SEMIFLEXIBLE POLYMERS IN STRAINING FLOWS

We introduce a model for semiflexible polymer chains based on the inte gral of an appropriate Gaussian process. The stiffness is characterize d physically by adding a bending energy. The degree of stiffness in th e polymer chain is quantified by means of a parameter and as this para meter tends to infinity, the limiting case reduces to the Brownian mod el of completely flexible chains studied in earlier work. The calculat ion of the partition function for the configuration statistical mechan ics (i.e., the distribution of shapes) of such polymers in elongationa l now or quadratic potentials is equivalent to the probabilistic probl em of finding the law of a quadratic functional of the associated Gaus sian process. An exact formula for the partition function is presented ; however, in practice, this formula is too complicated for most compu tations. We therefore develop an asymptotic expansion for the partitio n function in terms of the stiffness parameter and obtain the first-or der term which gives the first-order deviation from the completely fle xible case. In addition to the partition function, the method presente d here can also deal with other quadratic functionals such as the ''st ochastic area'' associated with two polymer chains.