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 q0, with E vanishing like q and K2,3 diverging like q2,3-. These exponents satisfy an exact scaling relation +2+3=1 in three dimensions, and are calculated to second order in =4-d, yielding =0.460.015, 2=0.280.015, and 3=0.210.015 in d=3. © 1992 The American Physical Society.