Description of the effect of temperature on food systems using the deformed Arrhenius rate law: deviations from linearity in logarithmic plots vs. inverse temperature

Modified Arrhenius Equation in Materials Science, Chemistry and Biology

The Arrhenius plot (logarithmic plot vs. inverse temperature) is represented by a straight line if the Arrhenius equation holds. A curved Arrhenius plot (mostly concave) is usually described phenomenologically, often using polynomials of T or 1/T. Many modifications of the Arrhenius equation based on different models have also been published, which fit the experimental data better or worse. This paper proposes two solutions for the concave-curved Arrhenius plot. The first is based on consecutive A→B→C reaction with rate constants k₁ ≪ k₂ at higher temperatures and k₁ ≫ k₂ (or at least k₁ > k₂) at lower temperatures. The second is based on the substitution of the temperature T the by temperature difference T − T₀ in the Arrhenius equation, where T₀ is the maximum temperature at which the Arrheniusprocess under study does not yet occur.

Topography of the free energy landscape of Claisen-Schmidt condensation: solvent and temperature effects on the rate-controlling step

Recent studies have found that hydroxide elimination and the C[double bond, length as m-dash]C bond formation step in base-promoted aldol condensation have a strong influence on the overall rate of the reaction, in contrast to the well-accepted first enolization or C-C bond formation step. Here, applying theoretical models to the prototypical reaction of chalcone formation, the complete free energy profile of Claisen-Schmidt condensation is assessed, revealing how a protic solvent and a slight increase in temperature can induce the second enolization as the rate-controlling step (RCS). It is also observed: i) the nonexistence of a step with a much higher energetic barrier than the others, making the concept of RCS debatable; and ii) that the overall inverse kinetic isotopic effect does not exclude second enolization as a RCS in protic continuum medium. We expect that these results can expand the understanding of the decisive role of physicochemical factors on the choose of the RCS in the aldol condensation.

From the Kinetic Theory of Gases to the Kinetics of Rate Processes: On the Verge of the Thermodynamic and Kinetic Limits

A variety of current experiments and molecular dynamics computations are expanding our understanding of rate processes occurring in extreme environments, especially at low temperatures, where deviations from linearity of Arrhenius plots are revealed. The thermodynamic behavior of molecular systems is determined at a specific temperature within conditions on large volume and number of particles at a given density (the thermodynamic limit): on the other side, kinetic features are intuitively perceived as defined in a range between the extreme temperatures, which limit the existence of each specific phase. In this paper, extending the statistical mechanics approach due to Fowler and collaborators, ensembles and partition functions are defined to evaluate initial state averages and activation energies involved in the kinetics of rate processes. A key step is delayed access to the thermodynamic limit when conditions on a large volume and number of particles are not fulfilled: the involved mathematical analysis requires consideration of the role of the succession for the exponential function due to Euler, precursor to the Poisson and Boltzmann classical distributions, recently discussed. Arguments are presented to demonstrate that a universal feature emerges: Convex Arrhenius plots (super-Arrhenius behavior) as temperature decreases are amply documented in progressively wider contexts, such as viscosity and glass transitions, biological processes, enzymatic catalysis, plasma catalysis, geochemical fluidity, and chemical reactions involving collective phenomena. The treatment expands the classical Tolman’s theorem formulated quantally by Fowler and Guggenheim: the activation energy of processes is related to the averages of microscopic energies. We previously introduced the concept of “transitivity”, a function that compactly accounts for the development of heuristic formulas and suggests the search for universal behavior. The velocity distribution function far from the thermodynamic limit is illustrated; the fraction of molecules with energy in excess of a certain threshold for the description of the kinetics of low-temperature transitions and of non-equilibrium reaction rates is derived. Uniform extension beyond the classical case to include quantum tunneling (leading to the concavity of plots, sub-Arrhenius behavior) and to Fermi and Bose statistics has been considered elsewhere. A companion paper presents a computational code permitting applications to a variety of phenomena and provides further examples.

"Transitivity": A Code for Computing Kinetic and Related Parameters in Chemical Transformations and Transport Phenomena

The Transitivity function, defined in terms of the reciprocal of the apparent activation energy, measures the propensity for a reaction to proceed and can provide a tool for implementing phenomenological kinetic models. Applications to systems which deviate from the Arrhenius law at low temperature encouraged the development of a user-friendly graphical interface for estimating the kinetic and thermodynamic parameters of physical and chemical processes. Here, we document the Transitivity code, written in Python, a free open-source code compatible with Windows, Linux and macOS platforms. Procedures are made available to evaluate the phenomenology of the temperature dependence of rate constants for processes from the Arrhenius and Transitivity plots. Reaction rate constants can be calculated by the traditional Transition-State Theory using a set of one-dimensional tunneling corrections (Bell (1935), Bell (1958), Skodje and Truhlar and, in particular, the deformed ( d -TST) approach). To account for the solvent effect on reaction rate constant, implementation is given of the Kramers and of Collins-Kimball formulations. An input file generator is provided to run various molecular dynamics approaches in CPMD code. Examples are worked out and made available for testing. The novelty of this code is its general scope and particular exploit of d -formulations to cope with non-Arrhenius behavior at low temperatures, a topic which is the focus of recent intense investigations. We expect that this code serves as a quick and practical tool for data documentation from electronic structure calculations: It presents a very intuitive graphical interface which we believe to provide an excellent working tool for researchers and as courseware to teach statistical thermodynamics, thermochemistry, kinetics, and related areas.

Temperature Dependence of Rate Processes Beyond Arrhenius and Eyring: Activation and Transitivity

Advances in the understanding of the dependence of reaction rates from temperature, as motivated from progress in experiments and theoretical tools (e. g., molecular dynamics), are needed for the modeling of extreme environmental conditions (e.g., in astrochemistry and in the chemistry of plasmas). While investigating statistical mechanics perspectives (Aquilanti et al., 2017b, 2018), the concept of transitivity was introduced as a measure for the propensity for a reaction to occur. The Transitivity plot is here defined as the reciprocal of the apparent activation energy vs. reciprocal absolute temperature. Since the transitivity function regulates transit in physicochemical transformations, not necessarily involving reference to transition-state hypothesis of Eyring, an extended version is here proposed to cope with general types of transformations. The transitivity plot permits a representation where deviations from Arrhenius behavior are given a geometrical meaning and make explicit a positive or negative linear dependence of transitivity for sub- and super-Arrhenius cases, respectively. To first-order in reciprocal temperature, the transitivity function models deviations from linearity in Arrhenius plots as originally proposed by Aquilanti and Mundim: when deviations are increasingly larger, other phenomenological formulas, such as Vogel-Fulcher-Tammann, Nakamura-Takayanagi-Sato, and Aquilanti-Sanches-Coutinho-Carvalho are here rediscussed from the transitivity concept perspective and with in a general context. Emphasized is the interest of introducing into this context modifications to a very successful tool of theoretical kinetics, Eyring's Transition-State Theory: considering the behavior of the transitivity function at low temperatures, in order to describe deviation from Arrhenius behavior under the quantum tunneling regime, a "d-TST" formulation was previously introduced (Carvalho-Silva et al., 2017). In this paper, a special attention is dedicated to a derivation of the temperature dependence of viscosity, making explicit reference to feature of the transitivity function, which in this case generally exhibits a super-Arrhenius behavior. This is of relevance also for advantages of using the transitivity function for diffusion-controlled phenomena.

