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Thermodynamically consistent forward and reverse degrees of rate control in reversible reactions
The net rate of a composite reaction is the difference between the forward and reverse reaction rates, which are kinetically distinct despite sharing elementary reaction steps and therefore have different rate-controlling transition states and species. Thus, degrees of rate control defined to identify rate-controlling transition states and species for the net rate confound contributions from the forward and reverse reactions. Herein, the forward and reverse degrees of rate control are defined to independently quantify the extent that species and transition states control the forward and reverse rates in reversible reactions. These degrees of rate control are defined as the relative change in the forward and reverse reaction rates per k B T decrease in the standard-state molecular free energies of transition states and species, and they are related to experimentally measurable quantities such as steady-state fractional coverages, reaction orders, and energies and entropies of activation of the forward and reverse reaction rates. The forward/reverse degrees of rate control represent stoichiometric coefficients for species and transition states in an equilibrium between the apparent initial states and the apparent transition states of the apparent rate-controlling steps of forward and reverse overall reactions. At equilibrium, the apparent transition states for the forward reaction and reverse reaction converge, and thus the forward and reverse rate-controlling steps combine to form a single apparent rate-controlling step at equilibrium. Here, this apparent rate-controlling step is comprised of an apparent initial state, transition state, and final state, where the apparent final state of the forward reaction is the apparent initial state of the reverse reaction. The apparent rate-controlling step behaves identically to an elementary step reaction at equilibrium with a pseudo-mass-action rate function given by the transition-state-theory (TST) form rate function (Foley and Bhan, 2020) with a stoichiometric number equal to the affinity-averaged stoichiometric number, $\bar{σ}$ The ratio of the forward and reverse TST-form rate functions is identical to the overall thermodynamic equilibrium relation, consistent with the principles of microscopic reversibility and detailed balance at equilibrium.
Concepts Relevant for the Kinetic Analysis of Reversible Reaction Systems
The net rate of a reversible chemical reaction is the difference between unidirectional rates of traversal along forward and reverse reaction paths. In a multistep reaction sequence, the forward and reverse trajectories, in general, are not the microscopic reverse of one another; rather, each unidirectional route is comprised of distinct rate-controlling steps, intermediates, and transition states. Consequently, traditional descriptors of rate (e.g., reaction orders) do not reflect intrinsic kinetic information but instead conflate unidirectional contributions determined by (i) the microscopic occurrence of forward/reverse reactions (i.e., unidirectional kinetics) and (ii) the reversibility of reaction (i.e., nonequilibrium thermodynamics). This review aims to provide a comprehensive resource of analytical and conceptual tools which deconvolute the contributions of reaction kinetics and thermodynamics to disambiguate unidirectional reaction trajectories and precisely identify rate- and reversibility-controlling molecular species and steps in reversible reaction systems. The extrication of mechanistic and kinetic information from bidirectional reactions is accomplished through equation-based formalisms (e.g., De Donder relations) grounded in principles of thermodynamics and interpreted in the context of theories of chemical kinetics developed in the past 25 years. Here, the aggregate of mathematical formalisms detailed herein is general to thermochemical and electrochemical reactions and encapsulates a diverse body of scientific literature encompassing chemical physics, thermodynamics, chemical kinetics, catalysis, and kinetic modeling.
Equilibrium spin polarization arising from chirality
Chirality-induced spin selectivity (CISS) describes how chiral molecules and materials generate spin polarization even at thermal equilibrium. This observation has challenged established principles of microscopic reversibility and Onsager reciprocity. We resolve this paradox by formulating a pseudo-Hermitian quantum framework that separates thermodynamic equilibrium from time-reversal symmetry. Within this approach, structural chirality and electron correlations, irrespective of their microscopic origin, are sufficient to produce CISS observables. Chirality enters through a non-local metric η that couples spin and spatial motion, leading to real spectra, unitary evolution, and thermodynamic consistency. The framework predicts a chirality-induced spin magnetic ordering characterized by a spin-displacement order, which reconciles equilibrium spin polarization with detailed balance and explains the persistence of CISS in materials composed of light elements. We derive generalized Onsager-Casimir relations that respect the observed CISS symmetry, i.e., parity $(\mathscr{P})$-odd and time-reversal $(\mathscr{T})$-odd, but exhibiting $\mathscr{PT}$-even symmetry. This approach establishes a coherent foundation for equilibrium CISS and provides a route to link chemical chirality with measurable spin-to-charge conversion effects.
