End-to-end displacement of fiber:

From different observables that characterize the size of a polymer configuration, we evaluate the end-to-end displacement vector , where  denotes the position of the filament at arc length s. The mean square value of  is then

,

(34.8)

Integrating the unit tangent vector

,

(34.9)

Substituting the expression for  from equation 34.9 in equation 34.8,

,

(34.10)

From equation 34.7, the correlation function  decays exponentially, to yield

,

(34.11)

The condition that the argument needs to be negative can be imposed by breaking the integration into two parts,

,

(34.12)

Above integration yields the following,

	(34.13)