A novel assessment of the role of the methyl radical and water formation channel in the CH3OH + H reaction

A number of experimental and theoretical papers accounted almost exclusively for two channels in the reaction of atomic hydrogen with methanol: H-abstraction from the methyl (R1) and hydroxyl (R2) functional groups. Recently, several astrochemical studies claimed the importance of another channel for this reaction, which is crucial for kinetic simulations related to the abundance of molecular constituents in planetary atmospheres: methyl radical and water formation (R3 channel). Here, motivated by the lack of and uncertainties about the experimental and theoretical kinetic rate constants for the third channel, we developed first-principles Car-Parrinello molecular dynamics thermalized at two significant temperatures - 300 and 2500 K. Furthermore, the kinetic rate constant of all three channels was calculated using a high-level deformed-transition state theory (d-TST) at a benchmark electronic structure level. d-TST is shown to be suitable for describing the overall rate constant for the CH₃OH + H reaction (an archetype of the moderate tunnelling regime) with the precision required for practical applications. Considering the experimental ratios at 1000 K, k_R1/k_R2 ≈ 0.84 and k_R1/k_R3 ≈ 15-40, we provided a better estimate when compared with previous theoretical work: 7.47 and 637, respectively. The combination of these procedures explicitly demonstrates the role of the third channel in a significant range of temperatures and indicates its importance considering the thermodynamic control to estimate methyl radical and water formation. We expect that these results can help to shed new light on the fundamental kinetic rate equations for the CH₃OH + H reaction.

Shelf Life of Food Products: From Open Labeling to Real-Time Measurements

The labels currently used on food and beverage products only provide consumers with a rough guide to their expected shelf lives because they assume that a product only experiences a limited range of predefined handling and storage conditions. These static labels do not take into consideration conditions that might shorten a product's shelf life (such as temperature abuse), which can lead to problems associated with food safety and waste. Advances in shelf-life estimation have the potential to improve the safety, reliability, and sustainability of the food supply. Selection of appropriate kinetic models and data-analysis techniques is essential to predict shelf life, to account for variability in environmental conditions, and to allow real-time monitoring. Novel analytical tools to determine safety and quality attributes in situ coupled with modern tracking technologies and appropriate predictive tools have the potential to provide accurate estimations of the remaining shelf life of a food product in real time. This review summarizes the necessary steps to attain a transition from open labeling to real-time shelf-life measurements.

A novel analytical potential function for dicationic diatomic molecular systems based on deformed exponential function

In this paper, we propose a new alternative analytical function aiming to better describe the potential energy curves of the doubly charged diatomic molecules. To achieve this goal, we modified an existing potential function in the literature to describe dicationic diatomic molecules using the deformed exponential function. We generated the potential energy curve of the testing group of dicationic diatomic molecules [Formula: see text], BH²⁺, [Formula: see text] and NH²⁺ by means of the CCSD(T)/aug-cc-pVQZ level of theory. To validate this new function, we also calculated the spectroscopic constants and the rovibrational spectra for the electronic state [Formula: see text]of the [Formula: see text] and [Formula: see text] systems using the Dunham and discrete variable representation methods. For BH²⁺ and NH²⁺ molecules, despite exhibiting a local minimum in the potential energy curve, no vibrational levels are supported, so the spectroscopic constants for these poorly bound systems are invalidated. The fitting accuracy had a better performance over the original potential for describing dicationic diatomic systems, considering that the discrete variable representation method resulted in a similar vibrational structure described in the literature. This fact can be explained due to the deformed function's flexibility.

Kinetics of low-temperature transitions and a reaction rate theory from non-equilibrium distributions