Olefin Coupling Catalyzed by (Pybox)Os Complexes via Osmacyclopentane Intermediates: Comparison with Isoelectronic (Phebox)Ir
(Pybox)Os is found to catalyze alkene hydrovinylation, effecting the dimerization of ethylene, tail-to-tail coupling of propene and 1-butene, and cross-coupling of ethylene with higher α-olefins. This reactivity contrasts with the previously reported dehydrogenative coupling of ethylene to give butadiene catalyzed by the isoelectronic fragment (Phebox)Ir. The reaction mechanism was investigated through computational and experimental means. Both the Os- and Ir-catalyzed reactions proceed through a [2 + 2 + 1] cyclization of the corresponding bis-olefin complex to yield an experimentally observed metallacyclopentane intermediate. In both cases, the metallacyclopentane undergoes β- H elimination, via a dechelated κ 2 -pincer-ligated intermediate, to yield a σ−π-but-3-enyl hydride complex or derivative. Both the greater reactivity and the distinct chemoselectivity of the Os system relative to the Ir system are attributable to C−H reductive elimination by the σ−π-but-3-enyl hydride having a barrier for Os much lower than that for Ir. This lower barrier to C−H elimination for Os is unexpected given that the thermodynamic driving force for elimination is much less for Os than for Ir. Computational studies of model complexes were conducted, comparing (Pybox)Os(L)(CH 3 )(H) with the isoelectronic (Phebox)Ir(L)(CH 3 )(H). The results indicate that the more facile kinetics with Os relative to Ir may be general for C−H elimination from six-coordinate d 6 complexes of the two metals, as well as for the microscopic reverse, i.e., C−H addition to the corresponding four-coordinate d 8 species.
Mixed quantum/classical theory for rotational energy exchange in symmetric-top-rotor + linear-rotor collisions and a case study of the ND 3 + D 2 system
The extension of mixed quantum/classical theory (MQCT) to describe collisional energy transfer is developed for a symmetric-top-rotor + linear-rotor system and is applied to ND 3 + D 2 . State-to-state transition cross sections are computed in a broad energy range for all possible processes: when both ND 3 and D 2 molecules are excited or both are quenched, when one is excited while the other is quenched and vice versa, when the ND 3 state changes its parity while D 2 is excited or quenched, and when ND 3 is excited or quenched while D 2 remains in the same state, ground or excited. In all these processes the results of MQCT are found to approximately satisfy the principle of microscopic reversibility. For a set of sixteen state-to-state transitions available from the literature for a collision energy of 800 cm –1 the values of cross sections predicted by MQCT are within 8% of accurate full-quantum results. A useful time-dependent insight is obtained by monitoring the evolution of state populations along MQCT trajectories. It is shown that, if before the collision, D 2 is in its ground state, the excitation of ND 3 rotational states proceeds through a two-step mechanism in which the kinetic energy of molecule–molecule collision is first used to excite D 2 and only then is transferred to the excited rotational states of ND 3 . Finally, it is found that both potential coupling and Coriolis coupling play important roles in ND 3 + D 2 collisions.
Rate coefficients for rotational state-to-state transitions in H 2 O + H 2 O collisions for cometary and planetary applications, as predicted by mixed quantum-classical theory
We present new calculations of collision cross sections for state-to-state transitions between the rotational states in an H 2 O + H 2 O system, which are used to generate a new database of collisional rate coefficients for cometary and planetary applications. Calculations were carried out using a mixed quantum-classical theory approach that is implemented in the code MQCT. The large basis set of rotational states used in these calculations permits us to predict thermally averaged cross sections for 441 transitions in para- and ortho-H 2 O in a broad range of temperatures. It is found that all state-to-state transitions in the H 2 O + H 2 O system split into two well-defined groups, one with higher cross-section values and lower energy transfer, which corresponds to the dipole-dipole driven processes. The other group has smaller cross sections and higher energy transfer, driven by higher-order interaction terms. We present a detailed analysis of the theoretical error bars, and we symmetrized the state-to-state transition matrixes to ensure that excitation and quenching processes for each transition satisfy the principle of microscopic reversibility. We also compare our results with other data available from the literature for H 2 O + H 2 O collisions.
