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Chromatographic Techniques for Characterization of Carbons and Carbon Composites
Published in Paweł K. Zarzycki, Pure and Functionalized Carbon Based Nanomaterials, 2020
Adam Voelkel, Beata Strzemiecka
Cohesive energy (Ecoh) related to a molar volume is called cohesive energy density c (equation 16): c=−EcohV and the square root of cohesive energy density is called solubility parameter δ (equation 17). This term proposed by Hildebrand for non-polar systems, used as a measure of intermolecular forces of different solvents, is related to the enthalpy of an evaporation ΔHw (equation 17): δ=c=EcohV=ΔHw−RTV where δ is the solubility parameter, Ecoh is the cohesive energy, V is the molar volume of a pure liquid, R is the gas constant, T is the temperature. The solubility parameter expressed by equation (17) is called the Hildebrand solubility parameter.
The Relevance of Solubility and Miscibility for the Performance of Organic Solar Cells
Published in John R. Reynolds, Barry C. Thompson, Terje A. Skotheim, Conjugated Polymers, 2019
Stefan Langner, Jose Dario Perea Ospina, Chaohong Zhang, Ning Li, Christoph J. Brabec
where V is the molar volume of the pure solvent, R is the ideal gas constant, T is the absolute temperature and ET is the energy of cohesion, which has been defined in terms of the enthalpy of vaporization ΔHv.24,25 For regular solutions, the solubility parameters and the molar volumes can be assumed to be constant for a wide temperature range. The Hildebrand solubility parameter can be further calculated by summing up the various attractive and distractive interactions among the molecular groups, as demonstrated in Equation (15.3), where ρ is the density, ΣF is the sum of the molar attraction constants of the molecule’s or polymer’s repeating unit and M is the molar mass of the repeating unit. δT=ρ∑FM,
A study of solubility parameters on dispersion, dissolution, and homogenization of reinforcement TiO2 and poly(4-methyl-1-Pentene) in different solvents for the fabrication of TiO2/PMP composite film
Published in Chemical Engineering Communications, 2023
Where E and V are the cohesive energy (vaporization energy) and molar volume respectively. For the minimum value of ΔHmix, solubility parameters of solute and solvent should be as close as possible (Gårdebjer et al. 2016). Also, equation 2 showed that ΔHmix could never be negative, but with the specific interaction, it could happen for a system (e.g., hydrogen bond) (Gårdebjer et al. 2016). The Hildebrand solubility parameter is based on a geometric mean approximation used for materials that interact through dispersion interaction only. However, molecule interactions may be due to polar, dispersion, or hydrogen bonding interactions. Charles Hansen explained these interactions using Hansen's solubility parameter (HSP), δd, δp and, δh (equation 4) (Burke 1984; Hansen 2007).