Organogels

In polymer chemistry, an organogel is a class of gel composed of an organic liquid phase within a three-dimensional, cross-linked network. Organogel networks can form in two ways. The first is classic gel network formation via polymerization. This mechanism converts a precursor solution of monomers with various reactive sites into polymeric chains that grow into a single covalently-linked network. At a critical concentration (the gel point), the polymeric network becomes large enough so that on the macroscopic scale, the solution starts to exhibit gel-like physical properties: an extensive continuous solid network, no steady-state flow, and solid-like rheological properties. However, organogels that are "low molecular weight gelators" can also be designed to form gels via self-assembly. Secondary forces, such as van der Waals or hydrogen bonding, cause monomers to cluster into a non-covalently bonded network that retains organic solvent, and as the network grows, it exhibits gel-like physical properties.

Gelation mechanism greatly influences the typical organogel properties. Since precursors with multiple functional groups polymerize into networks of covalent C-C bonds (on average 85 kcal/mol), networks formed by self-assembly, which relies on secondary forces (generally less than 10 kcal/mol), are less stable. Theorists also have difficulties predicting characteristic gelation parameters, such as gel point and gelation time, with a single and simple equation. Gel point, the transition point from a polymer solution to gel, is a function of the extent of reaction or the fraction of functional groups reacted. Gelation time is the time interval between the onset of reaction– by heating, addition of catalyst into a liquid system, etc.– and gel point. Kinetic and statistical mathematical theories have had moderate success in predicting gelation parameters; a simple, accurate, and widely applicable theory has not yet been developed.

Organogel formulation The formulation of an accurate theory of gel formation that correctly predicts gelation parameters (such as time, rate, and structure) of a broad range of materials is highly sought after for both commercial and intellectual reasons. As noted earlier, researchers often judge gel theories based upon their ability to accurately predict gel points. The kinetic and statistical methods model gel formation with different mathematical approaches. As of 2014 most researchers used statistical methods, as the equations derived thereby are less cumbersome and contain variables to which specific physical meanings can be attached, thus aiding in the analysis of gel formation theory. Below, we present the classical Flory-Stockmayer (FS) statistical theory for gel formation. This theory, despite its simplicity, has found widespread use. This is due in large part to small increases in accuracy provided by the use of more complicated methods, and to its being a general model which can be applied to many gelation systems. Other gel formation theories cased on different chemical approximations have also been derived. However, the FS model has better simplicity, wide applicability, and accuracy, and remains the most used.

The kinetic approach The kinetic (or coagulation) approach preserves the integrity of any and all structures created during network formation. Thus, an infinite set of differential rate equations (one for each possible structure, of which there essentially infinite) must be created in order to treat gel systems kinetically. Consequently, exact solutions for kinetic theories can be obtained for only the most basic systems. However, numerical answers to kinetic systems can be given via Monte Carlo methods. In general, kinetic treatments of gelation result in large, unwieldy, and dense sets of equations that give answers not discernibly better than those given by the statistical approach. A major drawback of the kinetic approach is that it treats the gel as essentially one giant, rigid molecule, and cannot actively simulate characteristic structures of gels such as elastic and dangling chains. A classic example of an analytical treatment and the ongoing work on simplification is Smoluchowski's coagulation equation.

The statistical approach The statistical approach views the phase change from liquid to gel as a uniform process throughout the fluid. That is, polymerization reactions are occurring all throughout the solution, with each reaction having an equal chance of occurring. Statistical theories try to determine the fraction of the total possible bonds that need to be made before an infinite polymer network can appear. The classic statistical theory first developed by Flory rested on two critical assumptions.

No intramolecular reactions occur. That is, no cyclic molecules form during polymerization lead-ing up to gelation. Every reactive unit has the same reactivity regardless of other factors. For example, a reactive group A on a 20-mer (a polymer with 20 monomer units) has the same reactivity as another group A on a 2000-mer. Using the above assumptions, let us examine a homopolymerization reaction starting from a single monomer with z-functional groups with a fraction p of all possible bonds already having been formed. The polymer we create follows the form of a Cayley tree or Bethe lattice – known from the field of statistical mechanics. The number of branches from each node is determined by the amount of functional groups, z, on our monomer. As we follow the tree's branches we want there to always be at least one path that leads onwards, as this is the condition of an infinite network polymer. At each node, there are z-1 possible paths, since one functional group was used to create the node. The probability that at least one of the possible paths has been created is (z-1)p. Since we want an infinite network, we require on average that (z-1)p ≥ 1 to ensure an infinitely long path. Therefore, the FS model predicts the critical point (pc) to be:

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