Improved temperature dependence of rate coefficients for rotational state-to-state transitions in H 2 O + H 2 O collisions
Aims. We present an improved database of temperature-dependent rate coefficients for rotational state-to-state transitions in H 2 O + H 2 O collisions. The database includes 231 transitions between the lower para-states of H 2 O and 210 transitions between its lower ortho-states (up toj= 7) and can be employed in cometary and planetary applications up to the temperature of 1000 K. Methods. We developed and applied a new general method that allows the generation of rate coefficients for excitation and quenching processes that automatically satisfy the principle of microscopic reversibility and also helps to cover the range of low collision energies by interpolation of cross sections between the process threshold and the computed data points. Results. We find that in the range of intermediate temperatures, 150
Magnetization reversal driven by electron localization-delocalization crossover in the inverse spinel Co 2 VO 4
Neutron diffraction, magnetization, and muon spin relaxation measurements, supplemented by density functional theory (DFT) calculations are employed to unravel temperature-driven magnetization reversal in inverse spinel Co 2 VO 4 . All measurements show a second-order magnetic phase transition at T C = 168 K to a collinear ferrimagnetic phase. Neutron diffraction measurements reveal two antiparallel ferromagnetic (FM) sublattices, belonging to magnetic ions on two distinct crystal lattice sites, where the relative balance between the two sublattices determine the net FM moment in the unit cell. As the evolution of the ordered moment with temperature differs between the two sublattices, the net magnetic moment reaches a maximum at T NC = 138 K and reverses its sign at T MR = 65 K. The DFT results suggest that the underlying microscopic mechanism for the reversal is a delocalization of the unfilled 3d -shell electrons on one sublattice just below T C , followed by a gradual localization as the temperature is lowered. Furthermore, this delocalized-localized crossover is supported by muon spectroscopy results, as strong T 1 relaxation observed below T C indicates fluctuating internal fields.
Electrolyte-Dependent, “Microscopically Irreversible” H-Atom Transfer Kinetics of Ce-Based Metal–Organic Framework, Ce-MOF-808
Redox reactions at the interface of metal oxides and protic electrolytes almost always involve protons and electrons in equal amounts. Given the stoichiometry, these proton-coupled electron transfer (PCET) reactions are thermochemically equivalent to net H-atom transfer (HAT) reactions. The correlation between the chemical nature of solid catalysts and HAT kinetics has been employed for decades as the design principle for energy-relevant reactions (e.g., reactions of 2H + /H 2 ). More recently, chemists have experimentally determined that a change in liquid electrolytes that alters the microenvironment at the redox-active sites has an equally profound impact on electrocatalysis involving PCET/HAT. Yet, precise correlations between the chemical nature of electrolytes and the PCET kinetics are, to date, rare in the literature. Herein, we report our findings using the Ce-based metal−organic framework, Ce-MOF-808, as a model system. Each Ce 6 (μ 3 −O) 4 (μ 3 − OH) 4 (OH) 6 (H 2 O) 6 node of this MOF undergoes a 1H + /1e − redox reaction. Using chronoamperometry and the Cottrell analysis, we have determined that the PCET hopping kinetics within the pores of Ce-MOF-808 can change by orders of magnitude by altering the buffer species and the proton activity of the electrolyte. Furthermore, in all buffers, reductive reactions were ∼3−10 times faster in kinetics than the reverse oxidative reaction with the same electrochemical driving force, suggesting that the system, at first glance, violates the principle of microscopic reversibility. Isothermal titration calorimetry (ITC) and computational simulations corroborated that the buffer-node binding thermodynamics are quite distinct, depending on the chemical nature of the buffer and the oxidation state of the node. Together, these results suggest that the substrate and the product during the oxidative vs reductive reaction of Ce-MOF-808 are chemically different species, which explains the apparent ‘microscopic irreversibility.’ Thus, the rational modulation of electrolytes can dramatically enhance PCET kinetics, even though the solid electrodes remain identical. Implications of these findings are contrasted with the electrochemical/electrocatalytic behavior of other redox-active MOFs, heterogeneous catalysts, and enzymatic systems at the solid−liquid interface.
