We present a model to calculate particle size distributions (PSDs) of colloidal ZnO nanoparticles from their absorbance spectra. Using literature values for the optical properties of bulk ZnO and correlating the measurement wavelengths in the UV-visible regime with distinct particle sizes by a tight binding model (TBM), an algorithm deconvolutes the absorbance spectra into contributions from size fractions. We find an excellent agreement between size distributions determined from TEM images and the calculated PSDs. For further validation, bimodal PSDs have been investigated and an approach to determine not only particle size but also solid concentration is introduced. We will show the applicability of our model by the determination of temperature-dependent ripening rates, which enables the calculation of solubilities, surface tensions, and the activation enthalpy of ripening. In principle, our methodology is applicable to different semiconductor nanoparticles in various solvents as long as their bulk properties are known and scattering is negligible.

Within the framework of the well-known curvature models, a fluid lipid bilayer membrane is regarded as a surface embedded in the three-dimensional Euclidean space whose equilibrium shapes are described in terms of its mean and Gaussian curvatures by the so-called membrane shape equation. In the present paper, all solutions to this equation determining cylindrical membrane shapes are found and presented, together with the expressions for the corresponding position vectors, in explicit analytic form. The necessary and sufficient conditions for such a surface to be closed are derived and several sufficient conditions for its directrix to be simple or self-intersecting are given.

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