Expected Square of the Length of a Hydrocarbon-Type Chain

Three successive bonds along a hydrocarbon chain may be in a planar trans configuration or in two nonplanar gauche configurations. The energy of the trans configuration is taken as zero and the energies of the two gauche configurations are each taken as ε (per mole). The mean square length of a hydrocarbon‐type chain of n links each of length l₀ is shown to be ${\mathrm{r̄}}^2{\text{=[(2+6a)/(3−3a)]nl}}_0^2$ , where $\text{a=1/[1+2\hspace{0.17em}}\exp \mathrm{(-\epsilon /RT)]}$ . The problem of excluded volume is not considered here.