Sketched Nanoscale KTaO 3 -Based Superconducting Quantum Interference Device
The discovery of two-dimensional superconductivity in LaAlO 3 /KTaO 3 (111) and (110) interfaces has raised significant interest in this system. In this paper, we report the first successful fabrication of a direct current superconducting quantum interference device (dc-SQUID) in the KTO system. The key device elements, superconducting weak links, are created by conductive atomic force microscope lithography, which can reversibly control the conductivity at the LAO/KTO (110) interface with nanoscale resolution. The periodic modulation of the SQUID critical current 𝐼 c (𝐵) with magnetic field corresponds well with our theoretical modeling, which reveals a large kinetic inductance of the superconducting two-dimensional electron gas in KTO. The kinetic inductance of the SQUID is tunable by electrical gating from the back, due to the large dielectric constant of KTO. The demonstration of weak links and SQUIDs in KTO broadens the scope for exploring the underlying physics of KTO superconductivity, including the role of spin-orbit coupling, pairing symmetry, and inhomogeneity. It also promotes KTO as a versatile platform for a growing family of quantum devices, which could be applicable in the realm of quantum computing and information.
How non-ohmic contact-layer diodes in perovskite pinholes affect abrupt low-voltage reverse-bias breakdown and destruction of solar cells
Perovskite solar cells (PSCs) rapidly degrade under reverse bias, a condition that may occur during partial shading. Here, in this study, we use electrical measurements, electron microscopy, and optical and thermal imaging to investigate abrupt breakdown and hotspotting under low reverse potentials (<|-2| V). We show that microscopic pinholes in the perovskite layer cause rapid, destructive breakdown under reverse bias despite minimally reducing power conversion efficiencies. Measurements on miniature (200-micrometer diameter) PSCs and perovskite-free transport-layer diodes indicate that abrupt, low-voltage breakdown occurs in nanoscale to micrometer-scale defects and that metal migration and filamentation are unlikely causes. Reverse-bias stability substantially improves when pinholes in the perovskite and transport layers are eliminated. Atomic layer deposition of tin oxide prevents abrupt breakdown by ensuring physical separation between electrodes-not by blocking metal ion migration. Perovskite researchers should adopt cleaner, more uniform deposition techniques to enable robust PSCs for further research and commercial applications.
Signal amplification in a solid-state sensor through asymmetric many-body echo
Electronic spins of nitrogen–vacancy centres in diamond constitute a promising system for micro- and nanoscale magnetic sensing, because of their operation under ambient conditions, ease of placement in close proximity to sensing targets and biological compatibility. At high densities, the electronic spins interact through dipolar coupling, which typically limits but can also potentially enhance sensing performance. Here we report the experimental demonstration of many-body signal amplification in a solid-state, room-temperature quantum sensor. Our approach uses time-reversed two-axis-twisting interactions, engineered through dynamical control of the quantization axis and Floquet engineering in a two-dimensional ensemble of nitrogen–vacancy centres. We observe that optimal amplification occurs when the backward evolution time equals twice the forward evolution time, in sharp contrast to the conventional Loschmidt echo. These observations can be understood as resulting from an underlying time-reversed mirror symmetry of the microscopic dynamics, providing key insights into signal amplification and opportunities for practical entanglement-enhanced quantum sensing.
Correlated nanoelectronics and the second quantum revolution
The growing field of correlated nanoelectronics exists at the intersection of two established fields: correlated oxide electronics and semiconductor nanoelectronics. The development of quantum technologies that exploit quantum coherence and entanglement for the purposes of computation, simulation, and sensing will require complex material properties to be controlled at nanoscale dimensions. Heterostructures and nanostructures formed at the interface between LaAlO 3 and SrTiO 3 exhibit striking behavior that arises from the ability to program the conductive behavior at extreme nanoscale dimensions. The active electronic layer, SrTiO 3 , exhibits a wide range of gate-tunable phenomena such as ferroelectricity, ferroelasticity, magnetism, superconductivity, and spin–orbit coupling, all of which can be controlled at the nanoscale using two reversible methods: conductive atomic force microscope lithography and ultra-low-voltage electron beam lithography. Mesoscopic devices such as single-electron transistors and quasi-one-dimensional electron waveguides can be “sketched” using these techniques, and the properties of these devices differ significantly from those created from traditional semiconductors, such as Si or GaAs. The strongly correlated nature of the SrTiO 3 system is evident from superconducting behavior as well as a state in which electrons are paired outside the superconducting state. A highly exotic phase was discovered in which a degenerate quantum liquid is formed from bound states of n = 2, 3, 4, … electrons. Further development of correlated nanoelectronics based on the LaAlO 3 /SrTiO 3 system can potentially lead to a general platform for quantum simulation as well as a pathway for the development of highly entangled states of multiple photons.
