Pre-exponential Term Research Articles

Structural Flexibility is a Decisive Factor in FLP Dihydrogen Cleavage with Tetrahedral Lewis Acids: A Silane Case Study.

Dihydrogen activation is the paradigmatic reaction of frustrated Lewis pairs (FLPs). While trigonal-planar Lewis acids have been well established in this transformation, tetrahedral Lewis acids are surprisingly limited. Indeed, several cases were computed as thermodynamically and kinetically feasible but exhibit puzzling discrepancies with experimental results. In the present study, a computational investigation of the factors influencing dihydrogen activation are considered by large ensemble sampling of encounter complexes, deformation energies and the activation strain model for a silicon/nitrogen FLP and compared with a boron/phosphorous FLP. The analysis adds the previously missing dimension of Lewis acids' structural flexibility as a factor that influences preexponential terms beyond pure transition state energies. It sheds light on the origin of "overfrustration" (defined herein), indicates structural constraint in Lewis acids as a linchpin for activation of weak donor substrates, and allows drawing a more refined mechanistic picture of this emblematic reactivity.

Drying kinetics of lemon (Citrus lemon) seeds on forced-air convective processing

The convective drying kinetics of Citrus lemon seeds at different air temperatures (60–160 °C, 0.3 m.s−1), as well as the effect of air velocity (v) and technology (tray and rotary drum (RD) drying), were investigated. Internal seed temperature profiles showed that most of the process would occur under internal mass transfer control. Each drying curve was fitted with a theoretical diffusion model to determine the effective diffusivity (Deff), and with nine empirical models. Deff were 0.65 × 10−10-13.10 × 10−10 m2.s−1 and the activation energy was 19.90 kJ.mol−1. Deff increased by 85% when v was raised by 50%; this effect was partially compensated by seed movement when using RD (62% increment). A two-term exponential model with arrangements over the pre-exponential terms demonstrated the complementarity of both terms in explaining the seed dehydration process. In addition, convective heat transfer coefficients were calculated (0.48–0.65 W.m−2 K−1). Overall, the results provide valuable kinetic parameters to characterize the dehydration process for further design and simulation of drying equipment.

The smallest nanodrop describable via macroscopic interfacial concepts: Testing classical heterogeneous nucleation theory with perfect wetting down to 3 nm

HypothesisThe smallest nanodrop tractable with macroscopic notions such as the interfacial energy could be determined by comparing heterogeneous nucleation observations and capillary theory predictions at decreasing drop diameters dp. AnalysisThis is done here for the condensation of n-butanol vapors on polyethylene glycol nano-globules (3 nm ≤ dp ≤ 9 nm). We use published activation probability measurements P(w,dp), where w is the accurately controlled saturation ratio of n-butanol vapor in a gas stream exiting a saturator. The maximal saturation ratio achieved in the nucleation region by cooling this gas-vapor stream in the apparatus of Gallar et al. satisfies Smax = Cw. The key unknown constant C and the preexponential term K governing the nucleation rate are determined by assuming that classical theory applies to the largest particles used. This yields P(Smax,dp) data, directly comparable with capillary theory with perfect wetting. FindingsExcellent agreement is found above 5 nm for the critical dependence Smax(dp) resulting from the constraint P(Smax,dp) = 0.5. The entire P(Smax,dp) curves also agree closely between 5 and 7 nm. Smaller particles depart only slightly from theory, even at dp = 3 nm. Capillary theory hence describes accurately the heterogeneous nucleation process above 3–5 nm, provides a reliable method to determine Smax, and yields experimentally the nucleation rate constant K.

Rheology of hydrated plagioclase at lower crustal conditions: Cataclasis, creep and transformational plasticity

