research consultancy
To address this gap, a team from Virginia Tech, the University of Delaware, and Aspen Technology compiled the first publicly available sigma profile database. This repository includes profiles for 1,432 compounds composed of 10 elements: H, C, N, O, F, P, S, Cl, Br, and I. Available for free online (www.design.che.vt.edu), the database also includes tools and documentation to enable researchers to generate sigma profiles for additional compounds.
The package includes:
Detailed procedures for generating sigma profiles.
FORTRAN code for sigma averaging and COSMO-SAC calculations.
Validation cases comparing COSMO-SAC predictions with experimental vapor-liquid equilibria, activity coefficients, and solubilities.
Theoretical Framework
COSMO-SAC Model Structure
COSMO-SAC computes the activity coefficient (γ) of a solute using two main contributions:
Electrostatic Restoration Free Energy: The difference between restoring induced charges in a solvent versus the pure solute phase.
Staverman-Guggenheim Combinatorial Term: Accounts for the entropy of mixing and cavity formation effects.
Mathematically:
lnγiS=ΔGi/Sres−ΔGi/iresRT+lnγi/SSG\ln \gamma_i^S = \frac{\Delta G_{i/S}^{res} – \Delta G_{i/i}^{res}}{RT} + \ln \gamma_{i/S}^{SG}
Where the restoring free energy is derived from the sigma profile and activity coefficient of each surface segment. The interaction energy between segments is modeled via:
ΔW(σm,σn)=R′2(σm+σn)2+chb⋅Hydrogen bonding terms\Delta W(\sigma_m, \sigma_n) = \frac{R’}{2} (\sigma_m + \sigma_n)^2 + chb \cdot \text{Hydrogen bonding terms}
These expressions capture the full spectrum of electrostatic and hydrogen-bonding interactions.
Applications and Validation
To validate the model and database, comparisons were made between sigma profiles generated by the VT-2005 implementation and those reported by Lin and Sandler. Compounds like water, acetone, n-hexane, and 1-octanol were analyzed, showing high consistency in charge distribution.
The COSMO-SAC model was used to predict:
Activity coefficients at infinite dilution.
Binary vapor-liquid equilibrium data.
Solubility limits.
In all cases, the model showed strong agreement with experimental data, confirming the reliability of both the theoretical approach and the sigma profile dataset.
