Hindered Rotation Chain

All bond lengths and angles are the same
Correlations among the bond angles are treated as before.
Torsional angles are not correlated and can assume continuous values. The mean torsional angle is calculated using Boltzmann weighting of the continuous distribution of U(φ), as in Figure 1

⟨R2⟩ = C nl2 (∞ ) ( ) C∞ = 1+-cosθ- 1-+-⟨cosφ⟩ 1- cosθ 1 - ⟨cosφ⟩ ∫2π cosφ exp(- U (φ )∕kT )dφ ⟨cosφ⟩ = -0∫-2π------------------- (10) 0 exp(- U(φ)∕kT )dφ