Plagioclase feldspar is one of the main rock-forming minerals of the lower continental crust. Assessing its rheology is therefore of particular importance for understanding the mechanical processes acting in convergence zones, where pressure and strain rate increases are often associated with metamorphic reactions and fluid fluxes. In this prospect, we performed axial shortening experiments on “as-is” (∼0.05 wt% H2O) and water-added (∼0.29 wt% H2O) natural plagioclase samples in a Griggs-type apparatus equipped with an acoustic emission monitoring system. Samples were deformed at ∼ 10−6 and ∼ 10−5 s−1, 700–800 °C, and 1.0 GPa in the plagioclase stability field. Experiments have also been performed at 1.5 GPa in order to study the rheological impact of the breakdown reaction Ca-rich plagioclase + water → zoisite + kyanite + quartz + Na-rich plagioclase. Mechanical data indicate that at the conditions studied, the rheology of plagioclase is strongly affected by water content. Microstructural observations confirm that under dry conditions, plagioclase aggregates deform by cataclastic flow. Under wet conditions, dislocation creep appears to be the dominant deformation mechanism, and plagioclase rheology is best described by the following equation, where strain rate, in s−1, is expressed as:ε·=Aσ3.0exp(−(168kJ/mol)/R/T), where σ is the stress in MPa, R is the gas constant, T is the temperature in K, and the pre-exponential term A=10−3.9MPa−3.0s−1. At 1.5 GPa, the reaction is faster under wet conditions but the rheology observed remains identical to that of wet plagioclase in its stability field. In the low water content experiments, plagioclase breakdown induces transient weakening due to fast zoisite nucleation and significant reaction volume change.

Length reduction kinetics of multiwalled carbon nanotubes correlated to planetary ball mill impact energy

Four commercial multiwalled carbon nanotubes with distinct lengths and diameters were subject to planetary ball milling to induce length reduction. The Burgio-Rojac energy model was employed to calculate the single impact energy and cumulative energy dissipated to the carbon nanotubes during milling. The ratio of sample mass to bead mass and the nanotube bulk density did not affect length reduction during grinding. The minimum impact energy barrier for carbon nanotube length reduction appeared directly proportional to nanotube diameter for parallel wall morphologies, although a nanotube sample with a cup-stacked wall morphology showed a much lower energy barrier. A normalized exponential equation relating carbon nanotube length and cumulative impact energy collapsed all data to a single exponential master curve described by the same scaling parameters, namely a pre-exponential term that includes the initial nanotube length and a scaling energy in the exponent.

Crystallization kinetics in a lithium disilicate glass revisited: Model-free and model-fitting approaches

The present work estimated the crystallization activation energy, Eα, the pre-exponential term, A, and the reaction model, g(α), of a lithium disilicate glass using model-free and model-fitting approaches. Samples with distinct granulometry (PD1: < 105 μm; and PD5: 600–850 μm) were heated at several rates (0.5 to 30 K/min). Our results show that Eα, A, and g(α) are susceptible to particle size. PD1 crystallizes in a single step, and the surface mainly governs it all β values. On the other hand, the overall crystallization of PD5 is more complex and can be described by different Avrami reaction models, with n = 1, 1.5, 2, and 3. In addition, we found that the crystallized fraction at the crystallization peak (αTp) varies significantly with the particle size and heating rate, which confirms that all the methods that assume that the αTp is constant are inadequate to describe the crystallization of glasses over a wide range of heating rates.

Phase Equilibria Simulation of Biomaterial-Hydrogen Binary Systems Using a Simple Empirical Correlation

This study proposes a simple correlation for approximating hydrogen solubility in biomaterials as a function of pressure and temperature. The pre-exponential term of the proposed model linearly relates to the pressure, whereas the exponential term is merely a function of temperature. The differential evolution (DE) optimization algorithm helps adjust three unknown coefficients of the correlation. The proposed model estimates 134 literature data points for the hydrogen solubility in biomaterials with an excellent absolute average relative deviation (AARD) of 3.02% and a coefficient of determination (R) of 0.99815. Comparing analysis justifies that the developed correlation has higher accuracy than the multilayer perceptron artificial neural network (MLP-ANN) with the same number of adjustable parameters. Comparing analysis justifies that the Arrhenius-type correlation not only needs lower computational effort, it also has higher accuracy than the PR (Peng-Robinson), PC-SAFT (perturbed-chain statistical associating fluid theory), and SRK (Soave-Redlich-Kwong) equations of state. Modeling results show that hydrogen solubility in the studied biomaterials increases with increasing temperature and pressure. Furthermore, furan and furfuryl alcohol show the maximum and minimum hydrogen absorption capacities, respectively. Such a correlation helps in understanding the biochemical–hydrogen phase equilibria which are necessary to design, optimize, and control biofuel production plants.

Shoreline Drying of Microseira (Lyngbya) wollei Biomass Can Lead to the Release and Formation of Toxic Saxitoxin Analogues to the Water Column.

