  The effect of network chain distribution on the mechanical behavior of
elastomers is one of the long-standing problems in rubber mechanics. The
classical theory of rubber elasticity is built upon the assumption of entropic
elasticity of networks whose constitutive strands are of uniform length. The
kinetic theories for vulcanization, computer simulations, and indirect
experimental measurements all indicate that the microstructure of vulcanizates
is made of polymer strands with a random distribution of length. The
polydispersity in strand length is expected to control the mechanical strength
of rubber as the overloaded short strands break at small deformations and
transfer the load to the longer strands. The purpose of the contributions
presented in this thesis is to present simple theories of rubber mechanics that
take into account the length distribution of strands and its effect on
elasticity and the onset of bulk failure in unfilled and filled elastomers. In
unfilled system, the population of short chains is identified as the culprits
for damage initiation. Upon deformation of a polydisperse network, shorter
strands break at considerably smaller stretches compared to the longer ones.
The network alteration continues concurrent with increasing deformation and
controls the onset of mechanical failure. In the filled networks, the
degradation in network mechanical behavior is assumed to be controlled by the
adhesive failure of the short strands adsorbed onto the filler surface. The
finite extensibility of the short adsorbed strands is a key determinant of
mechanical strength.
