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.