For some definitions, a polymer is a large molecule, or macromolecule, composed of many repeated subunits. Polymerization is a process of reacting monomer molecules together in a chemical reaction to form polymer chains or three-dimensional networks.
A condensation reaction, is a chemical reaction in which two molecules or moieties, often functional groups, combine to form a larger molecule, together with the loss of a small molecule. And in polymer science, the condensation reaction between monomers are called condensation polymerization. The condensation polymerization comprises 2 kinds of reactions - linear polymerization (LP) and three-dimensional polymerization (TDP). The difference between these two reaction types is that the former can lead to the formation of one-dimensional polymers, while the latter to the three-dimensional crosslinking networks (Figure 1). It is well-known that crosslinking network formed by TDP possess a larger contact area and higher mechanical strength. We thus decide to use monomers containing more than 3 functional groups, i.e., the poly-branching monomer Af (f>=3, where A stands for “functional group”, or “functionality”).
Fig. 1. Common kinds of polymerization. A: Linear Polymerization, B: Three-dimensional Polymerization. Functional groups a and b can react with each other. M can neither react with a nor b.
Gelation, reflecting a certain reaction extent polymerization would perform, is a common phenomenon of TDP, during which the physical properties like the degree of crosslinking, the viscosity and the “rigidity” of polymers increase a lot. Although the gel could collapse and be dissolved, what we really want to do in our project is to avoid gelation and increase the degree of crosslinking as much as possible.
Our SpyTag/SpyCatcher network surely belongs to the category of three-dimensional networks, which requires at least one kind of the reactant possess a functionality more than 2. We attempt to anticipate the gel point specific for the TDP with reaction extent p through Flory’s Theory.
For a more direct route from initial experimental parameter configuration to its prediction, the linkage between the initial solution state and final reaction extent (when it reaches equilibrium) may be established. A simple way to do this, with enough qualitative credibility, is to use the concentrations of the functional groups A and B, together with the equilibrium constant K of the condensation reaction between A and B:
