Application of the Baxter Model for Hard Spheres with Surface Adhesion to SANS Data for the U(VI)−HNO₃, TBP−n-Dodecane System

Small-angle neutron scattering (SANS) data for the tri- n -butyl phosphate (TBP)− n -dodecane, HNO 3 −UO 2 (NO 3 ) 2 solvent extraction system have been interpreted using the Baxter model for hard spheres with surface adhesion. The increase in the scattering intensity in the low Q range observed when increasing amounts of HNO 3 or UO 2 (NO 3 ) 2 are transferred into the organic phase has been interpreted as arising from interactions between solute particles. The SANS data have been reproduced using a 12−16 Å diameter of the hard sphere, d hs, and a 5.6 k B T −7.1 k B T stickiness parameter, τ -1 . When in contact with an aqueous phase, TBP in n -dodecane forms small reverse micelles containing three TBP molecules. Upon extraction of water, HNO 3, and UO 2 (NO 3 ) 2, the swollen micelles interact through attractive forces between their polar cores with a potential energy of about 2 k B T and an effective Hamaker constant of about 4 k B T . The intermicellar attraction, under suitable conditions, leads to third-phase formation. Upon phase splitting, most of the solutes in the original organic phase (water, TBP, HNO 3, and UO 2 (NO 3 ) 2 ) separate in a continuous phase containing interspersed layers of n -dodecane.