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In this work, we present in detail, in an accessible manner for undergraduate and graduate physics students, the model of spontaneous curvature, due to Helfrich, that quantitatively explains why the red blood cells in their natural state adopt a biconcave shape. The main hypothesis is that the equilibrium cell shape satisfies the principle of minimum free energy. Therefore, in the model, an expression for the membrane free energy is postulated based on the Helfrich theory. In that approximation, the membrane is modelled as a two-dimensional surface and the energy is written as a function of the surface principal curvatures and three parameters, including the spontaneous curvature, c0, which is associated with the chemical composition of the membrane. The negative values for c0 induce invaginations in the cell membrane. The model predicts the discocyte-spherocyte transition for the red blood cell. In the article, the concepts involved in the theory are developed in detail, and an algorithm that allows obtaining the contour of the cell is presented in detail as supplementary material.

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The degradation of organic molecules in an aqueous medium using heterogeneous photocatalysis depends on the chemical composition and concentration of the organic compound, the crystalline and morphological nature of the photocatalyst, the pH of the dye dilution, and the reaction temperature. Since photocatalytic degradation is a process that occurs on the surface of the catalytic material, it is desirable to induce maximum adsorption of the organic compound. One strategy to achieve this is to functionalize the surface of the catalyst to retain the molecule of interest. In this work, we studied the interaction of acid orange 7 (AO7) with commercial TiO2-anatase powder catalyst, and with a catalyst synthesized in house using titanium tetrachloride and ethanolamine (TiO2-et). Our results indicate that there is no adsorption of the AO7 dye on the TiO2-et particles. The infrared spectrum of the TiO2-et particles is presented.