Chemical Potential Difference Research Articles

General efficiency relation for dissipative molecular machines

Living systems use chemical fuel to process information, assemble structures and maintain fluxes. Many of these processes are dissipative: energy is consumed purely to maintain non-equilibrium steady-state outputs. How efficiently the input energy is transduced toward the output dissipation as opposed to being lost during intermediate steps, and whether the efficiency is constrained by general principles or specific fine-tuning, are open questions. Here, applying a recent mapping from non-equilibrium systems to battery-resistor circuits, an analytic expression for the efficiency of any dissipative molecular machine driven by a chemical potential difference is derived. This expression disentangles the chemical potential from the machine’s details, whose effect on the efficiency is fully specified by a constant called the load resistance. The efficiency passes through an inflection point separating totally inefficient machines from efficient machines if the balance between chemical potential difference and load resistance exceeds thermal noise. This explains all-or-none dynein stepping with increasing ATP concentration observed in single-molecule experiments. These results indicate that energy transduction in living systems is efficient not because of idiosyncratic optimization of biomolecules, but rather because the concentration of chemical fuel is kept above a threshold level.

Morphology and selectivity of hydrated alkali metal ions as depth of discharge in the 1T-MoS2 electrode with aqueous electrolytes.

Aqueous ion batteries have great commercial potential in green power and energy storage due to their green nature, safety and high ionic conductivities. Different from organic electrolytes, alkali ions (Li+, Na+, and K+) inevitably bring water molecules into the electrodes during the charging/discharging process due to the hydration of ions with water molecules. The selectivity of alkali ions and the mechanism of how water molecules are involved in the ion extraction/insertion process in the electrodes have not been clarified. In this study, we focus on the characteristics of the intra-layer distribution of different hydrated ions (Li+, Na+, and K+) and the quantitative analysis of the selectivity of hydrated cations in aqueous batteries. We found that the concentration of hydrated ions greatly affects their distribution within the 1T-MoS2 layers, and the presence of hydrogen bonding and O-O repulsive forces between water molecules causes the hydrated ions to gradually form chains from the dispersed state under the effect of hydrogen bonding and ionic bonding, then further form strips, and ultimately be densely dispersed within the whole layer. In addition, the chemical potential difference of hydrated ions is the key to the competitive reaction, and we quantitatively analyze the selectivity relationship between hydrated cations throughout the charging and discharging process; hydrated sodium ions will have better performance than lithium and potassium ions in aqueous batteries.

Morphology, phase composition, surface roughness evolution and growth mechanism of hot-dip aluminum coating on Mo substrate

The Al-rich hot-dip aluminum composite coatings were synthesized on Mo surface by hot-dip aluminizing under different deposition processes. The aluminide coatings present a very smooth dense coating structure with a lower surface roughness and fine grain size, the average surface roughness (RSa) values are only 0.118–0.869 μm, and the corresponding surface area growth rate (Sdr) values are 3.85–80.19 %. Increasing the deposition temperature is beneficial for the transition of low melting point compounds of the coating surface to high melting point compounds, and extending the hot dip time is profit for the diffusion and enrichment of Al atoms on the coating surface. Besides, increasing the deposition temperature or time can also promote the growth of Al4Mo grains, thereby significantly increasing the coating thickness. When the deposition temperature is 750 °C, the thicknesses of Al4Mo and Al8Mo3 layers increases in a parabolic law with deposition time, and the Kp values both of them are 3.46 × 10−13 m2/s and 1.47 × 10−15 m2/s, respectively. The growth of the coating depends on the continuous diffusion of Al atoms towards the substrate direction, and the difference in chemical potential between Al atoms in each phase is the main driving force for coating growth.

Physical origin of adsorption heat and its significance in the isotherm equation

Adsorption heat is a cornerstone concept underpinning almost all the existing theoretical isotherms for porous media. Yet, it remains elusive what this concept stands for and what are the physical sources for it. Here, a rigorous thermodynamic formulation is derived for the adsorption process with the aid of the law of mass action, leading to an expression of adsorption heat as the external chemical potential difference between two adjacent adsorbate layers. The interaction between adsorbent and adsorbates like van der Waals is theoretically identified as the intermolecular source for the change of adsorption heat. Thereby, adsorption heat is formulated as a spatially varied function of the distance to adsorbent surfaces. This adsorption heat function facilitates the establishment of a two-parameter sorption isotherm equation. The equation can be theoretically converted to two widely used adsorption isotherm equations, namely Brunauer–Emmet–Teller (BET) and Guggenheim-Anderson-de Boer (GAB) equations, and shows excellent performance in capturing experimental isotherm data of a wide array of materials. The comparative analysis demonstrates that the derived two-parameter isotherm equation outperforms the two-parameter BET equation and the three-parameter GAB equation in most cases. Such performance verifies the generality of the derived isotherm equation, thus further confirming the validity of the derived formulation of adsorption heat.