This article surveys the empirical information which originated both by laboratory experiments and by computational simulations, and expands previous understanding of the rates of chemical processes in the low-temperature range, where deviations from linearity of Arrhenius plots were revealed. The phenomenological two-parameter Arrhenius equation requires improvement for applications where interpolation or extrapolations are demanded in various areas of modern science. Based on Tolman's theorem, the dependence of the reciprocal of the apparent activation energy as a function of reciprocal absolute temperature permits the introduction of a deviation parameter d covering uniformly a variety of rate processes, from those where quantum mechanical tunnelling is significant and d < 0, to those where d > 0, corresponding to the Pareto-Tsallis statistical weights: these generalize the Boltzmann-Gibbs weight, which is recovered for d = 0. It is shown here how the weights arise, relaxing the thermodynamic equilibrium limit, either for a binomial distribution if d > 0 or for a negative binomial distribution if d < 0, formally corresponding to Fermion-like or Boson-like statistics, respectively. The current status of the phenomenology is illustrated emphasizing case studies; specifically (i) the super-Arrhenius kinetics, where transport phenomena accelerate processes as the temperature increases; (ii) the sub-Arrhenius kinetics, where quantum mechanical tunnelling propitiates low-temperature reactivity; (iii) the anti-Arrhenius kinetics, where processes with no energetic obstacles are rate-limited by molecular reorientation requirements. Particular attention is given for case (i) to the treatment of diffusion and viscosity, for case (ii) to formulation of a transition rate theory for chemical kinetics including quantum mechanical tunnelling, and for case (iii) to the stereodirectional specificity of the dynamics of reactions strongly hindered by the increase of temperature.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.

Non-linear van't Hoff behavior in pulmonary surfactant model membranes

Pulmonary surfactant exhibits phase coexistence over a wide range of surface pressure and temperature. Less is known about the effect of temperature on pulmonary surfactant models. Given the lack of studies on this issue, we used electron paramagnetic resonance (EPR) and nonlinear least-squares (NLLS) simulations to investigate the thermotropic phase behavior of the matrix that mimics the pulmonary surfactant lipid complex, i.e., the lipid mixture composed of dipalmitoyl phosphatidylcholine (DPPC), palmitoyl-oleoyl phosphatidylcholine (POPC) and palmitoyl-oleoyl phosphatidylglycerol (POPG). Irrespective of pH, the EPR spectra recorded from 5°C to 25°C in the DPPC/POPC/POPG (4:3:1) model membrane contain two spectral components corresponding to lipids in gel-like and fluid-like phases, indicating a coexistence of two domains in that range. The temperature dependence of the distribution of spin labels between the domains yielded nonlinear van't Hoff plots. The thermodynamic parameters evaluated were markedly different for DPPC and for the ternary DPPC/POPC/POPG (4:3:1) membranes and exhibited a dependence on chemical environment. While enthalpy and entropy changes for DPPC were always positive and presented a quadratic behavior with temperature, those of the ternary mixture were linearly dependent on temperature and changed from negative to positive values. Despite that, enthalpy-entropy compensation takes place in the two systems. The thermotropic process associated with the coexistence of the two domains is entropically-driven in DPPC and either entropically- or enthalpically-driven in the pulmonary surfactant membrane depending on the pH, ionic strength and temperature. The significance of these results to the structure and function of the pulmonary surfactant lipid matrix is discussed.

Deformed transition-state theory: Deviation from Arrhenius behavior and application to bimolecular hydrogen transfer reaction rates in the tunneling regime

A formulation is presented for the application of tools from quantum chemistry and transition-state theory to phenomenologically cover cases where reaction rates deviate from Arrhenius law at low temperatures. A parameter d is introduced to describe the deviation for the systems from reaching the thermodynamic limit and is identified as the linearizing coefficient in the dependence of the inverse activation energy with inverse temperature. Its physical meaning is given and when deviation can be ascribed to quantum mechanical tunneling its value is calculated explicitly. Here, a new derivation is given of the previously established relationship of the parameter d with features of the barrier in the potential energy surface. The proposed variant of transition state theory permits comparison with experiments and tests against alternative formulations. Prescriptions are provided and implemented to three hydrogen transfer reactions: CH₄  + OH → CH₃  + H₂ O, CH₃ Cl + OH → CH₂ Cl + H₂ O and H₂  + CN → H + HCN, widely investigated both experimentally and theoretically. © 2016 Wiley Periodicals, Inc.