Dear Muxue,

Hammett electronic effect constant (sigma) and Taft steric effect constant (Es) have been widely used in QSAR in drug discovery in order to understand the nature and mode of interactions between drugs and active sites of enzymes and receptor.

Similarly Hammett and Taft constants have been utilized for understanding the nature of interactions between a solute and a membrane (RO or NF). There are only few reports regarding this topic which demonstrated that using these constants allows a good predict ion of water flux.

For instance, the study by Bhattacharyya and coworkers entitled "Separation of Organic Pollutants by Reverse Osmosis and Nanofiltration Membranes: Mathematical Models and Experimental Verification (I&EC Research, September 1999) " revealed a linear correlation between water flux and pKa for a number of phenolic compounds.

The pka is the ability to donate proton, thus, free protons play dominant role in water flux presumably by hydrogen bonding between the solute and the membrane material.

Similarly bulky solutes interact differently with the membrane material from non-bulky solutes.

Attached please find the above mentioned paper along with other three publications which give an overview of QSAR models implemented with RO and NF membranes.

Regarding the limitation and accuracy: the attached publications documented a good accuracy in using the QSAR model. However, I believe that the limitations are the same as that reported for the QSAR in the drug discovery.

Hoping this might be helpful,

Rafik

I am not a membrane specialist, and the Rafik's answer is a good step to approach the substituent effects on membrane diffusion.

The Hammett and Taft approaches to substituent effects are empirical model based on similarity of rate and equilibria (in logarithmic forms, therefore related to Gibbs -or “free”- energies) and consequently were called Liner Free Energy Relationships (LFER). Hammett relation is for aromatic systems, for describing the changes in reactivity of a given functional group, under the influence of a series of substituent. It is a single-parameter equation, but ortho, meta, para positions need different parameters (however ortho substitution may pose specific problems). This is a good model for acidity/basicity of a molecule. Taft equation(s) (in the sense described by Rafik) is more adapted to reactivity problems for compounds bearing bulky substituents close to the reaction center. It is a two-parameter equation with an inductive and a steric (size) parameters.

There is other “Taft equations”. In addition to the inductive + steric model cited above, Robert W. Taft worked on substituent and solvent effects and devised a lot of equations and constants:

(i) A two parameter equation to replace the single parameter Hammett model, using inductive and resonance parameters; applicable to meta or para (and possibly ortho) positions in aromatic systems;

(ii) More complex equation for gas-phase basicities, probably not relevant to the diffusion problem;

(iii) A model of solvent effect or solvation (Kamlet-Taft equation, now popularized by M. H. Abraham) using hydrogen bonding parameters and polarity, polarizability, volume parameters, etc. widely used for solubility studies and chromatography. I am sure that his kind of approach may be useful for diffusion through membranes.

The C. Hansch “logP” constant (lipophilicity / hydrophilicity) constant should also be considered.

Finally “quantitative structure activity relationships” (QSAR, derived from medicinal chemistry approaches mostly for pharmaceutical activity) are a kind of synthesis of the empirical approaches, using electronic and steric substituent constants, as well as other more global parameters. These “many parameters” approaches should be better called “quantitative structure property relationships” or QSPR. The tendency is to use “theoretical” (calculated by quantum chemistry) parameters. The report “Membranes 4.pdf” cited by Rafik is a example of such approach. For me it is a pity that all the works of Hammett, Taft, Hansch, Abraham, etc. who initiated these methodologies are completely ignored in this and similar studies.

If you need more details on substituent and solvent effects, I’d be pleased to correspond on those matters.