(687c) Predicting Surface Area in Green Synthesis of Sol-Gel Materials

Rigidity Theory (J.C. Maxwell, 1864) explains why some physical structures are rigid and others not, by balancing the degrees of freedom of movement of the component parts, with the constraints on their movement effected by connections between them. We applied the theory to porous amorphous materials recently prepared without template molecules or organic solvents and can predict which precursors will and will not produce high surface area materials useful for adsorption and catalysis.

In sol-gel routes to porous materials, the precursors are hydrolyzed and then condensed to form a 3D polymeric network. During drying, the network substantially collapses due to strong capillary forces, unless something is done to prop it up. Our hypothesis is that, in the absence of pore-templating guest molecules or complex solvent-removal processes, the network must reach a critical level of rigidity in order to maintain a porous structure. We used rigidity theory to calculate the level of condensation present at the critical level.

For such a network to become critically rigid before collapse, it must form quickly (kinetics) and be stable (thermodynamics) under the conditions of drying. We developed descriptors for the time it takes for the network to achieve rigidity and for the level of solvent remaining in the gel at the rigidity transition. We further hypothesize that the amount of solvent remaining when rigidity is reached determines the total porosity as the originally solvent-filled volume becomes empty.

We show that the theory successfully distinguishes between precursors that exhibit very high levels of porosity and surface area (> 1000 m²/g), those that exhibit intermediate levels (~ 250 m²/g), and those that substantially collapse (< 50 m²/g). The theory is simple to implement for many precursors, and is being used to predict new precursors that might make useful materials.