A Physical Basis for Kinetic Compensation.

Kinetic compensation is a strong, positive correlation between the Arrhenius activation energy E and the frequency factor A for a reaction between the same reactants under similar experimental conditions or similar reactants under the same conditions, even though these parameters are supposed to be independent. The kinetic compensation effect (KCE) is demonstrated by a linear relationship between ln[A] and E/R in the eponymous Constable plot and has been the subject of more than 50 000 publications over the past 100 years, with no consensus opinion about the cause of this effect. In this paper, it is suggested that the linear relationship between ln[A] and E is the result of a real or spurious path dependence of the reaction history between the initial state of the pure reactant(s) and the final state of the pure product(s) having standard enthalpy and entropy differences, ΔH° and ΔS°, respectively. The single-step rate law approximation of a reversible reaction leads to T0 = H°/ΔS° as the dynamic thermal (thermodynamic) equilibrium temperature and 1/T0 = (ln[A̅/k0])/(E̅/R) as the slope of a Constable/KCE plot or the crossover temperature of Arrhenius lines in an isokinetic relationship (IKR), where A̅ and E̅ are mean values for the ensemble of compensating {Ei, Ai} pairs and k0 is a constant that accounts for the path dependence of the reaction history and reconciles the KCE with the IKR. This proposed physical basis for the KCE and IKR is supported by qualitative agreement between ΔH° and ΔS° calculated from the statistics of compensating {Ei, Ai} pairs in the literature, and the difference in the standard enthalpies and entropies of formation of the products and reactants for thermal decomposition of organic peroxides, calcium carbonate, and poly(methyl methacrylate).

Isokinetics.

The study of the rates of chemical reactions and their relationship to temperature began in the 19th century with empirical measurements of the time required to reach a particular reaction end point at a constant temperature. By the mid-20th century, the theory of reaction rates had advanced and instruments had been developed in which the temperature of the sample could be increased at a constant rate. These nonisothermal methods are now widely used to determine the kinetic parameters of reactions because of their convenience. In this paper, the mathematical relationship between measurements at constant temperature (isothermal) and constant heating rate (nonisothermal) is developed and it is shown that there is a point in the temperature history of a single-step reaction at which the isothermal and nonisothermal reaction rates are equal. This equal (iso) kinetic point occurs at a temperature early in the heating history of nonisothermal analyses at which the reaction rate begins to accelerate. The isokinetic temperature is the basis for a new method of nonisothermal kinetic analysis that provides a direct measurement of the Arrhenius frequency factor A and activation energy Ea for the elementary step of a solid-state reaction without any assumptions about the relationship between these parameters (i.e., kinetic compensation) or the reaction mechanism.

Energetics of lithium ion battery failure.

The energy released by failure of rechargeable 18-mm diameter by 65-mm long cylindrical (18650) lithium ion cells/batteries was measured in a bomb calorimeter for 4 different commercial cathode chemistries over the full range of charge using a method developed for this purpose. Thermal runaway was induced by electrical resistance (Joule) heating of the cell in the nitrogen-filled pressure vessel (bomb) to preclude combustion. The total energy released by cell failure, ΔHf, was assumed to be comprised of the stored electrical energy E (cell potential×charge) and the chemical energy of mixing, reaction and thermal decomposition of the cell components, ΔUrxn. The contribution of E and ΔUrxn to ΔHf was determined and the mass of volatile, combustible thermal decomposition products was measured in an effort to characterize the fire safety hazard of rechargeable lithium ion cells.

Thermal dynamics of bomb calorimeters.

The thermal dynamics of bomb calorimeters are modeled using a lumped heat transfer analysis in which heat is released in a pressure vessel/bomb immersed in a stirred water bath that is surrounded by a static air space bounded by an insulated (static) jacket, a constant/controlled temperature jacket (isoperibol), or a changing temperature (adiabatic) jacket. The temperature history of the water bath for each of these boundary conditions (methods) is well described by the two-term solution for the calorimeter response to a heat impulse (combustion), allowing the heat transfer coefficients and thermal capacities of the bomb and water bath to be determined parametrically. The validated heat transfer model provides an expression for direct calculation of the heat released in an arbitrary process inside a bomb calorimeter using the temperature history of the water bath for each of the boundary conditions (methods). This result makes possible the direct calculation of the heat of combustion of a sample in an isoperibol calorimeter from the recorded temperature history without the need for semi-empirical temperature corrections to account for non-adiabatic behavior. Another useful result is that the maximum temperature rise of the water bath in the static jacket method is proportional to the total heat generated, and the empirical proportionality constant, which is determined by calibration, accounts for all of the heat losses and thermal lags of the calorimeter.

A kinetic model for human blood concentrations of gaseous halocarbon fire-extinguishing agents.

A simple kinetic model for calculating the blood concentration history of humans exposed to time-varying concentrations of gaseous, halocarbon fire-extinguishing agents is described. The kinetic model was developed to extend experimental physiologically based pharmacokinetic (PBPK) models for arterial blood concentration of halocarbons, obtained from constant concentration exposure of dogs to time-varying exposure conditions for humans. In the present work, the simplified kinetic model was calibrated using published PBPK-derived arterial concentration histories for constant concentration exposure to several common fire-extinguishing agents. The calibrated kinetic model was then used to predict the blood concentration histories of humans exposed to time-varying concentrations of these fire-extinguishing agents in ventilated compartments and the results were compared with PBPK-derived data for the agents. It was found that the properly calibrated kinetic model predicts human arterial blood concentration histories for time-varying exposures as well as the PBPK models. Consequently, the kinetic model represents an economical methodology for calculating safe human exposure limits for time-varying concentrations of gaseous halocarbon fire-extinguishing agents when only PBPK-derived human arterial blood concentration histories for constant exposure conditions are available.