Modeling and measuring the absorption-induced expansion of swellable organically modified silica

We present a theoretical framework that describes the force generated by the expansion of swellable organically modified silica (SOMS) upon exposure to organic solvent. The total swelling force, produced from the differential contributions of localized swelling domains, is related logarithmically to the amount of material confined to a rigid space. The model is further parameterized according to the physical dimensions of that space and the intrinsic swellability of SOMS. This mathematical representation is validated experimentally using a piston force sensor apparatus, which shows that the solvent-induced force and pressure exerted by SOMS increase logarithmically with the amount of material that is present. Comparison with theory implies that the commercially available varieties of SOMS CyclaSorb(TM) and Osorb(TM) have Young's expansion moduli Y-C similar to 0.8 MPa and Y-O similar to 0.7 MPa, respectively, which succinctly quantifies their relative behavior. The theoretical model and experimental technique should be widely applicable to other swellable and stimuli-responsive materials.