Crystallization kinetics in stretched natural rubber

In thermally induced homogeneous crystallization from the molten state at a temperature T, the driving force for crystallization is the undercooling Delta T = T-m(0) - T (where T-m(0) is the melting temperature) and the free enthalpy barrier to form a stable crystal nucleus varies as 1/Delta T-2. It follows that the crystallization rate increases dramatically as Delta T increases, that is, as T decreases farther away from T-m(0). Crystallization induced under uniaxial tensile stress in a cross-linked natural rubber elastomer is a kinetic phenomenon as well. In this case, the driving force is the over-stress Delta sigma = sigma - sigma(0)(m), where sigma(0)(m) is the stress value at which the crystal and amorphous phases would coexist at equilibrium at a given temperature T. Equivalently, the driving force may be expressed as a function of the degree of overstretching Delta lambda approximate to Delta sigma/G where G is the Young's modulus of the elastomer in the amorphous state. Based on standard nucleation theory, the nucleation barrier can be expressed explicitly and it can be shown that it varies as 1/(Delta lambda)(2). It follows that the crystallization rate increases considerably as Delta lambda increases. Assuming that crystal growth is inhibited by the presence of crosslinks, the crystallization kinetics and concomitant stress relaxation can be described by an explicit, kinetic equation, at a given temperature and a fixed overall degree of overstretching. In tensile tests performed at a constant strain rate, the critical tensile strain at onset of crystallization depends on the strain rate. This dependence can be explicitly modelled as well.