1 Answers
The persistence length is a basic mechanical property quantifying the bending stiffness of a polymer.The molecule behaves like a flexible elastic rod/beam. Informally, for pieces of the polymer that are shorter than the persistence length, the molecule behaves like a rigid rod, while for pieces of the polymer that are much longer than the persistence length, the properties can only be described statistically, like a three-dimensional random walk.
Formally, the persistence length, P, is defined as the length over which correlations in the direction of the tangent are lost. In a more chemical based manner it can also be defined as the average sum of the projections of all bonds j ≥ i on bond i in an infinitely long chain.
Let us define the angle θ between a vector that is tangent to the polymer at position 0 and a tangent vector at a distance L away from position 0, along the contour of the chain. It can be shown that the expectation value of the cosine of the angle falls off exponentially with distance,
where P is the persistence length and the angled brackets denote the average over all starting positions.