Effective Bi-Layer Model Hamiltonian and Density-Matrix Renormalization Group Study for the High-T c Superconductivity in La3Ni2O7 under High Pressure

High-T c superconductivity with possible T c ≈ 80 K has been reported in the single crystal of La3Ni2O7 under high pressure. Based on the electronic structure given by the density functional theory calculations, we propose an effective bi-layer model Hamiltonian including both 3d z 2 and 3d x 2–y 2 orbital electrons of the nickel cations. The main feature of the model is that the 3d z 2 electrons form inter-layer σ-bonding and anti-bonding bands via the apical oxygen anions between the two layers, while the 3d x 2–y 2 electrons hybridize with the 3d z 2 electrons within each NiO2 plane. The chemical potential difference of these two orbital electrons ensures that the 3d z 2 orbitals are close to half-filling and the 3d x 2–y 2 orbitals are near quarter-filling. The strong on-site Hubbard repulsion of the 3d z 2 orbital electrons gives rise to an effective inter-layer antiferromagnetic spin super-exchange J. Applying pressure can self dope holes on the 3d z 2 orbitals with the same amount of electrons doped on the 3d x 2–y 2 orbitals. By performing numerical density-matrix renormalization group calculations on a minimum setup and focusing on the limit of large J and small doping of 3d z 2 orbitals, we find the superconducting instability on both the 3d z 2 and 3d x 2–y 2 orbitals by calculating the equal-time spin singlet pair–pair correlation function. Our numerical results may provide useful insights in the high-T c superconductivity in single crystal La3Ni2O7 under high pressure.

Unsaturated water flow-induced the structure variation of gas hydrate reservoir and its effect on fluid migration and gas production

Multi-phase (gas, saturated water, and unsaturated water) seepage is bound to exist in natural gas hydrates (NGHs) production process. The effect of water flow, especially for unsaturated water flow, on the permeability variation of hydrate reservoir and gas production behavior do not appear well understood. In this study, the unsaturated water flow in hydrate-bearing sediment and hydrate-free sediment is simulated by controlling water flow velocity. The hydrate phase distribution was monitored using visualization magnetic resonance imaging system. The variation of temperature, pressure, and gas production rate during the unsaturated water flow were analyzed. The results show that the changing trend of the pressure difference presented the three stages for the hydrate-free sediment. In contrast, the pressure difference followed a five-stage change for the hydrate-bearing sediment in the unsaturated water flow process due to the hydrate dissolution. The hydrate dissolution caused an increase in permeability (maximum of log10(Kr) was 0.5) and formed the obvious unsaturated water flow channel. Moreover, the higher water flow velocity, which increased the chemical potential difference between hydrate phase and water phase, accelerated the MH dissolution, and further induced the faster increase rate of permeability and gas production. Surprisingly, when the unsaturated water flow velocity was improved to 15 mL/min from 0.5 mL/min, the gas production rate increased by 35 times. Furthermore, the average gas production rate was mainly determined by the unsaturated water flow velocity, it was changing in a linear fashion with the increasing water flow velocity. The findings could provide new knowledge on the strategy design on NGHs production with high efficiency.

Holographic superfluid with excited states

We construct a novel family of solutions of the holographic superfluid model with the excited states in the probe limit. We observe that the higher excited state or larger superfluid velocity will make the scalar hair more difficult to be developed, and the higher excited state or smaller mass of the scalar field makes it easier for the emergence of translating point from the second-order transition to the first-order one. We note that the difference of the critical chemical potential between the consecutive states increases as the superfluid velocity increases. Interestingly, the “Cave of Winds” phase structure will disappear but the first-order phase transition occurs for the excited states, which is completely different from the holographic superfluid model with the ground state. This means that the excited state will hinder the appearance of the Cave of Winds. Moreover, we find that there exist additional poles in Im[σ(ω)] and delta functions in Re[σ(ω)] arising at low temperature for the excited states, and the higher excited state or larger superfluid velocity results in the larger deviation from the expected relation in the gap frequency.

