FINITE CHAIN EXTENSIBILITY AND TOPOLOGICAL CONSTRAINTS IN SWOLLEN NETWORKS

Uniaxial stress-strain properties of highly swollen and stretched rubb ers are discussed in the framework of a recently developed non-Gaussia n network model that considers the finite extensibility of network cha ins together with topological chain constraints. The finite extensibil ity is described by the well-known inverse Langevin function of the ne twork chain end-to-end distance. The model consequently distinguishes between topological constraints coming from packing effects of neighbo ring chains and from trapped entanglements. Whereas the latter act as additional network junctions, the packing effects are modeled in a mea n-field-like manner through strain-dependent conformational tubes. The calculated Gaussian contribution to the total modulus, the swelling d ependence of the infinite strain modulus, and the tube constraint modu lus of natural rubber (NR) samples are determined. It is found that th e infinite strain modulus varies linearly with the polymer volume frac tion phi, whereas the tube constraint modulus varies as phi(4/3). Both observations agree with the predictions of the presented model. Contr ary to literature data that were estimated from stress-strain experime nts on swollen networks in the framework of Gaussian statistics, the t ube constraint modulus (which is proportional to the C-2 value of the Mooney-Rivlin equation) is found to vanish in the limit phi --> 0, and not at a finite universal value phi approximate to 0.2.