A new force–extension formula for stretched macromolecules and polymers based on the Ising model

• A new force–extension formula taking into account of external effects is derived using an idea from Ising model.
• This formula is fitted with experimental data with and without conformational changes, and shows a good agreement.
• A Monte Carlo simulation is used to demonstrate a possible theoretical extension for the present model.

In this paper, we derive a new force–extension formula for stretched macromolecules and homogeneous polymer matrices. The Ising model arising from paramagnetism is employed, where the magnetic force is replaced by the external force, and the resistance energy is addressed in this model instead of the usual persistent length arising from the freely jointed chain and worm-like chain models. While the force–extension formula reveals the distinctive stretching features for stretched polymers, the resistance energy is found to increase almost linearly with the external force for our two polysaccharides stretching examples with and without ring conformational changes. In particular, a jump in the resistance energy which is caused by a conformational transition is investigated, and the gap between the jump determines the energy barrier between two conformational configurations. Our theoretical model matches well with experimental results undergoing no and single conformational transitions, and a Monte Carlo simulation has also been performed to ensure the correctness of the resistance energy. This technique might also be employed to determine the binding energy from other causes during molecular stretching and provide vital information for further theoretical investigations.