interaction patterns. In the low-${\cal M}_{\rm A}$ magnetic regime, the field is force-free, yet gas motion does not align with it. At intermediate ${\cal M}_{\rm A}$ (magnetic-kinetic transition regime), velocity and magnetic fields show peak alignment, likely due to rapid relaxation. In the high-${\cal M}_{\rm A}$ kinetic regime, both fields are irregular and unaligned. These regimes find observational counterparts in interstellar gas, highlighting the multifaceted nature of MHD turbulence and aiding future astrophysical interpretations.

Abstract This article attempts to summarize our understanding of heat flow in different solid materials and its relationship to atomistic structure of materials. This knowledge can be used to understand and design materials for electricity generation or cooling through the thermoelectric effect. We start with the fundamentals of heat transport in solids: mechanisms of phonon scattering in crystals, the role of interfaces and coherence, and the relationship between chemical bonding and heat transport will be elucidated. Theories used to model thermal conductivity of solids will be exposed next. They include the Green–Kubo formulation, Boltzmann transport equation and its recent quantum extensions, and Allen–Feldman theory of heat diffusion in noncrystalline solids and its recent extensions. In terms of phenomenology, we will distinguish between the kinetic regime based on independent single carriers and the collective or hydrodynamic one which occurs when normal or momentum-conserving processes dominate. Next, we will focus on advanced measurement and characterization techniques, and the knowledge extracted from them. Nanoscale thermal conductivity methods, such as the pump-probe thermoreflectance methods (TDTR/FDTR), have become fairly common allowing researchers to measure thermal conductivity of thin-film thermoelectrics. We will review recent advances of the method: the Gibbs excess approach, which measures thermal resistance across a grain boundary of polycrystals through mapping TDTR/FDTR measurements, and the transient Raman method, where pump-probe Raman spectroscopy realizes in-plane thermal conductivity measurements of two-dimensional materials even on a substrate. We will also review the progress in mode-resolved phonon property measurements, such as inelastic x-ray scattering for thin-film samples, which allows direct observation of the modulation of phonon band and lifetime by nanostructures, and thermal diffuse scattering for quick characterization of phonon dispersion relations. Finally, because the main focus of this issue is thermoelectrics, we will review different classes of materials and strategies to lower their thermal conductivities. Graphical abstract

Abstract The periphery surrounding oxide‐supported metal nanoparticles plays a crucial role in many catalytic reactions that exhibit strong metal‐oxide promotional effects. Engineering this catalytically active periphery, where kinetically relevant surface intermediates are efficiently turned over, offers a pathway to optimized performance, yet it remains challenging due to the need for precise control over nanospatial catalyst features. Herein, we address this subject for the relevant case of methanol synthesis by CO2 hydrogenation on Cu/ZrO2 catalysts. The methanol synthesis rate reaches a maximum at a surface‐to‐surface Cu interparticle distance of ca. 15 nm. Operando modulation–excitation diffuse reflectance infrared spectroscopy reveals that this optimal spacing maximizes the fraction of surface‐bound HCOO* intermediates, stabilized on coordinatively unsaturated Zr(IV) Lewis acid sites on the ZrO2 support, which are dynamically involved in catalysis. This particle spacing represents a shift in the reaction's kinetic control regime and the apparent activation energy for methanol synthesis. Engineering Cu interparticle spacing to the optimal value results in exceptionally high metal‐specific methanol formation rates under industrially relevant reaction conditions. More broadly, our findings highlight that, beyond metal particle size, interparticle spacing is a key design parameter for catalyst systems featuring functional metal‐oxide interfaces.

The periphery surrounding oxide‐supported metal nanoparticles plays a crucial role in many catalytic reactions that exhibit strong metal‐oxide promotional effects. Engineering this catalytically active periphery, where kinetically relevant surface intermediates are efficiently turned over, offers a pathway to optimized performance, yet it remains challenging due to the need for precise control over nanospatial catalyst features. Herein, we address this subject for the relevant case of methanol synthesis by CO2 hydrogenation on Cu/ZrO2 catalysts. The methanol synthesis rate reaches a maximum at a surface‐to‐surface Cu interparticle distance of ca. 15 nm. Operando modulation–excitation diffuse reflectance infrared spectroscopy reveals that this optimal spacing maximizes the fraction of surface‐bound HCOO* intermediates, stabilized on coordinatively unsaturated Zr(IV) Lewis acid sites on the ZrO2 support, which are dynamically involved in catalysis. This particle spacing represents a shift in the reaction's kinetic control regime and the apparent activation energy for methanol synthesis. Engineering Cu interparticle spacing to the optimal value results in exceptionally high metal‐specific methanol formation rates under industrially relevant reaction conditions. More broadly, our findings highlight that, beyond metal particle size, interparticle spacing is a key design parameter for catalyst systems featuring functional metal‐oxide interfaces.

