Equation for number of crosslinked polymer strand in rubber

[semc]

I am doing an experiment to estimate N, the number of crosslinked polymer strand in a piece of rectangular rubber. To do this, I attached weights to the rubber and measure the extension of the rubber when subject to the force. However, I found two equations that can be used to find N and they give different results hopefully someone can tell me which equation I should use.

Firstly, $$F=N(kb)T(\frac{x+X}{X^2}-\frac{X}{(X+x)^2})$$ where (kb) is the Boltzmann constant, T the temperature, X is the original length and x is the total length of the rubber after the weight is added.

The second equation is k=(3Nk_bT)/X² where k is the spring constant of the spring. I have totally no clue where this equation is derived from.

Thanks

 

[jbsteele]

!It really depends on how you want to estimate N. If you are looking for an accurate estimate, then it is best to use the first equation. This equation takes into account both the temperature and the length of the rubber before and after the weight was added. However, if you are just looking for a rough estimate, then the second equation might be simpler to use.