Knowledge of solution density as a function of levels of cyclodextrin (CDs), salt, and temperature is crucial in the production of cyclodextrins, evaluation of guest−host interactions, and many applications of CDs especially in aquifer remediation and advanced oil recovery where density affects hydraulics. Relatively high precision measurements (±1 μg·cm−3) of solution density at 1 atm were collected from 278.15 to 333.15 K for aqueous solutions of 2-hydroxypropyl-β-cyclodextrin and sodium chloride. A progressive
model (0.0021, 95% CI) based on observed trends in data was developed by observations of second-order relationships for temperature and salinity in molal and linear CD concentration. In a less biased manner, a novel approach to developing density equations involved creation of a series of ordinary least
squares (OLS) linear models based on a stepwise adoption of additional “best” terms from a pool of 3872 variants of terms commonly found in density and other rheological equations based on minimization of the Akaike information criterion. After evaluating the use of up to 83 terms, no improvement was gained for a molal-based concentration after 79 terms and mass fraction based after 77 terms with both having a 95% prediction interval of 32.4 μg·cm−3 being achieved. For potential end-users, the provided pool of 186 OLS models enables the choice of complexity versus performance for their application. More broadly, the methods used herein can be adopted for development of accurate equations for other rheological systems.
In this work, relatively high precision measurements of solution density at 1 atm were made of relatively degassed aqueous solutions of 2-hydroxypropyl-β-cyclodextrin and sodium chloride over temperatures of 278.15−333.15 K. For salt only solutions, regression analysis found linear increases in solution density with increasing salinity in mass fraction and molal concentration and the same was observed for the
examined cyclodextrin derivative. The slopes of these linear relationships were found to have an inverse relationship with temperature and were closely approximated with a second order model.
William J. Blanford*, David S. Jofat, and Adam D. Kapelner (2020) Solution Density Models as Functions of Sodium Chloride, Hydroxypropyl-β-cyclodextrin, and Temperature (278.15–333.15 K) via Progressive Linear and Stepwise Regression. J. Chem. Eng. Data 65, 10, 4735–4750
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