The persistence length is a critical measure of polymer flexibility, indicating the distance over which a polymer behaves elastically versus statically. It is defined as the characteristic length scale at which the correlation of tangent angles along the polymer decreases exponentially. For distances shorter than the persistence length, the polymer behaves like a rigid rod, while for longer distances, it behaves like a flexible noodle. The mathematical representation of this relationship is given by the equation (0)·u(i) = exp(-l/p), where 'l' is the distance and 'p' is the persistence length.
PREREQUISITESResearchers in biophysics, materials scientists, and students studying polymer physics will benefit from this discussion, particularly those interested in the mechanical properties of polymers and their applications in biological systems.
nancy189 said:Thanks Ryan. Could you further elaborate on that?
since the directions are opposite,how can i calculate the pl by '<u(0)·u（i）>=exp(-l/p)'.some values are negtive,so i can not fit the exponential line...what should i do?Ygggdrasil said:The persistence length of a long object (such as a polymer) is a measure of the flexibility of that object. Imagine a long cord that is slightly flexible. At short distance scales, the cord will basically be rigid. If you look at the direction the cord is pointing at two points that are very close together, the cord will likely be pointing in the same direction at those two points (i.e. the angles of the tangent vectors are highly correlated). If you choose two points on the this flexible cord (imagine a piece of cooked spaghetti that you've just tossed on your plate) that are very far apart, however, the tangent to the cords at those locations will likely be pointing in different directions (i.e. the angles will be uncorrelated). If you plot out how correlated the tangent angles at two different points are as a function of the distance between the the two points, you'll get a plot that starts out at 1 (perfect correlation) at a distance of zero and drops exponentially as distance increases. The persistence length is the characteristic length scale of that exponential decay.