Chemical potential formalism for polymer entropic forces

The entropic force is one of the most elusive interactions in macromolecules. It is clearly defined theoretically, but practically difficult to evaluate, thus restricting our knowledge of it often to a qualitative level. Here, we propose a formula for entropic force, f？=？f\({\hskip0.3pt}^{\rm -{\hskip-4.3pt}o}\)？+？T ln(α), for confined polymers and demonstrate its mathematical equivalence to the widely used chemical potential formula for solutions, μ？=？μ\(^{\rm -{\hskip-4.3pt}o} +R\tilde T\,{\mathrm{ln}}(a)\). A systematic analysis based on this formalism clarifies the force magnitudes obtained in several recent experiments on polymers and granular chains and elucidates the common force scales for polymers studied in nanoscience and biological systems. This work provides a practical tool for instantaneously evaluating the entropic forces in polymer science and indicates the possibility of using a reference-based strategy to tackle general entropic problems beyond chemical solutions