The harmful, filamentous cyanobacteria Microseira (Lyngbya) wollei produces several toxic analogues of saxitoxin (Lyngbya wollei toxins 1-6, or LWTs 1-6), grows in shallow water, and can deposit significant biomass on nearby shorelines. Here, we show that the LWTs are stable in the biomass during subsequent drying but that the process facilitates the later release of LWTs upon return to the water column. Under basic conditions, LWTs hydrolyzed to generate products that were significantly more neurotoxic than the initial toxins. Aqueous LWTs were subjected to conditions of covarying temperature and pH, and their degradation rates and products were determined at each condition. LWTs 1, 5, and 6 degraded faster at pH ≥ 8 at all temperatures. Their degradation products, which included decarbamoyl saxitoxin and LWT 4, were consistent with a base-catalyzed hydrolysis mechanism and represented a net increase in total biomass toxicity normalized against the equivalent toxicity of saxitoxin. The corresponding pre-exponential terms and activation energies for hydrolysis were obtained for pH 6-10 over the temperature range 10-40 °C. A locally weighted scatterplot smoothing (LOWESS) regression was developed to predict the loss of parent toxins and subsequent products in the water column under conditions corresponding to those commonly encountered in cyanobacterial blooms.

Quantitative estimation of chemical microheterogeneity through the determination of fuzzy entropy.

Chemical micro-heterogeneity is an attribute of all living systems and most of the soft and crystalline materials. Its characterization requires a plethora of techniques. This work proposes a strategy for quantifying the degree of chemical micro-heterogeneity. First of all, our approach needs the collection of time-evolving signals that can be fitted through poly-exponential functions. The best fit is determined through the Maximum Entropy Method. The pre-exponential terms of the poly-exponential fitting function are used to estimate Fuzzy Entropy. Related to the possibility of implementing Fuzzy sets through the micro-heterogeneity of chemical systems. Fuzzy Entropy becomes a quantitative estimation of the Fuzzy Information that can be processed through micro-heterogeneous chemical systems. We conclude that our definition of Fuzzy Entropy can be extended to other kinds of data, such as morphological and structural distributions, spectroscopic bands and chromatographic peaks. The chemical implementation of Fuzzy sets and Fuzzy logic will promote the development of Chemical Artificial Intelligence.

Reactivity of internal vs. external Brønsted acid sites in nanosponge MFI: H/D exchange kinetic study

The strength of Brønsted acid sites (BAS) affects the properties of 2D and hierarchical zeolites, but the relative contribution of internal and external BAS remains unknown. Accordingly, this study aims to assess the acidity of external and internal BAS in nanosponge-like MFI zeolites by comparatively analyzing hydrogen–deuterium exchange kinetics between zeolitic deuteroxyl groups and C 2 H 6 molecules monitored by in-situ FTIR spectroscopy. For this purpose, (i) a sample pre-treatment procedure was specifically developed to deuterate only internal or only external acid sites using 2,6-di-tert-butylpyridine (DTBP) as a masking agent and (ii) DFT modeling of surface BAS was performed. Theoretical models of the thin MFI layer revealed that the external surface of MFI crystals contains three types of BAS: (i) BAS positioned in 5-membered rings, either shielded by silanol nests, rendering the site inaccessible for DTBP or yielding a very low adsorption energy for ethane, (ii) BAS pointing into the pores, due to the presence of aluminol, which hinders DTBP accessibility, or the BAS undergoes transformation to a three-coordinate aluminium site, and (iii) BAS accessible to both DTBP and ethane. The results from our kinetics measurements showed that H/D exchange at external BAS of nanosponge MFI zeolites is faster than at internal BAS (rate constants at 425 °C: 3.8 10 −3 vs. 2.4 10 −3 s −1 for external and internal BAS, respectively), but this cannot be attributed to the effect of diffusion. Therefore, the differences in exchange kinetics between external and internal BAS are given by mutual interplay of subtle differences in the corresponding activation barriers (113 vs. 117 kJ/mol for external and internal BAS, respectively) and pre-exponential terms (1.09 10 6 vs. 1.45 10 6 s −1 for external and internal BAS, respectively). • Treatment procedure to discriminate internal and external Brønsted acid sites proposed. • Three types of external Brønsted acid sites was described based on DFT modeling. • Strength of internal and external Brønsted acid sites is the same.