While particle-laden flows are of great interest for a wide variety of applications, accurately accounting for particle–particle collisions can be challenging. In this work, three particle collision strategies based on the hard-sphere paradigm (event-driven (EDHS), time-driven (TDHS), and direct simulation Monte Carlo (DSMC)) are considered in order to gain insight into which method is best suited for use in aerospace applications. First, a spatially homogeneous 0-D setup was investigated in the kinetic regime to leverage theoretical results from kinetic theory. While the DSMC method showed excellent agreement with the theoretical kinetic collision rate, both the EDHS and TDHS methods displayed inaccurate collision rates due to an artificially increased particle volume fraction from the use of simulated particle bundles. Next, a particle-laden nozzle setup was considered using the Dust Simulation and Tracking plug-in for the US3D unstructured finite-volume CFD solver. Comparisons of the particle-induced surface erosion on the test article were made with both elastic and inelastic particle collision parameters using the DSMC and TDHS methods. Both the TDHS and DSMC methods agreed extremely well for both the elastic and inelastic setups, although there is a slight discrepancy in the results for the inelastic comparison. Based on the overall results of the two studies in this work, the DSMC method was determined to be the most suitable for aerospace applications (i.e., cases with low volume fractions) because of its accuracy, efficiency, ability to handle arbitrary particle weights, and ease of implementation on parallel architecture.

ABSTRACT A comprehensive understanding of solar coronal heating and charged particle acceleration remains one of the most critical challenges in space and astrophysical plasma physics. In this study, we explore the contribution of Alfvén waves – both in their kinetic (KAWs) and inertial (IAWs) regimes – to particle acceleration and solar coronal heating. Employing a kinetic plasma framework in the generalized Vlasov–Maxwell model, we analyse the dynamics of these waves with a focus on the perpendicular (i.e. across the magnetic field lines) Poynting flux vectors and the net resonant speed of the particles. We found the Poynting flux of KAWs decays rapidly, indicating short-range energy transport, while IAWs exhibit slower decay, enabling energy transfer over larger distances (R$_{\text{Sun}}$) in the solar corona. We also evaluate the electric potentials associated with KAWs and IAWs and find the KAW’s potentials are significantly enhanced at larger wavenumbers ($k_x \rho _i>0.1$) regimes, while IAWs exhibit reduced parallel and enhanced perpendicular electric potentials, governed by the perturbed electric fields (${E_x}$ and ${E_z}$) values. Additionally, we determine the net resonant speed of particles in the perpendicular direction and demonstrate that these wave–particle interactions can efficiently heat the solar corona over extended distances R$_{\text{Sun}}$. Finally, we quantify the power transported by KAWs and IAWs through solar flux loop tubes, finding that both wave types deliver greater energy with increasing ${T_e/T_i}$ and $c k_x/\omega _{pe}$ values. These insights not only deepen our theoretical understanding of wave-driven heating mechanisms but also provide valuable implications for interpreting solar wind, corona, heliospheric, and magnetospheric dynamics.

Generation and Dynamics of the Hall Magnetic Field during Sub-Alfvén Plasma Expansion in the Kinetic Regime

Force production by type-I myosins influences endocytic progression in many cell types. Because different myosin-I isoforms exhibit distinct force-dependent kinetic properties, it is important to investigate how these properties affect endocytic outcomes, and the mechanisms through which myosin-I contributes to endocytosis. To this end, we adapted our agent-based simulations of endocytic actin networks and incorporated nonprocessive, single-headed myosin motors at the base of the endocytic pit. We varied the unbinding rate and the force dependence of myosin unbinding. Our results revealed that the inclusion of myosin motors facilitated endocytic internalization, but only under kinetic regimes with rapid and less force-sensitive unbinding. Conversely, slow or strongly force-dependent unbinding impeded endocytic progression. As membrane tension increased, the boundary between assistive and inhibitory phases shifted, allowing the myosins to assist over larger regions of the kinetic landscape. Myosin-I's contribution to internalization could not be explained by direct force transduction or increased actin assembly. Instead, the myosins collectively bolstered the robustness of internalization by limiting pit retraction.

A new analytic model of isothermal evaporation of a sessile droplet in the form of a spherical cap is presented. This model is based on the rigorous theory of diffusion mass transfer and takes into account the intrinsic kinetics of the evaporation process. Due to its rigor, the presented model does not include the contact angle correction parameter f(θ) that is used in other models. An analysis of the presented model was conducted showing that a sessile droplet can evaporate in the diffusion-kinetic, diffusion, or kinetic regime. Each of these cases was considered separately. The case of sessile droplet evaporation in the constant contact radius mode (pinning) and the case of sessile droplet evaporation in the constant contact angle mode were also considered separately. A comparison of the calculated data obtained within the framework of the presented model with available experimental data on the evaporation kinetics of sessile droplets of ethanol and water into air was carried out. This comparison demonstrated that the presented model perfectly describes experimental data. In addition, this comparison demonstrated that to obtain correct results, a sessile droplet along with its surrounding gas must be isolated from the ambient atmosphere when an experiment to study the evaporation kinetics of the droplet is conducted.

