A functional integral formalism is used to derive the extension of a stiff chain subject to an external force. The force versus extension curves are calculated using a mean-field approach in which the hard constraint u(2)(s)=1 is replaced by a global constraint [u(2)(s)]=1 where u(s) is the tangent vector describing the chain and s is the arclength. The theory quantitatively reproduces the experimental results for DNA that is subject to a constant force. We also treat the problems of semiflexible chain in a nematic field. In the limit of weak nematic field strength our treatment reproduces the exact results for chain expansion parallel to the director. When the strength of the nematic field is large, a situation in which there are two equivalent minima in the free energy, the intrinsically mean-field approach yields incorrect results for the dependence of the persistence length on the nematic field. (C) 1997 American Institute of Physics. [References: 25]
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