Quantum rate theory and electron-transfer dynamics: A theoretical and experimental approach for quantum electrochemistry

Quantum rate theory is based on a first-principle quantum mechanical rate concept that comprises with the Planck–Einstein relationship E=hν, where ν=e2/hCq is a frequency associated with the quantum capacitance Cq and E=e2/Cq is the energy associated with ν. For a single state mode of transmittance, e2/Cq corresponds to the chemical potential differences Δμ between donor and acceptor state levels comprising an electrochemical reaction. A statistical mechanic treatment of E is required to compute the contribution of the thermal dynamics at finite temperature. The Arrhenius equation for the temperature dependence of the reaction rate was obtained, as well as Marcus’s Arrhenius-type electron-transfer rate constant as a particular setting of the quantum rate ν. Consequently, this ν concept provides the quantum mechanical foundations for electrochemical reactions at room temperature. The present work also demonstrates that the electron-transfer rate of heterogeneous (diffusionless) reactions can be studied in detail within this theory by measuring Cq using time-dependent electrochemical methods. Since the electron transfer follows a statistical mechanics version of the Planck–Einstein E=hν relationship, the electrochemical reaction dynamics cannot be appropriately modeled using non-relativistic Schrödinger wave mechanics, which is the ongoing quantum approach to electrochemistry. Accordingly, a relativistic analysis that takes into account the spin dynamics of the electron is more appropriate. The latter assumption implies quantum electrodynamics within a particular quantum transport mode intrinsically coupled to the electron-transfer rate of electrochemical reactions that have not been considered thus far. Here it is demonstrated that the consideration of this inherent quantum transport is key to obtaining an in-depth understanding of the electron transfer phenomenon. Finally, the theory is validated through its description of electron transfer, quantum conductance, and capacitance in different electro-active molecular films.

Understanding the role of polymers on the nucleating behavior of water in dilute supercooled solutions.

Understanding the nucleation behavior of water in dilute polymeric solutions is quintessential for the development of suitable artificial ice recrystallization inhibition (IRI) agents. Although poly(vinyl alcohol) (PVA) is found to be one of the most potent biomimetic IRI agents, the molecular understanding of the nucleation behavior of water in the presence of PVA is still lacking. Here, we use molecular dynamics to elucidate the role of concentration, degree of supercooling, degree of polymerization, and amphiphilicity of PVA and PVA-like polymers on the homogeneous nucleation of water in dilute polymeric solutions using the seeding method. Using classical nucleation theory (CNT), our simulations indicate an increase in the chemical potential difference between ice and melt that favors ice nucleation. However, it also predicts a significant increase in the ice-melt interfacial energy that impedes nucleation. The relative increase in the interfacial energy dominates the increase in the chemical potential difference, which results in a decrease in the nucleation rate of water with an increase in the solute concentration. This study contradicts the previous simulation study that suggested the promotion of homogeneous ice nucleation by PVA and supports the experimental observations of the heterogeneous origins of ice nucleation. Our results also suggest the non-classical origins of ice nucleation in polymeric solutions and the limitation of the CNT in predicting heterogeneous ice nucleation in polymeric solutions.

Fundamentals of liquid metal displacement reactions: Emf measurements of Na-Sn, Li-Sn, Mg-Sn, and Ca-Sn

