Bond forces in long-chain molecules

Theoretical formulas are developed for the mean and mean-square deviation of the forces in the bonds of a freely jointed long-chain molecule with arbitrary fixed end-to-end displacement r. The mean bond force is the same for all bonds in the molecule and is nonzero even when r=0 and the mean axial force on the molecule vanishes. The mean-square deviation of the bond forces is large and computer simulation results are presented to illustrate the time variation of these forces.