Cluster activation studies with a diffusive condensation particle counter: Effect of chemical composition

We use KanomaxFMT's Fast Condensation Particle Counter (CPC) to study the growth (activation) of purified singly charged cluster ions of several salts by condensation of n-butanol vapor. Salts investigated include 1-ethyl-3-methylimidazolium tris(pentafluoroethyl)trifluorophosphate (EMI-FAP), and four tetra-alkylammonium bromides (CpH2p+1)4N+-Br-, with p = 4, 6, 7, 12. The clusters studied contained up to 20 salt molecules, which were formed via a bipolar electrospray source, and were size-selected with a differential mobility analyzer. The CPC is operated at variable condenser and fixed saturator temperatures, Tc, Ts. It uses 75% sheath gas, such that most aerosol-containing fluid streamlines are near the channel center, and experience very similar maximal saturation ratios. This results in a steep initial dependence of the activation probability on Ts for selected particles. Therefore, a well-defined activation onset temperature Ts∗ is determined as a function of cluster composition, polarity (±), and mobility diameter (dp). Notwithstanding a modest material dependence found for the inferred Tc∗(dp) curves (±0.25 nm), the steepness of the activation curves measured permits determining particle size distributions for aerosols of known composition. There is some ambiguity in the precise temperature profile in the CPC channel. Nevertheless, using our best estimate, the onset condition for all but one of the seed particles studied agrees well with predictions from classical heterogeneous nucleation theory (Fletcher, 1962) when the pre-exponential term K in the nucleation rate is chosen appropriately. This enables the incorporation of materials properties into the sizing process in terms of only this single parameter K. This finding also provides a method to determine K experimentally, suggesting that the material dependence of the activation probability is due to the different interaction potentials between the clusters and the vapor. Tetraheptylammonium bromide is peculiar in that its cluster anions fit classical theory very much as all other materials studied, but its cluster cations do not.

Dynamics of oligomerization of silicate solution studied by Molecular Dynamics

The main route of silica powder production is the precipitation from sodium silicate solution in the 8–10 pH range. It was earlier established that the oligomerization of the silicate species is an important stage in silica nucleation. We performed Molecular Dynamics simulations of unsteady silicate solutions at T > 1000 K to overcome the difficulties encountered in oligomerization experiments (e.g. reliability of the obtained kinetic data). We studied the dynamics of oligomerization for various basic pH, temperature, and silicate concentration values. Based on the Becker–Döring theory of nucleation we now propose a simple reaction mechanism and a quantitative model explaining the evolution of the smaller oligomers concentration with time. The model requires fitting two physical parameters: the kinetic constants of oligomerization and hydrolysis; they depend on the temperature, but not on the size of the oligomer reacting with the monomer. Using the Arrhenius law, we deduce the activation energies for condensation and hydrolysis; we show that the pre-exponential term in the oligomerization rate follows Smoluchowski’s theory for Brownian aggregation. Applying the model to the silicate oligomerization at room temperature, we show that our model agrees with previously published modeling based on energetics considerations. The role of the counter-ions is also confirmed.

High Yield Poly(ethylene-alt-maleic acid) Grafting to Wood Pulp while Minimizing Fiber/Fiber Wet Adhesion.

Heating bleached kraft pulps treated with poly(ethylene-alt-maleic acid) (PEMAc) can lead to high yields of carboxylated polymer grafted to fibers. However, in many cases, the cured, dry pulp cannot be effectively repulped (redispersed in water) because the wet strength is too high. Impregnation with PEMAc solutions at pH 4 followed by high temperature (120-180 °C), catalyst-free curing for short times can give fixation yields >85% while maintaining repulpability. The combination of high fixation yields with low wet strength is possible because the extent of curing required for high grafting yields is less than the curing requirement for high wet strength. Two challenges in moving this technology to practicable applications are (1) identifying the optimum laboratory pulp curing conditions and (2) translating laboratory curing conditions to industrial processes. A modeling tool was developed to meet these challenges. The model is based on the observation that for curing conditions giving high fixation yields the wet tensile indices of grafted pulp sheets showed a power-law dependence on the βΓ product where β is the conversion of the succinic acid moieties in PEMAc to the corresponding succinic anhydride groups in the curing step and Γ is the amount of polymer applied to the pulp. For two PEMAc molecular weights and two pulp types, the power-law slopes were 0.6; however, the pre-exponential terms depended upon the specific polymer and pulp type combination. We propose that the relationships between the wet tensile index and βΓ, from polymer-treated, laboratory pulp handsheets, can be used to predict if proposed curing conditions for larger-scale processes will produce a repulpable product.

