Temperature dependence of the chain size

All results for chain size are now written in terms of the excluded volume. To understand how the chain size changes with temperature, we simply need the temperature dependence of the excluded volume. There are two important parts of the Mayer /-function, from which the excluded volume is calculated [Eq. (3.7)]. The first part is the hard-core repulsion, encountered when two monomers try to overlap each other (monomer separation r b). In the hard-core repulsion, the interaction energy is enormous compared to the thermal energy, so the Mayer /-function for r 6 is — I  

The second part is for monomer separations larger than their size (r b), where the magnitude of the interaction potential is small compared to the thermal energy. In this regime, the exponential can be expanded and the Mayer /-function is approximated by the ratio of the interaction energy and the thermal energy  

The excluded volume v can be estimated using Eq. (3.7) with these two parts of the Mayer 7-function  

The first term is the contribution of the hard-core repulsion, and is of the order of the monomer volume b. The second term contains the temperature dependence, and the coefficient of l/T defines an effective temperature called the -temperature ----------------------------------- 

Since U r) 0 in the attractive well, the -temperature is positive. This results in a very simple approximate temperature dependence of the excluded volume [Eq. (3.93)]  

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