The driving force of spontaneous displacement reactions between Na-Sn alloys and molten LiCl, MgCl2, and CaCl2 salts stems from the difference of chemical potential between Na and Li, Mg, or Ca in liquid Sn. However, fundamental thermodynamic data are absent. Herein, electromotive force (emf) values of Na-Sn, Li-Sn, Mg-Sn, and Ca-Sn alloys (electrodeposition of Na, Li, Mg, and Ca in liquid Sn via the coulometric titration) were measured in NaF-NaCl-NaI, LiF-LiCl, MgCl2-NaCl-KCl, and CaCl2-LiCl-NaCl salts respectively at 650 °C. The measured emf values of these alloys were normalized with respect to the Cl−/Cl2 potential that −3.14 V to −3.35 V for Na-Sn (mole fractions xNa = 0.02–0.30) alloy, −2.90 V to −3.21 V for Li-Sn (xLi = 0.02–0.30) alloy, −2.38 V to −2.45 V for Mg-Sn (xMg = 0.01–0.15) alloy, and −2.90 V to −3.06 V for Ca-Sn (xCa = 0.01–0.15) alloy. And Li20Sn, Mg10Sn, and Ca10Sn alloys were successful prepared by displacement reactions between Na20Sn alloys and LiCl-NaCl, MgCl2-NaCl, and CaCl2-NaCl salts, which offers theoretical guidelines for s-block elements extraction and separation.

Low chemical consumption of wastewater ammonium nitrogen recovery through Donnan dialysis-membrane stripping process

Wastewater ammonium nitrogen (NH4+-N) recovery is frequently associated with massive and ineffective chemical consumption due to the presence of bicarbonate (HCO3–), resulting in undesirable economic feasibility. In the present study, by incorporating energy-efficient Donnan dialysis (DD) as a pretreatment process for membrane stripping (MS), we developed a low-chemical consumption hybrid DD-MS process with two membranes (cation exchange membrane [CEM] and hydrophobic membrane) and three phases (wastewater, draw solution and acid solution). First, equimolar amount of ammonium was exchanged with sodium ions and passed through CEM into an alkaline draw solution, where it was immediately deprotonated to free ammonia. Finally, it was diffused across a hydrophobic membrane, absorbed by the acid solution, and recovered as an ammonium salt. Meanwhile, HCO3– was confined to wastewater due to electrostatic repulsion from CEM. Owing to the chemical potential difference, NaOH in the draw solution diffused into the wastewater, resulting in additional chemical consumption. Experiments and calculations based on the Donnan equilibrium revealed that using an alkaline draw solution at a slightly higher concentration than that of wastewater ammonium allowed high NH4+-N recovery and low NaOH diffusion simultaneously. In experiments on actual landfill leachate, the hybrid DD-MS process achieved 81.4% NH4+-N recovery from wastewater while reducing alkali and acid consumption by respectively 32.7% and 34.9% compared with the conventional MS process. The hybrid process reduced the cost of chemicals and amount of salt entering the wastewater and environment. Overall, the proposed hybrid process presents excellent application prospects for NH4+-N recovery from wastewater with high-strength HCO3–, such as landfill leachate and livestock wastewater.

Phase, chemical constitution and effective depth of oxide overgrowth and its influence on SmPrCo5 magnetic properties

Ternary Sm-Pr-Co magnets with CaCu5-type hexagonal structure exhibit superior magnetic properties and investigating their oxidation behavior is crucial for assessing their stability under the service conditions. In this regard, here thermal oxidation of sintered SmPrCo5 magnet is carried out by varying the oxidation temperature from 373 to 973 K for 5 hr under atmospheric pressure. Owing to their lower negative Gibbs free energy, rare earth oxides of Sm2O3 and Pr2O3 are found to initially form, making cobalt free from SmPrCo5 lattice. Cobalt is then observed to migrate to the oxide surface, because of the difference in chemical potential between the surface and inner layers, leading to Co3O4 formation. Moreover, here a comprehensive discussion on the occurrences of different oxide phases and their depth distributions in the oxide layer are being made. Finally, a correlation between these oxide phases and the alterations in their magnetic properties is discussed.

Thermodynamics Explains How Solution Composition Affects the Kinetics of Stochastic Ice Nucleation.

The freezing of aqueous solutions is of great relevance to multiple fields, yet the kinetics of ice nucleation, its first step, remains poorly understood. The literature focuses on the freezing of microdroplets, and it is unclear if those findings can be generalized and extended to larger volumes such as those used in the freezing of biopharmaceuticals. To this end, we study ice nucleation from aqueous solutions of ten different compositions in vials at the milliliter scale. The statistical analysis of the approximately 6,000 measured nucleation events reveals that the stochastic ice nucleation kinetics is independent of the nature and concentration of the solute. We demonstrate this by estimating the values of the kinetic parameters in the nucleation rate expression for the selected solution compositions, and we find that a single set of parameters can describe quantitatively the nucleation behavior in all solutions. This holds regardless of whether the nucleation rate is expressed as a function of the chemical potential difference, of the water activity difference, or of the supercooling. While the chemical potential difference is the thermodynamically correct driving force for nucleation and hence is more accurate from a theoretical point of view, the other two expressions allow for an easier implementation in mechanistic freezing models in pharmaceutical manufacturing.

