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We describe our extensive collective experience in the conduct of courses based on the use of advanced mathematical software to enhance the capabilities of students of chemistry to solve problems with a mathematical component. These courses have been based on an interactive electronic textbook Mathematics for Chemistry with Symbolic Computation that has been concurrently developed and expanded. The admirable performance of the students who have benefited from our courses leaves no doubt that mathematical software is an invaluable tool for the teaching, learning and practice of mathematics in a chemical context.

The anisotropy of molecular polarizability in liquid crystals is linked to the birefringence in these substances. The classic methods to compute the polarizabilities of liquid crystals assume an average number density of molecules that is equal in all directions. In the present work, a new model is proposed for the anisotropic molar polarization based on a virtual anisotropy of the number density of molecules in the liquid-crystalline material. This new strategy hence allows for the computation of both the anisotropic polarizabilities and the anisotropic thermal-expansion coefficients of liquid crystals. The model is applied to the liquid crystals 4-n-pentyl-4′-cyanobiphenyl and N-(4-methoxybenzylidene)-4-butylaniline, yielding polarizabilities similar to those reported for these materials. For these nematic liquid crystals, the results imply the existence of a positive thermal-expansion coefficient in the direction perpendicular to the director vector throughout the entire nematic temperature range and a negative thermal-expansion coefficient parallel to the director vector near the temperature of the nematic–isotropic transition. At the isotropization temperature, there exists divergent and critical behavior of the anisotropic thermal-expansion coefficients, consistent with the typical discontinuity of volume in first-order transitions. [ABSTRACT FROM AUTHOR]

Abstract: The article describes a new concept of an optical hybrid thin‐film material that exhibits reversible humidity‐driven light transmittance (scattering) properties. The film consists of a dispersive porous structure, with embedded hygroscopic and deliquescent compounds, that is able to scavenge water molecules from humid air to fill up the pores and become transparent to the incident light. Upon exposure to dry air, water is released from the structure and the material recovers its original light scattering properties. The developed thin films can change their transparency when exposed to air with different relative humidity (RH), adjusting the light throughput. This material can, therefore, be used to design new optical switching systems, having the advantage that they do not require liquid crystal, transparent conductive glass substrates, or complex layer‐by‐layer architectures for operation. In this work, a thin film was prepared by the sol–gel technique using calcium chloride as deliquescent substance embedded in a hybrid silica–titania matrix. At dry air, the thin films show a highly dispersive state, with a light transmittance T = 0.06, while at 51% RH the film exhibits a transparent state with a transmittance T =0.67 (measured at 633 nm). [ABSTRACT FROM AUTHOR]