Insights into organogelation and its kinetics from Hansen solubility parameters. Toward a priori predictions of...

Many small molecules can self-assemble by non-covalent interactions into fibrous networks and thereby induce gelation of organic liquids. However, no capability currently exists to predict whether a molecule in a given solvent will form a gel, a low-viscosity solution (sol), or an insoluble precipitate. Gelation has been recognized as a phenomenon that reflects a balance between solubility and insolubility; however, the distinction between these regimes has not been quantified in a systematic fashion. In this work, we focus on a well-known gelator, 1,3:2,4-dibenzylidene sorbitol (DBS), and study its self-assembly in various solvents. From these data, we build a framework for DBS gelation based on Hansen solubility parameters (HSPs). While the HSPs for DBS are not known a priori, the HSPs are available for each solvent and they quantify the solvent's ability to interact via dispersion, dipole-dipole, and hydrogen bonding interactions. Using the three HSPs, we construct three-dimensional plots showing regions of solubility (S), slow gelation (SG), instant gelation (IG), and insolubility (I) for DBS in the different solvents at a given temperature and concentration. Our principal finding is that the above regions radiate out as concentric shells: i.e., a central solubility (S) sphere, followed in order by spheres corresponding to SG, IG, and I regions. The distance (R0) from the origin of the central sphere quantifies the incompatibility between DBS and a solvent-the larger this distance, the more incompatible the pair. The elastic modulus of the final gel increases with R0, while the time required for a super-saturated sol to form a gel decreases with R0. Importantly, if R0 is too small, the gels are weak, but if R0 is too large, insolubility occurs-thus, strong gels fall within an optimal window of incompatibility between the gelator and the solvent. Our approach can be used to design organogels of desired strength and gelation time by judicious choice of a particular solvent or a blend of solvents. The above framework can be readily extended to many other gelators, including those with molecular structures very different from that of DBS. We have developed a MATLAB program that will be freely available (upon request) to the scientific community to replicate and extend this approach to other gelators of interest.