An analytical proof of Hardy-like inequalities related to the Dirac operator

We prove some sharp Hardy-type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.     

Numerical study of sliding wear caused by a loaded pin on a rotating disc

A computational approach is proposed to predict the sliding wear caused by a loaded spherical pin contacting a rotating disc, a condition typical of the so-called pin-on-disc test widely used in tribological studies. The proposed framework relies on the understanding that, when the pin contacts and slides on the disc, a predominantly plane strain region exists at the centre of the disc wear track. The wear rate in this plane strain region can therefore be determined from a two dimensional idealisation of the contact problem, reducing the need for computationally expensive three dimensional contact analyses. Periodic unit cell techniques are used in conjunction with a ratchetting-based failure criterion to predict the wear rate in the central plane strain region. The overall three dimensional wear rate of the disc is then determined by scaling the plane strain wear rate with a conversion factor related to the predicted shape of the wear track. The approach is used to predict pin-on-disc test data from an Al-Si coating using a tungsten carbide pin. The predicted results are found to be consistent with measured data.     

Ni5, Ni8, and Ni10 clusters with 2,6-diacetylpyridine-dioxime as a ligand

In the present work, novel coordination possibilities for the system dapdoH(2)/Ni(II) (dapdoH(2) = 2,6-diacetylpyridine-dioxime) have been explored. Depending on the starting reagents and solution conditions, several clusters with nuclearities ranging from Ni(5) to Ni(10) were achieved and structurally characterized, namely, [Ni(5)(R-COO)(2)(dapdo)(2)(dapdoH)(2)(N(CN)(2))(2)(MeOH)(2)] in which R-COO(-) = benzoate (1) or 3-chlorobenzoate (2), [Ni(8)(dapdo)(4)(NO(3))(4)(OH)(4)(MeOH)(4)] (3), and [Ni(10)(dapdo)(8)(N(CN)(2))(2)(MeO)(MeOH)](NO(3)) (4). For the first time, pentadentate coordination for the dapdo(2-) ligand has been established. All compounds show a combination of square-planar and octahedrally coordinated nickel atoms. According to the Ni(2)(sp)Ni(3)(Oh) (1 and 2), Ni(4)(sp)Ni(4)(Oh) (3), and Ni(4)(sp)Ni(6)(Oh) (4) environments, these systems magnetically behave as trimer, tetramer, and hexanuclear clusters, respectively. dc magnetic measurements in the 2-300 K range of temperature reveal antiferromagnetic coupling for all compounds, and the correlation of the superexchange interaction with the torsion angles involving the oximato bridges is experimentally confirmed.     

Donnan equilibrium revisited

The osmotic pressure, electric potential and final concentrations in the Donnan equilibrium of a 1-1 electrolyte and a charged species which cannot cross the membrane are calculated in the mean spherical approximation for the primitive model both for equal and different diameters. Large differences with the ideal and Debye-Hückel approximations are found and discussed.     

Front Cover: Critical Assessment of pH-Dependent Lipophilicity Profiles of Small Molecules: Which One Should We Use and In Which Cases? (ChemPhysChem 24/2023)

Lipophilicity is a physicochemical property with wide relevance in drug design, computational biology, food, environmental and medicinal chemistry. Lipophilicity is commonly expressed as the partition coefficient for neutral molecules, whereas for molecules with ionizable groups, the distribution coefficient (D) at a given pH is used. The logD_pH is usually predicted using a pH correction over the logP_N using the pK_a of ionizable molecules, while often ignoring the apparent ion pair partitioning . In this work, we studied the impact of on the prediction of both the experimental lipophilicity of small molecules and experimental lipophilicity-based applications and metrics such as lipophilic efficiency (LipE), distribution of spiked drugs in milk products, and pH-dependent partition of water contaminants in synthetic passive samples such as silicones. Our findings show that better predictions are obtained by considering the apparent ion pair partitioning. In this context, we developed machine learning algorithms to determine the cases that should be considered. The results indicate that small, rigid, and unsaturated molecules with logP_N close to zero, which present a significant proportion of ionic species in the aqueous phase, were better modeled using the apparent ion pair partitioning . Finally, our findings can serve as guidance to the scientific community working in early-stage drug design, food, and environmental chemistry.