Switching interlayer magnetic order in bilayer CrI 3 by stacking reversal
CrI 3 , a hot two-dimensional (2D) magnet, exhibits complex magnetism depending on the number of layers and interlayer stacking patterns. For bilayer CrI 3 , the interlayer magnetism can be tuned between ferromagnetic (FM) and antiferromagnetic (AFM) order by manipulating the stacking order. However, the stacking is mostly modified through translation between the layers, while the effect of rotation between the layers on the interlayer magnetic order has not yet been fully investigated. Here, we considered three energetically stable stacking patterns R$\bar3$ with combining macron], C2/m and AA in bilayer CrI 3 , and their reversed counterparts R$\bar3$ with combining macron]-r, C2/m-r and AA-r through rotating one layer by 180° with respect to the other layer. Our first-principles calculations suggest that the interlayer magnetic ground state can be switched from AFM to FM (or FM to AFM) by reversing the stacking pattern. A detailed microscopic analysis was carried out by magnetic force theory calculations on C2/m stacking which favors AFM and C2/m-r stacking which favors FM. The interlayer magnetic interactions and the origin of the magnetic order change were revealed through specific orbital analysis. Our work demonstrates that stacking rotation can also tune the interlayer magnetism of CrI 3 and provides insight into its interlayer magnetic properties at the microscopic level.
Imaging solid–electrolyte interphase dynamics using operando reflection interference microscopy
The quality of the solid–electrolyte interphase is crucial for the performance of most battery chemistries, but its formation dynamics during operation are not well understood due to a lack of reliable operando characterization techniques. Herein, we report a dynamic, non-invasive, operando reflection interference microscope to enable the real-time imaging of the solid–electrolyte interphase during its formation and evolution processes with high sensitivity. The stratified structure of the solid–electrolyte interphase formed during four distinct steps includes the emergence of a permanent inner inorganic layer enriched in LiF, a transient assembly of an interfacial electrified double layer and a consequent emergence of a temporary outer organic-rich layer whose presence is reversible with electrochemical cycling. Reflection interference microscope imaging reveals an inverse correlation between the thicknesses of two interphasial subcomponents, implying that the permanent inorganic-rich inner layer dictates the organic-rich outer layer formation and lithium nucleation. In conclusion, the real-time visualization of solid–electrolyte interphase dynamics provides a powerful tool for the rational design of battery interphases.
Theory of capillary tension and interfacial dynamics of motility-induced phases
The statistical mechanics of equilibrium interfaces has been well-established for over a half century. In the past decade, a wealth of observations have made increasingly clear that a new perspective is required to describe interfaces arbitrarily far from equilibrium. In this work, beginning from microscopic particle dynamics that break time-reversal symmetry, we derive the linear interfacial dynamics of coexisting motility-induced phases. Doing so allows us to identify the athermal energy scale that excites interfacial fluctuations and the nonequilibrium surface tension that resists these excitations. Our theory identifies that, in contrast to equilibrium fluids, this active surface tension contains contributions arising from nonconservative forces which act to suppress interfacial fluctuations and, crucially, is distinct from the mechanical surface tension of Kirkwood and Buff. Here we find that the interfacial stiffness scales linearly with the intrinsic persistence length of the constituent active particle trajectories, in agreement with simulation data. We demonstrate that at wavelengths much larger than the persistence length, the interface obeys surface-area minimizing Boltzmann statistics with our derived nonequilibrium interfacial stiffness playing a role identical to that of equilibrium systems.
Electronically reconfigurable complex oxide heterostructure freestanding membranes
In recent years, lanthanum aluminate/strontium titanate (LAO/STO) heterointerfaces have been used to create a growing family of nanoelectronic devices based on nanoscale control of LAO/STO metal-to-insulator transition. The properties of these devices are wide-ranging, but they are restricted by nature of the underlying thick STO substrate. Here, single-crystal freestanding membranes based on LAO/STO heterostructures were fabricated, which can be directly integrated with other materials via van der Waals stacking. The key properties of LAO/STO are preserved when LAO/STO membranes are formed. Conductive atomic force microscope lithography is shown to successfully create reversible patterns of nanoscale conducting regions, which survive to millikelvin temperatures. The ability to form reconfigurable conducting nanostructures on LAO/STO membranes opens opportunities to integrate a variety of nanoelectronics with silicon-based architectures and flexible, magnetic, or superconducting materials.