It takes quite some time (hundreds of ps) just to loose memory of the starting configuration. You may want to look at this paper:
Sen, S. and L. Nilsson (2001). "MD Simulations of Homomorphous PNA, DNA and RNA Single Strands: Characterization and Comparison of Conformations and Dynamics." J Am Chem Soc 123: 7414-7422.

Lennart Nilsson
Karolinska Institutet
Stockholm, Sweden