What is the Meaning of Persistence Length?

[nancy189]

I was reading an article which talked about measuring the persistence length of DNA and microtubules. I didnt understand what the term meant, tried wikipedia but it confused me further. So could anyone explain what persistence length means in layman terms?

Nancy

 

[Ryan_m_b]

Persistence length is a way of measuring the point at which a polymer ceases to be treated like elastically and can be treated statically.

 

[nancy189]

Thanks Ryan. Could you further elaborate on that?

 

[Ryan_m_b]

Thanks Ryan. Could you further elaborate on that?

What are you struggling with?

 

[Ygggdrasil]

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.

 

[nancy189]

Ryan, I didn't understand what you meant by treating a polymer statically.

Thanks Ygggdrasil. That definitely cleared things. I was also wondering what will be the behavior of the cord in the following cases.
1. Its length is lower than the persistence length.
2. Its length is higher than the persistence length.

If I understood it correctly, I think the cord will be rigid in case 1 and more flexible in case 2. Please correct me if I am wrong.

Nancy

 

[Ygggdrasil]

Yes, you are correct. When considering distances shorter than the persistence length, the cord acts much more like a stiff, rigid rod than a flexible noodle. For distances much longer than the persistence length, the cord acts much more like a flexible noodle than a rigid rod.

 

[eathon]

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.

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?
thank you

 

[edwardlu]

http://polly.phys.msu.ru/en/education/courses/polymer-intro/lecture2.pdf

good explanation with equation