Theoretical Calculations of Acid Dissociation Constants: A Review Article

Acid dissociation constants, or pKa values, are essential for understanding many fundamental reactions in chemistry. These values reveal the deprotonation state of a molecule in a particular solvent. There is great interest in using theoretical methods to calculate the pKa values for many different types of molecules. These include molecules that have not been synthesized, those for which experimental pKa determinations are difficult, and for larger molecules where the local environment changes the usual pKa values, such as for certain amino acids that are part of a larger polypeptide chain. Chemical accuracy in pKa calculations is difficult to achieve, because an error of 1.36 kcal/mol in the change of free energy for deprotonation in solvent results in an error of 1 pKa unit. In this review the most valuable methods for determining accurate pKa values in aqueous solution are presented for educators interested in explaining or using these methods for their students.

Planetary Gear Modal Vibration Experiments and Correlation against Lumped-Parameter and Finite Element Models

Experimental modal analysis techniques are applied to characterize the planar dynamic behavior of two spur planetary gears. Rotational and translational vibrations of the sun gear, carrier, and planet gears are measured. Experimentally obtained natural frequencies, mode shapes, and dynamic response are compared to the results from lumped-parameter and finite element models. Two qualitatively different classes of mode shapes in distinct frequency ranges are observed in the experiments and confirmed by the lumped-parameter model, which considers the accessory shafts and fixtures in the system to capture all of the natural frequencies and modes. The finite element model estimates the high-frequency modes that have significant tooth mesh deflection without considering the shafts and fixtures. The lumped-parameter and finite element models accurately predict the natural frequencies and modal properties established by experimentation. Rotational, translational, and planet mode types presented in published mathematical studies are confirmed experimentally. The number and types of modes in the low-frequency and high-frequency bands depend on the degrees of freedom in the central members and planet gears, respectively. The accuracy of natural frequency prediction is improved when the planet bearings have differing stiffnesses in the tangential and radial directions, consistent with the bearing load direction. (C) 2012 Elsevier Ltd. All rights reserved.