BREAKDOWN OF ELASTICITY THEORY IN NEMATIC POLYMERS

It is shown that linearized elasticity theory fails for nematic polymers in less than four dimensions. Instead, the polymer osmotic elastic modulus E and the elastic moduli K2 and K3 all become singular functions of wave vector q as \q\ --> 0, with E vanishing like q(eta-perpendicular-to) and K2,3 diverging like q-eta-2,3. These exponents satisfy an exact scaling relation eta-parallel-to + eta-2 + eta-3 = 1 in three dimensions, and are calculated to second order in epsilon = 4 - d, yielding eta-parallel-to = 0.46 +/- 0.015, eta-2 = 0.28 +/- 0.015, and eta-3 = 0.21 +/- 0.015 in d = 3.