Axial force fluctuations in long‐chain molecules

The fluctuations Δ f in the axial force f acting on a long‐chain molecule whose end‐to‐end displacement r is fixed are computed for a freely jointed model in which the covalent bonds are represented by stiff linear springs. It is found that the relative fluctuation Δ f / f remains large regardless of the length of the chain. A time‐dependent computer simulation of the model serves both to verify the theoretical calculation of Delta; f and to provide physical insight. The result helps to clarify the difference in behavior of the strain ensemble ( r is fixed and f fluctuates) and the stress ensemble ( f is fixed and r fluctuates) for which, in the absence of excluded volume, the strain ensemble predicts that f = 0 for r = 0, while for the stress ensemble with f = 0 it is found that 〈 r 2 〉 0 > 0.