Statistical Thermodynamics of Ideal Networks

Phenomenological thermodynamics describes changes in energies, temperatures, volumes, etc. Unless additional assumptions are made, however, it cannot give any information about the molecular phenomena that lie behind these processes. Statistical thermodynamics attempts to obtain such information through the use of probability functions. 

When a weakly cross-linked material is stretched, the molecular segments 

Poly(ethylene-co-propylene) -0.43 trans-1,4-Poly(isoprene) -0.09 

With one end of the chain at the origin of the coordinate system, the probability [li(x,y,z) dx dy dz of finding the other end point in a volume element dx dy dz it then [see also Equation (A4-37) for the corresponding expression for one direction] 

A is the number of segments in the chain and b is the segment length. Inserting Equation (11-24) into the Boltzmann equation 5, = In H, we obtain the following for the entropy of a chain  

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