Radius of Gyration of an H-polymer?

Sep 2019
1
0
Hello, I've been struggling with determining the radius of gyration of an H-polymer.

Show that the radius of gyration of an ideal H-polymer with all five sections containing an equal number (N/5) of Kuhn monomers of length b is:

\(\displaystyle (R_g)^2 = (Nb^2/6)(89/625)\)

I know the definition of the radius of gyration, but I've been having a difficult time deducing this particular equation from there.

Any help is appreciated.
 
Oct 2017
567
287
Glasgow
I don't know anything about physical chemistry, but it seems to me that there is a specific equation for the radius of gyration for a polymer based on the square of the distance between each point in the polymer chain and the centre of mass of the chain:

\(\displaystyle <R_g>^2 = \frac{1}{N} \sum_{i=1}^{N} (R_i - R_{cm})^2\)

So, perhaps you can draw the basic structure of a H-polymer with 5 sections and calculate this summation for each point on the polymer from its centre of mass?
 
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