A structural model for equilibrium swollen networks

S. K Sukumaran, G Beaucage
2002 Europhysics letters  
A tensile blob construction for branched structures is used to explain structural sizes larger than the strand length, as observed in neutron scattering data from equilibrium swollen networks. Under this model, equilibrium swollen networks display a base structural size, the "gel tensile blob" size, ξ, that follows the scaling relationship ξ ∼ l/(1/2 − χ) P , where l is the monomer length, χ is the Flory interaction parameter and P is a power determined by the connectivity of the network and
more » ... the network and the degree of interpenetration. The gel tensile blobs compose a large-scale linear structure, whose length, L, follows the scaling relationship L ∼ Q 1/2 Navg, where 1/N 2 avg = ((1/f N 2 c ) + (1/4N 2 e )), Q is the equilibrium swelling ratio, Nc is the strand length, Ne is the entanglement length and f is the functionality of the cross-links. The variation of the swelling ratio with molecular weight can now be expressed as Q ∼ N 3/5 avg , which reduces to the correct expressions under the limits Ne Nc and Nc Ne. 3/5 c , N c being the strand length. The prediction seems to be reasonably confirmed by experiments, especially for highly cross-linked networks [7] . A polymer chain in a semi-dilute solution does not follow Gaussian statistics c EDP Sciences
doi:10.1209/epl/i2002-00184-7 fatcat:i22wcsh4wfgc7o32aduo4evvpa