Equation for number of crosslinked polymer strand in rubber

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, [tex]F=N(kb)T(\frac{x+X}{X^2}-\frac{X}{(X+x)^2})[/tex] 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=(3NkbT)/X2 where k is the spring constant of the spring. I have totally no clue where this equation is derived from.


The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving