Designing Hydrogels by ATRP - In-Situ Gelling Polymers: For Biomedical Applications - page 74

their specific needs. Since its invention, ATRP has been broadly applied to the
preparation of well-defined polymers with controlled chemical compositions,
molecular weights and MWDs, chain sequence distributions, functionalities and
topologies.

3 Networks and Crosslinking in ATRP

Radical polymerization of monovinyl monomers with divinyl crosslinkers has
been broadly used for synthesis of various branched copolymers and gels. During
the copolymerization, incorporation of a free crosslinker unit into the growing
chain generates a pendant vinyl group which is consumed via its reaction with a
propagating radical to produce a crosslinkage. The molecular weight and/or size
of the branched polymers increase rapidly with the progress of intermolecular
crosslinking reactions, and finally reach an “infinite” value with the formation of
a polymeric network (gel). The transition from sol to gel is defined as the “gel
point”. It is evident that accurately predicting the gel point in a polymerization
reaction is critical when the synthesis is targeting either a soluble branched poly-
mer or an insoluble gel.
In the 1940's, Flory and Stockmayer developed a statistical mean-field theory
(FS theory) for an ideal polymer network based on two assumptions: (1) equal
reactivity of all vinyl species and (2) absence of intramolecular cyclization reac-
tions. The FS theory pointed out that the theoretical gel point should occur when
the weight-average number of crosslinking units per primary chain reached unity
[ 57 , 58 ] Eq. 1 , derived from the FS theory, indicates that the theoretical gel point
(p c ) based on the conversion of vinyl groups is determined by the concentration
of primary chains [PC] t at time t, the initial concentration of divinyl crosslinker
([X] 0 ), and the polydispersity of primary chains (M w /M n ) [ 59 ]

[ PC ] t
2 [ X ] 0

1
M w

p c =

M n

(1)

The theoretical gel point based on the FS theory provides important guide-
lines for experimental designs seeking to obtain branched polymers and gels,
although the assumptions, particularly the “no intramolecular cyclization”
assumption, are not completely valid during the experiments [ 8 , 60 - 62 ]. When
soluble branched polymers are targeted during the polymerization of mono-
mer and crosslinker, the reaction should be stopped before the critical gel
point ( p c ) in order to exclusively obtain soluble sols. Based on Eq. 1 , several
strategies are applicable in order to delay gelation in a system and push gela-
tion to higher conversion, including: (1) increasing the initial primary chain
concentration [ 63 - 67 ] e.g., using more initiator or chain transfer agent; (2)
using initiators with high initiation efficiency; [ 68 ] (3) using less crosslinker;
and (4) stopping the reaction at lower monomer conversion. Furthermore,