Cross-linking density and swelling ratio in the reaction solvent should be provided. What does it mean? Can you explain?
Cross-linking serves to connect an assembly of loose polymer molecules into a macroscopic network. This operation can be carried out either in solution, turning a polymer solution (fluid) into a gel (solid), or in an undiluted monomer mixture by co-polymerization. At a molecular scale, the cross-linking process results in creating permanent ‘junction zones’ (= linkages between two (or more) different molecules) into the polymer assembly. Although linkages can be of physical nature, like double helices or crystalline domains in biopolymers, I limit myself to chemical cross-linking.
There are 2 basic methods for chemical cross-linking:
The first type involves a co-polymerization reaction, generally conducted without dilution, where a small amount of e.g. a trifunctional monomer (= a monomer containing 1 branching point) is added to the bulk of bifunctional monomer. Polymerization without trifunctional monomer gives a linear polymer.
The second type involves a reaction between pre-existing linear polymer molecules and a bifunctional small molecule that links the polymer molecules together. This kind of cross-linking is generally conducted in solution.
The (molar) degree of cross-linking (DCL) is roughly calculated as the (molar) ratio tri-/bifunctional monomer or cross-linker/monomer applied. This gives a very rough approximation only, (1) because reaction efficiency is generally < 100 %, and (2) because small molecular assemblies may be produced with insufficient connection to take part of the network. A better approach is to wash the network exhaustively with a good solvent and analyse the purified network for the amount of cross-linker. This is hampered by the often very low DCL values applied and the lack of suitable analytical methods.
Variation of DCL is applied to tailor the mechanical and swelling properties of the network. At increased DCL the network structure becomes more dense. This results in a higher mechanical modulus (G) and a lower swelling power (q). Relationships between G or q and DCL have been derived, based on the theory of polymer physics. More often than not, DCL is not measured but estimated from G or q values. For details: despite its age I can still recommend the classical book of Nobel laureate Paul Flory: P.J. Flory, Principles of Polymer Chemistry, Cornell University Press, New York 1953 (at this time cited by 36241 according to Google Scholar).
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