## Water Sorption Isotherms

### Quick Start

Water sorption isotherms can be fitted to the GAB (Guggenheim- Anderson-de Boer) model. If you have a mix of materials (here we just use two) a weight-fraction average of the two seems to be an adequate approximation for the mixture.

### Water Sorption Isotherms

M1
C1
K1
Wt%1
M2
C2
K2

A water sorption isotherm shows the amount (or fraction, I have left the units vague) of water absorbed versus the water activity, aw or, if you prefer, %RH/100. To get these isotherms you need to be able to measure the weight increase as the %RH of the air is changed, allowing enough time for equilibrium to be reached before stepping to the next level. There is often hysteresis (not shown) between the values measured going from 0 to 100% and 100% going down to 0, with the descending isotherm showing more sorption that the ascending one.

The GAB model has three parameters: M which is what would be expected from a monolayer coverage, typically in the 0.05 to 0.2 range, then C which is in the 1-50 range, and K which is an adjustment parameter, typically in the 0.5 to 1 range. When K=1 the equation is formally equivalent to the well-known BET isotherm. The GAB model calculates the Sorption, S for a given water activity, aw. Because experimental data and GAB both have problems above 0.95 activity, the graph stops at that point.

S=(MCKa_w)/((1-Ka_w)(1-Ka_w+CKa_w))

Play with the two sets of three values to describe your different components (you can check values with the mouse readout) then alter the Wt%1 slider to see how the isotherm changes.