Semiflexible polymers in straining flows

We introduce a model for semiflexible polymer chains based on the integral of an appropriate Gaussian process. The stiffness is characterized physically by adding a bending energy. The degree of stiffness in the polymer chain is quantified by means of a parameter and as this parameter tends to infinity, the limiting case reduces to the Brownian model of completely flexible chains studied in earlier work. The calculation of the partition function for the configuration statistical mechanics (i.e., the distribution of shapes) of such polymers in elongational flow or quadratic potentials is equivalent to the probabilistic problem of finding the law of a quadratic functional of the associated Gaussian process. An exact formula for the partition function is presented; however, in practice, this formula is too complicated for most computations. We therefore develop an asymptotic expansion for the partition function in terms of the stiffness parameter and obtain the first-order term which gives the first-order deviation from the completely flexible case. In addition to the partition function, the method presented here can also deal with other quadratic functionals such as the “stochastic area” associated with two polymer chains.