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Some Underlying Physical Principles
Published in Clive R. Bagshaw, Biomolecular Kinetics, 2017
where A is the integration constant, normally termed the preexponential factor, and Ea is termed the activation energy. Ea is an experimentally determined value from the temperature dependence of a rate constant. Comparison with theory (Equations 3.18 and 3.24) shows that Ea provides an estimate to activation enthalpy, ΔH0+1. As discussed in Figure 3.5, the energy barrier that needs to be crossed to form product is defined by the free energy of activation, which also includes the activation entropy, which is part of the preexponential factor, A. It follows that a slow reaction has a small preexponential factor and/or large activation energy. For a constant value of the preexponential factor A, a reaction can be speeded up by increasing the temperature or decreasing the activation energy, the latter being invoked as a mechanism for catalysis (Figure 3.5b). The preexponential factor also has some temperature dependence, but generally, this is minor compared with the effect of the exponent term. The preexponential factor is a measure of the intrinsic rate of the reaction when the thermal energy (RT) greatly exceeds the activation energy. However, its estimation from an Arrhenius plot, where data have been obtained over a limited temperature range (Figure 3.4b), requires a large extrapolation of a function that is not strictly linear and is therefore prone to errors [11,72].
Dissolution of Silver Nanoparticles
Published in Huiliang Cao, Silver Nanoparticles for Antibacterial Devices, 2017
Erchao Meng, Qingbo Zhang, Feng Li, Tanya S. Peretyazhko
where κ is the rate constant, R is the gas constant, T is the temperature, A is a pre-exponential factor and Ea is the activation energy (Stumm and Morgan 2012). The obtained Ea was determined to be 35.1 ± 0.9 kJ/mol (Ho et al. 2010).
Thermal energy and tableting effects in benznidazole product: the impacts of industrial processing
Published in Drug Development and Industrial Pharmacy, 2023
Maria Betânia de Freitas-Marques, Talita Santos do Valle, Bárbara Caroline Rodrigues de Araujo, Rita de Cássia de Oliveira Sebastião, Wagner da Nova Mussel, Maria Irene Yoshida, Christian Fernandes
Thermodynamic factors involved in pharmaceutical systems have been identified and quantified using thermoanalytical techniques applied in the Quality by Design (QbD) approach for GMP [2,6,19] in the pharmaceutical industry. Therefore, it is possible to follow solid-state reactions from thermogravimetric (TG) data [20]. The conversion function of the material, α, is defined for the determination of kinetic parameters, such as the activation energy (Ea), mechanism, and pre-exponential factor (lnA) obtained by the Arrhenius equation for shelf-life estimation [21]. Thus, it is possible to determine the influence of excipients on drug thermodynamics by studying the compatibility kinetics of pharmaceutical solids [6] to determine the critical material attributes (CMA) and to define Critical Process Parameters (CPP) of pharmaceutical processing techniques [19]. Linking the necessary CMA and CPP to all changes in the properties of pharmaceutical materials, one may finally determine a product design space, followed by selecting an appropriate manufacturing process and developing a control strategy to produce consistent quality over the time of drug product market life [6,22].
Quantifying the relationship between biofilm reduction and thermal tissue damage on metal implants exposed to alternating magnetic fields
Published in International Journal of Hyperthermia, 2022
Bibin Prasad, Sumbul Shaikh, Reshu Saini, Qi Wang, Serena Zadoo, Varun Sadaphal, David E. Greenberg, Rajiv Chopra
The heat inactivation data were fit to an Arrhenius model to characterize the rate of inactivation for the different biofilm strains. The basic Arrhenius model can be expressed as [28] k is the rate constant, T is the absolute temperature in Kelvin, A is the pre-exponential factor, Ea is the activation energy for the reaction (in the same units as RT), R is the universal gas constant. Assuming the CFU reduction follows a log-linear reduction, where N is the log10 of CFU decrease log (CFU(t)/CFU(t = 0)) in a heat treatment of time t. The equation can be modified as, A and B are constants, B is defined as Ea/2.303R. This traditional log-linear model is the best-known primary survival model, and it is still widely used in sterility calculations in the food, pharmaceutical, and other industries [29,30]. A and B can be obtained through linear fitting by log(N/t) and 1/T. With A and B derived from this linear fit, a model for CFU reduction (N) as a function of temperature and time can be expressed as,
Proteomes of the past: the pursuit of proteins in paleontology
Published in Expert Review of Proteomics, 2019
The three resulting k values, one for each of three tested temperatures, are then plotted in a second logarithmic curve, the Arrhenius plot. It shows the natural logarithm of each decay constant, ln(k) versus the inverse temperature, 1/T. The slope of the line of best fit through those three points is used to obtain the variables Ea and A for the Arrhenius equation. Ea is the activation energy, and A is a pre-exponential factor unique to each reaction and partly expresses frequency of collisions between reactants. The slope of the Arrhenius plot equals – Ea/R, with R being the gas constant, 8.31446 J/(mol∙K). The y-intercept of the slope from that same Arrhenius plot equals ln(A). Finally, with all variables of the Arrhenius known, a form of the Arrhenius equation is then solved algebraically for the rate constant k at any given temperature.