Chemical Kinetics Bayesian Inference Toolbox (CKBIT)

The robust estimation of chemical kinetic parameters and their associated uncertainty is essential in the field of chemistry and catalysis. The Chemical Kinetics Bayesian Inference Toolbox (CKBIT) is a Python software library introduced to enable users to implement advanced Bayesian inference techniques for kinetic parameter estimation and uncertainty quantification. Leveraging functionalities of other open source Python packages and offering simplified implementation through minimal user-required coding and straightforward Excel input files, CKBIT aspires to make the inference method easily accessible for chemical kinetics. CKBIT provides maximum a posteriori, Markov chain Monte Carlo, and variational inference estimation options. Users may apply these functionalities to estimate activation energies, reaction orders, and pre-exponential terms from chemical reaction data from batch reactors, continuous stirred-tank reactors, and plug flow reactors. The availability of prior distribution specification and the implementation of hierarchical modeling in CKBIT provide a heightened level of accuracy in estimates of kinetic parameters and their uncertainties. Program summaryProgram title: CKBITCPC Library link to program files:https://doi.org/10.17632/tnzk2jvffs.1Developer's repository link:https://github.com/VlachosGroup/ckbitCode Ocean capsule:https://codeocean.com/capsule/8389927Licensing provisions: MIT licenseProgramming language: PythonNature of problem: Rigorous estimation and uncertainty quantification of kinetic rate parameters are necessary for chemical researchers to create physical models with explicit levels of certainty. Advanced statistical treatments of Bayesian inference meet this need with a high level of rigor. However, current software available for Bayesian inference is complex and nuanced in its implementation, preventing widespread adoption among researchers.Solution method: We present a Python package with a modular approach to applying different Bayesian inference techniques for kinetic rate parameter estimation and uncertainty quantification. Optimal point estimates can be obtained through maximum a posteriori estimation, while full probability distributions of parameters can be generated through Markov chain Monte Carlo estimation or variational inference. The code is straightforward to use in contrast to current Bayesian inference software, and it interfaces with Excel for ease of data entry.

Metadynamics simulations of strontium-vacancy diffusion in SrTiO3

The sluggish diffusion of strontium vacancies in the perovskite-oxide ${\mathrm{SrTiO}}_{3}$ was studied by means of classical metadynamics simulations. Two different mechanisms were examined: the migration of an isolated strontium vacancy and the migration of a strontium vacancy in a defect associate with an oxygen vacancy. Combining activation Gibbs energies of migration with the appropriate temperature-dependent pre-exponential terms, we obtained diffusivities of strontium vacancies by the two mechanisms for the temperature range $1000\ensuremath{\le}T/K\ensuremath{\le}2000$. Comparisons with experimental data (where available) yield excellent agreement, both in terms of the effective activation enthalpy of migration as well as the absolute rate of diffusion. In this way we demonstrate the ability of classical metadynamics simulations to predict diffusion coefficients quantitatively for extremely slow-moving defects in oxides, and we highlight the complexity of cation diffusion in perovskite materials.

Thermal reliability of deuterated AlGaN/GaN HEMTs

The reliability of the deuterated AlGaN/GaN High Electron Mobility Transistor (HEMT), which has an improved performance due to the deuterium passivation of point and extended defects, has been studied and compared to that of as-grown (non-deuterated), otherwise identical devices. The HEMT structure was grown by molecular beam epitaxy on Si substrates, and deuterium was in-diffused between the source and drain contacts, prior to the deposition of the gate. As-grown and deuterated transistors were simultaneously annealed at temperatures ranging from 300 °C to 700 °C, monitoring their charge transport properties after each anneal. It was observed that, even though both types of devices degraded, the degradation of the deuterated ones was less important. The evolution of their channel conductance reveals a different thermally stimulated degradation mechanism for each type of HEMT, with activation energies of 1.37 eV for the as-grown and 0.63 eV for the deuterated ones. Contrastingly, the pre-exponential term of the as-grown transistors was considerably higher than that of the deuterated ones, which explains their faster degradation. This study confirms that a proper deuteration improves the HEMT charge transport properties, making it more stable and reliable.