The role of quantum-chemical descriptors and sigma-profile overlapping of different co-solvents on tuning ethanolic extraction of soybean oil

Co-solvents can significantly improve ethanol efficiency in vegetable oil extraction, making their use a viable, cost-effective, and sustainable alternative to conventional solvents. The challenge, however, is to understand the complex interactions between the solvents and how this can affect the yield and quality of the extracted oil. In this study, the COnductor-like Screening Model with Segment Activity Coefficient and Hansen solubility parameters were combined and used to optimize soybean oil extraction using ethanol along with seven different co-solvents. In parallel, an experimental approach was carried out to verify the accuracy of the models. Both theoretical and empirical results indicated that the oil extraction yield decreased as the co-solvent polarity increased. The best performance in solubilizing non-polar lipids was observed for the mixture of 10 wt% of p-cymene, a non-polar solvent, with 90 wt% ethanol, reaching a yield of 24.35 g/100 g. According to the thermodynamic analysis, the effects of polarity weigh heavily on the standard entropy, which rules the driving force of mass transfer during the extraction. The interaction mechanisms were carefully investigated employing quantum mechanical calculations, revealing how the differences in chemical potential (μ), hardness (η), and electrophilicity (ω) underlie the macroscopic results and rule the efficiency obtained for different solvent ratios and combinations.

Effect of impurities on charge and heat transport in tubular nanowires

We calculate the charge and heat currents carried by electrons, originating from a temperature gradient and a chemical potential difference between the two ends of tubular nanowires with different geometries of the cross-sectional areas: circular, square, triangular, and hexagonal. We consider nanowires based on InAs semiconductor material, and use the Landauer-Büttiker approach to calculate the transport quantities. We include impurities in the form of delta scatterers and compare their effect for different geometries. The results depend on the quantum localization of the electrons along the edges of the tubular prismatic shell. For example, the effect of impurities on the charge and heat transport is weaker in the triangular shell than in the hexagonal shell, and the thermoelectric current in the triangular case is several times larger than in the hexagonal case, for the same temperature gradient.

Pore-scale Ostwald ripening of gas bubbles in the presence of oil and water in porous media

HypothesisOstwald ripening of gas bubbles is a spontaneous mass transfer process that can impact the storage volume of trapped gas in the subsurface. In homogeneous porous media with identical pores, bubbles evolve toward an equilibrium state of equal pressure and volume. How the presence of two liquids impacts ripening of a bubble population is less known. We hypothesize that the equilibrium bubble sizes depend on the surrounding liquid configuration and oil/water capillary pressure. Method and numerical experimentsWe investigate ripening of nitrogen bubbles in homogeneous porous media containing decane and water using a level set method that alternately simulates capillary-controlled displacement and mass transfer between bubbles to eradicate chemical-potential differences. We explore impacts of initial fluid distribution and oil/water capillary pressure on the bubble evolution. FindingsRipening in three-phase scenarios in porous media stabilizes gas bubbles to sizes that depend on their surrounding liquids. Bubbles in oil decrease in size while bubbles in water increase in size with increasing oil/water capillary pressure. Bubbles in oil reach local equilibrium before the three-phase system stabilizes globally. A potential implication for field-scale gas storage is that the trapped gas fractions in oil and water vary with depth in the oil/water transition zone.

Design of a Reverse Electrodialysis Plant for Salinity Gradient Energy Extraction in a Coastal Wastewater Treatment Plant.