Understanding the kinetics of zinc electrodeposition on current collectors is crucial for improving aqueous zinc-metal battery (AZMB) performance, yet it remains largely unexplored. A major challenge within the field is the inconsistent reporting of kinetic parameters, particularly the exchange current density (j0), which is essential for accurately modeling and simulating zinc electrodeposition reactions. In this study, fast scan voltammetry on tungsten ultramicroelectrodes (UMEs) is employed to decouple mass transfer effects and isolate charge transfer kinetics. This results show that while zinc electrodeposition is a two-electron process, the rate-limiting step involves a one-electron transfer, validated through Butler-Volmer and Marcus-Hush models. This work also identifies significant limitations of Tafel analysis for certain zinc electrolytes systemsl, as their kinetically quasi-reversible/irreversible nature prevents the existence of a true Tafel regime (±118 mV kinetic regime). For such systems, the Allen-Hickling approach is proposed as a more accurate method for probing zinc electrodeposition kinetics. We report j0 values for ZnSO4 (0.20 A/cm2), Zn(OTf)2 (0.42 A/cm2), and ZnCl2 (0.46 A/cm2) and provide clear guidelines for precise kinetic analysis based on the width of the kinetic regime. Finally, the impact of accurate kinetic parameter measurements on coin cell performance is demonstrated, revealing that lower accurately determinedj0 values correlate with improved long-term cycling stability, following the trend ZnSO4 > Zn(OTf)2 > ZnCl2, aligning with predictions from Sands' model. This work provides the first systematic kinetic investigation of counter anions in aqueous zinc-metal batteries, offering critical insights into how electrolyte composition influences charge transfer kinetics. These findings advance our fundamental understanding of AZMB kinetics and offer a framework for optimizing electrolyte compositions and electrode designs to enhance battery performance and durability.

Simulating solar flares requires capturing both large-scale magnetohydrodynamic (MHD) evolution and small-scale kinetic processes near reconnection sites. Bridging these scales has been a significant computational challenge. This study introduces a Particle-In-Cell (PIC) solver integrated within the DISPATCH framework, facilitating seamless embedding within MHD simulations. This development aims to enable self-consistent multi-scale solar flare simulations. Our PIC solver, inspired by the PhotonPlasma code, addresses the Vlasov–Maxwell equations in collisionless plasma. We validate its accuracy through fundamental plasma tests—including plasma oscillations, two-stream instability, and current sheet reconnection. To make kinetic simulations computationally feasible, we employ physical adjustment of constants (PAC), modifying the speed of light, elementary charge, and electron mass to shift plasma scales. Additionally, we implement and validate a coupling strategy that enables smooth transitions between kinetic and fluid regimes. The PIC solver successfully recovers expected plasma dynamics and electromagnetic field behaviour. Our analysis highlights the effects of PAC on reconnection dynamics, underscoring the importance of transparent and well-documented scaling choices. Test cases involving propagating waves across PIC-MHD interfaces confirm the robustness of our coupling approach. The integration of the PIC solver into the DISPATCH framework makes it possible to run self-consistent, multi-scale solar flare simulations. Our approach provides a computationally efficient foundation for investigating reconnection physics in large-scale astrophysical plasmas.

Heterogeneity in extrusion-based 3D-printed thermoplasticpolymersis generally both challenging to control and harmful to mechanicalperformance. Abrupt changes in material properties at the interfacesbetween roads are of particular interest due to the prevalence ofpoor inter-road adhesion. To gain insight into the origins of heterogeneitiesin 3D-printed parts, we report a combination of synchrotron-based in situ X-ray microdiffraction and infrared pyrometry tomap the formation and evolution of crystallinity in polyether etherketone (PEEK) in a series of single-road-width, two-road-tall prints.In all cases, the in situ maps show that crystallinityin the second road takes longer to form but reaches a higher degreeof order compared to that of single-road prints. Both trends are attributedto the observation from IR pyrometry that the first road cools fasterthan the second, which is itself attributed to the higher thermalconductivity of the (copper) print bed compared to that of the firstroad. Beyond these differences, detailed analysis of crystallizationkinetics suggests that crystallization in the first and second roadsoccurs in distinct kinetic regimes. Most remarkably, we find thatthe first road undergoes significant cold crystallization as the secondroad is deposited on top of it, leading to a sharp and persistentcrystallinity gradient between the first and second roads. We showthat this observation pertains not only to the two-road prints examinedhere but also to variations in crystallinity observed previously inmulti-layered, multi-road prints. Specifically, cold crystallizationinduced by newly deposited roads in adjacent, already-deposited roadsappears to be a general phenomenon and may contribute to poor inter-roadand interfacial adhesion.