Temperature‐dependent rate coefficients for the gas‐phase OH + furan‐2,5‐dione (C4H2O3, maleic anhydride) reaction

AbstractRate coefficients, k1(T), for the gas‐phase reaction of the OH radical with furan‐2,5‐dione (maleic anhydride (MA), C4H2O3), a biomass burning related compound, were measured under pseudo–first‐order conditions in OH using the pulsed laser photolysis–laser‐induced fluorescence method over a range of temperature (283‐374 K) and bath gas pressure (50‐200 Torr; He or N2). k1(T) was found to be independent of pressure over this range with k1(283‐374 K) = (1.55 ± 0.20) × 10−12 exp[(−410 ± 44)/T) cm3 molecule−1 s−1 and k1(296 K) = (3.93 ± 0.28) × 10−13 cm3 molecule−1 s−1, where the uncertainties are 2σ and the preexponential term includes the estimated systematic error. The atmospheric lifetime of MA with respect to OH reactive loss is estimated to be ∼15 days. The present results are compared with a previous room temperature relative rate study of the OH + MA reaction, and the significant discrepancy between the studies is discussed; the present results are approximately a factor of 4 lower. It is also noteworthy that the experimentally measured k1(296 K) value obtained in this work is nearly a factor of 110 less than estimated by a structure activity relationship based on trends in ionization potential. Based in part on a computational evaluation, an atmospheric degradation mechanism of MA is proposed.

Towards a comprehensive understanding of creep: Microstructural dependence of the pre-exponential term in Al

We show that the equation proposed by Takeuchi and Argon to explain the creep behavior of Al–Mg solid solution can be used to describe also the creep behavior of pure aluminum. In this frame, it is possible to avoid the use of the classic pre-exponential fitting parameter in the power law equation to predict the minimum creep strain rate. The effect of the fractal arrangement of dislocations, developed at the mesoscale, must be considered to fully explain the experimental data. These ideas allow improving the recently introduced SSTC model, fully describing the primary and secondary creep regimes of aluminum alloys without the need for fitting. Creep data from commercially pure Al99.8% and Al–Mg alloys tested at different temperatures and stresses are used to validate the proposed ideas.

Numerical comparison of usual Arrhenius-type equations for modeling ionic transport in solids

The primary objective of this work is to draw attention to the inherent differences between Arrhenius-type equations used for modeling ionic conductivity in solids. The used methodology comprises a comparison between the two most used Arrhenius-type equations by generating data applying one equation and fitting them by using the other equation. Data are generated in different conditions by varying input parameters such as the extent of the temperature range and the average temperature of this range, as well as the pre-exponential term and activation energy of the Arrhenius-type equation. The fitting procedure is performed by plotting the generated data based on the linearized form of those equations followed by the linear fitting. The results show a substantial difference between the activation energy value of those equations, which is mainly dependent on the average temperature of the range. In contrast with the widely held perception that differences in the activation energy of both equations usually can be neglected, this work reveals that relative differences between activation energy of these equations are usually significant. These relative differences are often around 10% and may reach over 15% depending on a combination of intrinsic and extrinsic input parameters such as low activation energy and high-temperature of measurement, respectively. An analytical equation that expresses the relative difference between activation energy calculated from both equations is also presented and discussed.

Complexity reduction for sign configurations through the KP II equation and its information-theoretic aspects

We provide a combinatorial setting to explore the information content associated with the fulfillment of the Kadomtsev-Petviashvili (KP) II equation. We start from a special family of solutions of KP II, namely, tau-functions of Wronskian type. A solution in this class can be expressed as a sum of exponentials, and we look at combinations of signs (signatures) for the nonvanishing terms in this sum. We prove a characterization of the signatures that return another solution of the KP II equation: they can be represented as choices of signs for columns and rows of a coefficient matrix, so we recover a function satisfying the whole KP hierarchy from this single constraint. The redundancy of this representation for different choices of the initial solution is investigated. Enumerative, information-theoretic, and geometric aspects of this construction are discussed.