The chemical potential difference at the discharge points of coastal Wastewater Treatment Plants (WWTPs) uncovers the opportunity to harness renewable salinity gradient energy (SGE). This work performs an upscaling assessment of reverse electrodialysis (RED) for SGE harvesting of two selected WWTPs located in Europe, quantified in terms of net present value (NPV). For that purpose, a design tool based on an optimization model formulated as a Generalized Disjunctive Program previously developed by the research group has been applied. The industrial scale-up of SGE-RED has already proven to be technically and economically feasible in the Ierapetra medium-sized plant (Greece), mainly due to a greater volumetric flow and a warmer temperature. At the current price of electricity in Greece and the up-to-date market cost of membranes of 10 EUR/m2, the NPV of an optimized RED plant in Ierapetra would amount to EUR117 thousand operating with 30 RUs in winter and EUR 157 thousand for 32 RUs in summer, harnessing 10.43 kW and 11.96 kW of SGE for the winter and summer seasons, respectively. However, in the Comillas facility (Spain), this could be cost-competitive with conventional alternatives, namely coal or nuclear power, under certain conditions such as lower capital expenses due to affordable membrane commercialization (4 EUR/m2). Bringing the membrane price down to 4 EUR/m2 would place the SGE-RED's Levelized Cost of Energy in the range of 83 EUR/MWh to 106 EUR/MWh, similar to renewable sources such as solar PV residential rooftops.

Zwitterionic Copolymers for Anti-Scaling Applications in Simulated Spaceflight Wastewater Scenarios.

Water reclamation in spaceflight applications, such as those encountered on the International Space Station (ISS), requires complex engineering solutions to ensure maximum water recovery. Current vapor compression distillation (VCD) technologies are effective but produce highly concentrated brines and often cause scaling within a separation system. This work evaluates initial steps toward integrating pervaporation, a membrane separation process, as a brine management strategy for ISS wastewaters. Pervaporation performs separations driven by a chemical potential difference across the membrane created by either a sweep gas or a vacuum pull. Pervaporation membranes, as with most membrane processes, can be subject to scaling. Therefore, this work studies the anti-scaling properties of zwitterions (polymeric molecules with covalently tethered positive and negative ions) coated onto sulfonated pentablock terpolymer block polymer (Nexar) pervaporation membrane surfaces. We report a method for applying zwitterions to the surface of pervaporation membranes and the effect on performance parameters such as flux and scaling resistance. Membranes with zwitterions had up to 53% reduction in permeance but reduced scaling. The highest amount of scaling occurred in the samples exposed to calcium chloride, and uncoated membranes had weight percent increases as high as 1617 ± 241%, whereas zwitterion-coated membranes experienced only about 317 ± 87% weight increase in the presence of the same scalant.

Thermodynamically and Kinetically Stabilized Pt Clusters Against Sintering on CeO2 Nanofibers Through Enclosing CeO2 Nanocubes.

Sintering is a major concern for the deactivation of supported metals catalysts, which is driven by the force of decreasing the total surface energy of the entire catalytic system. In this work, a double-confinement strategy is demonstrated to stabilize 2.6nm-Pt clusters against sintering on electrospun CeO2 nanofibers decorated by CeO2 nanocubes (m-CeO2 ). Thermodynamically, with the aid of CeO2 -nanocubes, the intrinsically irregular surface of polycrystalline CeO2 nanofibers becomes smooth, offering adjacent Pt clusters with decreased chemical potential differences on a relatively uniform surface. Kinetically, the Pt clusters are physically restricted on each facet of CeO2 nanocubes in a nanosized region. In situ high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) observation reveals that the Pt clusters can be stabilized up to 800°C even in a high density, which is far beyond their Tammann temperature, without observable size growth or migration. Such a sinter-resistant catalytic system is endowed with boosted catalytic activity toward both the hydrogenation of p-nitrophenol after being aged at 500°C and the sinter-promoting exothermic oxidation reactions (e.g., soot oxidation) at high temperatures over 700°C. This work offers new opportunities for exploring sinter-resistant nanocatalysts, starting from the rational design of whole catalytic system in terms of thermodynamic and kinetic aspects.

Thermodynamic bounds on ultrasensitivity in covalent switching

Switch-like motifs are among the basic building blocks of biochemical networks. A common motif that can serve as an ultrasensitive switch consists of two enzymes acting antagonistically on a substrate, one making and the other removing a covalent modification. To work as a switch, such covalent modification cycles must be held out of thermodynamic equilibrium by continuous expenditure of energy. Here, we exploit the linear framework for timescale separation to establish tight bounds on the performance of any covalent-modification switch in terms of the chemical potential difference driving the cycle. The bounds apply to arbitrary enzyme mechanisms, not just Michaelis-Menten, with arbitrary rate constants and thereby reflect fundamental physical constraints on covalent switching.